Millimeter-wave and terahertz imaging techniques

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In the using or citation of parts of the thesis it’s obliged to indicate the name of the author Millimeter-Wave and Terahertz Imaging Techniques Author Enrique Nova Lavado Thesis Advisor Jordi Romeu Robert AntennaLab Universitat Polit` ecnica de Catalunya Departament de Teoria del Senyal i Comunicacions Submitted to the Universitat Polit` ecnica de Catalunya (UPC) in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY April 26, 2013 Acta de qualificació de tesi doctoral Curs acadèmic: Nom i cognoms Programa de doctorat Unitat estructural responsable del programa Resolució del Tribunal Reunit el Tribunal designat a l'efecte, el doctorand / la doctoranda exposa el tema de la seva tesi doctoral titulada __________________________________________________________________________________________ _________________________________________________________________________________________. Acabada la lectura i després de donar resposta a les qüestions formulades pels membres titulars del tribunal, aquest atorga la qualificació: APTA/E NO APTA/E (Nom, cognoms i signatura) President/a (Nom, cognoms i signatura) Secretari/ària (Nom, cognoms i signatura) Vocal (Nom, cognoms i signatura) Vocal (Nom, cognoms i signatura) Vocal ______________________, _______ d'/de __________________ de _______________ El resultat de l’escrutini dels vots emesos pels membres titulars del tribunal, efectuat per l’Escola de Doctorat, a instància de la Comissió de Doctorat de la UPC, atorga la MENCIÓ CUM LAUDE: SÍ NO (Nom, cognoms i signatura) Presidenta de la Comissió de Doctorat (Nom, cognoms i signatura) Secretària de la Comissió de Doctorat Barcelona, _______ d'/de ____________________ de _________ Thesis written by Enrique Nova. Millimeter-Wave and Terahertz Imaging Techniques Ph. D. program on Signal Theory and Communications The work presented in this thesis has been supported in part by the Spanish Interministerial Commission on Science and Technology (CICYT) under projects TEC2010-20841-C04- 02, TEC2011-25865 and TEC2011-28201-C02-01, CONSOLIDER CSD2008-00068 and by the “Ministerio de Educaci´ on y Ciencia” through the FPU fellowship program. Copyright c 2012, Enrique Nova. All rights reserved. Reproduction by any means or translation of any part of this work is forbidden without written permission of the copyright holder. Requests for permission or further information should be addressed to enrique.nov[email protected] Dedicatoria Abstract This thesis presents the development and assessment of imaging techniques in the millimeterwave (mmW) and terahertz frequency bands. In the first part of the thesis, the development of a94 GHz passive screener based on a total-power radiometer (TPR) with mechanical beamscanning is presented. Several images have been acquired with the TPR screener demonstrator, either in indoor and outdoor environments, serving as a testbed to acquire the know-how required to perform the research presented in the following parts of the thesis. In the second part of the thesis, a theoretical research on the performance of near-field passive screeners is described. This part stands out the tradeoff between spatial and radiometric resolutions taking into account the image distortion produced by placing the scenario in the near-field range of the radiometer array. In addition, the impact of the decorrelation effect in the image has been also studied simulating the reconstruction technique of a synthetic aperture radiometer. Guidelines to choose the proper radiometer depending on the application, the scenario, the acquisition speed and the tolerated image distortion are given in this part. In the third part of the thesis, the development of a correlation technique with optical processing applicable to millimeter-wave interferometric radiometers is described. The technique is capable of correlating wide-bandwidth signals in the optical domain with no loss of radiometric sensitivity. The theoretical development of the method as well as measurements validating the suitability to correlate radiometric signals are presented in this part. In the final part of the thesis, the frequency band of the imaging problem is increased to frequencies beyond 100 GHz, covering the THz band. In this case the research is centered in tomographic techniques that include spectral information of the samples in the reconstructed images. The tomographic algorithm can provide detection and identification of chemical compounds that present a certain spectral footprint in the THz frequency band. Keywords:Aperture Synthesis, Optical Modulation, Passive Interferometry, W-band Radiometry, Near-Field Imaging, Radiometric Sensitivity, Passive Screeners, Terahertz Tomography, Terahertz Spectroscopy, Diffraction Tomography. Contents 1 Introduction 1 1.1 TeraSenseproject................................ 1 1.2 Stateoftheart.................................. 2 1.2.1 Millimeter-wave technology and applications . . . . . . . . . . . . . 2 1.2.2 Millimeter-wave passive imaging for personnel screening . . . . . . . 5 1.2.3 Terahertz systems and applications . . . . . . . . . . . . . . . . . . . 7 1.2.4 Terahertz spectroscopy and tomography . . . . . . . . . . . . . . . . 10 1.3 Objectives and scope of the thesis . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Objectives appearing in this document . . . . . . . . . . . . . . . . . 12 1.3.2 Objectives excluded from this document . . . . . . . . . . . . . . . . 12 1.4 Organization of the document . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Close-Range Millimeter-Wave Passive Systems 2 Millimeter-wave radiometric imaging 17 2.1 Millimeter-wave radiometry . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Thermal radiation and Plank’s law . . . . . . . . . . . . . . . . . . . 18 2.1.2 Antenna surrounded by a black body . . . . . . . . . . . . . . . . . . 18 2.1.3 Gray body radiation and apparent temperature . . . . . . . . . . . . . 19 2.1.4 Image temperature contrast . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Total-power radiometer with mechanical beam-scanning . . . . . . . . . . . 21 2.2.1 Total-power radiometer system design . . . . . . . . . . . . . . . . . 23 2.2.2 Calibration ............................... 24 2.2.3 Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.4 Description of the antenna system . . . . . . . . . . . . . . . . . . . 26 2.2.5 Beamdistortion............................. 27 2.2.6 Imaging Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3 Synthetic Aperture (SA) Interferometric Radiometry . . . . . . . . . . . . . 30 vii 4 Chapter 1 such large bandwidth, NTT has developed technology to convert an optical subcarrier data signal produced by photonics technology into electronic signals and radio waves using Uni-travelling Carrier Photodiode (UTC-PD) [3, 4]. It provides the photonics features such as wide bandwidth, good stability and ultrahigh frequency to generate electromagnetic waves in the mmW range. Current research has been performed using Amplitude Shift Keying (ASK) modulations, however it is expected that data rates up to 20 Gbits/scan be achieve if most sophisticated modulations schemes such as 16-state Quadrature Amplitude Modulation (16QAM) are used. •Active remote sensing: The main application in the area of active remote sensing at mmW frequencies is the automotive radar sensor [5, 6]. The radar is used as a driver assistant for various functions such as adaptive cruise control, automatic emergency braking and parking aid. The first generation of automotive radar sensors working at 77 GHz was introduced in 1998 by Daimler. Since then, several new generations of sensors have appeared from a number of manufacturers all relying on the Frequency- Modulated Continuous-Wave (FMCW) modulation technique. In Europe a total of 4 GHz are available for this purpose from 77 GHz to 81 GHz allowing a range resolution of 10 cm. The technology used to build the radar is usually based on Monolithic Microwave Integrated Circuit (MMIC) using GaAs semiconductor. Recently, implementations using 90 nm and 60 nm Complementary Metal-Oxide-Semiconductor (CMOS) technologies have been published [7]. Taking advantage of the wide bandwidth available for radar purposes in the mmW frequency region, other applications using radar techniques have appeared. As an example, in [8] a three-dimensional holographic imaging technique is shown to perform personnel screening for concealed weapon detection purposes. In [C7], an interferometric system is shown capable of detecting surface deformations on the order of tens of micrometers. Additionally, the W-band atmospheric window has been widely used to perform active remote sensing of the atmospheric properties such as the cloud formation and composition [9] [10]. •Passive remote sensing: Radioastronomy is the application concentrating the main efforts of the scientific community in the area of passive remote sensing. This effort is translated in examples like the Atacama Large Millimeter/Submillimeter Array (ALMA) international telescope [11]. It is situated on a dry place at 5000 m of elevation, allowing an excellent atmospheric transmission over the instrument frequency range from 30 GHz to 1 THz. The radio telescope consists of two antenna arrays: one of 64 antennas with 12 m diameter each being reconfigurable in multiple patterns ranging from 150 m to 15 km; and a second array consisting of a set of 4antennas with 12 m diameter and 12 antennas with 7 m diameter working in packed configurations of 50 m diameter [12]. ALMA will provide total power and interferometric information on molecular, atomic, ionized gas and dust in the solar system. A second example of a mmW instrument developed by the radioastronomy community the Planck radio telescope [13]. This instrument was launched in 2009 together with the Herschel radio telescope. Planck covers a frequency range from 30 GHz to 857 GHz and its objective is to map the entire sky by strip scanning with a spin rate of 1 rpm. The mmW frequency range is also used to retrieve environmental parameters such as 1.2 State of the art 5 Figure 1.3: Artist view of a passive scanner portal that is capable to detect objects concealed beneath the clothes. The working principle of this portal is to distribute in a vertical disposition a group of horizontal passive arrays in such a way that a 2D image is obtained. temperature, humidity and liquid water of the soil. In [14], total-power measurements at mmW are used to retrieve the aforementioned parameters. Additionally, passive remote sensing combined with image formation techniques is applied to solve several security issues: aircraft landing and guidance; low-visibility navigation and situational awareness; reconnaissance and surveillance; search and rescue and drug interdiction among others. An example can be found in a W-band radiometric imager that helps in the landing process of an helicopter. It provides real time imaging through the dust cloud when the helicopter is landing, thus reducing the probability of accident [15]. An additional application of the passive imaging is the personnel screening for concealed object detection. This application concentrates the research on mmW passive imaging presented in this thesis. The research undergoing in this area is described in the following section. 1.2.2 Millimeter-wave passive imaging for personnel screening Several companies have developed proprietary systems for concealed threat detection. These systems are designed either in a walkthrough portal configuration as the one shown in Fig. 1.3 or for stand-off operation. Portal systems are usually designed to detect small threats at short distances (<3 m), achieving spatial resolutions around 1 cm whereas stand-off systems are conceived for larger distances and larger threads. There are three different operating frequency ranges in use for personnel screening purposes: 1) 25 to 35 GHz; 2) 94 GHz; and 3) 200 to 300 GHz. Each corresponds to one of the windows that exist in atmospheric propa- 6 Chapter 1 (a) ThruVision T4000 passive scanning system (b) Brijot MobileScanPS passive scanning system Figure 1.4: Two examples of commercial passive scanning systems. gation. Atmospheric absorption is not a significant issue for the relatively modest distances used in people-screening applications, nevertheless by working in the same frequency ranges as some of the longer distance applications it is possible to benefit from more readily available and lower cost components. At the lower frequencies, equipment needs to be relatively large, or resolution is sacrificed. Higher frequencies enable more compact systems such as those developed by ThruVision [16]. Also, specially for passive systems, it is easier to detect dielectric threat materials at higher frequencies since their higher refractive indices at these frequencies makes them appear more metal-like and reflective. Another compact system, operating at 94 GHz for modest stand-off distances has been developed by Brijot. Figure 1.4 shows two photographs of the systems commented in this paragraph. A number of different scanning systems are in use with mechanical, electronic and hybrid configurations. The Smiths Detection system uses a pair of spinning tilted mirrors to scan in the x-axis and a third mirror to raster scan in the y-axis on to the detectors. The Qinetiq [17] system uses a different arrangement with a single rotating mirror to produce a conical scan on to a complete line array. It also exploits polarizers and a quarter-wave plate to enable a folded optic reducing the dimensions of the scanning system. The Trex Sago [18] approach is to create an azimuthal line scan through a frequency dependent coupling into an antenna. In the ST150, the second axis is provided by panning the main reflecting mirror. In their real-time imager, a phased array of some 230 receivers is deployed. The L-3 SafeView [19] system is an active system based on developments from PNNL using a holographic reconstruction from a fan-beam source and line array of detector antennas which rotate around the subject being scanned. This system measures both amplitude and phase of the reflected signal for use in the FFT-based holographic image reconstruction. 1.2 State of the art 7 A novel approach has been developed by Agilent [20] and demonstrated in prototype form. This employs a confocal arrangement of a single source and detector. The source is reflected from a configurable mirror made up of a 2-dimensional array of several thousand dipole reflectors. Each dipole is connected to a large, fast switching array which can place either a short or open circuit at the feed point of each dipole. This forms a programmable, reflecting Fresnel zone plate which can be used to focus the millimeter wave source and detector onto a chosen point in space in front of the mirror. The antennas can be switched so as to scan over 107pixels per second, leading to a solid state imaging system with a 15 Hz refresh rate or higher. Although the frequency employed is relatively low, 24 GHz in the prototype system, the programmable mirror is only a few centimeter thick, leading to relatively compact system. Development directions in mmW systems focus largely on methods to reduce the cost of systems, without sacrificing neither sensitivity nor resolution. Since most of these systems use a number of detectors in order to be able to capture moving images, the cost of multiple receivers dominates the total cost of the system. 1.2.3 Terahertz systems and applications The THz frequency range is comprised between 300 GHz and 3 THz as shown in Fig. 1.2, placed between the Radiofrequency (RF) spectrum and the infrared and optical spectrum. Either photonic or electronic techniques are used to generate THz electromagnetic waves depending on the type application. There are mainly 4ways of generating radiation in the THz range: •In order to generate a local oscillator for a THz transceiver in the range between 300 GHz and 1 THz usually electronic techniques are used. In this case, a mmW phaselocked oscillator is upconverted to the desired frequency by a multiplier chain [21]. •If a broadband pulsed radiation is required (e.g to perform spectroscopy) usually a Photoconductive Antenna (PCA) is used [22]. By exciting the PCA using a femtosecond laser pulse, a broadband THz pulse radiation is emitted [23]. The duration and therefore the spectral content of the emitted pulse depends basically on the duration of the laser pulse and on the relaxation-time of the photocarriers created by the laser pulse on the antenna semiconductor. •To generate a Continuous Wave (CW) signal beyond 1 THz usually a Photoconductive Switch (PCS) is used [24, 25]. The signals coming from two lasers are mixed in the PCS, giving an output frequency equal to the frequency difference between both lasers. This technique usually gives a power with a order of magnitude lower than the electronic generation, however it is suitable for higher frequencies. •If a CW high-power source (around 30 mW) is required, the solution is given by a Quantum Cascaded Laser (QCL) [26, 27]. This laser is a semiconductor device where the light emission is obtained through intersubband transitions in the quantum wells. This allows to radiate at lower frequencies than a typical optical laser. However the output frequency range is restricted to frequencies greater than 1.5 THz. 8 Chapter 1 Depending on the power requirements, the frequency and the application one among the aforementioned THz generation techniques should be chosen. The applications in the THz range can be distributed in the following areas: 1) Communications; 2) Remote sensing; 3) Spectroscopy and 4) Imaging •Terahertz communications: The THz frequency range is very attractive for communications due to the huge available bandwidth [28]. However, the signal path loss is a disadvantage. Figure 1.2 shows that atmospheric attenuation increases drastically beyond 100 GHz. Therefore, the research is focused on short-range Wireless Local Area Network (WLAN) and WPAN systems applied to wireless displays, HDTV distribution, backhaul traffic, etc. In addition, THz communications may interfere with the classical application of this frequency band: the radioastronomy [29]. This issue has been recently investigated and is concluded that the transmitter should be kept 55 km away from any radio telescope. Nevertheless, the research is still in an initial stage, and no relevant transceiver demonstrators working beyond 300 GHz have been published. •Active and passive remote sensing: As in the mmW frequency range, the main application for passive remote sensing in the THz range is the radioastronomy. An example is the Herschel radio telescope launched to the space in 2009 [30, 31]. The HIFI instrument carried by Herschel can retrieve a total power information of the sky in two polarizations over seven frequency bands between 480 GHz and 1.91 THz. Herschel has a cassegrain reflector antenna system with a main reflector of 3.5 m diameter and the instruments are cooled down to 80 K. The measurements are used by the scientific community to discern the weak signals from distant galaxies and to resolve among multiple forming stars and galactic clouds. On the other hand, the THz range is not widely used in passive remote sensing for security applications since the sensitivity of the available receivers beyond 300 GHz does not allow the acquisition of images in real-time. In order to improve the acquisition time, active approaches have been developed. An example is a FMCW radar developed by the Jet Propulsion Laboratory (JPL) of the National Aeronautics and Space Administration (NASA) [32] [33]. The system can acquire three-dimensional images at a standoff distances of 25 m in five seconds operating at 675 GHz. It relies on a 1 m diameter ellipsoidal main reflector to achieve an spatial resolution of around a centimeter at 25 m range. •Spectroscopy: Many materials presents vibrational or rotational modes at molecular level in the THz frequency range. This is translated in an absorption of the electromagnetic energy at the resonance frequency. In order to measure absorption frequencies, a broadband THz emission is produced and directed to the material. The absorption spectra of the received signal is analyzed to find absorption peaks. An absorption spectrum can completely characterize a material, therefore a certain material can be detected and its concentration can be calculated from an spectroscopic analysis [34,35]. The most extended THz spectroscopy system is the Terahertz Time-Domain Spectroscopy (THz-TDS). It relies on PCA to emit and receive the THz radiation and a femtosecond laser is used to excite the PCA. The amplitude and phase of the emitted pulse can be measured by sampling the THz pulse by using a delay stage that controls 1.2 State of the art 9 Spectrographic / tomographic Imaging Femtosecond Pulsed Laser •Spectral Range (min.) -0.1-3 THz •Dynamic Range ->50 dB (typ60) •Scan Range - 300 ps •Repetition Rate -100MHz •Wavelength -780 nm •Pulse Duration - 100 -120 fs •Output Port - •Total Average OutputP->65 mW Schematic Emitter Receiver λ/4 λ/2 PC Acq. Sample under test Delay Delay line THz Receiver Retina Emitter THz Figure 1.5: Schematics of a THz-TDS system with accessories to perform tomographic imaging (e.g. a rotor used to rotate the sample and a retina used to multiplex multiple points of view without necessity of mechanical movements). The main parts that intervene in the emission and reception of the THz pulse are depicted. the delay of the laser pulse. With this measurement system, the refractive index and the absorption coefficient of the material sample can be retrieved. •Imaging: Recently, a real-time CMOS camera has been published [36] [37] [38]. It consists on a 1 kPixel THz detector fully integrated in a 65 nm CMOS technology and it is capable of capture real-time video with up to 500 fps. The design achieves a bandwidth from 790 GHz to 960 GHz. This camera presents a great advance in the THz technology since it represents a cheap, compact and reliable instrument to acquire images in the THz range. Terahertz microscopy is also being developed and has been already applied to image semiconductor devices achieving down to 150 nm of spatial resolution [39]. The technique is based on capturing the near-field reflected by the sample using a very thin field probe. In this case the diffraction effect does not limit the resolution since the electromagnetic field has not been propagated, and therefore it has not lost information that limits the resolution in typical imaging. Additionally, THz imaging techniques are being developed to perform 3-dimensional imaging of biological, pharmaceutical and alimentary samples [40, 41]. The imaging information can be combined with the spectroscopic information to detect different materials dispersed over a sample. The following section describes in detail the current research on THz tomography. 10 Chapter 1 1.2.4 Terahertz spectroscopy and tomography Terahertz tomography refers to imaging by sections through the use of THz electromagnetic waves. Two main classifications of tomographic techniques are found in the literature: the diffractive techniques [42] and the non-diffractive techniques [43]. The diffractive techniques are based on illuminating the sample with an electromagnetic wave and measure the scattered field. From the measured information the currents that have been excited on the sample by the emitted field can be reconstructed, and thus the shape of the sample can be retrieved. The expressions that govern this method emanate from the Maxwell equations and cannot be solved analytically. In order to solve the expression for the scattered field, an approximation should be used. There are mainly two approximations to solve the problem: the Born approximation [44] and the Rytov approximation [45]. The Born approximation was introduced by Max Born in 1925. If the scattered field is much smaller compared with the incident field, the scattered field can be expressed by its first order approximation. The Born approximation can be applied if d∆n < λ 4where dis the target size and ∆nis the index of refraction difference between the air and the sample. From this approximation, one can observe that the approximation can be applied when the wavelength is several times the size of the object. Hence, in the THz frequency range the use of this approximation is unusual since the wavelength is usually smaller than the object. The Rytov approximation assumes that the incident field is perturbed by the sample only by introducing a phase shift along its propagation path. This approximation is considered more accurate than the Born approximation and it should provide a better estimate of the scattered wave. In addition, the approximation condition is less restrictive than the condition in the Born approximation and it just requires a slow variation of the refraction index of the sample over a wavelength. Additionally, Rytov approximation also has a better behavior when the measuring wavelength is longer than the sample. There are not many research publications using the aforementioned algorithms in the THz range since usually the conditions are not fulfilled and the resulting images do not reconstruct the shapes of the sample. The reconstruction algorithm commonly used in THz tomography is a non-diffractive method inspired from the x-ray: Computed Tomography (CT). The attenuation produced in the incident field by the object can be described by a line integral of the object function along its path called Radon transformation P(θ, t) = Z L(θ,t) f(x, y)dl =R(f(x, y)),(1.1) where P(θ, t)is the attenuation function of the incident ray along the path l, and tis the ray minimum distance from the sample origin. The attenuation function can be measured by rotating the the object along θand by sweeping the position of the ray along a line in order to obtain multiple samples on t. Hence, f(x, y)can be retrieved by applying the reverse Radon transformation to the measurements. In practice, a THz beam cannot be treated as a ray line as in in the x-ray CT. Therefore special attention should be taken to create a measurement environment where the assumptions of CT are still valid. The beam should be focused in the sample by using either lenses of parabolic mirrors. The resolution of the image cannot be better than the waist of the beam synthesized by the focusing element. Moreover, the sample 1.3 Objectives and scope of the thesis 11 Objectives mmW close-range passive imaging Preliminar work mmW close-range measurements with TPR Close-range mmW passive system performance asessment and study Improve the correlation method of large bandwidth radiometric signals applied to mmW interferometry Terahertz tomography and spectroscopy Introduction to the THz systems and the tomographic method Scene simulation and assessment of the tomographic algorithm Validation of the method by imaging samples with known spectral fingerprint Figure 1.6: Diagram showing the main objectives of both the mmW and THz parts of this thesis. should be small enough to fit in the focus depth of the beam, otherwise the size of the beam will vary along the sample and the assumption of rays is not further valid. The spectroscopic information appears directly in the reconstructed result by using all the aforementioned methods [46,47]. By using a THz-TDS system to measure the multiple point of views, the full spectral information of the sample is obtained. Therefore, the reconstructed image can reveal the different materials contained in the sample analyzing the spectrum. Figure 1.5 shows a THz-TDS system with the main components (e.g. femtosecond laser, two PCA, delay stage,...). This system is used, among other applications, to perform tomography of small samples. The dynamic range is around 65 dB in present commercial systems and its main advantage is that it can measure the complete THz spectral range at real time. 1.3 Objectives and scope of the thesis At the beginning of the research work in this thesis, the state of the art for the two main topics described above were analyzed to identify lacks or deficiencies. From the conclusions on the literature survey, the objectives stated in this section were chosen. A main division of the objectives has been done between the objectives that appear in this thesis and the ones that have been considered out of the scope. In addition, the objectives have been subdivided in two lists, the first related with mmW passive imaging and the second related with THz imaging. Each objective is related with its corresponding paper contribution either in a conference [Ci]or in a journal [Ji]. 12 Chapter 1 1.3.1 Objectives appearing in this document A summary of the objectives appearing in this document is presented in Fig. 1.6 depicting the timeline distribution among the objectives. •Millimeter-wave passive imaging – Passive imaging introduction and imaging: A simple demonstrator is built to test the passive imaging capabilities in indoor and outdoor conditions [C6, C8, C12]. – Close-range passive imaging performance analysis: A complete theoretical comparison including simulations of the close-range behavior of three radiometers in order to detect optimum configurations that can achieve better performance with lower overall cost [J2]. – Correlation method for large bandwidth radiometric signals: An optical correlation method is applied for correlating large bandwidth radiometric signals coming from mmW interferometric radiometers [C3,C4] [J1]. •THz spectroscopy and tomography – Diffractive spectroscopic tomography: A tomographic algorithm based on the Born approximation is applied to retrieve spectroscopic images. The spectral information of each pixel can be obtained to identify different compound types in the same image. Most of the THz tomographic systems use CT methods to retrieve the image and the diffractive techniques are not studied in deep in the literature [C1]. 1.3.2 Objectives excluded from this document •mmW systems and components: – Assessment of THz active Mills-Cross imaging: By placing two W-band headers from a Vectorial Network Analyzer (VNA) into two linear stages an active Mills-Cross setup is built. Measurements are obtained to assess the suitability of this imaging geometry in the mmW range. [C14–C16]. – Radiation pattern characterization of a mmW Cassegrain reflector: The radiation pattern of a Cassegrain has been characterized from near-field measurements. In addition, the return loss parameter has been adjusted by using a matching section formed by adjustable screws [C2]. •THz imaging: – Terahertz subsurface imaging system: By using a portable THz-TDS system, subsurface images of a ceramic sample are obtained with resolutions around 0.3 mm [C13]. 1.4 Organization of the document 13 1.4 Organization of the document This document has been divided in 4main parts: 1) the introduction; 2) the research on mmW passive systems; 3) the research on THz tomographic imaging techniques; and 4) conclusions and further discussion. The second part is sub-divided in three chapters whereas the third part is concentrated in one chapter. Each chapter has an introduction or abstract at the beginning followed by a description of the general concepts required to understand the core of the chapter. Measurement or simulation results are found at the end of the chapter and are used to validate the theoretical approach of the problem developed in the core of chapter. At the end of each chapter, with exception of the present one, the conclusions of the obtained results are written. The second part, Close-range Millimeter-wave Passive Imaging, is devoted to describe the advances achieved in the field of the mmW radiometry. The second chapter includes a total power and interferometric radiometry introduction. Furthermore, it includes a complete design of a total power radiometer used to study the behavior of the mmW components as a previous step to design the interferometric radiometer shown in the third chapter. Indoor and outdoor close-range measurements of persons with concealed objects are shown to study the detection capabilities of the system. The third chapter describes a theoretical study and comparison of three types of screeners and their behavior in close-range imaging: the Real- Aperture (RA) radiometer, the One-Dimensional Synthetic Aperture (1D-SA) and the Two- Dimensional Synthetic Aperture (2D-SA). The fourth chapter and the last one of the second part of this thesis is devoted to describe a method developed to correlate radiometric signals in the optical domain. Measurements of the system are shown validating the suitability of the method for passive mmW interferometric imaging. The third part, Terahertz Imaging and Spectroscopy, is devoted to describe the tomographic and spectroscopic imaging research performed in this thesis. The fifth chapter, introduces the terahertz imaging basic concepts, presents simulations of the method that is applied and finally show measurements validating the method. The last part concludes the document and presents further discussion on the achievements of this thesis. 20 Chapter 2 Emissivity Reflectivity Transmissivity Material 100 GHz 500 GHz 100 GHz 500 GHz 100 GHz 500 GHz Explosive 0.74 0.95 0.26 0.05 0 0 Metal 0 0 1 1 0 0 Skin 0.65 0.91 0.35 0.09 0 0 Denim 0.09 0.49 0.01 0.01 0.9 0.5 T-shirt 0.04 0.2 0 0 0.96 0.8 Table 2.1: Emissivity, reflectivity and transmissivity of typical materials related with radiometric security imaging [49]. will emit less power than a black-body. From this statement arises the relation among the emissivity e, reflectivity rand transmissivity tconcepts: e+r+t= 1.(2.6) Table 2.1 shows the emissivity, reflective and transmissivity values of various materials related with human body security imaging at 100 GHz and 500 GHz. When a gray-body is placed in a complex environment with other objects surrounding it, the power coming from the gray-body is not only related with its physical temperature. There are two additional effects that are included in the measured power coming from the body: 1) the reflected energy on the body surface; and 2) the energy that penetrates the body and is transmitted thorugh it. The total measured power is related with an apparent temperature TAseen from the body TA=eTph +rTbr +tTbb,(2.7) where Tbr is the brightness temperature of background which is reflected by the object and Tbb is the temperature of the background behind the object. 2.1.4 Image temperature contrast The power received by a radiometer coming from a body does not only depend on the body physical temperature but also on its absorption characteristics and the environment brightness temperature. Therefore the temperature contrast in an image acquired by a radiometer will strongly depend on the environment when imaging objects that are not purely absorptive. Table 2.1 shows that the usual object materials found in a security scene have a reflectivity coefficient greater that 0.2and in the limit, metal objects have a r= 1. Hence, the temperature contrast of objects that usually appear in security scenarios will strongly depend on the reflected radiation coming from the environment. In security image two types of scenarios, the indoor and the outdoor, are defined due two their different characteristics of background brightness temperature distribution. Figure 2.1.4 shows an artist view with the background radiation characteristics of both scenarios. The outdoor scenario is represented in Fig. 2.3(a) where three different background radiations are depicted: 1) the sky radiation has a brightness temperature of around Tsky = 100 K at mmW frequencies, although it depends on various parameters such as the incidence angle 2.2 Total-power radiometer with mechanical beam-scanning 21 (a) (b) Figure 2.3: Artist views of an outdoor scenario (a) and an indoor scenario (b) depicting the background temperatures that affect the result of the image contrast. and the cloud density; 2) the brightness temperature of the floor Tfloor is related on its physical temperature that will depend on the quantity of absorbed solar radiation; and 3) the scene brightness temperature Tscene depends on the ambient temperature. The effect of each background radiation is different on the each image portion. The sky temperature is reflected on the shoulders and on metallic objects appearing very cold in the image. The opposite effect is found from the knees to the feet, where the floor radiation is reflected appearing warmer than the rest of the human body. As a result, usually the images have a temperature gradient from cold to warm going from the head to the feet. Figure 2.3(b) corresponds to a indoor scenario where the brightness temperature of the environment Tscene is usually homogeneous and related to the ambient temperature, hence the effect on the image is uniform. The main difference between indoor and outdoor scenarios is the contrast level on the image. Outdoor scenarios experience higher contrasts since the reflection of the sky in the objects increase their apparent temperature difference. The dynamic range of the image also increases and goes from around 100 K to the ambient temperature (≈300 K). In an indoor scenario, the contrast is poor since the ambient temperature is very close to the body temperature and the dynamic range of the images is of around 20 K. In this case the radiometer should be more sensible in terms of received brightness temperature to be able to detect small changes in temperature. For a radiometer with a certain radiometric sensitivity indoor images are noisier than outdoor images and the detection capabilities are reduced in indoor scenarios. Measured images presented in section 2.2.6 are a good example to examine the aforementioned contrast differences. 2.2 Total-power radiometer with mechanical beam-scanning The TPR is a basic radiometer receiver that collects the scene radiation by using an antenna, filters and amplifies the Radiofrequency (RF) signal and detects its power by using a device 22 Chapter 2 Antenna Bandpass filter Amplifier Power detector Integrator ni(t) Vo=Pr nr(t) Figure 2.4: Block diagram of the basic components of a TPR. with a quadratic response. The final step is to average the signal at the output of the power detector in order to improve the Signal to Noise Ratio (SNR). Figure 2.4 shows a simplified block-diagram of the radiometer components. The TPR is the most common radiometer due to its simplicity and is the one chosen to introduce the basic radiometry concepts that will appear along the document.1 The voltage noise signal at the input of the power detector nr(t)can be modeled as nr(t) = nIr(t) cos (ωt)−nQr(t) sin (ωt) [V],(2.8) where Nr(t) = nIr(t) + jnQr(t)is the equivalent baseband of the input noise. The phase and quadrature components, nIr(t) and nQr(t)respectively, are independent stochastic processes with Gaussian probability density function and standard deviation σ. Hence, if a unitary resistor is considered at the input of the power detector, the voltage value at the output of the integrator is Vo=EkNr(t)k2= 2σ2=kBGBTsys [V],(2.9) where E{} is the expectation operator and Gis the gain of the amplifier. The system temperature Tsys =TA+TRincludes the contribution of the noise added by the receiver TRto the input noise. The receiver noise temperature TRdepends on the Noise Figure (NFI) of the receiver (usually fixed by the first amplifier) and can be calculated as TR= 290(NFI −1). The parameter Bis the equivalent noise bandwidth of the bandpass filter defined by B=1 Hmax Z∞ 0|H(f)|2df [Hz],(2.10) being H(f)the frequency response of the filter and Hmax its maximum value. The measurement standard deviation gives an estimation of the sensitivity of the system and can be calculated as std(Vo) = sE{kNr(t)k4}−E{kNr(t)k2}2 N=2σ2 √N[V],(2.11) where Nis the number of independent samples taken in the integration being equivalent to N=Bτ where τis the integration time. From (2.9) and (2.11) the radiometric sensitivity in terms of temperature resolution can be defined as ∆TN=Tsys √Bτ [K] (2.12) 1The following paragraphs of this section may contain verbatim text and figures from [C6,C8, C12]. 2.2 Total-power radiometer with mechanical beam-scanning 23 Ideally, ∆TNcan be arbitrarily low if the integration time is increased. However, the gain variability of the components in the receiver chain strongly reduces the sensitivity of the measurement. This is the main drawback of the TPR and can be solved using compensation techniques such as Dicke switching [50]. The effect of the gain variability on the system temperature is expressed as ∆TG=Tsys ∆G G[K],(2.13) being independent from the noise statistics. The receiver sensitivity taking into account the gain uncertainty is given by ∆T=q∆TN2+ ∆T2 G=Tsyss1 Bτ +∆G G2 [K],(2.14) The gain instability strongly increases ∆Treducing the radiometric sensitivity of the TPR. Usually, a thermal control is required on the radiometer components to minimize gain fluctuations. When acquiring an image, the fluctuation impacts along the whole image acquisition reducing the sensitivity. If no calibration is performed during the acquisition, the relation between brightness temperature and received power will vary from the first acquired pixel to the last one, yielding a distorted temperature map. 2.2.1 Total-power radiometer system design A mmW TPR has been designed to evaluate the passive imaging performance at W-band. The receiver architecture of the TPR is presented in Fig. 2.5(a) is based on a double-sideband heterodyne receiver with 64 dB gain. The NFI of the radiometer is mainly fixed by the first Low-Noise Amplifier (LNA), the 1.5 dB of the isolator losses and the phase noise introduced by the Local Oscillator (LO). A horn antenna is followed by an isolator that prevents the noise produced by the first LNA to be radiated by the radiometer. After the isolator, two LNA stages feed the W-band mixer achieving a chain gain of 64 dB. The LO of the system is based on a 15.16 GHz Phase- Locked Oscillator (PLO) multiplied by 6using a W-band multiplier. A LO signal of 91 GHz is mixed with the input noise signal, overlapping the RF bands from 88 GHz to 91 GHz and from 91 GHz to 94 GHz, since the baseband bandwidth of the system is 3 GHz. The baseband noise power is directly measured using a power detector that provides an output voltage proportional with the input Root-Mean-Square (RMS) voltage. The output/input relation is calibrated and expressed by Vo= 7.7V/Vrms. The video bandwidth of the detector is fixed to 2 kHz, however the signal is further averaged using a microcontroller. Therefore, the video bandwidth of the receiver can be selected by changing the averaging time in the microcontroller. The receiver temperature is stabilized by using a Proportional-Integral-Derivative (PID) controller with 3heating resistors, 2fan-coolers, 1PT100 temperature sensor and 6digital temperature sensors. Figure 2.5(b) shows a photograph of the radiometer with the parabolic reflector mounted on the pan-tilt scanner system. 24 Chapter 2 Conical Horn Antenna / Waveguide Termination LNA G: 32dB Δf: 90-98 GHz Below 15.5 GHz 94GHz components Power Supply and Temperature Control LNA G: 32dB Δf: 90-98 GHz ISOLATOR IL=1.5dB ISOLATION 20dB x6 Frequency multiplier Max. Output power: 15dBm Δf: 91-93 GHz Mixer Δf: 90-95 GHz IF: 0.1-2 GHz LO Power 13 dBm Conv. Losses: 8 dB AD8361 RMS power detector Δf: DC-2.7 GHz PLO Synth. Reference oscillator OX6749A-LZ-1 10MHz HITTITE HMC535LP4 Max. Output power: 9dBm Δf: 14.7-15.4 GHz x64 ADF4360-7 N-Synthesizer 240 MHz µC data and temperature acquisition, digital averaging High pass filter 2 x K band waveguide transitions A/D Converter TI-AD8344 16 bits A/D PIC18F2550 6 x temperature sensors MAXIM – DS1820B 220 to 15V Switched PS 8A max. XP POWER – JPM120PS15 PID Temp. Control EUROTHERM 2132 3x 10W Resistors 1x PT100 Sensor 2x FAN Coolers USB INTERFACE TO PC (a) (b) Figure 2.5: (a) Receiver schematic and hardware components of the TPR. (b) Photograph of the total power radiometer with the scanning system. 2.2.2 Calibration The radiometer has been calibrated using a method based on measuring a temperature sweep of a resistor block. The parabolic mirror is aimed sequentially to a resistor block and to an absorber with fixed temperature in order to compensate gain fluctuations of the receiver. In each measurement the resistor temperature is modified, starting with 100 ◦Cand reducing the temperature in different steps down to 30 ◦C, obtaining 7calibration points plus 7reference points. An infrared camera together with a K thermocouple sensor are used to measure the temperature of both the absorber and the resistor block. The relation between receiver power and brightness temperature of the scene is given by TB=aPo+b, (2.15) where the parameter TB≈Tph is the brightness temperature of the resistor block (where e has been considered 1), bbasically depends on the receiver noise temperature and Pois the corrected received power. The proportional constant adepends basically on the Boltzmann constant, the bandwidth of the receiver, the gain of both LNAs and the losses of the mixer. The correction of the received power is performed by multiplying the measured power the ratio between the reference measurement Pref and the absorber measurement Pabs yielding Po=Pref Pabs Pr.(2.16) Finally, the aand bparameters are obtained by inverting the simultaneous equations obtained 2.2 Total-power radiometer with mechanical beam-scanning 25 152 152.5 153 153.5 154 154.5 155 155.5 156 250 300 350 400 Received Power [mW] Antenna temperature [K] Regression curve Calibration points Figure 2.6: TPR calibration curve. from 7measurements a b=     Pc11 Pc21 . . .. . . Pc71      + ·     Tb1 Tb2 . . . Tb7     ,(2.17) where the symbol ”+”denotes the pseudoinverse of the matrix. The calibration result curve is depicted in Fig. 2.6 having a calculated variance of 0.24 K. 2.2.3 Performance Assessment The radiometric resolution ∆Tin K/√Hz of the radiometer has been characterized by measuring the radiometer output response, based on the ratio between the power detector output voltage spectral density ∆Vin V/√Hz and the power detector output Direct-Current (DC) voltage VDC. Two different regimes exist in the radiometer response separated by the so-called cornerfrequency. In the low frequency region the 1/f noise produced mainly by gain fluctuations in the receiver chain predominates whereas in the region beyond the corner-frequency ∆V/VDC converges to p1/(2B)in the case of using a linear power detector [51]. The characterization of the first region gives an information of the radiometer response drift for long radiometer acquisition times (e.g. the acquisition of an image). If no calibration is performed during the acquisition of an image, the ∆Twill depend on the radiometer stability and thus on the output 1/f noise, as described in [52] [53]. However, if the radiometer is calibrated at a faster frequency rate than the corner-frequency (e.g. with a Dicke switch), the ∆Tis constant with a relative value of p2/BRF. In this case, the relation between ∆V and ∆Tis given by ∆T Tsys = 2 ∆V VDC .(2.18) In order to obtain ∆V, the output voltage frequency spectrum of the detector has been acquired and normalized by the video bandwidth with a HP 3561A Dynamic Signal Ana- 26 Chapter 2 101102103 10−6 10−5 10−4 f [Hz] VAC/ VDC [ Hz -1/2] Band filtered digitally by the microcontroller Spurious tones created by fan coolers Figure 2.7: Measured radiometer response spectrum against video frequency. lyzer. The measurements have been performed with the radiometer input terminated with a temperature controlled matched load at a temperature of 298 K. Figure 2.7 shows the measured ∆V/VDC for video frequencies between 10 Hz and 1 kHz, corresponding to frequencies beyond the corner-frequency. The ∆V/VDC is flat from 10 Hz to 100 Hz with a mean value of 12.9·10−6Hz−1 2, giving equivalent noise RF bandwidth BRF of 3 GHz. Beyond 100 Hz, spurious tones created by the cooler fans appear. A better isolation between power supplies of the fans and the RF circuitry should be performed to avoid this effect. Nevertheless, the radiometer is operated with integration times greater than 1 ms, canceling these spurious signals. As a final result, the computed ∆Tfrom 10 Hz to 100 Hz is 83 mK/√Hz. 2.2.4 Description of the antenna system The antenna system mounted on top of the radiometer is shown in Fig. 2.8(b). A 90◦-offset parabolic reflector with 100 mm of diameter and a focal distance of 152 mm has been used to enhance the spatial resolution of the imaging system. Moreover, it has been mounted on a pan-tilt scanner to acquire images at close standoff distances. The scanner is moved by two servo motors, one per each axis, yielding a rotation resolution of 0.15 ◦for both axes. The reflector is fed by a horn antenna placed at 192 mm from the reflector. Adjusting the feeding point further away from the reflector focal distance allows a proper near-field focusing at 1 m. An approximated value of the angular resolution (-3 dB) is given by ∆θ=λ/D for an uniform illumination, where λis the wavelength at the center RF frequency of 91 GHz and D is the diameter of the reflector. From this equation, 1.9◦of beamwidth is obtained, translated to 3.3 cm at 1 m standoff distance. Figure 2.8(a) shows a simulation of the radiation pattern of the radiometer antenna. In order to obtain the radiation pattern of the horn-reflector group, two simulation steps have been followed: the first step is obtaining the radiation spherical modes of the horn using a Method of Moments (MoM) simulation; and the second step is to use the spherical modes of the horn as a point source in a Physical Optics (PO) simulation of the reflector. 2.2 Total-power radiometer with mechanical beam-scanning 27 −10 −8 −6 −4 −2 0 2 4 6 8 10 −40 −35 −30 −25 −20 −15 −10 −5 0 [deg] Normalized Amplitude [dB] E−plane H−Plane (a) (b) Figure 2.8: (a) Simulated radiation pattern of the radiometer antenna when focusing at 1 m. (b) Photograph of the antenna system specifying the main components. The simulation results show a beamwidth of 2.28 ◦, slightly wider than the theoretical since the taper caused by the horn illumination produces a reduction of the incident power at the edge of the reflector of 10 dB. This effect reduces the angular resolution of the antenna but improves the beam efficiency. The resulting beam efficiency ηbhas been calculated as ηb=R2π 0Rθb 0t(θ, φ) sin θdθdφ R2π 0Rπ 0t(θ, φ) sin θdθdφ ,(2.19) where t(θ, φ)is the normalized power pattern of the antenna system and θbis half of the beamwidth of the antenna. This calculation gives the ratio of power received by the imaged pixel over the total power received, achieving a 94 % for the current antenna system. It has to be pointed out the importance of the beam efficiency in our system, since either the spillover at the reflector or sidelobes effects caused by a sharp taper drastically increases the radiometer acquisition error. 2.2.5 Beam distortion In order to assess the distortion effect produced by the incidence angle and by the displacement of the reflector focus when aiming in elevation, the measurements shown in Fig. 2.9 have been performed. A resistor panel has been placed behind an absorber material having a hole of 1 cm of diameter, thus creating a hot spot. Two images have been obtained at 1 m distance: Fig. 2.9(a) shows an image of the hot spot when it is centered in the scene; additionally, a second image presented in Fig. 2.9(b) is acquired when the hot spot has been displaced to the coordinates (0.4,0.4) m in the scene, thus having the beam an incidence angle of 22 ◦. Two effects are observed when aiming to the border of the scene in Fig. 2.9(b), both the dynamic range of the image and the spatial resolution are worse than in Fig. 2.9(a). Specifically, the spatial resolution increases from approximately 4 cm to 6 cm due to the beam distortion. Moreover, the dynamic range is reduced by 15 K since the beam efficiency is reduced. 28 Chapter 2 (a) Centered point source (b) Displaced point source Figure 2.9: Acquired point source images to assess the beam distortion when aiming to the scene limits. 2.2.6 Imaging Performance The radiometer performs a continuous raster scan in elevation and a step scan in azimuth. For each pixel position, the radiometer microcontroller performs the desired integration of the signal provided by the power detector and sends the value via Universal Serial Bus (USB) to the computer. The computer software synchronizes the reflector aiming position with the power acquisition and stores the information in a 3-dimensional matrix with the elevation, azimuth and power values. Figure 2.10(a) shows a 50x50 pixels image of a person on a chair with a toy gun concealed under a T-shirt. As a reference, Fig. 2.10(b) shows an snapshot of the same scene recorded with an infrared camera from a different point of view. The image has been acquired with 70 ms of integration time per pixel. The calibration has been performed applying the curve given in Fig. 2.6 and using an absorber as a reference temperature. Even though the image has been acquired in an indoor environment, still there is enough contrast between the toy gun and the person to identify the shape of the object. The total acquisition time is 5 min, yielding a mean acquisition time per pixel of 120 ms taking into account the mechanical movement. The theoretical radiometric resolution of the image is 0.22 K calculated from the measured value of ∆Tin section 2.2.3. However, since only one reference calibration is performed, the radiometric resolution is degraded by drifts in the radiometer response. A second example of an indoor image from a standing person carrying a toy gun on the waist is shown in Fig. 2.11(b). It consists of a radiometric image with 100x40 pixels acquired in 7minutes. The radiometric image has 19 K of dynamic range, showing an apparent temperature of 295 K for the background and 305 K for the person. The toy gun and the belt buckle are recognizable as well as the mobile phone carried on the pocket. The apparent temperature of the person skin in the image will depend on the mean value between its physical temperature and the reflected brightness temperature of the environment. The metal surface of the gun however has a reflectivity value of r= 1, thus only reflecting 2.2 Total-power radiometer with mechanical beam-scanning 29 (a) (b) Figure 2.10: (a) W-band radiometric indoor image of a person on a chair with a concealed toy gun under a T-shirt. (b) Infrared image of the same scene. (a) (b) (c) Figure 2.11: (a) Optical, (b) radiometric and (b) infrared indoor images of a standing person with a concealed toy gun under a T-shirt. the environmental brightness temperature. As a result of the low contrast of the scenario, a noisy image is obtained and the gun is detected but hard to identify. An infrared image of the imaged scene is presented in Fig. 2.11(c). Even though the spatial resolution of the infrared image is greater than the radiometric image, the toy gun is harder to be detected since the T-shirt is more opaque to infrared frequencies. Fig. 2.12(b) presents a 100x50 pixels image of a person with a concealed toy gun as in 36 Chapter 2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 1.5 2 2.5 3 3.5 4 4.5 η ∆ T [K] RMS−TX RMS−TY 0.8 Figure 2.17: Radiometric sensitivity of the MIRAS/SMOS instrument over the ocean compared with the theoretical estimation as given in [62]. where ρri is the autocorrelation at the origin of the signal nri(t)and ρr1r2 is the crosscorrelation at the origin between nr1(t)and nr2(t). Hence, if TATsys, the temperature standard deviation of a visibility measurement is ∆Tv=Tsys √Bτ [K].(2.38) In order to calculate the standard deviation of the modified brightness temperature, the inversion equation (2.27) is discretized T0 B(ξ, η) = ∆sX mX n W(umn, vmn)V(umn, vmn)ej2π(umnξ+vmnη),(2.39) where ∆sis the elementary area in (ξ, η). Hence, if visibility errors are uncorrelated the standard deviation of the modified brightness temperature is ∆T0 B(ξ, η) = ∆s∆TvsX mX n W2 mn = ∆sTsys √Bτ αwpNv,(2.40) where αwis a parameter that depends on the window and Nvis the number of visibility samples. From (2.26) and (2.40), the radiometric resolution of a SA radiometer imaging an extended source of thermal radiation is [61]: ∆TB(ξ, η)=∆sTA+TR √Bτ Ωp t(ξ, η)p1−ξ2−η2αwαs αfpNv[K] (2.41) where αstakes into account the sensitivity loss due to non-analog correlation and αftakes into account the pre-detection filter shape. The accuracy of this formula has been recently validated by the MIRAS/SMOS instrument [62] launched on November 2009. Figure 2.17 shows a comparison between the radiometric sensitivity ∆TBof the Microwave Imaging Radiometer using Aperture Synthesis (MIRAS) instrument calculated with (2.41) (dotted lines) and measured by means of brightness temperature images over the ocean (continuous line) for both horizontal (Tx) and vertical (Ty) polarizations at the antenna plane. 2.4 Conclusion 37 2.4 Conclusion In this chapter, a brief description of classical radiometry concepts has been performed as an introduction of the research presented in this document. Special attention is paid to SA interferometric radiometry since the main research is done in this area. In addition, a practical study of mmW radiometry has been presented in this chapter, exposing the imaging capabilities of a mechanically scanned radiometer for concealing object detection. The simplicity of the receiver architecture and its good performance in terms of spatial resolution and radiometric sensitivity makes it appropriate for applications where the acquisition time is not constrained. The antenna subsystem achieves enough spatial resolution to detect objects with dimensions on the order of several centimeters. In addition, having radiometric sensitivity close to 1 K has allowed the acquisition of low-contrast indoor images that reveal concealed objects with only few degrees of temperature contrast. Nevertheless, it is unfeasible to use a single-receiver mechanically scanned system for real-time imaging purposes. The following chapters present performance studies and practical solutions with the objective of optimizing the acquisition time and the cost of the imaging system. 38 Chapter 2 CHAPTER 3 Millimeter-wave Performance Constraints for Passive Close-Range Screening INthis chapter, a theoretical study of the performance constraints appearing in passive closerange screening are studied. Three types of radiometers have been analyzed in terms of radiometric sensitivity and spatial resolution: 1) the Two-Dimensional Synthetic Aperture (2D-SA) radiometer; the One-Dimensional Synthetic Aperture (1D-SA) radiometer and the Real-Aperture (RA) radiometer. The analytical expressions for the radiometric resolution, the number of required antennas and the number of pixels in the image are derived taking into account the distortion produced by the Near Field (NF) geometry at non-boresight directions where the distortion is dominant. The image distortion caused by the NF geometry is assessed by using 2D-SA screener simulations. An screener geometry based on a sparse linear array is proposed as an optimum solution to achieve the best performance with the minimum number of receivers. If a moving walkway is used with a sparse linear array, no mechanical movements are needed on the receiver. Special attention is paid to this system since it solves problems regarding the number of receivers and acquisition time. Based on theoretical results a performance comparison among the studied systems is carried out to show the advantages and drawbacks when using the radiometers in a close-range screening application. Additionally the screener performance in a close-range environment is discussed from the results obtained in the aforementioned comparison. 1 3.1 Close-range aperture synthesis In this section the performance expressions for the 2D-SA, 1D-SA and RA radiometers are particularized for close-range screening. In the case of the interferometer systems, a T-shape array is the optimum configuration regarding a rectangular Field of View (FoV) as the one required by screening systems [60]. Therefore, the analytical expressions of sensitivity and 1The following sections of this chapter may contain verbatim text and figures from [J2]. 40 Chapter 3 Figure 3.1: Imaging setup used to compare different screening configurations. spatial resolution are derived for this geometry. Figure 3.1 shows the screener geometry and its disposition with respect the scene. The scene dimensions 2Wx2H together with the imaging range rdefine the FoV of the system. In order to use the inverse Fast Fourier Transform (iFFT) to obtain the image from the visibilities measured by the interferometric radiometer the targets of interest should be located in the Far Field (FF) range of the array [63]. For close-range operation, a Near-to-Far-Field correction is proposed in [64] [65] to use the Fast Fourier Transform (FFT) to retrieve images acquired in NF range if a certain degree of distortion at the edges of the FoV is allowed. It is considered that the scene is in the NF of the array if the distance between the array and the scene is r < 2D2 a/λ, where Dais the array physical size. The equality is given when the maximum phase error due to the paraxial approximation is π/8. In this situation, the phase error present in the visibilities should be compensated in order to avoid distortion if an iFFT is used as an image focusing technique. From the measured visibilities in NF VNF kj , an estimation of the FF visibilities is given by b VFF kj =VNF kj e−jk0(rk−rj)e−j2π(uξ+vη).(3.1) The correction consists of a phase compensation introduced by the term e−jk0(rk−rj), where riis the distance from the antenna “i”to the center pixel of the image. Hence, by using this correction, the center pixel is properly focused whereas the focusing level is decreased as the pixels are further from the center. Note that the target is in the FF of any single antenna 3.1 Close-range aperture synthesis 41 element in the array and close-range distortion is exclusively caused by non-paraxial imaging and by the projection of the screener beams on the image plane. The following points apply the formulation for 2D-SA, 1D-SA and RA radiometers developed in [64] to close-range applications. The general sensitivity equations for the different radiometers are elaborated for a NF geometry. These expressions can be directly compared at an equivalent imaging time (ts) depending on the system bandwidth, system temperature, scene range and dimensions and required resolution. In order to analyze several radiometer configurations, only boresight radiometric resolution is taken into account. 3.1.1 Single element constraints Equation (2.41) shows that boresight radiometric resolution is improved by minimizing the single element solid angle Ωe. However, since off-boresight radiometric resolution is degraded with the antenna pattern, a tradeoff is achieved by constraining this degradation to a maximum factor of 2 when the single element Half-Power Beamwidth (HPBW) matches the FoV. To assess the feasibility of this approach we must notice that the maximum size of a single element in the array is limited by the minimum antenna separation du and dv. In this case, according to (2.32), the single element HPBW for an aperture with uniform fields and size du ·dv is given by ∆θex =0.88 du = 0.88(2ξmax) ; ∆θey =0.88 dv = 0.88(2ηmax).(3.2) Therefore, in the case of practical antennas the HPBW of the single element antenna can be adapted to the scene FoV by using an aperture slightly smaller than the minimum antenna separation as described by the following expression: Lx∼ =0.88du Ly∼ =0.88dv (3.3) where Lxand Lyare the aperture dimensions of the single element antenna normalized to the system wavelength. 3.1.2 Particularized radiometric sensitivity For the sake of simplicity, rectangular tapering, analog correlation and ideal rectangular predetection filtering are considered in (2.41) yielding ∆TB=TA+TR √Bts du ·dv ·ΩepNuNv,(3.4) where the elemental sampling area given by ∆s=du·dv has been considered for rectangular sampling. It should be pointed out that according to (3.4) ∆TBis optimized if the single element solid angle Ωeis minimized by matching the HPBW of the single element antenna pattern to the FoV. In the case of a large number of elements in the array, from (2.30) and (2.34) the following equation is obtained du ·dv ∼ =4umaxvmax NuNv∼ =1 NuNv 4·0.602 ∆θx∆θy .(3.5) 42 Chapter 3 Now, if the synthesized solid angle is approximated by the product of the HPBW in the two orthogonal directions, Ωsyn ∼ =∆θx∆θy, and taking into account the relationship between solid angle and effective area (Ωsyn/Ωe=Ae/Asyn)the following expression is obtained ∆TB= 0.72TA+TR √Bts Asyn Ae 1 √NmuNmv ,(3.6) where Asyn and Aeare the effective areas of the synthetic aperture and the single element aperture. Note that (3.6) is consistent with the approximate expression usually found in the literature [66], where the number of measured visibility samples Nmu ·Nmv =Nu·Nv/4is used (the Hermitian visibility samples are not taken into account). 3.1.3 2D synthetic aperture interferometric radiometer In order to obtain the NF sensitivity expression, (3.4) is transformed using the following parameters: •Boresight spatial resolution in x: ∆x=r∆θx∼ =r∆ξ •Boresight spatial resolution in y: ∆y=r∆θy∼ =r∆η •Target size along x: 2ξmax = 2 sin(arctan(W r)) •Target size along y: 2ηmax = 2 sin(arctan(H r)) Since the synthesized image is computed as the FFT of the visibility samples, if Fourier interpolation is not used, the number of independent pixels in the synthesized image (Npx and Npy) is coincident with the number of visibility samples (Nvx and Nvy). In order to take into account the smearing of the image, the relation between the Effective Field of View (EFoV) and the Instantaneous Field of View (IFoV) is considered for the computation of the number of pixels. The angular resolution (∆θxand ∆θy) is approximated by the increment of the direction cosines (∆ξand ∆η) at boresight. If the single element HPBW matches the FoV: Ωe∼ = ∆θex∆θey ∼ =2ξmax2ηmax and Ωe∆s= 1. Thus if the NF distortion can be neglected ∆TB is independent on the imaging range as presented in point 3.1.6 and depends on the receiver parameters, the scene dimensions and the spatial resolution. Furthermore, as the antenna separation is also adapted to the FoV, the spatial resolution for a given number of antennas is approximately maintained independent of the range. Due to the pixel overlapping of the synthesized images given as a result of (2.35) and (2.36), the number of pixels related with the FoV and the spatial resolution is Nu=Npx = 1.22ξmax ∆θx + 1 ≈1.22ξmax ∆θx ;(3.7) Nv=Npy = 1.22ηmax ∆θy + 1 ≈1.22ηmax ∆θy .(3.8) 3.1 Close-range aperture synthesis 43 By substituting the aforementioned parameters in (3.4) the resulting expression is ∆TNF 2D = 2.4Tsys √Bts arctan(W r) arctan(H r) sin(arctan(W r)) sin(arctan(H r))ssin(arctan(W r)) ∆x r sin(arctan(H r)) ∆y r . (3.9) 3.1.4 1D synthetic aperture interferometric radiometer A 1D-SA radiometer that performs synthetic imaging in the vertical direction yand real aperture in horizontal direction xis studied. The 1D-SA radiometer must acquire a vertical line of pixels in ti=ts/Npx seconds in order to have a 2D image in tsseconds. In this case, the radiometric resolution is approximated by the following expression ∆TB=TA+TR √Bts ∆θydvpNvNpx.(3.10) The following equation is obtained if the parameters of (3.10) are transformed to consider the NF geometry ∆TNF 1D =√4.8Tsys √Bts arctan(H r) sin(arctan(H r))sarctan(W r) ∆x r sin(arctan(H r)) ∆y rrEFOV IFOV .(3.11) As in the 2D-SA case, the single element HPBW must match the FoV and the antenna separation dv is adjusted to the image FoV (dv = (2ηmax)−1). The number of mechanically scanned pixels depends on the scene distance for close-range imaging resulting in Npx =2 arctan (W r) ∆x r EFOV IFOV .(3.12) 3.1.5 Real aperture radiometer A system based on a single receiver radiometer with a beam-scanning antenna system has been considered for the RA screener configuration. In this case if Npx ·Npy pixels are imaged in tsseconds, the integration time for each pixel timust be reduced accordingly, yielding a radiometric sensitivity ∆TB=TA+TR √BtspNpxNpy.(3.13) Taking into account the number of pixels in NF, (3.13) develops into ∆TNF RA =Tsys √Btss2 arctan(W r) ∆x r 2 arctan(H r) ∆y r EFOV IFOV .(3.14) 44 Chapter 3 3.1.6 Far field radiometric sensitivity In the FF screening range (rW, H), the trigonometric functions of (3.9), (3.11) and (3.14) can be approximated by the angles, yielding the following expression ∆TFF B=TA+TR √Btss2W ∆x 2H ∆y EFOV IFOV .(3.15) Hence, the radiometric sensitivity ∆TBin the FF range tends to the same value for the three studied systems. Note that the Interferometric Radiometer Uncertainty Principle derived in [61] can be translated to the screener case by the following expression ∆TB·∆x·√ts=Tsys √B EFOV IFOV 2√WH. (3.16) The performance parameters have been grouped in the left hand side of the equation whereas the system parameters are in the right hand side. A clear tradeoff between spatial resolution and radiometric sensitivity is shown in the expression. 3.2 Screener design parameters In the following sections the expressions derived in section 3.1 are compared depending on several parameters. Additionally, a sparse array configuration is described for the 1D-SA radiometer. It should be pointed out that time delays caused by mechanical movements have been neglected in the comparison. 3.2.1 Radiometric sensitivity comparison The radiometric sensitivity ∆TBdescribes the capacity of the radiometer to distinguish among small scene contrasts in the image and hence, the capacity of detecting concealed objects with an apparent temperature similar to the background. The three radiometer systems are compared with similar front-end characteristics: TR= 300 K (3 dB noise figure), TA= 300 K, B= 500 MHz,∆x= ∆y= 3 cm, and a target size 2H= 180 cm and 2W= 90 cm (Fig.3.1). A relation between EFoV and IFoV is chosen as EFoV = 1.2IFoV for mechanical scanning to compare all systems in equal smearing conditions. These parameters will be used in the following points to compare the different radiometer architectures unless otherwise noted. Figure 3.2(a) shows the variation of ∆TBwith the imaging time calculated with (3.9), (3.11) and (3.14) at a range r= 1.25 m. In this particular case, ξmax = 0.33 and ηmax = 0.58 yielding an antenna separation of du = 1.51 and dv = 0.86. The spatial resolution sets umax =vmax = 25 and the number of pixels Nu= 34 and Nv= 59. The result is similar for the three radiometers and shows that with the studied system configuration the radiometric sensitivity is below 1.5 K for an image acquisition time of 1 s at a bandwidth of 500 MHz. Sub-second imaging or improved radiometric sensitivity requires larger predetection bandwidth (e.g. B= 2 GHz). 3.2 Screener design parameters 45 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 ts [s] ∆ T [K] 2D-SA 1D-SA RA B=500 MHz B=2 GHz (a) 0.5 1 1.5 2 2.5 3 3.5 4 0.9 1 1.1 1.2 1.3 1.4 1.5 Range [m] ∆ T [K] 2D−SA 1D−SA RA (b) 0.5 1 1.5 2 2.5 3 3.5 4 20 30 40 50 60 70 80 Range [m] Pixels Npx: 2D−SA Npy: 2D−SA Npx: 1D−SA Npy: 1D−SA Npx: RA Npy: RA (c) 1.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 Range [m] Antennas 2D−SA 1D−SA RA (d) Figure 3.2: (a) Radiometric sensitivity against integration time and bandwidth of the radiometers. Subsecond imaging and sub-Kelvin sensitivity requires a large bandwidth. (b) Radiometric sensitivity depending on the scene distance from the radiometer. (c) Number of pixels in the image for the different studied radiometers. (d) Number of antennas required to fulfill the FoV and spatial resolution specifications depending on the scene range. The range dependance of the radiometric sensitivity in passive NF imaging is pointed out in Fig. 3.2(b). For the aforementioned system characteristics and for a range between 0.5 and 2meters the sensitivity is dependent on the range. For a range larger than 2 meters the sensitivity tends to a value of 1.4 K, close to the FF value. The variation of the sensitivity in the NF range is due to the reduction of the number of pixels needed to acquire the image as presented in Fig. 3.2(c). This effect occurs since the projection of the beam on the scene degrades the spatial resolution at the edges and therefore the number of pixels required to fill the scene is reduced. Furthermore, as the number of pixels is reduced, the number of antennas is as well reduced in the case of the interferometric radiometers as shown in Fig. 3.2(d). Further discussion of NF distortion effects are carried out is section 3.3.2. Table 3.1 shows a comparison made according to a similar front-end configuration at 1.25 m range with 3 cm of spatial resolution. The RA screener needs one receiver antenna with an area of approximately 177 cm2to obtain the desired spatial resolution whilst the 1D filled (*) interferometric array is composed by 31 antennas of 3.4 cm2and the 2D array contains 65 antennas with an area of 0.13 cm2. The parameters specified for a 1D (**) array represent the performance of an array thinned to 10 antennas. The compared systems have nearly the same radiometric sensitivity if they are optimized for a specific range as shown in Table 3.1. 52 Chapter 3 −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=3cm / f0=94GHz y [m] (a) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=3cm / f0=94GHz y [m] (b) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=2cm / f0=94GHz y [m] (c) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=2cm / f0=94GHz y [m] (d) 0 5 10 15 [K] −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=1cm / f0=94GHz y [m] (f) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=1cm / f0=94GHz y [m] (g) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=3cm / f0=35GHz y [m] (h) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=3cm / f0=35GHz y [m] (i) 0 5 10 15 [K] −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=2cm / f0=35GHz y [m] (k) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=2cm / f0=35GHz y [m] (l) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=20GHz / ∆x=1cm / f0=35GHz y [m] (m) −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 x [m] B=10GHz / ∆x=1cm / f0=35GHz y [m] (n) 0 5 10 15 [K] Figure 3.10: 2D Screener simulations of the scene shown in Fig. 3.8(a) with r= 1.2 m. Decorrelation effects are taken into account. The simulations have been performed at two center frequencies f0= {94,35}GHz and two RF bandwidths B={10,20}GHz. The differential images reconstructed at f0= 94 GHz are: (a)(c)(f) with B= 20 GHz and ∆x= ∆y={3,2,1}cm respectively; (b)(d)(g) with B= 10 GHz and ∆x= ∆y={3,2,1}cm respectively. The results at f0= 35 GHz are: (h)(k)(m) with B= 20 GHz and ∆x= ∆y={3,2,1}cm respectively;(i)(l)(n) with B= 10 GHz and ∆x= ∆y={3,2,1}cm respectively. 3.3 Screener performance 53 effects produced by the beam projection on the image plane reduces the detection capability of the system at the edges. Figure 3.8(b) shows the distortion produced by the beam projection on a reconstructed image at r= 0.6 m, where the NF to FF correction has been applied. The edges of the image are affected by a blurring caused by a increment of the pixel dimension. The object placed in the ankle cannot be detected due to the distortion. In the case that this distortion level is unacceptable for the screener application, the radiometer should be placed at a further range, thus implying an increment of size of the imaging array. The second source of distortion is the assumption of the paraxial approximation in the reconstruction of the image. This assumption produces a phase error when imaging at closerange that should be corrected to properly reconstruct the image [64] [65]. Figure 3.9 is devoted to better illustrate the distortion effects produced in the close-range imaging. The effect predominating in the images appearing in the figure is the one produced by the paraxial approximation. An scenario with dimensions 2W= 90 cm and 2H= 180 cm has been used as a reference target to foresee the distortion produced by using standard interferometric techniques in the NF range. The scene contains a person at a differential temperature of 15 K with respect the background. The person carries 3metallic objects with different dimensions: 1) 4x10 cm2in the chest; 2) an L-shape object with 5 cm width in the waist and 3) 3x5 cm2 in the ankle. Figures 3.9(a)(d)(f) (i)(k) are retrieved differential images using standard iFFT with a boresight HPBW ∆x= ∆y={5,4,3,2,1}cm respectively. It can be appreciated that, as the spatial resolution is improved, the distortion is aggravated. This is due to the array enlargement needed to achieve the required resolution. Hence, if the array is larger, the phase error related to the paraxial approximation is increased. The phase error produces a distorted image not suitable for identification of concealed objects. Figures 3.9(b)(e)(g)(j)(l) are retrieved images after NF to FF correction with a boresight HPBW ∆x= ∆y={5,4,3,2,1}cm respectively. The reconstructed images after NF to FF shows a reduced level of distortion an are suitable to detect the objects, nevertheless the distortion level is increased at the edges as the spatial resolution is improved. The distortion correction capabilities are reduced when the array dimensions are increased to improve the spatial resolution. Hence, the Fig. 3.9(g) shows less distortion than 3.9(l). The results presented in Fig. 3.9 also show the detection capabilities depending on the spatial resolution. In Fig. 3.9(b), with ∆x= ∆y= 5 cm the object concealed in the ankle cannot be detected due to a lack of spatial resolution. However, in Fig. 3.9(l) the object is clearly identified. 3.3.3 Decorrelation effects Section 3.3.4 will show that a large predetection bandwidth Bis required to significantly improve the performance of the screener with relation to the example described in Table 3.1. However, although analog correlation allows very large bandwidth, decorrelation may degrade off-axis spatial resolution. Simulation of the NF visibilities in Fig. 3.10 has included the impact of decorrelation when an ideal rectangular bandpass filter in each receiver is taken into account. In this case, the fringe washing function for the baseline (u, v)given by a pair of receivers “k”and “j”has been modeled as: rkj(τd) = sinc B c0 (rk−rj)(3.20) 54 Chapter 3 where the delay τdbetween the radiation collected by antennas kand jis direction dependent, c0= 3 ·108m/sand rk,j the distance of each pixel in the image to antennas kand jrespectively. Figure 3.10 shows the impact of decorrelation effects in the reconstructed image for all combinations of f0={94,35}GHz,∆x= ∆y={3,2,1}cm and B={10,20}GHz. For f0= 94 GHz, the impact of decorrelation is negligible for predetection bandwidths of B= 10 GHz. However, the effects are noticeable for B= 20 GHz, mainly if ∆x= ∆y= 1 cm. For f0= 35 GHz, the decorrelation effects seriously impact the image, hindering the detection of objects at the edges of the image.At lower frequency bands the decorrelation impact of pre-detection bandwidth is higher due to the larger size of the array. This result justify that in order to avoid the NF distortion in the image Millimeter- Wave (mmW) frequency bands should be selected for close-range imaging. 3.3.4 Improved performance The results presented in Table 3.1 and Fig. 3.9 are related to a quite simple sensor design to show, as a first approach, the main performance parameters of a close-range screener. However, the enhanced performance that some applications may require can be achieved on penalty of higher cost and complexity. The improvement of any of the performance parameters of (3.16), while keeping constant the others, can only be achieved by improving the system parameters in the right hand side of the equation: •System temperature. Since the antenna temperature is fixed to TA∼ =300 K, system temperature can only be significantly improved if a cryogenic front end, either passive or active, is foreseen to reduce TR= 300 K. The theoretical maximum improvement factor in the ∆TB·∆x·√tsproduct is 2 when TR= 0 K. •Predetection bandwidth.Bcan be greatly increased if analog correlation, IF channelization or a combination of both is taken into account. The simulation in the previous section has shown that very large predetection bandwidths are feasible with negligible decorrelation effects in the W-band. If an effective bandwidth B= 10 GHz is used the sensor parameters would be improved by a factor of 4.5with respect the curves shown in section 3.2.1. •Redundancy. The radiometric resolution expressions given in [61] and [66] do not take into account any level of redundancy. Two baselines are said to be redundant one with the other when the distance and the direction of the two receivers involved in each one of the two baselines are the same. Unfortunately, the level of redundancy in 2D arrays is marginal (only in the direction of the axis). On the other hand, 1D-AS arrays have a large degree of redundancy but can be thinned to a large extent to minimize the number of antennas. Therefore, the most direct way to reduce radiometric noise by averaging simultaneous independent measurements is by replicating the whole sensor. This is particularly efficient in the case of 1D-SA sparse array. For instance in Table 3.1 2D-SA and 1D-SA sparse sensors require 65 and 10 antennas respectively to achieve the same radiometric resolution (∆TB= 1.3 K). If 61D-SA sparse arrays are placed together pointing to the same pixel (or adjacent pixels in the mechanically scanned direction), radiometric resolution is improved by a factor √6 with relation to the 2D case. 3.4 Conclusion 55 •Environment. The absorbers placed in front of the FoV can be cooled down to increase the contrast between reflective targets and the body temperature. For instance, surrounding temperature Tph = 12 ◦Cincreases the contrast from 15 K to 25 K and relaxes ∆TBrequirement by a factor 1.7. 3.4 Conclusion The theoretical framework developed in [66] for 1D, 2D and RA systems has been applied to analyze the performance and basic constraints of passive interferometric imaging for closerange applications. Close range system parameters have been set as a tradeoff between radiometric sensitivity, imaging rate and boresight spatial resolution, that has been presented as the close-range uncertainty principle. It has been shown that, when compared with the same front end parameters, spatial resolution and imaging rate, 2D-SA, 1D-SA and RA radiometric sensitivity is equivalent and not a driver to select one of the options. However, off-boresight radiometric resolution degrades as a function of ξ2+η2in the synthesized cases. Close attention has been paid to analyze close-range radiometric sensitivity, which is critical to achieve both high imaging rates and good spatial resolution. The accurate radiometric sensitivity expression recently validated within the Soil Moisture and Ocean Salinity (SMOS) project [61] has been used , and its consistency to the approximate formula widely used in passive interferometry [66] has been demonstrated. It has been shown that the optimum performance is achieved when imaging at a fixed range and the HPBW of each single antenna in the array matches the scene FoV. Also, that this condition is always feasible, in a first approach, independently of the imaging geometry and requirements. Simulations and theoretical analysis have shown that close-range imaging with moderate requirements is feasible with relatively simple front end configurations if some degree of offaxis performance degradation is allowed. Additionally, section 3.3 has discussed the path to achieve more stringent specifications (e.g. ∆x∼ =1 cm,∆TB∼ =1 K and ts1 s) on the penalty of higher cost and complexity. It is known that mmW screener applications benefits from the penetrating capability of the electromagnetic fields. The simulations in this work has been used to illustrate the main features and constraints of close-range synthetic aperture imaging to show that, due to the small array size, mmW operation also allows for very large predetection bandwidths and close-range configurations to improve radiometric sensitivity while minimizing decorrelation effects and NF distortion. It can be concluded that an sparse 1D-SA radiometer can be used with a moving walkway to perform personnel screening avoiding mechanical movements with an optimum number of mmW receivers. The performance of this screener in terms of ∆x,∆Tand tsis equivalent to the performance of an screener based on a 2D-SA or a 1D-SA radiometer. However, using interferometric radiometers at mmW frequencies is still a challenge due to the required Intermediate Frequency (IF) processing. This conclusion motivates the research presented in chapter 4, where a technique to reduce the complexity of a mmW screener system is described. 56 Chapter 3 CHAPTER 4 One-dimensional Synthetic Aperture Radiometer with Optical Signal Processing CHAPTER 3 concludes that the one-dimensional sparse interferometric radiometer achieves a good tradeoff between radiometric performance and number of receivers for closerange screening purposes. However, still a major drawback resides on this type of radiometer: the acquisition of multiple correlations of large bandwith signals required to retrieve the visibilities of the scene. This is a huge problem when the bandwith of the signals is on the order of several GHz if traditional techniques such as digital signal correlation or Intermediate Frequency (IF) analog correlation are used [68] [69]. Specifically, if digital correlation technique is chosen, Analog-to-Digital Converters (ADCs) with a sampling frequency of fs= 2B should be used in order to fulfill Nyquist criteria. Additionally, the correlations are performed in Field Programmable Gate Arrays (FPGAs) that should process the large amount of data incoming from the ADCs. If the bandwidth of the signals are on the order of several GHz, the hardware complexity required by the correlator system is unaffordable since neither FPGAs nor ADCs supporting such large digital speed rate are commercially available. This chapter describes a method to overcome the problem of routing and correlating all the antenna signal pairs in an interferometric radiometer by upconverting the Radiofrequency (RF) signal to the optical domain. Hence, the relative bandwidth of the modulated signal is small (even with a RF bandwidth consisting of tens of GHz) allowing the use of commercially available components for optical communications (e.g. Distributed Feedback (DFB) lasers, photodiodes, couplers...). In addition, the distribution of the signal is simplified in the optical domain with respect an RF distribution, since multiple optical signals can be guided either by fiber optics or free-space avoiding coupling effects. The first section of the chapter is devoted to describe the optical modulation and correlation process using LiNbO3 phase modulators. The working principle of the optical modulator is explained with the aim of understanding the characteristics of the modulated optical. Moreover, the resulting expressions for an optical correlation of two radiometric receivers are obtained for two different modulation schemes: 1) Double-Sideband (DSB) and 2) Single- Sideband (SSB) modulations. In the second section of the chapter, the expressions governing 58 Chapter 4 Ground Electrode Hot electrode LiNbO3 crystal Optical waveguide Induced E-Field Interaction length: l Electrode separation: d Figure 4.1: Perspective schematic view of an x-cut optical phase modulator where the main parts (RF electrodes, optical waveguide, LiNbO3 crystal...) are depicted. the method are related with the classical interferometric theory. Both sections are complemented with measurements that confirm the validity of the expressions. Additionally, final measurements consisting on one-dimentional images are acquired by moving two W-band radiometric receivers along a line in order to synthesize the required baselines. The third section is devoted to explain the optical distribution scheme that is able to obtain the signal combinations between all receiver pairs. Finally, considerations regarding the performance of the system are discussed at the end of the chapter for both types of optical modulations.1 4.1 Optical modulation In order to up-convert the RF signal to the optical domain, a laser optical source is modulated by the RF signal. There are mainly three types of commercially available optical modulator: 1) LiNbO3 modulators [70], 2) electro-absorption modulators [71] and 3) the direct modulation of a laser [72]. The study described in this chapter uses LiNbO3 modulators since they achieve the maximum bandwidth among all the options [73]. 4.1.1 LiNbO3 phase modulators The LiNbO3 optical phase modulators are based in the electro-optical effect that occurs in the LiNbO3 crystal. If the LiNbO3 crystal is placed between two electrodes, the phase of the optical signal going through the crystal is modulated by the voltage Vbetween the electrodes 1The following sections of this chapter may contain verbatim text and figures from [J1] [C3,C4]. 4.1 Optical modulation 59 as ∆Φ = πn3 0rV λ0 l d,(4.1) where dis the electrode separation, ris an electro-optic tensor that depends on the polarization of the optical beam, n0is the LiNbO3 index of refraction, lis the length of the interaction between the crystal and the optical signal and λ0is the optical wavelength. Figure 4.1 shows an schematic of a LiNbO3 phase modulator where the electrodes, the optical waveguide and the direction of the electric field are depicted. The voltage required to produce a phase shift of πis called half-wave voltage Vπ. The half-wave voltage is defined by the geometrical characteristics of the modulator and is obtained directly from (4.1) as Vπ=λ0 n3 0r d l.(4.2) The orientation of the crystal axes with respect the optical waveguides and the electrodes affects to the modulator efficiency and therefore to the half-wave voltage. The electric field should be aligned with the z-axis of the crystal since it is the axis presenting the highest electro-optic coefficient [70]. Figure 4.1 shows an schematic of an x-cut optical phase modulator where it is shown that the electric field created between the electrodes by the RF signal generates an electric field parallel to the z-axis of the crystal. Additionally, LiNbO3 crystals are birefringent and thus their refractive index depend on the polarization of the optical wave. A consequence of the birefringence in the LiNbO3 crystal is that the modulation efficiency of a LiNbO3 modulator also depends on the polarization of the incident optical wave. Hence, an optical polarization control is required to maximize the modulation efficiency. 4.1.2 Optical phase modulation by a CW signal If an RF Continuous Wave (CW) signal defined by x(t) = V0sin(ωmt+ψ)is used to modulate a laser beam with and electric field E(t) = E0ej(ω0t+φ0), the signal coming out of the LiNbO3 modulator is Em(t) = E0ej(w0t+φ0+msin(ωmt+ψ)),(4.3) where m=πV0 Vπand φ0=2πn0l λ0. The term ejm sin(ωmt+ψ)can be decomposed as ejm sin(ωmt+ψ)= ∞ X k=−∞ Jk(m)ejk(ωmt+ψ),(4.4) where Jkis the Bessel function of the first kind and order k. Therefore the resulting modulated signal spectrum contains multiple sidebands separated ωmfrom the optical center frequency ω0. If the RF signal amplitude fulfils the condition V0Vπ, the following approximations can be performed: Jk(m)≈0∀ |k|>1,J±1(m)≈ ±m 2and J0(m)≈1. Therefore (4.4) can be expressed as ejm sin(ωmt+ψ)≈1 + m 2(ej(ωmt+ψ)−e−j(ωmt+ψ)),(4.5) where only the carrier and the first sidebands are considered. Introducing (4.5) in (4.3) the optical signal is Emod(t)≈E0ej(ω0t+φ0)[1 + jm sin(ωmt+ψ)] .(4.6) 60 Chapter 4 Laser 3 dB Coupler LiNbO3 Phase Modulator LiNbO3 Phase Modulator 3 dB Coupler Photodiode TIA Transimpedance Amplifier Z=1200 Minicircuits VLF-7200+ VHF-6010+ B = 2 GHz fm= 7 GHz Power Detector x1(t) x2(t) E(t)=E0·ej·w0·t b1 DSB(t) b2(t) NEL NLK1556STG O ptical power = 0 dBm R=0.85 Lm= 1.5 dB Vπ=4.5 V Fujitsu FTM7921ER Agere 2860E Rohde & Schwarz NRP-Z21 Lm= 1.5 dB Vπ=4.5 V y (t) p (t) DSB DSB DSB Polarizer & Figure 4.2: Optical modulation and detection schematic for two receivers. The optical signal provided by a laser is modulated by the RF radiometric signals coming from the receivers. Two LiNbO3 modulators are used for this purpose. The DSB modulated signals are added and detected by a photodiode. The resulting photocurrent contains the correlation between both receiver signals. The component model of each part used in the measurement setup is specified. Equation (4.6) approximates the result of the optical signal phase-modulated by a single RF tone. 4.1.3 Cross-correlation of double-sideband optical modulated signals Figure 4.2 shows a block diagram of the proposed optical conversion system. The RF signals collected by the antennas in the millimeter-wave band are downconverted to provide x1,2(t) at an IF frequency compatible with the modulation bandwidth of the LiNbO3 phase modulator. The polarization of the optical signal produced by a DFB laser is adjusted by using an optical polarizer to maximize the modulation efficiency of the LiNbO3 modulators as described in the previous section. The optical signals bDSB 1,2(t)have been modulated respectively by the IF radiometric signals x1,2(t)and are combined and detected by a photodiode. The photodetected current is amplified using a Transimpedance Amplifier (TIA) and the power of the resulting signal is measured with a power detector. Although (4.6) is derived for a single tone, the results are also valid when the modulating signal is band-limited Gaussian noise with a small power [74] [75]. In this case, and going 4.1 Optical modulation 61 f fm B Sn1(f) l l0 So(l) Phase Modulation l l0l0+lm Sm1(l) l0-lm Sm2(l) Signal Coupling Sm1(l)+Sm2(l) Sm1(l)+Sm2(l) Photodiode + TIA Power Detector f fm B Sn1(f)+Sn2(f) RF Domain Optical Domain Optical Domain RF Domain DC Component with the correlation value Sidebands mixed with the carrier in the photodiode Figure 4.3: Spectrum of the signal in each step of the modulation and detection process. The RF spectrum of the signal coming from the receiver Sni(f)modulates an ideal optical laser source So(λ). The resulting modulated signal Smiis added to the modulated signal coming from other receiver Smj. The result is mixed in a photodiode producing a signal with spectrum centered at fmand bandwidth B proportional to Sni(f) + Snj(f). The final step is to measure the power of the signal with a power detector. This process yields a DC component with the correlation between the RF signals coming from both receivers. back to the block diagram of Fig. 4.2, for an input signal of the modulator x1,2(t)consisting of a band limited Gaussian noise of bandwidth B, the modulated optical signal is given by bDSB i(t)≈E0cos (ω0t+φi)−π VπLm xi(t) sin(ω0t+φi),(4.7) where Lmcorresponds to the optical losses in the modulator and xi(t)is defined as xi(t) = nIicos(ωmt)−nQisin(ωmt),(4.8) being ni(t) = nIi(t) + jnQi(t)the equivalent baseband signal of the noise. The following calculations are particularized for two front-ends and it is assumed that n1,2(t)are equal with a certain group delay difference n1(t) = n2(t−τ)e−jωmτand with equal power Pn1,n2=Pn. Hence the correlation level of the RF signals modulating the laser in each branch will depend on the delay difference τ. The effect of the receiver equivalent noise temperature and therefore the effect of additive uncorrelated noise in the result is discussed in Section 4.1.5. 68 Chapter 4 Receiver 1 Antenna 1 Receiver 2 Antenna 2 u D D x, x Point source R xPS t1t2 (a) (b) Figure 4.7: (a) Schematic of the setup used in Sections 4.2.2 and 4.2.3. A point source based on a hot resistor has been used as target to perform the measurements. (b) Photograph of the W-band and optical setup built to perform the measurements described in Sections 4.2.2 and 4.2.3. The components of two radiometric receivers are shown. The W-band components of each receiver are a conical horn antenna, a LNA, a mixer and a x6 multiplier. The schematics of the receiver chain is described in Fig. 4.8 whereas the optical part has been shown in Fig. 4.2. 4.2.3 One-dimensional image A one-dimensional brightness temperature distribution has been imaged using the optical correlation method proposed in this paper with the same receiver architecture as in Section 4.2.2. 4.2 Millimeter-wave interferometry measurements with optical signal processing 69 Conical Horn BW: 17.5 deg x6 15 GHz Bandpass Filter Minicircuits VLF-7200+ VHF-6010+ Bandwidth = 2 GHz Central frequency = 7 GHz xi(t) LNA HXI HLNAW-241 G: 28 dB NF: 6 dB Mixer Millitech MXP-10 CL: 12 dB X6 Multiplier Ducommun FMA-92 Output Power : 10 dBm @ 90 GHz IF Amp. Chain 2xMinicircuits ZX60-183+ G: 48 dB Phase shifter Hittite HMC929 Rohde & Schwarz SMB 100A Figure 4.8: Schematic of the W-band receiver components. A conical horn with 17.5 deg of beamwidth has been used as an antenna. A LNA with 28 dB gain and NF of 6 dB is placed before the mixer. The 7 GHz IF signal is filtered with 2 GHz of bandwidth and is amplified 48 dB. The last component before the optical modulator is a phase shifter used to perform the phase switching described in Section 4.2.1. −0.1 −0.05 0 0.05 0.1 −40 −20 0 20 40 ξ r(ξ) [nW] Measurement Theoretical Figure 4.9: Measured fringe pattern created by a point source at a distance of 25 cm with a fixed antenna baseline of u= 17.13. The center frequency of the RF signal is 97 GHz as described in Fig. 4.8. The measured values match with the analytical expression (4.23). The radiometric front-ends have been mounted on linear stages to synthesize the baselines corresponding to a linear array of antennas. The real part of the visibility samples have been obtained from the correlation of the signals given by both receivers as described by (4.22) integrating 200 ms for each visibility. In order to obtain the imaginary parts of the visibilities, a 90◦phase shift has been added to one receiver signal. Moreover, before obtaining the images a first calibration has been performed to retrieve the phase imbalance between both receivers. In order to obtain the reconstruction of the scene the phase imbalance has been 70 Chapter 4 0 5 10 15 20 25 −1 −0.5 0 0.5 1 u R(V) [K] 0 5 10 15 20 25 −1 −0.5 0 0.5 1 u I(V) [K] Measured: xsrc=2.5 cm Theoretical: xsrc=2.5 cm Measured: xsrc=3.4 cm Theoretical: xsrc=3.4 cm (a) −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.05 0.1 0.15 0.2 ξ T’B [K] Measured: x src =2.5cm Theoretical: xsrc =2.5cm Measured: x src =3.4cm Theoretical: xsrc =3.4cm −17.3 −13.0 −9.4 −6.1 −3.0 03.0 6.1 9.4 13.0 17.3 x[cm] (b) Figure 4.10: (a) Measured real and imaginary parts of the scene visibilities for two different scenes consisting on a point source placed at xPS =−2.5 cm and xPS =−3.4 cm from the origin. The visibilities from u= 0 to u= 6 cannot be measured since the minimum antenna spacing is given by the conical horn flange adapter of 22 mm. (b) The plot shows two reconstructed scenes obtained by applying (4.24) to the measured visibilities shown in Fig. 4.10(a). The two different scenes consist of a point source placed at xPS =−2.5 cm and xPS =−3.4 cm from the origin at a distance R= 30 cm from the antennas. corrected from the visibilities. An antenna separation of ∆u=λ/2has been chosen in order to avoid aliasing in the image as explained in Chapter 2. The same ceramic resistor used in the previous section has been used as the point source and it has been placed at a distance of R= 30 cm of the array. Two measurements have been taken corresponding to two positions of the resistor, xPS =−2.5 cm (ξPS =−0.08) and xPS −3.4 cm (ξPS =−0.12) from the center of the array. A total of Nmu = 42 visibilities have been measured corresponding to a synthetic array of 42 antennas. Figure 4.10(a) shows the visibilities for u > 0with an umax = 27. It must be noted that the visibilities in the range 0<u<6cannot be measured due to the flange of the conical horn antennas used in the measurement, which forces a minimum baseline umin = 6. Nevertheless, the measured visibility values agree with the simulated values. In order to retrieve the scene from the measured visibilities the inverse Fast Fourier Transform (iFFT) is applied: T0 B(ξ) = ZV(u)ej2πuξdu (4.24) giving as a result the linear reconstruction shown in Fig. 4.10(b). The reconstructed image matches with the position of the point source and roughly matches with the amplitude if the system parameters described in Section 4.2.2 are used to calculate constants Cand Sof (4.21). A second scene has been measured with two resistors placed at xPS =−5.5 cm (ξPS = −0.09) and xPS = 1.5 cm (ξPS = 0.02) from the center of the array at a distance R= 60 cm from the antennas. Fig. 4.11(a) shows an infrared image of the scene revealing the physical temperature of the resistors. After applying (4.24), the scene is reconstructed as shown in Fig. 4.11(b). A good agreement between the image and the scene is obtained. 4.3 Optical signal distribution for cross-correlation of multiple receivers 71 (a) −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 ξ T’B [K] −34.6 −26.1 −18.8 −12.2 −6.0 0 6.0 12.2 18.8 26.1 34.6 x [cm] (b) Figure 4.11: (a) Infrared image of a scene consisting on one resistor in vertical disposition placed at xPS =−5.5 cm from the origin and one resistor placed horizontally at xPS = 1.5 cm. The measured physical temperature of the resistors is around 200 ◦C. The scene distance from the antennas is R= 60 cm. (b) Reconstructed image from the scene shown in (a) obtained by applying (4.24) to the measured visibilities. The response of both resistors, centered at xPS =−5.5 cm and xPS = 1.5 cm from the center of the array respectively and at a distance R= 60 cm from the antennas. 4.3 Optical signal distribution for cross-correlation of multiple receivers The measurements presented in Section 4.1.5 have been performed with two receivers. Nevertheless the optical modulation method presented in this paper allows the combination of multiple receiver signals in the optical domain in order to perform the cross-correlation. The combination can be performed in the free-space due to the possibility of guiding optical beams with low divergence and with high spatial density. Moreover, the high level of integration of optical components and waveguides make the optical signal routing affordable with no constraint on the RF signal bandwidth [79] [80]. The following section proposes a free-space combination scheme for an arbitrary number of front-end receivers. 4.3.1 Distribution technique Figure 4.12 show an schematics of the signal distribution system. The optical signals coming from each modulator bi(t)are introduced to an optical splitter matrix having a number of inputs equal to the number of receivers Nrand a number of outputs of 2Nr. This matrix is equivalent to Nrsub-couplers, one for each optical channel, that is in charge of coupling the input signal to 2outputs with the same power level. The 2Nroutput channels are distributed using fiber optics towards collimating lenses that will emit the optical beam in a collimated way. The Nroptical beams split by the optical splitter matrix, containing one of the two beams split by each sub-coupler sbi2(t), carried and grouped into collimating lenses that will emit the beams with horizontal distribution. The Nrbeams are introduced to a diffractive beamsplitter that will divide each beam along the vertical axis in Nrsub-beams. The beams produced by a diffractive beamsplitter are emitted with a certain angle, there- 72 Chapter 4 Nr x 2Nr b1(t) s11, s12 ... s1Nr s21, s22 ... s2Nr sNr1, sNr2 ... sNrNr Ms hv1, hv2 ... hvNr hh1, hh2 ... hhNr b2(t) bNr(t) sb11(t) sb11(t) sb12(t) sb12(t) sb22(t) sbNr2(t) sb22(t) sbNr1(t) sb21(t) sbNr2(t) sbNr1(t) Optical splitter matrix Cylindrical lenses Beamsplitter View 2 View 1 Diffractive beamsplitter Diffractive beamsplitter Figure 4.12: Schematic of the distribution system. The optical signals bi(t)coming from the modulators enter to the optical splitter matrix placed at the left of the schematic. The output signal matrix beams sij are driven to photodiode matrix shown in Fig. 4.14. The schematics of the points of view “View 1” and “View 2” are shown in Fig. 4.13. hh1, hh2 ... hhNr s11, s21 ... sNr1 s12, s22 ... sNr2 s1Nr, s2Nr ... sNrNr Mh sb12(t) sbNr2(t) hv1, hv2 ... hvNr Mv sb12(t) sb22(t) sbNr2(t) View 1 View 2 Beamsplitter Beamsplitter Figure 4.13: Points of view “View 1” and “View 2” from the Fig. 4.12. rs21, rs22 ... rs2Nr rsNr1, rsNr2 ... rsNrNr Ms A/D PC rs11, rs12 ... rs1Nr fs11, fs12 ... fs1Nr fs21, fs22 ... fs2Nr fsNr1, fsNr2 ... fsNrNr Matrix Diode s11, s12 ... s1Nr s21, s22 ... s2Nr sNr1, sNr2 ... sNrNr Figure 4.14: Schematics showing the opto-electronic conversion matrix, the filtering and amplifying components and the power detector arrays. fore in order to avoid the divergence of the beams a cylindrical lens is used to collimate the beams along the vertical axis. This lens should be placed with the cylinder axis along the horizontal plane and with a distance from the diffractive splitter equal to its focal distance. In 4.3 Optical signal distribution for cross-correlation of multiple receivers 73 Figure 4.15: Artist view of the multiplexing scheme. The red beam represents b1(t)whereas the blue beam represents b2(t). The purple beam is the result of adding b1(t) + b2(t). The artist view is representative of the setup mounted in the laboratory to prove the suitability of the scheme. such way the beams are collimated and the matrix Mh is formed Mh=     b1b2··· bNr b1b2··· bNr . . .. . ..... . . bNrb2··· bNr     .(4.25) The remaining Nr channels sbi1(t)split by the optical splitter matrix are transported, grouped along the vertical axis, introduced in collimating lenses and emitted with vertical disposition. Using a diffractive beamsplitter the beams are divided along the horizontal plane creating Nrbeams from each original beam an therefore creating a matrix of NrxNrelements. Finally the beams are collimated using a cylindrical lens having the cylinder axis along the vertical axis of the system. The process is equivalent to the one described in the previous paragraph with the only difference that the resulting beam matrix Mvis rotated 90 ◦ with respect the matrix Mh Mv=     b1b1··· b1 b2b2··· b2 . . .. . ..... . . bNrbNr··· bNr     .(4.26) Figure 4.13 clarifies the beam distribution in this part of the system. In a final step, the beam matrices Mhand Mvare driven to a beamsplitter plate in order to combine the beams and 74 Chapter 4 obtain a sum matrix Ms Ms=     b1+b1b2+b1··· bNr+b1 b1+b2b2+b2··· bNr+b2 . . .. . ..... . . b1+bNrb2+bNr··· bNr+bNr     .(4.27) The final step in the correlation process is based on the detection of the signal contained in each optical beam. Figure 4.14 shows that a photodetector matrix is used to obtain the mixing between the optical carrier and the optical sidebands for each element of Ms. Each photodetector is followed by a TIA in order to convert the current signal given by the photodetector to a voltage signal with a certain transimpedance gain. Following the TIA a filter with the same passband as the original RF signal is placed. The resulting signal at this point is given by 4.9 or 4.14 if either DSB or SSB modulations are used respectively. The final step consists of measuring the power by using an array of power detectors. The resulting matrix contains the real part of the visibilities and is given by the following matrix for a DSB modulation Mv=C(Pn−S<              V11 V21 ··· VNr1 V12 V22 ··· VNr2 . . .. . ..... . . V1NrV2Nr··· VNrNr              ).(4.28) The following step is to perform the phase switching technique to remove Pnfrom the result. It should be pointed out that the lower triangular matrix is redundant and it is not necessary to be measured. The main drawback of this method is the strong alignment requirements of the optical devices. Moreover, the phase variations in the fiber makes the proposed scheme unfeasible without a phase control on each channel. Both issues can be solved if the scheme is integrated and implemented with photonic waveguides. Figure 4.15 shows a 3D representation of the proposed optical signal distribution scheme. 4.4 System Performance Considerations The performance of the system in terms of radiometric sensitivity is described in this section taking into account the contribution of optical correlation process and the phase switching technique. In addition, the image acquisition time is studied depending on the optical modulation scheme and system parameters to foresee the suitability of the method when real-time imaging is required. 4.4.1 Radiometric sensitivity The main noise sources in the system are the thermal noise generated in the receiver chain, the shot noise generated in the photodetector and the receiver gain variations falling in a phase switching period. The effect of the shot noise of the photodetector is neglected in front of the thermal noise generated in the receiver front-ends since this is pre-amplified in the RF stage. 4.4 System Performance Considerations 75 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 tv [ms] σv [K] Measured Theoretical (a) 0 50 100 150 200 250 0.85 0.9 0.95 1 1.05 1.1 ∆ψ [deg] σv [K] Moving average Theoretical (b) 0 10 20 30 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Nmu ts [s] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Angular resolution DSB SSB ∆θx [rad] (c) Figure 4.16: (a) Standard deviation of a visibility measurement σvdepending on the integration time tv. The noise received by the antennas is purely uncorrelated. The measurement is compared with the theoretical values provided by (4.29). (b) Standard deviation of a visibility measurement σvdepending on the signal correlation level for an integration time tv= 2 ms. The phase of the IF signal is shifted 260 deg with steps of 3 deg to sweep the correlation level of the noise radiatied from a resistor point source. A moving average of 20 samples is calculated from the measured points. The measurement is compared with a theoretical curve calculated using (4.29). (c) Image acquisition time tsdepending on the number of antennas Nmu for a ∆T= 1 K. The system parameters are TA= 300 K,TR= 1000 K and B= 1.8 GHz. The angular resolution ∆θxof the synthesized array is also depicted to show the tradeoff between spatial resolution and radiometric sensitivity. The phase switching rate is selected to avoid the gain fluctuations of the front-end receiver components as well as to avoid variations in the laser amplitude. If a high gain LNA is placed at the front of the chain as in our case, TRis mainly fixed by the noise figure of the LNA. The resulting standard deviation for a single visibility measurement if DSB modulation is used is given by σv=TAu +TR−TAc cos(∆ψ) √Btv [K],(4.29) where TAu and TAc are respectively the equivalent temperature of the uncorrelated and correlated noise captured by the receiver antenna. The visibility integration time tvis the sum of multiple phase switching periods. In the measurements performed in the previous sections, the integration time is tv= 200 ms corresponding to 10 repetitions of a phase switching period of 20 ms. In order to validate (4.29), the visibility standard deviation has been calculated from visibility samples measured with the system described in Section 4.1.5. 76 Chapter 4 Figure 4.16(a) shows the standard deviation of measured visibility samples for different integration times tv. An absorber has been used to have a constant source of uncorrelated noise in front of the antennas (TAc = 0 K). The values of Sand Cused to obtain the visibility value from the measured power (4.21) are those used in Section 4.1.5. The theoretical curve has been calculated using (4.29) with TAu = 300 K,TAc = 0 K,TR= 1400 K (corresponding to a NF = 7.7 dB) and B= 1.8 GHz. Additionally, the dependance of the visibility standard deviation with the correlation level (TAc = 60 K) of the signals is shown in Fig. 4.16(b). A point source consisting of a resistor has been used to radiate correlated noise. In order to modify the correlation level of the processed noise signals, a phase sweep of 260 ◦in steps of 3◦has been performed using the phase shifter placed in the receiver chain. A set of 1000 visibility samples has been measured consisting of two phase switching periods of 1 ms yielding a total integration time of tv= 2 ms. These samples have been used to calculate the standard deviation of the visibility for different values of phase shift. A moving average of 20 samples has been calculated to clearly observe the sinusoidal behavior. The measurement is compared with a theoretical curve calculated using (4.29) with TAc = 60 K,TAu = 400 K,TR= 1400 K and B= 1.8 GHz. 4.4.1.1 Image acquisition time If a DSB modulation is used in the conversion process the phase shift between receiver channels ∆φshould be maintained to {π 2,3π 2}as stated in Section 4.1.3. Therefore, an imaging system composed by Nmu >2receivers is not able to measure all the visibilities simultaneously since it is not possible to have the required phase shift between all the receiver pairs at once. A solution is to repeat the measurements in order to cover the whole set of combinations. It can be shown that for Nmu receivers, it is required a minimum of dlog2(Nmu)e steps, where d·e denotes the ceiling value. Therefore the image acquisition time tsdepends on the number of receivers as ts=tvdlog2(Nmu)e, leading to a radiometric sensitivity ∆TDSB = 1.4TA+TR √BtspNmudlog2(Nmu)e.(4.30) A different approach is either to use a SSB modulation or to filter one of the sidebands, thus adding complexity to the system. In this case the optical phase shift required to perform the correlation is ∆φ= 0, and the complete set of visibilities could be measured at once (ts=tv) yielding ∆TSSB = 1.4TA+TR √BtspNmu.(4.31) Figure 4.16(c) shows the image acquisition time and angular resolution depending on the number of receivers for a ∆T= 1 K. From the figure, it can be seen that for a particular case with an spatial resolution of 3 cm at a distance of 1 m from the antennas, the required number of antennas is Nmu = 36. For this system, a DSB modulation increases the acquisition time by a factor of 6compared with the SSB modulation. 4.5 Conclusions 77 4.4.1.2 Comparison with other available correlation techniques The optical correlation technique described in this paper is similar to an RF analog correlation [58]. In both cases the correlation is performed by measuring the power of the combination of the received signals. The main difference resides in which domain the signal is distributed in order to obtain the combination of all receiver pairs as required in aperture synthesis interferometry. There are several advantages of distributing the signals in the optical domain: 1) the signals can be distributed in the free space with collimated optical beams thus avoiding signal couplings and uncontrolled radiation that could appear with RF signal distribution; 2) photonic integrated devices can be used to incorporate the whole distribution system in a compact device; and 3) the bandwidth is limited by the optical modulator and can be of several tens of gigahertz whereas in the RF distribution the bandwidth would be limited by the complexity of the distribution components required to support large relative bandwidths. Nevertheless, in practice the optical system requires a real-time phase control to maintain fixed ∆φ, representing a drawback in front of the RF correlator. An additional technique commonly used in interferometric radiometry consists on sampling the RF signals with 1-bit precision and performing the correlation in a field programmable gate array (FPGA) [81]. In this case the number of receivers Nrand the capacity of the FPGA limits the bandwidth, and therefore limits the real-time imaging capabilities of the system. Taking into account that the signal should be digitized with a sampling frequency of fs= 2B to fulfill Nyquist criteria, the amount of internal data that the FPGA should manage is related with fsNrkbps. Hence, an interferometric system with a bandwidth of several GHz would require a huge processing system [82] that are not affordable for screening systems. 4.5 Conclusions This chapter presents a method to perform cross-correlation of RF radiometric signals in the optical domain. The expressions governing the method are derived relating the results to the classical interferometric imaging theory. In addition, the experimental validations prove the suitability of the method to perform millimeter-wave passive interferometric imaging: 1) the fringe pattern of a moving point source has been measured using a single baseline obtaining a result that matches with the theoretical expressions; and 2) linear interferometric images have been acquired by translating two receivers to sequentially synthesize the baselines of a filled array of receivers, where the whole set of visibility samples have been obtained performing the correlation in the optical domain. With respect to the performance of the system, it has been shown that the receiver temperature TRof the system is not critically degraded by converting the signal to the optical domain since the LNA placed at the front-end fixes the noise figure for the whole receiver chain. This statement is supported in Section 4.4 with the calculation of the standard deviation of a visibility measurement σv, showing that the optical processing has no significant influence on the radiometric performance of the system. In addition, the dependance of the visibility standard deviation with the signal correlation level has been also supported with measurements in Section 4.4. 84 Chapter 5 the currents radiating on a volume vbmultiplied by the electric field radiating from currents on the volume va[84] ZZva ~ Ja·~ Ebdva=ZZvb ~ Jb·~ Eadvb.(5.6) In the scenario shown in Fig. 5.1, it is assumed that Jbcorresponds to the currents induced on the sample by the electric field Ei(~r;ˆ θ0)and Jaare the currents on the transmitter antenna. In addition, Jbradiates the scattering field Es(~r)whereas Jaradiates a plane wave e−jk0ˆ θ·~r. Therefore, from (5.3) the currents induced in the sample from the incoming field E(~r;ˆ θ0)is described by Jb(~r) = −jω0C(~r)E(~r;ˆ θ0).(5.7) From (5.5) and using (5.6) the following expression is obtained ˜ C(k0(ˆ θ−ˆ θ0)) = jωµ0Zva Ja(~r, θ)Es(~r;ˆ θ0)dva.(5.8) If a cylindrical measurement geometry as presented in Fig. 5.1 is considered, (5.7) is expressed as ˜ C(k0(ˆ θ−ˆ θ0)) = jωµ0Z2π 0 I(θ−σ)Es(σ;ˆ θ0)Rdσ, (5.9) where I(θ−σ)is the current distribution along an angular position σof the antenna that radiates a plane wave with θdirection. This current distribution can be expressed, for an arbitrary radius of the cylinder geometry as I(θ−σ) = −2 ωµ0Rπ ∞ X n=−∞ j−n H(2) n(k0R)ejn(θ−σ),(5.10) where H(2) nis the Hankel function of the second kind and Ris the radius of the cylindrical geometry. In addition, the scattered field considering a plane wave impinging to the object can be expressed as Es(σ;ˆ θ0) = Z2π 0 I(θ0−σ0)Es(σ;σ0)Rdσ0,(5.11) where Es(σ;σ0)is the scattered field measured at an angle σand produced by a incident wave coming from the direction σ0. Considering that both receiver and transmitter antennas are placed further than the farfield distance from the sample (R >> 2D2 λ), (5.10) can be approximated asymptotically by I(θ−σ) = −s2k0 πRω2µ2 0 δ(θ−σ)e−j(k0R−π 4),(5.12) where δ() is the Dirac delta function. Finally, by applying (5.12) and (5.11) to (5.9), the resulting expression is ˜ C(k0(ˆ θ−ˆ θ0)) = 2Re−jk0R Z0πZ2π 0Z2π 0 δ(θ−σ)δ(θ0−σ0)Es(σ;σ0)dσdσ0,(5.13) 5.2 Imaging scenario simulations 85 kcx kcy -k0 kx< 0 kx> 0 -k0 2k0 (a) kcx [rad/cm] kcy [rad/cm] −20 −10 0 10 20 −20 −10 0 10 20 (b) Figure 5.2: (a) Angular spectrum of the contrast function C(~r)for a fixed incidence angle θ0. The black curve corresponds to the contrast profile given by the forward scattered field (−90 < θ < 90) deg. (b) Angular spectrum of a reconstructed image for θ0= 45ndeg where 1≤n≤8and -30 ≤θ≤ 30 deg. where the final result after the integration is ˜ C(k0(ˆ θ−ˆ θ0)) = 2Re−jk0R Z0πEs(θ;θ0).(5.14) Figure 5.2(a) shows an schematic that illustrates how the measured field is translated to the angular spectrum of the sample image contrast. The electric field value Es(θ;θ0), scattered by the sample in the direction θ0when an incident plane wave impinges from the direction θ, corresponds to the contrast spectrum value with angular coordinates ~ kc=k0(ˆ θ− ˆ θ0). It should be pointed out that the high frequency part of the spectrum is filled with the electric field values backscattered by the sample given by receiver antennas placed at θ≈ −θ0 (reflection geometry), yielding a maximum frequency of 2k0. The low frequency part of the spectrum corresponds to forward scattered electric field and is measured when the receiver antennas are placed at θ≈θ0(transmission geometry). Figure 5.2(b) shows the spectrum of a retrieved image. It corresponds to a reconstruction of a measurement with θ0= 45nwith n= 1...8and −30 < θ < 30 in steps of 1 deg. Note that the semi-circles are not well defined since the spectrum is convolved by the spectral response of the rectangular window applied due to the truncation of the reconstructed image. 5.2 Imaging scenario simulations This section includes electromagnetic simulations that are used to foresee the behavior of the algorithm in the THz range for a certain scenario. The Finite Element Method (FEM) 86 Chapter 5 simulator COMSOL Multiphysics [85] has been used to obtain the scattered fields for several incident and reception angles. In order to simplify the simulation and due to the high simulation frequency a two-dimensional geometry has been used. This geometry assumes uniformity in the z-axis, reducing the physical space where the electric field should be calculated. This simplification of the problem is crucial to enhance the acquisition speed in scenarios of several tens of wavelengths. 5.2.1 Simulation scenario Figure 5.3 shows the geometry introduced into the simulator to retrieve the scattered fields. It consists on several cylindrical sections that represents different materials in a two-dimensional geometry. The main sample consists on a 12 mm diameter cylinder of Rohacell material (r≈ 1.05) where two inner-cylinders have been filled with two different materials Ph1 and Ph2. Both materials have the same real permittivity but different loss tangent r= 1.7(1−jtan(δ) given by Fig. 5.4. The loss tangent is zero for all the simulated frequency range except at 500 GHz and 600 GHz for the material Ph1 and Ph2 respectively. The objective of introducing this dependance of the loss tangent with the frequency is to model absorption resonances in the materials. The scenario includes an air section that ends in a Perfect Matched Layer (PML). The PML absorbs the scattered radiation avoiding undesired back-reflections, thus emulating a free-space environment. As an excitation, a plane wave depending on the incidence angle θ0as Eiz(θ0) = e−jk0(xcos(θ0)+ysin(θ0)) (5.15) is included in the model. The currents induced by the plane wave in the outer part of the main cylinder are calculated by the solver. As a post-processing stage, the far-field radiated by the induced currents are evaluated and are given as a main output of the simulator. The algorithm presented in Section 5.1.1 is applied to the fields scattered by the object to reconstruct the image. The complete set of measurements are acquired in a three-dimensional matrix with indexes (f, θ0, θ), where f= 100,200...800 GHz;θ0= 0,45,90...315 deg and θ= 0,0.5,1, ...359.5 deg with a total number of 46080 electric field points. 5.2.2 Spectroscopic imaging In order to test the algorithm with a canonical shape, a first set of images that not include the materials Ph1 and Ph2 have been reconstructed. In this case, the inner-cylinders have been filled with air instead. Figure 5.5 shows the retrieved images frequency by frequency from 100 GHz to 800 GHz. The outer shape of the main cylinder is retrieved in all the images. However, the shape of the inner-cylinders change drastically with the frequency. As the frequency increases, the shape of the inner-cylinders is not well retrieved and for frequencies greater than 500 GHz there is no clear difference in the image that leads to the identification of the inner-cylinders. The image quality is reduced as the simulation frequency is increased since the Born approximation loses validity. As the frequency is increased, the scattered field is concentrated in values of θclose to the forward-scattering point (or pure transmission point). This causes that the high spatial frequencies of the image are not properly retrieved, translated into a poor reconstruction of the abrupt changes in the image. 5.2 Imaging scenario simulations 87 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] PML Air Rohacell Ph1 Ph2 Figure 5.3: 2D simulation geometry consisting on a Rohacell cylinder containing two cylinders filled with two different compounds Ph1 and Ph2. 100 200 300 400 500 600 700 800 0 0.02 0.04 0.06 0.08 f [GHz] Loss tangent (tand) Ph1 Ph2 Figure 5.4: Loss tangent against the frequency of the compounds Ph1 and Ph2. In a second simulation trial, the materials Ph1 and Ph2 have been introduced in the scenario in order to study the impact of the frequency-variable loss-tangent in the reconstruction. Figure 5.6 shows the retrieved images for each frequency. It should be pointed out a main difference with respect the reconstruction of the images appearing in Figure 5.5: the reception angle spans from −30 to 30 deg instead of covering the whole circumference. This restriction in the reception angle has been introduced to simulate the measurements capabilities of our system as will be described in Section 5.3.2. At first sight, it can be noted that the spatial resolution of the images strongly depends on the frequency. As the frequency increases the spatial resolution increases as well. This effect in the images is more noticeable in the images of Fig. 5.6 than in the ones appearing in Fig. 5.5 due to the restriction in the reception angle. Regarding the appearance of the materials Ph1 and Ph2 in the image, no change is observed depending on the frequency except at 500 GHz and 600 GHz where the absorption peaks of the materials are placed. The image retrieved at 500 GHz shows a clear attenuation 88 Chapter 5 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (a) 100 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (b) 200 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (c) 300 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (d) 400 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (f) 500 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (g) 600 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (h) 700 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (i) 800 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 Figure 5.5: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3, however in this simulation the pharmaceutical compounds have not been considered and the innercylinders are filled with a air. Each image corresponds to a reconstruction of the contrast at a single frequency: (a) 100 GHz, (b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz. −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (a) 100 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (b) 200 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (c) 300 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (d) 400 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (f) 500 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (g) 600 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (h) 700 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (i) 800 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 Figure 5.6: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3. In this case both compounds Ph1 and Ph2 have been considered in the reconstruction. Each image corresponds to a normalized contrast reconstruction at a single frequency: (a) 100 GHz,(b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz. in the zone where the material Ph1 is placed whereas at 600 GHz the attenuation is shown in the place where the material Ph2 is located. Hence, the variation in loss tangent has a clear effect on the images and can be foreseen that a material with a certain absorption peak can be 5.2 Imaging scenario simulations 89 100 200 300 400 500 600 700 800 0.4 0.5 0.6 0.7 0.8 0.9 1 f [GHz] Normalized Contrast Pharma 1 Pharma 2 Figure 5.7: Reconstructed contrast depending on the frequency for both materials. The contrast has been integrated along the area defined in Fig. 5.3 by the material Ph1 and Ph2 for the blue (continuous) and green (dotted) lines respectively. 100 200 300 400 500 600 700 800 20 30 40 50 60 f [GHz] Dynamic range [dB] Figure 5.8: Dynamic range of the imaging setup based on the THz-CW system depending on the frequency. identified in the image by using the proposed tomographic algorithm. Additionally, the frequency response of the materials can be obtained by integrating the zone where it is located against the frequency. Figure 5.7 shows the dependence with the frequency of integrating the contrast zone where the materials Ph1 and Ph2 are located. The attenuation points agree with the loss tangent peaks in each material. Thus, the spectroscopic response of the materials can be extracted from the images. However, since the Born approximation is not fulfilled due to the high contrast of the materials Ph1 and Ph2 with the Rohacell, the images do not provide quantitative information. Therefore parameters such material concentration cannot be provided by the images and only qualitative information can be obtained. An additional simulation has been performed introducing additive Gaussian noise to the simulated results in order to achieve the same dynamic range as the one provided by the measurement setup. Figure 5.8 shows the measured dynamic range of the imaging setup that 90 Chapter 5 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (a) 100 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (b) 200 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (c) 300 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (d) 400 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (f) 500 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (g) 600 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (h) 700 GHz −10 −5 0 5 10 −10 −5 0 5 10 x [mm] y [mm] (i) 800 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 Figure 5.9: Reconstructed images from the tomographic simulation of the scene shown in Fig. 5.3 adding complex Gaussian noise to the simulation to achieve the dynamic range shown in Fig. 5.8. Both compounds Ph1 and Ph2 have been considered in the reconstruction. Each image corresponds to a normalized contrast reconstruction at a single frequency: (a) 100 GHz,(b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz. 100 200 300 400 500 600 700 800 0.4 0.5 0.6 0.7 0.8 0.9 1 f [GHz] Normalized Contrast Pharma 1 Pharma 2 Figure 5.10: Reconstructed contrast depending on the frequency for both materials introducing additive Gaussian noise. The contrast has been integrated along the area defined in Fig. 5.3 by the material Ph1 and Ph2 for the blue (continuous) and green (dotted) lines respectively. is described in Section 5.3.1. It can be shown that as the frequency increases the dynamic range decreases, starting from 50 dB at 100 GHz to 25 dB at 800 GHz. If an additive Gaussian noise is added to the simulated electric field used to obtain the images shown in Fig. 5.6, the resulting reconstructed images are presented in Fig. 5.9. It can be noted that the reconstruction of the high frequency simulations yield noisy images since the dynamic range is reduced to about 25 dB. Nevertheless, the spectroscopic behavior of the samples is still perceived. This confirms the suitability of the measurement system, in terms 5.3 Measurements 91 of dynamic range, to measure the samples equivalent to the simulated ones. The result of integrating the zones where both materials are located is shown in Fig. 5.10. Despite the perception of the absorption characteristic of both materials is reduced, the peaks at 500 GHz and 600 GHz for Ph1 and Ph2 respectively can be noted. From these simulations can be concluded that, despite the reduction of dynamic range hinders the reconstruction of the spectral behavior of the sample by the algorithm, still the detection and identification of the materials can be performed. 5.3 Measurements In order to validate the simulations and to study the performance of the algorithm with real data, a set of measurements of different samples has been performed. The data required to reconstruct the image has been measured using a THz-CW spectroscopy system whereas the spectroscopic characterization of the sample has been performed using a Terahertz Time- Domain Spectroscopy (THz-TDS). Since both equipments are available in our laboratory, the most suitable one has been chosen for each operation. On the one hand the THz-TDS setup provides a better frequency accuracy than the THz-CW due to the high precision of the delay stage incorporated in the system [27]. In addition, the complete spectral response in amplitude and phase can be obtained from a sample using two measurements: a reference and sample measurements. As a result, a complete spectral information of the sample can be obtained in 15 minutes approximately and with high accuracy. On the other hand the THz-CW system used in this thesis relies on thermal tuning of the optical frequency to shift the photomixed THz frequency [86]. The system software incorporates a calibration file that associates a certain laser temperature to an output optical frequency. The resulting THz radiation is given as a result of the photomixing of two laser frequencies with a separation equal to the THz frequency: fTHz =fl2 −fl1 where fTHz is the THz frequency whereas fl2 and fl1 are the frequency of each laser source. Hence, by using thermal tuning fl2 can be increased and fl1 can be decreased yielding a increment of fTHz or viceversa. Hence, the frequency accuracy relies on calibration quality of the system and on its repeatability throughout time. In addition, due to the inherent inertia of the thermal tuning, once a certain objective temperature is set in the laser controllers, around 15 minutes should be waited until the frequency is properly set. Therefore, it makes extremely slow the acquisition of multiple frequency point with complex data information. Nevertheless, two main advantages makes this system a good choice for tomography: 1) the system is fiber-coupled, allowing a complete free movement of the photomixers as required by the tomographic algorithm; and 2) once a certain frequency is set, a complex data measurement lasts 1second whereas in the THz-TDS the whole frequency spectrum should be retrieved, even when only one frequency is required. The following sections describe the measurement methodology required to obtain the field scattered by the sample intended to be imaged. Additionally, several image reconstructions that validate the algorithm are shown. 92 Chapter 5 Distributed-feedback laser heads Figure 5.11: Photograph of the THz-CW system laser heads. Tx photoconductive switch Sample rotation servo RF absorber Horizontal linear stage Sample x y z (a) Sample Receiver rotor Rx lens Servo sample rotor Horizontal stage Rx photoconductive switch (b) Figure 5.12: Photographs of the tomographic measurement setup . The main components of the system are presented in the photographs. 5.3 Measurements 93 5.3.1 Setup and sample preparation The setup shown schematically in Fig. 5.1 has been implemented in the laboratory. As mentioned in the last section, a THz-CW system has been used to acquire the multiple field points required to reconstruct the image. The Distributed Feedback (DFB) lasers used to produce the two optical tones with frequency fl1 and fl2 are shown in Fig. 5.11. Both optical signals are coupled using a 2x2 optical coupling matrix, whose two outputs are the combination of the two inputs signals, and driven to the receiver and transmitter PCS using fiber optics. Figure 5.12 shows photographs of the measurement setup describing the main components. In Fig. 5.12(a), the transmitter photoconductive switch antenna. Note the fiber optics with blue protective cover that couples the laser power into the antenna. Also the coaxial cable in charge of biasing the antenna with a 13V,7 kHz square signal is shown. The photoconductive switch is mounted on two micrometer stages that allow vertical (z-axis) and horizontal (xaxis) displacement of the antenna. Furthermore, the whole antenna mount is held on a rail that allows a continuous displacement in y-axis. The sample is held by an optical post that is rotated by a winch servo. This servo, after a proper calibration, can be rotated 360 ◦with an accuracy around 1◦. The control of the servo is made by using a commercial control board Pololu Maestro 6-channel than can be connected to a computed by a Universal Serial Bus (USB) port. A Polyvinyl Chloride (PVC) structure holds the servo to a two-dimensional 300x300 mm2horizontal linear stage used to translate the sample. During the measurement, the sample is translated to two different positions: 1) the measurement position, where the servo rotation axis and the receiver rotation axis match; and 2) the empty chamber position, where the sample is translated to a maximum x-axis and z-axis value to avoid any intrusion of the sample in the measurement. Note in the Fig. 5.12(a) that an absorber has been placed covering the two-dimensional stage, trying to avoid undesired reflection from the metal parts that compose and hold the stages. A special care with undesired reflections has been taken at low frequencies where the transmitted beam covers a wide area. As the frequency is increased, the divergence angle of the beam is decreased and the amount of undesired reflections decrease. Figure 5.12(b) shows the receiver components of the setup placed on a rail. A Teflon plano-convex lens has been used to capture the plane wave scattered by the sample. The scattered radiation is then concentrated on the receiver photoconductive switch aperture. A fiberoptics is used, as in the transmitter PCS, to couple the laser in the receiver PCS. However, in the receiver antenna, the coaxial cable does not bias the antenna but collects the photoinduced current. The received current is amplified by a Transimpedance Amplifier (TIA) and driven to the input of the lock-in amplifier. Since the receiver components should be rotated around the sample, the rail is held on a rotation stage with the same rotation axis as the sample rotation servo. This rotation stage is controlled via a USB port with the computer. In the electronics reception stage, a lock-in amplifier is in charge of demodulate the received voltage given by the TIA. The THz electric field has been previously modulated at 7 kHz by the bias of the transmitter PCS, therefore the photo-induced current is as well modulated at the same frequency. The lock-in amplifier gets locked to the modulation frequency and retrieves the amplitude value of the signal. This technique is commonly used to improve the Signal to Noise Ratio (SNR) of the retrieved signal, that otherwise would be masked by 100 Chapter 5 eter response. The control has been achieved by purging with nitrogen gas the water vapor contained in the ambient air. Note that the purging system composed by a nitrogen tank and a purge control unit are also shown in Fig. 5.16. Since only the THz path should be purged, the transmitter and receiver optical paths are kept outside of the glovebox, introducing the laser beams through the acrylic back panel. The optical subsystem of the spectrometer is shown in Fig. 5.17. The femtosecond laser, the optical delay stage and the multiple optical mirrors and accessories composing the subsystem are shown in the photograph. In addition, the path of both receiver and transmitter laser beams are shown in blue and green respectively. At the right of the image, the beams are aimed directly to the photoconductive antennas placed inside the glovebox. The antennas are shown in Fig. 5.18 together with lenses in charge of collimating and focusing the THz beam, two mirrors that rotate the beam 90 ◦and a TIA. The Polaramine powder is placed using a sample holder in between both focusing lenses in order to perform the measurement. The technique used to measure the spectrum of the sample is the one usually used in a THz-TDS: •The THz pulse is sampled by using the optical delay stage. The linear step of the stage ∆xis translated to a temporal step in the sampled pulse of of ∆t= 2∆x/c, where cis the speed of light. •The voltage given by the TIA is processed by the lock-in amplifier and acquired using a ADC. For each step of the linear stage a voltage value is acquired, resulting in a total of Nppoints. •Once the complete pulse is retrieved, a Discrete Fourier Transform (DFT) is performed in order to obtain the frequency spectrum of the measurement. The maximum frequency value and the frequency resolution are given by the properties of the DFT. Therefore, the maximum frequency value is: fmax =1 2∆t; and the frequency resolution is given by the maximum time span: ∆f=1 ∆tNp. Figure 5.19 shows the measured spectrum of the system without sample with two different humidity levels: 30% and 2%. In this measurement, ∆t= 0.125 ps whereas the number of points is Np= 200. The water vapor absorption peaks appear in the curve corresponding to the measurement with 30% of humidity. Note the drastic reduction of the peaks in the purged measurement. This Figure shows that a purged measurement should be performed when the expected absorptions of the sample are close to the water vapor absorptions, otherwise the measurement will be masked. Figure 5.20 shows the measured absorption spectrum of a Polaramine sample. The measurement with the sample is normalized by the free-space measurement in order to eliminate the response of the system from the measurement. Moreover, the linear response of the scattering produced in the sample has been retrieved by using a linear regression and subtracted from the measurement. As expected, an absorption line appears at 525 GHz, confirming the pharmaceutical as a good candidate for spectroscopic imaging. It has to be pointed out that the response expected at the frequency of 0.993 THz is not noticeable since it is masked by noise. Despite the dynamic range of the system at 1 THz is close to 50 dB, the high scattering produced by the pharmaceutical powder attenuates the signal around 45 dB at 1 THz. This problem can be overcome by using a press to compact the powder. 5.3 Measurements 101 500 100 1000 1500 2000 2500 3000 3500 4000 −80 −60 −40 −20 0 f [GHz] Normalized Amplitude [dB] Ambient humidity: 30% Purged humidity: 2% Figure 5.19: Characterization of the signal spectrum produced by the THz-TDS system available in the AntennaLab THz laboratory. The spectrum has been measured with two different humidity levels: 30 % and 2 %. The reduction in the level of the water vapor absorption peaks is clearly noticeable. 300 400 500 600 700 800 900 1000 0 1 2 3 4 5 6 f [GHz] Absorbance [dB] Figure 5.20: Absorption spectrum of the pharmacological compound with commercial denomination Polaramine Repetabs. 5.3.5 Tomographic imaging Several measurements of different scenarios have been performed to test the imaging capabilities of the reconstruction algorithm in the THz frequency range. The difference among different scenarios resides in the type of sample and their disposition in the scene. The samples are based on a Rohacell structure as described Section 5.3.1 and may contain Polaramine depending on the test. Figure 5.21 shows the image reconstruction of a scenario consisting in a solid cylinder of Rohacell material with 12 mm diameter displaced from the center of rotation. Since the algorithm is based on a cylindrical geometry, it tends to easily reconstruct cylindric shapes at the center of the image, even if the algorithm is not properly implemented in the computer. Therefore, a first test with a sample displaced from the center has been performed in order to validate the implementation of the reconstruction algorithm. The cylinder is retrieved 102 Chapter 5 −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (a) 100 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (b) 200 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (c) 300 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (d) 400 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (f) 500 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (g) 600 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (h) 700 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (i) 800 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 Figure 5.21: Reconstructed images from the measurements of a Rohacell cylinder of 12mm diameter displaced from the center of rotation. Each image corresponds to a reconstruction of the contrast at a single frequency: (a) 100 GHz, (b) 200 GHz, (c) 300 GHz, (d) 400 GHz, (f) 500 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz. properly from frequencies up to 600 GHz. In the following frequencies the SNR of the measurements decreases, being translated to the image as an increment of noise. In addition, the shape of the cylinder tends to be concentrated to the center of the image. This is caused by the narrowing of both the illumination and reception THz beams as the frequency is increased. At high frequencies the THz beams illuminate the sample partially, and therefore the reconstruction shape does not perfectly match with the original sample. Additional tests have been performed without including the pharmaceutical compound in the sample. Figure 5.22 shows two reconstruction from different scenarios. In Fig. 5.22(a) a solid Rohacell block with triangular shape, and displaced from the center has been reconstructed. The shape obtained from the measurement does not completely match with the block shape. The main discrepancies occur at the edges that appear rounded instead of sharp. The main cause is the lack of spatial resolution to properly retrieve the edges. Either a higher frequency or a higher span of the reception angle θshould be used to improve the spatial resolution, and hence increase the reconstruction quality of the edges. A Rohacell cylinder of 12 mm diameter with an empty inner-cylinder of 6 mm diameter has been measured and the resulting image is shown in Fig. 5.22(b). The center hole is reconstructed with the proper dimensions, confirming the penetration capabilities of the THz radiation in the Rohacell material. Therefore, Rohacell is a proper material to be used as a sample holder to perform the spectroscopic imaging. The test on spectroscopic imaging has been performed using a centered Rohacell cylinder with 12 mm diameter and inner-cylinder of 6 mm filled with Polaramine. Figure 5.23 shows the reconstructed images of the sample. The cylinder is centered at the main rotation axis and therefore it appears centered in the image. The dynamic range of the images is fixed and the results have been normalized by the frequency response of the system, therefore the images 5.3 Measurements 103 −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] Rohacell with triangular shape 400 GHz (a) −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] 200 GHz Rohacell with center hole (b) Figure 5.22: (a) Reconstructed image of a Rohacell block with triangular shape; and (b) reconstructed image of a Rohacell cylinder with a hole of 6 mm diameter. can be compared among them. As in the images appearing in Fig. 5.21, as the frequency increases the level of noise in the images increases as well and reconstruction quality of the cylinder decreases. In general, only the outer shape of the cylinder is reconstructed and the polaramine contrast is not perceived. However in the images of Fig. 5.23(c) and 5.23(h), the contrast is slightly shown as a superposition of two circles. Note that the inner cylinder is not properly centered in the main cylinder, but a slight shifted to the positive x-axis. The main variation in the images appears in Fig. 5.23(f), where an attenuation in the zone of the image where the Polaramine is placed. However the zone corresponding to the Rohacell cylinder is still properly retrieved. It has to be pointed out that due to the slight shift in the frequency calibration of the THz-CW system, the attenuation occurs around 534 GHz instead of 525 GHz as measured with the THz-TDS system and presented in section 5.3.4. This attenuation zone appearing at the frequency where the Polaramine has an absorption line confirms the suitability of the algorithm to perform spectroscopic imaging since it is capable of showing in the image the attenuation of the materials that compose the scene, depending on the frequency. In order to check the attenuation level produced in the zone, an integration of the retrieved image contrast values in the zone where the Polaramine is placed has been performed. A result of the integration depending on the frequency is shown in Fig. 5.24. A clear absorption peak appears at 534 GHz, however the rest of the plot is not as flat as expected. This effect can be produced by the fact that the scenario does not fulfill the Born condition, since the relative permittivity of the Polaramine is around 2. The results obtained from the Polaramine are compared with the ones obtained from the Rohacell sample shown in Fig. 5.21. The result obtained from the Rohacell presents no significant absorption peaks since the Rohacell does not have an spectral footprint in the studied frequency band. These results reveal that the algorithm is useful when qualitative images are required, and no quantitative information can be obtained since the main assumption of the reconstruction algorithm is not fulfilled. Therefore, no information about concentration of the chemical substance can be obtained. The algorithm is limited to detect and identify the pharmaceutical compound. 104 Chapter 5 −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (a) 200 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (b) 300 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (c) 400 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (d) 500 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (f) 534 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (g) 600 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (h) 700 GHz −20 −10 0 10 20 −20 −10 0 10 20 x [mm] y [mm] (i) 800 GHz 0.3 0.4 0.5 0.6 0. 7 0.8 0.9 1 Figure 5.23: Reconstructed images from the measurements of a Rohacell cylinder of 12 mm diameter filled with Polaramine powder covering a diameter of 6 mm. Each image corresponds to a reconstruction of the contrast at a single frequency: (a) 200 GHz, (b) 300 GHz, (c) 400 GHz, (d) 500 GHz, (f) 534 GHz, (g) 600 GHz, (h) 700 GHz, (i) 800 GHz. 200 300 400 500 600 700 800 −6 −5 −4 −3 −2 −1 0 f [GHz] Relative absorption [dB] Polaramine Rohacell Figure 5.24: The blue curve shows the result of the integration of the image zone where the Polaramine is placed, depending on the frequency. The green curve shows the resulting integration of the zone where the Rohacell is placed from the set of images shown in Fig. 5.21. 5.4 Conclusions ATHz tomographic reconstruction technique has been presented in this chapter. The algorithm required to focus the measured scattered field from the sample has been described, and its suitability for imaging reconstruction at THz frequencies has been assessed. The spectroscopic capabilities of the algorithm have been validated at THz frequencies with a pharmaceutical compound having a molecular absorption resonance at 525 GHz. 5.4 Conclusions 105 A method to acquire complex electric field values with a THz-CW system has been developed. The method is based on modulating the laser current to shift the THz frequency and has been proven to be appropriate to measure the complex field values required to reconstruct the image. Acquisition speeds below 1 s can be easily achieved by using this method. However, a main drawback of the THz-CW has been found consisting of the large phase drift throughout time. A calibration method consisting of acquiring several calibration points and interpolating a phase calibration curve has been required to properly retrieve the images. Each acquisition has been normalized by the phase drift value corresponding to its acquisition time. This method have provided positive results on the image reconstruction since different sample shapes and distributions have been tested and reconstructed successfully. The spectroscopic capabilities of the algorithm have been validated by performing simulations and measurements. Only qualitative images can be obtained since the Born assumption of the algorithm is not fulfilled in the imaged scenarios. Therefore, the images do not provide information about concentration levels of the different materials and substances in the scene. Nevertheless, the detection and identification capabilities of the algorithm have been assessed yielding proper identification of the spectral footprint of the pharmaceutical compound under test. 106 Chapter 5 Thesis Conclusions CHAPTER 6 Conclusions and discussion THIS chapter describes the main contributions of this thesis in the areas of Millimeter- Wave (mmW) passive imaging and terahertz imaging. In addition, the CONSOLIDER project objectives that have been fulfilled thanks to the work presented in this thesis are also stated in the following lines. At the end of the chapter, the guidelines to continue with the work performed in the thesis are given. 6.1 Conclusions The work presented in this document is related with a research line that pursues two main goals: 1) the development of a mmW camera for real-time acquisition of close-range images; and 2) the development of a terahertz imaging system for detection and identification of chemical compounds. The author has encountered several problems when addressing the proposed goals. This has lead to a deep research on technology, techniques and methodology in the areas of mmW and terahertz imaging with the aim of solving the mentioned issues. The following list details the concluding remarks extracted in the pathway to the 94 GHz real-time camera development: •The several tests performed with a single-receiver mechanically-scanned screener based on a total-power radiometer have provided practical experience to the author, permitting to extract several conclusions: 1. Despite theoretically is feasible to obtain real-time (ts<1) images with a singlereceiver screener with a proper radiometric resolution, the mechanical complexity that presents the antenna aiming system makes this screener practically unfeasible. 2. In order to detect concealed objects in low-contrast scenarios, such as indoor environments, a radiometric resolution below 1 K is required. However, in outdoor 116 Acronyms FoV Field of View FPGA Field Programmable Gate Array FT Fourier Transform HDTV High Definition Television HPBW Half-Power Beamwidth iFFT inverse Fast Fourier Transform IF Intermediate Frequency IFoV Instantaneous Field of View iFT inverse Fourier Transform JPL Jet Propulsion Laboratory LNA Low-Noise Amplifier LO Local Oscillator MIRAS Microwave Imaging Radiometer using Aperture Synthesis MMIC Monolithic Microwave Integrated Circuit mmW Millimeter-Wave MoM Method of Moments NASA National Aeronautics and Space Administration NFI Noise Figure NF Near Field NTT Nippon Telegraph and Telephone Corporation PCA Photoconductive Antenna PCS Photoconductive Switch PID Proportional-Integral-Derivative PLO Phase-Locked Oscillator PML Perfect Matched Layer PO Physical Optics PVC Polyvinyl Chloride QCL Quantum Cascaded Laser Acronyms 117 RA Real-Aperture RF Radiofrequency RMS Root-Mean-Square SA Synthetic Aperture SMOS Soil Moisture and Ocean Salinity SNR Signal to Noise Ratio SSB Single-Sideband THz-CW Terahertz Continuous Wave THz-TDS Terahertz Time-Domain Spectroscopy TIA Transimpedance Amplifier TPR Total-Power Radiometer TSC Signal Theory and Communications Department UPC Polytechnic University of Catalonia USB Universal Serial Bus UTC-PD Uni-travelling Carrier Photodiode VNA Vectorial Network Analyzer WLAN Wireless Local Area Network WPAN Wireless Personal Area Network 118 Bibliography Bibliography [1] C. 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A. McIntosh, S. Calawa, W. F. DiNatale, E. Duerr, and K. A. Molvar, “Generation and detection of coherent terahertz waves using two photomixers,” Applied Physics Letters, vol. 73, no. 26, pp. 3824–3826, 1998. [87] S. Saito, T. M. Inerbaev, H. Mizuseki, N. Igarashi, R. Note, and Y. Kawazoe, “First principles calculation of terahertz vibrational modes of a disaccharide monohydrate crystal of lactose,” Japanese Journal of Applied Physics, vol. 45, no. 43, pp. L1156–L1158, 2006. Author Publications and Patents Journal articles [J1] Nova, E., J. Romeu, S. Capdevila, F. Torres, and L. Jofre, “Optical Signal Processor for Millimeter Wave Interferometric Radiometry,” Geoscience and Remote Sensing, IEEE Transactions on, vol. In press. [J2] Nova, E., J. Romeu, F. Torres, M. Pablos, J. Riera, A. Broquetas, and L. Jofre, “Radiometric and Spatial Resolution Constraints in Millimeter-Wave Close-Range Passive Screener Systems,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 51, no. 4, pp. 2327–2336, 2013. Conference articles [C1] Nova, E., G. Roqueta, J. Romeu, and L. Jofre, “Characterization of Pharmaceuticals using Terahertz Time Domain Spectral-Tomography,” in Antennas and Propagation (EUCAP), 2013 7th European Conference on, 2013. [C2] Nova, E., D. Rodrigo, J. Romeu, and L. Jofre, “94 GHz cassegrain reflector antenna performance characterization,” in Antennas and Propagation (EUCAP), 2012 6th European Conference on, march 2012, pp. 3442 –3445. [C3] Nova, E., J. Romeu, F. Torres, A. Broquetas, and L. Jofre, “Optical Cross-Correlation of Millimeter Wave Signals Applied to Interferometric Radiometry,” in Infrared, Millimeter and Terahertz Waves (IRMMW-THz), 2012 37th International Conference on, 2012. [C4] Nova, E., J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “Optical Cross-Correlation of W- band Radiometric Signals,” in XXVII Simposium Nacional de la Uni´ on Cient´ ıfca Internacional de Radio (URSI 2012), 2012. [C5] M. Alonso, C. Guerra, Nova, E., J. Abril, J. Romeu, N. Llombart, and L. Jofre, “100 GHz retina for THz tomographic imaging,” in Infrared, Millimeter and Terahertz Waves (IRMMW-THz), 2011 36th International Conference on, oct. 2011, pp. 1 –2. [C6] Nova, E., J. Abril, J. Romeu, A. Broquetas, F. Torres, and L. Jofre, “Characterization of a 94 GHz radiometric imager with mechanical beam-scanning,” in Microwave Workshop Series on Millimeter Wave Integration Technologies (IMWS), 2011 IEEE MTT-S International, sept. 2011, pp. 164 –167. [C7] J. Abril, Nova, E., A. Broquetas, A. Aguasca, J. Romeu, and L. Jofre, “Deforming and relief interferometric sar imaging at W-band,” in Infrared, Millimeter and Terahertz Waves (IRMMW- THz), 2011 36th International Conference on, oct. 2011, pp. 1 –2.