Polarimetric LiDAR for target characterization aiming at autonomous driving implementations
Abstract
LiDAR is an active sensor, used to measure distances. By illuminating obstacles and measuring retro-reflected light, LiDAR is able to measure the distance to a particular obstacle, as well as predict the shape of that obstacle. In autonomous driving, the high precision and accuracy of LIDAR is an enormous asset for decision making and safety. The fact that it is a fundamental technology for autonomous driving means that large companies are allocating resources (monetary and intellectual) to their development. The project in which this dissertation is inserted aims to use the concept of polarization of light in the LIDAR system, in order to allow the classification of targets and help their recognition. In the course of this work, different Mueller Polarimeters were built to consider and evaluate the importance and usefulness of polarization in the classification of materials. Two of the setups were developed, with a 1550 nm wavelength laser, in the facilities of the School of Sciences of the University of Minho, being different by using distinct polarimetric components to generate and analyse states of polarization: quarter wave plates or liquid crystals variable retarder and linear polarizers . The two 1550 nm setups and the obtained polarimetric information are described in this document. The work presented here also involved the construction of a fourth setup: a LIDAR demonstrator, whose objective was not only to measure distances with high precision and accuracy, but also to introduce polarimetric components and to recognize the importance of using polarization in the differentiation of materials. The results obtained in this work allow us to conclude that polarization at 1550 nm of wavelength has very significant importance in the classification and recognition of road scene objects. Moreover, a Polarization 1D LiDAR at a 1550nm is capable of distinguishing between at least some relevant materials of great importance in autonomous vehicle safety. Therefore, it is proposed to continue this path of work on polarization in LIDAR systems, in order to increase the capabilities of recognizing the environment, in the context of autonomous driving.
Full text
DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial-SemDerivações CC BY-NC-ND https://creativecommons.org/licenses/by-nc-nd/4.0/
i Acknowledgments Without any particular order, I would like to leave it imprinted my most sincere appreciation, gratitude and recognition to the ones that either paved my academic path or somehow interfered positively in my life: • To my advisor, Professor Eduardo Jorge Nunes Pereira, for giving me the opportunity of working in this project which allowed me to understand and fell the academic and company worlds, for the availability of always sparing his time with me, for always insisting on showing me the reality, despite my naivety, and for triggering my interest in the optics field. • To my co-advisor, Irene Estévez Caride, for all tireless work spent in the lab, for showing me be beauty behind light polarization, for actively motivate me, and for always keeping my curiosity satiated and, somehow, craving for more, at the same time. For showing me that the lab can also be a joyful place. • To all my team colleagues, in Bosch Chassis System Control and in the University of Minho, for embracing me in this internship and for the constant availability to listen and help me, and for the financial support offered by the company • To my Bosch colleague, Luís Martins for his words of advice, for offering me one (not yet signed) copy of his book, and for the speared time between laughs and work in the lab. • To my parents, Rosa Maria and Fernando, for the culture, education, opportunities, values, critical though, sacrifices and even for the discussions in our the dining table about politics or human rights, for agreeing and disagreeing with me, and most importantly for never letting me fell nulled and making our dining table the most warm. • To my brother, Tiago, for not only being a brother but for being also a friend, for supporting and loving me unconditionally even if I stole his food, for teaching me how to walk, to teaching me the meaning and the necessity of protecting the ones we love the most. • To my friend, D. Celeste, that since a youth fed me curiosity and discipline, for our snack breaks, and for giving me her most valuable “ q j é q j z q ”. • To my teachers, Carlos Pereira e Maria Cavaco, for the tenderness in their classes and for having encouraged my joy in science.
ii • To all my friends, for the dinners, for the trashy tv shows, for the most idiotic and non-sense talks, for the laughs, for the tears, for the making every moment a stunning memory, for somehow making my academic years a joyful and valuable path. • To my best friends, Lau e Mi, for 13 years of friendship, for no-one standing us when we are together, for the confidence, esteem, respect and the protection, for never letting me alone and keeping my heart full of love for all this years, and for the unhealthy meals full of heathy thoughts. • To my best friend Tiago, that never left me being and always pushed me forward. For the laughs, confidence, respect and protection. For being the brat that always makes me get out of my safe bubble and enjoy life as it is. • To my one and only, for always letting me proud, for being my service psychologist and for making y w y y “ y ”, for being the shell to my shell and for loving me with all my flaws, but most importantly for being the reason my eyes smile. For being my person. This work is supported by European Structural and Investment Funds in the FEDER component, through the Operational Competitiveness and Internationalization Programme (COMPETE 2020) [Project nº 037902; Funding Reference: POCI-01-0247-FEDER-037902].
iii STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho.
iv LiDAR Polarimétrico de Caraterização de Alvos para Implementações na Condução Autónoma Resumo O LiDAR é um sensor ativo, utilizado para medir distâncias. Iluminando os obstáculos e medindo a luz retrorefletida, o LiDAR é capaz de medir a distância até um determinado obstáculo, bem como de prever a forma desse mesmo obstáculo. Na condução autónoma, a elevada precisão e exatidão do LIDAR constituem uma enorme mais-valia para a tomada de decisões e para a segurança. O facto de ser uma tecnologia fundamental para a condução autónoma faz com que grandes empresas estão a alocar recursos ao seu desenvolvimento. O projeto em que esta dissertação se insere tem como objetivo utilizar o conceito de polarização da luz no sistema LIDAR, a fim de permitir a classificação de alvos e facilitar o reconhecimento dos mesmos. No decorrer deste trabalho, foram construídos três diferentes Polarímetros de Mueller para considerar e avaliar a importância e utilidade da polarização na classificação de materiais. Dois setups foram desenvolvidos, com lasers de 1550 nm, nas instalações da Escola de Ciências da Universidade do Minho, sendo estes diferenciados pela utilização de diferentes componentes polarimétricos na geração e análise de estados de polarização: lâminas de quarto de onda ou cristais líquidos de atraso variável e polarizadores lineares. Os dois setups referidos e a informação polarimétrica obtida são apresentados neste documento. O trabalho aqui apresentado envolveu, também, a construção de um quarto setup demonstrador de LIDAR, cujo objetivo era não só medir distâncias com elevada precisão e exatidão, como também introduzir componentes polarimétricas e reconhecer a importância da utilização de polarização na diferenciação de materiais. Os resultados obtidos neste trabalho permitem concluir que a polarização, a um comprimento de onda de 1550 nm, tem uma importância muito significativa na classificação e reconhecimento de objetos. Conclui-se também que, um LiDAR de polarização a 1550 nm é capaz de distinguir entre pelo menos alguns materiais de elevada importância para a segurança de veículos autónomos. Assim, propõe-se que seja prosseguida a linha de trabalho na polarização em sistemas LIDAR, de forma a aumentar as capacidades de reconhecimento do ambiente, em contexto de condução autónoma. Palavras-chave: condução autónoma, LIDAR, LIDAR de polarização, classificação de materiais, matriz de Mueller, polarímetro de Mueller, polarização, vetor de Stokes.
v Polarimetric LiDAR for Target Characterization aiming at Autonomous Driving Implementations Abstract LiDAR is an active sensor, used to measure distances. By illuminating obstacles and measuring retro-reflected light, LiDAR is able to measure the distance to a particular obstacle, as well as predict the shape of that obstacle. In autonomous driving, the high precision and accuracy of LIDAR is an enormous asset for decision making and safety. The fact that it is a fundamental technology for autonomous driving means that large companies are allocating resources (monetary and intellectual) to their development. The project in which this dissertation is inserted aims to use the concept of polarization of light in the LIDAR system, in order to allow the classification of targets and help their recognition. In the course of this work, different Mueller Polarimeters were built to consider and evaluate the importance and usefulness of polarization in the classification of materials. Two of the setups were developed, with a 1550 nm wavelength laser, in the facilities of the School of Sciences of the University of Minho, being different by using distinct polarimetric components to generate and analyse states of polarization: quarter wave plates or liquid crystals variable retarder and linear polarizers . The two 1550 nm setups and the obtained polarimetric information are described in this document. The work presented here also involved the construction of a fourth setup: a LIDAR demonstrator, whose objective was not only to measure distances with high precision and accuracy, but also to introduce polarimetric components and to recognize the importance of using polarization in the differentiation of materials. The results obtained in this work allow us to conclude that polarization at 1550 nm of wavelength has very significant importance in the classification and recognition of road scene objects. Moreover, a Polarization 1D LiDAR at a 1550nm is capable of distinguishing between at least some relevant materials of great importance in autonomous vehicle safety. Therefore, it is proposed to continue this path of work on polarization in LIDAR systems, in order to increase the capabilities of recognizing the environment, in the context of autonomous driving. Keywords: autonomous driving, LiDAR, Mueller matrix, Mueller polarimeter, material classification, polarization, polarization LiDAR, Stokes Vector.
vi List of acronyms Acronym – Meaning FoV – Field of View HWP – Half Wave Plate HLP – horizontal linear polarization IEC – International Electrotechnical Commission LiDAR - Light Detection and Ranging LC – Liquid Crystal LCP – Left Circularly Polarized LCVR – Liquid Crystal Variable Retarder LP – Linear Polarizer LP±45°– linearly polarized at ±45° MCP – microchannel plate MEMS – Microelectromechanical systems MMT – Micro Motion Technology M – Mueller matrix ℳ – Normalized Mueller matrix 𝑀𝑖𝑗 – Mueller matrix 𝑖𝑗 element 𝑚𝑖𝑗 – Normalized Mueller matrix 𝑖𝑗 element OPA – Optical Phased Array PMT – Photomultiplier Tube PSA – Polarization State Analyzer PSG – Polarization State Generator QWP – Quarter Wave Plate
xiii Figure 45. Normalized Mueller matrix image at 20 of SRA for 1550 nm of leaves, determined with the LCVRs Mueller setup. ................................................................................................................................................ 95 Figure 46.Normalized Mueller matrix image at 20 of SRA for 1550 nm of a rock (granite) , determined with the LCVRs Mueller setup. ...................................................................................................................................... 96 Figure 47. Normalized Mueller matrix image at 20 of SRA for 1550 nm of clothing fabric (cotton) , determined with the LCVRs Mueller setup. ................................................................................................................................ 97 Figure 48. RGB picture and normalized Mueller matrix image at 20 of SRA for 1550 nm of a) LEMONGRASS-MET., b) BLUEHIT and c) REFLEXSILBER metallic car paints, determined with the LCVRs Mueller setup. ........................ 98 Figure 49. SRA (°) dependence on the normalized averaged Mueller matrix at 1550 nm for multiple samples of each materials: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively), determined with the QWP Mueller setup. ........................................................................................................................................ 99 Figure 50. Chosen Mueller matrix components and sample rotation angle, SRA (°), represented in a threedimensional space of multiple samples of each material: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), asphalt (yellow), wood (magenta), metallic and non-metallic car paints (green and cyan, respectively). The Mueller components were determined with the QWP Mueller setup. ............................... 101 Figure 51. Diattenuation (a) and polarizance (b) norm dependence on the SRA for the Mueller matrices shown in Figure 49: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively). The components were determined with the QWP Mueller setup. ........................................................................................................ 102 Figure 52. 𝑀𝛥, 𝑀𝑅 and 𝑀𝐷 resulting from the decomposition of the Mueller matrix at 1550 nm at an SRA of 20 of one sample of each group of materials. The Mueller decomposition matrices were determined with the QWP Mueller setup. .......................................................................................................................................................... 103 Figure 53. Depolarizer matrix, 𝑀𝛥, as a function of the SRA (°), resulting from the decomposition of the Mueller matrix at 1550 nm, for multiple samples of each material: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively), determined with the QWP Mueller setup. ............................................................................ 105 Figure 54. Retardance matrix, 𝑀𝑅, as a function of the SRA (°), resulting from the decomposition of the Mueller matrix at 1550 nm, for multiple samples of each materials: retro-reflective traffic signals (blue), traffic signals without
xiv retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively) , determined with the QWP Mueller setup. ........................................................................... 106 Figure 55. Diattenuator matrix, 𝑀𝐷, as a function of the SRA (°), resulting from the decomposition of the Mueller matrix at 1550 nm, for multiple samples of each materials: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively), determined with the QWP Mueller setup. ............................................................................ 107 Figure 56. Experimental one-point LiDAR setup. The pulsed laser (1) generates a linearly polarized pulse that is collimated by the collimating lens (5). The existing pulse is divided by two glass cover slips (9) in order to reduce the intensity of the existing beam. One part of the beam is focused by a focusing lens (6) on the ADP1 (2). The portion of the laser beam with higher intensity, by the first glass cover slips, is directed to the target by a MEMS Mirror (4). The backscattered light is focused by a camera lens (7) and a focusing lens (8), to be detected by the ADP2 (3). ....... 110 57. “ L-K08-LP-015-005-010-1550-T1-ET0-PK26D-C ”.............. 111 Figure 58. Reference (blue) and Retroreflected (red) signals of specular and diffuse reflections. The 1550 nm pulse laser was fed at 1.3 mW (specular refection) and 2 mW (difusse reflection). ...................................................... 113 5 . “ L-K08-LP-015-005-010-1550-T1-ET0-PK26D-C ” w from the Test Report made by Keopsys [178]. ................................................................................................ 114 Figure 60. Standard deviation of 1000 measured pulses of the Reference (blue) and Retroreflected (red) signals of specular and diffuse reflections, the laser was electrically fed at 1.3 mW and 2 mW, respectively. ....................... 115 Figure 61. The electrical response to Specular Reflection (of the reference APD (blue) and the Retroreflected signal measured by the APD2 (red) to a Specular Reflection after passively suffering a differential inversion................... 116 Figure 62. Schematic representation of the optical path inside the experimental one-point LiDAR setup and the reference for distance measurement. ............................................................................................................. 117 63. ’ : C C y ( ) (orange dashed line). .................................................................................................................................... 120 Figure 64. Graphical representation of the distinction between accuracy and precision (adapted from reference [192]). ......................................................................................................................................................... 121 65. L ’ : 𝜎 𝑚, (blue) of the Gaussian distribution at 1.257 m and the ADC discretization resolution (orange) as a function of the measurable distance range (in m). ............................. 123
xv Figure 66. Experimental Polarization 1D LiDAR setup upgrade of the previous 1D LiDAR. ................................... 124 Figure 67. Photograph of the three samples that were subjects of the polarization 1D LiDAR study: (a) metallic car paint, and traffic signals (b) without and (c) with retroreflectors. ........................................................................ 125
xvi List of Tables Table 1. Summary of the qualitative performance of the different technologies using the five levels scale: Needs Improvement (red), Barely Satisfactory (orange), Good (yellow), Very Good (green) and Ideal Solution (blue) (adapted from reference [49]). ...................................................................................................................................... 26 Table 2. Brief Summary of the associated risk of each laser product class (adapted from reference [80]). .............. 38 3. C y’ L . ................................................... 55 Table 4. Calibration states summary for the Mueller polarimeter with rotating QWPs and LPs................................ 83 Table 5. Calibration states summary for the Mueller polarimeter using LCVR and LPs. The values were obtained from Eq. (44). ........................................................................................................................................................ 85 Table 6. PSG and PSA calibration states for the Mueller Polarimeter based on LCVRs retarders. The colours range from blue to red to describe the changes in the electric field with the propagator. ................................................ 86 Table 7. Comparison of the ToFs measured in the setup with the range finder measured distance. The measured ToF (left column) precision was considered to be the greatest time difference between two consecutive recorded times, and due to the handling of the range finder, its precision was estimated to be 4 times the range finder precision.. 119 Table 8. Set of experimental measurements in relation with the LiDAR selected range, and its Gaussian fits according to the determined mean value (Range (m)) and the estimated Standard Deviation (𝜎 𝑚). ................................... 122 Table 9. Normalized Mueller Matrix images, their respective average normalized Mueller Matrix and calculous of the HLP Stokes vector after interacting with the referred Mueller matrices, for three different materials (metallic car paint, regular traffic signal and retroreflector traffic signal) at a sample rotation of 0° (specular reflection). ................... 126 Table 10.Comparation of Stokes vector of the specular reflection of HLP light in a metallic car paint, a regular traffic signal and a retroreflector traffic signal. Predicted normalized Stokes vectors calculated from the experimental Mueller matrices measured with our polarimeter are shown in the middle column, and experimentally normalized Stokes vectors measured with our 1D LiDAR are show in the right column. .................................................................. 127 Table 11. Normalized Evaluation of the 1D Lidar precision as a function of the distance range (Range (m)). Experimental Results Distributions and their best Gaussian fits. ........................................................................ 144
17 1. Introduction 1.1. Context There might be no greater invention, in the last century, which has influenced human behaviour as deeply as transportation vehicles. The majority of us uses automobiles on our daily basis, as our primary way of transportation. In fact, it is estimated that over one billion passenger cars are on the road worldwide [1]. y’ “ y ” w w k human health, energy or human productivity [2]. Only in the last year, there were over 2.5 million car accidents recorded of which resulted in around 400 thousand injured passenger or pedestrians and 3 thousand fatalities [3], moreover transportation directly generated about 23% of global carbon dioxide emissions [4], [5]. The presented problems made automakers ideate new vehicle designs to keep up with the consumer necessities [6]–[11]. These demands have conducted human development to the introduction of autonomous driving, improving safety, comfort, convenience and energy efficiency [6], [8]. Statistics predict that Automated Vehicles will come with improved engines and designs, as well as better traffic management. These improvements will result in a lot less fuel usage [12]–[14]; accident savings, either in healthcare-related costs or car repairs [12]; and productivity gains, since the time used to drive can be then used to develop deskwork and goods transport can be made by analysing traffic and improving traffic flow, avoiding daytime traffic [12], [13] . Lately there has been an increasing amount of publications on this subject matter, driven by the engagement of the market player to develop their own expertise. It is expected that, the global ADAS (Advanced Driver Assistance System) market will reach approximately USD 67 billion by 2025, at considerable annual growth rate of 19% [15].The enormous efforts being made by companies like BOSCH Group made possible that experts plan to market the first autonomous vehicles in the coming years (such as BMW [16], Volvo [17] and the PSA Group [18]) [8].
18 1.1.1. The Levels of Automated Driving Although there is not a completely autonomous car yet, some technology advances in Automated Driving have been developed and some automated functions have been implemented in modern vehicles. For this reason, in order to provide a taxonomy for vehicle automation, the Society of Automotive Engineers (known as SAE), conceived the standard J3016TM in 2014 [19]. This document has the intent of promoting a common language for discussions and a foundation to further development activities in the automotive field [20]. This “ ” x ( ) 5 ( ) evolving continuously. The latest J3016 graphic, shown in Figure 1, was presented in 2019. The scope of this y y “L ” . “ ” ptive and technical, rather than normative or legal standards. Figure 1. SAE Standard J3016 automatedy y “L ” ( [21] ). In a level 0 of automation, the human driver makes the full-time performance and all the driving tasks (see Figure 1). More precisely, the system can intervene shortly, but the control of the vehicle is always in charge
19 . “ ” y may take control of some variables, such as acceleration and deceleration, taking into account the information acquired about the environment, but always with the expectation that the human driver is still in charge [22]. The human driver has to constantly monitor the vehicle and, in case of system failure, the driver has to be capable of taking corrective actions immediately, at any time [23]. “ ” system takes full control of the execution of steering and acceleration or deceleration under certain conditions, considering the environment. The system controls longitudinal and lateral vehicle motion in defined use cases [23], and the driver must be aware to interfere immediately in case of the occurrence of a failure in the automated system [22]. At the level 3 “C ” y k are in the system responsibility, but only in defined use cases [23]. Meaning that the human driver is only needed to intervene in case of a system request [22] (i.e., a failure occurs or system limitations are reached [23]). At the level 4 “H ” [22], the driver is no longer needed to be watchful, even if the limits of the system are reached or a failure occurs [23]. The vehicle is self-driving in most scenarios and, if not, it is capable of correct a not appropriated response of the driver to a request to intervene. The level 5 is the last level, “ ” [22], and it contemplates the full-time performance by the automated system. Note that in case of a system failure, the system is still responsible of the driving task ’ y e [23]. In this sense, the system is capable of handling every possible scenario, meaning that, at this stage, the pedals and the steering wheel are no longer included. At this moment, several ADAS levels (1 and 2) are being implemented by multiple companies, progressively achieving autonomy. For example, it was estimated that Tesla ’ 3 billion kilometres in October 2019 [24]. Concerning level 3 systems, it was claimed that Hyundai Motor, in partnership with Glovis , completed 40 km on highway in South Korea in August 2018 [25]. In addition, the Audi A8, launched in 2018, claimed to be a level 3 automated driving system that can take control of the majority of the driving tasks below 60 Km/h [26]. Since 2016, Renault-Nissan has been collaborating with Microsoft and later with Waymo to work on self-driving car technology for its vehicles, planning to release autonomous cars in urban conditions in 2020 [27]. Tesla ’ C O k uggested that Tesla will be fully autonomous by the end of 2020 [27].
20 1.1.2. Perception Sensing and the Autonomous Vehicle The much needed autonomous vehicles incorporate various technologies such as processors, mapping, software algorithms and sensors. The referred technologies are designed to remove the onus from the human driver. To complete this goal, certain requirements are necessary, such as obstacle detection and trustworthy processing, decision-making, and possible obstacle avoidance, all in real-time. As one might realize, sensing systems for autonomous driving technology are an essential and challenging task. In this sense, one of the main open challenges is to detect and recognize different kinds of static or moving objects, as pedestrians, road signals or cars; or to analyse the road conditions. To improve the detection process, multiple sensors might be included in autonomous vehicles providing data diversity and redundancy [28]. This is called Sensor Fusion [29]. Sensors to automotive purposes are divided into two categories: active and passive [30]. Passive sensors simply gather information about and from the environment without the need to emit a wave [30]. In this category, cameras might be the most accurate way to create a visual representation of the world [28]. On the other hand, active sensors emit energy in the form of waves onto its surrounding, acquire the reflected wave and analyse it to position various objects within the Field of View (FoV) of the sensor. As examples of ’ egory are Radars, Sonars and LiDARs [31], [32] (see Figure 2).
21 Figure 2. a) Chart of Surroundings Sensors. b) Schematic representation of Surrounding Sensors capability of self-driving vehicles (dark and light blue denote LongRange Radars and Short/Medium-Range Radars, respectively, red denotes LiDARs and grey denotes cameras). Image from reference [33]. Cameras As referred above, cameras are passive sensors. The majority of nowadays vehicles feature some sort of visible light cameras to provide video streaming to the driver. Stereo cameras are incorporated for detecting and recognizing small obstacles and for 3D mapping in a range greater than 15 meters [34].
22 By far, between the most common driving sensors, cameras are the most inexpensive and available optical sensors in the market. Different sensing functions are implemented by combining cameras and smart algorithms [35]. For example, stereo cameras capture scenes from more than one viewpoint and, by using various techniques such as triangulation, frame differencing or background subtraction, and based in the arrangement of pixels [34]–[36], it is possible to obtain depth perception of the surroundings, providing information about the position, distance and the speed of objects [28], [31], [37]. Figure 3. Frame differencing with a static camera. The moving cars are determined by calculating the difference between consecutive images (Figure from reference [35] ). However, cameras have some significant drawbacks, such as night-time and bad weather conditions that might not allow an efficient recognition or may even not be capable of recognizing street objects [34]. These disadvantages are expected of being compensated by integrating other types of sensors. In addition, cameras also have an enormous amount of data, which implies slow algorithms cannot make them real-time reliable [37]. Radars Nowadays, automotive radars are already used in adaptive cruise control, allowing them to supplement cameras in low visibility conditions, improving object detection [31], [36]. Note that since radars are active sensors, they work by emitting either electromagnetic pulses or frequency modulation (FMCW) in the radio frequency (RF) spectrum, covering 360 degrees of the horizontal FoV . Once those waves hit an object, they are reflected and detected by the sensor, providing accurate j ’ . pieces of information are determined either through the Time-of-Flight ( ToF ) or through the frequency shifts between the emitted and detected signal.
29 and recognizing objects. The processing unit evaluates the scene and decides about how to proceed and act in each situation. Figure 6 discretizes the elements predicted for higher levels of automated driving. Figure 6. Elements of autonomous driving system. From reference [53] . In short, none of the sensors alone completely fits every case scenario and so, multiple various sensors are y z y ’ .
30 2. Motivation and Objectives As one can understand from the chapter 1, LiDAR sensors are a key element to achieve greater levels of automations and it is expected having a major role in the sensors fusion for autonomous driving. Although LiDARs are already used in different fields, their application in the automotive market is not mature once compared with stereo cameras or radars, that are used intensively in other industries. Hence, the lack of development of this technology leads to current high price solutions, and without a doubt, compromises the development of a driverless vehicle. The goal of the present work ( y ’ j ) w to implement a single point LiDAR capable of measuring distances and distinguish materials through polarization. To understand how the polarization of light should be implemented, a comprehensive polarization study was pursued. The motivation behind this study is that polarization properties of light may vary once interacting with matter. These changes depend on the wavelength and the sample rotation angle of the incident beam, and the characteristic properties of ( …). k n provide information about the target material, supporting object recognition. In addition, the objective of this work is also to suggest an implementation of scanning system using a MEMS scanning micromirror to steer the beam vertical and horizontally, providing a 3D polarimetric LiDAR. The final objective of this thesis dissertation is not to implement a fully working LiDAR, but to acquired critical knowledge in LiDAR, polarization and the capabilities of integrating them as one. A fully apt LiDAR is an optical system of high complexity addressed by complete teams of multiple interdisciplinary areas of knowledge.
31 3. Framework and Content This master thesis dissertation is composed of nine chapters that discuss subjects like: an introduction to LiDAR, a contextualization of LiDAR systems, the light polarization and its benefits to LiDAR, experimental work, conclusions of this thesis and recommendations of work to be done in the future. • The first chapter aims to give a background of what an autonomous vehicle system is and the elements that should include, demonstrating the relevance of LiDAR in self-driving applications. • The second chapter, that is a brief chapter, refers the motivation and objectives within the present master thesis dissertation. • The third chapter explains the framework and content of this master thesis. • In the fourth chapter, the LiDAR system is presented in greater detail and it is discussed the working principle of lasers and the safety classification y L ’ systems and the main scanning technologies. • The fifth chapter reports the geographical comp ’ distribution investing in automotive LiDAR systems and the state-of-the-art of the automotive LiDAR sensors. A comparison of some of the current systems in the market is summarized to show the variety of the available products. Some soon to entering in the market products is also referred. In this chapter, it is also discussed the polarization LiDARs and their current applications. • The sixth chapter starts by giving a contextualization of the physical conceptualization of light waves, the concept of polarization and the Stokes-Mueller formalism. In addition, it is also discussed the experimental polarimetric measurement principle, two experimental 1550 nm Mueller polarimeter setups, and some conclusions derived from the study of the acquired data. • In the seventh chapter, L ’ x presented. An accuracy calibration is sought, and the system precision is evaluated. • The eighth chapter features the experimental Polarization 1D LiDAR and presents a brief experimental study of its capabilities on distinguishing different material. • The last chapter (ninth chapter) contains the conclusion of this project and some guidelines for future work.
32 4. The context of LiDAR As it was introduced in Chapter 1, a LiDAR (Light Detection and Ranging) system consists on a laser or an array of laser sources [47], [55], [56] capable of emitting either continuous light either electromagnetic pulses over the desired FoV [47], [56], [57], and an efficient detector to accurately detect and track objects [58]. Furthermore, LiDARs typically work in visible and near infrared frequency ranges [47], [55], [56] (NIR wavelengths are usually used for terrestrial mapping [59]). Figure 7 presents a conceptual diagram of a LiDAR system. The laser purpose is to emit light waveforms in order to obtain range information. In addition, specific electronic devices, capable of generating the desired waveform, control this element. The laser together with a high-precision clock only allows the detection of distance to an obstacle in its line of sight. In this sense, to acquire a two-dimensional field of view, a prospect system (scanning or non-scanning) is implemented to regulate horizontal and vertical directions [60]. Figure 7. LiDAR Conceptual diagram [55] : The transmitter (Tx) and receiver (Rx) components are in blue and red respectively and in green are the electrical components. Note that Figure 7 represents a bistatic system, where the transmitter (Tx) and the receiver (Rx) are completely separated, while in monostatic implementations, the light is emitted and received by the same aperture. The optical systems (Tx and Rx optics) in Figure 7 are integrated separately into the generator and receiver ends, respectively, to improve the Signal-to-Noise Ratio, i.e. to improve the sensing performance [55]. These systems are responsible for collimating and shaping the output beam (e.g. beam expanders [57]), focusing the reflected one into the detection system and filtering it to eliminate background noise (developing a better
33 Signal-to-Noise Ratio [55]), improving the ’ y [55], [57]. Under the bistatic scenario, the background signal is significantly reduced and fewer photons that suffered multiple scattering can be manipulated to less likely to be detected [57], leading to a more precise system. In addition, a detection system is needed. The detected beam from the outcome light from the reflection reaches the light sensor and it is converted into an electrical signal. The signal is now amplified and stored, for it to be then digitally filtered and manipulated to achieve its purpose [55], [57], [61]. This is further processed by analog of digital analysis to eventually obtain the targets distance. The now obtained signal together with its direction is stored and processed to construct a point cloud [30] and then, to reconstruct the surrounding environment through recognition algorithms [30], [35]. The system is protected by housing [62], [63] to protect LiDAR from external damaging and thermal oscillations, which creates the need to have at least one optical aperture so that the generated light is able to reach the environment and come into the detector [55], [57]. The communication between the central processor, responsible for taking into account the data acquired from all sensors, and the information determined by LiDAR should be done by wired interface communication to avoid shielding by a metallic housing [62], [63]. A CAN (Controller Area Network) interface could be used to acquire the fastest and the most reliable results [64]. 4.1. Major Devices in a LiDAR In this section, the major devices in a LiDAR are described. 4.1.1. Laser Source Physical Principle “ y ” ( ) monochromatic, coherent and highly collimated light through a process of optical amplification based on the stimulated emission within an amplifying medium, population inversion and on optical resonators [65]. To understand the physical principle behind these concepts, one shall recall that quantum mechanics forces electrons to take a discrete energy level once orbiting an atom [65]. Taking this into ponderation, one can consider two energy levels of electrons of which 𝐸1 is the ground state and 𝐸2 is the excited state (a higher electronic
34 energy level). Whenever a photon, with energy equal to the energetic difference between the ground state and the excited one, is focused on an atom, the ground state electron gains enough energy to jump to the excited state 𝐸2 (see Figure 8 (a)). In non-metal crystals, this phenomenon generates a pair electron-hole where one can consider there is an electron in the higher energy state and a hole in the lower energy state [65]. The electron, now in the excited state, can decay either by spontaneous emission (where electrons move naturally from one state to another, so the photon emission occurs naturally, meaning there is no control over the emitted light – incoherent light, see Figure 8 (b)), either by stimulated emission (it occurs when a passing photon is absorbed by an electron in the excited state and triggers the recombination of an electron with a hole, emitting a second photon with the same frequency, momentum and phase [65], [66] – coherent light, see Figure 8 (c)) [65]. The probability of a stimulated emission event to happen is inversely proportional to its time constant of decay [67]. Figure 8 . Electron transition in an atom. From reference [68] . Stimulated emission occurs when a passing photon is absorbed by an electron in the excited state and triggers the recombination of an electron with a hole, emitting a second photon with the same frequency, momentum and phase [66], [69], [70]. Unlikely spontaneous emission, stimulated emission guarantees that the big majority of the emitted photons have the same energy, phase and direction [69], [70]. This is because the system is designed in a way that the time decay of spontaneous emission is very long when it is compared with stimulated emission [69]–[71]. Note that in any real crystal’ case of study, the probability of stimulated emission is very small. Furthermore, the majority of the electrons are in the 𝐸1 energy ground state [70], [72]. y z ’ w y equilibrium
35 at a temperature 𝑇, the population at the excited energy level (𝑁2) in terms of the population at the energy ground state (𝑁1) and the energy of the two different levels (𝐸1 and 𝐸2) is [73] 𝑁2=𝑁1∙𝑒−𝐸2−𝐸1 𝑘𝐵𝑇 (1) where 𝑘𝐵 is the Boltzmann's constant. One can rearrange this equation and substituting 𝐸2−𝐸1 for the energy of the photon (ħ𝜔), obtaining 𝛥𝑁≡ 𝑁1−𝑁2= 𝑁1∙(1−𝑒−ħ𝜔 𝑘𝐵𝑇) (>1) (2) where 𝜔 is the angular frequency, and ħ is the reduced Planck constant. Thus, it is possible to conclude that in a normal population of atoms there will always be more electrons in the ground state than in the higher energy levels [72]. Meaning that amplification will not be possible because the probability of the absorption of a photon and the probability of spontaneous emission is the same. Consequently, to achieve a laser, a “ ” is required to happen [70], [72]. Population inversion of the gain medium occurs once the higher energy state has a greater electronic population than the lower energy state [70], [72]. This kind of event is only possible if one considers more than two energy level in a crystal, and the greater the number of energy states, the greater the optical gain will be. To a better understanding of this concept, let us consider a three energy levels system with energy levels 𝐸1, 𝐸2, 𝐸3, so that 𝐸1<𝐸2<𝐸3, and let 𝑁1, 𝑁2 and 𝑁3 be the number of electrons in its respective energy level (see Figure 9 (a)) [69], [70]. Under normal conditions, a lower energy level will have a greater number of electrons occupying its state. For that reason, it can be concluded that 𝑁1>𝑁2>𝑁3 in normal circumstances [69], [70]. Whenever provided the energy Δ𝐸1,3= 𝐸3−𝐸1 to excite the ground state electrons, referred to as pumping, it is possible to achieve a greater population in the third energy state. Such an arrangement is k w “ ” (see Figure 9 (b)) [69], [70]. A medium suitable for laser operation has to have the shortest lifetime constant from the third to the second level, transferring the energy of this decay to the crystal lattice by processes without radiation emission [69], [70]. Due to the short lifetime, only a small population of electrons will accumulate in the 𝐸3 energy state (see Figure 9 (c)) [69], [70]. As a result, the population of the 𝐸2 energy state will become, not only greater
36 than the population of the energy states 𝐸3 but also, greater than the population of the 𝐸1energy state [69], [70]. If this condition is guaranteed and if a photon with a frequency of 𝐸2−𝐸1 ħ is now inserted in the system, an electron in the second energy state level will be stimulated to decay to the first level by stimulated emission (see Figure 9 (d)) [69], [70]. Figure 9 . Population Inversion in a 3-level crystal (adapted from reference [74] ). One way to significantly amplify the output signal of this process is via a positive feedback mechanism called optical resonator [72]. An optical resonator is a system of mirrors that reflects undesirable (off-axis) photons out of the system and reflects on-axis photons back into the system [72], [75]. Meaning that emitted photons have an opportunity to stimulate new decays emitting another photon. As the on-axis are reflected back and forth, they will interact, each time, with more excited electrons increasing the stimulated emission [72]. However, to have a laser beam, the optical resonator needs to let a small percentage of the reflected light out of the system. To execute this purpose, one of the mirrors has a considerably lower reflectance, allowing a certain amount of photons getting out of the cavity [72].
37 Laser systems safety classification Lasers are devices categorized by their wavelength and for public general usage theirs maximum power has k “ y ” [76], [77]. For the purpose of most terrestrial LiDAR applications, the laser source makes use of near infrared (NIR) wavelengths [78] because, for long ranges, a better resolution is achieved by providing shorter wavelength light pulses [76]. In this sense, the used infrared wavelengths are those that avoid eye injury. One of the most used wavelengths is 905 nm and it was chosen for early LiDARs because: pulsed diode laser emitters were readily available and relatively inexpensive; silicon detectors could be used to detect the referred wavelength; and also, because the solar spectrum at sea-levels reaches a low irradiance at a wavelength of 905nm . But as this wavelength can penetrate the interior of the eye and reach the retina, the allowed power density is limited. Nevertheless, lasers with a wavelength of 1550 nm are presented as an alternative, as they are absorbed in the cornea instead of the retina [79], which makes “ y ” (by the IEC standard 60825-1 [80]) at much higher power levels [76]. The International Electrotechnical Commission, IEC, is an organization responsible for standardization comprising all national electrotechnical committees. In 2001, IEC published the standard 60825-1 regarding ’ y that has the intention of: • Protecting people against hazards from radiation, by reducing injuries from radiation and by introducing a system of classification of laser products and working spaces according to their degree of hazard [80]. • Ensuring adequate warnings of hazard to individuals, by improving the precautions taken into account and through protective safe protocols [80]. Any laser product carries legible, permanent and clearly visible labels in accordance with its class and some self-explanatory cautions. Table 2 presents the laser classes and their functionalities to evidence the risks associated with each laser product class.
38 Table 2. Brief Summary of the associated risk of each laser product class (adapted from reference [80] ). Laser Product Class Wavelength Range Associated Risks 1 - Safe under reasonably foreseeable conditions of operation. 1M 302,5 nm – 4000 nm Safe under reasonably foreseeable conditions of operation, but may be hazardous if the user employs optics within the beam 2 400 nm – 700 nm (visible) The blink reflex may be expected to provide adequate protection under reasonably foreseeable conditions of operation. 2M 400 nm – 700 nm (visible) The blink reflex may be expected to provide adequate protection under reasonably foreseeable conditions of operation, but it can be compromised if optics are employed within the beam. 3R 302,5 nm – 106 nm Direct intrabeam viewing is potentially hazardous but the risk is lower than for Class 3B lasers. The accessible emission limit is within five times the accessible exposure limit of Class 2 in the wavelength range from 400 nm to 700 nm and within five times the AEL of Class 1 for other wavelengths. 3B - Lasers that are normally hazardous when direct intrabeam exposure occurs. Diffuse reflections are normally safe. 4 - Lasers that are also capable of producing hazardous diffuse reflections. They may cause skin injuries and could constitute a fire hazard. Their use requires extreme caution. 4.1.2. Spatial Resolution of an Optical System Diffraction is an optical effect in regard to the wave nature of the light that has a great impact in the resolution of an optical system [81]. Spatial resolution is directly connected to angular resolution, because starting by the second one might have a much more intuitive approach: Angular resolution describes the reasonable ability of an image-forming device to distinguish small details of an object [81]. The angular resolution of an
45 The Single Photon Avalanche Diode is capable of detecting a single photon up to 50% of probability with 0.8 of quantum efficiency and a time accuracy of down to 30 picoseconds [87]. Hybrid Photomultiplier Tube Hybrid PMTs are vacuum tubes integrated with photocathodes and avalanche diodes [89], [103], [104]. A scheme of a hybrid photomultiplier tube is represented in Figure 15. As in PMTs, whenever a photon is absorbed by the photocathode, there will be electrons emitted and accelerated by a high electrical field to the semiconductor avalanche diode [89], [103], [104]. By taking this type of approach, one first obtains an electron-bombardment gain and afterward an avalanche gain [89], [103], [104]. The combination of these two technologies offers beneficial features like a high speed, a high pulse height resolution, a time uncertainty on the order of 50−100 𝑝𝑠, small latency and, in addition, it allows to develop a compact device [87], [89], [103], [104]. O ’ ined in one step, which means that they will deliver singlephoton narrow pulses, allowing them to distinguish one or multiple detected photons [89], [103], [104]. More than that, the absence of an electron multiplication system made it possible to successfully not having electrons getting neither absorbed nor reflected [89], [103], [104]. The major advantage of this detector is that there is no afterpulsing in its measures [89], [103], [104]. The afterpulsing are the background pulses that appear a few milliseconds after the detection of a photon in the detected signal [89]. It is a phenomena believed to be caused by ion feedback, by luminescence of the dynode material, by the glass of the PMT or by the electrons and holes in the previous avalanches of SPADs [89].
46 Figure 15. Schematic of a Hybrid Photomultiplier Tube. 4.1.5. Scanning system The scanning mechanism is conceived to consistently steer laser pulses in order illuminate surroundings with laser light and to measure the reflected pulses [78]. There are different methods of scanning the scenery available, granted for different purposes, such is achieved by regulating the azimuth and elevations, dual-axis scanner, dual oscillating plane mirrors and polygonal mirrors [77]. It is important to note that this system will determine the range and resolution of the device, but the speed at which images can be built up will be affected by the speed of scanning [77]. In 3D scanning, the scanning mechanisms are the systems responsible to direct laser beams with a range finder within the FoV. By taking the distance measured in various directions and from different viewing angles the device is able to capture the surroundings point cloud. The scanning systems available are presented in Figure 16. The following subsections briefly summarize some of them.
47 Figure 16. Probing Systems for 3D LiDAR. Mechanical Macro-Scanners Mechanical scanner systems are rotating systems that, in order to cover a 360° horizontal FoV, rotate their fixed laser-receiver assemblies around their vertical axis [105], [106]. Meaning this that each frame is obtained by completing a turn. That is, the point cloud density is placed vertically and the horizontal is a function of the rotation speed (see Figure 17). The vertical scanning of this kind of systems is achieved by aligning multiple laser-receiver assemblies covering different angular directions, meaning this, that vertically the resolution and point density are established by the used number of laser-receiver assemblies and the angular spacing between them. Probing Systems Macromechanical Scanning Mirror Gavanometer Scanner MEMS Mirror and MOEMS OPA (Optical phased Array) Flash Micro Motion Technology (MMT)
48 Figure 17. Representative scheme of a Mechanical Scanning System Due to the simple scientific background, it is easy to control and predict the behaviour of mechanical macroscanners [105]. Thanks to these characteristics, these systems are usually used to make the minimum viable LiDAR product [105]. For this reason, mechanical scanning might be the most used scanning system. As an example, one of the most used mechanical macro-scanner LiDARs is Velodyne with Alpha PrimeTM LiDAR (see reference [107]). Note that this kind of mechanism is the only one to be presented that is not a steering beam scanner, meaning this is the only system that does not use optical elements to control the beam vertically and horizontally. Scanning mirrors The majority of beam steering scanners use moveable mirrors to direct the light beam. In a system using scanning mirrors, a stationary laser beam is controlled through an optical system of lens and mirrors to redirect the light beam. One of these mirror systems is the galvanometers scanner represented in Figure 18.
49 Figure 18. Galvanometer Module from SCANLAB AG. From reference [108] . A Galvanometer Scanner, also called Galvo, is a system that consists of galvanometers, mirrors and a controller to regulate the system [109]. A Galvo uses at least 2 galvanometer mirrors in order to capture the vertical and horizontal dimensions of the FoV. Galvanometer mirrors are electromechanical devices constituted by a galvanometer and a mirror, combined to deflect the light whenever an electric current is sensed [110]. Galvanometer scanners are widely used in laser scanning because the provide the easiest way of steering a laser beam [111] and also for its incredible accuracy and precision [110]. However, the simplicity of making the beam travel across the FoV is, accompanied by the bulkiness of the system [111], and it might probably be the architecture most affected by the car movements and vibrations. Microelectromechanical System - MEMS Mirror Another way of realizing a scanning mirror apparatus is by using a micro scanning mirror, which is a more compact, lighter and lower power consumption way of steering a light beam. A MEMS mirror (see Figure 19) can be made, depending on the MEMS morphology, either by translation or rotation, on one or two axes, by electrically derived from repulsive force actuators [112]. This type of system also has some downfalls as, for example, the efforts made to align it are much intricate, the V y ’ x the resolution of the system depends on the
50 minimum measurable quantity variation of the mirror controller electrical signal. Modern LiDAR systems for the automotive industry are using MEMS mirrors that operate by being controlled by a system called MEMS Driver [113]. Figure 19. MEMS scanning mirror of Preciseley Microtechnology Corp (from reference [114] ). A scanning MOEMS (Micro-opto-electro-mechanical system), or scanning optical MEMS, is a special class of a MEMS and it is a combination of a MEMS with micro-optical elements [115]. Solid-State probing There are two types of solid-state probing systems: The Optical Phased Array (OPA) and the Flash technique. Using the OPA beam steering technique, the beam is precisely steered without any moving part [116], [117]. This device is used for aiming laser beams on a macroscopic scale by firstly splitting ’ through a power splitter tree, followed by aiming each segment of the light to a phase shifter, and lastly adjusting the phase of light waves, reflected or transmitted, through a surface of phase modulator crystals, called the array [116], [117]. The wavefront of the combined elements will then have the desired shape and direction of propagation and, consequently, redirecting the laser beam in a desire direction [116], [117]. Some examples of the referred capability of this method are represented in Figure 20.
51 Figure 20. Waves emanating from discrete sources in a phased array interfere to create a) a plane wave that appears to come from a distant source behind the array; b) a plane wave that propagates at an angles from the array surface; c) a spherical wave that appears to come from a point behind the array surface; d) a wavefront that appear to originate in empty space in front of the array (Adapted from reference [118] ). Furthermore, a Flash probing technique uses a single light source that illuminates the entire FoV in a single pulse that will posteriorly be detected by a 2D array of detectors. Each pixel of the 2D array detects the time it takes each laser pulse to hit the target and return to the sensor, as well as the location and intensity of the reflected pulse [119], [120]. The returned signal is processed by embedded algorithms to generate the fastest way to create a 3D rendered image of the FoV of the sensor [120]. One can understand that this is a high accuracy tool for applications in highly precise real-time imaging [121]. Figure 21 compares a beam steering scanner and a the briefly presented flash scanner in order to illustrate their differences.
52 Figure 21. Comparative scheme of a Beam Steering Scanner and a Flash LiDAR. Micro Motion Technology - MMT The US start-up company Cepton patented Micro Motion Technology (MMT) in 2016 [122]. This technology is supposed to minimize the use of mechanical components making the system frictionless[123], which translates into reducing costs and increasing reliability [124], [125]. At present, it is not exactly known how the MMT system works but it is said that it allows smalls movements of the laser sources and the detectors by making the use of coils [124], [125].
53 5. State of The Art It is suggested to consider that this research was made in February 2020 and because the automotive market is such a ferocious demand, new products and improvements are constantly being brought to the public eye. Also, one must consider that there are more marketplaces to LiDAR than automotive, such as agriculture, urban planning, astronomy, pollution modelling and meteorology, species conservation management, geology and mining, and green energy safety management [126]. 5.1. Automotive LiDARs The majority of the global k y ’ C y countries like the United States of America and Canada, being the first, the one with either the most promising start-ups and either the most established veteran companies [127]. European countries like Germany, Sweden, United Kingdom and Austria; along with Canada, Israel, and Japan; are constantly making significant progresses[127], [128]. Moreover, although China and Korea are in preliminary stages of LiDAR production and R&D, they are blooming, and they are expected to have a great contribution in this sector [127]. Figure 22. Global automotive LiDAR Manufacturers (adapted from reference [129] ).
54 On August 14th, 2019, the International Society for Optics and Photonics (SPIE) published a proceedings paper in recent developments of automotive LiDAR technology, its industry and trends. This study also identifies OEMs tech companies, suppliers and manufacturers of the necessary components, such as illumination sources, photodetectors, and optical elements integrated circuits [127]. Following this report j y w L ’ w w as an object of study and the results are discussed below. To this purpose, the main comparison criteria were the technology, range, horizontal and vertical FoV, angular resolution and range resolution. Due to different technologies have been implemented in different products, a complete comparison is limited and not viable. For this reason, an attempt was made to approach all the technological implementations referred to in chapter 4 “The context of LiDAR”. 5.1.1. Comparison of Automotive Current Products y’ . that are going to be the object of study in this state of the art are Velodyne, Ouster, Innoviz, Aeye, Omron, Quanergy, Cepton and LeddarTech. In Table 3, an attempt was made to do a summary of some of the best LiDARS, approaching multiple wavelengths and all the scanning technologies. Due to the diversity of the technologies being implemented in prototypes and commercial LIDARs targeted for automotive applications, a complete comprehensive (of all the possible LIDARs) is not viable. For this reason, the referred table criteria selected to analyse the presented products were wavelength, technology, range, horizontal and vertical FoV, angular resolution and range resolution. Bearing in mind the evaluation done in Table 3 of some of the best current products, Velodyne is still leading the mechanical LiDAR market with Alpha PrimeTN, in terms of performance. Its 128 channels allow high-speed support for autonomous driving, but this product still is not available to mass production. In addition, Velodyne “C ” , organized by the Consumer Technology Association, that the company was ready to start mass production of their other products such as VelarrayTM and VelabitTM [130]. The latest is the most recent announced product but there is not yet any information about the working principle of the device beyond working with metamaterials. Moreover, Velodyne informed that VelabitTM is able to work with cheap
61 so, as for the transmitter, four light detectors were used, each one analysing a different polarization state [146]. A simplified experimental layout was drawn in Figure 25. The architecture proposed in reference [146] enables the whole processing in some nanoseconds with a ≤ 8% error. Figure 25. Tested demonstrator layout. LPLinear polarizer, EOMelectro-optic modulator, QWP – quarter wave plate, PBS -polarizing beam splitter. In this chapter, some of the most recent state-of-the-art was presented and, although lots of LiDARs are being produced to reach the automobile market, there is still no proposal of an automotive LiDAR including a material detection and classification via the use of the Mueller matrix elements. Moreover, the Stokes-Mueller formalism has been multiple times used in the sense of discriminating different materials (see references [139], [141], [147]). Based on the idea that a polarimetric LiDAR, able to measure the Mueller matrix, can be used for autonomous driving, this master thesis is focus on characterizing the most relevant road scene objects and designing a polarimetric LiDAR, in order to bridge these elements. In addition, from the different applications discussed in this chapter, polarization has shown great results in remote sensing, enhancing the obtained results.
62 6. The Concept of Polarization To understand the study of polarization and its interaction with matter, one must start to consider the wavelike properties of light. This will be the case where the electric and magnetic fields, that describe light, must obey xw ’ q . xw ’ q in a homogeneous, isotropic, linear dielectric (non-conductor) material are [148] { 𝛻∙𝐸=0 𝛻∙𝐵=0 𝛻×𝐸= −𝜕𝐵 𝜕𝑡 𝛻×𝐵= 𝜇𝜀𝜕𝐸 𝜕𝑡 (5) where 𝐸 and 𝐵 are the imaginary vector description of the electric and the magnetic fields, respectively; 𝜇 is the permeability tensor of the optical medium and 𝜀 is the electric permittivity tensor of the optical medium. Since usually, the source of light is an almost monochromatic source, a monochromatic plane wave propagating along a general direction is going to be considered. Its electric and magnetic field vectors can be expressed as {𝑬=𝐸0.𝑒𝑖(𝒌∙𝒓−𝜔𝑡+𝜑𝐸) 𝑩=𝐵0.𝑒𝑖(𝒌∙𝒓−𝜔𝑡+𝜑𝐵) (6) where, 𝐸0 and 𝐵0 represent the complex amplitudes of the electric and magnetic fields, and 𝜑𝐸 and 𝜑𝐵 are their displacements, respectively. Also, 𝒌 is the imaginary wavenumber vector, 𝒓 is a specific position in space in a certain referential, ω is the angular frequency and 𝑡 is a specific time moment. Since the electric and the magnetic fields have a similar behaviour, Eq. (6) , one can work only with the electric field and generalize its conclusions to the magnetic field. It should also be considered that the light propagation medium is air, so attenuation effects can be ignored and 𝒌 becomes a real vector (𝒌). By doing these assumptions, a lot of constraints are imposed, and the electric field of a monochromatic collimated beam of light will be 𝑬(𝒓 ,𝑡)=𝑬𝟎.𝑒𝑖(𝒌∙𝒓−𝜔𝑡+𝜑𝐸) (7) Considering the cartesian z-axis as the light propagation axis, the Maxwell equations guarantee that there will be no magnetic nor electric field in the direction of the light propagation and, therefore, 𝑯 =(𝐻𝑥,𝐻𝑦,0)
63 and 𝑬=(𝐸𝑥,𝐸𝑦,0). Now, taking into account only the part of the solution that has a physical meaning, i.e. the real part, one finally achieved the components of transverse electrical field [149] {𝐸𝑥(𝑧,𝑡)=𝐸0𝑥∙𝑐𝑜𝑠(𝜏+ 𝛿𝑥) 𝐸𝑦(𝑧,𝑡)=𝐸0𝑦∙𝑐𝑜𝑠(𝜏+ 𝛿𝑦) 𝐸𝑧=0 (8) where 𝐸0𝑥 and 𝐸0𝑦 are the maximum amplitudes of the electric field in its cartesian components, x and y, respectively; 𝛿𝑥 and 𝛿𝑦 are arbitrary phases and 𝜏=𝑘∙𝑧−𝜔𝑡 is called the propagator. Note that the propagator is used only to simplify Eq. (7), since it is easier to consider a general change in the propagator than time and spatial variations. 6.1. Introduction to polarization As the electromagnetic wave propagates, the electric field components will construct a pattern. Using simple trigonometric relations and attending that 𝛿=𝛿𝑦−𝛿𝑥, one can demonstrate that the sum of the square of Eq. (8) can be written as 𝐸𝑥2 𝐸0𝑥2+𝐸𝑦2 𝐸0𝑦2−2𝐸𝑥 𝐸0𝑥 𝐸𝑦 𝐸0𝑦𝑐𝑜𝑠𝛿= 𝑠𝑖𝑛2𝛿 (9) Equation (9) is recognized as the equation of an ellipse, which means that at any instant of the propagation, the locus of points is described as an ellipse. For this reason, Eq. (9), known as the polarization ellipse equation, discriminates the polarization state. Figure 26 shows multiple representations of the polarization ellipse for different relative phases, 𝛿, assuming normalized and equal amplitudes (𝐸0𝑥=𝐸0𝑦). The polarization states in Figure 26 are: a) linearly polarized at +45° (LP+45°), 𝛿=0° ; b) right elliptically polarized, 𝛿=𝜋4 ⁄ ; c) right circularly polarized (RCP), 𝛿= 𝜋2 ⁄ ; d) right elliptically polarized (𝛿=3𝜋4 ⁄), e) linearly polarized at -45° (LP-45°), 𝛿=𝜋; f) left elliptically polarized (𝛿=5𝜋4 ⁄), g) left circularly polarized (LCP), 𝛿=3𝜋2 ⁄ ; and h) left elliptically polarized (𝛿=7𝜋4 ⁄). It can be observed that the area of the polarization ellipse is zero for 𝛿=0 and 𝜋, i.e. light is linearly polarized, and for 𝛿=𝜋2 ⁄ and 3𝜋2 ⁄ the area is a maximum and the obtained state of polarization is circularly polarized.
64 Figure 26. Polarization ellipses for different relative phases 𝛿=𝛿𝑦−𝛿𝑥 . The electric field magnitudes are equal ( 𝐸0𝑥=𝐸0𝑦 ) and normalized. Arrows indicate polarization direction (adapted from Ref. [150] ). The latest formulation has a serious limitation, for only being able to describe completely polarized light. Nevertheless, a formalism able to describe not only completely polarized light is needed. Note that polarized beams interacting with real-world materials can result in completely unpolarized or partially polarized light. On the one hand, unpolarized light is described as the superposition of multiple waves randomly polarized, resulting in rapid and random changes in polarization. On the other hand, partially polarized light has a randomly changing polarization state but has a tendency toward a particular state of polarization. For this reason, in order to describe not only fully polarized light, a more suited formalism is needed. 6.2. Mueller-Stokes Formalism There are different mathematical formalisms to describe polarization states of light beams and their interactions with matter. Based on different authors as Goldstein [149], Azzam [151] and Chipman [152], we have proposed to study polarization by using the Mueller-Stokes formalism. The main reason is because it is the most appropriate representation of polarization when considering not fully polarized light. Along this section, this formalism is presented.
65 6.2.1. Stokes Parameters In literature, there are different ways of describing light and its polarization. As stated above, one particularly interesting method of representing light is the Stokes parameters. The Stokes parameters are a method for characterizing the polarization properties of light beams. This method, presented itself as the most valuable in this study, not only represents polarized and unpolarized light but also represents them in terms of observables or measurable quantities. The Stokes parameters are four observables that can be obtained from the time average values of the squared optical field. Since the square of the electric field was already considered in the polarization ellipse equation (Eq. (9)) and, taking into account that for a monochromatic electromagnetic plane wave the amplitudes (𝐸0𝑥,𝐸0𝑦) and phase (𝛿) remain constant at all time, the time dependence can be written as 𝐸𝑥2(𝑡) 𝐸0𝑥2+𝐸𝑦2(𝑡) 𝐸0𝑦2−2𝐸𝑥(𝑡) 𝐸0𝑥 𝐸𝑦(𝑡) 𝐸0𝑦 𝑐𝑜𝑠𝛿= 𝑠𝑖𝑛2𝛿 (10) Taking the average value over time, Eq. (10) can be represented in terms of the optical observables as (𝐸0𝑥2+𝐸0𝑦2)2− (𝐸0𝑥2−𝐸0𝑦2)2− (2𝐸0𝑥𝐸0𝑦𝑐𝑜𝑠𝛿)2=(2𝐸0𝑥𝐸0𝑦𝑠𝑖𝑛𝛿)2 (11) The four observable quantities inside the parentheses in Eq. (11) are the Stokes parameters [149] { 𝑆0= 𝐸0𝑥2+𝐸0𝑦2 𝑆1= 𝐸0𝑥2−𝐸0𝑦2 𝑆2= 2𝐸0𝑥𝐸0𝑦𝑐𝑜𝑠𝛿 𝑆3= 2𝐸0𝑥𝐸0𝑦𝑠𝑖𝑛𝛿 (12) that can completely describe any state of polarization. Note that Eq. (11) can be rewritten as 𝑆02=𝑆12+ 𝑆22+𝑆32. In addition, Eq. (12) can be redefined in terms of polarized flux measurements as [153] {𝑆0= 𝑃0+𝑃90 𝑆1= 𝑃0−𝑃90 𝑆2= 𝑃45−𝑃135 𝑆3= 𝑃𝑅−𝑃𝐿 (13) where 𝑃𝛼 represents the polarized flux measurements whenever it is analysed the 𝛼 polarization, being 𝛼 either a number that characterises the azimuth of the linear polarizer light (0°, 45°, 90° and 135°), either a letter that represents the direction of the circularly polarized light, being clockwise, R, or counterclockwise,
66 L. Therefore, the first Stokes parameter, 𝑆0, is the total intensity of the light beam; 𝑆1 is a way of describing the amount of linear horizontal (0°) and vertical (90°) polarization; 𝑆2 describes the amount of linear +45° or -45° polarization; and the parameter 𝑆3 is the description of the amount of right (R) or left (L) circular polarization. One might also understand that the derivation to obtain the Stokes parameters was made by using a case of totally polarized light, and so, in order to consider every single case (partially polarized and unpolarized light), Eq. (11) must be written y w z’ q y [149] 𝑆02≥𝑆12+𝑆22+𝑆32 (14) If the light beam is completely polarized, Eq. (14) will be an equality. However, for unpolarized light 𝑆02>0 (there is no preference for any particular polarization state, i.e. 𝑆1=𝑆2=𝑆3=0), and for partially polarized light “≥” is replaced by “>” (i.e., 𝑆02>𝑆12+𝑆22+𝑆32 ). Additionally, the Stokes parameters can be concatenated in a vector (known as Stokes vector). A simple way of generalizing it, to describe every state of polarization, is by separating the Stokes vector (𝑺) in two different vectors. These two vectors represent the completely polarized content (𝑺𝒑) and the fully unpolarized content (𝑺𝒖) of the light beam [152] 𝑺= 𝑺𝒑+𝑺𝒖 ⟺ (𝑆0 𝑆1 𝑆2 𝑆3)= ( √𝑆12+𝑆22+𝑆32 𝑆1 𝑆2 𝑆3 ) +(𝑆0−√𝑆12+𝑆22+𝑆32)(1000) (15) The degree of polarization (𝐷𝑜𝑃) for any state of polarization is, by definition, the fraction of the intensities sum of the polarization components (𝐼𝑃𝑜𝑙) by the total intensity of the beam (𝐼𝑡𝑜𝑡) [149], 𝐷𝑜𝑃=𝐼𝑃𝑜𝑙 𝐼𝑡𝑜𝑡=√𝑆12+𝑆22+𝑆32 𝑆0 0≤𝐷𝑜𝑃≤1 (16) If 𝐷𝑜𝑃=0, the measured light is completely unpolarized and whenever 𝐷𝑜𝑃=1, the beam measured is fully polarized. The intermediate states, 0<𝐷𝑜𝑃<1, correspond to partially polarized light [149]. In order to describe not only polarized light but also depolarized or partially polarized light, Eq. (12) is generalized as
67 𝑺= (𝑆0 𝑆1 𝑆2 𝑆3)= ( 〈𝐸𝑝𝐸𝑝∗+𝐸𝑠𝐸𝑠∗〉 〈𝐸𝑝𝐸𝑝∗−𝐸𝑠𝐸𝑠∗〉 〈𝐸𝑝𝐸𝑠∗+𝐸𝑠𝐸𝑝∗〉 𝑖〈𝐸𝑝𝐸𝑠∗−𝐸𝑠𝐸𝑝∗〉 ) (17) where the electric field subscripts, 𝑠 and 𝑝, describe its perpendicular and parallel components with respect to the plane of incidence, respectively. 6.2.2. Poincaré Sphere The Poincaré sphere is a concept that, using a unit sphere centred in the Cartesian coordinate system, and as orthogonal axis the three components of the Stokes vector (𝑆1,𝑆2,𝑆3), represents any state of polarization as a punctual site in this three-dimensional space (see Figure 27). To the concept is given this name because any normalized Stokes vector (𝑠1=𝑆1 𝑆0, 𝑠2=𝑆2 𝑆0, 𝑠3=𝑆3 𝑆0) will be comprehended inside this sphere of radius 1. This representation helps us to quickly visualize any state of polarization. Figure 27 shows an example of an elliptical polarization state over the surface of the Poincaré Sphere. Note that any point over the surface of the Poincaré sphere corresponds to a fully state of polarization. More specifically, linear polarization states are represented along the equator, while north and south poles ( 𝑆3 axis) are the right and left circularly polarized states, respectively. In addition, the polarization state centred in the origin of the Poincaré sphere (0, 0, 0) is a totally depolarized state, meaning that any intermediate state between the origin and the Poi é ’ partially polarized state
68 Figure 27. A polarization state represented in the Poincaré Sphere (adapted from reference [154] ). As can be seen in Figure 27, any state of polarization can be represented in terms of the components named ellipticity angle, 𝜒, and the orientation angle, 𝛹, given by 𝑠𝑖𝑛(2𝜒)= 𝑠3 , −𝜋4≤ 𝜒≤𝜋4 (18) 𝑡𝑎𝑛(2𝜓)=𝑠2𝑠1 ⁄ , 0≤𝛹≤𝜋 (19) Arranging equations (18) and (19), the Stokes vector can be written as 𝑺=𝑆0(1 𝑐𝑜𝑠2𝜒𝑐𝑜𝑠2𝛹 𝑐𝑜𝑠2𝜒𝑠𝑖𝑛2𝛹 𝑠𝑖𝑛2𝜒 ) (20) 6.2.3. Mueller Matrices The interaction of a light beam with a medium was described by Mueller in 1948. In this formulation, Mueller defined all polarizing properties of a sample (diattenuation, retardance and depolarization) in a four-by-four matrix, 𝑀, that allows a simple correlation between the incident (𝑺𝒊𝒏) and exiting (𝑺𝒐𝒖𝒕) Stokes vectors as [152]
69 𝑺𝒐𝒖𝒕=(𝑀00 𝑀01 𝑀10 𝑀11 𝑀02 𝑀03 𝑀12 𝑀13 𝑀20 𝑀21 𝑀30 𝑀31 𝑀22 𝑀23 𝑀32 𝑀33)∙𝑺𝒊𝒏=𝑀∙𝑺𝒊𝒏 (21) Figure 28 shows an incident beam interacting with a sample in transmission and in reflection. In addition, if a light beam goes through a series of polarization elements or interacts with multiple elements, these interactions are taken into account by the multiplication of each individual Mueller matrix 𝑀𝑞, where 𝑀𝑞is the q-th of the Q elements that interact with the light beam. In a mathematical way, this is placed as 𝑀=𝑀𝑄∙𝑀𝑄−1∙…∙𝑀𝑞∙…∙𝑀2∙𝑀1= ∏𝑀𝑄−𝑞 𝑄−1 𝑞=0 (22) Figure 28. Schematic representation of different unique interactions light-matter: a) a light transmission over a sample, and b) a simple reflection, or scatter. 𝑺𝒊𝒏 and 𝑺𝒐𝒖𝒕 are the incident and exiting Stokes vectors, respectively, and 𝑀 is the characteristic Mueller matrix of the sample. It should be noted that, from a Mueller matrix, one can extract light properties such as how an interaction light-matter changes the light intensity (𝑀00) and the three fundamental polarization properties, which are diattenuation, retardance and depolarization [149]. 𝑀00 The beam intensity changes once the light interacts with matter [155]. This happens due to the different properties of a present material, as for example, the material in study can absorb some part of the light, or it can also disperse the light in a way that the detector can not sensor it [155].
70 The 𝑀00 element of a Mueller Matrix is the element responsible to scale the output intensity with respect to the input intensity [155]. This component can also be seen as the transmittance or reflectance if the system is being analysed in transmission or reflection, respectively [155]. Diattenuation Diattenuators are optical components that attenuate differently the amplitude of the orthogonal components of the electric field vector [149], [156]. In this sense, the diattenuation 𝐷 is the change in the intensity transmittances 𝑇 of the incident polarization state [149], [156], 𝐷=𝑇𝑚𝑎𝑥−𝑇𝑚𝑖𝑛 𝑇𝑚𝑎𝑥+𝑇𝑚𝑖𝑛 0≤𝐷≤1 (23) where the subscript 𝑚𝑎𝑥 and 𝑚𝑖𝑛 are mean maximum and minimum, respectively [149], [156]. Linear polarizers are diattenuators that extinguish one of the orthogonal components of the electric field vector (𝑇𝑚𝑖𝑛 = 0 and 𝐷 = 1). Since the diattenuation causes different changes in the different polarization states, this characteristic is usually represented as a vector 𝑫 that provides a complete description of the diattenuation properties. Its components are called horizontal, 𝐷𝐻, 45° linear, 𝐷45, and circular, 𝐷𝑐, diattenuation [149], [156] and their direct relations with the Mueller matrix are [149] 𝑫=(𝐷𝐻 𝐷45 𝐷𝐶)=1 𝑀00(𝑀01 𝑀02 𝑀03) (24) Note that Eq. (23) is still valid and can be used to determinate each one of the 𝑫 components, as a simple experimental determination method. In terms of the Poincaré sphere, perfect diattenuators act like a polarization filter that project different polarization states into a chosen one. A frequent kind of diattenuators used in optics are Linear Polarizers (LP). Retardance Retardance is the optical property that describes how the orthogonal electric field components are delayed once interacting with a retarder. These elements have a preferential path that is called the fast axis orientation, and a slow axis orientation where the electric field is delayed, i.e. retarded. Meaning that the retardance
77 Figure 30. Laboratorial setup illustration of our Mueller Polarimeter with rotating QWPs and LPs. In addition, the PSA and the detection system are placed over a rotation stage ( Thorlabs [163], Model RBB450A/M) to allow measurements in transmission, to calibrate the system, and in reflection, to take the so needed measurements. The setup also includes a motorized rotation stage ( Thorlabs [163], Model HDR50/M) in order to change the sample rotation angle of the sample. This rotation stage allows to measure polarization properties of specular reflection and scattering light in relation to the Sample Rotation Angle (SRA) [167]. In this setup the laser and camera are maintained fixed as close as possible to each other. This was made in order to try to mimic a LiDAR’ . SRA is described as the angular offset from the specular light detected in the camera (see Figure 31), i.e. when SRA = 0°, the camera will detect the specular reflection. In our polarimeter, the light source and the detection arms have a bistatic angle, 𝛽 in Figure 31, between them of 13.3° (𝛽=13.3°).
78 Figure 31. The sample rotation angle (SRA) is measured with respect to the specular reflection condition. The bistatic angle between the light source and the detection arm is 𝛽=13.3° (adapted from reference [167] . In this sense, firstly it is needed to use a highly reflective sample to do an angle calibration, i.e. look for the angle where highest detected intensity was shown and mark it as the 0° of the system. The referred Mueller polarimeter setup is shown in Figure 32. Its main components are labelled. Figure 32. Experimental implementation of the Mueller polarimeter designed with QWP developed in the University of Minho (the main components are labeled).
79 6.3.2. Mueller Polarimeter based on liquid crystal variable retarders (LCVRs) A downside in the setup presented in section 6.3.1, predicted in the literature [152], [153], [157], is that mechanically rotating elements setups cause beam wandering and positioning errors, due to the high dependency on the alignment, introducing errors in the calculated Mueller matrices. In addition, to rotate each optical element consumes a large amount of time. For these reasons, this setup was improved by using a static configuration for the PSG and the PSA. We have introduced variable retarders, liquid crystal variable retarders (LCVRs), depending on the applied voltage and the orientation on the fast axis, without requiring any mechanical movement [152], [153], [157]. Liquid Crystal (LC) retarder cells are used to dynamically change the polarization properties by imposing an external electric field to the cell being, in this sense, considered as static. Figure 33 shows a retardance versus voltage curve of a linear retardance modulator with axis along x and y. As the voltage changes, the transparent molecules are rotating in the x-z plane, but remaining nearly constant in y. Since it is considered that light is traveling in the z axis, the refractive index will cause a retardation in the x component in relation to the y component. Figure 33. Schematic of the ’ orientation on a nematic retardation modulator liquid crystal in accordance to the increasing applied, adapted from reference [157] . The representation of the referred setup is shown in Figure 34. In this setup, a 1550 nm laser light source that goes through the PSG, constituted by a static LP ( Thorlabs [163], Model LPNIR100-MP2) followed by two LCVRs ( Meadowlark Optics [168], LRC-300-IR3), is reflected by the sample. Then, it passes through the PSA, that contains two LCVRs ( Meadowlark Optics [168], LRC-300-IR3) followed by a fixed LP ( Thorlabs [163],
80 Model LPNIR100-MP2), being finally detected by a camera (Allied Vision [165], Model GolEye G-033 TEC1C) with a camera lens ( Kowa [166], with a focal length of 35 mm , Model SWIR Lens - CBC-IP2-M3514) to image the sample. Figure 34. Laboratorial setup illustration of a Mueller Polarimeter with rotating liquid crystal variable retarders (LCVRs) and static LPs As the setup in section 6.3.1, this setup includes a rotation stage that rotates each sample, in order to change the sample rotation (SRA). Note that the SRA is described as in the previous subsection (see section 6.3.1). In this type of setup, there is not verified beam wandering and this approach is considerably less timeconsuming than the Mueller Polarimeter with rotating QWPs and LPs. However, LCs material have a dependency on temperature, approximately -0,4% per °C [169]. To maintain the systems behaviour constant and solve this possible problem, in the construction of the laboratorial setup, we have used full-wave LC retarders from Meadowlark Optics [168] and periodically we calibrate and test our Mueller polarimeter. The changes imposed by the temperature in the built setup were unnoticed. The final experimental setup is shown in Figure 35 and its main components are labelled.
81 Figure 35. Experimental implementation of the Mueller polarimeter designed with liquid crystal variable retarders (LCVRs) developed in the University of Minho (the main components are labeled). 6.3.3. Setup Calibration To have accurate polarimetric measurements, it is needed to calibrate the setup, that it is done by calibrating the PSG and the PSA individually. To perform accurate polarimetric measurements there is no need to have ideal polarization elements, but it is needed to know with great accuracy the states exiting the PSG and the states analysed by the PSA. If this requirement is met, systematic errors due to non-ideal components are removed during the data reduction process. To this end, a commercial polarimeter (PAX1000IR2/M [163] from Thorlabs) is used to accurately determine the PSG exiting states and the analysing PSA states. There are multiple ways of calibrating the PSG and PSA (see references [149], [151]–[153], [170]). Based on the mathematical formalism described in section 6.2.4, we decided to characterize the PSA in reverse to its usage, meaning that the light should be going through it in the opposite direction. Although it is only need four linearly independent states of polarization generated by the PSG and analyzed by the PSA, with the purpose of generating easy to find polarization states and roam the entire Poincaré
82 sphere, it was decided to use the 6 standard polarization states: HLP (horizontal linear polarization), VLP (vertical linear polarization), LP+45 (+45° linear polarization), LP-45 (-45° linear polarization), RCP (right circularly polarization) and LCP (left circularly polarization). The theoretical CN of this configuration is √3 (see section 6.2.5). Calibration of the Mueller polarimeter with rotating QWPs and LPs in section 6.3.1. In order to select the PSG and PSA states, a mathematical prediction is made. In ideal conditions, the PSA and PSG calibration Mueller matrix are the same 𝑆𝑜𝑢𝑡=𝑀𝑃𝑆𝐺/𝑃𝑆𝐴∙𝑆𝑖𝑛= 𝑀𝐿𝑅(𝜃2,𝛿)∙𝑀𝐿𝑃(𝜃1)𝑆𝑖𝑛= =[1 0 0 𝑐𝑜𝑠2(2𝜃2)+𝑠𝑖𝑛2(2𝜃2)𝑐𝑜𝑠(𝛿)0 0 𝑠𝑖𝑛(2𝜃2)𝑐𝑜𝑠(2𝜃2)(1−𝑐𝑜𝑠(𝛿)) −𝑠𝑖𝑛(2𝜃2)𝑠𝑖𝑛(𝛿) 0 𝑠𝑖𝑛(2𝜃2)𝑐𝑜𝑠(2𝜃2)(1−𝑐𝑜𝑠(𝛿)) 0 𝑠𝑖𝑛(2𝜃2)𝑠𝑖𝑛(𝛿)𝑠𝑖𝑛2(2𝜃2)+𝑐𝑜𝑠2(2𝜃2)𝑐𝑜𝑠(𝛿)𝑐𝑜𝑠(2𝜃2)𝑠𝑖𝑛(𝛿) −𝑐𝑜𝑠(2𝜃2)𝑠𝑖𝑛(𝛿)𝑐𝑜𝑠(𝛿)] ∙12[1 𝑐𝑜𝑠(2𝜃1) 𝑐𝑜𝑠(2𝜃1)𝑐𝑜𝑠2(2𝜃1)𝑠𝑖𝑛(2𝜃1)0 0.5𝑠𝑖𝑛(4𝜃1)0 𝑠𝑖𝑛(2𝜃1)0.5𝑠𝑖𝑛(4𝜃1) 0 0 𝑠𝑖𝑛2(2𝜃1) 0 0 0]∙𝑆𝑖𝑛 (40) where 𝑆𝑖𝑛 and 𝑆𝑜𝑢𝑡 are the Stokes vectors that represent the light before and after the PSG/PSA, respectively, and 𝑀𝑃𝑆𝐺/𝑃𝑆𝐴 is the Mueller matrix corresponding to the PSG/PSA. 𝑀𝐿𝑅 is the Mueller matrix of a Linear Retarder, which in this case is a QWP, and 𝑀𝐿𝑃 is the Mueller matrix of a Linear Polarizer. 𝜃1 is the angle of the transmission axis of the Linear Polarizer, 𝛿 is the retardance of the Linear Retarder, which is 𝛿=𝜋2 for a QWP, and 𝜃2 is the angle of the fast axis of the QWP. If we consider that the light from our source is completely right circularly polarized, due to the presence of the first QWP (see Figure 30), and normalized to its intensity, 𝑆𝑖𝑛=(1 0 0 1)𝑇, and Eq. (40) becomes 𝑆𝑜𝑢𝑡=𝑀𝑃𝑆𝐺/𝑃𝑆𝐴∙(1001) ⟺ 𝑆𝑜𝑢𝑡=12 [ 1 cos2(2𝜃2)cos(2𝜃1)+12sin(4𝜃2)sin(2𝜃1) sin(2𝜃2)∙cos(2𝜃1−2𝜃2) −sin(2𝜃1−2𝜃2) ] (41) In an ideal optical system, Table 4 shows some 𝑆𝑜𝑢𝑡 values for a set of 𝜃1 and 𝜃2 as guidance to generate the desired calibration states.
83 Table 4. Calibration states summary for the Mueller polarimeter with rotating QWPs and LPs HLP (1100) VLP (1 −1 00) LP+45° (1010) LP-45° (10 −1 0) RCP (1001) LCP (100 −1) 𝜃1=0 𝜃2=0 𝜃1=𝜋2 𝜃2=𝜋2 𝜃1=𝜋4 𝜃2=𝜋4 𝜃1=−𝜋4 𝜃2=−𝜋4 𝜃1=𝜋4 𝜃2=𝜋2 𝜃1=−𝜋4 𝜃2=𝜋2 Due to the need of introducing the less mistakes possible while rotating the polarization elements, an automatic setup using motorized precision rotation stage was sought. Owing to automating the system and only having available two Motorized Precision Rotation Stages (PRM1/MZ8 from Thorlabs [163] ) , it is not possible to generate and analyses the 6 desired states. For this reason, it was decided to generate and analyses 11 polarizations states of each. The Mueller polarimeter shown in Figure 30 is calibrated with the obtain the states of polarization illustrated in the Poincaré Sphere in Figure 36. Figure 36.Illustration of the a) PGS and b) PSA experimentally achieved polarization states (yellow), represented in the Poincaré sphere, of the QWP Mueller setup.
84 G’ ’ calculated CN is 3.6123. The experimental CNs of this Mueller polarimeter are not close to the best theoretical CN of √3 (see section 6.2.5), therefore, we can conclude that this Mueller polarimeter is lacking some precision. Calibration of Mueller Polarimeter based on LCVRs retarders in section 6.3.1. In this setup, the incident light beam passes through a LP followed by two LCVRs. As it has been shown in reference [171], the optimal arrangement to generate or analyse any state of polarization is by having the fast axis of the LCVRs displaced at 45° and 0° from the LP’ transmission axis, sequentially (see Figure 37). Since LCVRs are, as QWP, also linear retarders, the Mueller matrices associated to these two optical components are 𝑀𝐿𝑅(𝜃+45°,𝛿1) and 𝑀𝐿𝑅(𝜃+0°,𝛿2), where 𝛿1 and 𝛿2 represent their retardances and 𝜃+45° and 𝜃+0° represent the angle of their fast axis. Here, to predict and select the PSG and PSA states, a mathematical prediction is made regarding this setup. In ideal conditions, the PSA and PSG calibration Mueller matrix are the same 𝑆𝑜𝑢𝑡=𝑀𝑃𝑆𝐺/𝑃𝑆𝐴∙𝑆𝑖𝑛=𝑀𝐿𝑅(𝜃,𝛿2) ∙𝑀𝐿𝑅(𝜃+45°,𝛿1) ∙𝑀𝐿𝑃(𝜃)∙𝑆𝑖𝑛 (42) where 𝑀𝐿𝑃 represents the Mueller matrix of the LP and 𝜃 is its transmission angle axis. To simplify the mathematical prediction, 𝜃 was placed at 0°. Figure 37. Scheme of a PSG constituted by a linear polarizer (LP) with the transmission axis at 0° followed by two liquid crystal variable retarders (LCVRs) with the fast axis at 45° and 0°, consecutively. 𝛿1 and 𝛿2 represent the retardance of both LCVRs.
85 Then, 𝑆𝑜𝑢𝑡=[1 0 0 1 0 0 0 0 0 0 0 0 cos𝛿2sin𝛿2 −sin𝛿2cos𝛿2]∙[1 0 0cos𝛿10 0 0 −sin𝛿1 0 0 0 sin𝛿11 0 0cos𝛿1]∙12[1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0]𝑆𝑖𝑛 ⟺ ⟺𝑆𝑜𝑢𝑡=12 ( 𝑆𝑖𝑛,0 𝑆𝑖𝑛,1cos𝛿1 𝑆𝑖𝑛,1sin𝛿1sin𝛿2 𝑆𝑖𝑛,1sin𝛿1cos𝛿2 ) (43) In theory, if the input state of polarization is normalized, 𝑆𝑖𝑛=(1 1 0 0)𝑇, Eq. (43) is rewritten as 𝑆𝑜𝑢𝑡=12(1 cos𝛿1 sin𝛿1sin𝛿2 sin𝛿1cos𝛿2) (44) This means that to generate the desired calibration states in an ideal optical system, one can look at the Table 5 as a screenplay. Table 5. Calibration states summary for the Mueller polarimeter using LCVR and LPs. The values were obtained from Eq. (44). HLP (1100) VLP (1 −1 00) LP+45° (1010) LP-45° (10 −1 0) RCP (1001) LCP (100 −1) δ1=0 δ2=0 δ1=𝜋2 δ2=𝜋2 δ1=𝜋4 δ2=𝜋4 δ1=−𝜋4 δ2=−𝜋4 δ1=𝜋4 δ2=𝜋2 δ1=−𝜋4 δ2=𝜋2 After analysing the best theoretical PSG and PSA polarization states, the Mueller polarimeter shown in Figure 34 is calibrated to obtain the states of polarization presented in Table 5. Due to the LCVRs supplier does not provide a prediction of the retardance versus voltage to the wavelength in use, firstly a huge series of combinations of different applied voltages in the LCVRs was detected with the Thorlabs [163] polarimeter to choose the polarization states that best represent the desired ones (see Table 5). The chosen states are indicated in
86 Table 6 and illustrated in the Poincaré Sphere in Figure 38. G’ C .75 7 ’ CN is 1.8179. As stated above, the best theoretical CN is √3 ≈1.7321 (see section 6.2.5), i.e., our experimental CNs are close to the theoretically expected. Therefore, we can conclude that our Mueller polarimeter is precise and accurate. Table 6. PSG and PSA calibration states for the Mueller Polarimeter based on LCVRs retarders. The colours range from blue to red to describe the changes in the electric field with the propagator. Calibration Theoretical Polarization State Calibration Experimental Polarization States Polarization Ellipse PSG PSA PSG PSA HLP (𝟏𝟏𝟎𝟎) (1.0000 0.9997 0.0254 0.0013) (1.0000 0.9998 −0.0201 0.0009) VLP (𝟏 −𝟏 𝟎𝟎) (1.0000 −0.9999 −0.0108 0.0028) (1.0000 −0.9880 −0.1526 0.0238) LP+45 (𝟏𝟎𝟏𝟎) (1.0000 −0.0021 1.0000 0.0040) (1.0000 0.0044 1.0000 −0.0008) LP-45 (𝟏𝟎 −𝟏 𝟎) (1.0000 −0.0040 −1.0000 −0.0081) (1.0000 0.0018 −1.0000 0.0039)
93 Figure 43. Normalized Mueller matrix image at 20 of SRA for 1550 nm of a retro-reflector traffic signal, determined with the LCVRs Mueller setup.
94 Figure 44. Normalized Mueller matrix image at 20 of SRA for 1550 nm of agglomerated wood, determined with the LCVRs Mueller setup.
95 Figure 45. Normalized Mueller matrix image at 20 of SRA for 1550 nm of leaves, determined with the LCVRs Mueller setup.
96 Figure 46.Normalized Mueller matrix image at 20 of SRA for 1550 nm of a rock (granite) , determined with the LCVRs Mueller setup.
97 Figure 47. Normalized Mueller matrix image at 20 of SRA for 1550 nm of clothing fabric (cotton) , determined with the LCVRs Mueller setup.
98 Figure 48. RGB picture and normalized Mueller matrix image at 20 of SRA for 1550 nm of a) LEMONGRASS-MET., b) BLUEHIT and c) REFLEXSILBER metallic car paints, determined with the LCVRs Mueller setup. Now that polarimetric differences were acknowledge, the dependence of the Mueller matrix on the SRA was studied. To this purpose, a LiDAR-like behaviour was considered. As referred in section 4.1.4, LiDARs rely on detectors and, in order to mimic its technology restrains and providing more accurate data, the image ’ x were averaged. It was studied that the spot-size of different LiDARs (from Velodyne [172], LeddarTech [173], Quanergy [174], Valeo [175], Ouster [176] …) divergence (the spot-size area can change from 10×10 mm2 to 300×200 mm2), for this reason, as a preliminary stage, we decided to use a pixel window of 40×40 mm2, which is comprised between the expected illuminating area. The single Mueller matrix of each sample was determined by averaging the entire illuminated area. The Mueller matrices of multiple samples were measured at 11 different angles of incidence, equally spaced 10 by 10 degrees, varying from −50 to +50 (in the clock-wise direction). The obtained averaged results are presented in Figure 49.
99 Figure 49. SRA (°) dependence on the normalized averaged Mueller matrix at 1550 nm for multiple samples of each materials: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively), determined with the QWP Mueller setup.
100 From Figure 49, it is deduced that not only the polarization properties have a dependence on the SRA, but also that similar materials have similar quantitative responses. Figure 49 also allows understanding that some Mueller matrix elements are more important than others to distinguish different materials, as for example the diagonal elements 𝑀11,𝑀22 and 𝑀33. After concluding that there are Mueller elements more suitable to distinguish materials, some combinations of three Mueller matrix components were plotted in different threedimensional spaces (see Figure 50). From the representations in Figure 50, it is deducible that small changes in only one Mueller element can represent a significant change in a three-dimensional space of Mueller elements coordinates, allowing a better material discrimination. Although materials discrimination is clearly possible using only three Mueller elements, some Mueller components, as referred before, are more suitable than others to this end. By Figure 50, one can clearly understand that the angle dependency does not add relevant distinction for material classification (Figure 50 a) and b)), likewise the selected elements represented in Figure 50 c) and d) does not provide as good classification as Figure 50 e) and f), since, in the last, materials are distanced from each other. For that reason, one has to choose the elements that maximize the distance between different material groups. From our preliminary conclusions, it is plausible that the diagonal matrix elements have a greater importance (see Figure 49). Due to the potential of polarimetry observed from the measured samples, this study has not come to an end, meaning that more samples are being measured daily and some Mueller parameters might become relevant. The idea is to analyse more samples, in order to deepen more on the best Mueller coefficients. Nevertheless, from the obtained results, we can clearly differentiate between the measured materials, by using the proposed 3D spaces in Figure 50. One might also extrapolate that material discrimination might enhance by using more than three Mueller matrix coefficients. Note that, in Figure 50, greater differences between materials are observed even without representing the SRA. Figure 50 allows deducing that, although the polarization properties depend on the SRA, the knowledge of the SRA might be unnecessary. After realizing that some elements show a greater relevance to material classification, a study was made to determine the dependence of the relevant elements on the 𝑀𝐷, 𝑀𝑅 and 𝑀Δ matrices, and on criteria as diattenuation |𝐷| and polarizance |𝑃| (see chapter 6.2.6). Note that, the decomposition of the Mueller matrix allows a further and simple discussion of the type of polarimetric response.
101 Figure 50. Chosen Mueller matrix components and sample rotation angle, SRA (°), represented in a three-dimensional space of multiple samples of each material: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), asphalt (yellow), wood (magenta), metallic and non-metallic car paints (green and cyan, respectively). The Mueller components were determined with the QWP Mueller setup. Firstly, the diattenuation and the polarizance were calculated, and then, they were plotted in Figure 51. As expected, due to the Mueller matrix having a quite symmetric behaviour [155], their diattenuation and polarizance have to be quite similar too.
102 Figure 51. Diattenuation (a) and polarizance (b) norm dependence on the SRA for the Mueller matrices shown in Figure 49: retro-reflective traffic signals (blue), traffic signals without retro-reflectance properties (red), Asphalt (yellow), Wood (magenta), metallic and non-metallic car paints (green and cyan, respectively). The components were determined with the QWP Mueller setup. Now, a qualitatively study was then made to better understand the polarization changes that every group of materials presents, i.e. depolarization, retardance and diattenuation. The results are shown in Figure 52, where the decomposition of the Mueller matrix image of several samples at an SRA of 20° are presented. By pure observation of Figure 52, one can conclude that in terms of the depolarization matrix, 𝑀Δ, some materials significantly depolarize more than others, being metallic car paint and solid traffic signals the ones that depolarize the less. In addition, the retro-reflective traffic signal presents a considerable displacement from the other groups of materials in terms of its retarder matrix 𝑀𝑅. In terms of the diattenuation matrix, the material groups that apparently show some dependence on 𝑀𝐷 are solid traffic signal and metallic car paint.
109 7. 1D LiDAR 7.1. Experimental configuration of the one-point LiDAR prototype The starting point of developing the polarization LiDAR proposed in this project is the implementation of a pulsed ToF LiDAR system in one spatial dimension. The conception of this architecture consists of a laser, two high-speed APDs, electronics behind that allows us to control the laser and to make the acquisition of the time of flight, and the optical components responsible to collimate the laser light beam and to focus the reflected light into the detectors’ detection area. The high-speed APD were used instead of single photon detectors (see section 4.1.4), because the automotive market is searching for less expensive LiDAR solutions so that it is viable to implement in vehicles. Nevertheless, a linear analog detector, like a high-speed APD, will provide amplitude signals which depend linearly on the optical power. The systems architecture can be observed in Figure 56. The setup was built thinking about the implementation of the next steps, i. e., to implement the scanning technology and to achieve a 3D LiDAR. Firstly, one should focus its mind on the setup part consisting on a pulsed laser “ L-K08-LP-015-005-0101550-T1-ET0-PK26D-C ” Keopsys [178] (λ = 1550 nm) and the two InGaAs APD detectors “ 3 ” (bandwidth 850-1650 nm) from MenloSystems [179]. The laser emits linearly polarized pulsed light beams at a 10-20 kHz frequency, so that a START signal is recorded by one of the ADPs and the STOP signal is recorded by the second ADP. The time interval between the START and STOP signal gives the needed information to determine the distance of an obstacle in the direction of the outcoming laser beam. Due to electronic constrains, the timing electronics are used in the reverse mode (see section 4.1.3), meaning that the input STOP signal is our reference from the laser and the input START signal is the signal incident in the obstacle.
110 Figure 56. Experimental one-point LiDAR setup. The pulsed laser (1) generates a linearly polarized pulse that is collimated by the collimating lens (5). The existing pulse is divided by two glass cover slips (9) in order to reduce the intensity of the existing beam. One part of the beam is focused by a focusing lens (6) on the ADP1 (2). The portion of the laser beam with higher intensity, by the first glass cover slips, is directed to the target by a MEMS Mirror (4). The backscattered light is focused by a camera lens (7) and a focusing lens (8), to be detected by the ADP2 (3). The ADP responsible for recording the reference signal is the ADP1 in Figure 56. Since the maximum power of the light pulse prevenient from the laser source is greater than the maximum power that the ADP can detect, without getting permanently damaged, two microscope glass cover slips were used to reflect a small percentage of light, into the ADP1. This principal is theoretically expected by Fresnel equations, for polarized light [149]. Having this in mind, to guarantee that the APD1 detects a significantly small light intensity, the laser was positioned so that it emits HLP in the lab referential. Also, the fibre laser source has a F240APC1550 [180] collimating lens, from Thorlabs , in its output placed and marked by the supplier to ensure and to help the user find the best collimation of the fibre laser. The ADP2 is responsible for detecting the incoming light from the reflection in the obstacle and, since the obstacle might absorb some light intensity and, more importantly, the ADPs transimpedance gain was adjusted so that, in the specular reflection, the detector was never close to its breakdown limit. High-speed APDs, in order to have a fast response, have a very small detection area ( ’ 0.03 mm [179]). Therefore, before each ADP, a lens is placed to focus the incoming light into the detection
111 area of the detector. Prior to ADP1, the placed lens is a LA1289-B-ML [181]. Nevertheless, before the ADP2, an optical system formed by a TEC-M55 lens [182] and a LA1540-B-ML lens [181] is placed. 7.2. Monitoring and Laser Control The proposed LiDAR uses “ L-K08-LP-015-005-010-1550-T1-ET0-PK26D-C ” Keopsys [178] that needs to be controlled and electrically fed by an interface platform [178]. In the development of this project, the used interface is a “ - K 6 ” Keopsys [178] with a “SubD25/Micro Sub-D25" connector cable and a supplied voltage of 25 𝑉 (see Figure 57). The interface has a pulse distributed feedback trigger input connected, via a BNC connector, to an external signal generator. The last is required to generate an input TTL signal characterized as: a square wave with a 𝑉𝐶𝐶=5 𝑉, a frequency of 10 𝐾𝐻𝑧 and a duty cycle of 20%. Finally, the interface platform is connected to a computer, via a Sub-D9/USB cable, which is in charge of the control of w “K ” [178], provided by the interface supplier. This software allows us to turn the laser on and off, set the current supplied to the laser and monitoring parameters, such as the current supplied to laser preamplifier and its booster, the distributed feedback frequency and the laser temperature. Figure 57. Electrical scheme of the laser module “ L-K08-LP-015-005-010-1550-T1-ET0-PK26D-C ”.
112 7.3. Photodetection electronics The ADP is a user-friendly complex sensor that integrates its own internal circuitry that comprises a temperature compensation circuit and an integrated amplifier with a continuously adjustable gain setting [179]. The ADPs have an included power supply with a country specific wall plug adapter that only needs to be directly plugged into the mains electricity network [179]. These sensors also have an output BNC connector that returns the sensors electrical response from the detected light. 7.4. Signal Characterization To understand and predict the systems behaviour, a signal characterization was pursued. Firstly, the signals from the ADP1 and ADP2 were analysed in the oscilloscope (model “H O4 34 ” y L C y [183]). The measured signals of specular and diffuse retroreflection are represented in Figure 58. The current intensity supplied to the laser was adjusted to guarantee that a measurable signal was detected but also it did not saturated nor damaged the detectors.
113 Figure 58. Reference (blue) and Retroreflected (red) signals of specular and diffuse reflections. The 1550 nm pulse laser was fed at 1.3 mW (specular refection) and 2 mW (difusse reflection). The recorded reference pulses (shown in Figure 58) have a waveform similar to the one provided by the laser manufacturer (see Figure 59). To understand the represented electrical behaviour, one must consider that the electrical response in Figure 58 w ’ function [184]. Note that, after the high amplitude pulse, there is an extension of the response time. This response duration is extended due to the high avalanche gain of the detector [184]. Furthermore, during the response duration, the waveforms exhibit ringing due to signal line reflections (for more technical information read reference [184]). In addition, the waveforms in Figure 58 also present a non-expected behaviour, since it does not reach
114 negative values in manufacturer report (see Figure 59). Regardless, this ringing type of behaviour is predicted in the literature whenever the stability of the APD system is compromised to increase the photoreceiver speed and sensitivity [184]. After the electrical signal reaches the ground state, there is an oscillator behaviour [179] caused by the APD feedback system electronics [185], responsible for carrying the sensor back to the ground state level, as quick as possible [185]. Also, the specular retroreflected signal has a slower transit time due to a lower transimpedance gain selected, in order to measure the specular signal without damaging the APD. Figure 59. “ L-K08-LP-015-005-010-1550-T1-ET0-PK26D-C ” w y K y [178] . After the first evaluation of the obtained signal, 1000 pulses were recorded. The mean of the waveform and its standard deviation (STD) were produce in Figure 60.
115 Figure 60. Standard deviation of 1000 measured pulses of the Reference (blue) and Retroreflected (red) signals of specular and diffuse reflections, the laser was electrically fed at 1.3 mW and 2 mW, respectively. The timing electronics used to the time-tag recording is the “SPC-160” “ y-Box-3 ” from Becker & Hickl GmbH [186]. The chosen system requires that the input pulses have a negative polarity. To achieve this condition, the TCSPC supplier recommend the use of the passive differential pulse inverter “ -PPI- ” [187]. Therefore “ -PPI- ” is connected to each of the APDs output. Hence, the electric signals resulting from the inversion of the specular signals descripted in Figure 58, y “ -PPI- ” passive differential pulse inverter, are presented in Figure 61.
116 Figure 61. The electrical response to Specular Reflection (of the reference APD (blue) and the Retroreflected signal measured by the APD2 (red) to a Specular Reflection after passively suffering a differential inversion. 7.5. LiDARs Spatial Calibration As one can predict, there are multiple factors that can influence the systems accuracy. On the one hand, there is an uncharted difference in the optical path between the path length travelled by the reference signal and the path travelled by the emitted light pulse (including the optical paths by traversing the lens). The optical path in the LiDAR setup can be observed in Figure 62. On the other hand, there is also an uncharted difference between the transit time of the two electrical signals due to, not only the delay imposed by the
117 delay box, but also the cable length difference between the two ADPs. Therefore, the system is in need of correcting the systematic spatial displacement, thereupon a distance calibration was sought. Figure 62. Schematic representation of the optical path inside the experimental one-point LiDAR setup and the reference for distance measurement. Afterwards, the timing system was implemented, and the calibration of the LiDAR prototype was performed by measuring the recorded ToF for multiple target positions, between 1.0612 m and 5.5750 m, in a way that the specular reflection light was detected. There are two different ways of measuring the time difference between two pulses: either using a time-todigital converter (TDC), either by using and analog-to-digital converter (ADC). TAC/ADC implementations use a Time-To-Amplitude converter (TAC), and the output is an amplitude proportional to the interval between two detected events, which is sampled in a digital format by the ADC.
118 The architectures by TDCs use a start-stop system, similar to a TCSPC system, where the electronic system starts and stops a timer whenever it detects an incoming signal. In this type of system, more than one ion arriving at the detector generates the same response as a single ion or ions that arrive slightly later in time. The two different implementations have some limitations in terms of the accuracy and precision of the ToF measured. The TAC/ADC architecture range of detection is determined by minimum and maximum available C y y C’ z ( C/ C cannot time interva C ’ ) [188]. C’ the ToF via will be limited by the range, accuracy and precision of their clocks. C’ y are simpler and straightforward to determine the ToF [189]. The time difference between the detection of the two pulses was recorded with a SPC-160 electronic board that makes use of an ADC implementation (TAC-Biased Amplifier-ADC), and the results were presented by the Becker & Hickl GmbH software [190]. Since the system is in reverse measuring mode, one should expect that the measured ToF (𝑇𝑜𝐹 𝑇𝐶𝑆𝑃𝐶) depends on the selected time range and on the total delay of the reference signal in the system [89]. This relation is given by 𝑇𝑜𝐹=(𝑡𝑖𝑚𝑒 𝑟𝑎𝑛𝑔𝑒+𝑡𝑜𝑡𝑎𝑙 𝑑𝑒𝑙𝑎𝑦)−𝑇𝑜𝐹 𝑇𝐶𝑆𝑃𝐶 ⇔ ⇔𝑇𝑜𝐹=(50 ns+𝑡𝑜𝑡𝑎𝑙 𝑑𝑒𝑙𝑎𝑦)−𝑇𝑜𝐹 𝑇𝐶𝑆𝑃𝐶 (45) As referred in the beginning of this chapter, there is an uncharted difference in the reference and emitted light pulses optical path. In addition, due to the use of a delay box, it became quite difficult to forecast the influence of the cable length and of the delay box system itself without the right tools. For those reasons, one should consider all of these delay parameters as one, called total delay. The recommendation is that the total delay introduced in the system is one order of magnitude less than the selected time range [89]. For these reasons, the search for a distance calibration system was solely made by relating the measured ToF, converted into a distance (see section 1.1.2), and comparing it to a reference position (see Figure 62) for measuring all distances. The referred distance was measured by a calibrated “ Range Finder GLM 5 V ” with a precision of 0.1 mm. The current intensity of the laser was adjusted, so that the APD2 measures specular light pulses with the highest intensity possible and compatible with the linear response in the APD2 output signal. The collected data is exhibited in Table 7.
125 Figure 67. Photograph of the three samples that were subjects of the polarization 1D LiDAR study: (a) metallic car paint, and traffic signals (b) without and (c) with retroreflectors. The main reason to choose the referred materials is that their Mueller matrices behaviour is clearly distinguishable (see Figure 49). In addition, the determination of the Mueller matrix is time consuming to be functional in autonomous driving. In contrast, the Stokes vector detection can be instantaneous [149], [152]. To this purpose, it was decided to illuminate the three samples with an HLP light state. The complete Stokes vector of the light beam reflected by the samples was measured at its specular reflection (i.e. SRA = 0°). At this moment, the setup is not able to measure the full Stokes vector simultaneously, so the measurements were taken sequentially in time. Firstly, the Stokes vector from the HLP light reflected by the selected samples were mathematically predicted from the Mueller matrix images previously obtained with our complete Mueller polarimeter. The results from this study are summarized in Table 9.
126 Table 9. Normalized Mueller Matrix images, their respective average normalized Mueller Matrix and calculous of the HLP Stokes vector after interacting with the referred Mueller matrices, for three different materials (metallic car paint, regular traffic signal and retroreflector traffic signal) at a sample rotation of 0° (specular reflection). Material Normalized Mueller Matrix Image Average Normalized Mueller Matrix (𝑴) 𝑺𝒐𝒖𝒕 =𝑴∙(𝟏𝟏𝟎𝟎) Metallic Car Paint (1.0000 −0.027±0.006 −0.030±0.005 0.977±0.005 0.011±0.008 −0.008±0.007 −0.001±0.005 −0.020±0.01 −0.011±0.007 −0.021±0.007 0.009±0.006 −0.010±0.009 −0.980±0.004 −0.01±0.02 0.01±0.01 −0.976±0.006) (1.000±0.006 0.973±0.007 −0.03±0.01 0.00±0.01) Regular Traffic Signal (1.000 −0.033±0.007 −0.028±0.006 0.974±0.007 0.015±0.007 −0.003±0.008 0.006±0.006 −0.03± 0.01 −0.013±0.007 −0.016±0.007 −0.0012±0.007 −0.011±0.009 −0.973±0.006 0.01±0.02 0.02±0.02 −0.971± 0.007) (1.000±0.007 0.978±0.009 −0.030±0.01 −0.01±0.01) Retroreflector Traffic Signal (1.000 −0.1±0.1 0.1±0.1 0.4±0.3 0.11±0.09 −0.1164±0.09 0.00±0.07 −0.0836±0.07 0.10±0.09 −0.04±0.07 0.1±0.1 0.00±0.06 −0.4±0.2 −0.0967±0.1 0.1±0.1 −0.6585±0.1) (1.0±0.1 0.46±0.3 0.1±0.1 0.1±0.1) To generate the HLP state and to measure the Stokes vector from the specular reflection of each sample, the LiDAR proposed in Figure 56 was upgraded. To this end, on one hand, a calibrated linear polarizer (LP1), WP25M-UB [193] from Thorlabs w HL L ’ x . On the other hand, a quarter wave plate (QWP), Thorlabs WPQ05M-1550 [194], and a linear polarizer (LP2),
127 Thorlabs WP25M-UB [193] , were placed at the entrance of the detection system to analyse the six standard polarization states (HLP, VLP, LP+45°, LP-45°, RCP and LCP). The six analysed polarization states were calibrated using the Thorlabs polarimeter [163]. The final experimental implementation can be observed in Figure 66. The light intensities measured from the backscattered light was recorded by using a digital oscilloscope (HDO4034 from Teledyne Lecroy) . To calculate the normalized Stokes vector reflected by the samples, Eq. (13) was used in respect to the maximum intensity. The comparation of the complete Stokes vectors measured experimentally with the calculated ones (from Table 9) is shown in Table 10. Table 10.Comparation of Stokes vector of the specular reflection of HLP light in a metallic car paint, a regular traffic signal and a retroreflector traffic signal. Predicted normalized Stokes vectors calculated from the experimental Mueller matrices measured with our polarimeter are shown in the middle column, and experimentally normalized Stokes vectors measured with our 1D LiDAR are show in the right column. Material Predicted calculated normalized Stokes vector Experimentally measured normalized Stokes vector Metallic Car Paint (1.000±0.006 0.973±0.007 −0.030±0.010 0.000±0.010) (1.0000 0.9841±0.0002 −0.0500±0.0400 −0.0200±0.0900) Regular Traffic Signal (1.000±0.007 0.978±0.009 −0.030±0.010 −0.010±0.010) (1.0000 0.9509±0.0002 0.0200±0.0600 0.0650±0.0070) Retroreflector Traffic Signal (1.00±0.1 0.46±0.3 0.10±0.1 0.10±0.1) (1.0000 0.4180±0.0007 0.0600 ±0.0800 0.0500 ±0.0200) Before analysing Table 10, one must consider that none of the materials is homogenous. On the one hand, the traffic signals are real world samples with some dirt and scratches. On the other hand, although the metallic “ w ” x -flakes that grant it the metallic look. Therefore, one must consider that the data in Table 10 are not from the same exact area, meaning that the obtained differences between Stokes vectors are expected. In addition, the errors observed in Table 10 are due to fluctuations of the intensity of the lasers, small errors in the orientation of
128 the QWPs and LPs, as well as phase variations in the LCVRs, and more importantly, the illuminated area in the two systems is not the same ( w ’ beam size difference and to the fact that the lasers could be pointing at different regions in the sample). Nevertheless, the metallic car paint shows similar results, as it is the most homogeneous sample. However, although the predicted and experimentally measured Stokes vectors present small differences between them, there are significant differences between some materials, such as between the retroreflector traffic signal and the two other samples. Consequently, it is perfectly possible to distinguish a retroreflector traffic signal from a regular traffic signal or a metallic car paint using a horizontal linear polarization state in a Polarization 1D LiDAR. At this point, an extensive study of the generated polarization state, that better distinguishes the majority of the classified materials, is proposed. For this purpose, for future steps of this project, we suggest to characterize polarimetrically a great number of samples, and then, to study the best Stokes vectors to distinguish targets.
129 9. Conclusion The present manuscript summarizes and reports the main work developed the academic year 2019/2020, in the facilities of the School of Sciences of the University of Minho. Multiple worldwide companies are investing in developing a LiDAR system to implement in autonomous driving. LiDARs are active sensors that, by illuminating obstacles and measuring the retro-reflected light, can measure with great precision distances to obstacles in its surrounding, as well as, their shape. These characteristics make LiDARs a promising technology to the autonomous driving market. Light polarization is a physical property that describes the transversal (to the direction of propagation) behaviour of a light wave. Whenever light interacts with matter, the polarization state of light might change. By means of this, a classification of materials through polarization is pursued. In this sense, a LiDAR that can distinguish materials through polarization can enhance the capability of making a more prudent decision in case of obstacle avoidance in autonomous driving. Due to the referred reasons, this project furthers the idea of a LiDAR that can execute polarization measurements. The first chapters are focused on describing the autonomous driving model, and the necessities surrounding sensor fusion. The components and techniques that are, nowadays, used in current LiDARs are also presented, as much as the state-of-the-art of the current developed LiDARs. Then, two different types of Mueller polarimeters setups were built and described to appraise the capabilities of distinguishing between different materials, using a wavelength of 1550 nm. The Mueller polarimeters are distinguished by the method that they use to produce the PSG and PSA states. One of them makes use of linear polarizers and quarter wave plates and the other makes use of linear polarizers and liquid crystal variable retarders. The Mueller polarimeter setups allowed to conclude that by means of light polarization at 1550 nm of wavelength, different materials have different polarimetric responses allowing material discrimination. In this sense, the diagonal elements of the Mueller matrix present more significant differences than the 𝑀03 and 𝑀30 components of the Mueller matrix. The graphical representations in Figure 50, allow clear distinction of materials, even if the sample rotation angle is unknown, and let extrapolate that material discrimination might enhance by using more than three Mueller matrix coefficients. The depolarization, diattenuation and
130 retardance of each sample were also object of this study. Their determination proved to be time consuming, compared to the determination of Mueller matrix. For this reason, we conclude that these parameters do not show satisfactory results for autonomous driving. The last part of this thesis is focused on the design, implementation and characterization of a Polarization 1D LiDAR. Firstly, the one-point LiDAR setup was presented, and a spatial calibration was sought. After that, an accuracy test was made, and afterwards the polarization concept was introduced to the already built setup. Due to the determination of a full Mueller matrix being too time consuming to be implemented in autonomous driving, we choose to only generate a polarization state and determine the full outcome Stokes vector from the light reflected by different targets. To test the Polarization One-Point LiDAR, we choose 3 different samples (metallic car paint, retroreflector traffic signal and regular traffic signal) and a horizontally linearly polarized state to be generated. The measurement was made detecting the specular reflection (sample rotation angle of 0°). The Polarization 1D LiDAR setup allows to conclude that polarization at a 1550nm LiDAR is capable of distinguishing between at least some relevant materials of great importance in autonomous vehicle safety. The polarimetric response of the reflected light add information that does not depend on the reflectance of the targets, but on the materials constitution (note that the analysed Stokes vectors were normalized). The studies reported in this present document allow to infer that polarization used in LiDAR must help a vehicle to make a more trustworthy decision and to avoid possible obstacles with lower time response.
131 10. Future Work The results obtained in this thesis show that to combine polarimetric techniques with distance measurements can enhance the detection of road scene objects in autonomous driving applications. For this reason, future work that aims to improve the obtained results is proposed, in order to continue this project. For future work, it is vital to increase the number of measured samples to enhance the plausibility of the present conclusions. The study should be kept by analysing the Mueller matrix of a great number of samples, and then, to determine the most adequate polarization state of emission that will cause a more distinguishable polarimetric response in the detection. Furthermore, it could be interesting to study real-w “ oratory” y can introduce relevant information to identify material classes. Note that there are various road scene objects that can not be measured in our laboratory (such as walls or crosswalks). Moreover, after assembling an extensive data basis of different materials, a machine learning algorithm could and should be implemented to allow a quick material determination. In addition, it can be studied if it is necessary to know the sample rotation to distinguish road scene objects. Also, it is important to continue working on the present Polarization 1D LiDAR, by upgrading it into a 3D Polarization LiDAR by means of controlling the MEMS mirror already implemented in the setup.
132 Bibliography [1] w “C w - W ” worldometers . [Online]. Available: https://www.worldometers.info/cars/. [Accessed: 07-Nov-2019]. [2] . “ w ” Commun. ACM , vol. 53, no. 4, pp. 99–106, 2010, doi: 10.1145/1721654.1721679. [3] . “ ” Destastis . [Online]. Available: https://www.destatis.de/EN/Themes/Society-Environment/Traffic-Accidents/_node.html. [Accessed: 11-Nov-2019]. [4] WHO “C ” WHO . [Online]. Available: https://www.who.int/sustainabledevelopment/transport/health-risks/climate-impacts/en/. [Accessed: 11-Nov-2019]. [5] “WHO C ” WHO , 2016. [6] . k j “ ’ ” Texas Instruments , pp. 1–7, 2017. [7] . K. . z . Z w jk “ k : literature review and ” Transp. Res. Part B Methodol. , vol. 107, pp. 212–228, Jan. 2018, doi: 10.1016/j.trb.2017.10.016. [8] . w . z . K K. . K “ y w rs ” Int. J. Syst. Assur. Eng. Manag. , 2020, doi: 10.1007/s13198-020-00961-4. [9] . G “ C : O z Transportation Plans, and Au V ” J. Plan. Educ. Res. , vol. 36, no. 2, pp. 210–224, 2015, doi: 10.1177/0739456X15613591. [10] K G “ V x Q k ” KPMG Int. , 2019. [11] M. Maurer, J. C. Gerdes, B. Lenz, and H. Winner, Autonomous driving: Technical, legal and social aspects . Springer Berlin Heidelberg, 2016. [12] j Z “ y: C y ” Business Insider , 2014. [Online]. Available: https://www.businessinsider.com/morgan-stanley-autonomouscars-trillion-dollars-2014-9?IR=T. [Accessed: 11-Nov-2019]. [13] . K . . V H . V z “H w V C y? C C C ” Urban Policy Res. , vol. 37, no. 4, pp. 442–457, 2019, doi: 10.1080/08111146.2019.1674646. [14] D. Feng, L. . K. y “L uncertainties for robust realL 3 j ” IEEE Intelligent Vehicles Symposium, Proceedings , 2019, vol. 2019-June, pp. 1280–1287, doi: 10.1109/IVS.2019.8814046. [15] G V w “ k z W $67 ” Grand View Research , 2018. [Online]. Available: https://www.grandviewresearch.com/press-release/global-advanced-driver-assistancesystems-adas-market. [Accessed: 11-Nov-2019].
133 [16] BMW Group, “ O O H W G O .” [O ]. : https://www.bmwgroup.com/en/NEXTGen/automated_driving.html. [Accessed: 22-Jul-2020]. [17] V “ x V C ” Volvo Cars , 2016. [Online]. Available: https://www.volvocars.com/en-kw/own/own-and-enjoy/autonomous-driving. [Accessed: 22-Jul2020]. [18] G . “ & : G .” [O ]. : https://www.groupe-psa.com/en/story/en-route-vers-la-voiture-autonome/. [Accessed: 22-Jul2020]. [19] SAE International, Surface Vehicle Information Report - Alternative Automotive Fuels . 2017. [20] “ V ” SAE Int. , p. 30, 2016. [21] “ J3016 automated- ” SAE International , 2019. [Online]. Available: https://www.sae.org/news/2019/01/sae-updates-j3016-automated-driving-graphic. [Accessed: 11Nov-2019]. [22] “ x L ” Www.Sae.Org/Autodrive , 2014, doi: P141661. [23] “ y ” Bosch Mobility Solutions , 2019. [Online]. Available: https://www.boschmobility-solutions.com/en/highlights/automated-mobility/. [Accessed: 11-Nov-2019]. [24] . “ H w f- ? ” Forbes , 2019. [Online]. Available: https://www.forbes.com/sites/greatspeculations/2019/11/08/just-how-far-ahead-is-tesla-in-selfdriving/#224f5d481b24. [Accessed: 13-Nov-2019]. [25] . O “Hy y k K ” Traffic Technology Today , 2019. [Online]. Available: https://www.traffictechnologytoday.com/news/autonomous-vehicles/hyundai-successfullydemonstrates-autonomous-truck-platooning-in-korea.html. [Accessed: 13-Nov-2019]. [26] J. Hughes “C y L x - ” TheDrive , 2017. [Online]. Available: https://www.thedrive.com/sheetmetal/15724/what-are-these-levels-of-autonomy-anyway. [Accessed: 13-Nov-2019]. [27] . W k “ -Driving Car Timeline – Predictions from the Top 11 Global Automakers | Emerj - ” Emerj , 2019. [Online]. Available: https://emerj.com/ai-adoption-timelines/self-driving-car-timeline-themselves-top-11-automakers/. [Accessed: 13-Nov-2019]. [28] K. Burk “H w - C ? ” NVIDIA Blog , 2019. [Online]. Available: https://blogs.nvidia.com/blog/2019/04/15/how-does-a-self-driving-car-see/. [Accessed: 15-Nov2019]. [29] L. A. Klein, Sensor and data fusion: A tool for information assessment and decision making: Second edition , Second Edi. Spie, 2012. [30] . wk “ V L ” Level Five Supplies , 2019. [Online]. Available: https://levelfivesupplies.com/sensors-used-in-autonomous-vehicles/. [Accessed: 15-Nov-2019].
134 [31] . wk “ V L ” Level Five Supplies , 2019. [Online]. Available: https://levelfivesupplies.com/sensors-used-in-autonomous-vehicles/. [Accessed: 18-Nov-2019]. [32] H. K. He G. . k “O ” Proc. - IEEE Int. Conf. Robot. Autom. , pp. 731–736, 2011, doi: 10.1109/ICRA.2011.5980509. [33] . . “W W k y V y? ” Viviota , 2018. [Online]. Available: https://blog.viviota.com/what-will-it-take-for-fully-autonomous-vehicles-to-becomea-reality. [Accessed: 19-Feb-2020]. [34] . k . . “ ” Analog Devices . [Online]. Available: https://www.analog.com/en/technical-articles/autonomous-industrialrevolution.html?gclid=EAIaIQobChMIsNeq5tfz5QIVBLDtCh2VdgLKEAAYASAAEgI7GvD_BwE#&as_qdr =y15. [Accessed: 18-Nov-2019]. [35] “C O j ” . –10, 2017. [36] K. k “H w - C ? ” nvidia , 2019. [Online]. Available: https://blogs.nvidia.com/blog/2019/04/15/how-does-a-self-driving-car-see/. [Accessed: 18-Nov2019]. [37] . Y . L . C K. k “ y : C ” arXiv Cornell Univ. , 2019. [38] M. Hansard, S. Lee, O. Choi, and R. Horaud, Time of Flight Cameras : Principles , Methods , and Applications . 2012. [39] G. V. . k . . K “ y ” Advanced Microsystems for Automotive Applications 2003 , Springer Berlin Heidelberg, 2007, pp. 215–221. [40] H. H. “ radar - y ” 8th European Conference on Antennas and Propagation, EuCAP 2014 , 2014, pp. 3107–3114, doi: 10.1109/EuCAP.2014.6902486. [41] C “ y ’ ” European Commission . [Online]. Available: https://ec.europa.eu/digital-single-market/en/node/329. [Accessed: 23-Jul-2020]. [42] . K . V. “ V ” 2018 26th Telecommunications Forum, TELFOR 2018 - Proceedings , 2018, doi: 10.1109/TELFOR.2018.8612054. [43] G. . . w “ ” Sensors (Switzerland) , vol. 15, no. 6, pp. 14661–14678, Jun. 2015, doi: 10.3390/s150614661. [44] L. z “ : C - ” Electronic Design , 2018. [Online]. Available: https://www.electronicdesign.com/industrial-automation/ultrasonicsensors-smart-choice-shorter-range-applications. [Accessed: 18-Nov-2019].
141 [157] . . . C “ y ” Handbook of Optical Metrology: Principles and Applications , Second., 2015, pp. 627–675. [158] . L z . é z . C. z . . C “ performance of an ink x y ” Appl. Opt. , vol. 54, no. 29, p. 8758, Oct. 2015, doi: 10.1364/ao.54.008758. [159] K. . w y . . C “O z x ” Opt. Express , vol. 16, no. 15, p. 11589, 2008, doi: 10.1364/oe.16.011589. [160] N. C. Bruce, J. M. López-Téllez, O. Rodríguez-Núñez, and O. G. Rodríguez-H “ experimental errors for optimized variable-retarder Muellerx ” Opt. Express , vol. 26, no. 11, p. 13693, 2018, doi: 10.1364/oe.26.013693. [161] G. H. Golub and C. F. Van Loan, Matrix Computation , Fourth. JHU Press, 2013. [162] R. A. Horn and C. R. Johnson, Matrix Analysis , Second. 2012. [163] “ .” [O ]. : ://www. . /. [ : 3-Jun-2020]. [164] . V. . W j w “C z roducing maximum polarized light y ” AIP Conference Proceedings , 2016, doi: 10.1063/1.4943751. [165] V “ C ” Allied Vision . [Online]. Available: https://www.alliedvision.com/en/digital-industrial-camera-solutions.html. [Accessed: 07-Aug-2020]. [166] K w “K w V CC V.” [O ]. : https://www.kowa-lenses.com/en/. [Accessed: 21-Jul-2020]. [167] . . . . . . C “ z n of diffusely reflecting man-made j ” Appl. Opt. , vol. 44, no. 26, pp. 5434–5445, Sep. 2005, doi: 10.1364/AO.44.005434. [168] . O “ w k O .” [O ]. : ://www. w k. /. [ : 03-Jun-2020]. [169] L. C. “L q C y V ” Meadowlark Opt. [170] A. De Martino, Y.-K. Kim, E. Garcia-C . L . é “O z w q y ” Opt. Lett. , vol. 28, no. 8, p. 616, Apr. 2003, doi: 10.1364/ol.28.000616. [171] . . y “ : x z -to-noise ratio and minimization of y ” Appl. Opt. , vol. 41, no. 4, pp. 619–630, 2002, doi: 10.1364/AO.41.000619. [172] V y “V y L ” Http://Velodynelidar.Com/ , p. 2800, 2013. [173] L “L .” [O ]. : :// . /. [ : -Aug-2020]. [174] Q y “Q y – L .” [O ]. : https://quanergy.com/. [Accessed: 01-Aug-2020]. [175] V “V - y ” Valeo . [Online]. Available: https://www.valeo.com/en/. [Accessed: 01-Aug-2020]. [176] O “H -resolution digital lidar: autonomous vehicles, rob .” [O ]. : https://ouster.com/. [Accessed: 01-Aug-2020].
142 [177] . H z . W z “ j - ” Comput. Aided. Des. Appl. , vol. 15, no. 4, pp. 501–508, Jan. 2018, doi: 10.1080/16864360.2017.1419638. [178] K. C y “K y y y .” [O ]. : https://www.keopsys.com/. [Accessed: 17-Jun-2020]. [179] . y “H y y ” Menlo Systems . [Online]. Available: https://www.menlosystems.com/products/photodetectors/apd310/. [Accessed: 17-Jun2020]. [180] “ - F240APC-1550 1550 nm, f = 8.18 mm, NA = 0.49 FC/APC Fiber Collimation k .” [O ]. : ps://www.thorlabs.com/thorproduct.cfm?partnumber=F240APC-1550. [Accessed: 30-Jun-2020]. [181] “ -BK7 Plano-Convex Lenses (AR Coating: 650 - 5 ).” [O ]. : https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6278. [Accessed: 25-Jun-2020]. [182] C “ C-55 : : L : .” [O ]. : https://computar.com/product/561/TEC-55. [Accessed: 25-Jun-2020]. [183] . L C y “ y L C y O yz .” [O ne]. Available: https://teledynelecroy.com/. [Accessed: 30-Jun-2020]. [184] A. S. Huntington, InGaAs Avalanche Photodiodes for Ranging and Lidar . 2020. [185] Jorge Leite Martins de Carvalho, Sistemas de controle automático . Livros Téc. e Cient. Editora, 2020. [186] . & H. G H “ k & H k G H.” [O ]. : ://www. k -hickl.com/. [Accessed: 27-Jun-2020]. [187] k & H k G H “ -PPI-D - k & H k G H.” [O ]. : https://www.beckerhickl.com/products/a-ppi-d/. [Accessed: 30-Jun-2020]. [188] . “W C C? ” 3. [189] . j “ -ofy.” . [190] . & H. G H. “ C C k - k & H k G H ” Becker & Hickl GmbH . [Online]. Available: https://www.becker-hickl.com/products/tcspc-package/#product-download. [Accessed: 03-Jul-2020]. [191] “ O 57 5-1:1994(en), Accuracy (trueness and precision) of measurement methods and results — Part 1: General principles and definit ” International Organization for Standardization , 1994. [Online]. Available: https://www.iso.org/obp/ui/#iso:std:iso:5725:-1:ed-1:v1:en. [Accessed: 06-Jul2020]. [192] . “ y ” All Sensors , pp. 1–5. [193] “ - WP25MØ 5. W G z 5 4 µ ” 7. [Online]. Available: https://www.thorlabs.com/thorproduct.cfm?partnumber=WP25M-UB. [Accessed: 11-Jul-2020].
143 [194] “ - WPQ05M-1550 Ø1/2" Zero-Order Quarter-W Ø " 55 .” [Online]. Available: https://www.thorlabs.com/thorproduct.cfm?partnumber=WPQ05M-1550. [Accessed: 11-Jul-2020].
144 Annex A Table 11. Normalized Evaluation of the 1D Lidar precision as a function of the distance range (Range (m)). Experimental Results Distributions and their best Gaussian fits. 𝑹𝒂𝒏𝒈𝒆 (𝐦) 𝐄𝐱𝐩𝐞𝐫𝐢𝐦𝐞𝐧𝐭𝐚𝐥 𝐑𝐞𝐬𝐮𝐥𝐭 𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐚𝐧𝐝 𝐢𝐭𝐬 𝐛𝐞𝐬𝐭 𝐆𝐚𝐮𝐬𝐬𝐢𝐚𝐧 𝐟𝐢𝐭 𝑹𝒂𝒏𝒈𝒆 (𝐦) 𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 𝑹𝒆𝒔𝒖𝒍𝒕 𝑫𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒂𝒏𝒅 𝒊𝒕𝒔 𝒃𝒆𝒔𝒕 𝑮𝒂𝒖𝒔𝒔𝒊𝒂𝒏 𝒇𝒊𝒕 0.4999 29.92 0.7498 38.96
145 1.500 44.99 3.749 59.84
146 7.498 74.98 11.98 90.11
147 14.96 103.5 22.49