Laser excited super resolution thermal imaging for nondestructive inspection of internal defects [original]

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Laser excited super resolution

thermal imaging for nondestructive

inspection of internal defects

Samim Ahmadi1*, Julien Lecompagnon1, Philipp Daniel Hirsch1, Peter Burgholzer2,

Peter Jung3, Giuseppe Caire3 & Mathias Ziegler1

A photothermal super resolution technique is proposed for an improved inspection of internal defects.

To evaluate the potential of the laser-based thermographic technique, an additively manufactured

stainless steel specimen with closely spaced internal cavities is used. Four different experimental

configurations in transmission, reflection, stepwise and continuous scanning are investigated. The

applied image post-processing method is based on compressed sensing and makes use of the block

sparsity from multiple measurement events. This concerted approach of experimental measurement

strategy and numerical optimization enables the resolution of internal defects and outperforms

conventional thermographic inspection techniques.

The nondestructive testing (NDT) of internal defects such as blowholes, inclusions or delaminations is of huge

interest in industry. There are several ways to detect internal defects without destroying the specimen such as

ultrasonic testing (UT) or radiographic testing (RT). UT is typically not contact-free and suffers from reconstruc-

tion accuracy if defects are not oriented perpendicular to the coupled ultrasound. In contrast, RT methods like

computed tomography provide reliable and accurate results1 and are contact-free, but end up to be costly, slow,

complex and only suitable ex-situ. Unlike UT and RT, active thermographic testing (TT) represents a contact-

less, simple, less expensive and in-situ suitable alternative by measuring the infrared (IR) radiation intensity of

the specimen with IR cameras2.

In active TT, light sources such as lasers can be used to generate heat in the specimen3,4. Compared to other

light sources such as flash lamps, halogen lamps or LED, lasers do not exhibit spectral overlap with the IR camera5

and can be tightly focused which helps to realize structured illumination (SI). Beside light sources, other energy

sources, e.g. induction coils and ultrasonic transducers are possible as well for thermal NDT6.

The diffuse nature of heat propagation in the material causes a degradation in spatial resolution and therefore

also in reconstruction accuracy7. To solve this problem, various measurement and thermal image processing

strategies were applied such as pulsed-phase thermography8 or lock-in thermography9, making use of the rela-

tive amplitude or phase change to a reference area. A relatively new method to circumvent spatial heat blurring

is the introduction of virtual waves, which increases the signal-to-noise ratio (SNR) in the measured thermal

images by transforming diffuse thermal waves into virtual propagating waves10–12.

Apart from that, so-called optical super resolution (SR) imaging—serving as an alternative measurement

strategy to enhance the spatial resolution—gained attention in fields of structured illumination microscopy13,14.

These SR techniques rely on multiple measurements with a small position shift. The result is a spatial frequency

mixing of the illuminated target pattern and the illumination pattern enabling an improvement in spatial resolu-

tion. While these optical SR techniques aim to enhance the optical diffraction limit of the imaging system, geo-

metrical SR techniques aim to enhance the resolution of the digital imaging sensors. While the latter approach

is known15,16 and already implemented in commercial IR camera systems, a method to overcome the diffusion

limit of TT by means of an optical SR analogue was out of reach so far.

Compressed sensing (CS) based algorithms can be used in post-processing which benefit from multiple

measurements all referring to a reconstruction result that is sparse17. Since defects are sparse in space and CS

algorithms rely on reconstructing a sparse data set from given measurements, CS is highly attractive and appli-

cable in NDT scenarios as well. Thus, CS based algorithms based on sparsity regularization with

ℓ1

-minimization

or Orthogonal Matching Pursuit (OMP) have been successfully employed to thermographic data improving

the thermal image quality18,19. However, the application of a simple

ℓ1

-minimization or OMP would not benefit

OPEN

1Bundesanstalt für Materialforschung und -prüfung (BAM), 12200 Berlin, Germany. 2Research Center for Non

Destructive Testing, 4040 Linz, Austria. 3TU Berlin, Communications and Information Theory, 10587 Berlin,

Germany. *email: [email protected]

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from multiple measurements as generated by the proposed SI experiments. In contrast, Block CS would be more

suitable20 so that algorithms such as Block-FISTA21 or Block-OMP22 could profit from many measurements

exhibiting a so-called joint or block sparsity domain.

Novel photothermal SR approaches combine the SI measurement strategy and CS based processing algo-

rithms, such as the iterative joint sparsity algorithm (IJOSP) to better separate two closely spaced defects7,23–25.

So far, the suitability of these techniques has been investigated in transmission configuration with anomalies on

the backside of the specimen. This paper focuses on the applicability of laser excited super resolution thermal

imaging to an additively manufactured stainless steel sample with internal defects as test specimen.

The major contributions of this paper are listed as follows.

• Different SI experiments (laser step and continuous scan in reflection and transmission configuration) are

shown to create suitable data to perform SR and to resolve all internal defects (so far in literature: SR suitable

experiments only in transmission configuration examining sample surface anomalies).

• The thermal image processing and the application of the model-based IJOSP algorithm is described in

details and adopted for the investigation of a specimen with internal defects in transmission and reflection

configuration (so far in literature: photothermal SR image processing description only available based on

transmission setups analyzing sample surface anomalies).

• The SR reconstruction results are compared qualitatively as well as quantitatively with conventional laser

thermography reconstruction results based on homogeneous illumination. The comparison shows that the

proposed SR techniques outperform conventional photothermal techniques resolving internal defects in steel

with an at least four times better spatial resolution.

• It is discussed which of the proposed SR techniques—based on different experimental setups—exhibits the

most promising results in improving the spatial resolution for TT of metals with internal defects.

Methods

Experimental setup. In the following we focus on the measured data obtained by using the transmis-

sion and reflection setup shown in Fig.1a,b, both performed in step scan and continuous scan measurements,

respectively. An exemplary experimental thermographic setup is shown as a photograph in Fig.2 which would

correspond to the shown configuration in Fig.1a.

As shown in our previous work25, step scan means that we use laser pulses (

tpulse

=500ms) to heat up the sam-

ple, wait until the sample is cooled down (

tcooling

=20s), shift the position slightly with a distance of

r

=0.2mm

and repeat for around 250 individual measurements. In all our measurements we have used a fiber-coupled

high-power diode laser with a maximum output power of 530W, a linear shaped spot (

0.4 mm ×17

mm) and a

wavelength of

940 ±10

nm. Furthermore, we have used a mid-wave IR camera (Infratec IR9300,

fcam

=100Hz,

full frame:

1280 ×1024

pixel, sensitive in 3–5

m wavelength range, NETD—noise equivalent temperature

difference of

∼30

mK) which was triggered by a photodiode that recognizes when the laser is switched on.

We have measured around 1000 frames from the beginning of the pulse for each measurement with a pixel

resolution of

rcam =54



m/pixel. This leads to a huge amount of data. In contrast, the continuous scanning

method provides a smaller measured data set, since the specimen is scanned continuously while the IR camera

is measuring without any intermediate cooling process. Thus, the size of the measured data is controlled by the

chosen scanning velocity. The power of the laser has been adjusted in each measurement configuration so that

we reach temperature differences of around

T

=3–5K for an assumed emissivity of

ǫ=1

(since only relative

changes in temperature are of interest, this parameter was not considered critical).

Mathematical model for super resolution laser thermography. Without restricting the general-

ity of our approach, we simplify the 3dim problem to a 2dim one by using a set of linear defects and a lin-

ear laser. We calculate the mean over the vertically arranged pixels (see dimension y in Fig.1) and end up

with a problem formulation in the r–z-domain. In addition, the mean over 315 pixels provides a better SNR of

�T/NETD ·√315 ≈4K/30 mK ·18 =2400

(a)(b)

Figure1. The IR camera and the specimen were placed for both configurations on a linear table so that

both components are moved with a certain velocity

vscan

. (a) Transmission configuration: the additively

manufactured stainless steel specimen (sandblasted from both sides to increase the emissivity) is shown with

details inside. (b) Schematic of the setup in reflection configuration. The specimen with eight cavities and

different distances is shown (a=0.5mm, b=40mm, c=4.5mm, d=7mm). The arrows in (a, b) represent the

direction of the motion.

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To describe the measured temperature difference values

Tmeas =T

, we make use of a Green’s function with

rectangular coordinates as a solution for the heat diffusion equation for a line source and a plate with a finite

thickness. In our previous studies24,25, we investigated steel samples which have been blackened on the front side

so that the measured temperature from the backside could be described for each measurement i=

1...Nmeas

whereby



represents the heat diffusion followed from illumination and

xi=Ii◦a

represents the element-wise

(Hadamard) product of the illumination

and absorption pattern a which represents the defects in space7,24,25.

In contrast to our previous model, there is no analytical solution for the case of internal defects to be investigated

now, i.e. the



required now is unknown. Since we are not interested in an exact reconstruction of the internal

geometry, but only in the best possible separation of closely adjacent internal defects, we can continue to use this

approach as an approximation. This means, we pretend to have an exactly describable sample without defects by



and allow the internal defects sparsely distributed in the r–z-domain to lead to a sparsely distributed contrast

in the result

Tmeas

, which we interpret as defect position in the r-domain. Thus,



can be described by25,26

for step scanning

step =

, whereby we set z=0 for reflection and z=L for transmission configuration, r stands

for the position of the horizontally arranged pixels and t stands for the time. Thus, Eq. (2) describes a thermal

point spread function that considers the convolution with the laser pulse length in step scanning by

(convolu-

tion in time with the variable t). For continuous scanning

cont

we have to substitute

:=1 since the laser is

switched on continuously, r:=

r−v·t

due to motion consideration and to add an integral over the previous

time stamps25,27 instead of having an integral due to the pulse length consideration as shown in Eq. (2).

stands

for the mass density,

for the specific heat,

for the thermal diffusivity, R for the thermal reflectance from the

material to air, and L for the thickness of the specimen. We have identified the following values for the material

parameters of our investigated additively manufactured stainless steel 316L 1.4404 sample:

=

4×10−6

m

/s,

=7990kg/m

=500J/kg/K and R=1. Indeed, R=1 was chosen for the sake of simplicity, but it is a very good

approximation since R actually should be around 0.95. It should be noted that the lal-tetrahydropalmatineser

line width is not taken into account in



, which means that this quantity has to be considered in x25.

Figure3 shows

step

and

cont

in reflection and transmission configuration, respectively. To reduce the huge

amount of data generated by performing step scanning measurements, we applied the maximum thermogram

(MT) method24 to the step scanning data which eliminates the time dimension from

Tmeas,step ∈

×N

×Nmeas

selecting the time stamp

t=tMT

where the maximum temperature amplitude is reached (c.f. Fig.4). Effectively,

this leads to

Tstep ∈

×Nmeas

and a vertical section through

�step := �step(r,z=0|L,t=tMT)

in Fig.3a,b),

represented by the dashed vertical lines. Consequently, we reformulate Eq. (1) and describe the measured data

for step and continuous scanning by the following two equations:

(1)

meas =



∗r,txi,

(2)

�(

r,z,t)=2

4π αρcp

It(t−˜

t)e−r2

4α˜

t·

∞



n=−∞

R2(n−1)e−(2nL+z)2

4α˜

Figure2. Exemplary transmission configuration for laser excited super resolution thermography from our

laser laboratory at BAM: (a) IR camera, (b) dichroic mirror (used to protect the IR camera from laser beam

fractions), (c) investigated stainless steel specimen shown in Fig.1, (d) high-power fiber-coupled laser. (a–c) are

mounted on a linear stage using an optical breadboard. The position of the linear stage is shifted by a motion

controller in submillimeter range which is necessary for optical super resolution.

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These are sets of 1dim problems in the r-domain. Since we are measuring the data, we have to describe the

measured data by discrete values

step/cont[

step/cont

�rcam

)

with

k=1...Nr

. It should be noted that

the measured continuous scanning data indeed considers the time, but here we interpret each time stamp as a

measurement i.

Inspection of internal defects using IJOSP. The iterative joint sparsity (IJOSP) approach promotes

joint sparse solutions and is particularly of interest if blind illumination is used21,28. In this work, the data is

treated as if we had measured blindly, since we consider the position of the illumination in x and not in



. This

is a worst-case scenario, which is of practical nature, because we do not always know the exact position of the

illumination. Therefore, the IJOSP approach empirically enables us to find a solution

ˆx≈x

and to describe the

defect pattern in space considering the following minimization problem:

(3)

step

[

]=

step

∗

step

[

]

cont

[

]=

i

cont

∗

cont

[

(4)

min



i=1



k=1





i∗ˆxi



[k]−Ti[k]



2+1�ˆx�2,1 +2

2�ˆx�2

Figure3. Diagrams of



for (a) step scanning, reflection configuration, (b) step scanning, transmission

configuration, (c) continuous scanning, reflection configuration, (d) continuous scanning, transmission

configuration [

vscan

=1mm/s in (c, d)]. Dashed vertical lines indicate the position of the maximum

thermograms used for time dimension reduction.

Figure4. Flow chart depicting the data analysis procedure discussed in this work. The chart is split in two

halves by a dashed line: the bottom half describes the necessary steps for continuous scanning data, while the

top half shows the steps for data generated by step scanning. The direction of data flow is from left to right. The

inspection of intermediate results is marked by empty circles. Tx= Transmission,

step := [T1

step

,...,T

meas

step ]

�cont

:= [�1

cont

,...,�

cont]

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for step scanning (

i=

step,T

step,

i=ˆ

IJOSP, step

meas

) and continuous scanning

(

i=



cont

i=ˆ

IJOSP, cont

), respectively.

1

and

2

are controlling the regularizers, more

precisely, the impact of block sparsity

�ˆ

�

2,1

=

k=1

i=1

ˆ

[

]



and Tikhonov regularization

�ˆx�2

To find a good solution with

ˆx≈x

, there are several ways to solve the minimization problem in Eq. (4). In

this work we have used the optimization algorithm Block-FISTA (does not make use of Tikhonov regulariza-

tion) and Block-Elastic-Net method25,29,30. Both optimization methods use an updating step size related factor

within the gradient descent implementation which is richly described in literature as the Lipschitz constant

for the gradient of the least squares error term shown in Eq. (4). The number of updates is described by the

number of iterations

Niter

Quantitative evaluation of the final reconstruction result. The final reconstruction result

ˆx1D

shown in the flow chart in Fig.4 is calculated by the sum over all measurements of

ˆx

. Since SR experiments are

performed with multiple measurements and small position shifts resulting in overlaps between the measure-

ments, the normalized sum of all illuminations

over the number of measurements equals an one-array over all

pixels. This means that the sum over all measurements of

ˆx

would approximately equal to a. In the following we

work with

arec =ˆx1D

max ˆx1D=iˆxi

max iˆxi

as final result to quantitatively evaluate and compare

with the originally manufactured a of the specimen.

For quantitative nondestructive evaluation (QNDE), the following metrics are used:

δT

and

δr

. Fig.5 explains

these metrics.

Thus,

δT

represents the contrast between defective and non-defective area investigating one specific defect

pair. Further,

δr

denotes the distance between one peak in

arec

to the real defect position in a referring to the full

width half maximum (FWHM). Moreover,

δT1/2∈[0, δT1/2, max

] with

δT1/2, max =1

due to the implemented

normalization and

δr1/2/3/4∈[0, δr1/2/3/4, max

]. Assuming that

rA1

and

rA2

limit the investigated area according to

Fig.5, the maximum values can be calculated by:

δr1, max =rA2−rD1

δr2, max =rA2−rD2

δr3, max =rD3−rA1

and

δr4, max =rD4−rA1

. The reconstruction accuracies (ra) for

δT

and

δr

can then be given by:

The overall reconstruction accuracy for an area A covering one defect pair is further determined by:

raA=0.5 ·(raδT+raδr)

Results and discussion

Figure4 shows the processing steps from the raw data averaged along y to the final 1dim reconstruction results

of the investigated internal defects shown in Fig.6. To obtain these final results (red curves), we have used the

parameters listed in Table1.

Analyzing Fig.6 clearly shows that we are able to resolve all internal defects in reflection and transmission

configuration for the additively manufactured stainless steel specimen. Especially in the step scanning reflection

case (see Fig.6a) we obtain outstanding results being able to reconstruct each internal defect almost perfectly.

Even with continuous scanning (Fig.6c,d) we are able to resolve the internal defects, but not as accurate as in

step scanning. Here, the most prominent peaks indicate the correct positions of the investigated internal defects,

but sometimes some minor peaks occur as small artifacts as well. But of course we also have to take into account

that we have to measure two to three orders of magnitude longer for the step scan (c.f. Table1). Furthermore, it

is noticeable that the red result curves in diagrams (a,b) exhibit broader peaks than the narrow peaks in (c,d).

This comes from the fact that in (a,b) we have used the Block-Elastic-Net optimization within IJOSP approach

that makes use of the Tikhonov regularization (

2>0

, c.f. Table1) which smoothens the signal in the spatial

sparsity domain, whereas the Block-FISTA (

2=0

) algorithm is used in (c,d).

(5)

δT

(δT1

δT2), raδr

4

δr1, max

−

δr1

r1, max

δr2, max

−

δr2

r2, max

δr3, max

−

δr3

r3, max

δr4, max

−

δr4

r4, max .

Figure5. Explanation of metrics for QNDE:

δT

and

δr

. The red curve illustrates an exemplary

arec

and the grey

defect pattern shows the corresponding exemplary a.

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The results can be further examined quantitatively by using the reconstruction accuracy as defined in the Eq.

(5). Table2 shows all calculated values based on the resolution accuracy given by the specification of the used IR

camera in terms of spatial resolution

rcam =54 µ

m and temperature resolution

Tcam =25

mK.

Table2 confirms the above mentioned statements based on the qualitative analysis. In addition, it can be seen

that the use of SR results in reconstruction accuracies of over 90% whereas conventional methods fail completely

(see

raA3

and

raA4

). Even the reconstruction based on continuous scanning data, that is of particular interest for

industrial applications, exhibits reconstruction accuracies of around 70–80%. Consequently, the quantitative

analysis shows that very high reconstruction accuracies (

>90%

) can be achieved with the proposed method

only for laser step scan measurements. If an exact reconstruction is not necessary, but only defects should be

detected, the continuous scanning could be sufficient as data basis, which has the advantage that these data can

be generated much faster than with the step scan.

Table 1. Chosen experimental and processing parameters to obtain the IJOSP results (red curves) in Fig.6.

Parameters (a) (b) (c) (d)

Position shift

r

(mm) 0.2 0.2 – –

tpulse

(ms) 500 500 – –

vscan

(mmps) – – 1 50

Measurement duration (min) 30 30 1 1/30

Lipschitz const.

(a.u.) 1.41 4.24 7.07 4.95

1

(a.u.) 2.38 20 50 14

2

(a.u.) 0.05 0.0005 0 0

Niter

(a.u.) 500 500 500 2500

Computation time (s) 41.67 57.06 132.23 18.8

Figure6. Normalized IJOSP results: (a) step scanning + refl.; (b) step scanning + trans.; (c) continuous

scanning + refl.; (d) continuous scanning + trans. The diagrams in (a, b) show additionally the conventional

result obtained by simply applying the maximum thermogram method to the raw data of a measurement where

the whole sample surface is illuminated—here we illuminated the whole sample surface with a laser square

60 ×60 mm2

tpulse =2

s.

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Conclusion and outlook

In this study we could show that we are able to resolve closely spaced internal defects inside an additively manu-

factured stainless steel specimen. We obtained accurate results in 1D reconstruction outperforming conventional

thermographic methods realized by homogeneous illumination of the whole sample surface. The resulting dia-

grams after applying IJOSP show an at least four times better spatial resolution since we could easily separate

defects with a defect depth to defect distance ratio up to 4:1 instead of 1:1 in conventional thermographic inspec-

tion techniques. The best results have been obtained in step scan reflection mode but the very fast continuous

scanning mode does lead to convincing results as well. To obtain these outstanding results, we have used standard

measurement technology, as found in many thermography laboratories, but upgraded with a SR measurement

strategy and a CS-based post-processing. Thus, these studies encourage the use of SR laser thermography in metal

industry for an accurate inspection of e.g. production samples with blowholes or other inclusions.

However, the regularization parameters within the IJOSP approach have been chosen manually. Therefore, as

an outlook, we are working on a deep neural network approach to figure out the optimal regularization parameter

based on simulated and/or experimental training data.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable

request.

Received: 10 June 2020; Accepted: 17 November 2020

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Table 2. Calculated reconstruction accuracies

ra ∈[0, 1]

with

ra =0.25 ·(raA1+raA2+raA3+raA4)

for each

shown result in Fig.6, A1 indicates the area of the defect pair with the largest distance to each other and A4

the defect pair area with the shortest distance to each other. Table cells with a dash inside mean that it was not

possible to identify two defects. The defect geometries in the last column are speciefied by the distance between

two defects within a defect pair, the width of one defect (all defects have the same width) and the depth of the

defects (all defects have the same depth). A graphical visualization of the investigated defect geometries is shown

in Fig.1b).

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Acknowledgements

The work of P. Burgholzer was supported by the Austrian Science Fund (FWF), projects P 30747-N32 and P

33019-N.

Author contributions

S.A., P.B. and M.Z. conceived the idea of super resolution laser thermography; S.A., P.B., P.J. and G.C. contributed

to the compressed sensing based signal processing; S.A., P.D.H. and M.Z. designed the specimen; S.A. and J.L.

conducted the experiments; S.A. wrote the manuscript with support from M.Z.; P.D.H. and J.L. contributed to

the preparation of Figs.1, 2 and 4. All authors reviewed the manuscript.

Funding

Open Access funding enabled and organized by Projekt DEAL.

Competing interests:

The authors declare no competing interests.

Additional information

Correspondence and requests for materials should be addressed to S.A.

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