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Abstract
A system and method for non-destructive detection of cracks of different width and depths based on digital speckle interferometry coupled with pulsed laser excitation is introduced and tested. Based on photoacoustic effect, acoustic waves are induced onto the rear of the samples by pumping a pulsed laser beam on it. The generated mechanical wave propagates from the rear surface of the sample to the front while front surface is monitored by speckle interferometry. In order to acquire information about surface deformation, the front surface is illuminated by continuous wave laser and interference are imaged onto the camera as speckle images. After processing the produced fringe patterns, it indicates the presence and location of the cracks in qualitative way. In this study, the system and method mentioned above are validated by detecting medium density fiberboard with simulated cracks. The fringe patterns from areas with or without defects are compared and discussed. Besides, the system and method to distinguish and predict cracks sizes is proposed and validated.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Defects are significant factors of structural deterioration which pose threat to the integrity of precious objects of cultural heritage (CH). Enormous cultural relics were standing for decades and centuries in the natural environment before being discovered. Exposure to natural environment means that on the surface and in internal bulk a number of defects, characterized by randomly distribution and location, are formed due to constantly changing environmental conditions. Crack [1–3] is a representative type of defect causing material separation and its presence weakens the construction and introduces material degradation. The involved risk of deterioration caused by cracks has led to the research for detecting and locating them before further irreversible damage is caused. In the context of CH, non destructivity is a serious factor in experimental design.
For detecting subsurface or internal bulk defects in the cultural heritage, due to the different kinds of objects, materials and construction, various measurement methods with distinct features have been developed over the course of last decade. These vary from ultrasonic imaging (UI) [4,5], optical coherence tomography (OCT) [6–9], non-linear microscopy (NLM) [10–13], digital holographic speckle pattern interferometry (DHSPI) [14–16]. These techniques investigate the cultural heritages from different perspective, but there are limitations to the application needs. UI is able to accomplish real-time image and fast imaging speed, but it is not contact-less due to using adhesives such as medical ultrasonic couplant. OCT is characterized by high imaging resolution and sensitivity, but the detectable depth is limited by the optical diffraction limits. NLM have advantages such as high spatial resolution and large penetration depths, but the number of signals that can be captured is limited [17]. DHSPI is a high-resolution and full-field dynamic detection technique, but it lacks the ability to detect defects in large depths over 2.5 cm.
Speckle pattern interferometry (SPI) is an efficient non-contact technique characterized by the best features of non-contact, full-field, fast detection and material-free selectivity. In the published study, SPI coupled with other excitation techniques have served as an effective means of detecting different types of surficial or sub-surficial defects [18–23]. SPI coupled to an infrared laser as excitation source can induce deformation on the object surface, thus providing information about the surface and subsurface hidden defects. In this paper it is suggested to obtain internal information by selecting suitable carrier signals and the acoustic waves generated by photoacoustic effect [24] is proved to provide an effective carrier. Considering that defects could affect the uniformity and continuity of the internal structure, using acoustic waves as the carrier signals is a feasible scheme to convey internal information which indicating location and depth of the defects.
This paper aims at inspecting the cracks of the object and distinguish the width and depth by photoacoustic speckle pattern interferometry (PA-SPI). Medium density fiberboard pieces were used as specimens including slots with different width and depth on the rear surface for simulating cracks. In research, a pulsed and a continuous wave laser served as excitation and detection source, respectively. The photoacoustic signal generated by pulse laser excitation is a mechanical wave and it goes through less energy attenuation propagating through object inner parts. Less energy attenuation indicates more energy left for incurring enough deformation to be detected to form apparent interferometry fringes. Differentiated interferometry fringes were acquired to indicate the presence of cracks and linear fit of the maximum phase changes was adopted to discriminate and predict different cracks width and depths.
2. Fundamental principle
Fourier spatial carrier method is a common method for obtaining phases from speckle interferograms, achieved by using an off-axis optical path with a reference light. The reference beam is primary requisite to create a stable fringe pattern so an interferogram with higher resolution in spatial domain.
The reference beam wave was tilted at an angle to the object wave, thus introducing the carrier frequency to separate the positive and negative 1st order spectra from the level 0 spectrum of the frequency domain of the speckle interferogram. After intercepting the 1st order spectrum and processed by inverse Fourier transform, the complex amplitude of object wave was acquired, leading to simply calculate the object surface phase changes.
Speckle interferograms record the phase and amplitude information of the detected object surface at the mean time, and the intensity distribution of it can be expressed as follows:
After the excitation of the pulsed laser, the front surface of the object undergoes deformation due to the propagation of acoustic waves. After aquisition of interferograms in both undeformed and deformed state is performed Fourier transform, the 1st order spectrum was intercepted and the center of the 1st order spectrum was moved to the center of the whole spectrum map. After the inverse Fourier transform, the complex amplitude of the object light before and after deformation can be obtained as $c({x,y} )$ and $c^{\prime}({x,y} )$, respectively. By conjugate multiplying the complex amplitudes of the object light before and after the deformation, formula (5) can be expressed as:
3. Experiment
3.1 Experimental set-up
In this experiment, a Q-switched Nd:YAG nanosecond laser source (Changchun new industry photoelectric technology AO-U-532: wavelength: 532 nm, single pulse energy: 1.24mJ, pulse duration: ∼10 ns) is used for the efficient excitation of photoacoustic effect. The pulsed laser is triggered and controlled by an arbitrary waveform generator (RIGOL TECHNOLOGIES DG822). A continuous wave laser (Changchun new industry photoelectric technology MSL-FN-532: wavelength: 532 nm, output power: 50 mW) is used for illuminating the front surface of specimen. A CCD (The Imaging Source DMK 41BU02: pixel size: 4.65µm × 4.65µm, resolution: 1280 × 960) is used for acquire speckle images. A computerized numerical control (CNC) drilling machine (Haas Automation VF 1) is used for processing slots to simulate cracks.
The schematic diagram of the optical system based on speckle interferometry coupled with photoacoustic system is shown in Fig. 2. The system consists of two main parts: the excitation part and the detection part. The excitation part includes laser 2, mirror 1, mirror 2 and aperture 2. The detection part includes laser 1, fiber coupler, attenuator, convex lens, aperture 1, beam coupler and camera.
The excitation path is guided by two mirrors, mirror 1 and mirror 2, in order to adjust excitation area to ensure that the speckle fringes acquired from interferograms are always in the center of the camera's view. And the aperture 2 is used to eliminate stray light from the light source and keep the diameter of laser spot at 3 mm.
For speckle interferometry, the backscattered laser beam by the surface of the object under consideration is called object beam (OB) and the twin beam derived from splitting the same laser beam by fiber coupler is called reference beam (RB). Firstly, the OB is reflected by the object and passes through the convex lens, the aperture 1, and enters into the beam combiner. Meanwhile, the RB passes through the attenuator and enters into the beam combiner, where the OB and RB interfere with each other to form the interferogram.
When the pulse laser starts to excite the rear surface of the object, photoacoustic signals, which are essentially acoustic waves, are generated and propagate to the front surface through the volume of the sample. The deformation of the front surface occurs due to the propagation of the acoustic waves and it is imaged onto the CCD chip as speckle interferogram.
A series of detection data consist of a stack of images with phase differences. Every single image corresponds to 1 sec accumulated laser excitation time of 44.6 mW laser energy deposition of frequency 600 Hz and one image acquisition. To record complete and valid information of the surface deformation during the accumulated laser excitation time, excitation laser and CCD are synchronized through computer control with the exposure time and frame rate of CCD is set to be 1s and 1fps, respectively. The initial phase measurement ${\Phi _0}$ is taken before excitation pulse to be compared to the next position after provoking a phase change. The strategy [22] is therefore shown as Fig. 3.
3.2 Sample preparation
As the specimen for the first presented measurement, a piece of medium intensity fiberboard which length, width and height are 10 cm, 10 cm and 5 mm, respectively was built as shown in Fig. 4(a). The slots with different sizes for simulating cracks in the rear surface were performed by means of CNC drilling machine as shown in Fig. 4(c). The length of all set slots is 10 mm but the width and also the depth are set to the gradient. From the left column to the right, the depth is 4 mm, 3 mm, 2 mm and 1 mm, respectively, and the depth is measured from the front surface, as shown in Fig. 4(d), hence the less the depth the closer to the surface is positioned the crack. From the top row to the bottom, the width is 4 mm, 3 mm, 2 mm and 1 mm, respectively.
Fig. 4. Medium fiber board: (a) the overall size of specimen; (b) the front surface of specimen; (c) the rear surface of specimen; (d) illustration for the definition of depths
The detailed illustration setting for excitation and detection processing is shown in Fig. 5, and images are from areas of one crack at each acquisition. In Fig. 5, one simulated crack with 3 mm width is taken for example. The view in CCD is marked by red rectangular solid line and the corresponding area on the other side surface is marked by red rectangular dashed line.
A 3-axis stage is used to fix the sample and move the sample horizontally and vertically to make the simulated cracks detected and excited in order.
4. Results
4.1 Different speckle images between cracked and non-cracked areas
According to the simplified model [25], the compression wave mode of sound waves is taken into consideration mainly and the other wave types or mode conversation are negligible. So as to generate efficient photoacoustic effect and apparent experimental phenomena, the operating voltage of the pulsed laser was set to 9 V and repetition frequency to 600 Hz by preliminary experimental proof. The whole excitation time of the rear surface was set to 30s to guarantee to generate enough and detectable deformation of the front surface. The detected photoacoustic signal and the temperature changes of the front surface during the 30s excitation time on non-cracked areas indicate that the deformation is caused by both acoustic waves and thermoelastic waves.
Prior to the start of the investigation on the cracks, the investigation was performed on the non-crack areas of the specimen to obtain a control group of speckle images. As the camera exposure time and frame rate were 1s and 1fps, respectively, 30 images were obtained and the first 3 images were selected to be shown for comparison. The result is shown in Fig. 6(a). The most significant characterization is the whole field deformation (Fig. 6(a)) compared to the local field deformation indicative of defect detection shown in Fig. 6(b).
And as shown in Fig. 7, these phenomena were more obvious in terms of phase changes. In the areas without simulated cracks, the phase changes were uniformly spread with small phase values. In the areas with simulated cracks, the phase changes are locally restricted but the phase changes values are large.
After identifying features of speckle images corresponding to areas on the fiberboard with or without simulated cracks, influence caused by the crack depth is taken into consideration. Figure 8(a)–8(d) represents changes of speckle images due to the presence of 3 mm width simulated cracks. The closer the crack is to the front surface, the faster the occurrence of circular fringes developed. Especially in the situation of the 1 mm depth crack, the fringe pattern formed earlier and fringe numbers formed more than any other situation even if the depth difference is all the same one millimeter between two adjacent comparison groups.
Fig. 8. Speckle images: (a) section with crack depth of 4 mm; (b) section with crack depth of 3 mm; (c) section with crack depth of 2 mm; (d) section with crack depth of 1 mm.
The results mentioned above indicate restrictive effect on the distribution of speckle fringes. The restrictive effect is defined as density and spread of speckle fringes influenced by the presence of simulated cracks. The development of speckle fringes is retarded by the simulated crack shape, thus making the deformation concentrated and leading to more phase changes.
4.2 Different speckle images due to varying simulated crack sizes
In order to interpretate exactly, phase changes are calculated and experiments are duplicated five times for every single depth and error bar was calculated. As shown in Fig. 9, the scatter plot illustrates changes of the maximum phase during the accumulated excitation time.
Fig. 9. Maximum phase changes due to varying simulated crack sizes: (a) 4 mm width with different depth; (b) 3 mm width with different depth; (c) 2 mm width with different depth.
It is apparent that on account of diverse simulated crack width and depth, the scatter distribution and variation tendency present different features. The situation of width 4 mm is similar with width 3 mm in consequence of the same excitation energy which is because that the diameter of excitation light spot is controlled as 3 mm, so the analysis focused on the same depth but different width experimental group (Investigation A) is evident that the reduced width resulted in excitation energy and phase changes reduction. And when it comes to the same width but different depth (Investigation B), the results can be concluded as depth increase leading to slope rising and phase changes ascending. For exploring intrinsic connections between simulated crack size changes and phase changes, the following numerical calculations and analysis had been finished.
As for the Investigation A, the aim is to figure out how exactly the excitation energy reduction had influence on the maximum phase changes because of the width loss, so the maximum phase changes from 15s to 30s during the pulsed excitation were chosen because the tendency of phase changes had stabilized and errors in the initial stage had been excluded meanwhile. To clarify mathematical relationships among data, functions with less parameters and more concise expression were considered, so linear fit was carried and confidence band was marked eventually.
As shown in Fig. 10, there are four different experimental group where had the same set, the same depth but various width. In Fig. 10(a), due to absorbing the same laser energy, the slope and intercept of linear function in width 4 mm and width 3 mm test groups are almost the same, which are 0.133 and 28.362, 0.136 and 28.299, respectively. And with the width decreasing, the intercept of linear function representing width 2 mm becomes small (21.271) but the value of slope (0.136) remains.
Fig. 10. Maximum phase changes during excitation time: (a) 1 mm depth with different width; (b) 2 mm depth with different width; (c) 3 mm depth with different width; (d) 4 mm depth with different width.
The investigation A (same depth but different width) indicates the absorbed energy loss sparked by simulated crack width reduction resulting in the overall value decrease in terms of the maximum phase changes, thus leading to the decreasing slope and remaining intercept. The detailed parameters comparison is shown in Table 1, making it possible for predicting other simulated crack width in the following research.
Table 1. Parameters of slope and intercept
As for the Investigation B, the width of simulated crack remains but depth varies. The objective is to explore influence generated by depth reduction in the case of constant excitation energy. As shown in Table 2, the linear fit functions represent cracks of the same width but different depth.
Table 2. Parameters of linear fit function
With the increased depth, which means the crack becomes further measured from the front surface, the intercept of linear function becomes to fall while the slope increases to varying degrees. Fell intercept indicates that, with depth increasing, deformation propagated over longer distance resulting in increased loss of energy. Increased slope indicates that the rising time of phase changes is delayed due to the longer distance mentioned above. But this illustrated law was not preferred to serve as basis for prediction due to the two simultaneously changed parameters.
From the perspective of discovered phenomenon, on the one hand, loss of excitation energy due to width variations affects intercepts but not slope. On the other hand, variation of depth actually represents the change of excitation energy propagation distance, which contributes to varying slope and intercept at the same time, but it is the change in slope ultimately.
From the perspective of detection mechanism, acoustic waves need to be taken into consideration. The mathematical relationship between initial acoustic source ${p_0}(\mathbf{r})$ and the measured data ${p_d}({\mathbf{r}_\textrm{0}},t)$ can be expressed as [26]:
4.3 Prediction and verification
4.3.1 Prediction for phase changes of 1 mm width with different depth cracks
According to the law aforementioned, which is the width reduction resulting in the overall value decrease but slope remaining, so it will be possible for predicting the unknown crack size through the linear fit. And the situation of 1 mm width crack was taken. As shown in Fig. 11, the predicted linear function and linear fit of experimental data were plotted for comparison to validate the effectiveness of the proposed method. And the detailed parameters and mean square error (MSE) were given in the Table 3. The predicted slope and intercept were the average values in Table 1.
Fig. 11. Comparison between predicted and experimental fit function: (a) 1 mm depth with 1 mm width; (b) 2 mm depth with 1 mm width; (c) 3 mm depth with 1 mm width; (d) 4 mm depth with 1 mm width.
Table 3. Parameters and MSE
From the data in Fig. 11 and Table 3, the variability between predicted linear functions and experimental linear fit are little. The average value of RMS is 0.00166, which as well indicates the little difference between prediction and experiment. Overall, the proposed method was proven to be effective and applicability by the experimental corroboration.
4.3.2 Further verification of the relevant laws
After the prediction for simulated cracks of 1 mm width with different depths, the proposed method is proved to work. But in order to exclude coincidence in the experiments, the No. 2 specimen was developed to further verify the relevant laws. And as shown in Fig. 12, the set width is 0.5 mm, 1.5 mm, 2.5 mm, respectively.
The prediction and experiment results of 2.5 mm width are taken for example to illustrate relevant laws, as shown in Fig. 13. The average MSE is 0.011, which indicates the proposed method is working.
Fig. 13. No.2 specimen for further verification: (a) 1 mm depth; (b) 2 mm depth; (c) 3 mm depth; (d) 4 mm depth.
And other prediction and experiment detailed results are shown in Table 4.
Table 4. Parameters of linear fit function
4.3.3 Feasibility of detecting internal closed defects
To create and simulate internal defects, we have covered the rear face with a piece of paper using glue and the schematic is shown in Fig. 14(a). The areas with or without simulated crack are excited and detected using the same experiment procedure mentioned in the manuscript and the speckle pattern is shown in Fig. 14(b). Similarly, influenced by the simulated cracks under the paper, the shown speckle fringe pattern is consistent with the laws mentioned above. The linear fit of detected maximum phase change is drawn in Fig. 15, due to the absorption of laser energy by the paper and the increase in deformation propagation distance, the value of detected deformation of the front surface decreased, leading to fallen slope and intercept. And according to the linear fits mentioned above, 1 mm width with different depths are predicted as shown in Fig. 16 and the average MSE is 0.0055. The experiment and prediction results verify the feasibility of the proposed method.
Fig. 15. Internal closed crack detected results: (a) 1 mm depth with different width; (b) 2 mm depth with different width; (c) 3 mm depth with different width; (d) 4 mm depth with different width.
Fig. 16. Comparison between predicted and experimental fit function: (a) 1 mm depth with 1 mm width; (b) 2 mm depth with 1 mm width; (c) 3 mm depth with 1 mm width; (d) 4 mm depth with 1 mm width.
5. Conclusions
This paper presents a digital speckle interferometry experiment coupled with photoacoustic system and method for non-destructive cracks inspection. Through the calculation of the maximum phase changes in time domain, the influences caused by simulated crack depth and width became digitization and different crack sizes were distinguished by scatter plot. Based on the obtained data, it is quite possible for predicting other crack sizes using linear fit curves for selected time periods of data and the comparison results between captured data and predicted data further verified validity of this analysis strategy. The exploration in this paper for influence by width and depth changes is pre-study for detecting inner part cracks and this pre-experience may assistance to identify crack sizes only by the phase changes.
Due to the acoustic waves serving as carrier signal, the most promising application lies in optical tomography analysis on internal defects. Reconstructing the complex acoustic amplitude generated by transducer at different planes in the interior volume of sample had been accomplished for visualizing interior defects. However, it is not actually non-destructive because of the touch between transducer and specimen, and samples such as artworks were not taken into consideration.
In future work, the non-destructive detection and location for internal defects of artworks will be carried out. Optical tomography based on the digital speckle interferometry coupled with photoacoustic system will be explored for three-dimensional visualization of defects inspection. Photoacoustic signal is a useful carrier for defects information and digital speckle interferometry coupled with photoacoustic may be an effective technique to solve the challenge of imaging internal defects.
Funding
National Natural Science Foundation of China (52075314).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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