1. Introduction

For industrial measurement, the full-field strain distribution of core structures is the basis for evaluating system performance and fault diagnosis, which requires the support of high-precision dynamic three-dimensional (3D) deformation measurement [1–3]. Digital holography interferometry (DHI) has the potential to realize the 3D deformation measurement with wavelength accuracy and has been widely studied in practical applications [4].

In principle, the corresponding relationships between phases and deformations in three dimensions would be established by setting different sensitivity vectors, as given in Eq. (1), $(\overrightarrow {{e_x}} ,\overrightarrow {{e_y}} ,\overrightarrow {{e_z}} )$ relates to the sine or cosine of angles between different imaging and illumination directions [5]. The classical system setups of one-dimension deformation, as a basic case, include the out-of-plane structure (OS) and the dual-beam in-plane structure (DIS) [6,7]. Thus, at least three groups of equations should be formulated to achieve 3D deformation calculation, indicating that the measurement system must contain three imaging or illumination parts with inconsistent spatial locations [8–10]. Such a problem increases the complexity of the system setup, which becomes one of the difficulties of 3D deformation measurement and further limits its practicability. Meanwhile, to ensure the correspondence of phases and deformations, the interferences should occur between the specific wave fields and be apart from each other. Studies have been conducted in terms of this issue, kinds of multiplexing techniques were introduced to realize the simultaneous recording and independent calculation of 3D deformation phases, such as wavelength multiplexing [11,12], spatial carrier multiplexing [13,14], spatial-division multiplexing [15,16], and the fusion of the above [17,18]. Notably, to meet the dynamic demands, Fourier transformation (FT) was widely chosen as the demodulation method, which degrades the spatial resolution and accuracy at the same time compared with phase-shifting methods [19]. To combine the phase-shifting methods with the 3D measurement for improving the measurement accuracy and spatial bandwidth, synchronous phase-shifting based on the polarization camera was introduced to achieve the 3D measurement of the unstable temperature fields, three polarization cameras are used to record the holograms from different views [20]. However, the complexity and cost of the measurement system are troubling, and it only suits for the phase measurement of transmissive objects.

The core advantage of holography is the ability to obtain the complex amplitude of objects from numerical computation. Since the traditional holographic interferometry only relies on the phase information, it is reasonable to find that the amplitude information can be fully used to retrieve the in-plane deformations based on digital image correlation calculation (DIC), while the out-of-plane deformation still be obtained from phase measurement [21–28]. As a result, the system structure can be greatly simplified to the OS, thus conquering an obstacle in traditional 3D deformation measurement methods. Facing the dynamic requirement, the interference fields $I = {O^2} + {R^2} + O{R^\ast } + {O^\ast }R$ and the object amplitude ${O^2}$ should be obtained at once in theory, nevertheless, hardly be realized in practice within a single shot by one camera due to the introduction of the reference light. So, the alternative scheme was proposed regarding the background term ${O^2} + {R^2}$ or modulation term $|{O{R^\ast }} |$ calculated from one off-axis hologram $I$ as the true object amplitude distribution. Apparently, the quality of the approximate object intensity would be obviously disturbed by the intensity and divergence of the reference wave, as well as the error in the numerical calculation [24,28], making it become an ignorable factor that decreases the DIC-based in-plane deformation measurement accuracy [29,30]. Meantime, the out-of-plane phase demodulation deals with the same accuracy and resolution limitations as the traditional DHI as mentioned before.

Table 1 summarizes the current methods of DHI-based dynamic 3D deformation measurement. It could be concluded that the ideal condition for the complex amplitude-based method should be the direct recording of object intensity gram (OIG) and the phase-shifting interferograms (PSIG), which have already been realized by us with the adoption of polarization multiplexing principle and dynamic polarization imaging technique [31], the improvement on the quality of OIG and 3D measurement accuracy was also validated. With the deepening of the research, a comprehensive mathematical model of dynamic 3D deformation measurement has been built and extended, the effect mechanism of different polarization modulation strategies of light fields on 3D deformation measurement has been discussed according to theoretical analysis and experimental verification, the better choice of object light and reference light polarization states is identified. Compared with our previous method, which is a special case of the measurement model, the measurement accuracy and range of out-of-plane deformation are improved by realizing “phase subtraction” with the specific phase-shifting algorithm. On the other hand, the excess reference light due to the extinction ratio of the micro-polarization array and the limited dynamic range of the camera can be further suppressed in the non-interference polarization channel, resulting in optimization of intensity gram quality and in-plane measurement accuracy.

Table 1. Comparison of current DHI 3D Deformation Measurement Methods

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In this paper, detailed theoretical and experimental analysis will be shown to give a full view of our idea, the thermal deformation experiment of the circuit board pin will be carried out to illustrate the dynamic measurement capability.

2. Method

The schematic diagram of our 3D deformation measurement method is shown in Fig. 1. The system was established based on the Michelson interference structure. Linear polarized spherical wavefront was emitted from a fiber laser and collimated by CL. The illumination beam was then modulated into circular polarized light by P1 and QWP1, to maximize the utilization of the light energy. NPBS divided the object light and reference light and combined them to generate the interferogram. The speckle field formed by the object with a rough surface was imaged by the 4f system composed of L1 and L2. To be clear, the imaging of the reference light would not affect the 3D deformation measurement. An adjustable AD was introduced as the spatial filter to make the speckle size meet the sampling requirement and block out some stray light at the same time.

 

Fig. 1. Schematic Diagram of the Method. (M - mirror, CL - collimating lens, P - polarizer, QWP - quarter wave plate, NPBS - non-polarized beam splitter, L - lens, AD - aperture diaphragm, Pol-C - polarization camera).

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The main idea of the method is to record the phase and amplitude of the object at each deforming state simultaneously within a single shot. The former would be demodulated from PSIGs to get the deformation based on the “phase subtraction” principle, and the latter should be directly captured with the optimal contrast instead of estimated from the numerical diffraction calculation. To achieve so, the dynamic polarization imaging technique known as the polarization camera (Pol-C) was adopted. Pol-C owns a micro-polarized array with each superpixel composed of two groups of orthogonal polarization directions (0°,45°,90°,135°), making it possible to record different information by polarization modulation.

2.1 Polarization-multiplexing mathematical model of 3D deformation measurement

The core concept of polarization-multiplexing was given out in the dashed box of Fig. 1. In order to get PSIG and OIG at once, the speckle field needs to be elliptically polarized at least to distribute across the four polarization channels of Pol-C simultaneously, while the polarization state of the reference light must be consistent with one of the four directions of the microarray. Interference only occurs in three channels, whereas OIG is recorded in the rest one channel which is orthogonal to the polarization state of the reference light. For definiteness and without loss of generality, two polarization modulation ways of reference light were discussed: 90° linear polarized or 45° linear polarized (the other two options of reference light polarization are equivalent respectively). According to the Jones Matrix, the complex amplitude of the desired speckle field ${E_{o1}}$ and reference field ${E_{r1}}$ are expressed as:

Both situations could satisfy the purpose of dynamic measurement. The flowcharts of 3D deformation recovery process corresponding to these two models are shown in Fig. 2. Each raw image is recorded by Pol-C with a single shot at each deformation state, from which the PSIGs and one OIG are obtained after downsampling and interpolation. The detailed measurement process of model(1) has been demonstrated in our related research [31]. The differences between two models are categorized into two aspects:

 

Fig. 2. Deformation Recovery Process under Two Models. (a1-a2) raw images captured at two deformed states. (b-c) two series of 2-step PSIGs. (d)3-step phase-shifting speckle fringe patterns obtained by intensity subtraction. (e1) wrapped phase obtained by fringe-based phase-shifting algorithms. (f) two OIGs. (h-i) two series of 3-step PSIGs. (k1) wrapped phase obtained by subtraction of (j) two speckle phases. (m) two quality-improved OIGs. (e2, k2) out-of-plane deformation(dz). (g1-g2, n1-n2) in-plane deformations(dx,dy).

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When the reference light is 45° polarized (model(1)), a linear relationship ${I_{45}} + {I_{135}} = {I_0} + {I_{90}}$ exists due to the singular coefficient matrix $C$ of Eq. (6) (its determinant is always equal to 0 independent of the value of $a$ and $\theta$). Thus, only two PSIGs $({I_0},{I_{90}})$ contribute to solving the out-of-plane deformation. To solve such an ill-posed problem, the “intensity subtraction” operation between $({I_0},{I_{90}})$ and $({I_0}^d,{I_{90}}^d)$(PSIGs captured at the next deformation state) needs to be done to generate three-step phase-shifting speckle fringe patterns, as shown in Fig. 2(b-d), from which the deformation phase could be demodulated. Trapped by the heavy speckle noise in Fig.(d), multiple filtering operations on speckle fringe patterns and wrapped phase patterns would be carried out to guarantee accuracy [32,33], and the fringe number needs to be considered for the former and the fringe-based phase-shifting algorithms [34].

With the reference light transferred into 90° polarized (model(2)), the coefficient matrix $C$ of Eq. (7) becomes full rank. All three PSIGs can be used to recover a speckle phase at each deformation state, as shown in Fig. 2(h-j). Thus, the deformation phase would be obtained by the “3 + 3” phase-shifting method in the principle of “phase subtraction”, which is simpler and theoretically more accurate than “intensity subtraction”[35,36]. With the determination of a, the speckle phase $\phi = ({\varphi _o} + \theta - {\varphi _r})$ could be demodulated from the 3-step PSIGs with inconsistent phase shifts and background intensities based on the Least Square (LS) method:

Then the out-of-plane deformation was calculated by subtracting the speckle phases before and after deformation (corresponding to subscripts b and a):

The in-plane deformations are obtained by correlation analysis between two OIGs (${I_{0b}}$ and ${I_{0a}}$) recorded before and after deformation. The deformation vector ${p} = {\left\{ {\begin{array}{{llllll}} u&v&{{u_x}}&{{u_y}}&{{v_x}}&{{v_y}} \end{array}} \right\}^T}$ used to express the relationship between reference points $({{x_{b(i )}},{y_{b(j )}}} )$ and deformed points $({{x_{a(i )}},{y_{a(j )}}} )$ in the region of interest (ROI) of ${I_{0b}}$ and is figured out based on Eq. (10). Full-field distributions then be formed by interpolating on the sparse measured points $({{x_{b(c )}},{y_{b(c )}}} )$[37].

Comparing ${I_{135}}$ (in Eq. (4)) and ${I_0}$ (in Eq. (5)), it could be found that the intensity of OIG can be raised by changing a, only when the reference light is 90° polarized(model(2)). It means that object light in the non-interference polarization channel can occupy more dynamic range under the same reference light intensity and camera conditions, and the improvement of OIG quality is of great significance for the DIC calculation accuracy, which is also expected to eliminate the fringe-liked error of in-plane deformation distribution in our previous research.

In summary, the 3D measurement mathematical model with reference light of 90° polarized has higher theoretical measurement accuracy, with the purpose of dynamic measurement well satisfied. Eventually, the 3D deformation $(dx,dy,dz)$ can be obtained based on the illumination angle $\beta$ and the magnification M of the system:

2.2 Simulation about the effect of polarization states on deformation accuracy

The value of a plays a crucial role in 3D deformation measurement accuracy, cause it not only determines the phase-shifting amount (${\delta _1}$, ${\delta _2}$) and background intensity of PSIGs, but also influences the imaging quality of the speckle amplitude. Thus, simulations about model(2) were conducted to find out the reasonable polarization angle $\theta$ of P2, which essentially determines the value of a. The interference fields and amplitude fields were generated based on Eq. (5). $\theta$ varied between 5° and 90° with the intervals of 5°. The speckle phase was distributed randomly in the range of $[{ - \pi ,\pi } ]$, with speckle size adjusted to 4 pixels by spatial frequency filtering method. The amplitude terms ${A_r}$ and ${A_o}$ were set to 1. The function peaks() was used to describe the out-of-plane deformation phase.

First, we analyzed $Ma = {{{a^2}} / {({a^2} + 1)}}$ (the intensity of OIG) and $Md = \frac{{{{({a^2} + 2)} / {({a^2} + 1)}}}}{{{2 / {\sqrt {{a^2} + 1} }}}}$ (the interference quality of PISG) as $\theta$ changes, the normalized curves are given in Fig. 3(a). These two parameters theoretically reflect the direct influence of $\theta$ on the amplitude and phase of the measured speckle field. These two curves intersect at the point where $\theta = {30^\mathrm{^\circ }}\left( {a = \sqrt 3 } \right)$, which means that the quality of PSIG and OIG can be taken into account at the same time. Subsequent analysis will focus on comparing the differences at $\theta = {30^\mathrm{^\circ }}$ and $\theta = {45^\mathrm{^\circ }}({a = 1} )$, the latter indicating a circularly polarized speckle field, the simplest case adopted in Ref. [31].

 

Fig. 3. Influence of the Polarization State on 3D Deformation Measurement Accuracy. (a) Ma and Md of the simulated speckle fields and interference fields. (b) Out-of-plane deformation phase demodulation accuracy. (c) Wrapped phase patterns obtained from (b). (d) MGG of the simulated speckle pattern.

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Then, the precision of out-of-plane deformation phase recovered by the LS-based “3 + 3” phase-shifting method (Eq. (8–9))was evaluated, as shown in Fig. 3(b), the root mean square error (RMSE) decreased rapidly when $\theta$ changes from 0°∼25° or 55°∼90°, but exhibited slightly differences of RMSE in the range of 30°∼45°, for the true values of Md are rather close to 1 (theoretical optimal value), which further confirmed that the LS-based deformation phase demodulation method is insensitive to the nuances of $\theta$. Some wrapped deformation phase patterns (without filtering) listed in Fig. 3(c) offered an intuitive demonstration of the change in calculation accuracy.

Dealing with the in-plane deformation, the mean gray value gradient (MGG) operator was introduced to comment on the impact of $\theta$ on the correlation calculation accuracy [38]. MGG is an operator used for evaluating the quality of the speckle grams, $MGG = \frac{{\sum\limits_{i = 1}^W {\sum\limits_{j = 1}^H {|{\nabla f({x_{ij}})} |} } }}{{W \times H}}$, W and H denote the resolution of the images, $|{\nabla f({x_{ij}})} |$ is the modulus of gray value gradient vector of each pixel ${x_{ij}}$, which can be calculated based on the common gradient operator. The larger the MGG is, the higher the quality of the recorded speckle pattern is, which is more conducive to high-precision in-plane deformation analysis, the results are given in Fig. 3(d). In contrast to the out-of-plane simulation, MGG showed a significant downward trend with fast speed when is between 30° and 45°, indicating that DIC-based in-plane deformation measurement puts a stricter requirement on the choice of $\theta$.

In terms of the simulations, it is reasonable to take 30° as the most suitable value of $\theta$, as a result of which the accuracy of 3D deformation measurement can be well balanced.

3. Experiments

To illustrate the necessity and advancement of polarization model analysis as well as optimizing the polarization modulation strategy, we first conducted some validation experiments of out-of-plane deformation and in-plane deformation separately, results obtained from different polarization states were compared with the reference values.

Figure 4 shows the experimental setup of the measurement system. A single longitudinal mode fiber laser with a wavelength of 633 nm was adopted as the light source. The illumination beam was formed after passing a collimating lens. This part was omitted here but could be seen in Fig. 7. The 90° linear polarization state of the reference light was controlled by P3. The speckle field generated by an aluminum plate was modulated into an elliptic polarization state by P2(30°) and QWP2 (0°), and then imaged with the appropriate size on Pol-C through the 4f system(L1-AD-L2). Thus, the desired intensity distribution was formed and used for 3D deformation calculation. At each deformation stage, Pol-C records a raw image, which contains three PSIGs with phase shift and varying intensity and one OIG according to model(2). The speckle phase of the current state is recovered by LS-based 3-step phase-shifting method, and the wrapped phase of out-of-plane deformation would be formed from the subtraction with other states. By recording and analyzing multiple deformation states, the complete deformation process of the object can be obtained. In the experiment, the wrapped deformation phase was unwrapped by a fast and noise-robust algorithm [39], while the DIC-based deformation computation was completed with the OpenCorr[40].

 

Fig. 4. The Experiment Setup and Measurement Flowchart of a Single Raw Image.

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3.1 Out-of-plane accuracy experiments

In order to explain the difference in measurement accuracy of out-of-plane deformation under different polarization states of reference light, two kinds of deformation that approach the measurement limitation were discussed. The aluminum plate with a micrometer screw loaded from the back was utilized to generate the out-of-plane deformation. The deformation measurement results (reference light = 90° polarized) were compared with those demodulated from the “4 + 4” phase shifting method and the “intensity subtraction”-based method (reference light = 45° polarized), as shown in Fig. 5. The first column under each deformation list represents the unfiltered wrapped deformation phase patterns, and the second column denotes the filtered wrapped deformation phase patterns. All the wrapped phases were filtered by the same sin-cos filtering process.

 

Fig. 5. Comparison of Out-of-plane Deformation Measurement Results.

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Based on the quality and RMSE of the wrapped phase patterns, it could be seen that the results provided under the 90° polarized reference light (shown in the second row of Fig. 5) outperform in both deformation cases and could be comparable with those of 4 + 4 phase shifting method. While the fringe-based phase shifting method corresponding to 45° polarized reference light failed to give acceptable results (shown in the third row of Fig. 5), because the speckle fringe patterns are always covered with speckle noises and too few (less than three) or too many (larger deformation indicates heavier speckle noises) fringes will reduce the signal-to-noise ratio of the images, therefore making high demand of the speckle fringes filtering process and limiting the precision of the multi-frame interference fringe phase demodulation algorithms. The phase measurement error between our method and 4 + 4 phase-shifting method mainly comes from two aspects, one is the reduction of the valid phase shifting patterns [41], the other is the uneven phase shifting amounts and background intensity of the three PSIGs as expressed in Eq. (5), increasing the difficulty of calculation based on the least square.

Such an experiment verified the significant effect of modulating the polarization state of the reference light on improving the measurement accuracy of out-of-plane deformation. The reference light changed from 45° to 90°, resulting in an increase in the number of PSIGs and the evolution of the deformation phase measurement principle, which was consistent with the theoretical analysis in section 2.1. Meanwhile, the out-of-plane deformation measurement accuracy was illustrated, indicating that the optimized polarization strategy can provide accurate deformation measurement results.

3.2 In-plane accuracy experiments

The direct recording of amplitude of object field is one of the advantages of our method, and The in-plane deformations are acquired by DIC calculation based on OIGs. However, both the polarization state of the object and reference light would affect the quality of OIG in practice. Through such an experiment, we aimed to demonstrate the effect of optimized object light and reference light polarization modulation strategy on enhancing image quality and further improving in-plane deformation measurement accuracy. In terms of the simulation analysis (section 2.2), a thin aluminum sheet and the USF1951 resolution board were tested to verify the improvement of imaging quality when the value of a changed from 1 to $\sqrt 3$ (corresponding to P2 (45°) or P2(30°), while the reference light remained 90° linear polarized. The normalized values of MGG of Fig. 6(a1-c) were 0.352, 0.721, 0.446, 0.803, respectively. Subsequently, the aluminum sheet was mounted on the electrical-controlled translation stage, moving 10 times in the X direction with an interval of 10µm. The deviations between the mean displacements in ROI and the feedback values of the stage were plotted in Fig. 6(e). Benefiting from the better quality of the OIG when P2 was at the designed angle of 30°, the errors at each deformation were less than that of P2 (45°), the peak-to-valley value of the measurement errors did not exceed 0.5µm, and might be improved by optimizing the DIC operation process.

 

Fig. 6. Comparison of In-plane Deformation Measurement Results. Recorded intensity grams of aluminum sheet and USAF1951 with (a1, b) P2(45) and (a2, c) P2(30). (d) Recorded intensity gram of USAF1951 by previous method. (c1), (d1) Partially enlarged view of (c) and (d). (e) Mean displacement error curves. Previous method-based in-plane deformation results in the Y direction (f1) and X direction (f2) of a blade [31]. (f3) Corresponding out-of-plane deformation fringe pattern. (g1-g2) Optimized in-plane deformation results.

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On the other hand, the change of the reference light polarization state from 45° to 90° would also do good for the quality of OIG, when considering some unideal experimental parameters. Due to the limitation of the processing technology, the extinction ratio of the micro-polarization array (300:1) is lower than that of the single polarizer (Lbtek, FLP25-VIS-M, 5000:1), and the polarization-maintaining ability of NPBS (Daheng Optics, GCC-403102) described by $|{{T_s} - {T_p}} |,|{{R_s} - {R_p}} |\le 10\%$, depends on the polarization angle of the incident light. The polarization state remains unchanged only when it is 0° or 90° polarized, with maximum deviation happening at 45°. Therefore, the 45° polarized reference light became slightly elliptical polarized after passing through NPBS. Such depolarization caused the leakage of the reference light intensity on the 135° polarization channel, which would get more serious considering the low extinction ratio of micro-polarization array. The interference with low contrast could be observed in the actual captured images, as shown in Fig. 6(d-d1). This phenomenon will not only affect the image quality of the OIGs, but also form fringe-liked errors in the in-plane deformation distribution, as shown in Fig. 6(f1-f3), the shape of which is related to the out-of-plane deformation fringes, because the correlation calculation is also a way to generate speckle interference fringes. Once the reference light was transferred to 90° polarized, these problems were well conquered. With the intensity leakage on the orthogonal channel being suppressed, which can be concluded by comparison of Fig. 6(c1) and Fig. 6(d1), the in-plane deformation measurement result of the same blade shown in Fig. 6(g1-g2) would not be disturbed by the special error. In summary, experiments have shown that refining the polarization state of speckle field and reference field can both improve the in-plane deformation measurement results by providing the OIG with higher quality. Thus, it can be concluded that, to realize the high-accuracy 3D deformation measurement, the optimal polarization modulation strategy should be “elliptical polarized object field with an amplitude ratio of $\sqrt 3$+ 90° polarized reference field”.

3.3 Dynamic 3D deformation measurement

Our method owns the ability to achieve the dynamic 3D deformation measurement by utilizing the complex amplitude of the speckle field simultaneously, the results of which are always taken as fundamental for performance analysis and faulty diagnosis. On the basis of the measurement accuracy verified by the experiments carried out in sections 3.1 and 3.2, to illustrate the dynamic measurement ability of our proposal, we conducted the experiment by testing the real-time 3D thermal deformation of the circuit pin, which was heated by a heat gun from room temperature to 500°C, as shown in Fig. 7(a). The polarization state of the object light and reference light were well adjusted to the optimal conditions. A long working distance microscope objective (MO) was introduced to magnify the testing area by 15 times. The resolution and pixel size of Pol-C (Baumer VCXU.2-50MP, Sony IMX250 Gen2 COMS image sensor) is $2048 \times 2448$ and $3.45\mu m$. The heating process lasted about 2 minutes, and the frame rate was set as 10fps with the resolution of $2000 \times 2000$ pixels (field of view ${\approx} 0.46 \times 0.46m{m^2}$). Only the results of the initial deformation stage were selected for illustration, the computation was carried out in MATLAB software with an Inter Core i7 processor with a clock rate of 3.3 G Hz and a memory size of 16GB.

 

Fig. 7. Dynamic Thermal Deformation Measurement of the Circuit Board (Visualization 1). (a) Experiment setup. (b) Out-of-plane deformations. (c),(d) In-plane deformations.

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Three states of the 3D deformations are given in Fig. 7(b-c). From the very beginning, the deformations were rather small, and the growth rate was slow. As the temperature of the object's surface gradually approached the melting point, the deformation speed started to accelerate. At the end of the chosen stage, the out-of-plane deformation reached $3.02\mu m$, the maximum deformations in X and Y directions are $- 3.16\mu m$ and $4.26\mu m$, the specified positive directions of which are indicated by arrows separately in the diagram. The whole deformation process was shown in Visualization 1. Based on the accurate dynamic 3D testing results, the relationship model between micro-deformations and temperature load can be established, which is helpful to analyze the dangerous area and failure reasons of welding joints.

For the sensitivities of the interferometry measurement and DIC measurement, the former depends on the relationship between the phase and the deformation: $dz = {{4\pi \cdot \Delta \varphi } / \lambda }$. In our experiment, $\lambda \textrm{ = }633\textrm{nm}$, so the sensitivity of out-of-plane deformation is about 316 nm (corresponding to the phase change of one fringe). The latter depends on the pixel size, and magnification of the imaging system, as well as the post-process algorithms, such as the choice of the matching window size and the subpixel algorithms. Usually, it can reach 0.5 pixels at least and achieve 0.01 pixels when the parameters are reasonably optimized. Thus, within the diffraction limit, the sensitivity of our experimental system can reach 690 nm (0.2 pixels), and the difference with the out-of-plane deformation sensitivity can be further reduced by optimizing the DIC algorithms.

4. Conclusion

This paper presented a compact and accurate DHI-based dynamic 3D deformation measurement method that utilizes the complex amplitude of the object simultaneously by employing the dynamic polarization imaging technique. First, the polarization modulation strategies of the object field and reference field were discussed by presenting a sufficient polarization-multiplexing mathematical model, from which the “elliptical polarized object field with an amplitude ratio of $\sqrt 3$+ 90° polarized reference field” was determined as the optimal combination. The utilization of all polarization channels was maximized, so that the dynamic requirement could be satisfied by directly recording the 3-step PSIGs and one OIG within a single shot. The 3D deformations were finally obtained by the specific LS-based phase-shifting algorithm and general correlation computation, in which the out-of-plane deformation recovery had been evolved into the “phase subtraction” method, while the better-quality object intensity data were provided for in-plane deformation measurement. Through comparing the accuracy of 3D deformations under different polarization states combination modes, the correctness of theoretical modeling and simulation analysis had been verified, furthermore, the advancement and necessity of the optimized strategy had been intuitively demonstrated. The experiment about the thermal deformation of the circuit pin reveals the dynamic measurement ability of the proposed method and its value in real industrial testing applications. Further research would be focused on vibration isolation based on the common-path structure [42], to suppress the influence on deformation measurement accuracy.