# Denoising of Wrapped Phase in Digital Speckle Shearography Based on Convolutional Neural Network
## 3 Experiments
### The Denoising Effect on Experimental Data  
To demonstrate the denoising effect of the model in structural damage detection, data were obtained using the digital speckle-shear interferometry system shown in Figure 1 to validate the performance. The experimental setup depicted in Figure 9 utilizes a 120 mm diameter circular plate made of 6061 aluminum alloy, with a thickness measuring 4 mm. Furthermore, coherent light from a helium-neon laser, characterized by a wavelength of 632.8 nm, is employed.  
In Figure 10, the contour pattern obtained by the four-step phase-shifting method is shown. In addition, since there is no ground-truth image for a real noisy image, visual comparison is employed to evaluate the performance of SDCNN. We choose the BM3D and DNCNN method for comparison because it is widely accepted as a benchmark for denoising applications.  
Figure 10: Experimental speckle-pattern image: (**a**) fringe pattern with phase shift \(-3\)a; (**b**) fringe pattern with phase shift \(-\alpha\); (**c**) fringe pattern with phase shift \(\alpha\); and (**d**) fringe pattern with phase shift \(3\)\(\alpha\).  
Figure 9: Digital speckle-shear interferogram: (**a**) speckle-pattern image before deformation; (**b**) speckle-pattern image after deformation.  
Figure 11 compares the denoising results of BM3D, DNCNN, and SDCNN on wrapped-phase maps. Visually, all three methods, BM3D, DNCNN, and SDCNN, effectively remove a significant amount of speckle noise. BM3D and DNCNN show comparable denoising results, but they are slightly outperformed by SDCNN. Regarding detail preservation, the red border in the lower right corner of the image demonstrates the effects on details. BM3D and DNCNN reduce noise but may introduce blurring in details, potentially impacting subsequent phase unwrapping. Figure 12a,b demonstrates the phase unwrapping effect of BM3D and DNCNN, from which the boundary blurring caused by poor noise reduction can be clearly seen. In contrast, SDCNN not only removes noise but also keeps important details intact, avoids interference between fringes, and shows better generalization abilities. Figure 12c shows the effect of phase unwrapping after noise reduction, and the unwrapping is significantly smoother and clearer.  
Figure 13 provides additional insight into the denoising capabilities of SDCNN on a series of authentic experimental maps. The visual results are notably effective. From Figure 13b, it is obvious that the SDCNN presents good results in both stripe preservation and noise-reduction effects, while Figure 13c unpacks the phase of the parcels after noise reduction. The unpacked phase information can be more intuitively seen in Figure 13d.  
Figure 11: Denoising results on experimental speckle-pattern map: (**a**) noise map; (**b**) denoising result of BM3D; (**c**) denoising result of DNCNN; and (**d**) denoising result of SDCNN.  
Figure 12: The unwrapped phase of Figure 11: (**a**) the unwrapped phase of BM3D; (**b**) the unwrapped phase of DNCNN; and (**c**) the unwrapped phase of SDCNN.  
**Data Availability Statement:** The original contributions presented in the study are included in the article material, further inquiries can be directed to the corresponding author/s.  
**Conflicts of Interest:** The authors declare no conflicts of interest.