In the process of using digital laser shearing speckle interferometry technology for measurement and detection, owing to the different interference characteristics of the laser and the measurement environment, there will be multiplicative and additive noise of different properties in the phase map wrapped in the measurement results. However, noise presented in the wrapped phase diagram makes it difficult to conduct and ensure accurate subsequent phase unwrapping. Therefore, investigating how best to suppress and remove noise contained in wrapped phase diagrams is crucial for measurement applications involving shear speckle interferometry. Currently, problems remain with noise suppression and the removal of speckle interference-wrapped phase maps. For example, traditional noise suppression methods (such as sine cosine full variation filtering) consistently fail to fully suppress both multiplicative and additive noise while protecting wrapped phase information, which makes the analysis error from subsequent processing either too large or complex to conduct. Hence, in this study, we propose a homomorphic filtering-based sine cosine full variation fusion filtering method that effectively removes multiplicative and additive noise while protecting wrapped phase map information. Subsequently, the effectiveness of the proposed method is experimentally verified.

This study proposes the suppression and removal of wrapped phase map noise during digital laser shearing speckle interferometry measurements using a homomorphic filtering-based sine cosine full variation fusion filtering method. First, homomorphic filtering is performed on the original wrapped phase image containing noise to suppress and remove multiplicative noise components from the wrapped phase image. Subsequently, the filtering results undergo sine and cosine decomposition to remove the periodic noise components in the wrapped phase diagram. Finally, the decomposed sine and cosine images are subjected to full variational filtering to remove the remaining additive noise components. Simultaneously, the speckle suppression index is introduced as a criterion to determine whether the filtering process has completed while suppressing the noise. Subsequently, the decomposed sine and cosine images are subjected to arctangent transformation to achieve filtering recovery of the final wrapped phase image. Additionally, the effectiveness of the filtering method is verified through simulation experiments and composite test pieces with preset defects.

It was confirmed that the proposed fusion filtering method achieved the goal of protecting phase information while removing multiplicative and additive noise in wrapped phase images. By simulating the wrapped phase diagram and its corresponding noisy image, noise suppression results were obtained using the proposed method alongside other traditional methods (Fig.3). From their speckle suppression indices , it can be observed that the speckle suppression index obtained using the proposed fusion filtering method was the smallest, indicating that this noise suppression effect is the best, Thus, verifying the feasibility of the proposed method. The proposed filtering method was validated using composite materials with preset defects. According to the filtering results, it can be observed that the speckle suppression index of the image obtained using the proposed method after filtering was approximately 10.7% lower than that of traditional sine cosine full variation filtering. After phase unwrapping the filtering results, the number of phase residual points in the noise suppression image obtained using the proposed method was the smallest, and the phase unwrapping results stabilized, thus, verifying the stability and superiority of the proposed fusion filtering method.

This study proposed a sine cosine full variation fusion filtering method based on homomorphic filtering to address the issue of noise in a wrapped phase map obtained from shear speckle interference. By considering different noise properties, we effectively achieved the suppression and removal of various noises, ensuring smooth future phase unwrapping. Compared to the traditional full variation denoising process based on sine cosine decomposition, this solution reduces the speckle suppression index by approximately 10.7% and protects phase information for subsequent phase unwrapping processes. Moreover, the filtering effect stabilized with fewer phase residual points during the unwrapping process. First, the feasibility and effectiveness of the method were verified by manually adding noise through a wrapped phase simulation. Subsequently, the actual wrapped phase map containing noise obtained by detecting the composite specimen plate with preset defects was filtered, and the filtering effect was quantitatively evaluated using the speckle suppression index. The phase information protection effect was also evaluated through phase unwrapping, and the effectiveness and superiority of the proposed method were verified using both simulation and practical detection experiments.