We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.

The denoising of electronic speckle pattern interferometry (ESPI) fringe patterns is a key step in the application of ESPI. In this paper, we propose a method for batch denoising of ESPI fringe patterns based on a convolution neural network (CNN). In the proposed method, the network is first trained by our training dataset, which consists of the noisy ESPI fringe patterns and the corresponding noise-free images. We propose a new computer-simulated method of ESPI fringe patterns to create our training dataset. After training, the other multi-frame ESPI fringe patterns to be processed are fed to the trained network simultaneously, and the corresponding denoising images can be obtained in batches. We demonstrate the performance of the proposed method via application to 50 computer-simulated ESPI fringe patterns and three groups of experimentally obtained ESPI fringe patterns. The experimental results show that our method can obtain desired results even when the quality of ESPI fringe images is considerably low because of variable density, high noise, and low contrast, and our method can denoise multi-frame fringe patterns simultaneously. Moreover, we use the computer-simulated ESPI fringe patterns to train the network; after training, the trained network can be used to denoise either computer-simulated ESPI fringe patterns or the experimentally obtained ESPI fringe patterns. The proposed method is especially suitable for processing a large number of ESPI fringe patterns.

In optical metrology, state of the art algorithms for background and noise removal of fringe patterns are based on space-frequency analysis. In this Letter, an approach based on variational image decomposition is proposed to remove background and noise from a fringe pattern simultaneously. In the proposed method, a fringe image is directly decomposed into three components: a first one containing background, a second one fringes, and a third one noise, which are described in different function spaces and are solved by minimization of the functional. A simple technical process involved in the minimization algorithm improves the convergence performance. The proposed approach is verified with the simulated and experimental fringe patterns.

We propose the oriented spatial filter masks for filtering in electronic speckle pattern interferometry (ESPI) phase fringe patterns. We establish the oriented derivative operator that only highlights noise without edges of an image. The noise in the image can be removed while still preserving the edges simply by subtracting the oriented derivative image from original image, which can be implemented with one pass of the oriented spatial filter mask. Further, we make an improvement on the oriented spatial filter mask for enhancing the smoothness. The performance of the oriented spatial filter masks is demonstrated via application to a simulated speckle phase fringe pattern and an experimentally obtained phase fringe pattern and comparison with other directional filtering methods.

We derive the new oriented-couple partial differential equation (PDE) models based on the variational methods for filtering in electronic speckle pattern interferometry phase fringe patterns. In the filtering methods based on the oriented PDE models, filtering along fringe orientation for the entire image is simply realized through solving the PDEs numerically, without having to laboriously establish the small filtering window along the fringe orientation and move this filtering window over each pixel in an image. We test the proposed models on two computer-simulated speckle phase fringe patterns and an experimentally obtained phase fringe pattern, respectively, in which the fringe density is variable, and compare our models with related PDE models. Further, we quantitatively evaluate the performance of these PDE models with a comparative parameter, named the image fidelity. We also compare the computational time of our method with that of a traditional filtering method along the fringe orientation. The experimental results demonstrate the performance of our new oriented PDE models.