Objective : With the development of optical imaging technology, the advantages of digital holography have gradually emerged in the fields of surface contour inspection, industrial inspection, microscopic particle imaging and biomedical interferometry. Realizing high-precision phase unwrapping is the main key technology in the process of digital holography reconstruction. Phase unwrapping is to restore the phase information wrapped in the (−π,π interval to the real phase information which changes continuously. Many phase unwrapping methods have been proposed in domestic and foreign related researches, including the research of algorithms and the application of deep learning techniques. But for the under-sampling problem due to the fast phase change, the classic phase unwrapping methods can solve the undersampling problem only within a certain range, and the difficulty lies in how to correctly recover the accurate phase distribution when the undersampling is more serious and the phase change is too fast. In order to solve the above problems, this paper proposes a spatial phase unwrapping method based on the DC-UMnet networks.

Methods A large number of simulated datasets are used to establish mapping relationships between wrapped and unwrapped phases by means of supervised learning. To address the problem of undersampling, this paper proposes a spatial phase unwrapping method based on the DC-UMnet network to unwrap the undersampling wrapped phase. The DC-UMnet network utilizes the U-net network as the framework. In order to reduce the complexity of the model, the number of parameters, and the cost of computation, it is integrated into the lightweight deep learning network of Mobilenetv1 in the encoding part. And it is integrated into the decoding part by the Dual-Channel block. The Dual-Channel convolution mode used in the Dual-Channel block better fuses the extracted features, so that the demodulated undersampling parcels phase information will have a higher accuracy. Finally, the optimal loss function and activation function suitable for this network are explored. The ReLU6 activation function is used to inhibit the maximum value in the process of feature extraction, which helps to maintain the accuracy in the quantization of the model. The SmoothL1 Loss loss function is used to calculate the loss value, which is robust to the outliers and outlying points in the training data, and is able to control the gradient magnitude to avoid affecting the final training effect of the network due to the special points. The undersampling simulated dataset is trained and the undersampling parcels phase diagram obtained from the experiments is verified. Comparing the proposed method with the U-net network and the DCT method, the results shows its superiority in the under-sampling problem.

Results and Discussions The simulation results in Fig.6-Fig.7 show the feasibility of the undersampling phase unwrapping of the method proposed, and the evaluated results according to the structural similarity index are more satisfactory. Comparing with the U-net network and the DCT method, the simulation results show that the structural similarity index values of the DC-UMnet network are improved by about 4.38 and 0.77 times. After adding noise, the test results show that the structural similarity index of DC-UMnet network increases about 4.68 times and 0.86 times. The experimental results with undersampling microscopic hole as the object shows that the proposed method has a smaller error. And the lateral error of the undersampling microscopic hole size obtained by the proposed method was 2.1 μm and the longitudinal error was 86.7 nm. The accuracy of this paper's method for extracting undersampling phase information is proved, which promotes its further development in the field of optical phase imaging and other fields.

Conclusions  A novel method is presented to solve the problem of unwrapping the phase of an undersampling parcel. The proposed method is based on the decoder-encoder framework of the U-net network. It incorporates the lightweight deep learning network of Mobilenetv1 and uses the dual-channel module to fuse the extracted features for the undersampling problem. The comparative analysis with existing phase unwrapping methods not only proves the feasibility of the method, but also demonstrates the excellence of its phase unwrapping ability under undersampling conditions. The experimental validation of the real object further affirms the superior performance of the proposed method, which is not only able to perform phase unwrapping with higher accuracy for objects without undersampling, but also able to accurately perform phase unwrapping under undersampling conditions with an accuracy of 91.2%. Simulation and experimental results show that the accuracy of the phase unwrapping results of the proposed method is greatly improved under the undersampling conditions. This is of great significance in optical phase imaging and provides new ideas and methods for solving the phase unwrapping problem under undersampling conditions.