Phase retrieval with physical constraints in coherent imaging systems

Abstract

Coherent imaging systems aim at detecting both the amplitude attenuation and phase shift of the coherent light after the transmittance of target object. However, conventional imaging sensors can only capture the amplitude information. With optical design, the connections between the measurements and the target objects are known. For example in the coherent diffractive imaging (CDI) setup, coherent light transmits through the object and diffraction patterns are captured in the far field, which is the squared Fourier modulus of the object.

Phase retrieval (PR) is important for reconstructing the image of the target object from the diffraction patterns. Since PR problem is ill-posed and non-convex, prior knowledge is critical. In this dissertation, we try to jointly design both the optical and computational parts to the coherent imaging systems. Coded masks incorporated into the imaging systems are used as physical constraints to help with the PR algorithms.

In conventional PR algorithms, the object support is important as it shows the region where no transmitted light exists. To extend this idea, we consider the masked CDI setup where a mask is set in front of the object plane, and its pattern on the object plane can be calculated by propagation. This pattern can be used as physical constraints for the PR algorithm. We propose a PR algorithm for this setup based on the alternating direction method of multipliers (ADMM). Besides, we design a regularization function for complex-valued images based on the structure tensor and Harris corner detector. Experimental results on real data show the superiority of our method.

For CDI system with high sampling rate, dimension of the original PR problem is high since the size of the diffraction pattern is large. Its scale can be reduced by introducing a binary sensor mask to discard some of the pixels in the diffraction patterns. The status of this sensor mask can be used as physical prior knowledge in the PR problem. Numerical results show that sensor masks with proper sampling rate can improve the speed and quality of our PR algorithm. To make this setup more stable, we refer to the learning-based method to design sensor masks according to the diffraction patterns, which can provide better reconstruction results.

Based on conventional ADMM method, we propose the dual ADMM method by incorporating a second iteration process to solve the dual problem. Since the solution of the dual problem is related to the non-trivial lower bound of the objective function, the iterative solutions of the dual problem can help with the primal iterations. Besides, we build a learning-based PR algorithm with dual recursive scheme based on this idea. The same network is shared in both the primal and dual iterations. For the optical setup, we refer to the coded holographic CDI system, where the coded mask is set in the object plane for reference as physical constraints. The coded mask is also designed by a neural network with reference to the intensity information of the object. Numerical results show the efficiency of this setup.