Efficient Gerchberg–Saxton algorithm deep unrolling for phase retrieval with a complex forward path

Phase retrieval problems occur in a wide range of optical systems characterized by different forward path complexities. The Gerchberg–Saxton algorithm deep unrolling technique is a state-of-the-art phase retrieval method. Its inference speed is determined by the complexity of the forward path. We propose FourierGSNet, an efficient Gerchberg–Saxton algorithm deep unrolling method, to achieve faster phase retrieval for applications with high forward path complexities. FourierGSNet does not directly unroll Gerchberg–Saxton iterations with the forward path of the system. Instead, it extracts physics knowledge from unrolled iterations using the Fourier transform as a simplified forward path and injects the knowledge into a cascaded neural network for phase retrieval for the actual system. We evaluated FourierGSNet on three applications with three degrees of complexities: (i) coherent diffractive imaging with Fourier transform as a simple forward path, (ii) near-field X-ray imaging with Fresnel diffraction as a medium-complexity forward path, and (iii) laser beam shaping with the entire simulated optical train as a complex forward path. We compare FourierGSNet with direct unrolling, two fitting methods, and state-of-the-art data-driven methods. Experiments show that FourierGSNet is significantly faster in inference than direct unrolling on high-complexity applications while achieving equal or higher accuracy than compared methods.