Phase Retrieval by Designed Hadamard Complementary Coded Apertures.

Phase retrieval (PR) is a challenging problem with applications in various fields, ranging from microscopy to astronomy. Currently, novel computational imaging systems for PR exploit the modulation of the optical field through \acrfull{rcca} to recover the amplitude and phase from a distorted beam without prior knowledge, solving an ill-posed optimization problem using the conventional phaseLift algorithm. However, these conventional approaches recover the phase and amplitude by using at least 20 coded apertures, which poses a great challenge for performing real-time acquisition and estimation of varying optical fields. To overcome this issue, in this work, we design eight binary Hadamard complementary coded apertures that reduce the acquisition time and enhance the amplitude and phase recovery quality. Through simulations, we compare our approach against traditional random complementary coded aperture using peak-signal-to-noise ratio as spatial fidelity metrics; we use 23 images from the Kodak dataset, PhaseLift as the phase retrieval reconstruction algorithm, and Fresnel as a light propagator in the near field. Extensive simulations using different noise levels prove that our approach Hadamard complementary coded aperture, outperforms conventional methods random complementary coded aperture in reducing the number of masks. Moreover, experimental results using our optical test bed demonstrate that our approach recovers the phase with a significantly improved visual quality.