Multiple-Level Green Noise Mask Design for Practical Fourier Phase Retrieval

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy, researchers introduce extra constraints to the measuring procedure by including a random aperture mask in the optical path that randomly modulates the light projected on the target object and gives the coded diffraction patterns (CDP). It is known that random masks are non-bandlimited and can lead to considerable high-frequency components in the Fourier intensity measurements. These high-frequency components can be beyond the Nyquist frequency of the optical system and are thus ignored by the phase retrieval optimization algorithms, resulting in degraded reconstruction performances. Recently, our team developed a binary green noise masking scheme that can significantly reduce the high-frequency components in the measurement. However, the scheme cannot be extended to generate multiple-level aperture masks. This paper proposes a two-stage optimization algorithm to generate multi-level random masks named OptMask that can also significantly reduce high-frequency components in the measurements but achieve higher accuracy than the binary masking scheme. Extensive experiments on a practical optical platform were conducted. The results demonstrate the superiority and practicality of the proposed OptMask over the existing masking schemes for CDP phase retrieval.

I. Introduction

PHASE retrieval aims to reconstruct a complex-valued optical wavefield from intensity-only measurements. It is known that, in coherent optical systems, the phase changes of the receiving light carry a lot of information about the measuring object that cannot be found in the intensity of the light. However, traditional imaging devices (charge-coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) sensors) can only detect the intensity of optical waves but not the phase information [1]. The need for phase retrieval algorithms thus naturally arises. Phase retrieval is a key problem in crystallography, optical imaging, astronomy, X-ray, electronic imaging [2], [3], [4], [5], [6], [7], [8], etc. Recently, substantial progress was made in the development of phase retrieval algorithms due to the advance in optimization theories [1]. Specifically, optical masks (also named coded apertures), acting as an extra constraint to the optimization process, are adopted in optical phase retrieval systems to improve reconstruction performance. It is shown in [9] and [10] that the introduction of random masks significantly improves the accuracy of the reconstructed signals.