Single-shot pixel super-resolution phase imaging by wavefront separation approach

Abstract

We propose a novel approach for lensless single-shot phase retrieval, which provides pixel super-resolution phase imaging. The approach is based on a computational separation of carrying and object wavefronts. The imaging task is to reconstruct the object wavefront, while the carrying wavefront corrects the discrepancies between the computational model and physical elements of an optical system. To reconstruct the carrying wavefront, we do two preliminary tests as system calibration without an object. Essential for phase retrieval noise is suppressed by a combination of sparse- and deep learning-based filters. Robustness to discrepancies in computational models and pixel super-resolution of the proposed approach are shown in simulations and physical experiments. We report an experimental computational super-resolution of 2μm, which is 3.45× smaller than the resolution following from the Nyquist-Shannon sampling theorem for the used camera pixel size of 3.45μm. For phase bio-imaging, we provide Buccal Epithelial Cells reconstructed with a quality close to the quality of a digital holographic system with a 40× magnification objective. Furthermore, the single-shot advantage provides a possibility to record dynamic scenes, where the frame rate is limited only by the used camera. We provide amplitude-phase video clip of a moving alive single-celled eukaryote.

Unfolding-Aided Bootstrapped Phase Retrieval in Optical Imaging

“…Reconstruction of the object wavefront. Lensless single-shot phase retrieval for pixel super-resolution phase imaging in the middle zone [5]. Noise is suppressed by a combination of sparse-and deep learning-based filters.…”

“…In optical applications such as radio astronomy [34] and microscopy [5], the scene x is naturally sparse in some orthogonal domain Ψ, i.e. Ψ H Ψ = I; common examples include wavelet or discrete cosine transform).…”

“…The advantage of the DOE lies in its imaging capability to successfully recover the phase without additional optical elements (such as lenses) leading to even more compact imaging devices [5]. The eschewing of the lens, which is the case in phase retrieval from CDP, makes the system not only light and cost-effective but also lens-aberration-free and with a larger field of view.…”

“…Considering the spatial distribution of DOE, the observation model [5] for the scene x and DOE D is y = |P z2 (D • P z1 (x))| 2 , where z 1 and z 2 are object-mask and mask-sensor distances, correspondingly (see Table I).…”

“…Phase retrieval in diffractive optical imaging (DOI) deals with the estimation of a complex domain signal from magnitude-only data in the form of its diffraction patterns. This problem has been at the center of exciting developments in DOI [1]- [3] during the last decade to improve achievable spatial resolution [4]- [6], lighter optical setups [5], and better detection [1]. When the diffraction patterns (phaseless data) are acquired through a setup that employs coherent light and a diffractive optical element (DOE) (also as coded aperture) to modulate the scene, phase coded diffraction patterns (CDP) are obtained.…”