Single-shot diffraction-limited imaging through scattering layers via bispectrum analysis

Abstract

Recently introduced speckle-correlations based techniques enable noninvasive imaging of objects hidden behind scattering layers. In these techniques the hidden object Fourier amplitude is retrieved from the scattered light autocorrelation, and the lost Fourier phase is recovered via iterative phase-retrieval algorithms, which suffer from convergence to wrong local-minima solutions and cannot solve ambiguities in object-orientation. Here, inspired by notions used in astronomy, we experimentally demonstrate that in addition to Fourier amplitude, the object phase information is naturally and inherently encoded in scattered light bispectrum (the Fourier transform of triple-correlation), and can also be extracted from a single high-resolution speckle pattern, based on which we present a single-shot imaging scheme to deterministically and unambiguously retrieve diffraction-limited images of objects hidden behind scattering layers.

Single-shot multispectral imaging through a thin scatterer

“…The solution is to use instead process the recorded speckle data using bispectrum processing (e.g. [8]) which recovers the absolute phase of the object up to an overall phase gradient. The recovered object from bispectrum processing can then be used as an initial-guess in further runs of an iterative phase retrieval algorithm to further refine the result.…”

Imaging objects through scattering layers and around corners by retrieval of the scattered point spread function

“…Indeed, it has been demonstrated that a speckle pattern propagated through clear space contains enough information to reconstruct the image of an object [5]. Recently, a variety of approaches have been demonstrated to solve this problem, such as time-of-flight imaging [6], time reversal or phase conjugation [7][8][9][10][11][12][13][14], transmission matrix measurement [15][16][17][18], wavefront shaping technique [19][20][21][22][23], digital holography [24][25][26][27], speckle auto-correlation method [28][29][30][31][32][33][34], and other speckle correlation methods [35,36]. The transmission matrix fully characterizes the effect of a scattering medium.…”

Single-shot memory-effect video

“…To further improve the accuracy of the resulting ME video and potentially make it more robust to imperfect recovery of the associated speckle subframes, alternative approaches to the image recovery may be used. 28 , 29 …”