Speckle-Correlation Scattering Matrix Approaches for Imaging and Sensing through Turbidity

Abstract

The development of optical and computational techniques has enabled imaging without the need for traditional optical imaging systems. Modern lensless imaging techniques overcome several restrictions imposed by lenses, while preserving or even surpassing the capability of lens-based imaging. However, existing lensless methods often rely on a priori information about objects or imaging conditions. Thus, they are not ideal for general imaging purposes. The recent development of the speckle-correlation scattering matrix (SSM) techniques facilitates new opportunities for lensless imaging and sensing. In this review, we present the fundamentals of SSM methods and highlight recent implementations for holographic imaging, microscopy, optical mode demultiplexing, and quantification of the degree of the coherence of light. We conclude with a discussion of the potential of SSM and future research directions.

Single‐Shot Reference‐Free Holographic Imaging using a Liquid Crystal Geometric Phase Diffuser

“…From the measured speckle pattern, the SSM method is applied using the designed TM. [ 9,10 ] To describe the reconstruction sequence, let us consider the orthonormal basis of the input field, $$U = \{{\bf{e}}_1,{\bf{e}}_2,\ldots,{\bf{e}}_N\}$$. The basis can freely be defined such that it satisfies $${\bf{x}} = \sum\nolimits_{i = 1}^N {{x_i}{{\bf{e}}_i}}$$, where $${\bf x}\in {\mathbb C}^{N}$$ is an unknown input field.…”

“…[ 3 ] To address this, various reference‐free holographic imaging techniques have been developed. [ 4–9 ] Because phase is not a directly measurable quantity, most reference‐free phase imaging methods must either make a priori constraints on an input field or conduct multiple measurements. For example, coherent diffractive imaging utilizes sample support, [ 4 ] integration methods assume a well‐defined phase (no dark points) over the entire field of view, [ 5 ] and the transport of intensity equation methods [ 6 ] and ptychography exploit axial and lateral sample scanning to increase the number of sampling points.…”

“…The constraint‐free feature is derived from the reconstruction algorithm, which only utilizes the given transmission matrix (TM) of the used diffuser and the mathematical relation between the diffused speckle fields. [ 9,10 ]…”

Direct high-resolution X-ray imaging exploiting pseudorandomness

“…In CSI, we transform the sample field into a random speckle before the measurement using an X-ray diffuser 36 . Although the phase of the speckle is immeasurable either, the complex-valued sample field can be uniquely reconstructed from the magnitude image through the pseudorandomness of speckle [37][38][39][40] . Our CSI exploits a designed X-ray diffuser after the sample instead of a zone plate (Fig.…”

Improving Compressed Sensing Image Reconstruction Based on Atmospheric Modulation Using the Distributed Cumulative Synthesis Method

“…This method requires auxiliary equipment in most cases, which limits its application in practice. Speckle correlation imaging [10][11][12] based on the "memory effect" [13] of the scattering medium has also attracted research interest. The experimental requirements of speckle-related methods are relatively simple, but the imaging field of view is limited by the memory effect range, which is inversely proportional to the medium thickness.…”