Sparsity-based single-shot subwavelength coherent diffractive imaging

Abstract

Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely diffracting intensity pattern. An important goal of such lensless imaging methods is to study the structure of molecules that cannot be crystallized. Ideally, one would want to perform CDI at the highest achievable spatial resolution and in a single-shot measurement such that it could be applied to imaging of ultrafast events. However, the resolution of current CDI techniques is limited by the diffraction limit, hence they cannot resolve features smaller than one half the wavelength of the illuminating light. Here, we present sparsity-based single-shot subwavelength resolution CDI: algorithmic reconstruction of subwavelength features from far-field intensity patterns, at a resolution several times better than the diffraction limit. This work paves the way for subwavelength CDI at ultrafast rates, and it can considerably improve the CDI resolution with X-ray free-electron lasers and high harmonics.

Compressive phase retrieval via generalized approximate message passing

“…When the sparsity rate λ in (18) is unknown, it can be learned using the EM-BG procedure described in [44]. In most cases, improved performance is obtained when a Gaussian mixture (GM) pdf is used in place of the Gaussian pdf in (18) [44].…”

“…For example, when all coefficients x n are known to be real-valued or positive, the circular-Gaussian pdf in (18) should be replaced by a real-Gaussian or truncated-Gaussian pdf, respectively, or even a truncated-GM [45]. Furthermore, when certain coefficient subsets are known to be more or less sparse than others, a non-uniform sparsity [46] rate λ n can be used in (18).…”

Speckle correlation resolution enhancement of wide-field fluorescence imaging

“…2(g)]. Fortunately, it is often possible to infer the lost phase information using an iterative phaseretrieval algorithm [31][32][33][34]. In essence, our approach relies on reducing the light-scattering problem to a phase-retrieval problem.…”

Subsampled phase retrieval for temporal resolution enhancement in lensless on-chip holographic video

“…Examples include a known finite sample support [18,19], sparsity [20], non-negativity or an intensity histogram [21]. Several recent works examine how sample sparsity permits accurate sample reconstruction from a limited number of holographic measurements [15,[22][23][24][25][26][27][28][29][30]. To the best of our knowledge, no work has yet examined whether prior knowledge of sample support alone may also relax required in-line holographic image readout rates, nor has demonstrated that such a modified phase retrieval process can improve the frame rate of on-chip holographic video.…”