Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework

Abstract

The estimation of phase errors from digital-holography data is critical for applications such as imaging or wave-front sensing. Conventional techniques require multiple i.i.d. data and perform poorly in the presence of high noise or large phase errors. In this paper we propose a method to estimate isoplanatic phase errors from a single data realization. We develop a model-based iterative reconstruction algorithm which computes the maximum a posteriori estimate of the phase and the speckle-free object reflectance. Using simulated data, we show that the algorithm is robust against high noise and strong phase errors.

Imaging through distributed-volume aberrations using single-shot digital holography

“…The resulting data are sensitive to phase errors caused by index-of-refraction perturbations in, for example, the atmosphere or optical systems. With this in mind, we can estimate these phase errors directly from the DH data for wavefront sensing purposes or to digitally correct aberrated images [2][3][4][5][6].…”

“…Recently, we developed a model-based iterative reconstruction (MBIR) algorithm for jointly computing the maximum a posteriori (MAP) estimates of the phase errors, ϕ, and the real-valued reflectance, r, from a single data realization-a process referred to here as single-shot DH [5]. We define the reflectance as r Ejgj 2 , where E· indicates the expected value [7].…”

“…Reconstructing r, rather than g, allows us to leverage its higher spatial correlation to better constrain the estimation process and produce more accurate estimates of the phase errors with fewer data and less signal, compared to IS algorithms [5,6].…”

“…[2] and the MBIR algorithm in Ref. [5] were designed for the estimation and correction of phase errors that are isoplanatic. In general, isoplanatic phase errors (IPEs) result in a shift-invariant point spread function (PSF) in the image domain.…”

“…Importantly, the IS and MBIR algorithms in Refs. [2] and [5] can only correct for a single PSF across the entire image field of view (FOV). Thus, in the presence of APEs, these algorithms cannot obtain diffraction-limited performance.…”