Quantitative phase imaging via the holomorphic property of complex optical fields

TL;DR

This paper explores the use of the holomorphic property of complex optical fields to improve quantitative phase imaging, employing analytic continuation and complex analysis theorems to understand and validate imaging conditions.

Contribution

It introduces a novel interpretation of phase imaging via the Hilbert transform as analytic continuation and proves imaging conditions using Rouche's theorem, linking complex analysis with holography.

Findings

Validated imaging conditions with computational and experimental data

Identified deviations from Kramers-Kronig holography conditions

Provided a new perspective for holographic imaging based on complex analysis

Abstract

An optical field is described by the amplitude and phase, and thus has a complex representation described in the complex plane. However, because the only thing we can measure is the amplitude of the complex field on the real axis, it is difficult to identify how the complex field behaves throughout the complex plane. In this study, we interpreted quantitative phase imaging methods via the Hilbert transform in terms of analytic continuation, manifesting the behavior in the whole complex plane. Using Rouche's theorem, we proved the imaging conditions imposed by Kramers-Kronig holographic imaging. The deviation from the Kramers-Kronig holography conditions was examined using computational images and experimental data. We believe that this study provides a clue for holographic imaging using the holomorphic characteristics of a complex optical field.