Abstract
We propose a new method for phase retrieval that uses partially coherent illumination created by any arbitrary source shape in Köhler geometry. Using a stack of defocused intensity images, we recover not only the phase and amplitude of the sample, but also an estimate of the unknown source shape, which describes the spatial coherence of the illumination. Our algorithm uses a Kalman filtering approach which is fast, accurate and robust to noise. The method is experimentally simple and flexible, so should find use in optical, electron, X-ray and other phase imaging systems which employ partially coherent light. We provide an experimental demonstration in an optical microscope with various condenser apertures.
Highlights
IntroductionIntensity images contain no information about the phase of ψ(x, y)
The ‘phase problem’ can be summarized as the need to recover a sample’s complex-field, ψ(x, y), from measurements of intensity, I(x, y) = |F{ψ(x, y)}|2, in an optical system described by the operator F{·}
We demonstrate our methoEdxpeexrpimereinmtaelnrteaslulylt ignivaenNsiokuornceTsEha3p0e0 microscope (Fig. 1) with broadband illumination centereidnfaorromuantidonwavelength 550 nm
Summary
Intensity images contain no information about the phase of ψ(x, y). With a suitable choice of optical system, F, the sample’s phase variations cause intensity variations at the camera. The first goal of phase imaging is to design an optical system for transferring phase into intensity information (the forward problem). Any complex transfer function will induce phase contrast; the ideal choice of F involves tradeoffs between experimental complexity, cost, accuracy, and the sample itself [1]. The transfer function for defocus is well-studied [8, 9] and can be tuned by varying defocus distance, z. Though we use here a stack of images at varying defocus (Fig. 1), we note that our algorithm is general and can be adapted to any appropriate optical system
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