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Journal ArticleDOI

Quantitative phase imaging via the holomorphic property of complex optical fields

TL;DR: In this article , the authors 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, and proved the imaging conditions imposed by Kramers-Kronig holographic imaging.
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.

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References
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Journal ArticleDOI
TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.
Abstract: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

5,210 citations

Journal ArticleDOI
TL;DR: An imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image, which can also correct for aberrations and digitally extend a microscope's depth-of-focus beyond the physical limitations of its optics.
Abstract: We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope’s depth of focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 µm, a field of view of ∼120 mm^2 and a resolution-invariant depth of focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

1,363 citations

Journal ArticleDOI
TL;DR: Off-axis holograms recorded with a CCD camera are numerically reconstructed with a calculation of scalar diffraction in the Fresnel approximation and the zero order of diffraction and the twin image are digitally eliminated by means of filtering their associated spatial frequencies in the computed Fourier transform of the hologram.
Abstract: Off-axis holograms recorded with a CCD camera are numerically reconstructed with a calculation of scalar diffraction in the Fresnel approximation. We show that the zero order of diffraction and the twin image can be digitally eliminated by means of filtering their associated spatial frequencies in the computed Fourier transform of the hologram. We show that this operation enhances the contrast of the reconstructed images and reduces the noise produced by parasitic reflections reaching the hologram plane with an incidence angle other than that of the object wave.

948 citations

Journal ArticleDOI
TL;DR: This Review presents the main principles of operation and representative basic and clinical science applications of quantitative phase imaging, and aims to provide a critical and objective overview of this dynamic research field.
Abstract: Quantitative phase imaging (QPI) has emerged as a valuable method for investigating cells and tissues. QPI operates on unlabelled specimens and, as such, is complementary to established fluorescence microscopy, exhibiting lower phototoxicity and no photobleaching. As the images represent quantitative maps of optical path length delays introduced by the specimen, QPI provides an objective measure of morphology and dynamics, free of variability due to contrast agents. Owing to the tremendous progress witnessed especially in the past 10–15 years, a number of technologies have become sufficiently reliable and translated to biomedical laboratories. Commercialization efforts are under way and, as a result, the QPI field is now transitioning from a technology-development-driven to an application-focused field. In this Review, we aim to provide a critical and objective overview of this dynamic research field by presenting the scientific context, main principles of operation and current biomedical applications. Over the past 10–15 years, quantitative phase imaging has moved from a research-driven to an application-focused field. This Review presents the main principles of operation and representative basic and clinical science applications.

847 citations

Journal ArticleDOI
TL;DR: In this paper, the authors explore propagation through the Poynting vector and find two classes of phase, one of which is topological in origin, and even then only in specific well-defined circumstances.
Abstract: We demonstrate that interferometric imaging may be replaced by noninterferometric propagation-based techniques in many experiments. We explore propagation through the Poynting vector and find two classes of phase, one of which is topological in origin. Only this latter class may require interferometry to be determined, and even then only in specific well-defined circumstances. Our alternative definitions of phase are readily generalized to partially coherent radiation. Our analysis leads to an approach that is able to determine the absolute phase and the amplitude of a wave.

705 citations