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Digital Holography and Phase Retrieval

Profile image of TATIANA ALIEVATATIANA ALIEVA

2011, Holography, Research and Technologies

https://doi.org/10.5772/13993
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Related papers

Realization of holographic optics based interferometer for study of phase objects
Amit Kumar Sharma

2004

The paper describes different configurations for realization of a simple, compact and robust holographic optics based interferometer, which makes use of minimal bulk optical components. The optical arrangements in the proposed interferometer set-ups involve a very simple alignment procedure and conventional holographic recording material is used in the formation of holographic optical elements. Recording schemes for the formation of holographic optical elements and the related techniques for the realisation of three different interferometer set-ups along-with the experimental results have been presented. The proposed interferometer set-ups are quite suitable for performing optical test studies on phase (transparent) objects in real time.

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Reconstruction of Digital Holograms by Iterative Phase Retrieval Algorithm:Improvements and Analysis
john sheridan

Digital Holography and Three-Dimensional Imaging, 2016

Iterative phase retrieval usually requires a good initial guess for the phase. In this paper, we consider two improvements to a recently proposed scheme (Opt. Eng. 55 (3), 033106 (2016)) to acquire the initial guess from a digital holographic system. This setup is simpler than phase-shifting interferometry, and suppresses the twin image and dc terms without the resolution trade-off involved in off-axis holography. In this paper, we show the benefits of ensuring the propagation algorithm is unitary. We also use a recently proposed iterative phase retrieval algorithm which uses a combination of the Gerschberg-Saxton and hybrid input-output algorithms, and demonstrate the benefit of this algorithm for avoiding stagnation of the algorithm.

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Phase-shifting digital holography in image reconstruction
Vivi Tornari

Journal of Shanghai University, 2006

A phase-shifting digital holography scheme developed to investigate internal defects in artworks is described. Phase-shifting is utilized to obtain a clear reconstructed object wave from a rough surface texture. A reverse-transform algorithm is employed to reconstruct the object wave on its original position of unknown distance or the imaging position from the object wave information on the holographic plane. To get the clearest reconstruction the exact registration of the unknown distance is determined by applying the intensity sum as the auto-focusing function. The spatial resolution of the reconstruction image is also investigated for a variety of affecting factors. Laboratory results of reconstruction images under deformation are presented.

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Phase measurement via in-line digital holographic microscopy
Weijuan Qu

2008

In-line digital holographic microscopy as a phase measurement tool for the inspection of micro-components is presented. Light diffracted by the micro-components interferes with the directly propagating beams to give the in-line digital hologram recorded by the CCD camera. The convolution method is used to calculate the diffractive propagation of the light in order to reconstruct the wavefront of the test specimen. A reference hologram without the test specimen is recorded for the phase reconstruction. Finally, the method is applied on a phase grating to test its refractive index of the coating material.

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Phase Retrieval in Two-Step Quadrature Phase-Shifting Holography
Hongbo Zhang

This paper presents a simple and effective method, without the need for any additional recording of the intensity maps or tremendous iterative computations, to remove the complex zeroth-order term in the complex hologram for phase retrieval in two-step quadrature phase-shifting holography by utilizing the intensity in certain area in the complex hologram. We select a particular area in the complex hologram where there is negligible diffraction from the test sample to calculate the intensity. The calculated intensity value allows us to eliminate the complex zeroth-order term from the complex hologram. Exact phase distribution can then be reconstructed by using the new complex hologram without the zeroth-order and twin image noise. Experiment results have been performed to verify the effectiveness and feasibility of our proposed method.

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The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement
yimo Zhang

Frontiers of Electrical and Electronic Engineering in China, 2007

Phase-shifting measurement and its error estimation method were studied according to the holographic principle. A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period (N-step phase-shifting function for short) was proposed. In N-step phase-shifting measurement, the interferograms are seen as a series of in-line holograms and the reference beam is an ideal parallel-plane wave. So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave. In ideal conditions, the proposed method is a kind of synchronous superposition algorithm in which the complex amplitude is separated, measured and superposed. When error exists in measurement, the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method. In the above method, the N+1-step phaseshifting function can be obtained from the N-step phaseshifting function. It shows that the N-step phase-shifting function can be separated into two parts: the ideal N-step phase-shifting function and its errors. The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function. The difficulties of the error estimation in phaseshifting phase measurement were restricted by this error estimation method. Meanwhile, the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.

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Holography: an interpretation from the phase-space point of view
Guohai Situ

Optics letters, 2007

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phase-retrieval techniques.

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Infrared Holography for Wavefront Reconstruction and Interferometric Metrology
Massimiliano Locatelli

Advanced Holography - Metrology and Imaging, 2011

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Phase recovering algorithms for extended objects encoded in digitally recorded holograms
Patrice Tankam

EPJ Web of Conferences, 2010

The paper presents algorithms to recover the optical phase of digitally encoded holograms. Algorithms are based on the use of a numerical spherical reconstructing wave. Proof of the validity of the concept is performed through an experimental off axis digital holographic set-up. Two-color digital holographic reconstruction is also investigated. Application of the color set-up and algorithms concerns the simultaneous two-dimensional deformation measurement of an object submitted to a mechanical loading.

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Physical phase compensation in digital holographic microscopy
Oi Choo Chee

2009

In digital holographic microscopy (DHM), using microscope objective for sample imaging may introduce additional spherical phase curvature. It can be physically compensated by introducing a same phase curvature in the reference beam. A theoretical analysis of the wavefront interefence between the reference beam and object beam is provided to indicate the physical phase compensation. The spatial frequency spectra of the hologram are involved for the judgement of the physical phase compensation status. Different DHM setups are presented in order to fulfill the physical compensation of the introduced spherical phase. In the DHM setups based on the Michelson interferometric configuration, an adjustable lens is used to perform the quasi physical phase compensation during the hologram recording. In the common-path DHM setups, digital off-axis holograms are recorded by using a single cube beam splitter in a non-conventional configuration so as to both split and combine a diverging spherical wavefront emerging from a microscope objective. A simple plane numerical reference wavefront is used for the reconstruction and the correct quantitative phase map of the test object is obtained after phase unwrapping. Its simplicity of the presented setups make it easy to be well aligned and with lower cost.

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Digital holography and phase retrieval: a theoretical investigation
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Iterative Phase Retrieval (PR) techniques represent an alternative means to Digital Holography (DH) for estimating the complex amplitude of an optical wavefront. To achieve a high-resolution reconstruction from a digital hologram, one must use Phase-Shifting Interferometric (PSI) techniques to remove the DC and twin image terms that are a feature of holographic recordings. Unfortunately this approach is not suitable for imaging dynamic events, since a minimum of 3 sequential captures, are typically required and the scene cannot change during this recording process. PR algorithms may provide a solution to this dynamic imaging problem, however these algorithms provide solutions that are not unique and hence cannot ensure an accurate solution to the problem.

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Phase map retrieval in digital holography: avoiding the undersampling effect by a lateral shear approach
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In Digital Holography (DH) the numerical reconstruction of the whole wavefront refracted or reflected by a sample object allows one to extract the wrapped phase map mod, 2π. In fact, since the hologram is coded numerically as a digitized image, both the wavefront amplitude and phase can be reconstructed simultaneously to provide amplitude and phase contrast imaging. The resolution in the image plane is the reconstruction pixel size that depends on wavelength, reconstruction distance and the size of the CCD recording area. Efforts to improve the resolution of DH reconstructions have been accomplished, following various strategies: increasing of the hologram aperture by moving the camera in different positions or even by using synthetic aperture approaches, using a diffraction grating to record digital holograms with a wider solid angle in the object beam, or using multiple sources and/or multiple acquisitions. Although all of these methods allow one to increase the spatial resolution, one more complication exists concerning the loss of resolution that occurs in the usual DH reconstruction approaches. It can occur that the reconstructed wrapped phase map in the image plane is undersampled because of the limited pixel size which limits the spatial bandwidth of the reconstructed image. In such a case the phase distribution cannot be retrieved correctly by the usual unwrapping procedures. We show that the use of the digital Lateral-Shearing Interferometry (LSI) approach in DH provides the correct reconstruction of the phase map in the image plane, even in extreme cases where the phase profile changes very rapidly. We demonstrate the effectiveness of the method in a particular case where the profile of a highly curved silicon micro-electromechanical system membrane has to be reconstructed.

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Phase retrieval without unwrapping by single-shot dual-wavelength digital holography
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A phase retrieval method by using single-shot dual-wavelength digital holography is proposed. Each single wavelength hologram is extracted from the color CCD recorded hologram at one exposure, and the unwrapped phase image of object can be reconstructed directly. Different from the traditional multiple wavelength phase unwrapping techniques, any single complex wavefronts at different wavelengths have no need to be calculated any more. Thus, the phase retrieval is computationally fast and straightforward, and the limitations on the total optical path difference are significantly relaxed. The practicability of the proposed method is demonstrated by both simulated and experimental results.

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We propose a technique in which intensity images are reconstructed from a digital hologram to provide inputs for the transport-of-intensity equation for unwrapped phase recovery. By doing this, we avoid shifting of the sample or the camera in the experiment, a method commonly employed while using the method of transport-of-intensity equation for phase retrieval. Computer simulations as well as experimental results have been demonstrated to verify the effectiveness of the proposed idea. The underlying numerical technique can also be viewed as an alternative to existing phase-unwrapping algorithms.

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This study presents an optical assembly and digital reconstruction method that is based on digital holography for characterizing transparent objects. The image-plane optical setup is based on a versatile Mach-Zehnder interferometer for the formation of controlled parallel fringe patterns, of tens micrometers of separations or less. The numerical reconstruction of the propagated wavefront by the hologram is performed by the Fresnel-Kirchhoff transform, and it is used of three ways: (a) interferometric phase reconstruction (as in interferometry) in the phase object position, (b) reconstruction of the wavefront amplitude at a determined distance from the object (shadowgraph technique), and (c) a composed digital reconstruction process of the wavefront amplitude, defined by a digital optical assembly for the selection of angular deflections produced by the phase object (schlieren technique). The resolving power of holographic reconstruction methodology proposed is determined by the sens...

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    Phase retrieval,i.e.the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications, such as X-ray crystallography, diffraction imaging, optics, quantum mechanics and astronomy. This problem has confounded engineers, physicists, and mathematicians for many decades. Recently, phase retrieval has seen a resurgence in research activity, ignited by new imaging modalities and novel mathematical concepts. As our scientific experiments produce larger and larger datasets and we aim for faster and faster throughput, it is becoming increasingly important to study the involved numerical algorithms in a systematic and principled manner. Indeed, the past decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval. In this paper we will review these recent advances from a numerical viewpoint.

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