Object Wave Reconstruction Research Articles

Enhanced fixed plane phase retrieval using wavelength-to-distance transformation and unordered propagations

Stagnation errors in iterative smooth object wavefront reconstruction occur because of insufficient intensity variation despite employing experimental methods that increase intensity variation such as the use of multiple illumination wavelengths. In this study, an algorithmic technique for optimized multiple wavelength phase retrieval that uses wavelength-to-distance transformation and unordered wave propagations sequence is demonstrated. Simulations show that the technique significantly accelerates the reconstruction compared to conventional methods based on sequential propagations. The number and tuning range (or spacing) of the illumination wavelengths are also optimized resulting in the enhanced reconstruction of the test object waves used. The main advantage of the technique is the reduced number of illumination wavelengths needed for enhanced object wave reconstruction.

Compressive complex wave retrieval from a single off-axis digital Fresnel hologram for quantitative phase imaging and microlens characterization

A compressive sensing (CS) approach is proposed for the complex wave retrieval algorithm from single off-axis digital Fresnel holography to improve the accuracy of quantitative phase measurement. The linear model of non-linear holographic process used in the complex wave retrieval algorithm is utilized to meet the linearity requirement of the proposed CS implementation presented in this paper. The error in object wave reconstruction due to the approximations used in complex wave retrieval algorithm is compensated by combining it with CS approach. A Mach–Zehnder interferometric geometry in transmission and off-axis mode in the Fresnel domain is used to record the digital hologram. The numerical simulations and experimental results are presented to demonstrate and validate the proof of the concept and to compare CS frame work with conventional complex wave retrieval algorithm. The proposed algorithm is tested for the microlens sample characterization by considering the parameters such as height, diameter and radius of curvature. A Haar wavelet based object wave sparsification is used in the experiment for the prudent phase reconstruction in the CS approach. The proposed method enables an improved and accurate object phase reconstruction, with minimal noise such as distortions or speckles with respect to the conventional complex wave retrieval method.

High-precision phase-shifting interferometry with spherical wavefront reference

An advanced phase-shifting interferometry approach with a spherical wavefront reference is proposed to improve the quality of the holographic image by avoiding errors caused by noncollimated reference and lowering the resolution of the recording device. By considering not only the real amplitude but also the phase distribution of a spherical wavefront reference, a singular object-wave reconstruction formula is deduced. The suggested method here can work without using the collimator in the reference wave and can then remove all the errors incurred by it. Computer simulations demonstrate that this technique is more convenient in the recording process and can improve the precision of the reconstructed wavefront by more than one order of magnitude after considering the real reference amplitude. Optical experiment results show the feasibility and effectiveness of this method.

Analysis and correction of object wavefront reconstruction errorsin two-step phase-shifting interferometry

The method of calculating and correcting object wave reconstruction errors caused by phase shift errors in two-step phase-shifting interferometry is studied systematically. Based on the principle of random distribution and the amplitude-phase independence of diffractive object wave, the expression of objective wave reconstruction error is introduced and the formula for that in the two-step standard algorithm is deduced. The automatic error correction method is suggested by further analyzing the structures, the characters of those errors caused by phase shift errors, and the objective expression. By the proposed method, the reconstructive amplitude and phase errors can be corrected at the same time through simple operation on the objective complex amplitude reconstructed by the standard two-step method without the additional measurement or the acknowledge of phase shift. The computer simulations are carried out to verify the effectiveness of this method, and the results show that the method is robust and reduces the effect of phase shift error on object wave-front reconstruction by about 2 orders of magnitude. Optical experiments also indicate that this method is effective and efficient.

Object-wave Reconstruction by Carbon-Film-Based Zernike- and Hilbert-Phase Plate Microscopy: A Theoretical Study Not Restricted to Weak Phase Objects

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.

Object wave reconstruction by phase-plate transmission electron microscopy

A method is described for the reconstruction of the amplitude and phase of the object exit wave function by phase-plate transmission electron microscopy. The proposed method can be considered as in-line holography and requires three images, taken with different phase shifts between undiffracted and diffracted electrons induced by a suitable phase-shifting device. The proposed method is applicable for arbitrary object exit wave functions and non-linear image formation. Verification of the method is performed for examples of a simulated crystalline object wave function and a wave function acquired with off-axis holography. The impact of noise on the reconstruction of the wave function is investigated.

Object wave reconstruction by speckle illumination and phase retrieval

An innovative setup for the speckle-based phase retrieval method is proposed. In the conventional setup, a plane wave illuminates the test object and the transmitted wavefront is incident on a diffuser aperture generating a speckle field. The sampled speckle intensities at axially displaced planes are input into a phase retrieval algorithm based on a wave propagation equation. In the new setup, the arrangement of the diffuser and the object is reversed. A plane wave incident on the diffuser generates a speckle field which, in turn, is used to illuminate the object. The transmitted wavefront is then directed to the camera sensor. The advantage of the proposed setup is the increased resolution since the limiting aperture is the full area of the sensor.

A non-iterative method for phase-shift estimation and wave-front reconstruction in phase-shifting digital holography

This paper derives an analytical formula for extracting the amount of phase-shift in phase-shifting digital holography when the object wave intensity can be measured, which is obtained by simply solving the object wave reconstruction equation. Since it eliminates the requirements of approximation and iteration in existing techniques, a much faster processing speed can be obtained. It also has higher estimation accuracy than those iterative methods with a large iterative step size.

Effects of measurement errors on both the amplitude and the phase reconstruction in phase-shifting interferometry: a systematic analysis

In many applications of phase-shifting interferometry (PSI) the actually recorded object wave is the diffraction field of an object surface. In this case not only the phase error but also the amplitude error in the retrieval process have effects on the object wave reconstruction in its original plane. In this paper, for the first time that we know, the amplitude errors in wave reconstruction in PSI are discussed systematically. Some general relations between the amplitude errors and the phase errors for three commonly encountered error sources, namely the phase shift error, the light source intensity fluctuation and the detector nonlinearity, are revealed. The analytical expressions of the amplitude and phase errors for six frequently used algorithms in PSI are derived. The statistical variances of the two kinds of error are introduced to describe the overall performance of these algorithms and are quantitatively calculated. A series of computer simulations are also given as a verification of our analyses. These results can be used for evaluating the complete wave errors in PSI and developing new methods for their correction.

Development and performance of a fast fibre-plate coupled CCD camera at medium energy and image processing system for electron holography

A new slow-scan CCD camera with a readout speed of either 2 MHz or 150 kHz has been developed for electron microscopy at medium energy. Rules for the design of electron image converters will be presented, and the most relevant data - such as sensitivity, modulation transfer function (MTF), and detective quantum efficiency (DQE) - of two different scintillator types (single-crystal YAG and poly-crystal P20) are measured. The camera is fully integrated into the image processing system VIPS-1000, which is designed for electron microscopy including remote control functions. The modular software package EM-MENU contains a broad range of functions optimized for fast and user-friendly operation of the TEM. Two application programs for object wave reconstruction by off-axis holography or focus variation will be presented.