Phase-shifting real-time holographic interferometry that uses bismuth silicon oxide crystals

A bismuth silicon oxide crystal is used in the diffusion regime as a dynamic recording medium in a real-time holographic interferometer based on anisotropic self-diffraction. This device is connected with an interferogram-analysis method that uses the phase-shifting technique for quantitative measurement of diffusive-reflecting object deformations. In addition to the usual error sources in phase shifting, the temporal interferogram erasure is studied and is found weakly perturbative for the measured phase. It is shown that quantitative measurements are possible for low-intensity object beams (8 μW/cm(2)) and a large observed area. Apractical situation of defect monitoring in a composite structure is presented.     

Phase-shifting real-time holographic interferometry applied to load transmission evaluation in dried human skull

Phase-shifting real-time holography with photorefractive Bi(12)SiO(20) crystal as holographic recording medium applied to load transmission evaluation and tension dissipation on a dried human skull under loading is presented. The applied loading stands as a simulation of isolated contraction (SIC) of some masticatories muscles. The four-frames phase-shifting technique and the unwrapping branch-cut technique were used to obtain the phase map. The quantitative results show the feasibility of the employed system in the study of microdisplacements in the skull structure provided by SIC.     

Phase-shifting interferometry immune to vibration

A modification of phase-shifting interferometry is proposed for microsurface profiling of flat surfaces under vibrating conditions. With this technique the required phase shift, achieved by quarter-wave plates and polarizers, is free of errors associated with motion. A nearly common optical-path configuration is achieved, and the effect of environment is reduced. The effect of environment on the optical system is also studied. Moreover, the measurement of phase is instantaneous, which increases the versatility of this technique to measure vibrating objects. Experiments were carried out on a smooth mirror surface excited with high-frequency vibrations, and the technique was found to be immune to vibrations of both high and low frequency.     

Phase-shifting algorithms for electronic speckle pattern interferometry

A set of innovative phase-shifting algorithms developed to facilitate metrology based on electronic speckle pattern interferometry (ESPI) are presented. The theory of a phase-shifting algorithm, called a (5,1) algorithm, that takes five phase-shifted intensity maps before a specimen is deformed and one intensity map after a specimen is deformed is presented first. Because a high-speed camera can be used to record the dynamic image of the specimen, this newly developed algorithm has the potential to retain the phase-shifting capability for ESPI in dynamic measurements. Also shown is an algorithm called a (1,5) algorithm that takes five phase-shifted intensity maps after the specimen is deformed. In addition, a direct-correlation algorithm was integrated with these newly developed (5,1) or (1,5) algorithms to form DC-(5,1) and DC-(1,5) algorithms, which are shown to improve significantly the quality of the phase maps. The theoretical and experimental aspects of these two newly developed techniques, which can extend ESPI to areas such as high-speed dynamic measurements, are examined in detail.     

Phase-shifting interferometry and maximum-likelihood estimation theory

A novel means of quantitatively assessing the performance of a phase-shifting interferometer is presented. We show how maximum-likelihood estimation theory can be used to estimate the surface-height profile from four noisy phase-shifted measurements. Remarkably, the analytical expression for the maximum-likelihood estimator is identical to the classical four-step algorithm, thereby rooting the traditional method on a statistically sound foundation. Furthermore, a Monte Carlo experiment shows the maximum-likelihood estimator is unbiased and efficient, achieving the theoretical Cramer-Rao lower bound on the variance of the error. This technique is then used to show that the performance is a function of the ratio of the irradiances from each arm, with the optimal performance occurring, not surprisingly, when the irradiances from the two arms are equal.     

Phase-shifting interferometry with uncalibrated phase shifts

A computationally efficient algorithm for phase-shifting interferometry with imprecise phase shifts is developed. It permits the use of an uncalibrated phase shifter and is also insensitive to spatial intensity variations. The measurement has both spatial and temporal aspects. Comparisons are made between pixels within the same interferogram, and these comparisons are extended across a set of interferograms by a maximum-minimum procedure. A test experiment is performed and confirms the theoretical results. An additional advantage of the algorithm is that an error measure can be developed. This error measure is used to implement an error correction scheme.     

Phase-shifting point-diffraction interferometry at 193 nm

Phase-shifting point-diffraction interferometry at the 193-nm wavelength suitable for highly accurate measurement of wave-front aberration is introduced. The interferometer preserves the advantages of the previously described extreme-ultraviolet phase-shifting point-diffraction interferometer but offers higher relative efficiency. Wave-front measurement of an imaging system, operating at the 193-nm wavelength, is reported. Direct measurement of the refractive-index change in a deep-ultraviolet radiation-damaged fused-silica sample is also presented as an application.     

Phase-shifting interferometry by a covariance-based method

A novel generalized approach to phase-shifting interferometry in which phase distribution in an interferogram is evaluated in the presence of nonsinusoidal waveforms and piezoactuator device miscalibration is proposed. The approach is based on the underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets. The advantage of the proposed method lies in its ability to identify arbitrary phase-step values pixelwise from an interference signal buried in noise. The robustness of the proposed method is investigated by addition of white Gaussian noise during the simulations.     

Real-time color holographic interferometry

A new optical technique based on real-time color holographic interferometry has been developed for analyzing unsteady aerodynamic wakes in fluid mechanics or for measuring displacements and deformations in solid mechanics. The technique's feasibility is demonstrated here. It uses three coherent wavelengths produced simultaneously by a cw laser (mixed argon and krypton). Holograms are recorded on single-layer panchromatic silver halide (Slavich PFG 03C) plates. Results show the optical setup can be adjusted to obtain a uniform background color. The interference fringe pattern visualized is large and colored and exhibits a single central white fringe, which makes the zero order of the interferogram easy to identify. An application in a subsonic wind tunnel is presented, in which the unsteady wake past a cylinder is recorded at high rate.     

In-line digital holographic interferometry

An optical system based on in-line digital holography for the evaluation of deformations is described. In-line holograms are recorded on a CCD chip. The problem of overlapping twin images typical for the in-line arrangement is solved by digital reconstruction and filtering of the unwanted wave fronts. Two separate interferograms of an object under test in its undeformed and deformed states are recorded each on a CCD chip. The phases of the two wave fronts are obtained from the complex amplitudes of the digital reconstructed wave fronts, and the deformation is calculated from the phase differences. Experimental results are presented.     

High-speed digital holographic interferometry for vibration measurement

A system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser (10 W) and a high-speed CCD camera are used. Hundreds of holograms of an object that has been subjected to dynamic deformation are recorded. The acquisition speed and the time of exposure of the detector are determined by the vibration frequency. Two methods are presented for triggering the camera in order to acquire at a given phase of the vibration. The phase of the wavefront is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object.     

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Abstract

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.     

Modulation-enhanced sensitivity of holographic interferometry

A modulation-demodulation scheme substantially enhances diffusion-dominated-adaptive-interferometric sensitivity. The path length sensitivity is improved by converting a quadratic small-signal response, easily drowned in system noise, to a linear response by mixing with a strong phase modulation. This conversion also shifts low-frequency signals away from 1/f noise. Experimental results show 180 fm/ [square root]Hz displacement sensitivity for a 5 Hz signal with a few milliwatts of optical power, an improvement of 3 orders of magnitude over the unenhanced system.     

Eight-frame holographic interferometry system for transient plasma diagnostics

A multiframe technique that uses Fresnel holography is described. Splitting of the initial pulse by means of 50/50 beam splitters provides two sets of eight consecutive pulses with approximately the same energy but with different angles. Each interferogram is recorded separately. The technique has been used to obtain time-resolved Fresnel holographic interferograms of transient electrical discharges, such as Z pinch. A frequency-doubled, Q-switched Nd:YAG laser (6-ns FWHM) is used. A delay between consecutive pulses of 10 ns is achieved, and it is mainly limited by the physical size of the laboratory. Interferograms obtained on a gas-embedded Z pinch are shown.     

Orthographic double-beam holographic interferometry for limited-view optical tomography

A simultaneous algebraic reconstruction technique (SART) that was first applied to limited-view optical tomography reconstruction of a three-dimensional asymmetric refractive-index field or a temperature distribution is presented and numerically simulated. Within two orthographic-view directions and limited view ranges, the reconstruction speed and accuracy of the SART are adequate. A new orthographic double-beam holographic-interferometric system from which multidirectional interferometric data can be obtained is first built. An asymmetric heat air-flow field is experimentally investigated by the use of orthographic double-beam holographic interferometry with double exposures. The temperatures reconstructed with the SART are consistent with those measured with a thermocouple.     

Time-averaged in-line digital holographic interferometry for vibration analysis

Time-averaged in-line digital holography is applied for vibration analysis. In particular, by use of a double-exposure approach, simultaneous determination of vibration mode shape and mean static state deformation during a vibration cycle are obtained. The subtraction of two numerically reconstructed digital holograms recorded at the same resonant frequency but with a small difference in amplitude shows the mixing of Bessel-type time-averaged fringes owing to vibration and of the double-exposure fringes owing to differences in the mean deformation of the object. It is shown that separation of these fringe patterns can be readily accomplished numerically. An experimental demonstration of this effect by use of in-line digital holography for relatively small membranes is demonstrated.