Uncertainty analysis of temporal phase-stepping algorithms for interferometry

We have addressed the problem of the uncertainty evaluation of phase values rendered by two popular algorithms: the N-bucket and the (N + 1)-bucket, both used to exploit temporal phase-stepping techniques. These algorithms, are mainly affected by errors in the calibration of the piezoelectric transducers used to achieve the phase shift, external vibration and optical noise. We have characterized and compared the influences of these errors on the phase uncertainty. We applied a Monte Carlo-based technique of uncertainty propagation that allowed us to consider in the uncertainty evaluation the simultaneous contributions of different error sources. The uncertainty evaluation was performed for phase values in the range (0, 2π), with different values of N and assuming that the phase was calculated from fringe patterns generated by using either Moiré interferometry or electronic speckle-pattern interferometry. We found that the uncertainties associated with the phases rendered by both algorithms are similar and they can be significantly affected by the optical noise and the value of N.     

Instantaneous velocity measurement of dynamic deformation by digital holographic interferometry

A novel method for the instantaneous velocity measurement of dynamic deformation by digital holographic interferometry is proposed. During dynamic deformation, a series of digital holograms is recorded by a high-speed camera. At each pixel of the phase difference maps, phase and amplitude information are combined as complex phasor (CP). Each pixel can be then considered as an independent sensor and a sequence of complex phasors of such a sensor is analyzed by short time Fourier transform (STFT) along the time axis. A fast iterative algorithm is developed for the computation of instantaneous velocity. The displacement of each pixel can also be obtained by integration of the instantaneous velocity over time and phase unwrapping process is thus avoided. The performance of the proposed CP method is compared experimentally with the commonly used digital phase subtraction method.     

Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals

We report on processing the spectral interference signals by a new method based on a windowed Fourier transform applied in the wavelength domain. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral signal. Second, the feasibility of the method is confirmed in processing experimental data from a dispersive Michelson interferometer comprising a cube beamsplitter made of BK7 glass. From the retrieved spectral phase difference, the effective thickness of the beamsplitter is determined precisely.     

Determination of displacement derivative in digital holographic interferometry

Digital holography (DH) and digital shearography (DS) both play an important role in non-destructive evaluation. In this paper, a novel method based on digital holographic interferometry (DHI) and complex phasor (CP) is proposed to determine displacement derivative. An algorithm is employed to filter the imaginary and real parts of complex values without the need of direct phase manipulation. Two-dimensional short time Fourier transform (STFT) is employed subsequently to process wrapped phase maps. An experiment is conducted to demonstrate the validity of the proposed method.     

Evaluation of dynamic speckle activity using the empirical mode decomposition method

The empirical mode decomposition (EMD) method is used to process sequences of dynamic speckle patterns to segment the differential activity that presents a sample as a function of the spatial coordinates and time. The application of the method is illustrated by segmenting bruised regions in fruits. A discussion of the obtained results and a comparison with the use of the filter bank technique are also presented.     

Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography

Phase-shifting digital holographic technique is a powerful tool for the measurement of various physical parameters, such as object deformation and liquid or cell’s refractive index change. However, for an accurate measurement, phase-shifting error in the reference wave path is still a major issue. In this paper, three novel and simple algorithms are proposed to quantitatively detect and correct phase-shifting error for a pure phase object in two-step phase-shifting digital holography. Influence of phase-shifting error is illustrated, and the effectiveness of the proposed algorithms is demonstrated by numerical simulation results.     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

The Gouy phase shift of the highly focused radially polarized beam

The Gouy phase shift in the focal field of high-NA focused radially polarized beam has been investigated in detail. Analytical expression for the Gouy phase shift can be derived using tilted wave interpretation, which provides a reasonable prediction compared to vectorial diffraction numerical simulation. Using this method, irregular wave spacing in the vicinity of the focus can be revealed.     

Generalization of Carré equation

The present work offers new equations for phase evaluation in measurements. Several phase shifting equations with an arbitrary but constant phase shift between captured intensity signs are proposed. The equations are similarly derived as the so-called Carré equation. The idea is to develop a generalization of Carré equation that is not restricted to four images. Errors and random noise in the images cannot be eliminated, but the uncertainty due to their effects can be reduced by increasing the number of observations. An experimental analysis of the mistakes of the technique was made, as well as a detailed analysis of mistakes of the measurement. The advantages of the proposed equation are its precision in the measures taken, speed of processing and the immunity to noise in signs and images.     

Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample

This study demonstrates a simple method for attenuating the speckle noise generated by coherent multiple-scattered photons in optical-coherence tomography images. The method could be included among the space-diversity techniques used for speckle reduction. It relies on displacing the sample along a weakly focused beam in the sample arm of the interferometer, acquiring a coherent image for each sample position and adding the individual images to form a compounded image. It is proven that the compounded image displays a reduction in the speckle noise generated by multiple scattered photons and an enhancement in the intensity signal caused by single-backscattered photons. To evaluate its potential biomedical applications, the method is used to investigate in vitro a caries lesion affecting the enamel layer of a wisdom tooth. Because of the uncorrelated nature of the speckle noise the compounded image provides a better mapping of the lesion compared to a single (coherent) image.     

Optimally discriminant moments for speckle detection in real B-scan images

The paper presents and evaluates a speckle detection method for B-scan images. This is a fully automatic method and does not require information about the sensor parameters, which is often missing in retrospective studies.The characterization and posterior detection of speckle noise in ultrasound (US) has been regarded as an important research topic in US imaging, for improving signal-to-noise ratio by removing speckle noise and for exploiting speckle correlation information. Most of the existing methods require either manual intervention, the need to know sensor parameters or are based on statistical models which often do not generalize well to B-scans of different imaging areas. The proposed method aims to overcome those limitations.The main novelty of this work is to show that speckle detection can be improved based on finding optimally discriminant low order speckle statistics. In addition, and in contrast with other approaches the presented method is fully automatic and can be efficiently implemented to B-scan images.The method detects speckle patches using an ellipsoid discriminant function which classifies patches based on features extracted from optimally discriminant low order moments of the uncompressed intensity B-scan information. In addition, if the uncompressed signal is not available, we propose and evaluate a method for the estimation of this factor.The computation of low order moments using an optimality criteria, the decompression factor estimation and other key aspects of the method are quantitatively evaluated using both simulated and real (phantom and in vivo) data. Speckle detection results are obtained using again phantom and in vivo studies which show the validity of our approach. In addition, speckle probability images (SPI) are presented which provide valuable information about the distribution of speckle and non-speckle areas in an image.The presented evaluation and results show the effectiveness of our approach. In particular, the need for using discriminant analysis to determine the optimal discriminant power of the statistical moments and that this optimal value strongly depends on the characteristics and imaged tissues in the B-scan data.     

Fourier transforms method for measuring thermal lens induced in diluted liquid samples

Drawing on interferometry and Fourier analysis, this paper describes the use of a two-beam thermal lens technique for measuring thermo-optical properties in optical materials. The procedure consists of yield interference patterns deformed by a localized photothermal effect. The photothermal phase shift is locally induced by the pump beam focused on a tested sample located on an on-axis probe beam, which is the first arm of a Mach-Zehnder interferometer. The plane where the effect is localized is imaged onto a CCD camera. Then two interferograms are recorded: one without effect and the other one with the induced photothermal phase. Fourier analysis performed on these interferograms allow us to plot the thermal lens map and, therefore, to estimate thermo-optic constant of Malachite Green in water solution. The method is applied to measure low linear absorptions of a diluted sample of Rhodamine B in water solution at 633 nm, showing that the proposed technique allows to measure photothermal phase shift as low as 3.1 mrad at 8 mW of input power in diluted materials.     

Analysis of reflection speckle holograms in a BSO crystal

A theoretical and experimental study of speckle registering in photorefractive BSO crystals through reflection hologram geometry is implemented. The three-dimensional speckle nature is considered in the diffraction efficiency calculations. The interference process produces index-of-refraction gratings in the speckle volume via the photorefractive effect. It is demonstrated that the coupled-wave theory for reflection geometry allows explaining the diffraction efficiency behavior when the interaction length is properly taken into account. It means that the speckle depth is related with the interaction length. The speckle depth can be controlled by the imaging system pupil aperture diameter. Under this condition, the influence of the speckle depth on the diffraction efficiency is analyzed. An agreement between the numerical model based on the coupled-wave theory and the experimental results is obtained.     

Quality assurance in nano-scale analysis

Some methods of nano-scale analysis are on the threshold of being a standard method in industry and therefore quality assurance becomes important. But, at the present time, there are deficits in standardisation and validation of these methods. Therefore, we have organised method comparisons and interlaboratory comparisons to overcome these deficits. We report the results of an interlaboratory comparison in step-height determination by atomic force microscopy and the development of a reference material for laterally resolving methods of material analysis. Received: 2 September 2002 / Accepted: 2 September 2002 / Published online: 5 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-30/8104-1827, E-mail: mathias.senoner@bam.de     

Optimization of phase objects in 4f coherent imaging system for nonlinear refraction measurements

We numerically analyze the effects of radius and phase shift of phase objects on the diffraction image of the 4f coherent imaging system, a system used for measuring the third-order nonlinear refractive index. The selection of the aperture radius is discussed. We prove that when the phase object radius is 0.1 time of the aperture radius and the phase change of the phase object is 0.57π, one can get the highest sensitivity for nonlinear refraction measurement.     

Digital holographic interferometry applied to the study of tympanic membrane displacements

Quantitative studies of the mechanical properties of tympanic membrane (TM) are needed for better understanding of its role in detailed clinical evaluation, its research being of extreme importance because it is one of the most important structures of the middle ear. By finding the membrane's vibration patterns and quantifying the induced displacement it is possible to characterize and determine its physiological status. Digital holographic interferometry (DHI) has proved to be a reliable optical non-invasive and full-field-of-view technique for the investigation of different mechanical parameters of biological tissues, i.e., DHI has demonstrated an ability to detect displacement changes in quasi-real time and without the need to contact the sample's surface under study providing relevant information, such as clinical and mechanical sample properties. In this research fresh tympanic membrane specimens taken from post-mortem cats are subjected to acoustic stimuli in the audible frequency range producing resonant vibration patterns on the membrane, a feature that results in an ideal application for DHI. An important feature of this approach over other techniques previously used to study the tympanic membrane vibrations is that it only requires two images and less hardware to carry out the measurements, making of DHI a simpler and faster technique as compared to other proposed approaches. The results found show a very good agreement between the present and past measurements from previous research work, showing that DHI is a technique that no doubt will help to improve the understanding of the tympanic membrane's working mechanisms.     

Development of the Technique for Fabricating Submicron Moire Gratings on Metal Materials Using Focused Ion Beam Milling

A focused gallium ion （Ga＋） beam is used to fabricate micro/submicron spacing gratings on the surface of porous NiTi shape memory alloy （SMA ）. The crossing type of gratings with double-frequency （25001/mm and 50001/mm） using the focused ion beam （FIB） milling are successfully produced in a combination mode or superposition mode. Based on the double-frequency gratings, high-quality scanning electron microscopy （SEM） Moird patterns are obtained to study the micro-scale deformation of porous NiTi SMA. The grating fabrication technique is discussed in detail. The experimental results verify the feasibility of fabricating high frequency grating on metal surface using FIB milling.     

Uncertainty analysis of whole-field phase-differences retrieved from ESPI fringe patterns by using the Fourier transform method (FTM)

We have evaluated the uncertainty associated with the whole-field phase-differences retrieved by using the Fourier transform method (FTM), from a fringe pattern generated by electronic speckle pattern interferometry (ESPI). The phase-differences were induced by applying load to an elastic sample. The FTM involved the Fourier transform application to the fringe pattern, the isolation of the term carrying the phase information by applying a band-pass filter in the spatial frequency domain, and then the inverse Fourier transform application. Since the fringes in the analyzed pattern were adequately open, the FTM outcomes were presumed to be mainly affected by errors in the determination of both the width and the location of the applied filter mask. The influence of these error sources was assessed by using a Monte Carlo-based computer simulation. It implied evaluating the phase-differences a large number of times under the influence of the involved error sources. We found that the phase uncertainty depends strongly on the width of the applied filter mask; the influence of the other error sources considered into the uncertainty propagation was significantly smaller.     

A new possible method for decreasing the wavelenght of Gyrotron

The weak transverse shear magnetic field is first proposed to decrease the working wavelength of Gyrotron. Using Lie perturbation method, we give the modified wave particle resonant relation in guiding magnetic field with weak transverse shear magnetic field.     

一种测量液膜高度的方法

给出一种测量液膜高度的新方法,利用此方法测定液体表面张力系数时发现,计算液膜重量时,液膜厚度不能用金属丝直径代替,否则液体表面张力系数会出现负值。