Fringe visibility analysis with different scale apertures in speckle photography

Abstract

The use of different scale aperture pupils for image recording in speckle photography is analysed. In particular a double-exposure specklegram is considered. The ensemble-average intensity in the Fourier plane is analytically derived and fringe visibility is investigated. The theoretical results are verified by in-plane displacement translation experiments.     

Additive-subtractive phase-modulated electronic speckle interferometry: analysis of fringe visibility

Fringe-visibility issues of additive-subtractive phase-modulated (ASPM) electronic speckle pattern interferometry (ESPI) are explored. ASPM ESPI is a three-step method in which additive-speckle images are acquired rapidly in an analog fashion in every frame of a video sequence, a speckle phase modulation is intentionally introduced between frames, and a digital subtraction of consecutive pairs of additive-speckle images is performed. We show that this scheme has the good high-frequency noise immunity associated with additive-ESPI techniques as well as the good fringe visibility associated with subtractive-ESPI techniques. The method has better fringe visibility than can be obtained with purely additive ESPI and also does not suffer from the fringe distortions that can occur with subtractive ESPI in the presence of high-frequency noise. We show that even if full speckle decorrelation were to occur between the two additive speckle images that are to be subtracted, the visibility of ASPM ESPI fringes can be made to approach unity by suitable adjustment of the reference-to-object beam-intensity ratio.     

Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method

Electronic speckle pattern interferometry fringe patterns usually have poor contrast so it is important to enhance fringe contrast for the extraction of phase from a single fringe pattern. We present new enhancement methods based on differential equations (called DE enhancement methods) to electronic speckle pattern interferometry fringes. The DE enhancement methods transform the image processing to solve differential equations. With the proposed methods, the visibility of the correlation speckle fringe patterns can be improved significantly. We tested the proposed methods on computer-simulated speckle correlation fringes and experimentally obtained fringes, and we compared the new method with other contrast enhancement techniques. The experimental results illustrate the performance of this approach.     

Squeezed States in Non-ideal Interferometers: The Effect of Aberrations

Abstract

We extend a previous study of the usefulness of squeezed states of light for noise reduction in a non-ideal interferometer to the case where fringe visibility that is less than unity is caused by non-absorptive processes such as aberrations or misalignment of the beams. The main differences and similarities between this system and our earlier study of an interferometer with unbalanced losses in both arms are presented and discussed. An expression is given for the minimum detectable phase change in this system, in the presence of squeezing, as a function of fringe visibility.     

Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method

The ordinary differential equation (ODE) and partial differential equation (PDE) image- processing methods have been applied to reduce noise and enhance the contrast of electronic speckle pattern interferometry fringe patterns. We evaluate the performance of a few representative PDE denoising models quantitatively with two parameters called image fidelity and speckle index, and then we choose a good denoising model. Combining this denoising model with the ODE enhancement method, we make it possible to perform contrast enhancement and denoising simultaneously. Second, we introduce the delta-mollification method to smooth the unwrapped phase map. Finally, based on PDE image processing, delta mollification and some traditional techniques, an approach of phase extraction from a single fringe pattern is tested for computer-simulated and experimentally obtained fringe patterns. The method works well under a high noise level and limited visibility and can extract accurate phase values.     

Comprehensive influence of in-plane displacement,double-aperture orientation and wedge-shearing direction on slope fringe formation in speckle shearing interferometry

Abstract

The comprehensive influence of the in-plane displacement, double-aperture orientation and wedge-shearing direction on the slope fringe formation in speckle shearing interferometry is discussed in this paper. The results show that the two in-plane displacement components have an influence on the slope fringe formation and that the double-aperture orientation and wedge-shearing direction also have an important influence on the slope fringe formation. A theoretical analysis and experimental results are given. The experimental results are in good agreement with the theoretical analysis.     

Theory of Ultra-high-resolution Optical Raman Ramsey Spectroscopy

A non-perturbative theoretical analysis of Ramsey interference lineshapes in three-level lambda systems excited by laser fields has been developed for the general case of several interaction regions. In conventional Ramsey excitation, two laser fields excite the lambda system each in two separate spatial interaction regions. Here we examine how increasing the number of interaction regions or altering the interaction times change and improve the lineshape characteristics such as fringe visibility. For short interaction times the fringe pattern is strongly dependent on the number of interaction regions, with the n = 2 sinusoidal fringes replaced by sharper fringes of greater visibility. With larger interaction times, the fringe pattern is virtually unchanged on increasing the number of interaction regions. The optimum fringe pattern is obtained with short interaction times and a larger (n a 9) number of regions.     

Electronic speckle pattern interferometry based on spatial information using only two sheets of speckle patterns

Abstract

Speckle interferometry is an important deformation measurement method for an object with a rough surface. In this paper, a novel fringe analysis method is proposed that uses a new optical system, which uses a plane wave as the reference beam of the speckle interferometer. When the optical system is employed in fringe analysis, the deformation information and the bias components of the speckle patterns are clearly separated in the frequency domain. Therefore, the deformation information can be readily extracted using a Fourier transform, which gives a pair of real and imaginary components concerning the information. The specklegram is calculated using such a pair of components, and the phase map is obtained from the specklegram. Experimental results confirmed that the resolution power of this measurement method is higher than 1/261 of the wavelength of the light source of the optical system.     

Fast,common-path,switchable, achromatic phase-shifter for polarization interferometry

Abstract

A fast switchable phase-shifter using a pair of liquid-crystal devices with a switching angle of 60° is described. This phase-shifter can be placed in the common path traversed by the two orthogonally polarized beams emerging from a polarization interference microscope and used for digital phase measurements over a wide range of wavelengths. It can also be used in a stellar interferometer with orthogonally polarized beams for measurements of fringe visibility with white light.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

Vibration measurement by the time-averaged electronic speckle pattern interferometry methods

Three different image-processing methods based on the time-averaged technique were compared by the electronic speckle pattern interferometry (ESPI) technique for vibration measurement. The three methods are the video-signal-addition method, the video-signal-subtraction method, and the amplitude-fluctuation method. Also, errors introduced by using the zero-order Bessel function directly into the analysis of the fringe pattern were investigated. The video-signal-addition method has been the most generally used ESPI technique for vibration measurement. However, without additional image and/or signal-processing procedures, the fringe pattern obtained directly by the video-signal-addition method is rather difficult to observe. The reason for poor visibility of the experimentally obtained fringe pattern with this method is explained. To increase the fringe pattern's visibility without additional image and/or signal processes, we tried two video-signal-subtraction methods. One of the two methods is the video-signal-subtraction method that has normally been used in the static applications. The other method, called the amplitude-fluctuation method, and its associated theory are reported here.     

Phase extraction from electronic speckle pattern interferometry addition fringes

Addition fringes are obtained in real time from electronic speckle pattern interferometry (ESPI) by use of a twin-pulsed laser when two pulses are fired during a single field of a CCD camera. This enables object deformations to be studied in harsh environmental conditions. However, the fringe patterns have poor visibility because optical noise is additive. To our knowledge automatic phase extraction from addition fringes has not previously been achieved: Low-pass filtering to suppress random speckle noise also eliminates the fringes because of their low visibility. Two phase-stepping algorithms that calculate phase from ESPI fringes without the need for a preprocessing filter are presented. In the first ESPI subtraction fringes are considered, for which an improvement in accuracy is seen, and in the second ESPI addition fringes are considered, which, we believe, has enabled the phase to be extracted for the first time. The algorithms are demonstrated with theoretical data and with experimental ESPI fringepatterns recorded with a cw laser. As presented, they form the first step toward a procedure that can beused with twin-pulsed ESPI.     

White-light spectral interferometric technique to measure the wavelength dependence of the spectral bqandpass of a fibre-optic spectrometer

Abstract

A spectral-domain white-light interferometric technique with channelled spectrum detection is used to measure the wavelength dependence of the spectral bandpass of a fibre-optic spectrometer. In an experimental setup comprising a halogen lamp, a non-dispersive Michelson interferometer and the spectrometer to be measured, spectral interferograms are recorded for different optical path differences (OPDs) between interfering beams. By processing the recorded spectral interferograms using discrete filtering and a fringe amplitude demodulation method, spectral fringe visibilities, first, as a function of the wavelength for given OPDs, and second, as a function of the OPD at given wavelengths, are obtained. It is confirmed, in accordance with theory, that the latter spectral fringe visibility functions are Gaussian functions with maxima and widths dependent on the wavelength. From the widths of the Gaussian spectral fringe visibility functions the wavelength dependence of the spectrometer bandpass is determined over a wide spectral range.     

Recording of In-plane Surface Displacement by Double-exposure Speckle Photography

Local displacements in the plane of an object surface illuminated by coherent light may be measured by recording double-exposure photographs of it. When the surface is illuminated symmetrically by two oblique beams, ‘speckle correlation fringes’ appear in the doubly exposed negative, due to the non-linear nature of the photographic recording. Factors affecting the visibility of these fringes and the range of displacement which can be measured are discussed. The fringe visibility falls to zero for displacements larger than a speckle width, but measurements can then be performed upon the optical transform of the negative image. With uni-directional object illumination, the in-plane displacement can be measured on a point-by-point basis in magnitude and in direction from Young's fringes observed. With two symmetrical oblique illuminating beams the effect of a small surface strain is displayed, even if large lateral displacement has occurred, by using spatial filtering when viewing the photographic image.     

Additive-Subtractive Two-Wavelength ESPI Contouring by Using a Synthetic Wavelength Phase Shift

The addition correlation of two speckle fields by simultaneousillumination at different wavelengths is used for object contouring ina Twyman-Green-type interferometer. Fringe visibility is enhancedwhen the stochastic speckle background intensity obtained from areference plane modulation is subtracted. We calculate the contourphase map by using a phase-shift algorithm in the syntheticwavelength. A comparison with a sequential illumination, phasedifference method based on a laser wavelength phase shift isgiven. The test setup does not need to be stable on aninterferometric scale, and therefore a method is provided that lendsitself to applications in noisy environments.     

Contrast enhancement of electronic speckle pattern interferometry addition fringes

The electronic speckle pattern interferometer in the double-pulse addition mode can be used to measure physical parameters in unstable environmental conditions. Owing to additive optical noise, however, the fringe patterns obtained have poor contrast. Some methods that use subtraction of addition double-pulsed fringe patterns improve fringe visibility but impose a limitation in measurement time ranges. To increase this range, to be limited by only the pulse separation, the contrast enhancement of double-pulsed addition-fringe patterns with a spatial filter based on local-standard-deviation measurements is investigated. Computer simulations and experimental results are presented.     

Simulation of Time-evolving Speckle Patterns Using Kolmogorov Statistics

Abstract

We present a new approach for simulating time-evolving speckle patterns, by combining the shift of a rigid phase screen with its evolution. Thus, the two time-scales associated with speckle boiling and speckle motion can be adjusted independently. The statistical properties of the phase perturbation and the speckle pattern are investigated by using the temporal phase structure function and the temporal intensity correlation. We found a very good agreement with experimental results.     

Three-wavelength Speckle Interferometry: A Theoretical Study

Abstract

In this paper we discuss from a theoretical point of view the statistical properties of the rough-surface interferometry (ROSI) if more than two wavelengths are used. Starting from the Gaussian statistics of several correlated speckle fields we derive and discuss the probability density functions of the statistical errors induced by speckle noise for two different techniques involving three wavelengths. We show that the use of more than two wavelengths may only be advantageous if these statistical errors are small compared to the errors induced by the measuring equipment.     

Denoising in digital speckle pattern interferometry using fast discrete curvelet transform

In digital speckle pattern interferometry, the denoising of speckle fringe patterns is of vital importance for quantitative extraction of phase distribution. A filtering method of fast discrete curvelet transform based on weighted average thresholding technique is proposed in this paper for noise removal in speckle fringe patterns. Both computer-simulated and experimental digital speckle pattern interferometry fringe patterns are adopted to evaluate the performance of the proposed filtering method. In addition, a widely used and representative filtering method, windowed Fourier filter, is introduced for making a comparison and validation in the image processing effect, and the parameter of peak signal noise ratio is also used for assessment of denoising effect. It is shown from the filtered results that the filtering method of fast discrete curvelet transform is effecitve to remove speckle noises and simultaneously preserve fringe structure information.     

De-correlation Effects in Speckle-pattern Interferometry. 1. Wavelength change dependent de-correlation with application to contouring and surface roughness measurement

A theoretical investigation of the de-correlation of speckle pattern with change of wavelength has been performed with particular reference to the electronic speckle-pattern interferometer. A method of measuring surface roughness using speckle de-correlation is proposed and some preliminary results presented. In addition, the loss of fringe visibility in two-wavelength speckle-pattern interferometric contouring is investigated and experimental confirmation of the theory given.