Speckle Correlation Fringes Research Articles

Analysis of double aperture hololens imaging system through simulation and experimentation for its application in speckle metrology

In-plane displacement measurement using Double exposure Speckle photography involves illumination of a rough surface by coherent source of light and formation of image of the object containing speckles on a high-resolution photosensitive film using imaging lenses corresponding to undeformed and deformed state of object. When doubly exposed and properly processed specklegram is illuminated with an unexpended laser beam, two slightly displaced speckles behave as two-point scatterer giving rise to young's type of speckle correlation fringes. From the measured value of fringe spacing, in-plane displacement occurred between the two exposures is measured. Monochromic aberrations of the imaging system lead to formation of deteriorated curved fringes which introduces error in measurement. Further, to measure in-plane displacement component with enhanced sensitivity of measurement, Duffy's double aperture interferometer is used where diffraction limited performance almost free from all monochromatic aberration is required over the two apertures. Sensitivity of measurement depends on separation between the two apertures. For achieving higher sensitivity of measurement, separation between the twin apertures should be large requiring low f-number imaging lens of large diameter for given focal length of the imaging lens. Conventional diffraction limited and almost aberration free lenses are costly and require tedious processing for their production. Present work presents detailed analysis of a four-hololens imaging system through simulation and experimentation to show that properly recorded and played back hololens imaging system may be used advantageously to achieve diffraction limited imaging performance almost free from all monochromatic aberrations. Further, it is shown that to minimize aberration for extended object field, a two-hololens imaging configuration corresponding to each aperture has to be utilized and to obtain appreciable illumination over the image plane the two lenses of each aperture should be kept in contact making the system compact. The experimentally obtained values of in-plane displacement using the compact version of the low f- number four-hololens imaging system are found to be in good agreement with theoretical predictions as well as results obtained for similar experimentation where Duffy's double aperture imaging configuration comprising of conventional imaging lens was used.

Estimation of phase derivative from a single fringe pattern using Riesz transforms

We propose a technique to estimate the phase derivative in both x and y directions based on Riesz transform from a single speckle correlation fringes. The originality of this technique is to exploit Riesz transform for phase derivatives estimation, spatial modulation, speckle denoising, and measure of features similarity. Phase modulation process is realized by combining a digital spatial carrier and Riesz quadrature; speckle denoising is computed using Riesz wavelets transform, and the performance is evaluated by Riesz features SIMilarity. Before applying our method on real speckle correlation fringes, its performance is tested by numerical simulation.

Two-dimensional discrete wavelets transform for optical phase extraction: application on speckle correlation fringes

A method for optical phase extraction based on two-dimensional discrete wavelets transform (2-DWT) decomposition is shown. From modulated fringe pattern, phase distribution is extracted by the ratio between detail and approximation. Modulation process is realized digitally by introducing high-frequency spatial carrier, and this process needs two π /2 -shifted fringe patterns. We propose to use only single fringe and generate its quadrature by spiral phase transform (SPT). After validation by computer simulation, we apply the 2-DWT algorithm on experimental speckle fringe correlation taken for hard disk surface. The extracted phase using SPT quadrature was compared with that given using this time experimental quadrature, and we show a good performance by multiscale structural similarity metric.

Design and analysis of modified version of double aperture speckle interferometer consisting of holographic optical element: Application to measurement of in plane displacement component

Duffy's double aperture speckle interferometer consists of two apertures placed symmetrically over an imaging lens and is used to measure in plane displacement component parallel to the line joining the two apertures using speckle photography. Diffraction limited imaging performance almost free from all monochromatic aberration over the two apertures is desirable for accurate measurement. In present work twin apertures are placed over a compact holographic lens (hololens) system. Lens system consists of two properly recorded and played back holographic lenses cemented together with proper alignment. Recording and play back geometry of holographic lenses has been designed for ease of alignment similar that of an on-axis imaging performance obtained by a conventional lens. Experimental results on measurement of in plane displacement along a line joining the two apertures using the designed interferometer is presented and compared with the actual displacement given to a diffuser between the two exposures. Further, results on measurement of in-plane displacement by analyzing speckle correlation fringes contained in zero order and ±1st order are presented to show that measurement made by analyzing fringes contained in ±1st order give better result than that of results obtained by analyzing speckle correlation fringes contained in zero order. In plane displacement measurement carried out by measuring fringe width of young's fringes contained in ±1st order provides an experimental technique to avoid cumbersome mathematical calculation for correction in the measured value of fringe spacing as suggested by several researchers.

Filtering of Electronic Speckle Correlation Fringes

Speckle correlation fringes include a large quantity of speckle noise. It is first to consider how to reduce speckle noise before using phase formula to calculate. Filter is usually used to reduce speckle noise. From two aspects of frequency domain and space domain, we adopted mean filter, medium filter, Butterworth low-pass filter and homomorphism filter to process the speckle correlation fringes obtained by experiment. It is shown that the speckle correlation fringes are clearer and more easily interpreted and automatic processed after being filtered.

电子散斑干涉条纹图的变分去噪方法

Traditional speckle fringe patterns by electronic speckle pattern interferometry (ESPI) are inherently noisy and of limited visibility, so denoising is the key problem in ESPI. We present the variational denoising method for ESPI. This method transforms the image denosing to minimizing an appropriate penalized energy function and solving a partial differential equation. We test the proposed method on computer-simulated and experimental speckle correlation fringes, respectively. The results show that this technique is capable of significantly improving the quality of fringe patterns. It works well as a pre-processing for the fringe patterns by ESPI.

Adaptive optics interferometer using superspeckles for high resolution deformation measurement

Digital speckle pattern interferometry (DSPI) is a well-known technique for measuring deformations, but it is limited in range by speckle decorrelation. We developed an adaptive interferometer with increased measurement range by combining the DSPI set-up with a pupil filter that generates optical superresolution. As a result, a decrease in the transverse speckle size is observed accompanied with a substantial increase in the longitudinal speckle size. The increase in the speckle correlation length along the optical axis allows for obtaining an out-of-plane deformation measurement over a significantly extended depth. An experimental verification of this concept of superspeckles is presented with an intensity-only LCD spatial light modulator (SLM) acting as a pupil filter. Comparison of speckle correlation fringes with and without the superresolution filter confirms the proposed concept. The present work demonstrates a doubling of the measurement range when using the superresolution interferometer. A standard set-up in which the speckle length is comparably elongated by stopping down the lens has a similar loss of intensity, but its lateral resolution is only half as good.

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.

Adaptive correction to the speckle correlation fringes by using a twisted-nematic liquid-crystal display

An innovative technique for reducing speckle noise and improving the intensity profile of the speckle correlation fringes is presented. The method is based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concept is presented both analytically and by simulation by using computer-generated speckle patterns. The experimental verification is performed by using an amplitude-only spatial light modulator (SLM) in a conventional electronic speckle pattern interferometry setup. The optical arrangement for tuning a commercially available LCD array for amplitude-only behavior is described. The method of feedback to the LCD SLM to modulate the intensity of the reference beam in order to reduce the modulation intensity values is explained, and the resulting fringe pattern and increase in the signal-to-noise ratio are discussed.

Phase shift calibration in speckle photography—a first step to practical real-time analysis of speckle correlation fringes

The paper is focused on the implemention of phase shift calibration in speckle photography with a view to introducing the possibility of realtime analysis of displacement data obtained by the method. Phase reversal is accomplished by varying pressure within an air-filled quartz cell inserted in the pump beam in a conventional two-beam coupling arrangement. It is shown that phase reversal is achieved when a π-shifted speckle pattern overlaps on an unshifted speckle pattern at the observation plane. This phenomenon is exploited for calibration of the phase shift. Experimental results show good agreement with the theory.

Phase shift calibration in speckle photography--a first step to practical real-time analysis of speckle correlation fringes

Phase shift calibration in speckle photography--a first step to practical real-time analysis of speckle correlation fringes

Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photorefractive BaTiO 3 crystal

A technique has been proposed for the measurement of tilt of a diffuse object using speckle fanning in a photorefractive BaTiO 3 crystal. Free space geometry has been used for recording in which the axis of rotation of the object lies away in three-dimensional space. The method is based on recording of two exposures, one before- and another after the tilt, thus producing speckle correlation fringes due to overlapping of two speckle fans. We consider a generalized case of tilt, generating curved fringes with center shifted in the transverse direction. The axis of rotation lies perpendicular to the optical axis in three-dimensional space having the transverse and axial components of the shift in the center of rotation with respect to the diffuser plane. Fourier transform of the curved fringes produces correlation output. Measure of separation between the correlation peaks in transverse and axial directions provides information about the tilt angle, the direction of tilt, and the distance of rotation axis from the optical axis. Experimental results have been presented to validate the theoretical predictions.

Three-dimensional rigid body motion measurement using speckle fanning in a photorefractive BaTiO 3 crystal

Summary A simple speckle technique, utilizing speckle fanning in a BaTiO 3 crystal, is demonstrated for the measurement of rigid body displacement in an arbitrary direction. Collimated laser beam illuminates a diffuser to generate speckles, which are then recorded inside a photorefractive barium titanate crystal thus producing speckle fan. Speckle correlation fringes are formed due to interference between the reconstructed speckle fans corresponding respectively to the initial- and final positions of the diffuser. Displacements occurring in a direction making small angles with the optical axis have been measured by profiling the fringes. The measurement of displacement in a direction making large angle with the optical axis is possible only by taking the Fourier transform of the fringes. This facilitates the separation of transverse and axial correlation peaks giving the transverse and axial components of the motion.

Out-of-plane displacement measurement by using speckle fanning in a photorefractive BaTiO 3 crystal

Summary We propose a method for the measurement of out-of-plane object displacement by a speckle technique utilizing the speckle fanning in a photorefractive barium titanate crystal. A portion of the converging incident beam has been used to illuminate the diffuser to generate speckles, while the remaining portion is allowed to fall directly on the crystal. Coupling of scattered beam with incident beam inside the crystal generates speckle fan of light after diffraction from the complex gratings formed in the volume of the crystal. Semi-circular speckle correlation fringes are formed due to the interference between reconstructed speckled fan beam recorded for an initial position of the diffuse surface, and directly transmitted speckled beam after introducing the out-of-plane displacement in the diffuser. Fringe diameter has been measured after ‘profiling’ operation on the fringes, for the calculation of out-of-plane displacement.

Effect of low-frequency vibrations on speckle interferometry fringes

The effects of low-frequency vibrations on speckle correlation fringes have been investigated. The relatively short capture time of the camera in the low-frequency case may yield usable fringe contrast in spite of vibration. It has been shown that the fringes also shift due to the vibration. The study is in agreement with experimental observations of good-contrast correlation fringes even if the object is not on a vibration- isolated table. Some such experimental observations are also presented.

Quantitative verification of laser-modulated phase-stepping digital shearography for monofrequency vibration measurement

An offspring of holographic and shearing interferometry, digital shearography is a full-field, optical technique. Its full-field nature allows examination of approximately a one square foot area, requiring no scanning. In its usual implementation for vibration studies, time-averaged speckle correlation fringes are formed. While sufficient for observing mode shapes, these fringe patterns carry several disadvantages when quantitative interpretation is attempted. Digital shearography, combined with stroboscopic laser illumination and optical phase stepping, overcomes these limitations. The differential displacement field during monofrequency vibration is calculated independently at each point, and is no longer dependent upon fringe interpretation. The system, a new combination of several well-established techniques, has not been validated in either the optics or acoustics literature. The goal of the current work is to verify the technique via side-by-side measurements made with shearography and laser vibrometry. A simple cantilever beam is vibrated at several resonance and antiresonance frequencies and examined by both methods. Analysis techniques for comparing velocity output of the vibrometer to differential displacement output from shearography will be discussed. Agreement between the two systems is excellent, demonstrating the potential usefulness of this new method. [Work supported by the Penn State University Applied Research Lab.]

Digital polarization sensitive speckle pattern interferometer

The polarization characteristics of a Digital Speckle Pattern Interferometric (DSPI) arrangement are investigated. The influence of this parameter on the visibility of the speckle correlation fringes is pointed out. A theory is outlined and compared with experimental measurements showing the validity of the approach.

Application of an optically addressed spatial light modulator to real-time speckle photography

The application of a bistable, binary, amorphous silicon ferroelectric liquid crystal optically addressed spatial light modulator to speckle photography is described. The system presented has a higher space-bandwidth product than a television system and can operate at greater than 500 Hz frame rates. The output is also amenable to further optical processing. The spatial light modulator is characterised for sensitivity, contrast ratio and resolution and speckle correlation fringes from a moving object are successfully obtained. Measurement of displacements in the range 20 μm to 70 μm with an rms error of 3 μm is demonstrated and the suitability of these devices to practical optical metrology is discussed.

Differential Fourier analysis of speckle correlation fringes

A method consisting of the median filtering and the differential Fourier analysis is proposed to analyze the speckle correlation fringes. In the method, these two operations act effectively as a band-pass filter since the speckle noise with high frequencies is suppressed by the median filtering and the pedestal variation with low frequency is removed through the differentiation of fringe signals. In computer simulations, the performance of the method is compared with that based on the ordinary Fourier analysis and examined with respect to the window size of median filters used. It is revealed that speckled fringes with the low visibility can be successfully analyzed with high accuracy. The validity of the method is also experimentally shown by applying it to the analysis of speckle correlation fringes obtained in speckle photography.

Digital phase stepping speckle interferometry

A variation of electronic speckle pattern interferometry (ESPI) is presented whereby phase fringes are produced in contrast to speckle correlation fringes. Digital phase stepping speckle interferometry uses a phase measurement technique developed for holographic interferometry, which involves phase shifting of the reference beam in a conventional speckle interferometer. Saw-tooth phase fringes are produced by subtracting the phases of the speckle fields before and after object deformation in a digital frame store. This enables the sign of the deformation to be distinguished. After application of a special low-pass digital filter, the phase fringes are of adequate quality to be counted automatically.