Development of Matlab filtering techniques in digital speckle pattern interferometry

In interferometric fringe pattern analysis, specular and speckle fringe patterns are the two main divisions. While specular fringes are characterized by quality fringes, speckle (that obtains due to the diffuse scattering of the coherent radiation from an optically rough surface) fringe patterns are characterized by noisy fringes. This paper concentrates on this aspect and the Matlab based filtering methods to improve the quality of speckle fringe patterns by developing the appropriate software. Further, the newly developed software “Macurv” will be presented which can give the second order derivative (curvature) fringe information. A software with several functions is written using Matlab. The objective of the software is to provide a more effective way for the post-processing of speckle interferometric fringes. The algorithm and functions of the developed software “Macurv” will be explained.     

Holographic contouring using double-source technique and Fourier transform analysis

This paper describes a double-exposure holographic contouring technique by the movement of the object beam through fibre optics. Single-mode optic fibres are used to transfer both object and reference beams. Between two exposures the object illumination beam is displaced. The contouring fringes can be visualised on the object surfaces. The fringe patterns are automatically processed by the fast Fourier transform (FFT) method, which produces a 3D perspective plot. Examples are given for different objects.     

Contrast and sensitivity of the vibration fringes in time-averaged electronic speckle-pattern interferometry: effect of variations of force level

The time averaged frame subtraction technique is improved by subtracting two Bessel fringe patterns at two different force levels. The technique enables significant enhancement of fringe contrast and increased measurement sensitivity. The contrast and sensitivity of the fringes obtained at different force ratios are investigated. Both theoretical and experimental results are presented.     

Young's fringes analysis with a computer image-processing system

A two-dimensional Fourier transform analysis is presented for numerically processing the Young's fringes diffraction pattern from a double- exposure speckle photograph. The fringe spacing and orientation are determined using only one Young's fringes pattern without any other diffraction halo patterns. This algorithm is based on the 2-D FFT of the fringe pattern with 256 × 256 pixels. Therefore, it enables automatic analysis to be performed on specklegram with noisy and poor fringe patterns. The measurement of deformation by the laser speckle method can be carried out with high accuracy, reliability and speed.     

An improved stair phase encoding method for absolute phase retrieval

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.     

The identification of fringe positions in speckle patterns

This paper two methods of identifying fringe positions in speckle patterns. The first uses local directional averaging to track fringes, while the second uses standard image processing techniques to connect the patterns into a form where the fringes can be identified.     

Window fringe pattern demodulation by multi-functional fitting using a genetic algorithm

We present a new way to demodulate complicated fringe patterns containing closed fringes using a genetic algorithm (GA). The entire fringe pattern is divided into a set of partially overlapping smaller sub-image windows. Each of these has a lower dimensionality and as a consequence is faster and can be demodulated more reliably. The demodulation process proceeds row-by-row way passing from one sub-image in a neighborhood until the whole interferogram is processed. The modulating phase of each sub-image is modeled as a parametric analytic function whose parameters are optimized using a GA. The technique is demonstrated demodulating some normalized fringe patterns that have two main difficulties: closed fringes within the interferogram and regions of under-sampled fringes. These fringe images cannot be demodulated by techniques such as the regularized phase tracker (RPT).     

Application of the holographic carrier fringe and FFT technique for deformation measurement

This paper describes a holographic system based on the use of fibre optics and automatic spatial carrier fringe pattern analysis. Carrier fringes are generated by simply translating the object beam between two exposures. Single-mode optical fibres are used to transfer both the object and reference beams. The fast Fourier transform method is used to process the interferograms: it extracts phase from fringe patterns resulting from the interference of tilted wavefronts. The method is illustrated by measuring the deformation of an arbitrarily clamped, uniformly loaded circular plate. The results are given for the perspective plot of the out-of-plane deformation field, the maps of wrapped and unwrapped phase, and a contour map of the unwrapped phase.     

High-resolution time-average electronic holography for vibration measurement

Time-average electronic holography (also known as TV holography) is a widespread technique used in real-time, non-contact, whole-field vibration measurement. The quantitative interpretation of time-averaged fringe patterns is difficult because of speckle noise and of the decreasing visibility of higher-order Bessel fringes. Speckle noise may only be reduced during image acquisition, by multiple-frame averaging.The objective of this paper is to present two new methods allowing to obtain time-averaged fringe patterns presenting a high resolution and a high contrast between dark and bright fringes, as well as the associated quantitative interpretation. They are based on the elimination of the random phase component and on the reduction of the random intensity component of the time-averaged fringe pattern. The fringe patterns obtained by this method may be efficiently filtered in order to provide the precise locations of the Bessel-type fringes associated with the object vibration. The methods rely on the use of the simplest standard equipment, without any need for modulators or stroboscopic devices. Quantitative fringe interpretation is straightforward and based on the method of fringe skeletonizing and indexing. Fringe contrast is so high that skeletonizing may be done by simple thresholding.     

Smoothing of speckle and moire fringes by computer processing

Moire and speckle pattern fringes are usually readily identifiable by eye: when the intensity of such a pattern is digitised and fed into a computer, it is by no means easy to identify the fringe positions because of the presence of optical noise in the fringe patterns. Three techniques for digital smoothing of such fringe patterns are discussed here.     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

Variational denoising method for electronic speckle pattern interferometry

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.     

A flexible 3D profilometry based on fringe contrast analysis

This paper proposed a flexible 3D profilometry based on fringe contrast analysis. A series of sinusoidal fringes are projected on the surface of the testing object that is laid in front of the imaging plane of the fringes, and captured through a beam splitter by a CCD camera in the same direction as the axis of the projection. After the fringe contrast obtained using phase-shifting technique, the height of the object can be restored through searching the look-up table of the contrast and the height. In the measurement process, we only need to capture fringe patterns in one position, without changing the imaging plane of the fringes, so it is faster and more convenient than the existing method based on fringe contrast analysis. Our system is simple and flexible by reason of no special devices used. In this paper, the principle of this method, the setup of the measurement system and primary experiment results are given. The experimental results prove this method can restore the height of the complex object accurately and effectively.     

Measurement of dynamic crack tip displacement field by speckle photography and interferometry

Speckle interferometry has been used to measure the transient displacement field around a crack due to stress wave loading. Double exposure interferograms are recorded with a pulsed ruby laser, and correlation fringes formed by spatial filtering of the developed film. A new technique is presented for reducing the noise level in spatially filtered speckle interferograms. Independent fringe patterns, obtained from one interferogram but with the filtering aperture sampling different regions of the Fourier transform plane, are digitised by a CCD camera and combined numerically. It is demonstrated that accurate analysis of fringe patterns by the Fourier transform method can be carried out, even if no carrier fringes are present. The measurements are compared with those obtained by speckle photography. Least-squares fitting of the theoretical displacement field is used to calculate the stress intensity factor at the crack tip as a function of time.     

Unstable resonator alignment based on the fringe analysis

The existing cavity mirrors alignment method aligns cavities according to the symmetry of the near-field interference fringes of the guided lights by the unstable resonator. Its precision is restricted due to the lack of objective criterion for the fringe symmetry. This article proposes a high-precision cavity mirrors alignment method using the grey projection of fringe patterns as a solution to the problem. First, vertical and horizontal grey projection on the concerned fringe patterns; then an evaluation function for the cavity mirrors alignment is established using the distances between peak/valley values of all the levels in the projection curve as variables; finally, the function value is employed to characterize the fringe symmetry and thus to provide an objective criterion for the alignment effect of the stable resonator cavity mirrors. Experiments show that the proposed method is able to give effective evaluation for the symmetry of the near-field interference fringes of the guided lights and improve the alignment precision greatly.     

傅里叶变换条纹位相分析技术中移频消去载频法对位相分析的影响

在理论上分析了傅里叶变换位相分析技术中的移频消去载频法,由于采样的离散化,不同的条纹周期对位相分析将产生不同的影响。利用计算机仿真,模拟了不同周期的条纹图以及形变条纹图,根据傅里叶变换频移法,获得了不同周期条纹图的位相分布及误差,同时与"减基准条纹法"获得的位相分布及误差进行比较,验证了不同条纹周期对位相分析产生的影响。以花瓶为目标物体,在实验中进一步验证了采样的离散化对位相分析带来的误差和影响。并且讨论了两种减弱这种误差的方法。     

Image fusion by color texture extraction

In this paper, we present a method to extract shape and color information simultaneously of a colorful object by projecting sequentially sinusoidal fringe patterns onto object's surface. Distorted fringe patterns are captured by digital CCD color camera. It is applied the phase shifting method to evaluate the phase of the projected fringes. We obtain both topography details and color texture information.     

A composite-structured-light 3D measurement method based on fringe parameter calibration

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in composite-structured-light 3D measurement systems. For a composite-structured-light 3D measurement system, spectrum overlapping causes parameters of each deformed phase-shifting fringe to change, and therefore leads to phase measurement errors. The proposed fringe parameter calibration method is based on the fact that variations in each deformed fringe's parameters are independent of height and reflectivity of the measured object. Three frames of composite grating are projected on the reference plane, and each carrier channel includes the information of three phase-shifting sinusoidal gratings used in Phase Measuring Profilometry (PMP). With the parameter calculation formulas of PMP, the parameters of fringes demodulated from the same carrier channel can be calculated, and therefore parameter relation coefficients between fringes demodulated from different carrier channels may be obtained. When an object is measured, these relation coefficients can be used to calibrate the parameters of the deformed phase-shifting fringes. A new 3D measurement mathematical model is established to reconstruct the shape of the object. Experimental data proved that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy by more than three times.     

Identifying a dot-matrix hologram with the fringe-overlapping phenomena of grating dots

Dot-matrix holograms created by two-beam writers contain many grating dots. Because the phase difference between two laser beams for interference cannot be controlled accurately, the fringe positions of grating dots are randomly determined. Therefore, fringe positions are a good kind of tool to identify dot-matrix holograms. In this paper, a number difference between two special fringes of a target grating dot is used to identify a dot-matrix hologram. The two special fringes are determined by three grating dots with parallel fringes. The first special fringe is corresponding to a fringe pair with the best matching for the fringes of the target grating dot and the fringes of the second grating dot. The second special fringe is corresponding to a fringe pair with the best matching for the fringes of the target grating dot and the fringes of the third grating dot. An experiment has proved the proposed method practical and feasible. Because reproducing a grating dot with a specified fringe number difference is difficult, the proposed method is excellent for anti-counterfeiting.