Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping

A high-speed phase-shifted speckle interferometer has been developed recently for studying dynamic events. Speckle interferograms are continuously recorded by a CCD camera operating at 1 kHz with temporal phase shifting carried out by a Pockels cell running at the same frequency. Temporal phase unwrapping through sequences of more than 1000 frames allows the determination of time-varying absolute displacement maps. This paper presents the application of this speckle interferometry system to the detection and measurement of sub-surface delamination defects in carbon fibre specimens. The influence of re-referencing the temporal phase unwrapping algorithm after different time intervals is analysed to reduce the random phase errors produced by speckle decorrelation and vibration. The performance of several phase-shifting algorithms to minimize the influence of the vibration noise caused by the vacuum pump used to load the specimen is also investigated.     

Speckle photography combined with speckle interferometry

By combining speckle interferometry (SI) measurements with speckle photography, the fringe visibility can be kept high despite the presence of a large bulk or rotating motion of the object. This combined technique improves the usability and measuring range of both pulsed and phase-stepped SI-methods. This paper reviews the theory of fringe formation in SI and shows some recent applications of this combined technique.     

A comparative study of phase-shifting algorithms in digital speckle pattern interferometry

Digital speckle pattern interferometry (DSPI) is a tool for making qualitative as well as quantitative measurements of deformation of objects. Phase-shifting algorithms in DSPI are useful for extracting quantitative deformation data from the system. Comparative studies of the different phase-shifting algorithms in DSPI for object deformation measurement are presented. Static and quasi-dynamic deformation of the object can be measured using these algorithms. Error compensating five-step phase-shifting method is used for the algorithms.     

Continual deformation analysis with scanning phase method and time sequence phase method in temporal speckle pattern interferometry

If a laser beam illuminates a continual deformation object surface, it will lead to a temporal speckle pattern on the observation plane. Recording this time-dependent speckle pattern the deformation of the surface of an object can be obtained. Two methods, scanning phase method (SPM) and time sequence phase method (TSPM), have been introduced for measuring the displacement caused by the deformation in temporal speckle pattern interferometry (TSPI). Their principle is that by capturing a series of speckle interference patterns related to the object deformations, the fluctuations in the intensity of the interference patterns can be obtained. Through scanning these fluctuations and estimating both the average intensity and modulation of the temporal speckle interference patterns, the phase maps for whole-field displacements are calculated. In this way one is capable of quantitatively measuring continual displacements simply using a conventional electronic speckle pattern interferometry (ESPI) system without phase shifting or a carrier. The elaboration on the new methods is given in this paper and experiments are performed to demonstrate their performance with a conventional ESPI system.     

Deformation field induced by spherical indentation: numerical analysis and experimental measurement by speckle interferometry

The present paper describes an experimental procedure for the measurement of the displacement field around a spherical indentation. The measurements were performed by a speckle interferometer designed for the detection on small areas of one or more oblique components of displacement; the indentations were made by a standard durometer used for metals.The experiments were carried out on a hardened and tempered steel, previously characterized by a standard tensile test; the results are in accordance with the numerical results obtained by an elasto-plastic FEM analysis.     

Simulation of dynamic speckle sequences and its application to the analysis of transient processes

Dynamic speckle has been used in recent years to analyse several transient processes that are produced in industrial and biological applications. We present here a numerical simulation to generate a temporal sequence of dynamic speckle patterns which is based on a model used for speckle formation by the superposition of waves from discrete scattering centres. It is demonstrated that the first and second statistics of the intensity of each speckle image, the time history of the speckle pattern, the temporal evolution of the correlation coefficient, and the power spectral density of the intensity generated by the proposed model reproduce quite well those obtained from experimentally recorded data. The process of a fast drying paint is presented as an example of the application of the proposed numerical model.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

Self-marking phase-stepping electronic speckle pattern interferometry (ESPI) for determining a phase map with least residues

Different from most of the electronic speckle pattern interferometry (ESPI) approaches, which involve the correlation fringe formulation followed by speckle noise elimination (or filtering), to develop a wrapped phase map, this study adopts the approach proposed by Creath in 1985 instead. However, Creath's approach is so critical of its applying interferograms, the influence of which is dependent on the robustness of the applied phase-shifting algorithm and the accuracy of the phase shifter. The self-marking technique proposed by Huang and Chou in 2000 is adopted herein to help overcome any unfavorable conditioning, including hysteresis, nonlinearity or plane tilting, of the pieozo-electrical transducer (PZT), to enable the successful implementation of the Creath's method. With its help, the whole phase stepping history of a practical work (i.e., an ESPI experiment for the present study) can be fully recorded and monitored. Thus, the required phase stepping frames can be accordingly decided and their further calculation will yield a phase map with least number of residues.     

Measuring velocity of speckle fields with digital speckle pattern interferometry

We investigate a digital method for detecting the velocity of a diffusing object. The technique is based on Digital Speckle Pattern Interferometry (DSPI). A set of reference fringes is generated externally through the reference beam in a digital interferometer. As the object moves, subsequent frames are acquired and subtracted according to the normal DSPI procedure and stored. By means of the theory of first order speckle statistics applied to speckle intensity correlation, we relate the visibility variations in the reference fringes with the object velocity. Thus, by measuring the fringe visibility variation in the resulting DSPI stored frames the mean object velocity can be obtained. The theoretical results are experimentally verified.     

Measurement of tilt of a diffuse object by double-exposure speckle photography using speckle fanning in a photorefractive BaTiO3 crystal

A technique has been proposed for the measurement of tilt of a diffuse object using speckle fanning in a photorefractive BaTiO₃ 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.     

Digital speckle interferometry for assessment of surface roughness

In this work, the principle of interferometry is used to assess the surface roughness of the machined surfaces. Interferometry produces an interference fringe pattern when two or more light waves interact with each other. It is one of the important tool for precision optical metrology and testing. Well-known advantages of the phase shifting interferometry include high measurement accuracy, rapid measurement, good result even with low contrast fringes and that the polarity of the wave front can be determined. In fringe projection techniques, a known optical fringe pattern is projected onto the surface of interest. The fringe pattern on the surface is perturbed in accordance with the profile of the test surface, thereby enabling direct derivation of surface profile.In this work, an attempt has been made to assess the surface roughness using a speckle fringe analysis method of five frame phase shift algorithm for machined surface (ground surface). As these fringes are too noisy, advanced filtering technique has been used so as to reduce noise and to get improved wrapped phase map from the phase shifted fringes. A phase unwrapping software has been developed using discrete cosine transform (DCT) to generate the three-dimensional (3-D) profiles. Finally, it is compared with R_a values measured using a mechanical stylus instrument, showing good agreement.     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.     

Analysis of mechanical vibrations through speckle interferometry: A phase-space approach

The goal of this paper is to determine hidden periodicities (spatial frequencies) into speckles patterns obtained in a diffuser after reflection of an unexpanded laser beam over an aluminum membrane by means of the so-called Wigner Distribution Function (WDF). These spatial frequencies are used to find the temporal frequencies at which the mechanic system is vibrating.     

Signal processing method of phase correction for laser heterodyne interferometry

A novel signal processing method of movement direction identification and phase correction is presented for laser heterodyne interferometry. Based on the reference signal, four intervals with phase difference of 90° each other are set up. The real-time movement direction identification and the integer fringe counting are realized by detecting the times that the rising-edge of the measurement signal crosses the intervals. The phase correction approach is proposed in detail to solve the fraction phase compensation when the initial phase difference is not equal to the zero phase difference. Three experiments of the stability test, the nanometer and micrometer displacement tests on bi-directional movement were performed to demonstrate the usefulness and feasibility of the presented signal processing method.     

Phase retrieval in two-wavelength DSSI using a combined filtering method

Phase retrieval in two-wavelength DSSI (digital speckle shearing interferometry) using a combined filtering method is proposed for small deformation derivative measurement. A simultaneous two-wavelength illumination and 3-CCD camera are employed in the experimental setup. The proposed method, which uses a two-wavelength technique does not require the conventional spatial phase unwrapping and has the advantage of good noise suppression for phase retrieval. Experimental results obtained show that using the proposed combined filtering method sensitivity similar to the single wavelength technique can be achieved.     

Temporal heterodyne shearing speckle pattern interferometry

Shearing speckle pattern interferometry is a full-field speckle interferometric technique used to determine surface displacement derivatives. In this paper, a new measurement system of real-time heterodyne shearography interferometry is presented. This system combined with heterodyne measurement, shearography interferometry and time domain signal processing technology can dynamically detect the out-of-plane displacement gradient. The principles and system arrangement are described. Using the Jones matrix, the mathematical expression of light intensity distribution passing through this system is deduced. A preliminary experiment was performed to demonstrate the performance of this new device, and simulations were conducted using the finite element method. Comparison of results shows that quantitative measurement of the displacement derivative has been achieved.     

Comparison between instantaneous and integral intensities in dynamic speckle pattern interferometry

A new speckle measurement technique called temporal speckle pattern interferometry or time sequential speckle pattern interferometry has been developed recently. Its principle is that by capturing the temporal speckle patterns related to the object deformation or displacement, the whole-field displacement, the amplitude of the vibrating object and the shape of the tested object can be calculated through speckle intensity fluctuation scanning technique or Fourier-transforming method. In this paper, we combine the analytical and numerical methods to simulate the properties of the time demodulation in temporal speckle patterns interferometry techniques. The performance of three kinds of temporal phase sequences, power, exponential and harmonic phase sequences, are studied with the parameters of temporal speckle intensity fluctuation, the value of the spatial phase term, optical integral time of the recording camera and the initial phase of the temporal speckle intensities. The results indicate that the normalized value and period change of the instantaneous intensity are nearly coincident with that of the integral intensity for the harmonic temporal phase sequences and are different for the power and exponential temporal phase sequences.     

Real-time visualisation of deformation fields using speckle interferometry and temporal phase unwrapping

A real-time system for analysing data from speckle interferometers, and speckle shearing interferometers, has been developed. Interferograms are continuously recorded by a digital camera at a rate of 60 frames s⁻¹ with temporal phase shifting carried out at the same rate. The images are analysed using a pipeline image processor. With a standard 4-frame phase-shifting algorithm (phase steps of π/2), wrapped phase maps are calculated and displayed at 15 frames s⁻¹. These are unwrapped using a temporal phase unwrapping algorithm to provide a real-time colour-coded display of the relevant displacement component. Each camera pixel (or cluster of pixels) behaves in effect as an independent displacement sensor. The reference speckle interferogram is updated automatically at regular user-defined intervals, allowing arbitrarily large deformations to be measured and errors due to speckle decorrelation to be minimised. The system has been applied to the problem of detecting sub-surface delamination cracks in carbon fibre composite panels.