Pierre Jacquot

Deformation measurement with object-induced dynamic phase shifting

A simple, yet powerful, means of computing the phase of fringe patterns depicting dynamic phenomena is presented. It is shown that the basic principle of the phase-shifting methods can be extended to the case of dynamic situations. The crux is to recognize that the phenomenon under examination can itself provide the necessary incremental phase shifts. This new method possesses a very wide range of applications in the field of deformation measurement.

Speckle motions induced by rigid-body movements in free-space geometry: an explicit investigation and extension to new cases

In line with the current interest in speckle motion in free-space propagation, it is proposed to investigate new aspects of the induced speckle motion due to rigid-body movements of a model using as a starting point the well-known concept of homology, first stated in holographic interferometry, the importance of which has only recently been realized in speckle metrology. At the outset, stating the homology conditions leads to a general expression relating the speckle shift to the geometrical parameters at the recording and to the six degrees of movement of the object surface. The expression presented in this explicit form is found to be true for both opaque and thin transparent diffusing models and for different conditions of illumination and observation. The study is then extended to (1) when the object is at rest, subjecting the illuminating source to a small displacement and (2) when the wavelength of the illuminating beam is changed between the two exposures. The case of the rigid-body displacement of the object is experimentally verified and the results are found to be in good agreement with theory. The viability of the method to make measurements is assessed, several applications are envisaged, and some advantages are pointed out.

Wavelet processing of interferometric signals and fringe patterns

The measurement of shape, displacement and deformations is often performed using interferometric methods, featuring nm to mm sensitivities and very high spatial and temporal resolutions. We first give a brief overview of interferometric techniques. Emphasis is laid on the wide purposes of these techniques. Then, we present a novel method using wavelet analysis to process live interference patterns. Further developments of the method are then presented. Finally, through two practical examples, we intend to highlight the interest of fringe processing by wavelet transform.

Measurement of difference deformation using speckle interferometry

An application of speckle interferometry is presented that allows one to compare the resistance to stress of two nominally identical specimens. The interference pattern gives contours of equal differences in displacements of the two stressed specimens. The method is briefly developed, and its experimental feasibility is demonstrated by comparing the deflections of two square plates clamped along the edges and subjected to centrally concentrated loads.

The empirical mode decomposition: a must-have tool in speckle interferometry?

In a wider and wider range of research and engineering activities, there is a growing interest for full-field techniques, featuring nanometric sensitivities, and able to be addressed to dynamic behaviors characterization. Speckle interferometry (SI) techniques are acknowledged as good candidates to tackle this challenge. To get rid of the intrinsic correlation length limitation and simplify the un-wrapping step, a straightforward approach lies in the pixel history analysis. The need of increasing performances in terms of accuracy and computation speed is permanently demanding new efficient processing techniques. We propose in this paper a fast implementation of the Empirical Mode Decomposition (EMD) to put the SI pixel signal in an appropriate shape for accurate phase computation. As one of the best way to perform it, the analytic method based on the Hilbert transform (HT) of the so-transformed signal will then be reviewed. For short evaluation, a zero-crossing technique which exploits directly the extrema finding step of the EMD will be presented. We propose moreover a technique to discard the under-modulated pixels which yield wrong phase evaluation. This work is actually an attempt to elaborate a phase extraction procedure which exploits all the reliable information in 3D, - two space and one time coordinates -, to endeavor to make the most of SI raw data.

Simulation of speckle complex amplitude: advocating the linear model

The basic convolution integral, Uf = Uo crossed circle h where Uo is a random object complex amplitude and h the impulse response of the system under consideration, serves to model the observed speckle field Uf. Depending on the choice of h, the simulated field is an objective or a subjective speckle pattern. The computation makes use of two consecutive Fast Fourier Transforms. In the reported examples, the object function represents a pure phase diffuser ruled by a uniform distribution. The probability density functions (PDF) of the simulated intensity and phase patterns fit very well with their analytical counterparts obtained under the classical Gaussian hypotheses. Phase maps exhibit the awaited singularities. Moreover, elements of second order statistics, as the autocorrelation functions, are in very good agreement too. Furthermore, subtle effects, as the dip of contrast in the focused image plane of partially developed speckle patterns, are also suitably disclosed. The linear model thus appears, all together, as conceptually easy, very flexible, computationally simple, very accurate for a wide range of experiments, and endowed with excellent predictive and speculative potentials.

Influence of out-of-plane deformation and its elimination in white light speckle photography

Abstract The aim of this paper is to present the white light speckle method as a practical tool in metrology and to search for the optimum conditions for its application. In particular, the study provides evidence that the white light speckle technique is not exclusively sensitive to the in-plane components of displacement. Consequently, the interpretation of the Youngs fringes as pure in-plane fringes is prone to inaccurate measurements. The errors so introduced are systematically analysed for various optical parameters. Some practical considerations are then pointed out to aid in the design of an error-tolerance limited white light displacement measurement system to suit a particular need. two complementary techniques are next proposed which promise to eliminate the influence of the out-of-plane movements on the measurement of the lateral components of displacement. The proposed methods not only allow an increase in the accuracy of in-plane measurements, but also permit mapping of the out-of-plane movements undergone by the object surface. The techniques presented, apply equally to coherent speckle photography where the same problems are manifest, and should pave the way for the application of these methods to concrete engineering problems.

Speckle Metrology Techniques: A Parametric Examination Of The Observed Fringes

Considerable interest in speckle metrology and a consistent search to refine these techniques to suit the intricate engineering environment has led to an active investigation into the basic aspects of speckle movements in three-dimensional space induced by small displacements and deformations of the object surface. The model exploited in this paper is based on the notion of the local invariance of the speckle structure in such a case; it is thus intimately related to the concept of homology and draws closely on the theories aiming to reconcile speckle metrology and holographic interferometry techniques. The laws of speckle motions issuing from this model are applied to major known techniques in speckle photography (focused or defocused), speckle interferometry, and speckle shearing interferometry in an attempt to make as objective an assessment as possible of these methods. The study unveils the influence of parasite movements, field angles, and the geometrical parameters at the recording on the measured component, thereby paving the way for the optimization of a method to a given deformation problem and forging a better understanding of the phenomenon underlying these techniques.

Phase shifting of whole field speckle photography fringes.

A phase shifting readout system is used to analyze whole field fringes in dual plate speckle photography and preliminary results obtained with a first prototype are presented.

Multiple optical trapping in high gradient interference fringes

In biological investigations, many protocols using optical trapping call for the possibility to trap a large number of particles simultaneously. Interference fringes provide a solution for massively parallel micro-manipulation of mesoscopic objects. Concurrently, the strength of traps can be improved by raising the slope of fringe profiles, such as to create intensity gradients much higher than the ones formed by sinusoidal fringes (Youngs fringes). We use a multiple-beam interference system, derived from the classical Fizeau configuration, with semitransparent interfaces to generate walls of light with a very high intensity gradient (Tolansky fringes). These fringes are formed into a trapping set-up to produce new types of trapping templates. The possibility to build multiple trap arrays of various geometries is examined; a high number of particles can be trapped in those potential wells. The period of the fringes can easily be changed in order to fit traps sizes to the dimensions of the confined objects. This is achieved by modifying several parameters of the interferometer, such as the angle and/or the distance between the beam-splitter and the mirror. It is well known that optical trapping presents a great potential when used in conjunction with microfluidics for lab-on-a-chip applications. We present an original solution for multiple trapping integrated in a microfluidic device. This solution does not require high numerical aperture objectives.