Moire methods are optical neasurernent methods , that are based on the effect of superposition ofgrating lines and have been widely used in the context of industrial applications for shape analysis for non-contact measurements and for quality control of industrial components . In apf)hcations the following computations: image filtering fringe skeletonising and fringe numbering have to be performed for each test object , before comparison between the numerically reconstructed test object shape and its CAD. inodel . in oider to ieduce the computing time required by the preceeding computations , the inverse nioiré technique has been intoduced by Harthong. Instead of using a grating made of parallel straight lines , the inverse moire technique uses a pre-computed specific grating , that is formed of curved lines such that the moire pattern is composed of parallel straight fringes if the test object shape is conform to its CAD. model . Defects are then characterized by a deformation and a curvature of these parallel fringes . In this paper , we present examples showing tlia.t standard fringe extraction by automatic thresholding is not that. easy. ic) OV(ICOfl1( this (liihcultv, wc propose a four stage process a.lgorithrnical approach that. al lows fri nge det.ect.ioi i i i nverse n ot r i m ages with high sensitivity and sJ)ecificity. lirs we used the well-known image processing technique called urisharp masking , to enhaiice moire iiiage and to emphasize low contrasted fringes. The second SteJ) is to extract bright fringes by image segmentation and constrained contour modeling. After deletion of these bright fringes inside the zone of interest of the moire image, we get the thick skeleton of adjacent background and of dark fringes. The third step is to skeletonize this thick skeleton of adjacent background and of dark fringes, using morphological thinning of well-composed sets , that assures that each fringe skeleton will be one pixel thick ,at the difference of standard thinning techniques . The fourth step is to apply a graph technique to isolate the individual dark fringes. When all these four steps have been followed , one is left with a binary iniage showing the dark fringe pattern skeleton . The experimental results that have been obtained have shown the robustness of this algorithmical approach for the analysis of noisy iiiverse nioiré 111 iages 1 Introduction Moire methods are optical measurement metho(ls [2], [7] , [8] , [12], that are based oii the effect of superposition of grating lines . These techniques have 54 / SPIE Vol. 2786 0-8194-21 72-3/96/$6.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/21/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
We present a mathematical analysis of moiré sensing in which the basic theoretical concept-and tool-is the concept of the contour function. We show that the mathematical analysis is simplified greatly by systematic recourse to this tool. The analysis that is presented permits a simultaneous treatment of two different modes of implementing the moiré technique: the direct mode (widely used and well known) and the converse mode (scarcely used). The converse mode consists of computing and designing a grating especially for one model of an object in such a way that if (and only if) the object is in conformity with theprescribed model, will the resulting moiré fringes be parallel straight lines. We give explicit formulas and algorithms for such computations.
Among all the parameters that characterize a phase grating, the most difficult to control is the modulation profile of the refractive index. In fact, it covers many scalar parameters that are the Fourier coefficients of the profile. To study the influence of processing baths on the modulation profile, in phase holographic gratings made of dichromated gelatin, we have observed that the shape of the profiles obtained sometimes presents a slight concavity or a convexity in the middle, leading to an increase or a decrease in the diffraction efficiency. We present the experimental results and a numerical study in the form of a theoretical prediction, which confirms the experimental observations.
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