About the Efficiency of Using "Extended" Fourier Transforms for Surface Characterization by the Deconvolution Technique

摘要: Deconvolution of echoes scattered by a surface tends to give the response function Dirac pulse incident on surface. In some cases, this is easily related geometry scatterer and could be used characterize it. practical, situation with infinite bandwidth not realized even broad band transducer which acts as band-pass filter. We propose here simple arguments extend Fourier spectrum in order improve results deconvolution. Experiments are performed targets consisting either small plane surfaces various shapes or randomly rough surfaces. Results good agreement those expected using Kichhoff-Helmholtz integral. INTRODUCTION The signal reflected insonified very short ultrasonic contains, rather large range frequencies, information scattering properties study variation frequency can as, for example, defects metals.l,2 Indeed, when dimensions target same magnitude wavelengths waves, obeying diffraction laws highly varying one infer (lengths estimated within few percent). generally far field transducers that wave approximation va 1 i d. analysis time domain imaging techniques3 echo methods get size cracks. high techniques.4•5 For instance, it was shown Lloyd 4 who Freedman 6 theory mechanism formation generated each part object where discontinuity appears solid angle under sees object. This formulation gives excellent at much greater than wavelength so coming from different discontinuities well separated domain. extract whole axis given experiment. method proposed Haines Langston' characterization. It recreate transfer electronic equipment constant. But delivering band-limiting signals cannot total axis; therefore follows result deconvolution operation strongly affected spurious oscillations. comp ement extrapolation amplitude toward zero and, moreover, frequencies connection complex first second transducer; latter working higher but connected former. technique applied immersed water. THEORY Plane Targets assume approximated (experimentally we use placed transducer). Using Neubauer 8 Johnson9 Kirchhoff approximation, pressure backscattered rigid A is: 359 pr(k) = k~~a IJ R(e) cos e exp (-2ikz) da (1) phase factor depending choice coordinates, B coefficient including frequency; an elementary area z position element along propagation ultrasound Oz; incidence da; reflection e. smooth constant expression becomes: R( e)~~B If exp(-2ikz) (2) normalize value Pr0 (k) obtained normal calibrateo Acal z0 comes: pr(k)/Pro(k) 8R(a) exp(-2ikzl AcalR(OJ (3) (4) exp(2ikz l pure o~ origin coordinates. tilted respect beam axis, choose coordinates Ox' Oy (Fig. 1). y r------.::.;--~~ I