Computer reconstruction of a periodic surface by means of the scattered and transmitted acoustic fields

The profile of a periodic surface for which an analytical expression in Fourier series exists is computer reconstructed. The surface is considered as a sum of sinusoidal gratings because of the fact that each surface can be presented in Fourier series. A periodic surface is chosen for testing of the mathematical model based on the solution of the Helmholtz integral equation in the case for which the Kirchhoff condition is realized for each harmonic. The surface profile is reconstructed using the acoustic field scattered from the surface as well as the transmitted acoustic field. In both cases all acoustic fields are registered (to the left and to the right relative to the central peak of the mirror reflected field) by a piezoelectric transducer moved by a computer controlled table. The fields are registered at a frequency of the radiating transducer of 1.1 MHz (A = 1.3636 mm at acoustic velocity 1500 m s(-1) in water). The surface profile is reconstructed from the fields registered to the left as well as to the right according to the mathematical model based on Kirchhoff's inequality. In both cases the reconstructed profile has the same form, period and distance from peak to valley as the real surface profile.