M. Stankova et al., Computer reconstruction of a periodic surface by means of the scattered and transmitted acoustic fields, MEAS SCI T, 12(8), 2001, pp. 1330-1335
The profile of a periodic surface for which an analytical expression in Fou
rier series exists is computer reconstructed. The surface is considered as
a sum of sinusoidal gratings because of the fact that each surface can be p
resented in Fourier series. A periodic surface is chosen for testing of the
mathematical model based on the solution of the Helmholtz integral equatio
n in the case for which the Kirchhoff condition is realized for each harmon
ic. 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 t
o the central peak of the mirror reflected field) by a piezoelectric transd
ucer moved by a computer controlled table. The fields are registered at a f
requency 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 recon
structed profile has the same form, period and distance from peak to valley
as the real surface profile.