Abstract:
Detection of periodic structures, hidden in random surfaces has been
addressed by us for some time and the `extended matched filter' method,
developed by us, has been shown to be effective in detecting the hidden
periodic part from the light scattering data in circumstances where
conventional data analysis methods cannot reveal the successive peaks due to
scattering by the periodic part of the surface. It has been shown that if
$r_{0}$ is the coherence length of light on scattering from the rough part
and $\Lambda$ is the wavelength of the periodic part of the surface, the
extended matched filter method can detect hidden periodic structures for
$(r_{0}/\Lambda )\ge 0.11$, while conventional methods are limited to
much higher values ($(r_{0}/\Lambda) \ge 0.33$). In the method
developed till now, the detection of periodic structures involves the
detection of the central peak, first peak and second peak in the scattered
intensity of light, located at scattering wave vectors $v_{x} = 0$, $Q$, $2Q$,
respectively, where $Q = 2\pi/\Lambda$, their distinct identities
being obfuscated by the fact that the peaks have width $\Delta v_{x} =
2\pi/r_{0} \gg Q$. The relative magnitudes of these peaks and the
consequent problems associated in identifying them is discussed. The
Kolmogorov--Smirnov statistical goodness test is used to justify the
identification of the peaks. This test is used to `reject' or `not
reject' the null hypothesis which states that the successive peaks do exist. This
test is repeated for various values of $r_{0}/\Lambda$, which leads to
the conclusion that there is really a periodic structure hidden behind the
random surface