Proceedings of Topical Meeting on Optoinformatics (pdf-format, 1.21 ...

SAINT-PETERSBURG, October 17 – 20, 2005 23
THE APPLICATION OF DIRECT INTEGRAL-GEOMETRIC
METHODS FOR THE ANALYSIS OF SOME EXPERIMENTAL
INTERFEROMETRIC IMAGES
A.A. Aliverdiev
Institute <strong>of</strong> Physics, Daghestan Scientific Center <strong>of</strong> Russian Academy <strong>of</strong> the Science
367003, Russia, Daghestan, Makhachkala, 94 Yaragskogo Street
E-mail: aliverdi@frascati.enea.it, URL: http://aliverdi.rusf.net
Here we present our approach to apply the direct integral-geometric methods in
analysis <strong>of</strong> interferometric images. These approaches give the possibility to
increase the precision <strong>of</strong> further physical analysis, and the automation <strong>of</strong> some
steps <strong>of</strong> analysis.
In our resent works we have considered the use <strong>of</strong> the back [1-4] and direct [4-10] Radon
transform for the different physical applications. Here we report some new data about the
application <strong>of</strong> the direct Radon transform for the interferometric image analysis, which we
already tested for the experimental data diagnostic <strong>of</strong> laser plasma and for the ESPI
measurements.
We already reported [11] some results <strong>of</strong> an experimental investigation <strong>of</strong> the
temporal evolution <strong>of</strong> plasmas produced by laser irradiation. The experimental set up
includes a Nd:glass high power laser system with typical intensity <strong>of</strong> 10 14 W/cm 3 and
duration 600 ps, a probe beam (Nd:YAG converted to 2ω) coupled to an interferometer
and to a streak-camera with ps/µm resolution. The density <strong>of</strong> free electrons in that
conditions could be considered proportional to the phase shift in the interferometric a
streak-camera image. So, the precision <strong>of</strong> the determination <strong>of</strong> phase shift is the crucial
point <strong>of</strong> the analysis. But unfortunately the quality <strong>of</strong> real experimental interferograms is
not good. The separate time-dependence <strong>of</strong> the streak-camera image intensity for the
certain x 0 doesn't contain the full information about the real phase shift cause <strong>of</strong> presence
<strong>of</strong> a strong noise, which can be resulted and in the neglecting or shift <strong>of</strong> a real extremes,
both in the appearance <strong>of</strong> a false extremes. But from other hand, the averaging by axis x
doesn't give the good results, because <strong>of</strong> it smoothes the picture. To overcome this problem
we <strong>of</strong>fer the averaging with time shifts, with a characteristic velocity more or less
correspondent to real velocity. The peculiarities <strong>of</strong> this method are discussed in the present
report for the first time.
We also present the method <strong>of</strong> image analysis for the automatic set up <strong>of</strong> an
Electronic Speckle Pattern Interferometry (ESPI). The idea <strong>of</strong> our method is to make a
direct Radon-like transformation for each pixel (x 0 , y 0 ) a 2D field <strong>of</strong> an image brightness
s0
B(x,y): g( x y s = ∫ B x + s ⋅ − p ⋅ y + s ⋅ + p ⋅ dp
0,
0 )( , φ ) ( 0 cos( φ)
sin( φ),
0 sin( φ)
cos( φ))
, where
−s0
( s , φ)
are the normal co-ordinates <strong>of</strong> the Radon-like transformation, p is the variable <strong>of</strong>
integration, and then we calculate the rms spatial deviation by s
2
2
σ s ( φ)
= ( g(
s,
φ)
− g(
s,
φ)
) , the maximum <strong>of</strong> which determines two value: (i)
s
s
immediate max φ ( σ s ), and (ii) the corresponded angle φ (( σ s )
max
) . Similar transformation
we already used in some other applications. So, from 2D function B(x,y) we have two