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Real-time measurement of surface roughness by correlation of speckle patterns

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Dominique Leger at Office National d'Études et de Recherches Aérospatiales
Dominique Leger
J. C. Perrin
J. C. Perrin
J. C. Perrin
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Abstract and Figures

In a previous article we have shown that the two speckle patterns produced from the same rough surface illuminated by two coherent plane waves under two different angles of incidence are correlated. The correlation depends on the surface roughness. In this paper a method is described where the rough surface is illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-time measurement of the surface roughness in the range of large roughness (σ > λ). The theoretical calculations have been performed for a normally distributed surface. The experimental results are in good agreement with theory. We describe the optical arrangement of an instrument based on this principle.
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Real-time measurement of surface roughness by correlation of speckle patterns
D. Leger and J. C. Perrin
Laboratoire d'Optique Coh6rente, Centre d'Etudes et de Recherches de la Compagnie Electra-Mgcanique, 49,
rue du Commandant Rolland- 93350 Le Bourget-France
(Received 25 April 1976)
In a previous article we have shown that the two speckle patterns produced from the same rough surface
illuminated by two coherent plane waves under two different angles of incidence are correlated. The
correlation depends on the surface roughness. In this paper a method is described where the rough surface is
illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the
correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-
time measurement of the surface roughness in the range of large roughness (a- > X). The theoretical calculations
have been performed for a normally distributed surface. The experimental results are in good agreement with
theory. We describe the optical arrangement of an instrument based on this principle.
I. INTRODUCTION
It is well known that the two speckle patterns scat-
tered by a rough surface under two different conditions
can be correlated. This property is currently used in
holographic interferometry or in speckle interferome-
try' to form the interference fringes or correlation
fringes between these two correlated speckle patterns.
1210 J. Opt. Soc. Am., Vol. 66, No. 11, November 1976
The shape of these fringes gives some information
about the displacement field on the rough surface,
whereas their contrast depends on the degree of cor-
relation between the two speckle patterns. It has been
recognized for a long time that the degree of correla-
tion between these two speckle patterns depends, among
other things, on the surface roughness, but none seems
ods2,3 based on such a principle have been proposed for
Copyright i 1976 by the Optical Society of America 1210
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... The pixel-wise SSC of the defined window, SSC(i l , j b ), can be deduced from these images by using Eq. (1) [15,18,21,28]: ...
... Here, m and n denote an individual picture element of the AOI defined by an l × b window. In addition, the theoretical equation governing the relationship between the degree of correlation, SSC(i l , j b ), and the RMS surface roughness, R q (i l , j b ), can be written as [15,18,28] ...
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