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Autocorrelation functions from optical scattering for one-dimensionally rough surfaces.

E Marx, B Leridon, T R Lettieri

|August 31, 2010

Summary

This study experimentally validates a method linking surface roughness to scattered light patterns. The technique accurately measures surface height autocorrelation functions using optical scattering data, even for fine details.

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Area of Science:

Surface metrology
Optical physics
Scattering theory

Background:

Characterizing surface topography is crucial in many scientific and engineering fields.
Optical scattering methods offer non-contact alternatives for surface analysis.

Purpose of the Study:

To experimentally investigate the relationship between a 1D rough surface's height autocorrelation function and the Fourier transform of its scattered light intensity distribution.
To validate theoretical predictions derived using the Fraunhofer approximation.

Main Methods:

Derivation of theory using the Fraunhofer approximation, avoiding Kirchhoff boundary conditions.
Experimental testing using optical scattering data and comparison with stylus profilometry data.
Analysis of scattered light intensity distribution and its Fourier transform.

Main Results:

Good agreement was found between optical data and stylus data for surface height autocorrelation functions.
The method proved effective even for autocorrelation lengths comparable to the optical wavelength.
A limitation was identified: the method is best suited for surfaces with rms roughness less than approximately 0.14 times the optical wavelength.

Conclusions:

The experimental results support the theoretical model relating scattered light intensity to surface autocorrelation.
The optical scattering method provides a viable technique for surface characterization within specific roughness limits.
Further research may explore extending the method's applicability to rougher surfaces.