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Reflectance for an approximately one-dimensional rough surface that has rms roughness greater than a wavelength

A relation between the intensity reflectances of approximately one-dimensional and one-dimensional rough surfaces within the diffraction solid angle in the specular direction for normal incidence is derived for an rms roughness greater than a wavelength. The relation shows that the reflectance of an approximately one-dimensional rough surface is proportional to the reflectance of a one-dimension rough surface. The validity of the derived relation is studied for an approximately one-dimensional rough steel surface with an rms roughness of 1.3 μm and a correlation length of 15.2 μm. The wavelength was 0.6328 μm and the angle of incidence was 4°. The reflectance of the rough steel surface was measured and estimated from the derived relation. Satisfactory agreement was found between the estimated and measured reflectance values.