Relation between Surface Roughness and Specular Reflectance at Normal Incidence

TLDR: In this paper, the roughness of a plane surface is related to its specular reflectance at normal incidence, and expressions for the case when the root mean square surface roughness is small compared to the wavelength of light are presented.

Abstract: Expressions relating the roughness of a plane surface to its specular reflectance at normal incidence are presented and are verified experimentally. The expressions are valid for the case when the root mean square surface roughness is small compared to the wavelength of light. If light of a sufficiently long wavelength is used, the decrease in measured specular reflectance due to surface roughness is a function only of the root mean square height of the surface irregularities. Long-wavelength specular reflectance measurements thus provide a simple and sensitive method for accurate measurement of surface finish. This method is particularly useful for surface finishes too fine to be measured accurately by conventional tracing instruments. Surface roughness must also be considered in precise optical measurements. For example, a non-negligible systematic error in specular reflectance measurements will be made even if the root mean square surface roughness is less than 0.01 wavelength. The roughness of even optically polished surfaces may thus be important for measurements in the visible and ultraviolet regions of the spectrum.