SIMULATION OF LIGHT-SCATTERING BY TECHNICAL ROUGH SURFACES AS A BASIS OF METHODS FOR OPTICAL MEASURING OF ROUGHNESS

Many optical measuring methods for determining the roughness rest on the analysis of light scattered from the surface which has to be examined. The specific aim of these methods is the determination of the values of definite statistical parameters of the scattering surfaces. For this, these parameters have to be related to the stochastic properties of the scattered light. Therefore, besides the stochastic description of surface microstructures an optical theory of light scattering is needed as the basis of such measuring methods. For checking and evaluating analytical results which are obtained by statistical optics methods and which often use idealizing assumptions, a computer simulation of the process of light scattering may be carried out first. In this paper a corresponding simulation method is introduced. The development of this method starts with a well-known relation for the description of the electric far field of monochromatic light which has been scattered by a rough surface. This theoretical relation may be achieved by applying the Kirchhoff-theory of physical optics. Using mathematical functions h(j) which give the deviations of the surface heights from a medium height it is possible to determine the values of the corresponding intensities I(j) of the light scattered into the Fraunhofer region. In the present paper, this will be pointed out for fictive profiles h(j)(x) of surfaces which are rough in one direction only. These fictive profiles are generated numerically giving N sampled values of the surface heights. Based upon these sampled values a numerical integration method is introduced for the purpose of estimating the intensity values mentioned above. At last, this advance permits the realization of a Monte Carlo method which makes it possible to check statistical measuring methods for the optical determination of surface roughness values. This will be discussed on the example of roughness measurement by the method of Dichromatic Speckle Correlation.