Roughness measurement using threshold angle of image formation

Abstract

When the emitted light from a small object illuminates a rough interface, the image of the object is formed in reflection if the incident angle of the light is larger than a threshold angle. The threshold angle is the angle beyond which the specularly scattered light acquires a coherent component. The threshold angle depends on interface roughness and light wavelength. In transmission mode, the incident angle on the rough interface has an upper limit for image formation. The latter angle depends also on the refractive indices of the media surrounding the rough interface. We have determined the threshold angles and corresponding roughness for three different wavelengths using rough sheet-glass surfaces that were prepared by grinding sheet-glass surfaces by powders of different grain size. The roughnesses obtained by this method are in good agreement with those obtained by other methods. Our experimental studies also show that the threshold angle is practically independent of the illumination intensity. The presented method has the potential to be used in process measurement due to simplicity of the required optical system.