Measurement of the interface roughness by determining the image formation threshold angle

Abstract

As the emitted light from an object strikes a rough interface the scattered light in specular direction can form image only at incident angles beyond a threshold angle that depends on surface roughness and light wavelength. This is also the case in transmission mode, but in this case the image is observed below a threshold angle that depends also on refractive indices of the media surrounding the rough interface. In this work we show that the threshold angle is the angle beyond which the scattered light acquires coherent component in specular direction. Using glass surfaces roughened by powders of different grain sizes we have measured the threshold angles for roughnesses in the range of 0.420-4.23 μm with the precision of 5 arc minutes, which provides the measurement of the roughness, σ, with a precision in the range 0.002-0.15 μm. Our experimental studies show that the threshold angle is practically independent of the illumination intensity. We have also studied the dependence of the threshold angle on wavelength and the change in the image color with the change of incident angle in reflection and transmission. The theoretical predictions and experimental results are in good agreement.