A small dark ring is formed when laser radiation is incident normally on a thin slab of transparent material that has an index of refraction greater than one, a smooth, specularly reflecting front surface, and a white diffusely reflecting substrate. The dark ring, which is located on the substrate, increases in size as the thickness of the transparent medium increases. It is formed when (1) the ratio of transparent medium thickness to diameter and (2) the ratio of laser beam diameter to transparent medium diameter are small. Since the radius of the dark ring is a function of the transparent medium thickness (as well as the index of refraction), the problem is two-dimensional. Experimental data are presented for the backscattered radiation in the normal direction as a function of radial distance from the incident laser beam. A geometric optics development is used to explain (1) the ring formation and (2) the effect of finite-sized detection apertures. Comparisons with the experimental measurements are used to verify the theoretical analysis.
D. C. Look, Jr.,
H. F. Nelson,
"Reflection Of Laser Radiation From Transparent Media (N >1) With A Diffusely Reflecting Substrate," Optical Engineering 25(1), 251173 (1 January 1986). https://doi.org/10.1117/12.7973796