Experiments are currently in progress testing the optical quality of cryogenic targets made using the {beta}-layering process. This process uses the heat liberated from decaying tritium to sublimate thick parts of the DT layer. This sublimated DT is subsequently condensed on a thinner part of the shell thereby tending to equalize the layer thickness. The uniformity and stability of the ice layer formed on the inside of these capsules is of fundamental importance. The experiments now being performed simply photograph a capsule through a pair of transparent windows in the dewar as the temperature is lowered below the triple point and finally the sublimation point of the DT mixture. The analysis of these photographs is made difficult by the strong refraction and multiple reflections of the light by the sapphire shell and the relatively weak refraction at the vacuum solid DT interface. Photographs thus far obtained show very little difference between an empty shell and a shell which is believed to be uniformly layered with hydrogen ice. The difficulty in interpreting these data has led to the establishment of an effort to simulate these measurements by direct computational methods. The code which is the subject of this report is a …