Several applications, both on the ground and in space, are envisaged for large, light parabolic reflectors which are compact when folded. In this paper the aim is to calculate by a differential method the deformed meridian line and the creased zone of an elastic inflatable revolution membrane. Conversely, one can calculate the original meridian line which, under a given pressure, transforms into a selected meridian line, in this case parabolic. The theory is confirmed by the deformation measurements of a cap in 36-µm thick polyester film cut out of a sphere 4 m in diameter.
© 1982 Optical Society of America
P. Casal, C. Fayard, and B. Authier, "Calculation of the elastic deformations of the revolution membranes," Appl. Opt. 20, 1983-1989 (1981)