Interpretation of out-of-focus star images in terms of wave-front curvature

The wave-front-curvature-sensing method used by F. Roddier for the University of Hawaii’s curvature-adaptive-optics system is derived from the interpretation in 1979 of the out-of-focus images obtained by use of the Multiple Mirror Telescope. I summarize those original Multiple Mirror Telescope observations and the simple interpretation given in terms of wave-front curvature by use of geometrical optics at that time.