IMAGE STRUCTURE FROM MIRRORS WITH PRINT-THROUGH UNDULATIONS - THEORETICAL-ANALYSIS

The image structure produced by a periodic hexagonal pattern of mirror surface undulations has been analyzed. Such undulations form a two-di mensional phase grating that can result from the polishing of honeycom b mirrors or, for example, meniscus mirrors with a hexagonal pattern o f axial supports. For monochromatic light of wavelength lambda, undula tions having uniform peak-to-valley amplitude H << lambda and period L cause a decrease in the central intensity of the point spread functio n (PSF), and a fraction, similar to 13(H/lambda)(2), of the total powe r is diffracted into an infinite hexagonal array of satellite images. These have angular separations of 2 lambda/root 3L and intensity profi les in the form of perfect diffraction Limited PSF's, but with intensi ties decreasing with increasing diffraction order. The six innermost ( first-order) satellites each have central intensities approximately 2( H/lambda)(2) times that of the central image. If the am, plitudes of t he surface bumps are of random size with a normal frequency distributi on, then the intensity of the diffracted orders decreases, and an addi tional weak structure appears over the image plane; the positions and heights of the peaks in this grasslike structure depend on the particu lar two-dimensional distribution of the random bumps. When the input i s polychromatic, the diffracted orders other than zero give images tha t are elongated radially and decrease outward in intensity with a 1/la mbda(4) dependence. (C) 1997 Optical Society of America.