Image structure from mirrors with print-through undulations: Theoretical analysis

摘要

The image structure produced by a periodic hexagonal pattern of mirror surface undulations has been analyzed. Such undulations form a two-dimensional phase grating that can result from the polishing of honeycomb mirrors or, for example, meniscus mirrors with a hexagonal pattern of axial supports. For monochromatic light of wavelength lambda, undulations having uniform peak-to-valley amplitude H lambda and period L cause a decrease in the central intensity of the point spread function (PSF), and a fraction, similar to 13(H/lambda)(2), of the total power is diffracted into an infinite hexagonal array of satellite images. These have angular separations of 2 lambda/root 3L and intensity profiles in the form of perfect diffraction Limited PSF's, but with intensities 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 the surface bumps are of random size with a normal frequency distribution, then the intensity of the diffracted orders decreases, and an additional weak structure appears over the image plane; the positions and heights of the peaks in this grasslike structure depend on the particular two-dimensional distribution of the random bumps. When the input is polychromatic, the diffracted orders other than zero give images that are elongated radially and decrease outward in intensity with a 1/lambda(4) dependence. (C) 1997 Optical Society of America.