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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 λ, undulations having uniform peak-to-valley amplitude ℋ ≪ λ and period L cause a decrease in the central intensity of the point spread function (PSF), and a fraction, ∼13 (ℋ/λ)2, of the total power is diffracted into an infinite hexagonal array of satellite images. These have angular separations of 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/λ)2 times that of the central image. If the amplitudes 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/λ4 dependence.
© 1997 Optical Society of America
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