Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems.
Daniel K. Inouye Solar Telescope (formerly known as Advanced Technology Solar Telescope) will be the largest optical solar telescope ever built to provide greatly improved image, spatial and spectral resolution and to collect sufficient light flux of Sun. To meet the requirements of the telescope the design adopted a 4m aperture off-axis parabolic primary mirror with challenging specifications of the surface quality including the surface figure, irregularity and BRDF. The mirror has been completed at the College of Optical Sciences in the University of Arizona and it meets every aspect of requirement with margin. In fact this mirror may be the smoothest large mirror ever made.This paper presents the detail fabrication process and metrology applied to the mirror from the grinding to finish, that include extremely stable hydraulic support, IR and Visible deflectometry, Interferometry and Computer Controlled fabrication process developed at the University of Arizona.
Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.
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