23 August 1996 Minimization of astigmatism of toroidal strong off-axis holographic optical elements
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Abstract
The two principal radii of curvature of toroidally curved Holographic Optical Elements offer two extra parameters in the design and optimization of HOE's. It appears to be possible to reduce to zero the second order astigmatism term in the series expansion of the wavefront aberration, that is expressed in the coordinates of a plane normal to the principal ray to the gaussian image point. Analytic expressions are derived for the optimal principal radii of curvature of the HOE to fulfill this condition. The wavefront aberration, elaborated to the fourth order and reordered in Zernike polynomials, together with an exact expression of the total wavefront aberration offer tools for further analysis of the aberrations. As an example, a HOE applicated as a diffraction-mirror in a infrared spectrograph is calculated for zero second-order astigmatism.
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E. G. Skalli, E. Jan de Jong, Joseph J. M. Braat, "Minimization of astigmatism of toroidal strong off-axis holographic optical elements", Proc. SPIE 2774, Design and Engineering of Optical Systems, (23 August 1996); doi: 10.1117/12.246662; https://doi.org/10.1117/12.246662
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