21 September 2011 Development of optical design algorithms on the base of the exact (all orders) geometrical aberration theory
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The process of optical design today is both an art and a science mainly due to the lack of exact and suitable aberration theory. In this paper we propose an exact (without any approximations) analytical aberration theory. It describes exactly the relations between the on-axis image aberrations and on-axis object aberrations via so called relative parameters, real aperture incidence angles, real aperture slope angles, refraction indexes and object distance. The image field aberrations (distortion, astigmatism, tangential curvature, sagittal curvature and field curvature) are described in a mathematically exact way by means of relative parameters, real incidence angles and slope angles of the chief rays, refraction indexes, object distance and corresponding object aberrations. For the image tangential coma and image sagittal coma we propose differential formulae. To verify the correction of every single aberration we use the commercial program OSLO. The differences between our and OSLO results for each aberration (except for the tangential and sagittal coma) are less than 1x10-8 mm. In addition we propose some exact aberration's correction algorithms for a very distant object and variety of constructive design solutions which confirm the truth of the proposed theory.
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Boian A. Hristov, Boian A. Hristov, } "Development of optical design algorithms on the base of the exact (all orders) geometrical aberration theory", Proc. SPIE 8167, Optical Design and Engineering IV, 81670E (21 September 2011); doi: 10.1117/12.896887; https://doi.org/10.1117/12.896887

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