18 September 2007 Third order aberration solution using aberration polynomials for a general zoom lens design
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A mathematical approach for the third order solution for a general zoom lens design is proposed. The design starts with a first-order layout. Lens elements with the proper refracting power are placed at the proper distances to meet the physical constraints of the intended lens system. For the third-order design stage, a matrix notation called "Aberration Polynomial," which clarifies the linearity of the transformation from a normal thin group configuration to a general thin group configuration by pupil shift and conjugate shift theory is implemented. The purpose of the method is correcting low-order aberrations during the preliminary design of zoom lenses. The goal is to mathematically reduce to zero the four aberration coefficients of the third-order (spherical aberration, coma, astigmatism, and distortion) rather than searching for a minimum by commercial design software. Once this theory is proven and accepted, it becomes possible to determine how many groups are needed for a particular optical system. The method of aberration polynomials establishes the number of groups needed to correct a given number of aberrations at a given number of zoom positions. Furthermore, it provides the shape or bending of the elements, from where it will be possible to continue to optimize with standard methods.
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Hyun Kyoung An, Juan L. Rayces, Patrick J Reardon, "Third order aberration solution using aberration polynomials for a general zoom lens design", Proc. SPIE 6667, Current Developments in Lens Design and Optical Engineering VIII, 66670B (18 September 2007); doi: 10.1117/12.732206; https://doi.org/10.1117/12.732206

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