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16 June 2000 Using matrices to understand geometrical optics
Jose B. Almeida
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Proceedings Volume 3831, Sixth International Conference on Education and Training in Optics and Photonics; (2000) https://doi.org/10.1117/12.388749
Event: Education and Training in Optics and Photonics (ETOP'99), 1999, Cancun, Mexico
Abstract
The optimization of an optical system benefits greatly from a study of its aberrations and an identification of each of its elements' contribution to the overall aberration figures. The matrix formalism developed by one of the authors was the object of a previous paper and allows the expression of image-space coordinates as high-order polynomials of object-space coordinates. In this paper we approach the question of aberrations, both through the evaluation of the wavefront evolution along the system and its departure from the ideal spherical shape and the use of ray density plots. Using seventh-order matrix modeling, we can calculate the optical path between any two points of a ray as it travels along the optical system and we define the wavefront as the locus of the points with any given optical path; the results are presented on the form of traces of the wavefront on the tangential plane, although the formalism would also permit sagittal plane plots. Ray density plots are obtained by actual derivation of the seventh-order polynomials.
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Jose B. Almeida "Using matrices to understand geometrical optics", Proc. SPIE 3831, Sixth International Conference on Education and Training in Optics and Photonics, (16 June 2000); https://doi.org/10.1117/12.388749
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KEYWORDS
Wavefronts
Geometrical optics
Spherical lenses
Matrices
Refractive index
Ray tracing
Monochromatic aberrations
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