Abstract
We have seen in the previous chapter on optical aberrations how complicated the algebra can get. Recently a number of workers [1–4] have introduced formalisms using matrix methods to do nonlinear calculations (i.e., departures for Gaussian optics) and hence calculate aberrations up to any arbitrary order. However, the drawback of matrix methods when extended to the non-linear regime is that in general, large matrices are required. For example, if one were to go up to the 5th order, the size of the matrices are of the dimensions of 125 × 125 for any arbitrary conical surface. The size of the matrices can be reduced by the use of symmetries, but the method is still cumbersome.
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Lakshminarayanan, V., Ghatak, A.K., Thyagarajan, K. (2002). An Introduction to Lie Algebraic Treatment of Optical Aberrations. In: Lagrangian Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1711-5_8
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DOI: https://doi.org/10.1007/978-1-4615-1711-5_8
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