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- W1991623450 abstract "Abstract The need to achieve control of specific aberrations and to investigate theaberrational properties of lens systems, has led to the development of aninteractive design tool based on multi-dimensional quadratic extrapolation.A quadratic approximation to the non-linearly varying aberrations allowsthe step length of this differential correction technique to be extended andthe underlying relationships between goups of constructional parametersand aberrations are revealed. Examples are given. Introduction Mathematical optimization algorithms have been successfully used in the correction of lens systems for manyyears. The damped-least squares (DLS) algorithm [1], and its many enhanced forms [2,3,4], are the mostwidely used optimization techniques for lens design but there are several other methods which representsignificantly different approaches [5,6,7]. Although the method to be described here may appear to besimilar to the work of Meiron and Volinez [8] and Huber [3], it is fundamentally different. Both Meiron andVolinez and Huber approximate the variation of the merit function by a parabola whereas our quadraticapproximation is to the variation of the individual aberrations.The method to be described in this paper uses a quadratic function to approximate the variation of eachaberration along a vector of linearly generated parameter changes. These quadratic functions are then solvedfor the required aberration target values and the changes fed back to yield a solution vector which wouldachieve these targets if the quadratic approximations were valid.As in principle in any optimization method, the specification of targetted aberrations need not be restrictedin any way. For example, they can be specified as Seidel sums, ray intersection data from a finite ray trace,wavefront aberration coefficients etc. The variable parameters can be combined to allow grouped variablesto be defined, for example, as a thin lens bend. Methods of combining lens constructional parameters areonly ingenuity-limited, but are usually chosen with a potential for correcting one or more of the targettedaberrations. The only restriction in the method that we are reporting here is that the number of targettedaberrations and variables are identical. Although this appears to be a severe constraint, the examples atthe end of this paper demonstrate that this is not the case and what is more, the target values are reached,where possible, in a very few iterations.An important feature of this method is that it reports the feasibility of the correction strategy, so that if a" @default.
- W1991623450 created "2016-06-24" @default.
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- W1991623450 date "1991-01-01" @default.
- W1991623450 modified "2023-09-23" @default.
- W1991623450 title "Simple multidimensional quadratic extrapolation method for the correction of specific aberrations in lens systems" @default.
- W1991623450 doi "https://doi.org/10.1117/12.47886" @default.
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