Adaptive Automatic Correction in Optical Design

E. Glatzel; R. Wilson

doi:10.1364/AO.7.000265

Applied Optics
Vol. 7,
Issue 2,
pp. 265-276
(1968)
•https://doi.org/10.1364/AO.7.000265

Adaptive Automatic Correction in Optical Design

E. Glatzel and R. Wilson

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E. Glatzel and R. Wilson, "Adaptive Automatic Correction in Optical Design," Appl. Opt. 7, 265-276 (1968)

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Abstract

An adaptive technique for optical design with computers is described Its distinctive features are compared with those of the well known damped least squares (DLS) method. The system of adaptive control ensures a particularly certain and rapid convergence, often of an order of magnitude quicker than the DLS method. The convergence is illustrated for a number of examples. The adaptive method enables the designer to learn the fundamental potentialities and limitations of a given optical system.

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DLS	Glatzel adaptive method
1) (x) = [(A)^T(A) + K(I)]⁻¹(A)^T(f_s − f_o)	1) (x) = (A)^T[(A)(A)^T]⁻¹(f_s − f_o)
2)ϕ function	2) Aberrations are independently controlled
3) Weights on aberrations	3) No weights necessary
4) Normally n > m but no restriction	4) n ≤ m
5) All acceptable parameters are used in each matrix solution	5) As DLS
6) Target values normally used—but rarely to steer the course of correction	6) Target values are used to steer course of correction and are reduced automatically
7) Damping is normally to an optimum step for linearity. Usually, new matrix (A) for each step	7) No mathematical damping because of inner cycle technique. Matrix (A) used repeatedly
8) Choice of controlled aberrations normally remains fixed for a given system. Weights are changed to steer ϕ	8) The aberrations are controlled successively; the choice is continually adjusted to the state of the correction

DLS	Glatzel adaptive method
1) (x) = [(A)^T(A) + K(I)]⁻¹(A)^T(f_s − f_o)	1) (x) = (A)^T[(A)(A)^T]⁻¹(f_s − f_o)
2)ϕ function	2) Aberrations are independently controlled
3) Weights on aberrations	3) No weights necessary
4) Normally n > m but no restriction	4) n ≤ m
5) All acceptable parameters are used in each matrix solution	5) As DLS
6) Target values normally used—but rarely to steer the course of correction	6) Target values are used to steer course of correction and are reduced automatically
7) Damping is normally to an optimum step for linearity. Usually, new matrix (A) for each step	7) No mathematical damping because of inner cycle technique. Matrix (A) used repeatedly
8) Choice of controlled aberrations normally remains fixed for a given system. Weights are changed to steer ϕ	8) The aberrations are controlled successively; the choice is continually adjusted to the state of the correction

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Applied Optics