Aberration Theories for Semiautomatic Lens Design by Electronic Computers II A Specific Computer Program

Grey, David S.

doi:10.1364/josa.53.000677

Cited by 9 publications

(5 citation statements)

References 2 publications

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“…Except for the LS methods, Spencer [37] has specified that computers could only be regarded as a tool capable of offering optical designers temporary solutions because qualitative judgments and compromises were required in the optimization of optical systems. A novel concept of aberrations brought up by David S. Grey [38,39] is prominent, and this is principally due to the practical realization of his computer program, where a novel orthonormal theory of aberrations was applied in the optimization of optical systems. Moreover, the orthonormalization in this theory was improved through the Gram-Schmidt transformation proposed by Pegis et al [40].…”

Section: Overview Of Optical Imaging System Designmentioning

confidence: 99%

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

et al. 2022

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An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.

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Section: Overview Of Optical Imaging System Designmentioning

confidence: 99%

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

et al. 2022

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“…Our partitioning strategy is an input parameter to the program. It may range from blocks containing single variables (Grey's original [8]) to a single block containing all variables (Gauss-Newton-Hartley [9]). Since every program contains tactics peculiar to its author, two programs that purport to use identical strategy may perform somewhat differently.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

“…In addition, St. Clair and Rigler [8] have found the blocked orthogonalization process to be advantageous when fitting Lorentz functions to spectroscopic data.…”

Section: Acknowledgementmentioning

confidence: 99%

“…We have just described the Gauss-Newton-Hartley algorithm [9] for nonlinear regression, where QR decomposition may be used to solve the sequence of linear problems. Grey [8] used the Gram-Schmidt decomposition to transform the residual equations (2) into the system The vector tk is the kth column of T = S -1, at least one of which is a descent direction; further, gk is the kth column of G. l~or ~(x) quadratic, g [h(xo) represents the distance traveled in the t k direction. When ~(x) is nonquadratic, Xne w is computed in increments,…”

Section: Introductionmentioning

confidence: 99%

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An algorithm for least squares analysis of spectroscopic data

Clair

Rigler

1979

BIT

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Abstract.This paper describes a variant of the Gauss-Newton-Hartley algorithm for nonlinear least squares, in which a QR implementation is used to solve the linear least squares problem. We follow Grey's idea of updating variables at intermediate stages of the orthogonalization. This technique, applied in partitions identified with known or suspected spectral lines, appears to be especially suited to the analysis of spectroscopic data. We suggest that this algorithm is an attractive candidate for the optimization role in Ekenberg's interactive computer graphics curve fitting program.

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“…The coefficients of the linear combination of active constraints in (20) are the Lagrange multipliers. The magnitude of the multipliers is proportional to the sensitivity of the aberration function to changes in the constraint targets.…”

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confidence: 99%

Optimization Methodology

Hayford

1985

Geometrical Optics

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IntroductionProgress in optical design has always been a function of the computational tools available to the designer.In the last half of the Twentieth Century, progress in optical design has been propelled along by vast increases in the power of computing hardware.This development has led to a complete change in the way optical design is actually done.Modern optical design is intensely computer-dependent but still at a point where intelligent inputs from a human designer are essential to the process of optical design.The software tools available today are the result of over 25 years of research, development and use and can provide cost -effective solutions to increasingly complex problems.They can yield impressive results when used by an experienced optical designer and even, in some cases, the novice designer.1 At the same time, the software tools are by no means fail -safe, and the unknowing user may spend dearly for a solution to a problem or even find no solution at all. This paper is intended to review for the optical designer the basic optimization technology used in software tools for optical design.In terms of artificial intelligence, optimization programs are on the level of dumb beasts; in terms of mathematical sophistication, the best programs, in the hands of knowledgeable designers, are capable of large scale problem solving unequaled in the history of technology.The designer must appreciate what problems the algorithms are capable of solving.Indeed, an understanding of what problems an algorithm does not solve is as important in practice as knowledge of the positive attributes of an algorithm's performance.The discussion opens with a statement of the optical design optimization problem. Some preliminary background on the mathematical approach taken is given before the methods themselves are given. This is done in the two main sections: unconstrained and constrained optimization. Before summarizing, some final comments will be offered on the prospects for global optimization and on directions for future optimization research. Statement of problemThe optical design optimization problem is stated as follows:Given an initial optical system with a specified set of variable parameters, find a new set of parameters which improve an optical performance function subject to physical and optical constraints on the optical system. This is a fairly general statement but not unrealistic in terms of what is encountered in practical design. The problems found in optical design have certain characteristics which direct the choice of the algorithms of interest.Cogent points concerning the elements of the problem statement above are:All methods in use today optimize the performance of an optical system by using an algorithm which minimizes an aberration function expressed as a function of system constructional parameters, the problem variables. It is usually necessary to oversample the aberration function, i.e. have more data points than there are variables to get good correlation between the optical system performa...

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Aberration Theories for Semiautomatic Lens Design by Electronic Computers II A Specific Computer Program

Cited by 9 publications

References 2 publications

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System

An algorithm for least squares analysis of spectroscopic data

Optimization Methodology

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