Differential ray tracing in inhomogeneous media

Stone, Bryan D.; Forbes, G. W.

doi:10.1364/josaa.14.002824

Cited by 31 publications

(14 citation statements)

References 9 publications

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“…It is well known that the derivatives-based approaches of optimization methods are more promising for designing a wide variety of optical problems. There exist several publications of the Jacobian matrices of rays [7][8][9][10][11][12][13][14][15][16][17][18]. Unfortunately, they do not take into account all of the system variables.…”

Section: Jacobian and Hessian Matrices Of A Raymentioning

confidence: 99%

“…To overcome the limitations of FD methods, the differential method can be used for determination of the derivative matrices. This fact has been known in geometrical optics for many years and there exist several publications on the subject [7][8][9][10][11][12][13][14][15][16][17][18]. For examples, Shekhonin et al [17] derived the differential changes of the linear and angular coordinates of a ray, as well as the aberration function, with the changes of boundary variables of the system in most general case.…”

Section: Introductionmentioning

confidence: 99%

“…Brewer [18] developed a set of algorithms to compute partial derivatives of transverseray errors with respect to the boundary variables. However, the differential methods presented in [7][8][9][10][11][12][13][14][15][16][17][18] do not take into account all of the system variables (i.e., the six pose variables of an element in 3D space). Consequently, the proposed derivative matrices are applicable only to axis-symmetrical systems.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, that scheme is extended to determine the Hessian matrix of a skew ray as it is reflected or refracted at a surface with a spherical boundary. In contrast to the differential methods presented in [7][8][9][10][11][12][13][14][15][16][17][18], the proposed method is applicable to both axis-symmetrical and nonaxially symmetrical optical systems. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustrative purposes.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Lin

2014

Appl. Opt.

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In a previous paper [Appl. Opt.52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

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Section: Jacobian and Hessian Matrices Of A Raymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Lin

2014

Appl. Opt.

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“…8 of [14]). The literature contains various proposals for determining the Jacobian matrices of rays [4,5,[15][16][17][18][19][20][21][22][23][24]. Theoretically, these proposals can be extended to the derivation of the Jacobian matrix of the OPL.…”

Section: Introductionmentioning

confidence: 99%

Derivatives of optical path length: from mathematical formulation to applications

Lin

2015

J. Opt. Soc. Am. A

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The optical path length (OPL) of an optical system is a highly important parameter since it determines the phase of the light passing through the system and governs the interference and diffraction of the rays as they propagate. The Jacobian and Hessian matrices of the OPL are of fundamental importance in tuning the performance of a system. However, the OPL varies as a recursive function of the incoming ray and the boundary variable vector, and hence computing the Jacobian and Hessian matrices is extremely challenging. In an earlier study by the present group, this problem was addressed by deriving the Jacobian matrix of the OPL with respect to all of the independent system variables of a nonaxially symmetric system. In the present study, the proposed method is extended to the Hessian matrix of a nonaxially symmetric optical system. The proposed method facilitates the cross-sensitivity analysis of the OPL with respect to arbitrary system variables and provides an ideal basis for automatic optical system design applications in which the merit function is defined in terms of wavefront aberrations. An illustrative example is given. It is shown that the proposed method requires fewer iterations than that based on the Jacobian matrix and yields a more reliable and precise optimization performance.

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Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism

Hsueh

Lin

2009

Appl. Phys. B

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Differential ray tracing in inhomogeneous media

Cited by 31 publications

References 9 publications

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design

Derivatives of optical path length: from mathematical formulation to applications

Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism

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