Computationally efficient gradient matrix of optical path length in axisymmetric optical systems

Hsueh, Chun Che; Lin, Psang Dain

doi:10.1364/ao.48.000893

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…Furthermore, terms ∂OPL i ∕∂R i−1 and ∂OPL i ∕∂X i are derived in Eqs. (13) and (14) of this paper. Consequently, the following subsections present only the derivations of…”

Section: Hessian Matrix Of Opl Imentioning

confidence: 67%

“…Prior to 2009, the existing literature on the Jacobian matrix of optical quantities considered only axissymmetrical systems. To address this limitation, the present group derived the Jacobian matrix of the optical path length (OPL) with respect to all the independent system variables of a nonaxially symmetric system [13]. Notably, the proposed approach differs from the earlier work of Feder [4,5], in which the Jacobian matrix was defined with respect only to the curvatures, separations, and refractive indices of the system components.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the literature lacks any formal means of computing the Hessian matrix of the OPL. To circumvent this limitation, the present study extends the method proposed in [13,25] to determine the Hessian matrix of the OPL with respect to all of the system variables of a nonaxially symmetric system.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Furthermore, terms ∂OPL i ∕∂R i−1 and ∂OPL i ∕∂X i are derived in Eqs. (13) and (14) of this paper. Consequently, the following subsections present only the derivations of…”

Section: Hessian Matrix Of Opl Imentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Derivatives of optical path length: from mathematical formulation to applications

Lin

2015

J. Opt. Soc. Am. A

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“…In 1997, Stone and Forbes 28 generalized the standard Runge–Kutta method to solve the ray equation, thus performing ray tracing for nonuniform media. In 2009, Hsueh and Lin 29 developed a new mathematical method to determine the optical path length (OPL) gradient matrix associated with all system variables, which greatly reduces the time compared to the ray-tracing method approximated by finite difference. In 2013, Chen et al 30 .…”

Section: Introductionmentioning

confidence: 99%

3D ray tracing methods across inhomogeneous refractive indices using a transmission equation

Xiong

Ding

et al. 2022

Opt. Eng.

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. When an aircraft flies at high speed in a dense atmosphere, the airflow outside the optical window interacts to form a complex flow field structure with irregular and nonuniform refractive index distribution, which makes it difficult to accurately calculate the ray propagation path based on the refractive index field. To solve this challenge, three ray tracing implementation methods with fourth-order accuracy are proposed. By comparing with the spiral ray resolution results, it is found that the Adams method has the smallest computational error of 1.2 × 10 − 11 compared with the fourth-order Runge–Kutta method and the Richardson extrapolation method. The Adams method is the most computationally efficient in terms of computational time cost, followed by the Richardson extrapolation method, and finally the fourth-order Runge–Kutta method. The results show that the Adams method is the fastest and most accurate for different step sizes and grid volumes.

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“…Obviously, the optical antenna is the most important component of the optical system. The loss caused by the secondary mirror is a serious problem [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Hyperbola–parabola primary mirror in Cassegrain optical antenna to improve transmission efficiency

et al. 2015

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An optical model with a hyperbola-parabola primary mirror added in the Cassegrain optical antenna, which can effectively improve the transmission efficiency, is proposed in this paper. The optimum parameters of a hyperbola-parabola primary mirror and a secondary mirror for the optical antenna system have been designed and analyzed in detail. The parabola-hyperbola primary structure optical antenna is obtained to improve the transmission efficiency of 10.60% in theory, and the simulation efficiency changed 9.359%. For different deflection angles to the receiving antenna with the emit antenna, the coupling efficiency curve of the optical antenna has been obtained.

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Computationally efficient gradient matrix of optical path length in axisymmetric optical systems

Cited by 9 publications

References 9 publications

Derivatives of optical path length: from mathematical formulation to applications

Derivatives of optical path length: from mathematical formulation to applications

3D ray tracing methods across inhomogeneous refractive indices using a transmission equation

Hyperbola–parabola primary mirror in Cassegrain optical antenna to improve transmission efficiency

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