TY - JOUR
T1 - Application of derivative matrices of skew rays to direct and inverse problems of Risley and tilting orthogonal double-prism systems
AU - Lin, Psang Dain
AU - Johnson, R. Barry
N1 - Funding Information:
Acknowledgment. The authors wish to thank the anonymous referee who called their attention to the particular case of Risley systems. Special thanks are also extended to the Ministry of Science and Technology of Taiwan for the generous financial support of this study under grant number MOST 103-2221-E-006-033–MY3.
Publisher Copyright:
© 2017 Optical Society of America.
PY - 2017/12
Y1 - 2017/12
N2 - Risley systems and tilting orthogonal double-prism systems are optical systems consisting of two prisms in series. The analysis of such systems typically involves both direct and inverse problems. Problems of the former type can be easily solved using ray-tracing equations. However, inverse problems are comparatively more difficult if the search direction is not properly given prior to iteration. In the present study, the two optical systems are modeled using the homogeneous coordinate notation. A method is then proposed for solving the direct and inverse problems of both optical systems using a ray-tracing approach and the first- and second-order derivative matrices of the skew rays. In addition, four optimization methods based on the two derivative matrices are proposed for determining the search direction in the inverse problem. Eight illustrative examples are given. It is shown that the proposed method can not only determine the scan patterns and sensitivity coefficients in the direct problem, but also determine the search direction in the inverse problem.
AB - Risley systems and tilting orthogonal double-prism systems are optical systems consisting of two prisms in series. The analysis of such systems typically involves both direct and inverse problems. Problems of the former type can be easily solved using ray-tracing equations. However, inverse problems are comparatively more difficult if the search direction is not properly given prior to iteration. In the present study, the two optical systems are modeled using the homogeneous coordinate notation. A method is then proposed for solving the direct and inverse problems of both optical systems using a ray-tracing approach and the first- and second-order derivative matrices of the skew rays. In addition, four optimization methods based on the two derivative matrices are proposed for determining the search direction in the inverse problem. Eight illustrative examples are given. It is shown that the proposed method can not only determine the scan patterns and sensitivity coefficients in the direct problem, but also determine the search direction in the inverse problem.
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U2 - 10.1364/JOSAA.34.002203
DO - 10.1364/JOSAA.34.002203
M3 - Article
C2 - 29240095
AN - SCOPUS:85036661168
VL - 34
SP - 2203
EP - 2212
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
SN - 1084-7529
IS - 12
ER -