Abstract
The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.
| Original language | English |
|---|---|
| Pages (from-to) | 471-479 |
| Number of pages | 9 |
| Journal | Applied Physics B: Lasers and Optics |
| Volume | 98 |
| Issue number | 2-3 |
| DOIs | |
| Publication status | Published - 2010 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
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Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism. / Hsueh, C. C.; Lin, Psang-Dain.
In: Applied Physics B: Lasers and Optics, Vol. 98, No. 2-3, 01.02.2010, p. 471-479.Research output: Contribution to journal › Article
TY - JOUR
T1 - Gradient matrix of optical path length for evaluating the effects of design variable changes in a prism
AU - Hsueh, C. C.
AU - Lin, Psang-Dain
PY - 2010/2/1
Y1 - 2010/2/1
N2 - The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.
AB - The effects of variable changes on the optical path length (OPL) of optical elements such as a prism are generally evaluated by utilizing a ray tracing approach to determine the OPL before and after the variable change, respectively, and then applying a finite difference (FD) method to estimate the OPL gradient with respect to each individual variable. By contrast, this study constructs the gradient matrix of OPL of a prism which permits the effects of multiple variable changes to be determined in a single pass. The developed approach not only resolves the error inherent in the FD method as a result of the denominator being far smaller than the numerator, but also avoids the requirement for multiple ray tracing operations and therefore yields a substantial improvement in the computational efficiency. The validity of the proposed approach is demonstrated utilizing a Pechan prism for illustration purposes.
UR - http://www.scopus.com/inward/record.url?scp=73849096782&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=73849096782&partnerID=8YFLogxK
U2 - 10.1007/s00340-009-3716-4
DO - 10.1007/s00340-009-3716-4
M3 - Article
AN - SCOPUS:73849096782
VL - 98
SP - 471
EP - 479
JO - Applied Physics B: Lasers and Optics
JF - Applied Physics B: Lasers and Optics
SN - 0946-2171
IS - 2-3
ER -