Abstract
The local control of B-spline surfaces has the potential to provide better surface representation for free-form imaging optics; however, it also makes B-spline surface optimization more challenging. To solve this problem, we, for the first time to the best of our knowledge, present an algorithm to design free-form imaging optics with nonrational B-spline surfaces. In this method, the local z-coordinates of a set of data points on B-spline surfaces are defined as independent variables, and the location of each ray point in the image plane is considered as a nonlinear function of these independent variables. By this mathematical consideration, a prescribed imaging system design with B-spline surfaces can be converted into an overdetermined system of nonlinear equations, and the least-squares solution to this nonlinear problem is found by using the Gauss-Newton method based on a ray-tracing technique. An off-axis two-mirror system is presented to demonstrate the elegance of this method in imaging system design with B-spline surfaces.
| Language | English (US) |
|---|---|
| Pages | 2517-2522 |
| Number of pages | 6 |
| Journal | Applied Optics |
| Volume | 56 |
| Issue number | 9 |
| DOIs | |
| State | Published - Mar 20 2017 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Algorithm for designing free-form imaging optics with nonrational B-spline surfaces. / Wu, Rengmao; Sasián, José; Liang, Rongguang.
In: Applied Optics, Vol. 56, No. 9, 20.03.2017, p. 2517-2522.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Algorithm for designing free-form imaging optics with nonrational B-spline surfaces
AU - Wu,Rengmao
AU - Sasián,José
AU - Liang,Rongguang
PY - 2017/3/20
Y1 - 2017/3/20
N2 - The local control of B-spline surfaces has the potential to provide better surface representation for free-form imaging optics; however, it also makes B-spline surface optimization more challenging. To solve this problem, we, for the first time to the best of our knowledge, present an algorithm to design free-form imaging optics with nonrational B-spline surfaces. In this method, the local z-coordinates of a set of data points on B-spline surfaces are defined as independent variables, and the location of each ray point in the image plane is considered as a nonlinear function of these independent variables. By this mathematical consideration, a prescribed imaging system design with B-spline surfaces can be converted into an overdetermined system of nonlinear equations, and the least-squares solution to this nonlinear problem is found by using the Gauss-Newton method based on a ray-tracing technique. An off-axis two-mirror system is presented to demonstrate the elegance of this method in imaging system design with B-spline surfaces.
AB - The local control of B-spline surfaces has the potential to provide better surface representation for free-form imaging optics; however, it also makes B-spline surface optimization more challenging. To solve this problem, we, for the first time to the best of our knowledge, present an algorithm to design free-form imaging optics with nonrational B-spline surfaces. In this method, the local z-coordinates of a set of data points on B-spline surfaces are defined as independent variables, and the location of each ray point in the image plane is considered as a nonlinear function of these independent variables. By this mathematical consideration, a prescribed imaging system design with B-spline surfaces can be converted into an overdetermined system of nonlinear equations, and the least-squares solution to this nonlinear problem is found by using the Gauss-Newton method based on a ray-tracing technique. An off-axis two-mirror system is presented to demonstrate the elegance of this method in imaging system design with B-spline surfaces.
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U2 - 10.1364/AO.56.002517
DO - 10.1364/AO.56.002517
M3 - Article
VL - 56
SP - 2517
EP - 2522
JO - Applied Optics
T2 - Applied Optics
JF - Applied Optics
SN - 1559-128X
IS - 9
ER -