### 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

*Applied Optics*,

*56*(9), 2517-2522. DOI: 10.1364/AO.56.002517

**Algorithm for designing free-form imaging optics with nonrational B-spline surfaces.** / Wu, Rengmao; Sasián, José; Liang, Rongguang.

Research output: Research - peer-review › Article

*Applied Optics*, vol 56, no. 9, pp. 2517-2522. DOI: 10.1364/AO.56.002517

}

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.

UR - http://www.scopus.com/inward/record.url?scp=85016022117&partnerID=8YFLogxK

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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 -