Second-order derivatives of a ray with respect to the variables of its source ray in optical systems containing spherical boundary surfaces

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)

摘要

The second-order derivative matrix of a scalar function with respect to a variable vector is called a Hessian matrix, which is a square matrix. Our research group previously presented a method for determination of the first-order derivatives (i.e., the Jacobian matrix) of a skew ray with respect to the variable vector of an optical system. This paper extends our previous methodology to determine the second-order derivatives (i.e., the Hessian matrix) of a skew ray with respect to the variable vector of its source ray when this ray is reflected/refracted by spherical boundary surfaces. The traditional finite-difference methods using ray-tracing data to compute the Hessian matrix suffer from various cumulative rounding and truncation errors. The proposed method uses differential geometry, giving it an inherently greater accuracy. The proposed Hessian matrix methodology has potential use in optimization methods where the merit function is defined as ray aberrations. It also can be used to investigate the shape of the wavefront for a ray traveling through an optical system.

原文English
頁(從 - 到)1995-2005
頁數11
期刊Journal of the Optical Society of America A: Optics and Image Science, and Vision
28
發行號10
DOIs
出版狀態Published - 2011 10月

All Science Journal Classification (ASJC) codes

  • 電子、光磁材料
  • 原子與分子物理與光學
  • 電腦視覺和模式識別

指紋

深入研究「Second-order derivatives of a ray with respect to the variables of its source ray in optical systems containing spherical boundary surfaces」主題。共同形成了獨特的指紋。

引用此