Applied Physics B

, Volume 96, Issue 2, pp 517–525

A general calculation of the 3-D disk of least confusion using skew ray tracing


DOI: 10.1007/s00340-009-3515-y

Cite this article as:
Tsai, CY. Appl. Phys. B (2009) 96: 517. doi:10.1007/s00340-009-3515-y


A general and analytical method is proposed to determine the 3-D contour of the disk of least confusion (DLC) produced by an optical system for a point light source located at any arbitrary position in the object space. By using the skew ray tracing method, the sensitivity method, and the Jacobian matrix, we can analytically obtain the caustic and the marginal rays. Consequently, the DLC can be determined by the intersection of the obtained caustic and marginal rays. In addition, this proposed method covers common cases with special light sources, e.g. mutually parallel incident rays parallel to the optical axis, or a point light source located on the optical axis. This proposed methodology will be useful in the analysis of rays and in the design of optical systems with a general point light source. A general case is used as illustrative example to validate its applications.


42.15.-i 42.15.Eq 



the world coordinate frame


number to label boundary surfaces, i=1,2,…,n


the coordinate frame imbedded in the ith boundary surface


the ith boundary surface


incidence point at ri


reflected/refracted unit directional vector of a light ray at ri


The reflected/refracted ray at the ith boundary surface


pose of coordinate frame (xyz)i with respect to coordinate frame (xyz)j

Jacobian matrix

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Computer-Aided EngineeringNational Formosa UniversityHuweiTaiwan

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