Imaging with tilted surfaces: an efficient matrix method for the generalized Scheimpflug condition and its application to rotationally symmetric triangulation

Abstract

An efficient two-dimensional matrix method is presented that facilitates the design of optical systems with tilted surfaces for which the requirement or knowledge of the orientation of the image plane is necessary, i.e., for which a generalized Scheimpflug condition is needed. In more general terms, the method results in imaging properties of second-order expansion, but the method is linear. Therefore the complexity of the design process is considerably reduced. The strength of the design method is demonstrated in detail for a novel application in which a reflective optical system of several surfaces is required for rotationally symmetric triangulation.

© 2005 Optical Society of America

Analysis of imaging for laser triangulation sensors under Scheimpflug rule

Antonin Miks, Jiri Novak, and Pavel Novak
Opt. Express 21(15) 18225-18235 (2013)

Calibration methods for a camera with a tilted lens and a three-dimensional laser scanner in the Scheimpflug condition

Mingwei Shao
J. Opt. Soc. Am. A 37(7) 1076-1082 (2020)

Improvement of Scheimpflug systems with freeform surfaces

Yi Zhong and Herbert Gross
Appl. Opt. 57(6) 1482-1491 (2018)

Initial system design method for non-rotationally symmetric systems based on Gaussian brackets and Nodal aberration theory

Yi Zhong and Herbert Gross
Opt. Express 25(9) 10016-10030 (2017)

Second-order design methods for definitive studies of plane-symmetric, two-mirror systems

Bryan D. Stone and G. W. Forbes
J. Opt. Soc. Am. A 11(12) 3292-3307 (1994)