We study the imaging properties of windows that rotate the direction of transmitted light rays by a fixed angle around the window normal [A. C. Hamilton et al., J. Opt. A: Pure Appl. Opt. 11,085705 (2009)]. We previously found that such windows image between object and image positions with suitably defined complex longitudinal coordinates [J. Courtial et al., Opt. Lett. 37, 701 (2012)]. Here we extend this work to object and image positions in which any coordinate can be complex. This is possible by generalising our definition of what it means for alight ray to pass through a complex position: the vector from the real part of the position to the point on the ray that is closest to that real part of the position must equal the cross product of the imaginary part of the image position and the normalised light-ray-direction vector. In the paraxial limit, we derive the equivalent of the lens equation for planar and spherical ray-rotating windows. These results allow us to describe complex imaging in more general situations, involving combinations of lenses and inclined ray-rotating windows. We illustrate our results with ray-tracing simulations.

Date Published: 25 September 2014
PDF: 6 pages
Proc. SPIE 9192, Current Developments in Lens Design and Optical Engineering XV, 91920A (25 September 2014); doi: 10.1117/12.2061398

Published in SPIE Proceedings Vol. 9192:
Current Developments in Lens Design and Optical Engineering XV
R. Barry Johnson; Virendra N. Mahajan; Simon Thibault, Editor(s)