Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2 × 2 matrices acting on the height and slope of the rays. A known limitation of ray transfer matrices is that they only work for optical elements that are centered and normal to the optical axis. In this article, we provide an improved 3 × 3 matrix method for calculating paraxial ray traces of optical systems that is applicable to how these systems are actually arranged on the optical table: lenses and mirrors in any orientation or position (e.g., in laboratory coordinates), with the optical path zig-zagging along the table. Using projective duality, we also show how to directly image points through an optical system using a point transfer matrix calculated from the system's ray transfer matrix. We demonstrate the usefulness of these methods with several examples and discuss future directions to expand the applications of this technique.
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June 2023
PAPERS|
June 01 2023
Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates
Theodore A. Corcovilos
Theodore A. Corcovilos
a)
Department of Physics, Duquesne University
, Pittsburgh, Pennsylvania 15282
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a)
[email protected], ORCID: 0000-0001-5716-1188.
Am. J. Phys. 91, 449–457 (2023)
Article history
Received:
December 21 2021
Accepted:
February 14 2023
Citation
Theodore A. Corcovilos; Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates. Am. J. Phys. 1 June 2023; 91 (6): 449–457. https://doi.org/10.1119/5.0083069
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