Understanding Lens Aberrations
- 1 Department of Mathematics, Brock University, St. Catharines, Ontario, Canada
Abstract
In most textbooks, lens aberrations are usually described in the briefest possible manner, without any attempt for their proper derivation. At the same time, monographs which do go into more detail are often inaccessible to most students and non-specialists interested in deeper understanding of this topic. This article tries to fill this gap and provide an introduction to what happens when basic formulas of Geometrical Optics are extended by third-order terms in Taylor’s expansion of sin ( α ). The presentation is accessible to most undergraduate students as it requires only some knowledge of basic calculus and planar geometry. The resulting five aberrations are then described in detail, including a novel derivation of the exact shape of coma. A simple Mathematica program is included to facilitate numerical exploration of the magnitude of the resulting aberrations for various optical systems.
- Pedrotti, F.L., Pedrotti, L.M. and Pedrotti, L.S. (2017) Introduction to Optics. 3rd Edition, Cambridge University Press, Cambridge. https://doi.org/10.1017/9781108552493
- Welford, W.T. (1974) Aberrations of the Symmetrical Optical Systems. Academic Press, New York.
- Vrbik, J. (2020) Geometrical Optics from the Ground Up. Applied Mathematics, 11, 1021-1040. https://doi.org/10.4236/am.2020.1110068
- Herzberger, M. (1958) Modern Geometrical Optics. Interscience Publishers, New York.
- Buchdahl, H.A. (1993) An Introduction to Hamiltonian Optics. Dover Publications, New York.
- Smith, W.J. (2008) Modern Optical Engineering. 4th Edition. McGraw-Hill, New York.
- Mahajan, V.N. (1999) Optical Imaging and Aberrations, Part I: Ray Geometrical Optics. SPIE Press, Washington DC.