On the validity of the paraxial eikonal in catastrophe optics
- 1 January 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (1), 99-108
- https://doi.org/10.1088/0305-4470/17/1/013
Abstract
The paraxial eikonal Psi =Z-f(r)+(R-r)2/2Z is frequently used in catastrophe optics. The authors show that, except in the far-field limit, it can lead not only to quantitative errors, but to major qualitative errors unless the singularity involved is three-determinate. If at some point on the local optical axis (R=0) the exact eikonal has a cuspoid singularity or an umbilic singularity with nonzero four-jet, then the paraxial eikonal generically has a four-determinate singularity at that point. The consequences for cusp and swallowtail foci are explored in detail. They show that such errors do not result from any obvious failure to satisfy the conditions under which Psi is derived.Keywords
This publication has 5 references indexed in Scilit:
- The Double-cusp Unfolding of the 0 X 9 Diffraction CatastropheOptica Acta: International Journal of Optics, 1982
- Bifurcation and catastrophe theoryContemporary Mathematics, 1982
- Optical caustics from liquid drops under gravity: observations of the parabolic and symbolic umbilicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1979
- The elliptic umbilic diffraction catastrophePhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1979
- Optical caustics in the near field from liquid dropsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978