Abstract

In this work we use geometrical optics and the caustic touching theorem, introduced by Berry, to describe the internal structure of the null Ronchi grating for a plano–parabolic lens illuminated by a point light source placed on the optical axis. The aim of this work is to explain the role of the caustic region in the process of morphology change between image and object in computing the null Ronchi grating. To this end, we obtain the analytic expression of the null Ronchi grating, and after that we deeply study the change in morphology between a single straight fringe image at the Ronchigram and the multiple curve rulings that can generate it (one open and one closed). We analyze exactly how multiple rulings generate the same straight image fringe, or how an entire ruling collapses into a single point image. For this analysis, we take different observation planes at different positions with respect to the caustic region. Finally, we characterize this topological change as one of two possible kinds depending on the relative position between the observation plane and the caustic region.

© 2015 Optical Society of America

Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror

Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Jorge Velázquez-Castro
J. Opt. Soc. Am. A 27(4) 832-845 (2010)

Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens

Salvador Alejandro Juárez-Reyes, Magdalena Marciano-Melchor, Mariana Marcelino-Aranda, Paula Ortega-Vidals, Edwin Román-Hernández, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, Román Suárez-Xique, Gerardo Francisco Torres del Castillo, and Mercedes Velázquez-Quesada
J. Opt. Soc. Am. A 31(2) 448-459 (2014)

Wavefronts, caustics, and ronchigrams of a spherical wave reflected by a spherical mirror

Jorge Castro-Ramos, Magdalena Marciano-Melchor, Mariana Marcelino-Aranda, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, Román Suárez-Xique, and José Miguel Zárate-Paz
J. Opt. Soc. Am. A 30(2) 177-188 (2013)

Exact computation of image disruption under reflection on a smooth surface and Ronchigrams

Edwin Román-Hernández and Gilberto Silva-Ortigoza
Appl. Opt. 47(29) 5500-5518 (2008)

Curvatures of the refracted wavefronts and Ronchigrams for a plano arbitrary lens

Omar de J. Cabrera-Rosas, Paula Ortega-Vidals, Salvador Alejandro Juárez-Reyes, and Gilberto Silva-Ortigoza
J. Opt. Soc. Am. A 33(9) 1760-1768 (2016)