Abstract

Designing extended-depth-of-focus wavefronts is required in multiple optical applications. Caustic location and structure analysis offer a powerful tool for designing such wavefronts. An intrinsic limitation of designing extended-depth-of-focus wavefronts is that any smooth surface, with a non-constant mean curvature, unavoidably introduces a separation between caustic sheets, which is proportional to the ratio of change of the mean curvature along a curve embedded in the wavefront. We present a method to obtain extended-depth-of-focus wavefronts where the mean curvature variation ratio is reduced thanks to using a long circle-involute space curve effectively filling the wavefront surface. Additionally, we present a variant of the method in which the wavefront is modified within a small tubular neighborhood of the circle involute in order to partially meet the umbilical condition along that tubular region. Finally, we provide some numerical results showing the potential of our method in an application example.

© 2023 Optica Publishing Group

Smooth multifocal wavefronts with a prescribed mean curvature for visual optics applications

Sergio Barbero
Appl. Opt. 60(21) 6147-6154 (2021)

Caustics and wavefronts produced by multiple refraction-reflections through plane-parallel plates

Maximino Avendaño-Alejo, Jesús DelOlmo-Márquez, Ismael Velázquez-Gómez, Osvaldo Ponce-Hernández, Martín Jiménez-Rodríguez, Oliver Huerta-Carranza, Gabriel Castillo-Santiago, and Luis Castañeda
J. Opt. Soc. Am. A 40(12) 2119-2127 (2023)

Multifocal wavefronts with prescribed caustics in axially symmetric optical systems

Sergio Barbero
Opt. Express 30(9) 14274-14286 (2022)

The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface

Magdalena Marciano-Melchor, Esperanza Navarro-Morales, Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Román Suárez-Xique
J. Opt. Soc. Am. A 29(6) 1035-1046 (2012)

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)