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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 4 — Apr. 1, 2010
  • pp: 832–845

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  »View Author Affiliations


JOSA A, Vol. 27, Issue 4, pp. 832-845 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000832


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Abstract

In this work we use the geometrical point of view of the Ronchi test and the caustic-touching theorem to describe the structure of the ronchigrams for a parabolical mirror when the point light source is on and off the optical axis and the grating is placed at the caustic associated with the reflected light rays. We find that for a given position of the point light source the structure of the ronchigram is determined by the form of the caustic and the relative position between the grating and the caustic. We remark that the closed loop fringes commonly observed in the ronchigrams appear when the grating and the caustic are tangent to each other. Furthermore, we find that the caustic locally has singularities of the purse or hyperbolic umbilic type, and the ronchigram obtained when the grating is located at certain specific positions at the caustic locally is of the serpentine type. The main motivation of this work is that nowadays a quantitative analysis of the Ronchi test is applied only when the grating is outside the caustic, and we claim that by working at the caustic, the sensitivity of the Ronchi test will be improved. Therefore, a clear understanding of the properties of the ronchigrams when the grating is placed at the caustic will be needed to extend the Ronchi test to that region.

© 2010 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(110.4190) Imaging systems : Multiple imaging
(120.5700) Instrumentation, measurement, and metrology : Reflection
(220.4840) Optical design and fabrication : Testing

History
Original Manuscript: December 4, 2009
Manuscript Accepted: January 22, 2010
Published: March 24, 2010

Citation
Edwin Román-Hernández, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza, Ramón Silva-Ortigoza, and Jorge Velázquez-Castro, "Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror," J. Opt. Soc. Am. A 27, 832-845 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-4-832

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