OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (2711 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

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

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Malacara, A. Cornejo, and M. V. R. K. Murty, “Bibliography of various optical testing methods,” Appl. Opt.  14, 1065–1065 (1975). [CrossRef] [PubMed]
  2. A. Cornejo, H. J. Caulfied, and W. Friday, “Testing of optical surfaces: A bibliography,” Appl. Opt.  20, 4148–4148 (1981). [CrossRef]
  3. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt.  3, 437–451 (1964). [CrossRef]
  4. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 1978), Chap. 9.
  5. M. Mansuripur, “The Ronchi test,” Opt. Photonics News , 42–46 (1997).
  6. D. Malacara, “Geometrical Ronchi test of aspherical mirrors,” Appl. Opt.  4, 1371–1374 (1965). [CrossRef]
  7. A. A. Sherwood, “Quantitative analysis of the Ronchi test in terms of ray optics,” J. Br. Astron. Assc.  68, 180–191 (1958).
  8. A. A. Sherwood, “Ronchi test charts for parabolic mirrors,” J. Proc. R. Soc. New South Wales  43, 19 (1960).
  9. D. Malacara and A. Cornejo, “Null Ronchi test for aspherical surfaces,” Appl. Opt.  13, 1778–1780 (1974). [CrossRef] [PubMed]
  10. T. Yatagai, “Fringe scanning Ronchi test for aspherical surfaces,” Appl. Opt.  23, 3676–3679 (1984). [CrossRef] [PubMed]
  11. A. Cordero-Dávila, A. Cornejo-Rodriguez, and O. Cardona-Nuñez, “Null Hartmann and Ronchi-Hartmann tests,” Appl. Opt.  29, 4618–4621 (1990). [CrossRef] [PubMed]
  12. A. Cordero-Dávila, A. Cornejo-Rodriguez, and O. Cardona-Nuñez, “Ronchi and Hartmann tests with the same mathematical theory,” Appl. Opt.  31, 2370–2376 (1992). [CrossRef] [PubMed]
  13. A. Cordero-Dávila, J. Díaz-Anzures, and V. Cabrera-Peláez, “Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates,” Appl. Opt.  41, 3866–3873 (2002). [CrossRef] [PubMed]
  14. E. Román-Hernández and G. Silva-Ortigoza, “Exact computation of image disruption under reflection on a smooth surface and Ronchigrams,” Appl. Opt.  47, 5500–5518 (2008). [CrossRef] [PubMed]
  15. M. V. Berry, “Disruption of images: the caustic-touching theorem,” J. Opt. Soc. Am. A  4, 561–569 (1987). [CrossRef]
  16. O. N. Stavroudis and R. C. Fronczek, “Caustic surfaces and the structure of the geometrical image,” J. Opt. Soc. Am.  66, 795–800 (1976). [CrossRef]
  17. A. M. Kassim and D. L. Shealy, “Wave front equation, caustics, and wave aberration function of simple lenses and mirrors,” Appl. Opt.  27, 516–522 (1988). [CrossRef] [PubMed]
  18. D. L. Shealy and J. A. Hoffnagle, “Wavefront and caustics of a plane wave refracted by an arbitrary surface,” J. Opt. Soc. Am. A  25, 2370–2382 (2008). [CrossRef]
  19. E. Román-Hernández, J. G. Santiago-Santiago, G. Silva-Ortigoza, and R. Silva-Ortigoza, “Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface,” J. Opt. Soc. Am. A  20, 2295–2305 (2009). [CrossRef]
  20. D. L. Shealy and D. G. Burkhard, “Caustic surfaces and irradiance for reflection and refraction from an ellipsoid, elliptic paraboloid, and elliptic cone,” Appl. Opt.  12, 2955–2959 (1973). [CrossRef] [PubMed]
  21. D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance in an optical system,” Appl. Opt.  20, 897–909 (1981). [CrossRef] [PubMed]
  22. P. S. Theocaris, “Surface topography by caustics,” Appl. Opt.  15, 1629–1638 (1976). [CrossRef] [PubMed]
  23. P. S. Theocaris, “Properties of caustics from conic reflectors. 1: Meridional rays,” Appl. Opt.  16, 1705–1716 (1977). [CrossRef] [PubMed]
  24. G. Silva-Ortigoza, J. Castro-Ramos, and A. Cordero-Dávila, “Exact calculation of the circle of least confusion of a rotationally symmetric mirror. II,” Appl. Opt.  40, 1021–1028 (2001). [CrossRef]
  25. G. Silva-Ortigoza, M. Marciano-Melchor, O. Carvente-Muñoz, and Ramón Silva-Ortigoza, “Exact computation of the caustic associated with the evolution of an aberrated wavefront,” J. Opt. A, Pure Appl. Opt.  4, 358–365 (2002). [CrossRef]
  26. J. Castro-Ramos, O. de Ita Prieto, and G. Silva-Ortigoza, “Computation of the disk of least confusion for conic mirrors,” Appl. Opt.  43, 6080–6088 (2004). [CrossRef] [PubMed]
  27. D. L. Shealy and D. G. Burkhard, “Flux density ray propagation in discrete index media expressed in terms of the intrinsic geometry of the reflecting surface,” Opt. Acta  20, 287–301 (1973). [CrossRef]
  28. D. L. Shealy, “Analytical illuminance and caustic surface calculations in geometrical optics,” Appl. Opt.  15, 2588–2596 (1976). [CrossRef] [PubMed]
  29. A. M. Kassim, D. L. Shealy, and D. G. Burkhard, “Caustic merit function for optical design,” Appl. Opt.  28, 601606 (1989). [CrossRef]
  30. I. H. Al-Ahdali and D. L. Shealy, “Optimization of three- and four-element lens systems by minimizing the caustic surfaces,” Appl. Opt.  29, 4551–4559 (1989). [CrossRef]
  31. D. G. Burkhard and D. L. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt.  21, 32993306 (1982). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited