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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. 31, Iss. 2 — Feb. 1, 2014
  • pp: 448–459

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  »View Author Affiliations


JOSA A, Vol. 31, Issue 2, pp. 448-459 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000448


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Abstract

The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative positions to the caustic region, and third we describe in detail the structure of the null ronchigrating for this system; that is, we obtain the grating such that when it is placed at the flat surface of the axicon its associated pattern, at a given plane perpendicular to the optical axis, is a set of parallel fringes. We find that the caustic has only one branch, which is a segment of a line along the optical axis; the ronchigram exhibits self-intersecting fringes when the screen is placed at the caustic region, and the null ronchigrating exhibits closed loop rulings if we want to obtain its associated pattern at the caustic region.

© 2014 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(110.4190) Imaging systems : Multiple imaging
(120.5710) Instrumentation, measurement, and metrology : Refraction
(220.4840) Optical design and fabrication : Testing

ToC Category:
Geometric Optics

History
Original Manuscript: September 5, 2013
Revised Manuscript: December 23, 2013
Manuscript Accepted: December 23, 2013
Published: January 31, 2014

Citation
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, "Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens," J. Opt. Soc. Am. A 31, 448-459 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-2-448


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References

  1. V. I. Arnold, Catastrophe Theory (Springer-Verlag, 1986).
  2. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps (Birkhauser, 1995), Vol. I.
  3. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, 1980).
  4. O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics (Wiley, 2006).
  5. 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]
  6. 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]
  7. D. L. Shealy, “Analytical illuminance and caustic surface calculations in geometrical optics,” Appl. Opt. 15, 2588–2596 (1976). [CrossRef]
  8. G. L. Strobel and D. L. Shealy, “Caustic surface analysis for a gradient-index lens,” J. Opt. Soc. Am. 70, 1264–1269 (1980). [CrossRef]
  9. D. G. Burkhard and D. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt. 21, 3299–3306 (1982). [CrossRef]
  10. 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]
  11. A. M. Kassim, D. L. Shealy, and D. G. Burkhard, “Caustic merit function for optical design,” Appl. Opt. 28, 601–606 (1989). [CrossRef]
  12. 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 (1990). [CrossRef]
  13. P. S. Theocaris and E. E. Gdoutos, “Distance measuring based on caustics,” Appl. Opt. 16, 722–728 (1977). [CrossRef]
  14. P. S. Theocaris, “Properties of caustics from conic reflectors. 1: meridional rays,” Appl. Opt. 16, 1705–1716 (1977). [CrossRef]
  15. P. S. Theocaris and T. P. Philippidis, “Possibilities of reflected caustics due to an improved optical arrangement: some further aspects,” Appl. Opt. 23, 3667–3675 (1984). [CrossRef]
  16. P. S. Theocaris, “Multicusp caustics formed from reflections of warped surfaces,” Appl. Opt. 27, 780–789 (1988). [CrossRef]
  17. A. Cornejo and D. Malacara, “Caustic coordinates in Platzeck-Gaviola test of conic mirrors,” Appl. Opt. 17, 18–19 (1978). [CrossRef]
  18. M. R. Hatch and D. E. Stoltzmann, “Extending the caustic test to general aspheric surfaces,” Appl. Opt. 31, 4343–4349 (1992). [CrossRef]
  19. D. P. K. Banerjee, R. V. Willstrop, and B. G. Anandarao, “Improving the accuracy of the caustic test,” Appl. Opt. 37, 1227–1230 (1998). [CrossRef]
  20. G. Silva-Ortigoza, M. Marciano-Melchor, O. Carvente-Muñoz, and R. Silva-Ortigoza, “Exact computation of the caustic associated with the evolution of an aberrated wavefront,” J. Opt. A 4, 358–365 (2002). [CrossRef]
  21. 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]
  22. J. Castro-Ramos, O. de Ita Prieto, and G. Silva-Ortigoza, “Computation of the disk of least confusion for conic mirrors,” Appl. Opt. 43, 6080–6089 (2004). [CrossRef]
  23. 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]
  24. 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]
  25. M. Avendaño-Alejo and R. Díaz-Uribe, “Testing a fast off-axis parabolic mirror by using tilted null screens,” Appl. Opt. 45, 2607–2614 (2006). [CrossRef]
  26. M. Avendaño-Alejo, R. Diaz-Uribe, and I. Moreno, “Caustics caused by refraction in the interface between an isotropic medium and a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1586–1593 (2008). [CrossRef]
  27. M. Avendaño-Alejo, V. I. Moreno-Oliva, M. Campos-García, and R. Díaz-Uribe, “Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen,” Appl. Opt. 48, 1008–1015 (2009). [CrossRef]
  28. M. Avendaño-Alejo, L. Castañeda, and I. Moreno, “Properties of caustics produced by a positive lens: meridional rays,” J. Opt. Soc. Am. A 27, 2252–2260 (2010). [CrossRef]
  29. M. Avendaño-Alejo, D. González-Utrera, and L. Castañeda, “Caustics in a meridional plane produced by plano-convex conic lenses,” J. Opt. Soc. Am. A 28, 2619–2628 (2011). [CrossRef]
  30. 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 26, 2295–2305 (2009). [CrossRef]
  31. E. Román-Hernández, J. G. Santiago-Santiago, G. Silva-Ortigoza, R. Silva-Ortigoza, and J. 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). [CrossRef]
  32. E. Román-Hernández, J. G. Santiago-Santiago, G. Silva-Ortigoza, and R. Silva-Ortigoza, “Wavefronts, light rays and caustic of a circular wave reflected by an arbitrary smooth curve,” J. Opt. 13, 055705 (2011). [CrossRef]
  33. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954). [CrossRef]
  34. J. H. McLeod, “Axicons and their uses,” J. Opt. Soc. Am. 50, 166–169 (1960). [CrossRef]
  35. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005). [CrossRef]
  36. J. L. Rayces, “Formation of axicon images,” J. Opt. Soc. Am. 48, 576–578 (1958). [CrossRef]
  37. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–451 (1964). [CrossRef]
  38. A. Cornejo-Rodriguez, “Ronchi test,” in Optical Shop Testing, D. Malacara, ed. (Wiley, 1978), Chap. 9.
  39. D. Malacara, “Geometrical Ronchi test of aspherical mirrors,” Appl. Opt. 4, 1371–1374 (1965). [CrossRef]
  40. A. A. Sherwood, “Quantitative analysis of the Ronchi test in terms of ray optics,” J. Br. Astron. Assoc. 68, 180–191 (1958).
  41. 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]
  42. 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]
  43. M. Marciano-Melchor, E. Navarro-Morales, E. Román-Hernández, J. G. Santiago-Santiago, G. Silva-Ortigoza, R. Silva-Ortigoza, and R. Suárez-Xique, “The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface,” J. Opt. Soc. Am. A 29, 1035–1046 (2012). [CrossRef]
  44. M. V. Berry, “Disruption of images: the caustic-touching theorem,” J. Opt. Soc. Am. A 4, 561–569 (1987). [CrossRef]
  45. M. Avendaño-Alejo, D. González-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordoñes-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Express 18, 21131–21137 (2010). [CrossRef]

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