Journal of the European Optical Society - Rapid publications, Vol 10 (2015)

Point diffraction interferometry to measure local curvatures and caustics of noisy wave fronts: Application for determining optical properties of fish lenses

S. Vallmitjana, I. Ricart, S. Bosch, A. Gargallo, E. Acosta

Abstract


The study of caustics is important because they contain information about the image formation properties of optical systems. In this work we use the concept of caustic as a set of focal points, and we have developed a second order approach theory to determine local slopes and curvatures of a wavefront emerging from an optical system. The method is based on the use of a point diffraction interferometer, and the analysis of the interferograms allows us to compute the focal region. Experimental results obtained with a plano-convex lens demonstrate the accuracy of the combined theoretical-experimental method here developed. Application to noisy wavefronts such as those produced by biological samples, specifically in crystalline lenses of fish eyes, are also exposed.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2015.15010]

Full Text: PDF

Citation Details


Cite this article

References


D. Malacara, Optical shop testing (Wiley, New Jersey, 2007).

M. Avendaño-Alejo, ”Caustics in a meridional plane produced by plano-convex aspheric lenses,” J. Opt. Soc. Am. A 30(3), 501–508 (2013).

I. H. Al-Ahdali, and D. L. Shealy, ”Optimization of three- and fourelement lens systems by minimizing the caustic surfaces,” Appl. Optics 29(31), 4551–4559 (1990).

O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics: the k-function and its Ramifications (Wiley-VCH, Weinheim, 2006).

D. G. Burkhard, and D. Shealy, ”Formula for the density of tangent rays over a caustic surface,” Appl. Optics 21, 3299–3306 (1982).

M. F. Land, and D. E. Nilsson, Animal Eyes (Oxford University Press Inc., New York, 2002).

T. Mandelman, and J. G. Sivak, ”Longitudinal chromatic aberration of the vertebrate eye,” Vision Res. 23, 1555–1559 (1983).

G. L. Walls, The Vertebrate Eye and its Adaptive Radiation (Cranbrook Institute of Science, Bloomfield Hills, 1964).

R. H. H. Kröger, K. A. Fritsches, and E. J. Warrant, ”Lens optical properties in the eyes of large marine predatory Teleosts,” J. Comp. Physiol. A 195, 175–182 (2009).

R. H. H. Kröger, ”Multifocal Optics of the Fish Lens for Clear Color Vision,” in Frontiers in Optics 2011, FWV1 (Optical Society of America, San Jose, 2011).

M. C. W. Campbell, and A. Hughes, ”An analytic, gradient index schematic lens and eye for the rat which predicts aberrations for finite pupils,” Vision Res. 21, 1129–1148 (1981).

J. G. Sivak, ”Optical properties of a cephalopod eye (the short finned squid, Illex illecebrosus),” J. Comp. Physiol. A 147, 323–327 (1982).

J. E. Marsden, and A. J. Tromba, Vector calculus, 2nd ed. (W. H. Freeman&Co., S. Francisco, 1981).

C. Campbell, ”Generalized Coddington equations found via an operator method,” J. Opt. Soc. Am. A 23(7), 1691–1697 (2006).

V. Linikk, ”Simple interferometer for the investigation of optical systems,” C. R. Acad. Sci. USSR 1, 208-210 (1933).

S. Chamadoira, R. Blendowske, and E. Acosta, ”Progressive Addition Lens Measurement by Point Diffraction Interferometry,” Optometry Vision Sci. textbf89(10), 1532–1542, (2012).

E. Acosta, S. Chamadoira, and R. Blendowske, ”Modified point diffraction interferometer for inspection and evaluation of ophthalmic components,” J. Opt. Soc. Am. A. 23, 632–637 (2006).

S. Chamadoira, Point diffraction interferometer for inspection and characterization of progressive addition lenses, Ph.D. Dissertation (University of Santiago de Compostela, Santiago de Compostela, 2011)

S. Bosch, ”Ray tracing and scalar diffraction calculations of wavefronts, caustics and complex amplitudes in optical systems,” J. Mod. Optic. 58, 146–153 (2011).


Journal of the European Optical Society:Rapid publications - ISSN 1990-2573. JEOS:RP is subject to the EOS General Terms and Conditions.