Abstract
We discuss the use of nonconventional optical processors for generating irradiance distributions, which are useful for visualizing the characteristics of imaging devices that extend the depth of field. Our discussion starts with the use of binary masks for generating nonconventional irradiance distributions, which display the variations of the impulse response with focus errors. By using an anamorphic optical processor these irradiance distributions can easily be transformed into variations of the optical transfer function vs focus errors. Next, another anamorphic optical processor is used for generating the ambiguity function of a pupil aperture, which helps to visualize the variations of the optical transfer function with variable focus error. Finally, we translate the integral transform associated with the evaluation of the ambiguity function into tunable devices for controlling the depth of field, without modifying the size of the pupil aperture.
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References
Jacquinot, P.: Apodization, Appendix E, in concepts of classical optics, John Strong, pp. 410–418. W. H. Freeman, San Francisco (1958)
Marechal, A., Françon, M.: Diffraction Structure Des Images, pp. 152–155. Masson, Paris (1970)
Papoulis, A.: Systems and Transforms with Applications in Optics, pp. 442–444. McGraw-Hill, New York (1968)
Steel, W.H.: Interferometry, pp. 23, 234, 248–249. Cambridge University Press, Cambridge (1983)
Goodman, J.W.: Introduction to Fourier Optics, pp. 151–154. McGraw-Hill, New York (1996)
Ojeda-Castañeda, J., Berriel-Valdos, L.R., Montes E.: Bessel annular apodizers: imaging characteristics. Appl. Opt. 26(10), 2770–2772 (1987)
McCutchen, C.W.: Generalized aperture and three-dimensional diffraction image. J. Opt. Soc. Am. 54(2), 240–244 (1964)
Ojeda-Castañeda, J., Berriel-Valdos, L.R.: Arbitrarily high focal depth with finite apertures. Opt. Lett. 13(3), 183–185 (1988)
Ojeda-Castañeda, J., Andres, P., Diaz, A.: Strehl ratio with low sensitivity to spherical aberration. J. Opt. Soc. Am. A 5(8), 1233–1236 (1988)
Ojeda-Castañeda, J., Tepichin, E., Pons, A.: Apodization of annular apertures: Strehl ratio. Appl. Opt. 27(24), 5140–5145 (1988)
Mino, M., Okano, Y.: Improvement in the OTF of a defocused optical system through the use of shaded apertures. Appl. Opt. 10(10), 2219 (1971)
Hauesler, G.: A method to increase the depth of focus by two step image processing. Opt. Commun. 6(1), 38–42 (1972)
Chung, C.S., Hopkins, H.H.: Influence of nonuniform amplitude on the optical transfer function. Appl. Opt. 28(6), 90–91 (1989)
Ojeda-Castañeda, J., Yépez-Vidal, E., Gómez-Sarabia, C.M.: Multiple-frame photography for extended depth of field. Appl. Opt. 52(10), D84–D90 (2013)
Lohmann, A.W., Ojeda-Castañeda, J., Serrano-Heredia, A.: Trading dimensionality in signal processing. Opt. Laser Technol. 28(2), 101–107 (1996)
Ojeda-Castañeda, J., Lohmann, A.W.: Young’s experiment in signal synthesis, Chapter 14, Trends in Optic, Anna Consortini Editor, pp. 263–280. Academic Press, San Diego (1996)
Lohmann, A.W., Ojeda-Castañeda, J., Frausto, C.: Optical simulation of free-space propagation. Opt. Commun. 157(1–6), 7–12 (1998)
Ojeda-Castañeda, J., Castro, A.: Simultaneous Cartesian coordinate display of defocused optical transfer functions. Opt. Lett. 23(13), 1049–1051 (1998)
Woodward, P.M.: Radar ambiguity analysis, Technical Note No. 731. Royal Radar Establishment, London (1967)
Papoulis, A.: Ambiguity function in Fourier optics. J. Opt. Soc. Am. 64(6), 779–788 (1974)
Guigay, J.P.: The ambiguity function in diffraction and isoplanatic imaging by partially coherent beams. Opt. Commun. 26(2), 136–138 (1978)
Marks, R.J., Walkup, J.K., Krile, T.F.: Ambiguity function display: an improved coherent processor. Appl. Opt. 16(3), 746–750 (1977)
Brenner, K.-H., Lohmann, A.W., Ojeda-Castañeda, J.: The ambiguity function as a polar display of the OTF. Opt. Commun. 44(5), 323–326 (1983)
Ojeda-Castañeda, J., Berriel-Valdos, L.R., Montes, E.: Ambiguity function as a design tool for high focal depth. Appl. Opt. 27(4), 790–795 (1988)
Ojeda-Castañeda, J., Noyola-Isgleas, A.: High focal depth by apodization and digital restoration. Appl. Opt. 27(12), 2583–2586 (1988)
Dowski, E.R., Cathey, T.W.: Extended depth of field through wave-front coding. Appl. Opt. 34(11), 1859–1865 (1995)
Cook, C. E., Bernfeld, M.: Radar Signals: An Introduction to Theory and Applications, pp. 59–108. Arctech House, Norwood (1993)
George, N., Chi, W.: Extended depth of field using a Logarithmic asphere. J. Opt. Pure Appl. 5, s157–s163 (2003)
Muyo, G., Harvey, A.R.: Decomposition of the optical transfer function: wavefront coding imaging systems. Opt. Lett. 30(20), 2715–2717 (2005)
Sauceda-Carvajal, A., Ojeda-Castaneda, J.: High focal depth with fractional-power wave fronts. Opt. Lett. 29(6), 560–562 (2004)
Castro, A., Ojeda-Castaneda, J.: Asymmetric phase masks for extended depth of field. Appl. Opt. 43(17), 3474–3479 (2004)
Ojeda-Castañeda, J.: Focus error operator and related special functions. J. Opt. Soc. Am. 73(8), 1042–1047 (1983)
Ojeda-Castañeda, J., Boivin, A.: The influence of wave aberrations: an operator approach. Can. J. Phys. 63(2), 250–253 (1985)
Ojeda-Castañeda, J., Noyola-Isgleas, A.: Differential operator for scalar wave propagation. J. Opt. Soc. Am. A 5(10), 1605–1609 (1988)
Ojeda-Castañeda, J., Berriel-Valdos, L.R., Montes, E.: Ambiguity function as a design tool for high focal depth. Appl. Opt. 27(4), 790–795 (1988)
Marks, R.J. II, Walkup, J.K., Krile, T.F.: Ambiguity function display: an improved coherent processor. Appl. Opt. 16(3), 746–750 (1977)
Castro, A., Ojeda-Castaneda, J., Lohmann, A.W.: Bow-tie effect: differential operator. Appl. Opt. 45(30), 7878–7884 (2006)
Ojeda-Castañeda, J., Yépez-Vidal, E., García-Almanza, E.: Complex amplitude filters for extended depth of field. Photonics Lett. Pol. 2, 162–164 (2010)
Ojeda-Castañeda J., Ledesma S. and Gomez-Sarabia C. M., Hyper Gaussian Windows with fractional wavefronts. Photonics Lett. Pol. 5(1), 23–25 (2013)
Brenner, N., Rader, C.: IEEE Acoustics. Speech Signal Process. 24, 264–266 (1976)
Plummer, W.T., Baker, J.G., van Tassell, J.: Photographic optical systems with nonrotational aspheric surfaces. Appl. Opt. 38(16), 3572–2592 (1999)
Kitajima, I.: “Improvement in lenses”. British Patent 250, 268 (July 29, 1926)
Lohmann, A.W.: Lente a focale variabili. Italian Patent 727, 848 (June 19, 1964)
Lohmann, A.W.: Improvements relating to lenses and to variable optical lens systems formed for such a lens. Patent Specification 998,191, London (1965)
Lohmann, A.W.: A new class of varifocal lenses. Appl. Opt. 9(7), 1669–1671 (1970)
Alvarez, L.W.: Two-element variable-power spherical lens. US Patent 3, 305, 294 (December 3, 1964)
Alvarez, L.W., Humphrey, W.H.: Variable power lens and system. US Patent 3, 507, 565 (April 21, 1970)
Ojeda-Castañeda, J., Landgrave, J.E.A., Gómez-Sarabia, C.M.: The use of conjugate phase plates in the analysis of the frequency response of optical systems designed for an extended depth of field. Appl. Opt. 47(22), E99–E105 (2008)
Ojeda-Castañeda, J., Aguilera Gómez, E., Plascencia Mora, H., Torres Cisneros, M., Ledesma Orozco, E.R., León Martínez, A., Pacheco Santamaría, J.S., Martínez Castro, J.G.: Carlos Salas Segoviano R., U. S. Patent 8, 159, 573B2 (April 17, 2012)
Ojeda-Castañeda, J., Gómez-Sarabia, C.M.: Key concepts for extending the depth of field with high resolution. Opt. Pura Apl. 45(4) 449–459 (2012)
Ojeda-Castañeda, J., Yépez-Vidal, E., García-Almanza, E., Gómez-Sarabia, C.M.: “Tunable Gaussian mask for extending the depth of field”. Photonics Lett. Pol. 4(3), 115–117 (2012)
Lohmann, A.W., Paris, D.P.: “Variable Fresnel Zone Pattern” Appl. Opt. 6(9), 1567–1570 (1967)
Burch, J.M., Williams, D.C.: Varifocal moiré zone plates for straightness measurement. Appl. Opt. 16(9), 2445–2450 (1977)
Bernet, S., Jesacher, A., Fuerhapter, S., Maurer, C., Ritsch-Marte, M.: “Quantitative imaging of complex samples by spiral phase contrast microscopy”. Opt. Express 14(9) 3792–3805 (2006)
Jesacher, A., Fürhapter, S., Bernet, S., Ritsch-Marte, M.: “Spiral interferogram analysis”. J. Opt. Soc. Am. A 23(6) 1400–1409 (2006)
Bernet, S., Ritsch-Marte, M.: “Optical device with a pair of diffractive optical elements”. US Patent 0134869 A1 (June 3, 2010)
Ojeda-Castaneda, J., Ledesma, S., Gomez-Sarabia, C.M.: Tunable apodizers and tunable focalizers using helical pairs. Photonics Lett. Pol. 5(1), 20–22 (2013)
Ojeda-Castaneda, J., Gomez-Sarabia, C.M., Ledesma, S.: Tunable focalizers: axicons, lenses and axilenses, Tribute to H. John Caulfield, SPIE Proceedings 8833, 88330601–88330606 (2013)
Bryngdahl, O.: Radial- and circular-fringe interferograms. J. Opt. Soc. Am. 63(9), 1098–1104 (1973)
Ojeda-Castañeda, J., Ledesma, S., Gomez-Sarabia, C.M.: Hyper Gaussian Windows with fractional wavefronts. Photonics Lett. Pol. 5(1), 23–25 (2013)
Ojeda-Castaneda, J., Ledesma, S., Gomez-Sarabia, C.M.: Helical apodizers for tunable hyper Gaussian masks, Novel Optical System Design and Optimization XVI, SPIE Proceedings 8842, 88420N-1-88420N-6 (2013)
Acknowledgements
We gratefully acknowledge the financial support of CONACYT, grant 157673, Fondo: I0017, as well as the grant 1477-CIO-UG-2013, DAIP, University of Guanajuato.
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Ojeda-Castañeda, J., Ledesma, S., Yépez-Vidal, E., Gomez-Sarabia, C., Torres-Cisneros, M. (2015). Optical Processors as Conceptual Tools for Designing Nonconventional Devices. In: Shulika, O., Sukhoivanov, I. (eds) Advanced Lasers. Springer Series in Optical Sciences, vol 193. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9481-7_8
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