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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 9 — Sep. 1, 2014
  • pp: 2021–2029

Transformational volume holography

Hanhong Gao and George Barbastathis  »View Author Affiliations

JOSA A, Vol. 31, Issue 9, pp. 2021-2029 (2014)

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We analyze the bulk elastic transformation of volume holograms as a general approach for three-dimensional pupil engineering. The physical relationship between transformation and the resulting point spread function is discussed by deriving the corresponding analytical expressions. For affine transformations, an analytical solution is directly possible. However, for nonaffine transformations, the analytical solution is not straightforward and we must turn to quasi-analytical solutions using the approximation of the stationary phase. Transformational volume holography offers richer design flexibility and real-time adjustment capabilities for imaging systems.

© 2014 Optical Society of America

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(090.2890) Holography : Holographic optical elements
(350.6980) Other areas of optics : Transforms

ToC Category:

Original Manuscript: May 22, 2014
Manuscript Accepted: July 11, 2014
Published: August 20, 2014

Hanhong Gao and George Barbastathis, "Transformational volume holography," J. Opt. Soc. Am. A 31, 2021-2029 (2014)

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  1. H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, “New spectroscopic instrument based on volume holographic optical elements,” Proc. SPIE 2406, 260–267 (1995).
  2. G. Barbastathis and D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999). [CrossRef]
  3. A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt. 43, 1533–1551 (2004). [CrossRef]
  4. Y. Luo, I. K. Zervantonakis, S. B. Oh, R. D. Kamm, and G. Barbastathis, “Spectrally resolved multidepth fluorescence imaging,” J. Biomed. Opt. 16, 096015 (2011). [CrossRef]
  5. H. Gao, J. M. Watson, J. S. Stuart, and G. Barbastathis, “Design of volume hologram filters for suppression of daytime sky brightness in artificial satellite detection,” Opt. Express 21, 6448–6458 (2013). [CrossRef]
  6. K. Tian, T. Cuingnet, Z. Li, W. Liu, D. Psaltis, and G. Barbastathis, “Diffraction from deformed volume holograms: perturbation theory approach,” J. Opt. Soc. Am. A 22, 2880–2889 (2005). [CrossRef]
  7. H. Gao and G. Barbastathis, “Design of volume holograpic imaging point spread functions using multiple point deformations,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2012), paper DTu3C.6.
  8. H. Gao and G. Barbastathis, “Design and optimization of point spread functions in volume holographic imaging systems,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2013), paper DTh3A.6.
  9. H. Gao, “Design and transformation of three-dimensional pupils: diffractive and subwavelength,” Ph.D. dissertation (Massachusetts Institute of Technology, 2014).
  10. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006). [CrossRef]
  11. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef]
  12. G. Barbastathis, F. Mok, and D. Psaltis, “Non-volatile readout of shift multiplexed holograms,” U.S. patent5,978,112 (November2, 1999).
  13. J. T. Gallo and C. M. Verber, “Model for the effects of material shrinkage on volume holograms,” Appl. Opt. 33, 6797–6804 (1994). [CrossRef]
  14. P. Hariharan, Optical Holography: Principles, Techniques, and Applications, 2nd ed. (Cambridge University, 1996).
  15. D. H. R. Vilkomerson and D. Bostwick, “Some effects of emulsion shrinkage on a holograms image space,” Appl. Opt. 6, 1270–1272 (1967). [CrossRef]
  16. R. C. Hibbeler, Mechanics of Materials (Prentice-Hall, 2010).
  17. V. A. Borovikov, Uniform Stationary Phase Method (Institution of Electrical Engineers, 1994).
  18. H. Cheng, Advanced Analytic Methods in Applied Mathematics, Science, and Engineering (LuBan, 2007).
  19. J. C. Cooke, “Stationary phase in two dimensions,” IMA J. Appl. Math. 29, 25–37 (1982). [CrossRef]
  20. V. A. Borovikov and B. Y. Kinber, Geometrical Theory of Diffraction (Institution of Electrical Engineers, 1994).
  21. O. M. Conde, J. Pérez, and M. F. Cátedra, “Stationary phase method application for the analysis of radiation of complex 3-D conducting structures,” IEEE Trans. Antennas Propag. 49, 724–731 (2001). [CrossRef]
  22. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (The Institution of Engineering and Technology, 1979).
  23. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover, 1965).

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