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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. 28, Iss. 10 — Oct. 1, 2011
  • pp: 2014–2025

Trajectories in parallel optics

Iftach Klapp, Nir Sochen, and David Mendlovic  »View Author Affiliations


JOSA A, Vol. 28, Issue 10, pp. 2014-2025 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002014


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Abstract

In our previous work we showed the ability to improve the optical system’s matrix condition by optical design, thereby improving its robustness to noise. It was shown that by using singular value decomposition, a target point-spread function (PSF) matrix can be defined for an auxiliary optical system, which works parallel to the original system to achieve such an improvement. In this paper, after briefly introducing the all optics implementation of the auxiliary system, we show a method to decompose the target PSF matrix. This is done through a series of shifted responses of auxiliary optics (named trajectories), where a complicated hardware filter is replaced by postprocessing. This process manipulates the pixel confined PSF response of simple auxiliary optics, which in turn creates an auxiliary system with the required PSF matrix. This method is simulated on two space variant systems and reduces their system condition number from 18,598 to 197 and from 87,640 to 5.75, respectively. We perform a study of the latter result and show significant improvement in image restoration performance, in comparison to a system without auxiliary optics and to other previously suggested hybrid solutions. Image restoration results show that in a range of low signal-to-noise ratio values, the trajectories method gives a significant advantage over alternative approaches. A third space invariant study case is explored only briefly, and we present a significant improvement in the matrix condition number from 1.9160e+013 to 34,526.

© 2011 Optical Society of America

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(080.1010) Geometric optics : Aberrations (global)
(100.3190) Image processing : Inverse problems
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: March 16, 2011
Revised Manuscript: July 26, 2011
Manuscript Accepted: July 28, 2011
Published: September 9, 2011

Citation
Iftach Klapp, Nir Sochen, and David Mendlovic, "Trajectories in parallel optics," J. Opt. Soc. Am. A 28, 2014-2025 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-10-2014


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References

  1. I. Klapp and D. Mendlovic, “Improvement of matrix condition of hybrid, space variant optics by the means of parallel optics design,” Opt. Express 17, 11673–11689 (2009). [CrossRef]
  2. J. H. Wilkinson, Rounding Errors in Algebraic Processes (Her Majesty’s Stationery Office, 1963), Chap. 3, p. 91.
  3. G. H. Golub and C. F. Van-loan, Matrix Computation (North Oxford Academic, 1983).
  4. H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976). [CrossRef]
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  6. A. W. Lohmann and W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1151 (1978). [CrossRef]
  7. J. N. Mait and W. T. Rhodes, “Two-pupil synthesis of optical transfer functions: pupil function relationships,” Appl. Opt. 25, 2003–2007 (1986). [CrossRef]
  8. P. C. Hansen and J. G. Nagy, Deblurring Images Matrices, Spectra, and Filtering (SIAM, 2006).
  9. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
  10. R. G. Paxman, T. J. Schultz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992). [CrossRef]
  11. R. A. Gonsalves, “Nonisoplanatic imaging by phase diversity,” Opt. Lett. 19, 493–495 (1994). [CrossRef]
  12. M. G. Lofdahl, “Multiframe deconvolution with space variant point spread function by use of inverse filtering and fast Fourier transform,” Appl. Opt. 46, 4686–4693 (2007). [CrossRef]
  13. J. Bardsley, S. Jefferies, J. Nagy, and R. Plemmons, “Blind iterative restoration of image with spatially-varying blur,” presented at the Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, (September 5–9, 2005).
  14. R. G. Paxman and J. H. Seldin, “Phase-diversity data set and processing strategies,” in High Resolution Solar Physics: Theory, Observations, and Techniques, T.R.Rimmele, ed., ASP Conference Series (Astronomical Society of the Pacific, 1999), Vol.  183.
  15. M. R. Bolcar and J. R. Fienup, “Method of phase diversity in multi aperture systems utilizing individual sub aperture control,” Proc. SPIE 5896, 58960G (2005). [CrossRef]
  16. T. C. Zaugg and R. G. Paxman, “Complementary compensation in the presence of fixed aberrations,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings, Technical Digest (CD) (Optical Society of America, 2005), paper SMB5.
  17. E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995). [CrossRef]
  18. S. Mezouari and A. R. Harvey, “Phase pupil function for reduction of defocus and spherical aberration,” Opt. Lett. 28, 771–773(2003). [CrossRef]
  19. S. Mezouari, G. Moyo, and A. R. Harvey, “Circularly symmetric phase filter for control of primary third order aberration: coma and astigmatism,” J. Opt. Soc. Am. A. 23, 1058–1062(2006). [CrossRef]
  20. I. Klapp and D. Mendlovic, “Parallel optics for improving system matrix condition,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CWB3.
  21. I. Klapp and D. Mendlovic, “Optical design for improving matrix condition,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA7.
  22. I. Klapp and D. Mendlovic, “Imaging system and method for imaging object with reduced image blur,” U.S. patent WO/2010/103527 A2 (March 13, 2009).
  23. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1991).
  24. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
  25. I. Klapp and D. Mendlovic, “Trajectories by a blurred auxiliary system,” J. Opt. Soc. Am. A 28, 1796–1802 (2011).

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