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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 13 — May. 1, 2006
  • pp: 2924–2934

Signal-to-noise analysis of task-based imaging systems with defocus

Paulo E. X. Silveira and Ramkumar Narayanswamy  »View Author Affiliations

Applied Optics, Vol. 45, Issue 13, pp. 2924-2934 (2006)

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We analyze the signal-to-noise ratio (SNR) of arbitrary imaging systems in the presence of defocus. The modulation transfer function (MTF) and the mean SNR are combined to calculate the spatial-frequency spectrum of the SNR (the spectral SNR). Computational imaging methods are used for extending the depth of field (DOF) of the system. The DOF of a task-specific imaging system is defined as the range of defocus that causes the spectral SNR to drop below a minimum value within a band of spatial frequencies of interest. We introduce the polar-SNR plot as a tool for visualizing the spectral SNR of defocused imaging systems with asymmetric pupil functions. As an example, we perform the analysis of an imaging system used for biometric iris recognition.

© 2006 Optical Society of America

OCIS Codes
(100.5010) Image processing : Pattern recognition
(110.2960) Imaging systems : Image analysis
(110.3000) Imaging systems : Image quality assessment
(110.4100) Imaging systems : Modulation transfer function
(110.4280) Imaging systems : Noise in imaging systems

ToC Category:
Performance Analysis

Original Manuscript: September 8, 2005
Revised Manuscript: October 25, 2005
Manuscript Accepted: October 25, 2005

Virtual Issues
Vol. 1, Iss. 6 Virtual Journal for Biomedical Optics

Paulo E. X. Silveira and Ramkumar Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 45, 2924-2934 (2006)

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  1. See, for example, J. W. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, 1968), Chap. 6, pp. 122-125.
  2. J. Hall, "F-number, numerical aperture, and depth of focus," in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 556-559.
  3. W. J. Smith, Modern Optical Engineering, 3rd. ed. (McGraw-Hill, 2000), Chap. 6, pp. 154-157.
  4. R. Narayanswamy, G. E. Johnson, P. E. X. Silveira, and H. B. Wach, "Extending the imaging volume for biometric iris recognition," Appl. Opt. 44, 701-712 (2005). [CrossRef] [PubMed]
  5. R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. van der Gracht, "Extended depth-of-field iris recognition system for a workstation environment," in Biometric Technology for Human Identification II, A. K. Jain and N. K. Ratha, eds., Proc. SPIE 5779, 41-50 (2005).
  6. R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, "Applications of wavefront coded imaging," in Computational Imaging II, C.A.Bouman and E.L.Miller, eds., Proc. SPIE 5299, 163-174 (2004).
  7. W. T. Cathey and E. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002). [CrossRef] [PubMed]
  8. E. R. Dowski, Jr., and W. T. Cathey, "Extended depth of field through wavefront coding," Appl. Opt. 34, 1859-1866 (1995). [CrossRef] [PubMed]
  9. H. Wach, E. Dowski, and W. T. Cathey, "Control of chromatic focal shift through wavefront coding," Appl. Opt. 37, 5359-5367 (1998). [CrossRef]
  10. K. Kubala, E. Dowski, J. Kobus, and B. Brown, "Aberration and error invariant space telescope systems," in Novel Optical Systems Design and Optimization VII, J.M.Sasian, R.J.Koshel, P.K.Manhart, and R.C.Juergens, eds., Proc. SPIE 5524, 54-65 (2004).
  11. R. Fiete and T. Tantalo, "Comparison of SNR image quality metrics for remote sensing systems," Opt. Eng. 40, 574-585 (2001). [CrossRef]
  12. C. P. Cain, D. Courant, D. A. Freund, B. A. Grossman, P. A. Kennedy, D. J. Lund, M. A. Mainster, A. A. Manenkov, W. J. Marshall, R. McCally, B. A. Rockwell, D. H. Sliney, P. A. Smith, B. E. Stuck, S. A. Tell, M. L. Wolbarsht, and G. I. Zheltov, "Revision of the guidelines on limits of exposure to laser radiation of wavelengths between 400 nm and 1.4 μm," Health Phys. 79, 431-440 (2000). [CrossRef]
  13. W. J. Smith, Modern Optical Engineering, 3rd. ed. (McGraw-Hill, 2000), Chap. 8, pp. 219-230.
  14. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, 1983).
  15. See, for example, E. R. Dougherty, Random Processes for Image and Signal Processing (IEEE, 1998), Chap. 1, pp. 26-28.
  16. J. W. Goodman, "Fan-in and fan-out with optical interconnections," Opt. Acta 32, 1489-1496 (1985). [CrossRef]
  17. D. J. Brady, "Multiplex sensors and the constant radiance theorem," Opt. Lett. 27, 16-18 (2002). [CrossRef]
  18. J. G. Daugman, "High confidence visual recognition of persons by a test of statistical independence," IEEE Trans. Pattern Anal. Mach. Intell. 15, 1148-1161 (1993). [CrossRef]
  19. R. P. Wildes, "Automated iris recognition: an emerging biometric technology," in Proc. IEEE 85, 1348-1363 (1997). [CrossRef]
  20. J. G. Daugman, "The importance of being random: statistical principles of iris recognition," Pattern Recogn. 36, 279-291 (2003). [CrossRef]

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