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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 28 — Oct. 1, 2012
  • pp: 6753–6764

Order-of-scattering point spread and modulation transfer functions for natural waters

Deric J. Gray  »View Author Affiliations


Applied Optics, Vol. 51, Issue 28, pp. 6753-6764 (2012)
http://dx.doi.org/10.1364/AO.51.006753


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Abstract

The point spread and modulation transfer functions for natural waters are derived using the small-angle approximation to radiative transfer theory. The functional forms are expanded into a summation of terms that represent each order-of-scattering contribution to the total. The beam spread function is shown to be a product of an angle function that depends only on the phase function of the medium and a weighting factor that depends only on the optical properties and depth. The modulation transfer function is similarly shown as a product of a function depending only on the spatial frequency and a weighting function. These results are compared with Monte Carlo calculations using two different phase functions, with excellent agreement. The results suggest the small-angle approximation to be valid over a much larger angular range than previously thought.

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(290.4210) Scattering : Multiple scattering
(110.0113) Imaging systems : Imaging through turbid media
(010.4455) Atmospheric and oceanic optics : Oceanic propagation
(010.7295) Atmospheric and oceanic optics : Visibility and imaging
(010.5620) Atmospheric and oceanic optics : Radiative transfer

ToC Category:
Scattering

History
Original Manuscript: July 16, 2012
Manuscript Accepted: August 27, 2012
Published: September 25, 2012

Citation
Deric J. Gray, "Order-of-scattering point spread and modulation transfer functions for natural waters," Appl. Opt. 51, 6753-6764 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-28-6753


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References

  1. J. S. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Ocean Eng. 15, 101–111 (1990). [CrossRef]
  2. C. J. Funk, S. B. Bryant, and P. J. Heckman, Handbook of Underwater Imaging System Design (Ocean Technology Department, Naval Undersea Center, 1972).
  3. W. H. Wells, “Theory of small-angle scattering,” AGARD Lect. Ser. 61, 1–19 (1973).
  4. J. S. Jaffe, “Monte Carlo modeling of underwater-image formation: validity of the linear and small-angle approximations,” Appl. Opt. 34, 5413–5421 (1995). [CrossRef]
  5. E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer Through a Scattering Medium (Springer-Verlag, 1991).
  6. W. Hou, D. J. Gray, A. D. Weidemann, and R. A. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express 16, 9958–9965 (2008). [CrossRef]
  7. H. R. Gordon, “Equivalence of the point and beam spread functions of scattering media: a formal demonstration,” Appl. Opt. 33, 1120–1122 (1994). [CrossRef]
  8. L. E. Mertens and F. S. Replogle, “Use of point spread and beam spread functions for analysis of imaging systems in water,” J. Opt. Soc. Am. 67, 1105–1117 (1977). [CrossRef]
  9. D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. Zaneveld, “Comparison of near-forward light scattering on oceanic turbulence and particle,” Appl. Opt. 37, 4669–4677 (1998). [CrossRef]
  10. W. T. Scott, “The theory of small-angle multiple-scattering of fast charged particles,” Rev. Mod. Phys. 35, 231–313 (1963). [CrossRef]
  11. D. M. Bravo-Zhivotovskiy, L. S. Dolin, A. G. Luchinin, and V. A. Savel’yev, “Structure of a narrow light beam in sea water,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. (Engl. Transl.) 5, 160–167 (1969) (translated by P. A. Kaehn).
  12. R. E. Walker, Marine Light Field Statistics (Wiley, 1994).
  13. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  14. W. H. Wells, “Loss of resolution in water as a result of multiple small-angle scattering,” J. Opt. Soc. Am. 59, 686–691 (1969). [CrossRef]
  15. A. Gordon and M. R. Kittel, “Underwater multiple scattering of light for system designers,” Naval Undersea Center Technical Report 371 (National Technical Information Service, 1973).
  16. R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999).
  17. J. Markham and J.-A. Conchello, “Numerical Evaluation of Hankel transforms for oscillating function,” J. Opt. Soc. Am. A 20, 621–630 (2003). [CrossRef]
  18. T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Reference 72–78 (Scripps Institute of Oceanography, University of California, San Diego,1972).
  19. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, 1994).
  20. V. I. Haltrin, “Theoretical and empirical phase functions for Monte Carlo calculations of light scattering in seawater,” in Proceedings of the Fourth International Conference on Remote Sensing for Marine and Coastal Environments (Environmental Research Institute of Michigan, 1997).
  21. L. B. Stotts, “Limitations of approximate Fourier techniques in solving radiative-transfer problems,” J. Opt. Soc. Am. 69, 1719–1723 (1979). [CrossRef]
  22. N. L. Swanson, V. M. Gehman, B. D. Billard, and T. L. Gennaro, “Limits of the small-angle approximation to the radiative transport equation,” J. Opt. Soc. Am. A 18, 385–391 (2001). [CrossRef]
  23. N. L. Swanson, B. D. Billard, V. M. Gehman, and T. L. Gennaro, “Application of the small-angle approximation to ocean water types,” Appl. Opt. 40, 3608–3613 (2001). [CrossRef]

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