## Analytic beam spread function for ocean optics applications

Applied Optics, Vol. 41, Issue 30, pp. 6276-6288 (2002)

http://dx.doi.org/10.1364/AO.41.006276

Enhanced HTML Acrobat PDF (213 KB)

### Abstract

A discrete ordinates code is developed with which to compute the beam spread function (BSF) without invoking the small-angle scattering approximation or performing Monte Carlo calculations. The computed BSF is used to predict the response of a detector versus its distance to the origin of a highly collimated beam, its angle with respect to the beam, and the two local angles that specify the detector orientation. Numerical results have been obtained for water models that simulate a clear ocean, a coastal ocean, and a turbid harbor. Six orders of magnitude or more change in the detector response caused by scattered photons can be predicted for different detector locations while simultaneously obtaining small changes for different detector orientations. This capability is useful for assessment of the sensitivity of the detector response to the interpretation of time-independent underwater imaging systems or visibility models.

© 2002 Optical Society of America

**OCIS Codes**

(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics

(010.4450) Atmospheric and oceanic optics : Oceanic optics

(010.7340) Atmospheric and oceanic optics : Water

(030.5620) Coherence and statistical optics : Radiative transfer

**History**

Original Manuscript: January 4, 2002

Revised Manuscript: June 10, 2002

Published: October 20, 2002

**Citation**

Richard Sanchez and Norman J. McCormick, "Analytic beam spread function for ocean optics applications," Appl. Opt. **41**, 6276-6288 (2002)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-30-6276

Sort: Year | Journal | Reset

### References

- K. M. Case, F. de Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion (U.S. GPO, Washington, D.C., 1953).
- D. E. Kornreich, B. D. Ganapol, “The suite of analytical benchmarks for neutral particle transport in infinite isotropically scattering media,” Nucl. Sci. Eng. 125, 24–50 (1997).
- H. R. Gordon, “Equivalence of the point and beam spread functions of scattering media: a formal demonstration,” Appl. Opt. 33, 1120–1122 (1994). [CrossRef] [PubMed]
- K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
- W. H. Wells, “Theory of small angle scattering,” in Optics of the Sea (Interface and In-Water Transmission and Imaging), P. Halley, ed., Lecture Series no. 61 (North Atlantic Treaty Organization, Advisory Group for Aerospace Research and Development, Neuilly-sur-Seine, France, 1973).
- K. J. Voss, A. L. Chapin, “Measurement of the point spread function in the ocean,” Appl. Opt. 29, 3638–3642 (1990). [CrossRef] [PubMed]
- K. J. Voss, “Simple empirical model of the oceanic point spread function,” Appl. Opt. 30, 2647–2651 (1991). [CrossRef] [PubMed]
- R. E. Walker, Marine Light Field Statistics (Wiley, New York, 1994).
- N. L. Swanson, V. M. Gehman, B. D. Billard, T. L. Gennaro, “Limits of the small-angle approximation to the radiative transport equation,” J. Opt. Soc. Am. A 18, 385–391 (2001). [CrossRef]
- N. L. Swanson, B. D. Billard, V. M. Gehman, T. L. Gennaro, “Application of the small-angle approximation to ocean water types,” Appl. Opt. 40, 3608–3613 (2001). [CrossRef]
- C. D. Mobley, G. F. Cota, T. C. Grenfell, R. A. Maffione, W. S. Pegau, D. K. Perovich, “Modeling light propagation in sea ice,” IEEE Trans. Geosci. Remote Sens. 36, 1743–1749 (1998). [CrossRef]
- A. Laux, R. Billmers, L. Mullen, B. Concannon, J. Davis, J. Prentice, V. Contarino, “The a, b, cs of oceanographic lidar predictions: a significant step toward closing the loop between theory and experiment,” J. Mod. Opt. 49, 439–451 (2002). [CrossRef]
- J. J. Duderstadt, W. R. Martin, Transport Theory (Wiley, New York, 1979).
- E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport (American Nuclear Society, LaGrange Park, Ill., 1993).
- K. D. Lathrop, F. W. Brinkley, “twotran sphere: a fortran program to solve the multigroup transport equation in two-dimensional spherical geometry,” Los Alamos Report LA-4567 (Los Alamos Scientific Laboratory, Los Alamos, N. Mex., 1970).
- R. Sanchez, N. J. McCormick, “Discrete ordinate solutions for highly forward-peaked scattering,” Ann. Nucl. Energy, submitted for publication.
- R. Sanchez, “On the singular structure of the uncollided and first-collided components of the Green’s function,” Ann. Nucl. Energy 27, 1167–1186 (2000). [CrossRef]
- C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic, New York, 1994).
- N. J. McCormick, “Asymptotic optical attenuation,” Limnol. Oceanogr. 37, 1570–1578 (1992). [CrossRef]
- T. J. Petzold, “Volume scattering functions for selected ocean waters,” SIO Ref. 72–78 (Scripps Institution of Oceanography, La Jolla, Calif., 1972).
- J. W. McLean, J. D. Freeman, R. E. Walker, “Beam spread function with time dispersion,” Appl. Opt. 37, 4701–4711 (1998). [CrossRef]
- G. C. Pomraning, “The Fokker–Planck operator as an asymptotic limit,” Math. Models Methods Appl. Sci. 2, 21–36 (1992). [CrossRef]
- G. C. Pomraning, A. K. Prinja, J. W. VanDenburg, “An asymptotic model for the spreading of a collimated beam,” Nucl. Sci. Eng. 112, 347–360 (1992).
- C. Börgers, E. W. Larsen, “Asymptotic derivation of the Fermi pencil-beam approximation,” Nucl. Sci. Eng. 123, 343–357 (1996).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.