Standard Monte Carlo methods trace photon bundles in a forward direction, and may become extremely inefficient when radiation onto a small spot and/or onto a small direction cone is desired. Backward tracing of photon bundles is known to alleviate this problem if the source of radiation is large, but may also fail if the radiation source is collimated and/or very small. In this paper various implementations of the backward Monte Carlo method are discussed, allowing efficient Monte Carlo simulations for problems with arbitrary radiation sources, including small collimated beams, point sources, etc., in media of arbitrary optical thickness.

1.
Modest, M. F., 1993, Radiative Heat Transfer, McGraw-Hill, New York.
2.
Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, 3rd ed., Hemisphere, New York.
3.
Walters, D. V., and Buckius, R. O., 1992, “Monte Carlo Methods for Radiative Heat Transfer in Scattering Media,” in Annual Review of Heat Transfer, 5, Hemisphere, New York, pp. 131–176.
4.
Gordon
,
H. R.
,
1985
, “
Ship Perturbation of Irradiance Measurements at Sea: 1—Monte Carlo Simulations
,”
Appl. Opt.
,
24
, pp.
4172
4182
.
5.
Collins
,
D. G.
,
Bla¨ttner
,
W. G.
,
Wells
,
M. B.
, and
Horak
,
H. G.
,
1972
, “
Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging From Spherical-Shell Atmospheres
,”
Appl. Opt.
,
11
, pp.
2684
2696
.
6.
Adams
,
C. N.
, and
Kattawar
,
G. W.
,
1978
, “
Radiative Transfer in Spherical Shell Atmospheres—I. Rayleigh Scattering
,”
Icarus
,
35
, pp.
139
151
.
7.
Nishita
,
T.
,
Miyawaki
,
Y.
, and
Nakamae
,
E.
,
1987
, “
A Shading Model for Atmospheric Scattering Considering Luminous Intensity Distribution of Light Sources
,”
Comput. Graph.
,
21
, pp.
303
310
.
8.
Sabella
,
P.
,
1988
, “
A Rendering Algorithm for Visualizing 3D Scalar Fields
,”
Comput. Graph.
,
22
, pp.
51
58
.
9.
Edwards, D. K., 1983, “Numerical Methods in Radiation Heat Transfer,” in Proc. Second National Symposium on Numerical Properties and Methodologies in Heat Transfer, Shih, T. M., ed., Hemisphere, pp. 479–496.
10.
Walters
,
D. V.
, and
Buckius
,
R. O.
,
1992
, “
Rigorous Development For Radiation Heat Transfer In Nonhomogeneous Absorbing, Emitting And Scattering Media
,”
Int. J. Heat Mass Transf.
,
35
, pp.
3323
3333
.
11.
Cramer
,
S. N.
,
1996
, “
Forward-Adjoint Monte Carlo Coupling With No Statistical Error Propagation
,”
Nucl. Sci. Eng.
,
124
(
3
), pp.
398
416
.
12.
Serov
,
I. V.
,
John
,
T. M.
, and
Hoogenboom
,
J. E.
,
1999
, “
A Midway Forward-Adjoint Coupling Method for Neutron and Photon Monte Carlo Transport
,”
Nucl. Sci. Eng.
,
133
(
1
), pp.
55
72
.
13.
Ueki
,
T.
, and
Hoogenboom
,
J. E.
,
2001
, “
Exact Monte Carlo Perturbation Analysis by Forward-Adjoint Coupling in Radiation Transport Calculations
,”
J. Comput. Phys.
,
171
(
2
), pp.
509
533
.
14.
Case
,
K. M.
,
1957
, “
Transfer Problems and the Reciprocity Principle
,”
Rev. Mod. Phys.
,
29
, pp.
651
663
.
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