Chapter 22
RAY OPTICS APPROXIMATION FOR RANDOM
CLUSTERS OF GAUSSIAN SPHERES
K. Muinonen
Astronomical Observatory, Uppsals University, Uppsala, Sweden.
1.
INTRODUCTION
Scattering of light by natural particle clusters is one of the most important
current scattering problems. It is the goal of the present work to provide first
understanding about the differences in scattering by, on one hand, isolated
single particles and, on the other hand, clusters made of such single particles.
The fundamentals of the lognormal probability distribution are concisely
summarized by Aitchison and Brown (1963), including the multiplicative
analogues to the Central Limit Theorem for the normal probability
distribution. The lognormal distribution has been extensively used in studies
of various kinds of small particles. Only recently has the lognormal
distribution been applied in shape modeling (Muinonen et al. 1996,
Muinonen 1996, Peltoniemi et al. 1989). In these approaches, scattering by
random particles was studied in the ray optics approximation. Peltoniemi et
al. adopted a Markovian approach based on propagation probabilities for
stochastically rough particles. Muinonen et al. developed a spherical harmon
method for the generation of Gaussian random (or stochastically rough)
particles, and traced rays deterministically for sample particles, generating a
new sample particle for each ray. It has been hypothesized that, e.g., the
shapes of asteroids and cometary nuclei can be modeled by the Gaussian
random sphere (Muinonen 1997, Lagerros 1997).
Peltoniemi and Lumme (1992) showed important first results for
scattering by closely packed media. In close resemblance, but slightly
rephrasing the research goals, the current approach is directed toward
209
M.M. Verstraete et al. (eds.), Observing Land from Space: Science, Customers and Technology, 209–217.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
RAY OPTICS APPROXIMATION FOR RANDOM
CLUSTERS OF GAUSSIAN SPHERES
K. Muinonen
Astronomical Observatory, Uppsals University, Uppsala, Sweden.
1.
INTRODUCTION
Scattering of light by natural particle clusters is one of the most important
current scattering problems. It is the goal of the present work to provide first
understanding about the differences in scattering by, on one hand, isolated
single particles and, on the other hand, clusters made of such single particles.
The fundamentals of the lognormal probability distribution are concisely
summarized by Aitchison and Brown (1963), including the multiplicative
analogues to the Central Limit Theorem for the normal probability
distribution. The lognormal distribution has been extensively used in studies
of various kinds of small particles. Only recently has the lognormal
distribution been applied in shape modeling (Muinonen et al. 1996,
Muinonen 1996, Peltoniemi et al. 1989). In these approaches, scattering by
random particles was studied in the ray optics approximation. Peltoniemi et
al. adopted a Markovian approach based on propagation probabilities for
stochastically rough particles. Muinonen et al. developed a spherical harmon
method for the generation of Gaussian random (or stochastically rough)
particles, and traced rays deterministically for sample particles, generating a
new sample particle for each ray. It has been hypothesized that, e.g., the
shapes of asteroids and cometary nuclei can be modeled by the Gaussian
random sphere (Muinonen 1997, Lagerros 1997).
Peltoniemi and Lumme (1992) showed important first results for
scattering by closely packed media. In close resemblance, but slightly
rephrasing the research goals, the current approach is directed toward
209
M.M. Verstraete et al. (eds.), Observing Land from Space: Science, Customers and Technology, 209–217.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.