Monte Carlo Algorithms for Solving Nonstationary Problems of the Theory of Narrow-Beam Propagation in the Atmosphere and Ocean

Abstract

This chapter deals with calculational aspects of problems of utilizing high-power pulsed-laser lidary systems to obtain an information concerning the structures of the atmosphere and ocean. The problem can be formulated as follows. Consider a narrow light beam that propagates through an absorbing and scattering medium in a layer h ≤ z ≤ H. The light is emitted uniformly from a circular surface source of radius R _s situated in the plane

$${a_s}\left( {x - {x_s}} \right) + {b_s}\left( {y - {y_s}} \right) + {c_s}\left( {z - {z_s}} \right) = 0,$$

at a point (x _s, y _s, z _s). The emission is also assumed to be isotropic within a circular conic solid angle Ω _s [with an angle γ _s between its element and axis n = (a _s, b _s, c _s)]. The time distribution density of the emitted photons is a function p ⁽⁰⁾_t (τ) such that

$$\int\limits_0^\infty {p_t^{\left( 0 \right)}} \left( \tau \right)d\tau = 1.$$