Light scattering from water droplets in the geometrical optics approximation

The geometrical optics approach is used to derive i(1)(theta) = |S(1)(theta)|(2) and i(2)(theta) = |S(2)(theta)|(2), the angular intensity functions for light scattered by a spherical water droplet of a radius comparable with or larger than the wavelength of light. In contrast to previously published results, these functions are obtained in closed form and as functions of the scattering angle theta, which greatly enhance their usefulness in numerical work and in the reduction of large sphere scattering data. The range of validity of these expressions is investigated by graphical comparison of calculated angular intensity patterns with those obtained from rigorous Mie theory. Our main objective is to study the feasibility of using the geometrical optics expressions as a basis for practical laser water droplet sizing work. A criterion is established for the range of applicability of the relationship I(theta,R) = K(theta)R(2), which relates the scattering intensity at a particular angle theta to the radius R of the droplet. Accuracy of the laser water droplet sizing technique is thus quantitatively established.