A Mueller matrix M̃ is developed for a single-scattering process such that G(θ, ϕ) = T̃(ϕ a ) M̃T̃(ϕ p )u, where u is the incident irradiance Stokes vector transmitted through a linear polarizer at azimuthal angle ϕ p , with transmission Mueller matrix T̃(ϕ p ), and G(θ, ϕ) is the polarized irradiance Stokes vector measured by a detector with a field of view F, placed after an analyzer with transmission Mueller matrix T̃(ϕ a ) at angle ϕ a . The Mueller matrix M̃ is a function of the Mueller matrix S̃(θ) of the scattering medium, the scattering angle (θ, ϕ), and the detector field of view F. The Mueller matrix M̃ is derived for backscattering and forward scattering, along with equations for the detector polarized irradiance measurements (e.g., cross polarization and copolarization) and the depolarization ratio. The information that can be derived from the Mueller matrix M̃ on the scattering Mueller matrix S̃(θ) is limited because the detector integrates the cone of incoming radiance over a range of azimuths of 2π for forward scattering and backscattering. However, all nine Mueller matrix elements that affect linearly polarized radiation can be derived if a spatial filter in the form of a pie-slice slit is placed in the focal plane of the detector and azimuthally dependent polarized measurements and azimuthally integrated polarized measurements are combined.
© 1998 Optical Society of America
Original Manuscript: March 5, 1997
Revised Manuscript: September 2, 1997
Published: April 20, 1998
Avishai Ben-David, "Mueller matrices and information derived from linear polarization lidar measurements: theory," Appl. Opt. 37, 2448-2463 (1998)