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Derivation of phase statistics from the Mueller matrix
Author(s) -
Sarabandi K.
Publication year - 1992
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/92rs00195
Subject(s) - probability density function , mueller calculus , standard deviation , polarimetry , random matrix , gaussian , mathematics , matrix (chemical analysis) , statistics , scattering , statistical physics , phase (matter) , covariance matrix , physics , optics , materials science , eigenvalues and eigenvectors , quantum mechanics , composite material
To answer the question of what radar polarimetry has to offer to the remote sensing of random media, statistics of the phase difference of the scattering matrix elements must be studied. Recent polarimetric measurements of rough surfaces have indicated that the statistical parameters of the phase difference (mean, standard deviation, etc.) are very sensitive to some of the physical parameters. In this paper the probability density function of the phase differences is derived from the Mueller matrix, assuming that the elements of the scattering matrix are jointly Gaussian. It is shown that the probability density functions of the copolarized and cross‐polarized phase differences are similar in form, and each can be determined by two parameters (α and ς) completely. The expressions for the probability density functions are verified by comparing the histograms, the mean, and the standard deviations of phase differences derived directly from polarimetric measurements of a variety of rough surfaces to the probability density function, its mean, and standard deviation derived from the Mueller matrices of the same data. The expressions for the probability density functions are of special interest for noncoherent polarimetric radars and noncoherent polarimetric models for random media such as vector radiative transfer.