Estimating Polarization Purity with Noise

• Published in: IEEE transactions on geoscience and remote sensing 2024-01, Vol.62, p.1-1
• Main Authors: Kostinski, Alexander, Kestner, Daniel, Vivekanandan, Jothiram
• Format: Article
• Language: English
• Subjects: Atmospheric research; Calibration; Correlation coefficient; Correlation coefficients; Cross correlation; Electric fields; Ellipticity; imbalance; Meteorological radar; Monte Carlo simulation; Noise; Orthogonality; Parameter estimation; Poincare spheres; Polarimetry; Polarization; Probability density functions; Probability theory; Purity; Radar; Radar polarimetry; Receivers; Statistical analysis; Thermal noise; Thermal simulation; Vectors; Voltage measurement
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2024.3380531

We formulate a problem of estimating and monitoring mismatch (unwanted departure from orthogonality) of two ostensibly orthogonal polarization channels in a fully polarimetric general device such as a polarimetric weather radar. A statistical approach is proposed by using thermal noise or, more generally, a "polarimetric noise" class of sources. The suitable noise class of distributions is shown to be rooted in the complex multivariate Gaussian probability density function (pdf), the latter possessing a uniform pdf on the Poincare sphere, with a probability measure given by a fractional surface area. To that end, we develop a parameter to estimate polarization purity. By relating an inner (dot) product of noisy electric fields to their cross-correlation coefficient, we arrive at a simple relation between the ellipticity δ ϵ and tilt δ τ mismatches and the measured complex voltage cross-correlation coefficient ρ: ρ ≈ ∓ cos(2ϵ)δ τ ± i δ ϵ . Our results are confirmed by Monte Carlo simulations. Thermal noise microwave data collected by the S-band radar of the National Center for Atmospheric Research (NCAR) during solar calibration scans is used to set bounds on δ ϵ and δ τ , thereby characterizing polarization purity.