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The purpose of this paper is to discuss two polarimetric parameters which are widely used in synthetic aperture radar (SAR) polarimetry, namely, target entropy and alpha angle. We propose alternative parameters based on our analysis on how they are connected to covariance matrix similarity invariants and how they can be physically interpreted in optical polarimetry. The proposed alternatives can be computed by a fairly simple algorithm and even by the use of software without complex mathematics abilities. As an example, a NASA/Jet Propulsion Laboratory Airborne SAR L-band image of the San Francisco Bay is used to compare the proposed parameter schemes with the original entropy and alpha. A coherent rationale for these alternative parameters is formulated in order to provide insight to polarimetric parameter interpretation.