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This paper introduces the quadrant polarization parameters $Q_{000}$,$Q_{090}$, $Q_{180}$, $Q_{270}$ for Stokes $Q$ and $U_{045}$, $U_{135}$,$U_{225}$, $U_{315}$ for Stokes $U$ for the characterization of the azimuthaldependence of the scattering polarization of spatially resolved circumstellardisks illuminated by the central star. These parameters are based on thenatural Stokes $Q$ and $U$ quadrant pattern produced by circumstellarscattering. They provide a simple test of the deviations of the disk geometryfrom axisymmetry and can be used to constrain the scattering phase function foroptically thin disks without detailed model fitting of disk images. Theparameters are easy to derive from observations and model calculations and aretherefore well suited to systematic studies of the dust scattering incircumstellar disks.  It is shown for models of optically thin and rotationally symmetric debrisdisks that the quadrant parameters normalized to the integrated azimuthalpolarization or quadrant ratios like $Q_{000}/Q_{180}$ depend only on the diskinclination $i$ and the polarized scattering phase function of the dust, andthey do not depend on the radial distribution of the scattering emissivity.Because $i$ is usually well known for resolved disk, we can derive the shape ofthe phase function for the sampled scattering angle range. This finding alsoapplies to models with vertical extensions as observed for debris disks.  Diagnostic diagrams are calculated for normalized quadrant parameters andquadrant ratios for the determination of the asymmetry parameter $g$ of thepolarized Henyey-Greenstein scattering phase function. We apply these diagramsto measurements of HR 4796A, and find that a phase function with only oneparameter does not reproduce the data well, but find a better solution with athree-parameter phase function.

Quadrant polarization parameters for the scattered light of circumstellar disks. Analysis of debris disk models and observations of HR 4796A