How to use:
This tool generates simple formulae which may be used to compute Stokes I, Q, and U. These formulae may be applied to either observed aperture counts, or to entire images. One inputs the aperture, polarizer setting, and PA_V3 for each of three observed images. Optionally, aperture counts for the target in each image may be input, as well.
Clicking on "calculate" will then start the computations.
The results are a set of equations giving Stokes I, Q, and U as a function of the observed images. If aperture counts are input, the program also returns Stokes I, Q, and U (in units of counts), the fractional polarization, and the polarization position angle (E-vector).
Accuracy:
Accuracy is about 1-2% of I in the apertures PC1, WF2, WF3, and WF4. For reasons which are currently unclear, the accurracy in apertures POLQN33 and POLQP15W is poorer (2% to 5% of I).
How the tool works:
This tool uses Mueller matrices to generate equations relating the (unknown) Stokes vector incident on HST to the observed counts. Given parameters for three observed images, it uses these matrices to form a system of three equations in three unknowns (Stokes I, Q, and U). It then solves the equations for I, Q, and U.
Separate matrices are used for the rotation of HST on the sky, the 47 degree pick-off mirror in WFPC2, the rotations of the polarizer quads and filter wheel, and for the polarizer itself. These matrices are then multiplied together to produce a single matrix for each observed image.
The Mueller matrix for the pick-off mirror include the effects of diattenuation and linear retardance in the mirror. The mirror is modeled as bare aluminum; the 250 Angstrom MgF2 coating is thought to have little effect (<<1%). Further study of this issue is needed, and the mirror model will be improved if needed.
The polarizer matrix includes leakage terms for the perpendicular direction.
-J. Biretta, STScI