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and the Stokes parameters Q and U:The statistical uncertainties are obtained by straightforward propagation of errors:
The Stokes parameters can then be combined to yield the polarized intensity, Ip:
and the degree, P, and position angle of polarization, , using:
Figure 5.5: Polarimetry Decision Chart
Polarimetric Sensitivity
As with the imaging filters, sensitivity information for the two sets of polarizers may be obtained from the Exposure Time Calculator. It gives the same information as was described in Chapter 4: namely a sensitivity curve, plotted as flux against time for a constant S/N ratio and an exposure exclusion curve for both point and extended sources. To use these, look up the integration time required for your source flux on the sensitivity curve for the signal to noise you want (see Chapter 12 if you need to convert the units). Then go to the associated exclusion curve and check that you are not in the shaded areas. If you are, adjust your integration time appropriately until you are in the clear area. If you are to the left of the vertical dashed line then you must use bright object mode. Work out how many integrations you need to get your desired S/N. To get the total exposure time required for a polarimetric observation multiply your final answer by 3 to account for the fact that you need to use 3 polarizers to get a measurement. Note that the transmission curves are for a 100% polarized source while all the sensitivity information here is calculated for a single polarizer image, assuming an unpolarized source.
The polarizers have yet to be extensively tested or calibrated -- this will be accomplished as part of the Cycle 7 calibration program. Current estimates are than single observations will have ~1% uncertainties implying 3-5% accuracy for polarization measurements.
Camera 1, Polarizers
The polarizers consist of 3 identical elements at relative angles of 0, 120, and 240 degrees.
Central (microns) |
Mean (microns) |
Peak (microns) |
FWHM (microns) |
Range (microns) |
Principal Tr percent |
Pixel fraction |
---|---|---|---|---|---|---|
1.0450
|
1.0384
|
1.0245
|
0.4750
|
0.8-1.3
|
77.60
|
0.048
|
Figure 5.6: Throughput of Short Wavelength Polarizers
Camera 2, Polarizers
The polarizers consist of 3 identical elements at relative angles of 0, 120, and 240 degrees. Thermal background is important.
Central (microns) |
Mean (microns) |
Peak (microns) |
FWHM (microns) |
Range (microns) |
Principal Tr |
Pixel Fraction |
---|---|---|---|---|---|---|
1.9943
|
1.9946
|
1.9100
|
0.2025
|
1.9-2.1
|
96.67
|
0.33
|
Figure 5.7: Throughput of Long Wavelength Polarizers