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# Polarimetry: special conditions

Michelle's imaging polarimetry capabilities are described in detail in the Michelle-specific pages; here we outline the special S/N requirements for polarimetric measurements and the weather conditions necessary for these to be obtained.

Polarisation accuracy and signal-to-noise ratio

When carrying out polarimetric observations, the signal-to-noise ratio (S/N) must be high enough to get a precise measurement of the polarization. The S/N necessary in order to obtain a certain level of polarisation accuracy is given by:

S/N = √2 / ΔP

where ΔP is the required accuracy. For example, an observer attempting to measure the polarisation of a source suspected to be polarised at the 1% level would probably want measurements accurate to at least 0.3%, which would require S/N = 1.4 / 0.003 = 471. If one has an estimate of the percent polarization a target is likely to have, this sets a minimum S/N to reliably detect this level of polarization. If one wishes to detect 2% polarization in a target, for example, it is not sufficient to request time to obtain S/N of 50 since from the formula above that would given uncertainties in the measured p values of 1.2%, meaning that a 2% polarization would only be detected at a level of 1.6 sigma. The uncertainties can be reduced by binning the pixels in the images, which would be expected to improve the S/N (and thus the accuracy in the measured polarization values) by a factor of the square-root of the number of pixels being binned.

When preparing a polarimetry proposal PIs need to be certain that a sufficiently high S/N can be obtained in the time requested, and the PI needs to distinguish between the S/N per pixel and the S/N which is obtained within a given aperture. It is the latter value which is calculated by the Michelle ITC *kind of broken*.

Required weather conditions

As polarimetry is essentially very accurate differential photometry (between images with the waveplate at various angles), polarimetric observations require very stable observing conditions, otherwise the level of polarization will be overestimated. This means that the seeing and transparency of the atmosphere need to be changing only slowly (and overall not by too large an amount) during the observation. There is no sense in requesting polarimetry observations to be taken in poor conditions. These guidelines about which filters are more sensitive to water vapour changes should be kept in mind when requesting polarimetry observations, since changes in the water vapour level will affect the transparency of the atmosphere for those filters that are in the less favourable parts of the N- or Q-band windows.

Last update 2006 March 10; Rachel Mason