Corrections for Instrumental Effects

POLPACK expects your data to be calibrated so that the pixel values are proportional to the analysed intensity. You should therefore correct your data for any known instrumental effects such as non-linearity, variation of sensitivity across the detector, zero point offsets, etc., before proceeding to use POLPACK. The details will obviously depend on your detector, but if you are using a CCD camera, then the CCDPACK package will usually be able to perform these corrections.

If you are using dual-beam data, and target exposures are available at half-wave plate positions of 45.0 degrees and 67.5 degrees (as well as 0 degrees and 22.5 degrees), then POLPACK can make corrections for the following effects when calculating the Stokes vectors:

1. Differences in exposure times between the target exposures
2. A constant difference in sensitivity between the $O$ and $E$ ray channels.

These effects therefore do not need to be calibrated out of the raw data.

One aspect of calibration common to most detectors is flat-fielding. If your flat-fields are obtained in polarized light (such as produced by reflection or scattering, for instance), then the mean signals measured in the $O$ and $E$ ray images of dual-beam data will be different. When such a flat-field is used to calibrate your target exposures, these different mean levels will introduce an apparent difference in sensitivity between the $O$ and $E$ ray channels. If the same flat-field is used for all target exposures, then this difference in sensitivity will be constant and can be removed while calculating the Stokes parameters (provided you have target exposures at half-wave plate positions of 0, 22.5, 45 and 67.5 degrees). Go here for a mathematical description of the flat-fielding process for dual-beam data, and the corrections applied by POLPACK when calculating the Stokes parameters.

Whether you are using dual-beam or single-beam data, do not forget to use the same flat-field to correct all target exposures. This will usually be a master flat-field formed by co-adding several individual flat-field exposures. This reduces the noise in the master flat-field. This is important for two reasons:

1. Any noise in the flat-field gets passed directly into the final results.
2. Any noise in the flat-field appears in each of the flat-fielded intensity images, resulting in a degree of correlation between the noise in these images. This can cause any variance estimates for the final polarization parameters (see next paragraph) to be wrong. This is because the variance calculations assume that there is no correlation between the noise in different images.

Another aspect of instrumental calibration is the estimation of the uncertainty on every pixel value. If you know the noise characteristics of your detector, you may be able to store this information with your data in the form of an NDF VARIANCE component. This is an array holding an estimate of the variance at every pixel in your data. If present, POLPACK will process this information to obtain estimates of the uncertainty in the final polarization parameters. If you use CCDPACK to calibrate your data, then the DEBIAS application can be used to create a VARIANCE component.

If you are using single-beam data, there is an option to estimate the variances associated with the input data while calculating the Stokes vectors. This enables variances to be found for the Stokes vectors even if your input data has no usable variance information. Go here for details.