In this section, we calculate the accuracy of polarization measurement due to photon noise for two typical types of observations. It is assumed that the observations are made in the V-band ( photons ) using a telescope of effective area , the brightness of the sky is 20 mag per sq arcsec, and that the software aperture used for photometry is about 30 sq arcsec. The combined effect of the atmosphere, the telescope, the optics and quantum efficiency of the detector etc., is taken to result in an effective transmission of .
A classical example of polarimetric observations involves study of dark
molecular clouds with the light of stars shining behind their periphery
(e.g. Elvius 1970;
Joshi et al. 1985;
Kane et al. 1995). Typically the
polarization of these sources is in the range . Assuming stars
of apparent visual magnitude mv = 15, we see that the total number
of photo-electrons collected, due to the star (N) and the background
(NB), within the software aperture, for an exposure of 15 minutes are
and respectively. Therefore, the corresponding error in
polarization measurement is given by
If the observations are made with a filter which covers both the V and R bands (), there will be an improvement in the signal-to-noise ratio by a factor of , giving .
Study of extended objects like reflection nebulae, is another field in
which polarimetric observations are useful. Polarization in the light
scattered from these clouds can range from a few percent to as much 30%.
Assuming that the observation involves a reflection nebula of the same
surface brightness as the background sky, the integrated photoelectron count
from each, for an exposure of 15 minutes, will be and hence
for a solid angle defined by the software aperture. The wideband observations, in this case will give an error of about 0.34%.
Figure 3: The errors due to photon noise alone, as calculated in Sect. 4, for wideband measurements of fractional polarization p are shown as a function of the brightness of the source. The solid curve refers to the case of stars while the dashed curve is for an extended object, for which the x-axis represents the surface brightness of the source in magnitudes per sq arcsecs. The background is assumed to be magnitude per sq arcsec and a software aperture of 30 sq arcsec has been used during data reduction. The crosses represent the errors in actual polarimetric measurements made with instrument on a field at the periphery of the dark cloud B133
In Fig. 3 (click here) the solid and dashed curves show the estimated error in the measurement of polarization, due to photon statistics alone, for the two cases discussed above, namely stellar sources and reflection nebulae respectively. The crosses indicate how well actual measurements conform to the errors predicted by photon noise alone.