Polarimetric Principles and Instruments in Visual Studio .NET

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8 Polarimetric Principles and Instruments
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Fig 83 (a) shows the distribution of 3000 q, u pixel measurements centred on the origin of an NSP diagram for the unpolarized standard star, Bo , the data obtained from four CCD frames of the image of the telescope aperture (b) displays the histogram of (p / ) values for the adjacent data show-
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ing that it closely follows a Rice distribution corresponding to p o D 0 The slight displacement of the histogram pattern indicates the presence of a very small polarization which is generated by the outer annuli of the telescope mirror (The material is taken from Clarke & Naghizadeh-Khouei, 1997)
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The ultimate way of using CCDs to achieve the highest polarimetric accuracy for a single star is to consider a design whereby the source is isolated in the telescope focal plane, and then the radiation passed through the modulator and an imaging system so that the telescope aperture is focussed on the chip This has the advantage of the illuminated patch being xed, even if there is image movement in the telescope focal plane A further advantage of the system is that any patchy polarizing effects of the telescope mirrors contributing to the instrumental polarization can be explored by observing standard unpolarized stars and, in the subsequent data reductions, applying appropriate corrections to each pixel within the aperture image A prototype aperture imaging polarimeter of this kind was tested by Clarke & Naghizadeh-Khouei (1997) By using a Savart plate, the instrument was designed to produce two images of the telescope aperture on the same CCD chip Switching the orthogonally resolved polarizations was achieved by a rotatable half-wave plate For each stellar polarimetric measurement some 3000 pixels were used, and nal accuracies in NSPs of 00001 were readily achieved An example of measurements of a standard unpolarized star is shown in Figure 83 When the data are grouped together in zones across the image of the aperture, mean values of the measurements clearly indicated that the telescope mirror introduced small amounts of polarization with the outer annuli being the most affected in this way Also in Figure 83, a histogram of the p / values is depicted relative to the Rice distribution for p o D 0; the small disparity of the data relative to the theoretical distribution curve relates to a mirror-induced polarization Another novel approach to spatial imaging for recording stellar polarizations is by a method pioneered by Treanor (1968) Using a very simple arrangement, he
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Stellar P larimetry
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demonstrated that polarimetric information might be encoded as a spatial record for registration by a two-dimensional detector such as a photographic plate In his instrument, a polarizer was rotated together with a glass wedge prior to the telescope focus Stellar images were then recorded in the form of annuli If the light from a star is polarized, the corresponding annulus carries an intensity modulation with a variation of the form given by (83), i e S( ) D I f1 C p cos 2( )g , (840)
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where de nes the angular position around the annulus The principle was applied to star elds with many stars being recorded simultaneously on a single photographic plate The technique appeared to have been abandoned because of the poor quantum ef ciency of emulsion photography, and other problems associated with calibrations and data reduction procedures With the advent of CCD detectors, Treanor s idea has been reconsidered by Clarke & Neumayer (2002) and a system has been developed by Steele, Bates, Carter, et al (2006) for use on an automated telescope for immediate optical follow up of gamma-ray burster events As well as undertaking polarimetry of stellar elds, the technique can be applied to individual stars Using a large number of pixels near to full well capacity, a very large number of photons can be accumulated to achieve high accuracy for the measured value The modulator may be simply a rotating tilted disc of high quality sheet polarizer A rotating Rochon prism, with its weak spectral dispersion, might also be used to provide high accuracy, low spectral resolution spectropolarimetry, the annuli having a radial spread according to wavelength Oliva (1997) has designed a specially constructed wedged double Wollaston prism For the simple case of recording the polarization of star elds, by using the appropriate optics, it can be placed at the image of the telescope aperture By re-imaging the eld on a CCD chip, four images are produced simultaneously corresponding to the polarization directions 0 , 90 , 45 and 135 , from which both q and u can be determined Thus all the linear polarization characteristics can be measured from a single CCD frame By placing it at a pupil image within a spectrometer, single frame spectropolarimetry may also be undertaken
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