Simultaneous NSP Measurements in .NET framework

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86 Simultaneous NSP Measurements
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By rotating a quarter-wave plate prior to a xed polarizer, the signal for measurement is represented by Q 1 1 IC I 0 ( ) D C (Q cos 4 C U sin 4 ) V sin 2 (839) 2 2 2 Thus, the Q and U parameters are modulated four times per cycle while the V parameter is modulated twice per cycle; the mean level comprises the value of I plus half the Q intensity In principle, by recording this waveform, all of the NSPs may be determined, although there appears to be no reference to the use of this simple method A successful technique to measure both linear and circular polarization simultaneously by the continuous rotation of a quarter- and half-wave plate in opposite senses was suggested by Serkowski (1974b); it has been developed and implemented at the University of Cape Town (see Cropper, 1985) With this design, any circular component is modulated at six times the rotation rate, and the linear is split equally between four and eight times the rotation rate In the Cape Town instrument, the mechanical rotation was 10 Hz with the signal for each rotation split into 100 memory sectors At the end of the integration scheme, the data are tted to the 4th, 6th and 8th harmonics of the rotational frequency by least squares, and the Stokes parameters are calculated from the amplitudes and phases of the recorded harmonics
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Stellar P larimetry
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87 Spatial Recording of the Polarimetric Modulation
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In 1, it was suggested that stellar polarimetry began to ourish through the advent of the photomultiplier and it is fair to say that most of the accumulated data of interstellar and circumstellar polarization have been obtained using such detectors The advent of 2D detectors has now allowed observational research into polarimetry of individual stars, star elds, extended objects and stars at high spectral resolution, in a more ef cient way Using these detectors has also offered the challenge that measurements of improved accuracy might be pursued for broadband measurements Equation (52) shows that the ultimate accuracy of any measurement of an NSP, such as q, depends simply on the number of photons, n o , registered during the p integration with the uncertainty (1 ), q, given by 1/ n o Unfortunately, the photomultiplier carries a dead-time limitation when photon counting techniques are applied If the photon arrival rate is too high, counts are lost as a result of pulse overlap and, because of non-linearities, corrections for this can only be applied successfully when count rates are only just above the critical value Discussion on this problem is provided in Clarke & Naghizadeh-Khouei (1994) Generally, photon detection rates should not be allowed to be much greater than 105 s 1 At such a rate, an uncertainty of q 00001, requiring a photon count of 108 , can only be achieved by an integration 1000 s For large aperture telescopes and for the measurement of brighter stars, the potential photoelectron rate is embarrassingly high for photon counting techniques In some observational studies, the dead-time problem has been avoided by using neutral density lters to reduce the detectable ux, and then extending the experimental time to accumulate the necessary photon count a somewhat defeatist solution One approach for gleaning the maximum information from the collected photons and improving polarimetric detection limits is to use a solid-state detector such as a PIN diode The output requires digitization of the analogue signal by a voltage-to-frequency converter with the appropriate linearity and dynamic range (see Hough, Lucas, Bailey, et al, 2005, Hough, Lucas, Bailey, et al, 2006) An alternative is to consider the application of CCDs In accumulating the necessary large photoelectron counts, it is important that the pixel records of the CCD are well below saturation ( 5 105 electrons) to prevent non-linear effects, thus limiting the accuracy per pixel to q or u 001 For stellar images, atmospheric seeing spreads out the ux over several tens of pixels allowing more photoelectrons to be recorded in an image in any one frame Photometric experience shows that differential stellar brightness values can be achieved fairly readily to an accuracy 0m 001 By recording orthogonally resolved images simultaneously, the immediate potential accuracy of q or u is 00005 per frame For brighter sources, to prevent saturation, the images may be defocussed to spread the ux over a larger number of pixels, with the potential of further increasing polarimetric accuracy
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