Spectropolarimetry in VS .NET

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88 Spectropolarimetry
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In many polarimeters, spectral measurements can be made by the insertion of lters in the system The best location to do this is after the modulator system so that the lter does not introduce any spurious polarization into the measurements The spectral bandpass is dictated by the choice of lters and, in some instruments, high resolution has been achieved by narrow-band interference lters By tilt-tuning these devices (see Clarke, McLean & Wyllie 1975), it was possible to obtain p ( ) measurements across line pro les Instruments involving this technique have had particular success at H and H (see, for example, Clarke & McLean, 1975, 1976)
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8 Polarimetric Principles and Instruments
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With the advent of 2D detectors such as CCDs, measurements can be made simultaneously at multi-wavelength positions, and single-point sequential scanning has now been abandoned It is now possible to conduct spectropolarimetry at high resolution and over a broad spectral range By using a Savart plate prior to the entrance slit of a spectrometer, two spectra corresponding to the orthogonal beams can be produced which may be recorded side by side Insertion of an achromatic rotatable half-wave plate prior to the polarizing beam splitter allows the NSPs to be determined across the recorded spectra With the accuracies that such systems provide, problems of the wave plate polarizance and fringing have become apparent in the raw data The matrix written as [Wave Plate] in (815) describes the effect of the wave plate that, for a pure device, simply includes terms describing the effects of the phase delay In reality, as discussed in 6, it also needs to include the effects of a polarizance Its form is therefore represented by (65) or (66) Using the latter equation, and following multiplying out the matrices in (815), the signal for measurement, S ( ) may be organized to be written as 2S ( ) D k1 (I C Q cos 4 C U sin 4 ) k3 V sin sin 2 C k2 (I cos 2 C Q cos 2 C U sin 2 ) U sin 4 C (k1 C k3 cos ) Q sin2 2 2
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(841)
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In exploring the behaviour of (841), it is expected that k1 and k3 are both close to unity, with k2 0 If linear polarization is being measured, it can be seen that, in addition to the expected modulation of the Stokes parameters, the polarizance introduces a spurious signal according to 2 , however This problem is exacerbated by the effects of fringing caused by multiple beam interference within the wave plate The modulation ef ciency, dependent on the value of cos , is also subject to fringing In considering these issues, Clarke (2005) has provided observing strategies that help to alleviate the various troublesome effects For linear polarization measurements, the polarizance of the wave plate and its fringe structure can be calibrated out by making measurements at D /2 and 3 /4, in addition to D 0 and /4, for the determination of q (see (829)) Similarly, measurements made at D 5 /4 and 7 /4, in addition to those at D /8 and 3 /8, allow the polarizance calibration with respect to the u parameter (see (830)) As a result of linear-to-circular cross-talk with fringe structures, the spectral measurement of circular polarization is particularly prone to misinterpretations If fringing remains evident in the raw data, the reduction problem can only be dealt with properly by determining the elements of the matrix of the wave plate for each spectral point and performing inversion procedures rather than simple off-set subtractions Stability of the fringe structures is also an issue and it is important to operate with a modulator that is temperature stabilized
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