The Basics of Polarimetric Elements in .NET framework

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6 The Basics of Polarimetric Elements
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Two of the disadvantages of the simple Fresnel rhomb are that the light does not emerge along the same axis as the incident beam, and the retardance produced varies with the angle of incidence These problems are overcome by a system of two parellopipeds in series as suggested by Kizel, Krasilov & Shamraev (1964) They also describe a system using three TIRs in a ve-sided prism For a quarter-wave retardance, the angle of incidence is high in both devices and consequently, for the entrance aperture to be a reasonable size, the components must be long They are thus prone to the effects of stress birefringence in the direction of propagation, and the performance of the retarders is consequently impaired In its application, it must be remembered that, despite it sometimes being referred to as a quarter-wave device, the Fresnel rhomb has a phase delay of 3/4-wave This is con rmed by the statement of Wood (1947) who writes:
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In the case of TIR, the phase of the component of vibration parallel to the plane of incidence is retarded 135 , or a total retardation of 270 for two re ections This is virtually the equivalent of an acceleration of 90 and we can so consider it in all experimental work
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Knowledge of the true value of its retardance is important when it comes to the interpretation of the handedness of any investigated circular polarization An error in interpreting the sense of handedness will ensue if the device is treated as introducing a quarter-wave retardation, rather than three-quarters of a wave, in its circular-to-linear conversion It is the sign of U from conversion of V that is taken to give the handedness of the original V Application of the appropriate Mueller matrix on a Stokes column vector shows that a phase delay of /2 converts positive V to positive U, whereas a retardation of 3 /2 converts positive V to negative U An example of the use of Fresnel rhombs on the telescope is found in the instrument described by Miller, Robinson & Schmidt (1980) who used two of them to perform double-beam circular spectropolarimetry
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633 Tunable Wave Plates
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Birefringence can be generated in some crystals by the application of electric elds The Pockels effect, whereby the birefringence is in the direction of the eld, has been utilized to produce retarders A device is commercially available in the form of a cell with electrodes on its ends made of a mesh of transparent material to provide the eld The crystal normally used is potassium di-hydrogen phosphate, or KDP The retardance of the Pockels cell can be tuned by adjusting the voltage applied to the electrodes This voltage can be made to follow any desired waveform and the relationship between voltage and phase delay is linear Typical frequency responses can be as high as 100 kHz Because of the sensitivity of inef cient operation of the device to off-axis rays, the cells are best operated in a collimated beam Problems with the device when used to provide phase delays which are maintained for long periods have been found in some applications (see 8)
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Stellar P larimetry
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An important invention by Kemp (1969), particularly suited to the investigation of high accuracy circular polarimetry, is the photoelastic modulator (PEM) It comprises a block of glass that is made to resonate in its natural vibrational mode The oscillations of the bulk material induce a time-varying stress birefringence By controlling the amplitude of the applied stimulus, the birefringence can be controlled to produce a variable phase delay of /4, adjustable to any wavelength in the optical spectrum Linear polarization may be investigated by the prior insertion of a quarter-wave plate The resonant frequency is 50 kHz and, by applying synchronous gating techniques, the polarimetric signal produced at this very high frequency modulation can be readily recorded without it being subject to intensity scintillation noise produced by the Earth s atmosphere Because the birefringence is small (only of the order of 1 part in 40 000) the glass plate is thick to achieve the value of phase delay, but there is an advantage in that the device s spurious polarizance by re ection at the entry face is small Recently, tunable wave plates have become available involving nematic liquid crystals They operate with low driving voltages in the range of 0 to 15 V Within a transparent cell, the anisotropic liquid crystals form uniaxial birefringent layers The properties of nematic materials are such that the molecules tend to align with their long axes parallel and pointing in the same direction Unlike a solid crystal, they do not settle in regular planes and the molecule centres are distributed at random Electrical contacts are bonded to the windows of the cell which have a layer to align the molecules when no voltage is applied On applying an AC voltage, the molecules tend to tip with the long axis becoming parallel to the oscillating electric eld, this reducing the birefringence of the cell The degree of birefringence is controllable by the size of the applied voltage amplitude A minor disadvantage is the small residual retardance when the voltage is at its maximum as a result of some molecules being effectively pinned to the internal alignment layer of the cell window, but its effect can be removed by the addition of a xed compensation plate with its fast axis parallel to the slow axis of the cell The range of phase shift of the basic cell is just greater than /2 Typical response times are about 5 ms to switch from one-half to zero waves (low-to-high voltage change) and about 20 ms to switch from zero to one-half wave (high-to-low voltage change) Liquid crystal wave plates have potential in that a series of them in combination could provide a modulator, with an appropriate switching sequence, to record the Stokes parameters in turn without the need of mechanical rotations of any optical devices within the optical train A further improvement might be considered whereby the axes of the wave plates are orientated to follow a Pancharatnam con guration with a provision for achromatic switching of the phase delay
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