The Basics of Polarimetric Elements in .NET framework

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6 The Basics of Polarimetric Elements
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Centre (zero retardation) A O O A
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Fig 69 (a) shows the principle of the Babinet compensator involving two birefringent wedges with the optical axes set orthogonally (b) is for the Soleil Babinet compensator with two birefringent wedges set with their axes aligned but with their overall multi-order
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phase delay reduced by a rectangular prism of the same material with its optic axis set orthogonally Constant retardance covers the area between the wedge apexes and is marked by the dotted lines
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tertiary mirror set at an angle to the incident beam, the re ected radiation is made elliptically polarized by the induced phase delay This may be reverted by applying a phase delay of the opposite sense A device producing a controlled variable phase delay might comprise two opposed quartz wedges of equal angle, one wedge being movable along its length by a micrometer screw The wedges need to be cut so that their fast directions are along, and perpendicular to, the direction of motion Such a simple arrangement is the Babinet compensator as shown in Figure 69 The phase delay for this basic system varies across its aperture A more useful design is the Soleil Babinet compensator in which the wedges are cut and placed together with their axes parallel, effecting a multi-order wave plate By introducing a third element in the form of a rectangular prism of thickness matching that of the wedge combination, but with its axis set orthogonally, a zero-order wave plate is produced with an adjustable retardation from 0 to 2 which is constant over the aperture de ned by the interval between the wedge apexes
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632 Re ection Retarders
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It is well known that there are phase delays associated with TIR and that these are unequal for the orthogonal vibrations relative to the plane of incidence According to the geometry of the angles involved and the refractive index of the more dense material in which the TIR takes place, devices can be constructed for the production of some desired differential phase delay The most common device of this type is the Fresnel rhomb If a consistent sign convention is used to deal with the effects of TIR (see Clarke & Grainger, 1971, and Appendix A), it can be shown that the phase difference between components vibrating perpendicular to, and parallel to, the plane of incidence is greater than /2 throughout the range of angles for which TIR takes place within all dielectrics of refractive index less than 2414 If it is desired to produce a quarter-wave retarder, based on the difference in phase of the orthogonal vibrations de ned above, this is not possible using only one TIR in normal glasses Two such re ections, however, providing they are arranged so that the phase delays they
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Stellar P larimetry
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produce are cumulative, will produce a delay ranging between 2 and tan(3 /16) Thus glasses with refractive indices equal to or greater than 1496 can produce a retardation of the parallel component with respect to the perpendicular component of 3 /2 or more, i e an effective advance of the parallel component of /2 or less The Fresnel rhomb provides a phase delay of 3 /2 using two identical TIRs It consists of a parallelopiped of glass, the light passing normally through the entrance and exit faces If the glass has a refractive index of exactly 1496, then the 3 /2 phase difference occurs for only one angle of incidence (see Appendix A), namely s
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If the refractive index is greater than 1496, then two angles of incidence give a phase difference of 3 /2 Fresnel pointed out that the larger of these angles is preferred, as the effects of dispersion are smaller It is also preferred because the phase change of 3 /2 is less seriously affected by any small departures in the angle of incidence For the same reason, the less the refractive index exceeds 1496 the better Fresnel s rst rhomb was made of glass of refractive index 151, which required angles of incidence of 54 370 If the whole entrance face is illuminated and all this light is to emerge, the ratio of a long to short side of the parallelogram must be 2 sin i tan i , which, for i D 54 370 , is 23 Thus the original device is anything but a rhombus (see Figure 610) In fact, it is impossible for a rhombus to satisfy the condition that all the light entering normally should emerge and preserve the phase delay of 3 /2 One of the advantages of the Fresnel rhomb is that the phase delay is nearly achromatic Stress birefringence and surface lms may, however, reduce its performance It has been shown by King (1966) that the desired retardance can be restored and made more achromatic by coating the re ecting surfaces of the rhomb with magnesium uoride
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Fig 610 A basic Fresnel rhomb three quarter-wave retarder with the angle of incidence at TIR of i D 52 1 Note that the long side to short side ratio is 23 so that parallel rays entering the device are re ected with all of them passing through the exit face
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