The Basics of Polarimetric Elements in Visual Studio .NET

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6 The Basics of Polarimetric Elements
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623 Re ection Polarizers
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When light is incident on any dielectric material the intensity of the re ected and transmitted beams are sensitive to polarization If a dielectric plate is set at Brewster s angle relative to some incident light, the degree of polarization of the re ected beam should be unity (see Appendix A) Thus, it can act as a perfect polarizer It is, however, usually inconvenient to use such a re ecting plate as a polarizer because of the angle at which the polarized light beam emerges; the emergent beam also describes a cone as the polarizer is rotated The transmitted light is partially polarized, and by using a succession of plates set at Brewster s angle, the transmitted light becomes progressively more polarized This type of device is referred to as a pile-of-plates polarizer and, although it is not often used in the optical region, the principle still nds application in the infrared In optical texts, there is some confusion on the formulas promoted to describe the polarizance of the device and care should be taken in predicting the behaviour of any pile-of-plates system The problem has been addressed by Tuckerman (1947) By simply extending the number of involved plates to N, each of refractive index n and set at Brewster s angle, the polarizance, p K , of the device is 4N 2n n2 C 1 pK D 4N 2n 1C n2 C 1 1
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(61)
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This equation relates to a system with all the re ected components absorbed before they meet another plate of the system Although reference to the formula describing the polarizance may be found in earlier papers, the standard derivation is generally ascribed to De la Provostage & Desains (1850) In this more realistic treatment, the rays which have been re ected an even number of times are also included in the calculation of the polarizance of the emergent beam, and this may be expressed by pK D NC N 2n n2 1 2 (62)
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It can easily be seen that the polarizance is higher for the rst condition (61) than for the second (62) For a device used in the polarimetric calibrations of measurements of the Zodiacal Light, Weinberg (1964) has drawn attention to the distinct differences of the behaviour of a pile-of-plates polarizer depending on whether multiple beam re ections are taken into account or not The more ef cient design is hard to achieve in practice without the device becoming long in comparison with its aperture Conn & Eaton (1954) have pointed out that in some systems, only a small number of the multiple re ected rays pass through, and p K may be larger than that given by (62)
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The value of p K for the pile-of-plates polarizer is also affected by absorption in the materials This problem was investigated by Stokes (1862) and again by Tuckerman (1947) Interference effects are also likely to be present according to the optical quality of the plates but references as to how this affects the polarizance behaviour are elusive Drawbacks of the pile-of-plates polarizer are that the re ected components are lost, the emerging beam does not lie on the same axis as the entering beam, and surface lms on the plates alter the polarizing characteristics from those predicted by the Fresnel equations as applied to simple plates Growth of surface lms with time consequently changes the polarizance and transmittance of the system
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63 Retarders
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The purpose of a retarder is to alter the phase relation between orthogonally resolved components of a beam of light Such a change is generally necessary when light is being analysed to determine its complete state of polarization Devices that are able to produce a phase change are known as retarders If the effect of the device is simply that of retardation, then it is known as a pure retarder However, in some cases, the very mechanism which is utilized to bring about differential retardation also introduces a small polarizance which can affect the quest of high accuracy polarimetry These devices might be classed as impure retarders Although retarders of any desired phase delay can be constructed, the most common types introduce phase delays of either /2 or , and are called quarter-wave and half-wave retarders, respectively The differential retardation is produced between components resolved along two particular orthogonal directions xed in the device The directions with respect to which retardation is produced are referred to as the fast and slow axes, and the amount of retardation produced with respect to the axes is known as the retardance Quarter-wave retarders are often used to produce circularly polarized light from linearly polarized light and vice versa Half-wave retarders are often used to produce linearly polarized light from already linearly polarized light, but with a different direction of vibration, i e the direction of vibration is rotated The components of the incident linearly polarized light, along and perpendicular to the reference axis of the half-wave retarder, emerge with one of them changed in phase by with respect to the other They, therefore, recombine to give linear polarization again, but with the direction of vibration being inclined to that of the incident beam by twice the angle which the latter makes with reference axis of the retarder This is readily con rmed by multiplying out the appropriate Mueller matrices representing the situation Relative phase changes can be brought about by passing a beam through a birefringent material, or by making it suffer a re ection which produces phase change effects Retarders have been designed depending on both these principles, and it is convenient to discuss them accordingly This is done in the following subsections
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