Axis Determination of Wave Plates in .NET

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634 Axis Determination of Wave Plates
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In the application of wave plates in any optical system, it is important to be able to identify the orientation of the fast/slow axes of the device For the conversion of linear to circular polarization, the axes of the applied quarter-wave plate need
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6 The Basics of Polarimetric Elements
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to be known in order to establish which handedness of circular polarization will be generated Conversely, if the handedness of some circular polarization is being investigated, the result will be ambiguous unless it is known whether a phase delay of C /2 or /2 has been applied relative to the instrumental polarimetric axes Determining which is the fast or slow axis of a wave plate can sometimes cause problems It is useful to have devices available that have already been calibrated in terms of which are the fast and slow axes It is often convenient to have a device whose fast and slow axes are known so that it can be overlaid on any other retarder to see whether the phase delay of the combination increases or decreases In this way the fast and slow axes of the second retarder may be distinguished In the eld of optical crystallography, such a calibrating device is referred to as an accessory plate A simple means of producing such a device is to use Scotch tape or Selotape which has been adhered to a glass slide In the manufacturing process of the tape, the substrate is stretched with the introduction of stress birefringence According to Wood (1964), the long direction of the tape corresponds to the slow ray Experience shows that, in some cases, the slow axis may not be exactly aligned to the edge of the tape as the slicing of rolls from the bulk material may be misaligned to the original stretch direction Although mica is now not generally used in instrumentation, it can be applied as an accessory plate Any problem in deciding which are the fast and slow axes of a mica plate can be resolved quite easily as follows Set up crossed polarizers light from the exit face of the system will be extinguished Insert a mica plate between them, preferably a square one with its axes parallel to its edges, and rotate it, keeping it normal to the beam, so that the maximum intensity is achieved Now rst tilt it about one of the axes parallel to an edge and then about the orthogonal edge; the edge corresponding to the fast axis is revealed as that producing a blackening at a tilt of about 35
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64 Metallic Re ection
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Many of the pieces employed in optical instrumentation rely on re ections by metallic surfaces Most mirrors in telescope systems, for example, are coated with vacuum deposited aluminium Spectrometers attached to telescopes invariably employ metallic coated mirrors Both the optical and the astronomical literature reveal ambiguities and inconsistences in relation to the de nition of phase changes associated with metallic re ections Many papers suggest that there is a phase difference of between the resolved components for re ections at normal incidence This, of course, cannot be the case since, at normal incidence, the components are indistinguishable For this geometry, the phase difference must be zero The effect of re ection, however, affects the descriptive coordinate frame and imposes a handedness change such that the U and V parameters are subject to sign changes, making the optical interaction
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equivalent to there being a relative phase shift of between the components A more complete discussion of this is provided in Appendix A Following the conventions there, the matrix describing re ection from a metal surface may be written as 2 3 R C Rk R Rk 0 0 7 1 6 R Rk R C Rk 6 7 (68) p 0 p 0 0 0 2 R Rk cos 2p R Rk sin 5 24 p 0 0 2 R Rk sin 2 R Rk cos At normal incidence, with D 0, the matrix of (68) reduces to 3 2 1 0 0 0 60 1 0 07 7, R6 40 0 1 05 0 0 0 1
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where R is the re ection coef cient Thus, for any incoming radiation, the signs of U and V are ipped, the latter indicating that there is a change in handedness of any circularly polarized light This obviously occurs if observations are made at primary focus of a single mirror in a telescope system, so requiring correction when the records are expressed in a standard celestial coordinate frame For telescopes involving two on-axis mirrors, such as a regular Cassegrain system, there is a second ip of the U and V parameters, returning them to their original signs Typical variations of R , Rk and D k are illustrated in Figure A6 of Appendix A in respect of the optical coef cients determined by Capitani, Cavallini, Ceppatelli et al (1989) for the mirrors of a coelostat For 6500 they derived values for the real and imaginary parts of the refractive index of n D 1036 and D 589 for the metallic coating, assuming that the behaviour of the re ection with angle of incidence followed the classical theory If the fore optics contain mirrors set at an angle, the matrix of (68) may be applied with appropriate values for the re ection coef cients and phase change according to the optical constants of the re ecting material For example, for a re ection at 45 , as in a Newtonian or Nasmyth con guration, the derived polarization parameters show that R D 093, Rk D 087 and D 6 5, according to the values of n and above If a compensator is employed to correct this, a phase of 6 5 adjustment might be applied, with the recorded U, V corrected for sign to allow for the re ection of the reference axes Alternatively, the applied phase compensation might be set for (180 6 5), without sign corrections being required for the recorded U, V values
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