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On the use of polarization modulation in combined interferometry and polarimetry

S E Segre1998年Plasma Physics and Controlled FusionIF 2.2出版社

In this paper, in both the main text and the appendix, the expression for the quantity g is incorrect and should read g = sin2δsin4x2. Furthermore, in figures 1 and 2, all the plots of the additional phase as a function of ψ0 for various values of tan x0 are correct except for the two curves corresponding to the limiting values x0 = 0 and . These two curves are incorrect, the error being due to the ambiguity of π in the arctan function appearing in the expression for . In order to resolve this ambiguity, and so obtain the correct curves, consider the following useful expressions. If we put S0=2 sin x0 sin ψ0 and C0 = 2 cos x0 cos ψ 0, then from equations (4), (16) and (18) we have , , cos ψp = C/(S2 + C2)1/2 and sin ψ p= C/(S2 + C2)1/2, where S and C are given by equation (17) or by equations (23) and (24). Then using trigonometry, we have and with simple algebra we have which is equivalent to equation (25). 0C1  Figure C1. Corrected curves for . The ambiguity of π in can then be resolved by examining the signs of and , i.e. the signs of (C0C + S0S) and (C0S - S0C) or equivalently the signs of the denominator and the numerator in the expression given above for . Using this procedure, one finds for the limiting values x0 = 0 and for the example in the original paper (having and tan δ = 1) the correct curves for reported here in figure C1, where each dashed curve is equivalent to the corresponding full curve since they differ by 2π, starting from the discontinuity. It is therefore confirmed that if progressive modulation of the polarization is used, i.e. , then even for linear input polarization x0=0 one has large variations of . However, if one uses linear input polarization with an alternating azimuth, as in [7] of the original paper, the corresponding variation in can be small provided that ψ0, during its excursion, remains always far from the values where and is large, namely far from and ψ0=ψ/2, for x0=0, i.e. far from ψ0=0.795 and ψ0=1.571 in our example.

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