... experiment

PLANCK is the third medium-sized mission in the Horizons 2000 Scientific Program of the European Space Agency, http://astro.estec.esa.nl/Planck

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... plane

By the principle of reciprocity, modeling a feed transmitting from the focal plane to the sky is equivalent to modeling a detector horn, in the same position, collecting radiation from the sky, since, by time reversal, the transmission pattern is the same as the reception pattern.

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... telescope

We define an ideal telescope as one with rotationally symmetric reflectors and on-axis fully linearly polarized detectors.

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... of XPD

For simplicity of notation, XPD will always be expressed in dB units as a power difference, $\Delta W$.

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... sky

In fact, in a dual reflector system such as that of PLANCK, the rotation of the principal plane of polarization on the sky would be symmetric and not equal to the rotation of the feed, due to the "mirroring'' of the radiation pattern in the beam coordinate system when the signal is reflected from one mirror to the other. Equation (8) takes this symmetry into account.

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... angles

Note that, by symmetry, a feed rotation by $\psi _{{\rm FP}}$ is equivalent to a $\psi_{{\rm FP}} - 180^{\circ}$ rotation, so we need not consider cases with $\psi_{{\rm FP}}>180^{\circ}$.

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... telescope

By definition, the z-axis of the line-of sight coordinate system points to the direction of maximum power radiated (or received) by an on-axis detector.

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...$0\leq\phi<\pi$)

Note that $\theta$ is a latitude coordinate, while $\phi$ is a longitude coordinate.

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...before

These far field reference frames (mb1, mb4 and mb27) can be seen in Figs. A.1 and A.2. Note that they have a common origin with $C_{{\rm PM}}$, at the center of the primary mirror, but different orientations.

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