Several analyser arrangements are commonly used. POLPACK can handle data from the following forms:
A half-wave plate has a preferred axis. Light polarized parallel to this axis passes through the half-wave plate unchanged. Light polarized perpendicular to the axis is retarded by half a wavelength. The net effect of this is to rotate the plane of polarization of the light so that the axis of the half-wave plate bisects the angle between the planes of polarization in the incoming and outgoing light.
This form of polarimeter is shown diagrammatically in the next figure:
There will be a reference direction within the focal plane. The orientation of the rotating analyser or half-wave plate is specified by giving the angle between the reference direction and the analyser (or half-wave plate). In POLPACK, the reference direction is specified by giving the anti-clockwise angle from the first image axis to the reference direction. This angle is usually referred to as , and is specified in degrees.
The combination of a fixed analyser and a rotating half-wave plate can be thought of as equivalent to a single rotating analyser, in which the analyser rotates twice as fast as the half-wave plate. If the anti-clockwise angle from the reference direction to the half-wave plate is , then the effective analyser position is given by:
This is the angle from the reference direction to a hypothetical analyser which would give the same effect as the combination of the fixed analyser and half-wave plate (see the next figure).
Here , and are the Stokes parameters describing the incoming partially plane polarized light. is the total intensity, i.e. the sum of the polarized and unpolarized intensities. If a fraction of the incoming light is totally plane polarized, then:
where is the polarized intensity, and is the unpolarized intensity. Q measures the intensity polarized parallel to the reference direction, and U measures the intensity polarized perpendicular to the reference direction. They are given by:
Here, is the anti-clockwise angle from the reference direction to the direction of polarization of the incoming light.
The two other values, and in the above expression for the
record intensity, , are the analyser transmission and the
analyser efficiency. The transmission measures the total
throughput of the analyser, and the efficiency measures the ability of
the analyser to select a single state of polarization. A perfect analyser
would have a value of for both. A perfectly bad analyser
such as a piece of high quality glass, would have a transmission of
and an efficiency of zero. If you know the transmission and efficiency of
your analysers, then POLPACK can take account of them when estimating the
values of the Stokes parameters, , and . If you do not known
them, then don't worry... just use the default values of for both.
These will probably be acceptable since instrument makers usually go to
some trouble to make their analysers as perfect as possible. If in doubt,
you could try re-processing your data with different values for the
analyser transmission and efficiency. This will give you some idea of how
sensitive the final results are to the values used.