where is a fixed frequency known as the ``local oscillator
frequency''. In other words, the local oscillator frequency is always
mid-way between any pair of corresponding upper and lower sideband
frequencies16. If you want to describe the spectral axis
of such a spectrum using a SpecFrame you must choose whether you want the
SpecFrame to describe
or
- a basic SpecFrame cannot
describe both sidebands simultaneously. However, there is a sub-class of
SpecFrame, called DSBSpecFrame, which overcomes this difficulty.
A DSBSpecFrame has a SideBand attribute which indicates if the
DSBSpecFrame is currently being used to describe the upper or lower
sideband spectral axis. The value of this attribute can be changed at any
time. If you use the
astConvert
function to find the Mapping between two DSBSpecFrames, the setting for
the two SideBand attributes will be taken into account. Thus, if you take
a copy of a DSBSpecFrame, toggle its SideBand attribute, and then use
astConvert
to find a Mapping from the original to the modified copy, the resulting
Mapping will be of the form of equation (if the
DSBSpecFrame has its StdOfRest attribute set to ``Topocentric'').
In general, when finding a Mapping between two arbitrary DSBSpecFrames, the total Mapping is made of of three parts in series:
If an attempt is made to find the Mapping between a DSBSpecFrame and a basic SpecFrame, then the DSBSpecFrame will be treated like a basic SpecFrame. In other words, the returned Mapping will not be affected by the setting of the SideBand attribute (or any of the other attributes specific to the DSBSpecFrame class).
In practice, the local oscillator frequency for a dual sideband instrument may not be easily available to an observer. Instead, it is common practice to specify the spectral position of some central feature in the observation (commonly the centre of the instrument passband), together with an ``intermediate frequency''. Together, these two values allow the local oscillator frequency to be determined. The intermediate frequency is the difference between the topocentric frequency at the central spectral position and the topocentric frequency of the local oscillator. So:
The DSBSpecFrame class uses the DSBCentre attribute to specify the central
spectral position (), and the IF attribute to specify the
intermediate frequency (
). The DSBCentre value is given and returned
in the spectral system described by the DSBSpecFrame (thus you do not need to
calculate the corresponding topocentric frequency yourself - this will be
done automatically by the DSBSpecFrame when you assign a new value to the
DSBCentre attribute). The value assigned to the IF attribute should
always be a topocentric frequency in units of Hz, however a negative
value may be given to indicate that the DSBCentre value is in the upper
sideband (that is, if
then
). A positive
value for IF indicates that the DSBCentre value is in the lower sideband
(that is, if
then
).
AST A Library for Handling World Coordinate Systems in Astronomy