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
frequencies
. This is illustrated in
Figure 11. The astronomical signal received in the two
spectral windows (one corresponding to each sideband) are superimposed in
the final measured spectrum, with the signal from the USB window first being
reversed in frequency.
[width=0.9]sun211_figures/dsbspec1
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To describe the spectral axis of the final measured spectrum
using a SpecFrameSpecFrame you must choose whether you want the SpecFrame to
describe the frequency of the LSB window () or of the USB window
(
) - a basic SpecFrame cannot describe both sidebands
simultaneously. However, there is a sub-class of SpecFrame, called
DSBSpecFrameDSBSpecFrame, which overcomes this difficulty.
A DSBSpecFrame has a SideBandSideBand 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. A DSBSpecFrame knows how to transform frequencies between the two
sidebands. For instance, if you have two DSBSpecFrame objects that
describe topocentric frequency and are identical except that they
describe opposite sidebands, then the
astConvertastConvert
function will return a MappingMapping that implement equation
1. If the DSBSpecFrames
describe anything other than topocentric frequency, then the returned
Mapping will be more complicated since it will include conversions to and
from topocentric frequency.
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 DSBCentreDSBCentre attribute to specify the
central spectral position (), and the IFIF attribute to
specify the intermediate frequency (
). This is illustrated in
Figure 11, where the values of the DSBCentre and IF
attributes have been chosen to put an emission line at the centre of the
LSB window. The DSBSpecFrame determines LO from these two attribute values.
Note, in principle there is no reason why the attribute values should not have been chosen to put the spectral line in the USB instead of the LSB. The choice of which sideband to use for the observed feature is usually made in order to exclude any bright features from the other window. The sideband that contains the observation centre is known as the “observed” sideband, and the other sideband is known as the “image” sideband.
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. It's sign indicates whether the observation centre (given by DSBCentre) is in the LSB or the USB—a positive IF puts the observation centre in the LSB and a negative IF puts it in the USB.