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Handling Dual-Sideband Spectra

Dual sideband super-heterodyne receivers produce spectra in which each channel contains contributions from two different frequencies, referred to as the “upper sideband” (USB) frequency and the “lower sideband” (LSB) frequency. In the rest frame of the observer (topocentric), these are related to each other as follows:

170#170 (1)

where 171#171 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.

Figure 11: A dual-sideband spectrum is formed by superimposing the signal received from two spectral windows—the lower sideband (LSB) and upper sideband (USB). In topocentric frequency, the two sidebands are equally spaced on either side of the local oscillator (LO) frequency. In other spectral systems the width and placement of the windows may not be symetric about the LO.
[width=0.9]sun211_figures/dsbspec1

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 (172#172) or of the USB window (173#173) - 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:

174#174 (2)

The DSBSpecFrame class uses the DSBCentreDSBCentre attribute to specify the central spectral position (175#175), and the IFIF attribute to specify the intermediate frequency (176#176). 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.

Subsections

- Aligning Dual-Sideband Spectra