Observation and display of line spectra

There are two separate issues. First, we need to observe such that the line of interest actually occurs within the passband of the instrument (normally, but not always, at the centre of the passband). For a heterodyne receiver we do this by adjusting the local oscillator frequency by an amount equal to the total doppler frequency shift expected for the line. Second, we then need to display the spectrum. Unfortunately, the spectrometer is back on Earth, at the telescope, so we need to map the I.F. frequencies of individual spectrometer channels onto velocity (or frequency) space in some other chosen frame. This `display' frame need not necessarily be the same as the `observation' frame. For example, whatever the observation frame, we may wish to display the output in one of several standard frames:

1. In the telluric frame, where the frequencies of spurious responses in the I.F. passband (for example) can be measured, and with any luck, disposed of. Or we may wish to measure absolute frequency in this frame to identify telluric (atmospheric) emission and/or absorption features.
2. In the frame of the source (e.g., at a velocity of $V_{lsr}$ offset with respect to the LSR frame itself), when we wish to measure the absolute frequency of some spectral feature, in case it is a spectral line of some species other than the one we desired.
3. In the LSR frame, if we want to determine a velocity to use for distance measurements within the galaxy.
4. In a heliocentric frame for velocity determinations of external galaxies (I am told that this is the normal way of doing this.)

The solution adopted in SPECX is to view all calculations of velocity and/or frequency as a two stage process. In the first, the spectral header information is used to calculate the telluric centre frequency of the observation. That is, we deduce the true frequency as measured at the telescope of a signal appearing in the centre channel of the spectrometer. SPECX then produces an `X-array' which contains, for each spectrometer channel, the telluric frequency corresponding to that channel. Finally, this array is transformed back to the display frame. By default the display frame is the same as the observation frame, which is encoded in the SPECX and GSD scan headers, but it may be changed to any other frame if you like.

To summarize: SPECX will normally display the data using the velocity frame in which it was observed; however you can use SET-VELOCITY-FRAME to select another frame, and optionally you can use SET-LINE-REST-FREQ to choose another reference frequency for the velocity transformation. Current options for frames include LSR, Geocentric, Heliocentric and Telluric, and you have a choice of Radio, Optical and Relativistic velocity laws. Because of the bewildering number of combinations of these variables, the header on the X-axis of the plot has been modified to give a full specification.