Frequency and velocity scales

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Frequency and velocity scales

NOEMA operates with Doppler tracking. When the user provides a setup, with a given reference rest frequency, , and a source velocity, , within some referential (usually LSR referential) on one side and an IF frequency, , at which the rest frequency should appear on the other side. The Doppler tracking consists in modifying the LO1 frequency so that the two frequencies stay aligned to within one tenth of the smallest channel spacing of the spectral setup being observed.

The rest, , and topocentric frequencies, , are related through:

| (39)

where is the Doppler factor between the chosen referential and the topocentric referential, and is the source systemic velocity within this referential.

Since (+ for an USB conversion, - for a LSB conversion), we have:

| (40)

so by setting

| (41)

we ensure the Doppler tracking as defined above.

Table 4: Parameters for receiver tuning. For the source referential TYPE_VEL, 1 means LSR, 2 heliocentric, 3 geocentric, 4 no doppler tracking, 5 unknown.
Parameter | Freq | Frame | Notation | SIC variable
Reference rest frequency | RF | Rest |  | FREQUENCY
Sideband |  |  |  | ISB
Reference IF frequency | IF | Topo |  | FIF1
LO1 frequency |  | Topo |  | FLO1
Source referential |  |  |  | TYPE_VEL
Source velocity |  | Ref. |  | VELOCITY
Doppler factor |  |  |  | DOPPLER

The frequency value of channel from spectral window are defined as:

|  |  | (42)
|  |  | (43)

where is the channel spacing of the backend in the topocentric frame and

Table 5: Parameters for spectral windows and corresponding SIC variables
Parameter | Freq | Frame | Notation | SIC variable
Number of channels |  |  |  | N_CHANNELS
Channel number of (2) |  |  |  | REF_NUM
Center frequency | IF | Topo |  | LFCEN
Reference channel |  |  |  | REF_CHANNEL
Rest frequency | RF | Rest |  | F_OFFSET
Frequency spacing |  | Topo |  | LFRES
Frequency spacing |  | Rest |  | F_RESOLUTION