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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, $ F_{rest}^{ref}$ , and a source velocity, $ v$ , within some referential (usually LSR referential) on one side and an IF frequency, $ F_{IF}^{ref}$ , 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, $ F_{rest}$ , and topocentric frequencies, $ F_{topo}$ , are related through:

$\displaystyle F_{topo} = F_{rest} \left(1+\delta-\frac{v}{c} \right)$ (39)

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

Since $ F_{IF} = \pm(F_{topo}-F_{LO1})$ (+ for an USB conversion, - for a LSB conversion), we have:

$\displaystyle F_{IF} = \pm \left(F_{rest} \left(1+\delta-\frac{v}{c}\right) - F_{LO1}\right)$ (40)

so by setting

$\displaystyle F_{LO1} = F_{rest}^{ref}\left(1+\delta-\frac{v}{c}\right)\mp F_{IF}^{ref}$ (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 $ F_{rest}^{ref}$ FREQUENCY
Sideband       ISB
Reference IF frequency IF Topo $ F_{IF}^{ref}$ FIF1
LO1 frequency   Topo $ F_{LO1}$ FLO1
Source referential       TYPE_VEL
Source velocity   Ref. $ v$ VELOCITY
Doppler factor     $ \delta$ DOPPLER

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

$\displaystyle F_{IF}(j,k)$ $\displaystyle =$ $\displaystyle \left(k-i_{IF}(j)\right)*\delta F_{topo}+F_{IF}^0(j)$ (42)
$\displaystyle F_{rest}(j,k)$ $\displaystyle =$ $\displaystyle \left(k-i_{rest}(j)\right)*\delta F_{rest}+F_{rest}^0(j)$ (43)

where $ \delta F_{topo}$ is the channel spacing of the backend in the topocentric frame and $ \delta F_{topo} = \delta
F_{rest}\left(1+\delta- \frac{v}{c}\right)$

Table 5: Parameters for spectral windows and corresponding SIC variables
Parameter Freq Frame Notation SIC variable
Number of channels     $ n_{ch}$ N_CHANNELS
Channel number of (2)     $ i_{IF}$ REF_NUM
Center frequency IF Topo $ F_{IF}^0$ LFCEN
Reference channel     $ i_{ref}$ REF_CHANNEL
Rest frequency RF Rest $ F_{rest}^0$ F_OFFSET
Frequency spacing   Topo $ \delta F_{rest}$ LFRES
Frequency spacing   Rest $ \delta F_{topo}$ F_RESOLUTION

next up previous contents index
Next: Custom modifications Up: Modify Previous: Phases   Contents   Index
Gildas manager 2022-01-17