Sometimes confusion may arise on how to calculate the sky frequency for a given redshift or source velocity. This stems from the fact that optical and radio astronomers calculate radial source velocities from different formulas. (Remember that velocities are not directly measured but calculated from wavelength or frequency shifts). Optical astronomers deduce radial velocities from the measurement of a wavelength shift:
where c is the speed of light, 
(
) the unshifted
and 
(f) the shifted wavelength (frequency), respectively.
The astronomical redshift z is defined as
At low redshifts some radio astronomers use a different convention which presumably comes from the fact that frequency shifts rather than wavelength shifts are measured. The radio convention is
As a consequence, radio ``velocity'' and optical recession velocity are not the same for a given redshift:
This means that in order to calculate the correct sky frequency from a
given velocity one needs to know if the velocity was calculated using
the optical or radio convention. An optical velocity 
(or redshift z) requires another formula than a radio velocity
obtained e.g. from 21 cm HI measurements. The
sky frequency 
for a given source velocity and line rest
frequency 
is
At the IRAM 30m telescope the conversion is done in the following way:
the drive program calculates the velocity 
of
the telescope relative to the local standard of rest, takes the source
velocity 
(from the source catalogue), and
then calculates the sky frequency applying the optical convention:
If you want to observe e.g. a high-redshift object with redshift
z at line rest frequency 
,
the recommended procedure is to set the source velocity v (in the
source catalogue) to zero and give the corrected frequency (calculated
with the optical formula) 
to the
drive program by using the OBS command:
RECEIVER rx_name
/FREQUENCY 
LSB.
You might alternatively calculate the optical
source velocity 
, give this velocity in the
source catalogue, and use the line rest frequency 
in the OBS
command:
RECEIVER rx_name
/FREQUENCY 
LSB.
If you need to use the radio convention, it is best to set
the source velocity v (in the source catalogue) to zero and give the
corrected frequency (calculated with the radio formula)
using the OBS command:
RECEIVER rx_name
/FREQUENCY 
LSB
instead of the line rest
frequency.
Instead of giving frequencies directly in the RECEIVER command,
you can also define a line with the corrected frequency in your line
catalogue, and use the OBS command:
RECEIVER rx_name /LINE your_line.
Wolfgang WILD