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We summarize here the relations between the rms noise (
) and the
elapsed telescope time (
) derived by Pety et al. (2009) in the case of a
singlepixel heterodyne receiver. The results depends on a combination of
 The observation kind:
 Tracked observations
 where the telescope track the source, i.e.
it always observes the same position in the source referential. The
result is a single spectra.
 OnTheFly observations
 where the telescope continuously slew
through the source with time to map it. The result is a cube of
spectra.
 and of the switching mode:
 Position switch
 where the offmeasurement is done on a closeby sky
position devoid of signal. Wobbler switching is a particular case.
 Frequency switch
 where the telescope always points towards the the
source and the switching is done in the frequency (velocity) space. In
this case,
The formulas are
 for tracked observations

(1) 
 for OTF observations

(2) 
In these formulas

is the efficiency of the telescope. It includes the time
needed 1) to do calibrations (e.g. pointing, focus, temperature scale
calibration), and 2) to slew the telescope between useful integrations,
etc... Its value is decided by IRAM: It should not be changed by
the PI.

is the spectrometer efficiency.

is the frequency resolution.

is the number of polarizations tuned at the same frequency (1
or 2).

is the system temperature, which is a summary of the noise
added by the system. It is usual to approximate it (in the
scale)
with

(3) 
where
is the receiver image gain,
the telescope forward
efficiency,
the airmass,
the
atmospheric opacity in the signal band,
the mean physical
atmospheric temperature,
the ambient temperature in the receiver
cabine and
the noise equivalent temperature of the receiver and
the optics.

is the number of independent measurement in the map observed
in the OTF mode. It is given by

(4) 
where
is the map area,
is the area of the resolution
element in the map,
is the smoothing factor due to gridding
and
is the telescope full width at half maximum.

the number of submaps needed to cover the whole map area,
a submap being the area covered between two successive off
measurements.
is computed with

(5) 
where
is the telescope scanning speed and
is the
typical timescale of stability of the observing system.
The demonstrations and additional subtleties for the OTF case are fully
described in Pety et al. (2009).
Next: Generalization to a multipixel
Up: IRAM30m HERA time/sensitivity estimator
Previous: IRAM30m HERA time/sensitivity estimator
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20140701