21.3 Atmospheric behaviour and noise properties

Table 21.3 summarises the properties of the atmosphere and the resulting noise (including also the instrumentation) at both wavelengths.

Mm versus optical interferometry: Atmosphere & Noise properties

Item	Radio mm	Optical
$\lambda$	0.6mm to 1cm	0.4 to 30 $\mu$m
$\nu$	30 to 450 GHz	10 to 600 THz
Comparison given for	$\lambda \sim 1.3$mm	$\lambda \sim 1 \mu$m
Noise sources	background limited	photon limited
	(gaussian)	(poisson)$^*$
Main instrumental noise	Receiver (thermal)	Detector (read-out)
	thermal sky emission
Signal Detection	$T_{signal}/T_{sys} \sim 10^{-2}.10^{-4}$	photon limited
Seeing origin	Variation of W(H$_2$O)	Variation of $T_{atm}$
Fried Parameter $r_o$	$>$ antenna	$\leq$ telescope
(size of the coherence cell)
Coherence Time $t_o$	several 10 minutes	$\sim$ 10 milli-seconds
(time to reach $\Delta \Phi \approx 180^o$)
Equivalent to	Single-speckle	Multi-speckle
Atmospheric correction
Photometry	monitoring of T$_{sys}$	``standard'' photometry technics
Seeing	radiometric	tip tilt
	phase correction	adaptive optics
Phase Calibration	phase referenced	$t_o$ too short
	on nearby sources	closure phase on dual interferometer
Measurements	complex correlator rates: $r_i$,$r_r$	$V^{raw}_{12} = \frac{I_{max} - I_{min}}{I_{max}+I_{min}}$
	complex visibility $V$	fringe contrast
Information on	$\mid V \mid$ & $\Phi_V$	$\mid V \mid$, amplitude
Imaging	Complex visibilities	Phase retrieval by
		closure relations
Algorithms	all standard imaging	+ amplitude model fitting
		in the UV plane

$^*$ Note that for $\lambda \geq 2.5 \mu$m, the atmosphere and the telescope are starting to contribute as main sources of noise (thermal emission), therefore the noise becomes background limited.