5.4.4 Phase stability requirements

Short term phase errors in the local oscillators (jitter) will cause a decorrelation of the signal and reduce the visibility amplitude by a factor

$$\ensuremath{\eta_\mathrm{\scriptscriptstyle 12}} = e^{-({\sig... ...riptstyle 1}}\ensuremath{\eta_\mathrm{\scriptscriptstyle 2}} }$$ (5.22)

where $\sigma_1$ is the rms phase fluctuation of the LO in one of the antennas ($\sigma_2$ in the other). $\ensuremath{\eta_\mathrm{\scriptscriptstyle 1}} = e^{-{\sigma_1}^2 }$ is the decorrelation factor for one antenna; typical requirements on $\sigma_1$ are:

$\ensuremath{\eta_\mathrm{\scriptscriptstyle 1}}$	0.99	0.98	0.95	0.90
$\sigma_1$ (degrees)	5.75	8.1	13.0	18.5

The phase stability required on the LO2 is $\sigma_1/(\ensuremath{N_\mathrm{\scriptscriptstyle M}}\ensuremath{N_\mathrm{\scriptscriptstyle H}} ) \sim 0.1^\circ$ for a 0.95 efficiency at 1.3mm: very stable oscillators are needed.