# Limits on Phase Correction Performance Due to Differences Between Astronomical and Water-Vapour Radiometer Beams

## Abstract

Using high-resolution three-dimensional realisations of turbulent fields, we investigate the limits on achievable performance of atmospheric phase correction using water-vapour radiometers arising from following effects: the incoherent measurement of power from water by the radiometers (in contrast to coherent detection of the astronomical signal); the different tapers of the response patterns of the astronomical and radiometer receivers; and, the differences in the directions of the radiometer and astronomical beams. We quantify the limit on performance as the fraction of atmospheric phase fluctuations that is not tracked by the radiometers. We find that, for parameters relevant for ALMA, the performance in high-frequency bands will be limited in approximately equal parts by the two effects, i.e., the differences due the incoherent vs coherent processes measured by the two receivers, together with their different tapers, and the angular displacements of the beams. For the lower frequency bands, the angular displacements of the beams becomes the dominant source of error.

## Astronomical and WVR beams

The astronomical and WVR beams (without the relative offset in their direction) are available in this compressed FITS file.

These are certainly relevant:

• O. P. Lay, The temporal power spectrum of atmospheric fluctuations due to water vapor Astronomy and Astrophysics Vol. 122, 1997, ADS

## Figure 5

Created using pstricks and LaTeX. Adapt and reuse as you wish:

      \begin{pspicture}(0,0)(10,10)

\psframe[fillstyle=solid,fillcolor=lightgray,linewidth=0pt](1.5,4)(7.5,6)
\psline[dash=5pt 5pt,linewidth=1pt,linestyle=dotteddashed](1,5)(7.5,5)

\psline[linewidth=3pt]{->}(4,1)(4,8)\uput[0](4,8){Astronomical beam}
\psline[linewidth=3pt]{->}(4,1)(4.5,7.5)\uput[0](4.5,7.5){WVR Beam}

\psline[linewidth=1pt]{<->}(1,1)(1,5)\uput[0](1,3){$h=750\,\unit{m}$}
\psline[linewidth=1pt]{<->}(7.75,4)(7.75,6)\uput[0](7.75,5){$w=500\,\unit{m}$}
\psline[linewidth=1pt]{->}(7.5,2)(7.5,3)\uput[0](7.5,2.5){$z$-direction}

\uput[0](5,5.5){Turbulent layer}

\psframe[fillstyle=hlines,fillcolor=lightgray,linewidth=0pt](0,0)(9,1)

\end{pspicture}


The result: