Measuring the gravitational astigmatism of a radio telescope

Most conventional radio telescopes will show a strong astigmatism when tilted, resulting in surface degradation, which can be corrected with a mechanically deformable subreflector. Astigmatism means different focal lengths (
\Delta F
) in two perpendicular planes. A most direct way of measuring the astigmatism is to measure
\Delta F
with an elongated rotatable feed, illuminating only a central strip of the telescope. Equations are given for the relations between
\Delta F
, rim deviation
A
, and rms surface deviation
\Delta z
, and for the dependence of these quantities on elevation angle. This method was applied to the 140-ft. telescope. Between zenith and horizon, the measured range is
\Delta F = (51 \pm 2)
mm, yielding an astigmatic rim deviation of
A = 8.7
mm, and an astigmatic rms surface deviation of
\Delta z = 2.87
mm. The latter agrees with astronomical efficiency measurements, showing that the total gravitational deformation is mainly of a simple astigmatic shape, to be corrected by relatively simple means.