We present a technique for the accurate estimation of large-scale errors in
an antenna surface using astronomical sources and detectors. The technique
requires several out-of-focus images of a compact source and the
signal-to-noise ratio needs to be good but not unreasonably high. For a given
pattern of surface errors, the expected form of such images can be calculated
directly. We show that it is possible to solve the inverse problem of finding
the surface errors from the images in a stable manner using standard numerical
techniques. To do this we describe the surface error as a linear combination of
a suitable set of basis functions (we use Zernike polynomials). We present
simulations illustrating the technique and in particular we investigate the
effects of receiver noise and pointing errors. Measurements of the 15-m James
Clerk Maxwell telescope made using this technique are presented as an example.
The key result is that good measurements of errors on large spatial scales can
be obtained if the input images have a signal-to-noise ratio of order 100 or
more. The important advantage of this technique over transmitter-based
holography is that it allows measurements at arbitrary elevation angles, so
allowing one to characterise the large scale deformations in an antenna as a
function of elevation.Comment: 6 pages, 5 figures (accepted by Astronomy & Astrophysics