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There are three basic systematic surface/wavefront deformations (occasionally
associated with pointing errors) with which the observer may be confronted,
i.e. defocus, coma, and astigmatism (a transient feature on the IRAM 30-m
telescope).
- 1.
- The most important systematic wavefront/beam error is due to a defocus of the telescope. This error is easily detected, measured, and corrected
from the observation of a strong source at a number of focus settings. Figure
1.7 shows, as example, the beam pattern measured on Jupiter with the
telescope being gradually defocused. Evidently, the peak power in the main beam
decreases, the power in the side lobes increases, until finally the beam pattern has
completely collapsed. To be on the safe side for observations, the defocus of the
telescope should not exceed
.
A defocus does not introduce
a pointing error.
Figure 1.7:
Effect on the beam pattern (scans across Jupiter)
introduced by defocusing the IRAM 15-m telescope (shifts of the subreflector in
steps of a quarter of the wavelength (3 mm)).
![\resizebox{6cm}{!}{\includegraphics[angle=0.0]{greve7.eps}}](img127.gif) |
- 2.
- A telescope may have a comatic wavefront/beam error due to a
misaligned subreflector, shifted perpendicular off the main reflector axis.
Figure 8 shows, as example, a cross scan through a comatic beam of the IRAM
15-m telescope, especially produced by displacement of the subreflector.
A comatic beam pattern introduces a pointing error. It may be useful for the
observer to recognize this error, in particular if unexplained pointing errors
occur in an observations. [The IRAM telescopes are regularly checked for
misalignments, and correspondingly corrected.]
Figure 1.8:
Illustration of a comatic beam (scanned in the direction of the
coma) especially produced on the IRAM 15-m telescope. The shift of the subreflector
is indicated by S. The beam pattern is perfect at S = 0. Note the shift of the beam
(pointing error) when the subreflector is shifted.
![\resizebox{6cm}{!}{\includegraphics[angle=0.0]{greve8.eps}}](img128.gif) |
- 3.
- A telescope may have an astigmatic wavefront/beam error, usually
introduced by complicated mechanical and/or thermal deformations (a transient
feature on the IRAM 30-m telescope). While this beam deformation is easily
recognized by the observer from the difference in beam widths measured from
in-and-out-of-focus cross scans, the improvement of the telescope usually is
difficult, and out of reach of the observer. A focused astigmatic beam does not introduce a pointing error. Figure 1.9 shows the focused beam pattern
measured on a telescope which has a strong astigmatic main reflector (amplitude of
the astigmatism
0.5mm).
Figure 1.9:
Illustration of an astigmatic beam pattern; well focused.
![\resizebox{8cm}{!}{\includegraphics[angle=0.0]{greve9.eps}}](img129.gif) |
The beam deformation of systematic wavefront deformations occurs close to the main
beam, and the exact analysis should be based on diffraction calculations. A
convenient description of systematic deformations uses Zernike polynomials of order
(n,m) [Born and Wolf 1975]. Without going into details, the Zernike-type surface
deformation
[with (
) normalized coordinates of the aperture, and R special
polynomial functions] with amplitude
has a quasi rms-value
=
and introduces a loss in main beam
intensity of
![\begin{displaymath}{\epsilon}_{\rm sys}/{\epsilon}_{o}\ {\approx}\
{\rm exp[-(4{\pi}{\alpha}/{\lambda})^{2}/(n+1)]}
\end{displaymath}](img134.gif) |
(1.16) |
For primary coma n = 1, for primary astigmatism n = 2. Although the beam deformation
may be very noticeable and severe, the associated loss in main beam intensity may
still be low because of the reduction by the factor (n+1).
Next: 1.4.2 Random Errors
Up: 1.4 The real Single-Dish
Previous: 1.4 The real Single-Dish
S.Guilloteau
2000-01-19