The problem treated here is the evaluation of the loss of image quality caused by wind induced pressure fluctuations on the primary mirror of a large optical telescope. The primary mirror will experience significant optical aberrations already with deflections of the order of 200 nanometers. These aberrations depend strongly on the modal shapes of the deflections which in turn depend on the spatial distribution of pressure fluctuations on the surface and on the mirror eigenmodes. Therefore the study described here joins notions and methods of optics and wind engineering. This special problem will be tackled in the following manner:

- The features to be investigated are the pressure variations on
the mirror surface which shall be measured over times which are
somewhat longer than the basic integration time of the active optics
system (30 sec to 1 min). These measurements shall allow a decomposition
into the main optical aberrations modes of the mirror, described by
Zernike polynomials, of which the first eight are:
- When these optical modes are fitted to measurements of
the pressure field on the mirror, one obtains a set of modal pressure
coefficients which then characterize the spatial frequencies of the
fluctuating pressure field.
- The wavefront aberrations corresponding to each modal
component of
pressure can be computed from the modal pressure coefficients
with a knowledge of the elastic eigenmodes
of the mirror, which are quite similar to the aberration modes.
- The square root of the quadratic sum
of all components of the modal deformation gives finally the total
wavefront aberration (expressed in nanometers),
which is the measure of the overall optical quality of
the mirror shape.
- We will in particular study the variation of the overall mirror aberration with respect to the average values of fluctuating pressure in the different enclosure types and for various mirror orientations, with the aim to establish relationships suitable for parametric studies.

- [A]
- Wind tunnel tests on a 1/80 model of the telescope in open air.
- [B]
- Measurements of the pressure field on a 3.5-m dummy mirror located inside the NTT building (see fig. ) just in front of the telescope and in the inflatable dome prototype, also located at the La Silla observatory.
- [C]
- Wind tunnel tests on a 1/60 model of the telescope
surrounded by a cylindrical enclosure.

**Figure:** "Open air" telescope model in the LASEN wind tunnel

Lorenzo Zago, zago@elgc.epfl.ch, Sun Feb 26 22:57:31 GMT+0100 1995