In modern telescopes the secondary mirror (often called M2) is attached to electro-mechanic actuators which allow fine adjustment of the optical alignment and focusing. The latest telescopes projects also provide for fast motion of the secondary mirror, either to switch rapidly between the observed object and the sky background, or to correct guiding errors due to wind loading. All these systems produce some heat which, if it is not carried away by a cooling circuit, will dissipate right into the telescope light-beam and may then cause a seeing degradation.
In order to evaluate this issue, Jacques Beckers of ESO performed a series of measurements at the ESO 2.2-m telescope using a CCD array to measure FWHM image size ([Beckers 92]). For the tests three different types of heating gadgets were used to produce heat: a metal square box 222222 cm and a metal plate 22027.51.1 cm. They were mounted on top of the 2.2-m telescope, the plate across the light-beam, simulating two opposite spiders (cf. fig. ), and the box mounted on it on thermal insulating legs.
The measurements were performed on stars about 30 from zenith while either the box or the plate were heated. The box was heated with 135 Watts and the plate with 560 Watts. Both wattages resulted in a surface-air temperature difference of about 60 K. The mean heat transfer coefficient was respectively 7.5 W/m for the box and 7.8 W/m for the plate. The wind velocity was low during the experiment (3 m/s or less), which lets assume that the air flow motion near the top of the telescope was around 1 to 2 m/s (although no measurements were done inside the dome). A measurement cycle (heating to maximum temperature starting from ambient and cooling off to near ambient) lasted 2 hours. The CCD images were fit with a Gaussian profile and the FWHM were recorded. The natural seeing was recorded by the DIMM seeing monitor operating at La Silla and was near 0.8 arcsec during the three nights of the experiments.
The experimenters had expected to record a significant increase of
seeing with the heating elements in the telescope light-beam, and were
surprised when the effects were very small, barely noticeable through
the variability of natural seeing.
The measurements were analyzed by least square fitting of
where was the natural seeing measured by the DIMM and a general fixed error contribution from the telescope.
The factor a was the quantity of interest, as the FWHM contribution was assumed to be linear with , and was evaluated as:
Figure: Seeing caused by a free convection plume from the M2 unit.
We can transpose these experimental data also to telescopes of different sizes provided that a geometry similarity is approximately maintained in the proportions of the test. Consider the telescope configuration sketched in fig. . Heat is dissipated by the secondary mirror unit causing a vertical plume across the light-beam. Let us assume that the plume spreads in proportion to its distance from its origin. A circumferential cross-section at a distance r from the optical axis has then dimensions along the line of sight and across it. We assume further that the thermal turbulence in the plume is described by a relationship of type (). The seeing spread through a line of sight at a distance r from the optical axis (see fig. ) will be proportional to:
where and are respectively the average temperature structure coefficient and heat flux along a line of sight across the plume. The total seeing spread of the light beam will be obtained by integrating over the plume cross-section seen by the telescope, normalized by the mirror area:
where D is the pupil (mirror) diameter.
Since both and are proportional to r, it is:
Noting that the total heat flow Q from the secondary unit is proportional to , we obtain:
Therefore the scaling relationship based on the experimental results is:
This relationship may be used to specify the maximum allowable heat dissipation for a given seeing requirement. For instance, if we consider a 8-m telescope and a requirement that the seeing contribution shall be 0.025 arcsec, the allowable heat dissipation from the secondary mirror unit will be about 108 Watts.