We have in this work regarded mirror seeing only with respect to its global effect on image quality. It would however be of great interest to understand the mirror seeing effect also in terms of the mirror aberration modes, particularly in view of the further development of extended active and adaptive optics systems.
Some limited information is provided by Iye's 62-cm experiment in which it is verified that a large part of the image aberration appears as originated from wavefront tilt and defocus errors. The data, however, do not allow us to derive the spectral density of the fluctuations with respect to temporal frequency.
An estimation of the order of magnitude of
the peak frequency of these fluctuations may nonetheless be tried on
the base of mirror seeing geometry and physics.
Noting that the FWHM value of free convection mirror
seeing corresponds in the diagram of fig. to a Froude
number of about 0.1, one can evaluate a reference flow speed
from expression (
):
Assuming that the spectral density follows the Von Karman model, which is generally the case for spectra in turbulent flow phenomena, we would obtain:
where is the height of the viscous conductive layer where the
turbulence is strongest.
A numerical application with = 1K and
= 3 mm
gives for an 8-meter mirror a frequency of about 8.3 Hz.
While all caution should be taken concerning the absolute accuracy
of this result, it appears that the order of magnitude of the required
bandpass for active correction is likely in the range 5 to 15 Hz,
that is quite outside the bandpass
of active optics systems but well within the range aimed for advanced
adaptive optics systems.