The franco-Italian T.H.E.M.I.S. telescope (T.H.E.M.I.S. is a French acronym which stands
for "solar heliographic telescope for
the study of solar magnetism and atmospheric
instabilities") is designed to obtain very precise measurements of the solar
magnetic field vector from simultaneous observations of different polarized
spectral lines. Image stabilization and high image quality are requirements
for the observation of small solar magnetic features like magnetic flux tubes,
so that the light passing through the entrance of the spectrograph slit will
come from the same solar structure troughout the observation time (
0.4 second) which is longer than the caracteristic time of evolution of the terrestrial
atmospheric tubulence. One of the main optical elements integrated into
T.H.E.M.I.S. optical train is a tiltable mirror which corrects instrument vibrations
and steering as well as random wavefront caused by atmospheric turbulence
(Rayrole 1992).
Solar physics research requires observations of magnetic features in a range
from one tenth of an arcsecond, for flux tubes, to a few arc-minutes, for active
regions. Another demand on the image compensation system is that the observer
should be able to analyze a large field of view. So, an estimate of image
quality after correction using the T.H.E.M.I.S. image stabilizer system is
presented:
1) To analyze the compensation degradation by adaptive optics system across
large fields of view taking into account the effects of anisoplanatism.
2) To determine the usable limited field of view of the wavefront analysis
corresponding to the isoplanatic patch. Anisoplanatism poses a severe problem
if the field of view of the correlation tracker is not cut down to approximately the
isoplanatic patch. The new tracking method called granulation tracking described
in a previous paper (Molodij et al. 1996) is devoted to measure image motions
with extended incoherent sources. The granulation tracker, incorporated in the
T.H.E.M.I.S. optical arrangement is designed to work on a square field of
view of the granulation image which can be adjusted from 
arcseconds to
arcseconds, depending on the Fried parameter r0.
The favorable turbulence conditions at the Iza
a site in the canary
Island (r0 > 15 cm for 60% of the observation times)
(Barletti et al. 1973) suggests that
image stabilization system is well adapted for improving image resolution of
large field of view observations in visible wavelength with the use of a
tiltable mirror. This is due to the fact that T.H.E.M.I.S. is a 0.9 meter class
telescope (D/r0 < 6 for 60% of the observation times). So, atmospheric
perturbations are esentially caused by the wavefront tilts whose variances
represent 90% of the total variance phase
(Noll 1976).
However, it must be keep in mind that any correlation tracker makes wavefront
slope measurements in order to correct pure wavefronts tilts. Such problems
are analyzed in this paper when observing extended sources.
A new approach to wavefront sensing on extended, complex objects based on the curvature sensing technique while imaging the Sun has been recently proposed by R. Kupke, F. Roddier and D.L. Mickey (Kupke et al. 1994). The goal of this paper is also to investigate and compare the performances of image stabilizer optical system and adaptive optics system which will be able to correct the first aberrated modes as tilt, focusing and astigmatism for the 0.9 meter telescope.
In order to evaluate the limitations due to angular anisoplanatism and slope
measurements by correlation trackers, this paper presents a theoretical
analysis based on the modal control of the adaptive optics system. Modal control
is an helpful tool in adaptive optics in order to manage optimal correction
in terms of temporal and angular decorrelation of turbulent wavefront
(Rousset 1993; Gendron & Léna 1994).
The analysis uses Mellin transform techniques to evaluate the effects of
anisoplanatism upon the performance of adaptive optics system
(Chassat 1989;
Sasiela 1994; Molodij & Rousset 1997).
In Sect. 2, the residual wavefront distortions associated are evaluated
modally in terms of Zernike polynomials which are chosen for their simple
analytical form and because of the correspondance of the low-order Zernike
polynomials to physically controlable modes of correction, .i.e, tilt,
focusing, astigmatism, etc. The problem of the wavefront tilts correction
from wavefront slope measurements is considered in Sect. 3 using the modal
expansion on the Zernike polynomials (Primot et al. 1990).
These analysis are directly related to the Zernike coefficient angular
correlations between two plane waves (Chassat 1992). Numerical results are
presented in Sect. 4 for the modelized turbulence profile Cn2 resulting
from experimental measurements on the Izaa site by Arcetri
university (Barletti et al. 1973).
In Sect. 5, the optical transfer functions
are evaluated for a Zernike expansion following
the Wang and Markey approach
(Wang & Markey 1978). The statistics of the Zernike coefficients for an
expansion of Kolmogorov turbulence phase distortion have been derived by Noll
(Noll 1976) and applied to calculate the optical transfer function (OTF) for
a point source (Wang & Markey 1978). We develop the calculation of OTF
to cases when the observing source is extended in order to evaluate the
degradation in the field of view of the image due to anisoplanatism after
adaptive optics compensation. We compare the performances of image stabilizer
optical system and adaptive optics system which will correct aberrations as
tilt, focusing and astigmatism on solar granulation images.