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1 Introduction

Many authors reported and discussed variations observed in the Sun's diameter measurements performed during the last three centuries (Toulmonde 1997). These results added greater interests to the solar diameter measurements and long term variations. Thus, many programs were born for solar geometry goals. Visual and photoelectric measurements have been made using instruments dedicated to the solar diameter measurements (Brown et al. 1982; Bode et al. 1995; Laclare 1983; Laclare et al. 1980, 1996; Neckel 1995; Wittmann 1997; Wittmann et al. 1981, 1991). The mean values of solar radius reported from these programs were dispersed. The difference lied between a few tenths to more than two arcseconds. Moreover, variations have not always been noted from the observation series of the solar programs. Using the observations recorded with the solar diameter monitor (Brown et al. 1982) during the period 1982 to 1987, Brown & Christensen-Dalsgaard (1998) did not observe any variations. In their work, they used special methods in order to eliminate some atmospheric effects. However, in opposite, variations were observed in diameter measurements performed with the solar astrolabe (Delache et al. 1985; Laclare et al. 1996).

The astrolabe experiment of Calern Observatory (France) has begun in 1975, when the first measurements were obtained. Since the beginning of the solar program up to now, visual observations were made regularly while the CCD ones began in 1988. Figure 1 represents the visual solar data recorded at Calern Observatory astrolabe during the period 1975 to 1996. It is clearly shown an oscillation with a period of about ten years corresponding probably to the solar cycle but in opposite phase.

  
\begin{figure}
\includegraphics [height=2.2364in,width=3.2396in]{ds1705f1.eps}\end{figure} Figure 1: Solar radius measurements obtained using the Calern Observatory astrolabe during the period 1975 to 1996
Others new solar astrolabe programs have been then developed from these new exciting results (Laclare et al. 1996; Leister & Benevides Soares 1990; Noël 1995; Sanchez et al. 1995). Several studies were also developed in order to analyze (Moussaoui et al. 1998; Delache et al. 1985; Gavryusev et al. 1994) and to valide the recorded data (Laclare et al. 1996; Irbah et al. 1994). For this purpose and to improve the astrolabe experiment, all effects which are able to cause variations or degradations of the solar data, are required to be studied.

The present work is a study of the instrumental and atmospheric turbulence effects to the contribution to diameter measurement errors when observing with a solar astrolabe. It is developed using a numerical simulation where the principal atmospheric parameters are introduced. The effect of each parameter is studied separately in order to evaluate its proper contribution to the global diameter error. Section 2 presents the simulation of solar images as observed at the astrolabe through the atmospheric turbulence. In the simulation, a fractal model is used to generate randomly perturbed wavefronts and therefore point spread functions (psf) of the whole atmosphere-instrument. In Sect. 3, we present the steps leading to the instant of the Sun transit by the small circle needed for the diameter measurement with the astrolabe. Finally, we expose and discuss the results obtained for the contribution of each atmospheric parameter to the error on the diameter estimation.


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