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We have been investigating the scattered light properties of the San Fernando Observatory (SFO) Cartesian Full Disk Telescope (CFDT). Recently, Toner and Jeffries (1993, Ap. J. 415 , 852) have published a technique for the accurate determination of the solar limb position, based on the Hankel transform of a radial solar profile. They show that the Hankel transform of the observed solar limb profile yields a seeing-independent determination of the solar limb position and limb darkening profile. In principle, the ratio of the transform of the observed profile to that of the model, polynomial, solar limb darkening would then be the modulation transfer function (MTF) of the atmosphere and telescope. In practice, as with all such ratios of an observed power spectrum to an analytic one, the noise at high spatial frequencies makes the division difficult. We have taken a different approach. Using observed limb profiles from the SFO CFDT, we do a non-linear least-squares fit of the observed profile to the convolution of a model limb darkening profile and a model MTF. The model limb darkening is an expansion in orthonormal Legendre polynomials in $\mu$ rather than simple powers of $\mu$, as orthnormal polynomials have many desirable numerical features. The model MTF is a sum of short-range (typically Gaussian) and long-range (typically Lorentzian) parts (Lawrence, Chapman, Herzog, and Shelton 1985, Ap. J. 292 , 297). We will present results from these model fits and comment on their robustness.
We gratefully acknowledge Eric Hansen of Dartmouth College, who supplied us with a copy of his Hankel transform code. This work has been partially supported by NSF grant ATM-9115111 and NASA grants NAGW-2770 and NAGW-3017.
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