Scattered Light in Solar Images using Hankel Transforms
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**Session 59 -- Solar Surface and Corona**
*Oral presentation, Thursday, January 13, 10:15-11:45, Salon VI Room (Crystal Gateway)*

## [59.08] Scattered Light in Solar Images using Hankel Transforms

*S.R. Walton, G.A. Chapman, A.M. Cookson, D. Preminger (SFO/CSUN)*
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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