Various methods for obtaining the solar ultraviolet limb-darkening profiles are investigated in terms of their accuracy and adaptability for use on electronic computers. The experimental data consist of a series of spectra in the wavelengths shorter than 3000 Å taken with a somewhat astigmatic spectrograph flown in an Aerobee rocket and a similar set of carbon-arc spectra obtained with the same spectrograph shortly before the flight. For our particular purpose, the densitometer tracings of these spectra are made at right angles to the direction of dispersion. Special attention is directed to the possibility of determining the instrumental astigmatism profiles from the carbon-arc spectra on the basis of assuming a rectangular form for the carbon-arc profile unbroadened by astigmatism. It is found that this method is quite satisfactory. In order to correct the observed limb-darkening profiles for instrumental broadening, the Fourier inversion method appears to be superior to the other methods considered, although the direct numerical evaluation can also be satisfactorily applied.
ANDREW A. LACIS and SATOSHI MATSUSHIMA, "Method of Correction for Instrumental Astigmatism to Determine the Center-to-Limb Variation of the Solar Ultraviolet Continuum," J. Opt. Soc. Am. 56, 1239-1243 (1966)