On the Sharpeming of Observational Data with Special Application to the Darkening of the Solar Limb

Abstract

Numerical observations are sometimes blurred by convolution with some known scattering function, and it is desired to sharpen them so as to obtain the numbers that would have been observed in the absence of the blurring. It is suggested that a method of doing this by Fourier transformation has marked advantages. Although the method requires rather more arithmetical operations than are in principle necessary, the computation of the Fourier transforms on Lipson-Beevers strips so simplifies these operations that the method is economical. Moreover, when the calculation is made in this way, the effect of errors in the data is apparent both during the work and in the final result. These errors prevent complete sharpening, but a degree of sharpening can be chosen which minimizes the sum of the systematic and random differences between the reconstruction and the true distribution. This optimum sharpening depends on the statistical properties of the errors, and it is therefore suggested that in future work these properties should be measured in order that the required sharpening can be determined uniquely. The brightness near the solar limb is recalculated by the suggested method from the results of the Göttingen measurements at the partial eclipse of 1949 April 28. It appears that photoelectric measures of brightness distributions are preferable to photographic determinations.