On the use of total brightness measurements for tomography of the solar corona

A time series of polarized white light coronagraph images may be used to make a tomographic estimate of the electron density (N_e) in three dimensions, as has been demonstrated by several authors. This technique has come to be known as solar rotational tomography (SRI). SRT relies on the fact that the polarized brightness (pB) is dominated by the electron-scattered K corona. In contrast, the total brightness contains a large contribution from the dust-scattered F-corona with some signal from the K corona. The K-corona contribution to the total brightness (B) is of interest because the Thomson scattering has different angular dependences for the polarized and unpolarized components. This difference in angular dependence in principle allows one to exploit total brightness measurements as a source of independent information for SRT. In this paper the problem of making optimal tomographic estimates of N_e using both total and polarized brightness data is considered under the assumption that the F-corona contribution can be determined with a known level of precision. Formulae for the reconstructions and the likely errors are given in terms of the singular value decomposition of the weighted measurement operators. It is shown that in order for the total brightness measurements to be useful for SRT, the process of removing the F-corona contribution must be almost perfect in the sense that it contributes uncertainty that is not much greater than the measurement noise in the polarized images. This result holds at heights below roughly 15 solar radii, where the F corona is almost completely unpolarized. 2005. The American Astronomical Society. All rights reserved.