In the first part of this article a more general DEI equation was derived using simple concepts. Not only does the new DEI equation explain all the problems that can be done by the DEI equation proposed by Chapman, but also explains the problem that can not be explained with the old DEI equation, such as the noise background caused by the small angle scattering reflected by the analyzer. In the second part, a DEI-PI-CT formula has been proposed and the contour contrast caused by the extinction of refraction beam has been qualitatively explained, and then based on the work of Ando's group two formulae of refraction CT with DEI method has been proposed. Combining one refraction CT formula proposed by Dilmanian with the two refraction CT formulae proposed by us, the whole framework of CT algorithm can be made to reconstruct three components of the gradient of refractive index.
