X-ray refraction-based computer tomography imaging is a well-established method for nondestructive investigations of various objects. In order to perform the 3D reconstruction of the index of refraction, two or more raw computed tomography phase-contrast images are usually acquired and combined to retrieve the refraction map (i.e. differential phase) signal within the sample. We suggest an approximate method to extract the refraction signal, which uses a single raw phase-contrast image. This method, here applied to analyzer-based phase-contrast imaging, is employed to retrieve the index of refraction map of a biological sample. The achieved accuracy in distinguishing the different tissues is comparable with the non-approximated approach. The suggested procedure can be used for precise refraction computer tomography with the advantage of a reduction of at least a factor of two of both the acquisition time and the dose delivered to the sample with respect to any of the other algorithms in the literature.