Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography.

The unique tomographic imaging method based on refractive effects that was recently developed by Maksimenko et al. [Appl. Phys. Lett. 86, 124105 (2005)] exhibits an excellent imaging property in the hard-x-ray region for phase objects such as soft materials and biological samples. However, there seems to have been little consideration of the physical aspects of the underlying imaging principles. Also, as the method is similar to diffraction-enhanced-imaging (DEI)-based computed tomography (CT), the difference between these two methodologies has not been made clear. We theoretically consider the imaging principles starting from the measurement process to the reconstruction procedures from the viewpoint of geometrical optics and then clarify their difference in relationship to the physical quantities to be depicted. The major feature of this novel method is the in-plane two-dimensional vector-field reconstruction of the refractive-index gradient in an object, while DEI CT obtains the out-of-plane scalar-field gradient component. In other words, the novel method and DEI CT present the transverse and the longitudinal components, respectively, of the three-dimensional vector fields of the gradient refractive index. Therefore they can be considered complementary to each other.