Grating interferometric reconstruction in tomography: some considerations

The concept of reconstruction of an object by a grating interferometer1 is basically related to tomography. As an imaging device, the grating in terferometer images each Fourier component of each object slice onto a specific imaging plane. Imaging different object slices is akin to forming different projections at different angles in either the backprojection or the filtered backprojection processes, and imaging the different Fourier components of each object slice is akin to the Fourier decomposition in the Fourier reconstruction process of conventional tomography. The method of grating interferometric reconstruction which combines these two processes is essentially related to the diffraction tomography if both of them are within Born and Rytov’s approximation. Computational analysis and experiment both demonstrate that the fringe visibility distribution along the z axis is of the form sinc2z, centered at the localization plane. The curve of fringe visibility is also sinc2R shaped, where R is the radius of the light source. In accordance with these properties of grating imaging, we may define the depth of field of the fringes as the distance from the peak to the first zero of the sinc2 function, thereby obtaining the expression ∓ L / [ π R ( f + f n ) ] , where L is the distance between the light source and collimating lens. From this point of view, the expressions for the resolution of the object in the z direction and the resolution of the frequency components is readily derived. The optimal sampling spacing is also considered.