• We will assume parallel illumination, even though there are reconstruction algorithms [Tuy 1983, Feldkamp 1984] for cone beam tomography where the beam diverges from a point source.

• We will assume that we start with images that provide a linear response to the projected object thickness t(x, y) along each viewing direction. In the case of absorption contrast transmission imaging, this can be done by calculating the optical density D(x, y) = - ln[I(x, y)/I0] = μt(x, y) as given by Eq. 3.83, with μ being the material's linear absorption coefficient (LAC) of Eq. 3.75. In phase contrast imaging, one may have to use phase unwrapping [Goldstein 1988, Volkov 2003] methods to first obtain a projection image which is linear with the projected object thickness since (see Fig. 3.17).

• We will assume that there is no spatial-frequency-dependent reduction in the contrast of image features as seen in a projection image. That is, we will assume that the modulation transfer function (MTF) is 1 at all frequencies u (see Section 4.4.7). One can always approach this condition by doing deconvolution (Section 4.4.8) on individual projection images before tomographic reconstruction, or building in an actual MTF estimate into optimization approaches (Section 8.2.1).

• We will assume that the first Born approximation applies (Section 3.3.4): we can approximate the wavefield that reaches a downstream plane in a 3D object as being essentially the same as the wavefield reaching an upstream plane.