  Diffraction tomography is an inverse scattering technique used to reconstruct
the spatial distribution of the material properties of a weakly scattering
object. The object is exposed to radiation, typically light or ultrasound, and
the scattered waves induced from different incident field angles are recorded.
In conventional diffraction tomography, the incident wave is assumed to be a
monochromatic plane wave, an unrealistic simplification in practical imaging
scenarios. In this article, we extend conventional diffraction tomography by
introducing the concept of customized illumination scenarios, with a pronounced
emphasis on imaging with focused beams. We present a new forward model that
incorporates a generalized incident field and extends the classical Fourier
diffraction theorem to the use of this incident field. This yields a new
two-step reconstruction process which we comprehensively evaluate through
numerical experiments.
