  Chromatic properties of the multi-prism and prism-array X-ray lenses (MPL and
PAL) can potentially be utilized for efficient energy filtering and dose
reduction in mammography. The line-shaped foci of the lenses are optimal for
coupling to photon-counting silicon strip detectors in a scanning system. A
theoretical model was developed and used to investigate the benefit of two
lenses compared with an absorption-filtered reference system. The dose
reduction of the MPL filter was ~15% compared with the reference system at
matching scan time, and the spatial resolution was higher. The dose of the
PAL-filtered system was found to be ~20% lower than for the reference system at
equal scan time and resolution, and only ~20% higher than for a monochromatic
beam. An investigation of some practical issues remains, including the
feasibility of brilliant-enough X-ray sources and manufacturing of a polymer
PAL.
