New easy spectrally tunable backlighting schemes based on a
spherically bent crystal are considered. Contrary to traditional
backlighting scheme, in which the investigated objects should be placed
between the backlighter and the crystal, for the considered schemes an
object is placed downstream of the crystal, before the tangential or
after the sagittal focus and an image of the object is recorded at the
distance from the object corresponding to the needed magnification. The
magnification is defined by the ratio of the distances from the
sagittal focus to the detector and from the object to the sagittal
focus. A ray-tracing modeling and experimental images of test meshes,
obtained at incidence angles of the backlighter radiation of 10°
and 22°, are presented. It is demonstrated that a simple linear
transformation of the obtained astigmatic images allows reconstructing
them as a stigmatic with an accuracy of 5–15%. For the spectral
range around 9 Å a spatial resolution about 10 μm in a field
of view of some square millimeters is achieved experimentally and
confirmed by ray-tracing simulations.