Easy spectrally tunable highly efficient X-ray backlighting schemes based on spherically bent crystals

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 10degrees and 22degrees, 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 9Angstrom a spatial resolution about 10 mum in a field of view of some square millimeters is achieved experimentally and confirmed by ray-tracing simulations.