Use of combined zone plates as imaging optics for hard x-rays

We have carried out modeling of an image formation in hard x-ray coherent radiation using a Rayleigh-Sommerfeld integral. Combined zone plates have been used to form the image.
The resolution of the combined zone plate was numerically shown to increase up to 10 times (equaling 20 nm) when compared with a traditional Fresnel zone plate without any changes of the outermost zone width (205 nm). The zone plate consisted of 6 areas operating in 1, 3, 5, 7, 9 and 11 diffraction orders. An efficiency improvement of 42% has been numerically achieved in contrast to a traditional Fresnel zone plate used in the third diffraction order. For the combined zone plate, the efficiency of 3.7% has been achieved.