Design optimization of one-dimensional aberration-free x-ray gradually focusing lenses

In our previous work, we proposed a new design method for an aberration-free x-ray refractive focusing lens based on an ideal Cartesian oval shape to solve the aberration problem in x-ray compound refractive focusing. In this paper, we propose an optimization method for this new lens. By reducing the aperture of each lens, we achieve the objective of increasing the effective aperture and improving the focusing performance of the lens. The simulation of the beam propagation method shows that the focusing performance of the optimized lenses is better in compound refractive lens shape but worse in the kinoform shape. This is different from the results obtained with the conventional kinoform lens. After further comparison, we found that this is because the step height of the kinoform lens is small when the lens aperture is very small, resulting in a strong diffraction effect that weakens the focusing performance of the lens. Further modifications to the structure of the kinoform lens are needed to improve this phenomenon.