The Bragg and Fresnel scattering is realized by single crystals with e
lliptically-modulated surfaces that serve as point-to-point focusing l
enses for X rays. Analytical expressions for the focus characteristics
, namely: the ratio of peak intensity to background, focusing efficien
cy, and the focus width are derived. It is shown that the peak intensi
ty is proportional to the square of the total number of zones, while t
he focusing efficiency remains constant depending only on the Bragg sc
attering angle.