  We present a formalism of x-ray dynamical diffraction from volume diffractive
optics with large numerical aperture and high aspect ratio, in an analogy to
the Takagi-Taupin equations for strained single crystals. We derive a set of
basic equations for dynamical diffraction from volume diffractive optics, which
enable us to study the focusing property of these optics with various grating
profiles. We study volume diffractive optics that satisfy the Bragg condition
to various degrees, namely flat, tilted and wedged geometries, and derive the
curved geometries required for ultimate focusing. We show that the curved
geometries satisfy the Bragg condition everywhere and phase requirement for
point focusing, and effectively focus hard x-rays to a scale close to the
wavelength.
