  Diffractive lenses fabricated by lithographic methods are one of the most
popular image forming optics in the x-ray regime. Most commonly, binary
diffractive optics, such as Fresnel zone plates are used due to their ability
to focus at high resolution and to manipulate the x-ray wavefront. We report
here a binary zone plate design strategy to form arbitrary illuminations for
coherent multiplexing, structured illumination, and wavefront shaping
experiments. Given a desired illumination, we adjust the duty cycle, harmonic
order, and zone placement to vary both the amplitude and phase of the wavefront
at the lens. This enables the binary lithographic pattern to generate arbitrary
structured illumination optimized for a variety of applications such as
holography, interferometry, ptychography, imaging, and others.
