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.
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