A maskless, extreme ultraviolet (EUV) lithography scanner uses an array of microlenses, such as binary-optic, zone-plate lenses, to focus EUV radiation onto an array of focus spots (e.g. about 2 million spots), which are imaged through projection optics (e.g., two EUV mirrors) onto a writing surface (e.g., at 6× reduction, numerical aperture 0.55). The surface is scanned while the spots are modulated to form a high-resolution, digitally synthesized exposure image. The projection system includes a diffractive mirror, which operates in combination with the microlenses to achieve point imaging performance substantially free of geometric and chromatic aberration. Similarly, a holographic EUV lithography stepper can use a diffractive photomask in conjunction with a diffractive projection mirror to achieve substantially aberration-free, full-field imaging performance for high-throughput, mask-projection lithography. Maskless and holographic EUV lithography can both be implemented at the industry-standard 13.5-nm wavelength, and could potentially be adapted for operation at a 6.7-nm wavelength.