We used an approach based on the self-imaging property of gratings to fabricate high-resolution Fresnel zone plates (FZPs). Under certain conditions, the illumination of a parent ZP with a wideband EUV beam produces a radially oscillating intensity distribution with double the spatial frequency of the ZP. This intensity distribution is observed in a certain distance range, given by the local zone width, the focal length of the ZP, and the spectral bandwidth of the illuminating beam. This phenomenon has been used to lithographically record daughter ZPs that have approximately half the zone width, thus twice the resolution, of the parent ZP. FZPs with zone widths as low as 30nm have been fabricated in this way. Use of this technique in the extreme ultraviolet (EUV) region has the potential for high throughput production of FZPs and similar high-resolution diffraction optics with variable spatial frequency for the EUV and x-ray regions. © 2011 Optical Society of America.