By apodizing the cells of a zone plate and changing the opening ratio, it is possible to shape the relative power spectrum of its foci. We describe a novel procedure that leads to an analytical formula for shaping the focus power spectrum by using apodizers expressible as the Legendre series; these act on cells of arbitrary opening ratio. Our general result is used to design zone plates that have missing foci and to discuss a synthesis procedure using apodizers with various opening ratios. Our applications can also be used for shaping the power spectrum of 1-D gratings.
© 1990 Optical Society of America
Original Manuscript: July 10, 1989
Published: March 20, 1990
Jorge Ojeda-Castaneda, Pedro Andres, and Manuel Martinez-Corral, "Zone plates with cells apodized by Legendre profiles," Appl. Opt. 29, 1299-1303 (1990)