We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precision focusing, axial hyperresolution, or high focal depth.
© 1994 Optical Society of America
Original Manuscript: January 7, 1993
Revised Manuscript: August 23, 1993
Published: April 10, 1994
Manuel Martínez-Corral, Pedro Andrés, and Jorge Ojeda-Castañeda, "On-axis diffractional behavior of two-dimensional pupils," Appl. Opt. 33, 2223-2229 (1994)