title: On-axis diffractional behavior of two-dimensional pupils.
abstract: 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.
authors.forename: M
authors.initials: M
authors.lastname: Martínez-Corral
authors.forename: P
authors.initials: P
authors.lastname: Andrés
authors.forename: J
authors.initials: J
authors.lastname: Ojeda-Castañeda