Analytic expressions are given for the on-axis intensity predicted by the Rayleigh–Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.
© 2003 Optical Society of America
Original Manuscript: January 22, 2003
Revised Manuscript: June 2, 2003
Manuscript Accepted: July 14, 2003
Published: November 1, 2003
Colin J. R. Sheppard and Peter Török, "Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number," J. Opt. Soc. Am. A 20, 2156-2162 (2003)