Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory

Abstract

Abstract:In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM). 145-148 (1965). 6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento 9, 426-438 (1952). 7. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). 8. C. J. R. Sheppard, "Synthesis of filters for specified axial properties," J. Mod. Opt. 43, 525-536 (1996)

Shaping the focal field of radially/azimuthally polarized phase vortex with Zernike polynomials

“…Tight focusing behavior of polarized phase vortex beams [17,18] has been investigated to achieve sharp resolution [19,20], and to demonstrate spin-to-orbital angular momentum conversion [21], et al. In a previous publication [22] , we have demonstrated a method to generate elongated focal spot using Zernike polynomials. Zernike polynomials forms a complete and orthogonal set of polynomials on a unit circle, which form an ideal set to study the pupil engineering of normally circularly apertured optical imaging system.…”

“…By precalculating the focal fields of Zernike polynomials, we can optimise the focal field by only optimising the Zernike coefficients. However, in paper [22], scalar diffraction integral is considered, thus neither polarization nor phase vortices are investigated. In this paper, we first study the focal field properties of radially/azimuthally polarized Zernike polynomials.…”