Point-Spread-Function Engineering in MINFLUX: Optimality of Donut and Half-Moon Excitation Patterns

TL;DR

This paper develops a computational framework to identify optimal excitation patterns in MINFLUX super-resolution microscopy, confirming the donut shape's optimality and discovering new half-moon beam patterns that enhance localization precision.

Contribution

The work introduces a numerical and theoretical method to optimize PSF engineering in MINFLUX, revealing the optimality of donut beams and proposing new half-moon patterns for improved accuracy.

Findings

Donut beam is optimal under shape constraints.

Half-moon beams can double localization precision.

Framework enables efficient search for new beam patterns.

Abstract

Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the MINFLUX method achieves super-resolution by shaping the excitation point-spread function (PSF) to minimize the required photon flux for a given precision. Various beam shapes have recently been proposed to improve localization efficiency, yet their optimality remains an open question. In this work, we deploy a numerical and theoretical framework to determine optimal excitation patterns for MINFLUX. Such a computational approach allows us to search for new beam patterns in a fast and low-cost fashion, and to avoid time-consuming and expensive experimental explorations. We show that the conventional donut beam is a robust optimum when the excitation beams are all constrained to the same shape. Further, our PSF engineering framework yields two pairs of half-moon beams (orthogonal to each other) which can improve the theoretical localization precision by a factor of about two.