Point-Spread-Function Engineering in MINFLUX: Optimality of Donut and Half-Moon Excitation Patterns
Yan Liu, Doctoral Student at EPFL

Meeting • 2024-12-10

Abstract
Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. 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 based on the Cramer-Rao bound of the detection precision of the system to determine optimal excitation patterns for MINFLUX. Our framework is written in PyTorch to leverage its powerful auto-differentiation functionality. The performance is further enhanced by our custom FFT functions based on the chirp Z-transform to accurately compute the photon propagation. 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. Finally, we provide two mathematical results which relate the computational framework to properties of the electric field to offer insights and intuitions on the optimal beam shapes.