Super-localisation of a point-like emitter in a resonant environment: Correction of the mirage effect

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-07-13 DOI:10.3934/ipi.2022054

Lorenzo Baldassari, A. Vanel, Pierre Millien

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引用次数: 0

Abstract

In this paper, we show that it is possible to overcome one of the fundamental limitations of super-resolution microscopy: the necessity to be in an optically homogeneous environment. Using recent modal approximation results from [10, 7], we show, as a proof of concept, that it is possible to recover the position of a single point-like emitter in a known resonant environment from far-field measurements, with a precision two orders of magnitude below the classical Rayleigh limit. The procedure does not involve solving any partial differential equation, is computationally light (optimisation in \begin{document}$ \mathbb{R}^d $\end{document} with \begin{document}$ d $\end{document} of the order of \begin{document}$ 10 $\end{document}) and is therefore suited for the recovery of a very large number of single emitters.

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谐振环境中点状发射器的超局部化：海市蜃楼效应的校正

在本文中，我们表明有可能克服超分辨率显微镜的一个基本限制：必须在光学均匀的环境中。使用[10，7]的最新模态近似结果，我们表明，作为概念证明，可以从远场测量中恢复已知谐振环境中单个点状发射器的位置，精度比经典瑞利极限低两个数量级。该程序不涉及求解任何偏微分方程，计算量很轻（在\begin｛document｝$\mathbb｛R｝^d$\end｛document｝中的优化为\begin{document｝$d$\eend｛document}的阶数为\begin{document}$10$\end{document}），因此适用于大量单个发射器的恢复。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.