Manipulating the Point Spread Function of Light to Increase Quantum Limited Estimation Accuracy for Bio-Medical Applications

确定性和随机超分辨率技术可以定期实现远低于20 nm的分辨率。然而，这只能通过对荧光团发射的复杂控制来实现，并且它既耗时又有侵入性，因为超分辨率假设可以独立分辨的单个发射器。尽管如此，仍有一些情况下，人们希望定位同时发射的荧光团，这些荧光团太近而无法单独分辨。这部分是由于在确定未解决的集群中同时排放者的数目方面取得了进展。最初，我们只限于两个相同但不相干的来源。在常规强度成像中，两个点状源彼此越接近，估计这些源的位置就变得越困难。Tsang等人的工作表明，值得注意的是，这不一定是这样的：通过捕获成像系统中的相位信息，可以从辐射中提取的源的分离的信息量不取决于分离本身，只要发射器是不相干的。不幸的是，这种最佳方案的相应实现是繁琐的。它们涉及不适合显微镜的干涉测量安排，因为两个源的质心的位置需要事先知道，这在生物成像中是罕见的。作为一个实际的折衷方案，Paúr等人发现，将成像系统的点扩散函数（PSF）成形为强度为零，这是一种相对更容易的操作，可以显着改善分离的量子限制估计。虽然这种技术的分辨能力在短距离下仍然下降到零，但缩放比典型的高斯点扩散函数成像有利得多。虽然Paúr等人的原始工作集中在一维演示上，但我们对二维情况感兴趣，其中发射器之间的分离方向是先验未知的。通过操纵辐射光的相位，使得点扩散函数具有暗环，我们已经在分析和数值上示出了两个荧光团的分离可以被估计到比直接成像更高的精度。一个原理验证实验正在建设中，以证实这些预测。

Deterministic and Stochastic Super-Resolution techniques can regularly achieve resolutions well below 20nm. However, this is only achieved via sophisticated control of the emission of fluorophores, and it is both time-consuming and invasive because super-resolution assumes individual emitters that can be resolved independently. There are nonetheless scenarios where one would like to localise simultaneously emitting fluorophores that are too closed to be individually resolved. This is in part due to progress made in the determination of the number of simultaneous emitters in unresolved clusters. Initially we have restricted ourselves to two identical but incoherent sources. In conventional intensity imaging, estimating the positions of two point-like sources becomes harder the closer these sources are to each other. Work by Tsang et al showed that remarkably, this need not be the case: by capturing phase information in the imaging system, the amount of information on the separation of the sources that can be extracted from the radiation does not depend on the separation itself, provided the emitters are incoherent. Unfortunately, the corresponding implementations of such optimum scheme are cumbersome. They involve interferometric arrangements that are ill-suited to microscopy because the position of the centre of mass of the two sources would need to be known a priori, a rare occurrence in bio-imaging. As a practical compromise, Paúr et al found that shaping the point spread function (PSF) of the imaging system such that it exhibits a zero of intensity, a comparatively easier operation, significantly improves the quantum-limited estimation of the separation. While the resolving power of this technique does still drop to zero at short distances, the scaling is much more favourable than imaging with a typical Gaussian point spread function. While the original work of Paúr et al focused on a one-dimensional demonstration, we are interested in the two-dimensional case, where the direction of separation between the emitters is unknown a priori. By manipulating the phase of the radiated light such that the point spread function has a dark ring, we have shown analytically and numerically that the separation of two fluorophores can be estimate to an accuracy greater than direct imaging. A proof-of-principle experiment is under construction to confirm these predictions.