Lupo Cosmo, Huang Zixin, Kok Pieter
Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom.
Phys Rev Lett. 2020 Feb 28;124(8):080503. doi: 10.1103/PhysRevLett.124.080503.
We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent pointlike emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a passive linear interferometer feeds into an array of photodetectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the special case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.
我们解决了一个一般性问题，即通过成像确定处于任意空间构型的N个弱非相干点状发射器的三维位置。我们表明，一种结构化测量策略，其中无源线性干涉仪接入光探测器阵列，对于这个估计问题总是最优的，从它达到量子克拉美罗界的意义上来说。我们提供了一种明确构建最优干涉仪的方法。对于傍轴区域中一个和两个非相干发射器的特殊情况，还获得了关于量子费希尔信息以及达到该信息的最优干涉仪设计的进一步明确结果。这项工作为近来备受关注的通过非相干成像实现超分辨率现象提供了见解。我们的结果将在从荧光显微镜到恒星干涉测量等广泛的频率范围内找到广泛应用。
