论文标题
量子限制在一个和二维中扩展源的超级分辨率
Quantum Limited Superresolution of Extended Sources in One and Two Dimensions
论文作者
论文摘要
我们计算量子渔民信息（QFI），用于使用圆形成像光圈，均匀的明亮不一致的线源的长度，具有固定的中点和带有固定中心的均匀明亮不相互不相互不相互的磁盘形源的半径。中心线段上的pr酸球形波形（PSWFS）及其在中心磁盘上的广义版本提供了计算单光密度运算符的特征状态和特征值的相应碱基，我们随后从中计算出两个源的空间参数的QFI。 Zernike多项式提供了一个很好的集合来投射完整的源波前，并且这种经典的波前投影数据可以实现每种情况下限制的量子有限估计误差。随后，我们概括了我们使用与PSWF密切相关的一定类别的Bessel傅立叶函数来分析任意亮度分布和形状源的方法。我们通过计算QFI来估计均匀明亮，中心椭圆盘的主要轴的长度来说明一般方法。
We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the length of a uniformly bright incoherent line source with a fixed mid-point and the radius of a uniformly bright incoherent disk shaped source with a fixed center. Prolate spheroidal wavefunctions (PSWFs) on a centered line segment and its generalized version on a centered disk furnish the respective bases for computing the eigenstates and eigenvalues of the one-photon density operator, from which we subsequently calculate QFI with respect to the spatial parameters of the two sources. Zernike polynomials provide a good set into which to project the full source wavefront, and such classical wavefront projection data can realize quantum limited estimation error bound in each case. We subsequently generalize our approach to analyze sources of arbitrary brightness distributions and shapes using a certain class of Bessel Fourier functions that are closely related to the PSWFs. We illustrate the general approach by computing QFI for estimating the lengths of the principal axes of a uniformly bright, centered elliptical disk.
