论文标题
量子限制定位点对象与均匀明亮的磁盘的定位对象
Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk
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，即在理想的光子计数限制下，点源与已知中心和半径均匀明亮的磁盘的二维位置。我们介绍了背景亮度比的功能的QFI的扰动计算，也介绍了单光密度运算符的特征基础中QFI的数值确切计算。量子限制的相关问题，即估计小面积亮度孔在原本均匀的明亮磁盘中的位置，这是极性行星检测群落潜在兴趣的问题，也以孔区域和背景磁盘比率的能力进行扰动。然后，我们在三个单独的基础上对波前投影进行数值评估，包括Zernike，Fourier-Bessel和局部点源模式组成的波前投影，分别估算了两个问题的亮度孔中心的点源和亮度孔中心的两个位置坐标。通过将这些CRB与相应的量子限制的最小误差方差进行比较，通过反转QFI矩阵给出，以及与直接成像相关的CRB，我们评估了这些波前投影在执行此类估计中的最大效率。
We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the two-dimensional location of a point source against a uniformly bright disk of known center and radius in the ideal photon-counting limit. We present both a perturbative calculation of the QFI in powers of the background-to-source brightness ratio and a numerically exact calculation of the QFI in the eigen-basis of the one-photon density operator. A related problem of the quantum limit on estimating the location of a small-area brightness hole in an otherwise uniformly bright disk, a problem of potential interest to the extrasolar planet detection community, is also treated perturbatively in powers of the ratio of the areas of the hole and the background disk. We then numerically evaluate the Cramer-Rao lower bound (CRB) for wavefront projections in three separate bases, those comprised of Zernike, Fourier-Bessel and localized point-source modes, for unbiased estimation of the two position coordinates of the point source and of the brightness hole center, respectively, for the two problems. By comparing these CRBs with the corresponding quantum-limited minimum error variances, given by inverting the QFI matrix, and with the CRBs associated with direct imaging, we assess the maximum efficiency of these wavefront projections in performing such estimations.
