达到被动成像的量子极限
Attaining the quantum limit of passive imaging
摘要：
我们考虑的问题，其中一个相机的任务是确定两个假设之一：第一个与非相干辐射准单色点源，第二个与两个相同的紧密间隔的点源。我们给出了在任一假设下，在积分时间内收集的光子总数被假定为相同的。对于一个源的假设，该源被认为是轴上沿视线和两个源的假设，我们给自己的先验知识的角度分离的源，他们被假定为是相同的，并位于对称离轴。Helstrom在1973年研究了这个问题，他评估了使用次优光学测量可实现的错误概率，并没有指定结构化实现。在本文中，我们评估的量子的最小误差概率的下限，可实现的任何物理上可实现的接收器，这是指数紧的制度，积分时间是高的。我们给出了一个明确的结构化接收器，分离三个正交的空间模式的孔径场，然后由量子噪声有限的时间分辨光子测量，并表明，这实现了量子的Bundoff界。换句话说，我们的模式分辨探测器的经典的Bundoff界完全匹配这个问题的量子Bundoff界。最后，我们评估了经典的Beschoff界的错误概率实现使用一个理想的焦平面阵列-信号散粒噪声限制连续光子检测接收器与无限多的无限微小的像素-和量化其性能差距与量子极限。
英文摘要：
We consider the problem, where a camera is tasked with determining one of two hypotheses: first with an incoherently-radiating quasi-monochromatic point source and the second with two identical closely spaced point sources. We are given that the total number of photons collected over an integration time is assumed to be the same under either hypothesis. For the one-source hypothesis, the source is taken to be on-axis along the line of sight and for the two-source hypothesis, we give ourselves the prior knowledge of the angular separation of the sources, and they are assumed to be identical and located symmetrically off-axis. This problem was studied by Helstrom in 1973, who evaluated the probability of error achievable using a sub-optimal optical measurement, with an unspecified structured realization. In this paper, we evaluate the quantum Chernoff bound, a lower bound on the minimum probability of error achievable by any physically-realizable receiver, which is exponentially tight in the regime that the integration time is high. We give an explicit structured receiver that separates three orthogonal spatial modes of the aperture field followed by quantum-noise-limited time-resolved photon measurement and show that this achieves the quantum Chernoff bound. In other words, the classical Chernoff bound of our mode-resolved detector exactly matches the quantum Chernoff bound for this problem. Finally, we evaluate the classical Chernoff bound on the error probability achievable using an ideal focal plane array---a signal shot-noise limited continuum photon-detection receiver with infinitely many infinitesimally-tiny pixels---and quantify its performance gap with the quantum limit.
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