基于高阶关联函数的量子成像重建复合物体
Reconstructing compound objects by quantum imaging with higher-order correlation functions
摘要：
量子成像具有利用成像场的量子关联来提高物体重建精度的潜力。这对于需要低强度场到少光子水平的成像尤其重要。然而，量子成像通常会导致非线性估计问题。这些问题的复杂性随着描述对象的参数的数量而迅速增加。我们提出了一种方法来大大降低复杂性的广泛的一类问题。该方法的关键是将Fisher信息的特征与问题的参数局部性联系起来，并在每一步中只重构整个参数集的一个子集，从而建立高效的迭代推理方案。该迭代格式对参数总数是线性的。将该方案应用于量子近场成像，建立了相应的推理过程，实现了灰度复合透射物体的超分辨重建。该方法的功能与实验数据的测量获得的高阶关联函数与纠缠双光子和赝热光源的成像证明。通过分析测量的信息内容，可以预测最佳光子相关性的存在，从而在超分辨率机制中提供最佳图像分辨率。这一预测得到了实验证实。它还示出了如何从图像特征产生的估计偏差可能会大大提高分辨率。
英文摘要：
Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons. However, quantum imaging generally leads to nonlinear estimation problems. The complexity of these problems rapidly increases with the number of parameters describing the object. We suggest a way to drastically reduce the complexity for a wide class of problems. The key point of our approach is connecting the features of the Fisher information with the parametric locality of the problem, and building the efficient iterative inference scheme reconstructing only a subset of the whole set of parameters in each step. This iterative scheme is linear on the total number of parameters. This scheme is applied to quantum near-field imaging, the inference procedure is developed resulting in super-resolving reconstruction of grey compound transmission objects. The functionality of the method is demonstrated with experimental data obtained by measurements of higher-order correlation functions for imaging with entangled twin-photons and pseudo-thermal light sources. By analyzing the informational content of the measurement, it becomes possible to predict the existence of optimal photon correlations providing for the best image resolution in the super-resolution regime. This prediction is experimentally confirmed. It is also shown how an estimation bias stemming from image features may drastically improve the resolution.
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