Fundamental uncertainty limit of optical flow velocimetry according to Heisenberg's uncertainty principle.
Fundamental uncertainty limit of optical flow velocimetry according to Heisenberg's uncertainty principle.
复制标题
根据海森堡不确定性原理的光流测速的基本不确定性极限。
DOI：
10.1364/ao.55.008787
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发表时间：
2016
期刊：
影响因子：
1.9
通讯作者：
A. Fischer
中科院分区：
文献类型：
--
作者：
A. Fischer
光学流速测量对于理解流体的复杂行为是重要的。虽然存在各种各样的方法，但它们要么基于多普勒测量原理，要么基于飞行时间测量原理。多普勒测速法评估在移动粒子处散射的光的速度依赖性频移，而飞行时间测速法评估每个时间间隔的散射粒子的行进距离。关于实现最小测量不确定性的目标，尚不清楚是否有一个原则可以实现较低的不确定性，或者两个原则是否可以实现相等的不确定性。为此，自然的，基本的不确定性限制根据海森堡的不确定性原理推导出多普勒和飞行时间测量原理，分别。所获得的速度不确定性的极限在性质上是相同的，例如，速度的绝对值与32的幂成正比，而与散射光功率的平方根成间接正比。因此，由于光子的量子力学行为，这两种测量原理在基本不确定性极限方面具有相同的潜力。这个基本极限实际上可以用多普勒或飞行时间方法达到（至少是渐近地），因为主导光子散粒噪声的各自的克拉美-拉奥界限（被建模为白色泊松噪声）与海森堡不确定性原理的结论相同。
Optical flow velocity measurements are important for understanding the complex behavior of flows. Although a huge variety of methods exist, they are either based on a Doppler or a time-of-flight measurement principle. Doppler velocimetry evaluates the velocity-dependent frequency shift of light scattered at a moving particle, whereas time-of-flight velocimetry evaluates the traveled distance of a scattering particle per time interval. Regarding the aim of achieving a minimal measurement uncertainty, it is unclear if one principle allows to achieve lower uncertainties or if both principles can achieve equal uncertainties. For this reason, the natural, fundamental uncertainty limit according to Heisenberg's uncertainty principle is derived for Doppler and time-of-flight measurement principles, respectively. The obtained limits of the velocity uncertainty are qualitatively identical showing, e.g., a direct proportionality for the absolute value of the velocity to the power of 32 and an indirect proportionality to the square root of the scattered light power. Hence, both measurement principles have identical potentials regarding the fundamental uncertainty limit due to the quantum mechanical behavior of photons. This fundamental limit can be attained (at least asymptotically) in reality either with Doppler or time-of-flight methods, because the respective Cramér-Rao bounds for dominating photon shot noise, which is modeled as white Poissonian noise, are identical with the conclusions from Heisenberg's uncertainty principle.
影响因子：
35
作者：
Aasi, J.;Abadie, J.;Zweizig, J.
通讯作者：
Zweizig, J.