空间远场光束对准精度的量子极限

Quantum Limits of Far-Field Beam Pointing Accuracy in Space

根据标量亥姆霍兹方程和定态薛定谔方程的对等关系,指出平面波经透镜聚焦过程等同于光子态函数由坐标表象向动量表象转换的过程。受有限孔径的影响,光子在动量空间态函数无法精确再现,导致空间光束对准精度的存在一个量子极限。在量子极限条件下,空间光束对准精度大约是衍射极限角的26%,主要取决于光波长和接收透镜孔径,与透镜焦距无关。就光子在焦平面位置进行质心跟踪,测角精度所能达到的理想质心极限只略优于衍射极限分辨率,残留误差仍然是量子极限的3.24倍。

Based on the equality of Helmholtz equation and stationary state Schrdinger equation,focalizing plane wave is just the transformation of state function of a photonic from coordinate representation to momentum representation.However,as a result of limited aperture size,the state function in the momentum space could not be reconstructed exactly,which leads to the quantum precision limits of alignment.Under the conditions of quantum limits,the precision is approximately 26% of the diffraction limited angle.It depends on the aperture size only and is irrespective to the focal length.The centroid method on the focal plane could only reach the precision close to the diffraction limited angle.The root mean square of remained errors is still 3.24 times of the quantum limits.