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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。
According to the reciprocal relation between the scalar Helmholtz equation and the stationary Schrödinger equation, it is pointed out that the process of focusing the plane wave through the lens is equivalent to the conversion of the photon state function from the coordinate surface image to the momentum surface image. Due to the limited aperture, the photon can not reproduce accurately in the momentum space state function, resulting in the existence of a quantum limit in the spatial beam alignment accuracy. Under quantum confinement, the spatial beam alignment accuracy is about 26% of the diffraction limit angle, which depends mainly on the wavelength of the light and the acceptance lens aperture, regardless of the focal length of the lens. The centroid tracking of the photon at the focal plane shows that the ideal centroid limit achievable by the angular accuracy is only slightly better than the diffraction limit resolution and the residual error is still 3.24 times the quantum limit.