运用张量分析方法把轴对称系统中的空间频率域的柯林斯公式推广到一般的非轴对称光学系统,并推导了在空间频率域中适用于非轴对称光学系统的张量ABCD定律。空间频率域中的柯林斯公式和张量ABCD定律直接给出了像散光束的空间傅里叶频谱的传输规律。它们在处理与空间频谱有关的问题,如空间滤波、成像系统的传递函数、复杂像散高斯光束在自由空间的传输等问题时更为简便。

The Collins formula in spatial frequency domain is generalized into axially nonsymmetrical optical system in terms of tensor analysis method. Based on this formula, the tensor ABCD law in spatial frequency domain is derived. The Collins formula and tensor ABCD law in spatial frequency domain provide the relation between the input spatial Fourier spectrum and the output spectrum directly. They have advantages in treating the problems concerned with spatial Fourier spectrum, such as spatial frequency filtering, optical transfer function of imaging systems and the propagation of general astigmatic Gaussian beam in free space, and so on.