Peng Sun, Jin Guo, Tingfeng Wang
J Opt Soc Am A Opt Image Sci Vis. 2013 Jul 1;30(7):1381-6. doi: 10.1364/JOSAA.30.001381.
Based on the generalized Huygens-Fresnel diffraction integral (Collins' formula), the propagation equation of Hermite-Gauss beams through a complex optical system with a limiting aperture is derived. The elements of the optical system may be all those characterized by an ABCD ray-transfer matrix, as well as any kind of apertures represented by complex transmittance functions. To obtain the analytical expression, we expand the aperture transmittance function into a finite sum of complex Gaussian functions. Thus the limiting aperture is expressed as a superposition of a series of Gaussian-shaped limiting apertures. The advantage of this treatment is that we can treat almost all kinds of apertures in theory. As application, we define the width of the beam and the focal plane using an encircled-energy criterion and calculate the intensity distribution of Hermite-Gauss beams at the actual focus of an aperture lens.
基于广义惠更斯-菲涅耳衍射积分（柯林斯公式），推导了厄米-高斯光束通过具有有限孔径的复杂光学系统的传输方程。光学系统的元件可以是所有由ABCD光线传输矩阵表征的元件，以及由复透射率函数表示的任何类型的孔径。为了得到解析表达式，我们将孔径透射率函数展开为复高斯函数的有限和。因此，有限孔径被表示为一系列高斯形有限孔径的叠加。这种处理方法的优点是，理论上我们可以处理几乎所有类型的孔径。作为应用，我们使用环围能量准则定义光束宽度和焦平面，并计算厄米-高斯光束在孔径透镜实际焦点处的强度分布。
