We have derived a set of equations for beam waist at lens focus as a function of variable spot size and demonstrated their physical validity. The derived equations are useful for the estimation of the beam waist size of high peak power lasers focused with high numerical aperture lenses and for spot size measurement of long-range collimated Gaussian beams for several meters. We have described an indirect method to estimate the high peak power focused laser beam waist. The same treatment is extended to the Gaussian vortex beam for estimating its parameters at the beam waist. These results can be useful in the focused Gaussian beam and Gaussian vortex beam applications.

中文翻译：

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高峰值功率激光器的束腰测量方程

我们推导出了一组透镜焦点处的光束腰作为可变光斑大小的函数的方程，并证明了它们的物理有效性。导出的方程可用于估计用高数值孔径透镜聚焦的高峰值功率激光器的束腰尺寸，以及用于几米长的准直高斯光束的光斑尺寸测量。我们已经描述了一种估计高峰值功率聚焦激光束腰的间接方法。相同的处理扩展到高斯涡旋光束，以估计其在光束腰部的参数。这些结果可用于聚焦高斯光束和高斯涡旋光束应用。