提出了一种利用夏克-哈特曼波前传感器测量未知波前时确定其子孔径数目的新方法。首先将被测波前相位用傅里叶级数展开表示, 然后对展开表达式的复振幅进行贝塞尔展开, 并对它进行傅里叶变换计算出其远场光斑分布。分析表明, 波前相位频谱分量与远场光斑形态存在某种相互对应的关系, 可根据采样定理通过远场光斑的分布界限确定出夏克-哈特曼波前传感器的采样率。该方法为夏克-哈特曼传感器对未知波前进行测量时其子合理孔径数目的确定提供了理论依据, 有效避免了夏克-哈特曼传感器由于采样率不足而造成精度下降的问题, 结束了在确定夏克-哈特曼波前传感器的子孔径数目时只依靠经验的状态。

A method on how to decide the resolution of Shack-Hartmann sensor when it is used to measure an unknown incident wavefront is presented. The phase of incident wavefront can be according to Fourier progression, the complex amplitude of incident wavefront can be expanded according to Bessel progression, and then the distribution of intensity of far-field spot can be got through Fourier transform. The results indicate that the phase spectrum of incident wavefront have affiliation with the distribution of intensity of far-field spot. The resolution of Shack-Hartmann sensor can be decided through measuring the distribution of intensity of far-field spot. This method provides the theoretic support on the decision of the number of sub-aperture of Shack-Hartmann sensor. So the problem of the decrease in accuracy of Shack-Hartman sensor because of the lack of sub-apertures can be solved.