Direct measurement of wavefunctions has attracted great interest and many different methods have been developed. However, the precision of current techniques is limited by the use of Fourier transform lenses. These measurements require to shear cut the part of particles with momentum $P=0$, which greatly restricts the efficiency and application of the approaches. Here, a method to directly measure 2D photonic wavefunctions is proposed and experimentally demonstrated by combining the momentum weak measurement technology and the zonal wavefront restoration algorithm. Both the Gaussian and Laguerre–Gaussian wavefunctions are experimentally well reconstructed. This method avoids using the Fourier lens and post selection on the momentum $P=0$. This is further applied to measure wavefronts with ultra‐high spatial frequency and achieve a pixel resolution, which is difficult for traditional Shack–Hartmann wavefront sensing technologies. This work extends the ability of quantum measurement techniques and will be useful for high‐resolution wavefront sensing.

中文翻译：

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通过动量弱测量实现光子波函数的带状重构

直接测量波函数引起了极大的兴趣，并且已经开发了许多不同的方法。但是，当前技术的精度受到傅立叶变换透镜的限制。这些测量需要剪切动量的颗粒部分$P=0$，这极大地限制了这些方法的效率和应用。在此，提出了一种直接测量二维光子波函数的方法，并结合动量弱测量技术和纬向波阵面恢复算法进行了实验验证。高斯波函数和拉盖尔－高斯波函数都在实验上得到了很好的重构。该方法避免使用傅立叶透镜和动量后选择$P=0$。该技术可进一步用于测量具有超高空间频率的波前并获得像素分辨率，这对于传统的Shack-Hartmann波前传感技术而言是困难的。这项工作扩展了量子测量技术的能力，将对高分辨率波前感测有用。