In single-pixel imaging or computational ghost imaging, the measurement matrix has a great impact on the performance of the imaging system, because it involves modulation of the optical signal and image reconstruction. The measurement matrix reported in the existing literatures is first binarized and then loaded onto the digital micro-mirror device (DMD) for optical modulation, that is, each pixel can only be modulated into on-off states. In this paper, we propose a digital grayscale modulation method for more efficient compressive sampling. On the basis of this, we demonstrate a single photon compressive imaging system. A control and counting circuit, based on field-programmable gate array (FPGA), is developed to control DMD to conduct digital grayscale modulation and count single-photon pulse output from the photomultiplier tube (PMT) simultaneously. The experimental results show that the imaging reconstruction quality can be improved by increasing the sparsity ratio properly and compressive sampling ratio (SR) of these gray-scale matrices. However, when the compressive SR and sparsity ratio are increased appropriately to a certain value, the reconstruction quality is usually saturated, and the imaging reconstruction quality of the digital grayscale modulation is better than that of binary modulation.

在单像素成像或计算重影成像中，测量矩阵对成像系统的性能影响很大，因为它涉及光信号的调制和图像重建。现有文献中报道的测量矩阵首先进行二值化，然后加载到数字微镜器件（DMD）上进行光学调制，也就是说，每个像素只能被调制为开-关状态。在本文中，我们提出了一种用于更有效压缩采样的数字灰度调制方法。在此基础上，我们演示了一个单光子压缩成像系统。基于现场可编程门阵列（FPGA）的控制和计数电路，开发用于控制DMD进行数字灰度调制并同时计数从光电倍增管（PMT）输出的单光子脉冲。实验结果表明，通过适当提高这些灰度矩阵的稀疏比和压缩采样率（SR），可以提高成像重建质量。然而，当压缩SR和稀疏比适当地增加到一定值时，重建质量通常饱和，并且数字灰度调制的图像重建质量优于二进制调制的图像重建质量。