In order to harness diffractive neural networks (DNNs) for tasks that better align with real-world computer vision requirements, the incorporation of gray scale is essential. Currently, DNNs are not powerful enough to accomplish gray-scale image processing tasks due to limitations in their expressive power. In our work, we elucidate the relationship between the improvement in the expressive power of DNNs and the increase in the number of phase modulation layers, as well as the optimization of the Fresnel number, which can describe the diffraction process. To demonstrate this point, we numerically trained a double-layer DNN, addressing the prerequisites for intensity-based gray-scale image processing. Furthermore, we experimentally constructed this double-layer DNN based on digital micromirror devices and spatial light modulators, achieving eight-level intensity-based gray-scale image classification for the MNIST and Fashion-MNIST data sets. This optical system achieved the maximum accuracies of 95.10% and 80.61%, respectively.