Abstract To well reveal the imaging mechanism of ghost imaging (GI) with thermal light, we propose a probability theory using more general assumptions than existing theoretical explanations that the reference patterns obey an arbitrary identical distribution and the objects are of grayscale. It is not limited to a specific correlation function, even multi-functional variants of reference patterns can be used in correlation calculation. We have proven in both theory and experiments that the reconstruction means are linear transformations of original object's gray values and the probabilities of recovered pixel values in the pixel region of the same original gray value follow a Gaussian distribution, whose variance explains the appearance of reconstruction noise. We also derive the relationship between pattern variance and contrast-to-noise ratio under noisy conditions, which will be instructive for better pattern construction. This work will deepen the understanding of GI and enrich intensity correlation forms.

中文翻译：

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热光鬼成像强度相关的概率论

摘要 为了更好地揭示热光鬼成像（GI）的成像机制，我们提出了一种概率理论，该理论使用比现有理论解释更普遍的假设，即参考图案服从任意相同的分布并且物体是灰度的。它不限于特定的相关函数，甚至可以在相关计算中使用参考模式的多功能变体。我们在理论和实验中都证明了重构手段是原始对象灰度值的线性变换，相同原始灰度值的像素区域中恢复像素值的概率服从高斯分布，其方差解释了重构噪声的出现. 我们还推导出了噪声条件下模式方差与对比度噪声比之间的关系，这对于更好的模式构建具有指导意义。这项工作将加深对GI的理解，丰富强度相关形式。