A Statistical Model for Imaging Systems

Abstract: The behavior of photons is controlled by quantum mechanics, not as deterministic as classical optics shows. To this end, we defined a new statistic $Z$, which is equal to the variance minus the expectation or mean. Then, we established a statistical model for imaging systems and obtained three fundamental imaging formulas. Among them, the first formula is entirely consistent with the classic convolution equation. The second and third ones link the $Z$ quantities of the object and noise elegantly with the $Z$ image and covariance image, revealing new laws. Consequently, besides the flux density, the $Z$ quantity of an object is also imageable, which opens a new realm for imaging systems to explore the physical world.