We present here a synthesis of our previous work in order to provide an overall model that describes the infrared image of ground terrain in terms of the heat balance of each image pixel. This approach relates the pixel radiance to two physical invariant properties and to the external heat input (output) source. Thus, the temporal variations of the statistical and spatial properties can be accounted for. Specifically, the model predicts a non-Gaussian distribution of the radiance over the scene, as well as the change of the probability density function with changing external heat source (the sun). The probability density function can be asymmetric. The radiance statistics are related to the image resolution. We show that the distribution approaches the normal distribution as the resolution decreases. The radiance spatial behavior can be described by an exponential correlation function. The present discussion shows that the correlation length describing a given type of terrain is time dependent. It is predicted that the correlation length decreases as the intensity of the heat source increases, i.e., that higher spatial frequencies are more pronounced at noon than at sunrise or sunset. The model can be used to predict the infrared image of a given scene. Most of the model predictions are supported by experimental results.
"Measurement And Modeling Of Natural Desert Terrain In The Infrared," Optical Engineering 27(11), 271128 (1 November 1988). https://doi.org/10.1117/12.7976789