Head-Eye Coordination at a Microscopic Scale M.Rucci 2015 Current Biology ending with:

An interesting hypothesis now emerges. The nature of the spatiotemporal reformatting of visual input signals and, consequently, the range of spatial frequencies transmitted to the brain depends on the characteristics of retinal image motion. This phenomenon is well captured by a Brownian model of retinal drift, in which lower diffusion constants lead to transmission of a wider equalized range of spatial frequencies, but with a lower gain. The current work raises the possibility that this trade-off can be regulated by controlling the fixational head-eye compensation: a more precise compensation would lead to a decrease in the diffusion constant and vice versa. Further work is necessary to investigate whether humans use this mechanism to tune
retinal image motion to the task demands