"The frame rate of the digital high-speed video camera was 2000 frames per second (fps) in 1989, and has been exponentially increasing. A simulation study showed that a silicon image sensor made with a 130 nm process technology can achieve about 10^10 fps. The frame rate seems to approach the upper bound. Rayleigh proposed an expression on the theoretical spatial resolution limit when the resolution of lenses approached the limit. In this paper, the temporal resolution limit of silicon image sensors was theoretically analyzed. It is revealed that the limit is mainly governed by mixing of charges with different travel times caused by the distribution of penetration depth of light. The derived expression of the limit is extremely simple, yet accurate. For example, the limit for green light of 550 nm incident to silicon image sensors at 300 K is 11.1 picoseconds. Therefore, the theoretical highest frame rate is 90.1 Gfps (about 10^11 fps)."
After the simplifications of equations mostly based on the photocarriers travel time to the collection node, "the expression of the temporal resolution limit is reduced to an extremely simple form:"
Δτ = 6.12 δ
where δ is the average light penetration depth
∆τ is the temporal resolution limit
The units of ∆τ and δ are, respectively, ps and µm.
The paper's conclusion:
"The temporal resolution limit of silicon image sensors is theoretically derived. The limit is mainly governed by mixing of charges with different travel times caused by the distribution of penetration depth of light. The final expression is ∆τ = 6.12 δ, which may be unbelievably simple, but sufficiently accurate. Now, the target is clear. It is time to give it a try to break it."