Image sensors: Theory

The shutter efficiency reports how much the stored pixel value is distorted by incoming light (which will be typically light from an unrelated exposure period which falls on the pixel when awaiting readout). While reading out the sensor, additional electrons are moved. This shows in particular if the exposure time is much shorter than the readout time, e.g. if high image sensor gain settings are used to allow a short exposure time. It also shows if there is much light outside the exposure time, e.g. when trying to take images between light pulses.

A rolling shutter sensor has a constant readout time for each row and that is typically very short, which makes it unlikely to see the shutter efficiency causing an issue.

For a global shutter sensor, the readout time grows in readout direction, visible as a brightness gradient. In case of moving targets, the gradient may additionally present as motion blur. It also causes brightness non-linearity for short exposure times.

$$\text"shutter efficiency" = 1 - \text"sensitivity with shutter closed" / \text"sensitivity with shutter open"$$

This sample image was taken by a camera with 40 µs exposure time and a readout time of 242 ms using an integrating sphere with a constant illumination. The black level is calibrated to be 0. The top rows have an average of 8662 DN16 and the bottom rows have an average of 15377 DN16, which results in a difference of 6715 DN16 gained during readout (scaled for web presentation).

The resulting shutter efficiency is:

$$1 - { { { 6715 \text"[DN16]" } / { 242 · 10^{-3} \text"[s]" } } / { { 8662 \text"[DN16]" } / { 40 · 10^{-6} \text"[s]" } } } = 0.99997$$

That is actually a great value. The problem is the extreme ratio of exposure time and readout time. This issue becomes more serious with large global shutter sensors due to their high amount of data. The readout time is not just annoying in performance, but impacts the usability of the camera for short exposure times.

For calculating the leakage ratio is easier to use than the efficiency:

$$ { { 6715 \text"[DN16]" } / { 242·10^{-3} \text"[s]" } } / { { 8662 \text"[DN16]" } / { 40·10^{-6} \text"[s]" } } = 1.2·10^{-4} $$

If the leakage should be at most 1% (factor 100 less), the required exposure time would be at least:

$$\text"leakage" · \text"brightness [DN/s]" · \text"readout time [s]" < { \text"brightness [DN/s]" * \text"exposure time [s]" } / \text"factor"$$ $$\text"leakage" · \text"readout time [s]" < { \text"exposure time [s]" } / \text"factor"$$ $$\text"leakage" · \text"readout time [s]" · \text"factor" < \text"exposure time [s]"$$ $$1.2·10^{-4} · 242·10^{-3} \text"[s]" · 100 < 2.9·10^{-3} \text"[s]"$$

There appears to be a considerable inaccuracy, though, because using readout times led to significantly worse leakage ratios. But the learning is: If the exposure time is a few order of magnitudes less than the readout times, a global shutter may show light leaking through the closed shutter.

Image sensors: Shutter efficiency