An important characteristic of an image sensor is its ability to convert electrons into output signal. Most CMOS image sensors include on-chip ADCs which convert the analog signal coming from the pixel into digital numbers. The CCE (Charge Conversion Efficiency) defines the relationship between the number of electrons collected in the pixel and the resulting output signal in DNs (Digital Numbers).
This leads to the definition of the CCE: DN/e (digital numbers / electron)
As electrons are collected in the pixel, the on chip ADCs detect a potential difference, which is a result of the pixel capacity and gain introduced between pixel and the ADC.
While the introduced gain is fairly predictable with simulations and measurements, the sense node capacity and its voltage conversion is hard to accurately predict and measure.
Dummy pixel rows can be added to a design with its sole purpose to measure the pixel capacity and its voltage conversion. But that is not always feasible, especially in line scan applications.
A more convenient way to determine a sensor’s CCE is to plot the variance vs. mean output level:
With higher input light levels, the random noise at the sensor output starts to be dominated by shot noise and the read noise becomes insignificant. The arrival and collection of light within a fixed integration time and within a single pixel follows Poisson distribution. This is due to the fact that light arrives in the form of discrete and independent quanta (photons). If each absorbed photon generates no more than a single electron per photon (true for silicon until the deep UV and Xray) then the collected electrons also follow Poisson’s distribution. An important and useful characteristic of Poisson’s distribution is that the mean is equal to the variance.
Therefore, an increase of the light level (delta mean) in the shot noise limited region, leads to the same change in variance (delta σ2). The slope in the graph above, defined by Δ mean and Δ σ2 would need to be 1 in order to satisfy this relationship.
If now gain (CCE) is applied, and the graph above is measured at the sensor output, the increased light level leads to a change in digital numbers defined by CCE x Δ mean
Note: Δ mean represents the increase of electrons on the sense node
The change of the standard deviation (Δ σ) is multiplied by CCE as well and therefore the increase of the variance at the output is defined by CCE2 x Δ σ2
Note: Δ σ2 represents the increase of the variance on the sense node
Since Δ mean is equal to Δ σ2 on the sense node, the slope of the measured curve can be determined to define the CCE.
As mentioned above, this is only valid if the electrons follow a Poisson distribution on the sense node. And of course the images taken, need to be corrected for FPN (Fixed Pattern Noise) and PRNU (Photo Response Non-Uniformity). Mechanisms like blooming or saturation can quickly (earlier than expected!) influence and corrupt the Poisson distribution.
Therefore, it is good practice to plot the photon transfer curve (standard deviation vs mean in a log-log graph) to more accurately determine the valid region (slope=1/2).
It is interesting to note that only the electron signal enters into the above analysis – the optical properties, and in particular quantum efficiency, do not. A knowledge of the CCE allows for a calculation of the QE, but only if the absolute power of the incoming light can be measured.
More on that in a future post.