The dynamic range is an important camera specification related to the minimal and maximal signal that can be measured within a single image. It is most notably influenced by how many photons can be collected by a pixel in the image before saturation occurs (full-well depth) and the noise floor of the camera.
The most straightforward measure of the maximum signal that can be tolerated by a camera is the full-well capacity or depth. The full-well depth characterizes how many electrons can be stored by pixel. If this is exceeded, further exposure to light does not result in a linear increase of the signal; the pixel is saturated and the excessive amount of photoelectrons will result in pixel leaking.
On the opposite end, the minimal signal measured by the camera is limited by its noise. For many technologies, the readout noise will be the dominant noise source, although the dark current (i.e. thermal noise) will become dominant during long acquisitions. While the readout noise will be used for further demonstrations, the main noise source of an acquisition is highly specific to its unique context.
Once these two limits have been identified, the dynamic range is determined by dividing the full-well depth by the noise floor. For example, a full-well depth of 100 kē and readout noise of 40 ē would lead to a dynamic range of 2500:1. A 12-bit image (4096 levels) would be sufficient to cover this data range.
Both the full-well depth and noise specifications are given in electrons. This is because most imaging devices make use of the photoelectric effect; the generation of electrons following exposure to photons. This conversion occurs at a certain rate characterized by the sensor’s quantum efficiency. Hence a camera with a quantum efficiency of 90% and a full-well depth of 100 kē can be exposed to, on average, 110 000 photons/pixel before saturation. It must be noted that measures like full-well depth and quantum efficiency are averages and can change from pixel to pixel.
However, digital camera images are often presented in Analog-to-Digital Units (ADU) and not electrons. To relate ADUs to photons, a measure of the individual camera unit’s gain, often referred to as k-gain, is used. By using this ratio of ē/ADUs and then balancing the number of electrons with the quantum efficiency, a rough estimate of the number of photons captured per pixel can be obtained.
The usage of EMCCDs is geared towards extremely faint flux imaging down to the single photon per pixel. This is thanks to the use of electron-multiplication (EM) gain which makes readout noise negligible; more information on the EMCCD technology is available here.
The EM Gain adds another layer to the estimation of dynamic range. While EM Gain does not affect the imaging area’s full-well depth, the multiplication register, part of the sensor where electron multiplication occurs, has its own full-well capacity. When using EM Gain, this will often be the limiting factor. For example, a signal of 1 kē would not exceed an EMCCD’s imaging area’s full-well of 100 kē, but if an EM gain of 1000 is used the resulting 1000 kē would exceed the multiplication register’s full-well of 300 kē.
As such, the effective full-well capacity of an EMCCD can be estimated by dividing the multiplication register’s full-well by the EM gain used. Furthermore, while the calibrated EM gain is very precise it represents the mean gain applied to the image. On a pixel basis, the EM gain is stochastic and thus some pixels will be amplified more (or less) than others. As a rule of thumb, when using high EM gains, it is safer to use only <90% of the available dynamic range to limit saturation in strongly amplified pixels.
The EMCCD’s modulable EM gain allows to adapt the camera and its dynamic range to a specific acquisition’s requirements. This flexibility is part of what makes the EMCCD unmatched for low-light imaging.