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Calculating the Signal to Noise Ratio of a Camera

An important parameter that is often used to evaluate the sensitivity of a camera is the signal to noise ratio. This can be used to determine how different cameras may perform at light regimes that simulate those of a given research conditions. In this article we will look at the theoretical prediction of signal to noise for a typical CCD or sCMOS camera by looking at both signal and noise elements.

Signal

If we assume we have a number of photons P falling on a camera pixel with a Quantum Efficiency DQE this will generate a signal of Ne electrons as below

Noise – Photon Shot Noise

The incoming photons have an inherent noise variation or uncertainty to the signal itself. This is known as photon “Shot” noise. As the photons follow Poisson statistics the signal noise, may be described as:

Noise Sources from the Camera itself

The internal processes of the camera generate noise. Some of these are largely set by the sensor design itself, but also how the sensor has been implemented and packaged into the camera design will influence these.
These noise sources are:

readout which is the noise generated from the sensor readout process.

dark is the noise resulting from thermally generated electrons (often called dark signal as it is produced in the absence of light. Dark current can be reduced by cooling the sensor – click here to read about the effect of cooling on dark current in sCMOS cameras.

Other Noise Sources - EMCCD

For EMCCD cameras there is an additional noise factor that is called “EM noise” or “Excess Noise Factor”. This is a result of the EM gain amplification and effectively increases the shot noise by a factor of 1.41. Note that this is not an additional noise, but an increase in the variability of the signal. When EMCCD cameras are considered this additional noise factor must be considered.

Other Noise Sources - sCMOS

For sCMOS cameras, each pixel effectively has its own amplifier. An effect of this is that the some pixels will have a higher or lower read noise value. The read noise of sCMOS cameras has an asymmetric distribution that can be described as either a median and/or a rms value. Although the median value is often specified for sCMOS cameras, when considering signal to noise ratios it is the rms value that is used.

Another noise consideration for sCMOS sensor architectures is fixed pattern noise. Due to the very slight differences of each pixel they will in turn have very slight differences in their response to light. A correctly optimised camera uses “pixel maps” to account for these differences so that fixed pattern noise is not generally an issue. Fixed pattern noise is not a factor in signal to noise calculations so is covered in more detail in other articles.

Other Noise Sources

Spurious noise (also called Clock induced Charge or CIC) is another source of noise within sensors. Clock induced charge occurs as charge is shifted from pixel to pixel on its way to the output amplifier. This is due to a very small but finite possibility that the charges involved can induce additional charges due to impact ionization (Note that this is the same effect that is exploited in the EM gain register of EMCCD cameras that allows for signal amplification). In a well-designed camera the spurious noise effect is minimized and is effectively masked by the much higher read noise and dark current noise sources that will be present. Clock induced charge can however become relevant e.g. binning a very large number of pixels of a CCD camera, and for EMCCD cameras. Since EMCCD cameras are so effective at boosting even the lowest signals that occur in the image section of the sensor this would also be true of dark current and of clock induced charge that may be present. The spurious noise of the camera is represented as δcic.

Combining the Signal and Noise Components

We can put the signal and noise components together and generate an expression for the signal to noise ratio for a typical CCD or sCMOS camera:

Substituting for the expressions for Noise we can see the equation for signal to noise for a camera is as follows:

The thermal noise component Ndark is a function of temperature and exposure time.

Advanced Calculations for Signal to Noise

The above equation will allow for basic signal to noise estimations using the readily camera parameters, however we can make more detailed comparisons by including the modelling of spurious noise, and to account for the effect of amplifier gain when operating under different gain settings. The camera amplifier amplifies the low-level signal but also the noise components by the Gain value. The camera Gain value (also referred to as sensitivity) may be found on a camera performance sheet and there will be a value for each of the different gain modes applied in the available modes of operation. If we describe this gain as M we can thus define the noise factor F that would be attributed to this amplification process by the following relationship:

Note that an ideal amplifier would have a noise factor of 1. We can apply this to the signal for P photons falling on a pixel in the camera with a Quantum efficiency of DQE and for Gain M. The signal output from the camera would be expressed as:

The total camera noise is the sum in quadrature of the various noise sources i.e. the square root of the sum of the noises squared. Therefore, the total Noise would be as follows:

The noise due to the dark signal, light signal noise, and clock induced charge are all amplified in the above by the Gain (M) and by noise of the amplifier itself (F). We can then combine the signal and noise components as:

This can then be divided throughout by M to the following equation:

This advanced equation can therefore be used to make precise calculation of a cameras signal to noise under different modes of operation. Parameters can be obtained from the camera performance sheets and using the QE curve to calculate QE at the required wavelength. The noise factor for sCMOS and CCD cameras can be considered as 1, EMCCD cameras 1.41and for ICCD Gen III cameras 1.6.

  • For experiments with low exposure times such as live cell experiments with exposures in the order of 10-50 milliseconds. When coupled with moderate sensor cooling, in these applications the dark current will be negligible. These types of experiments are therefore often most suited to sCMOS cameras such as Andor Zyla, Sona or Marana with high sensitivity, low read noise and high frame rate capabilities.
  • For experiments where longer exposures of seconds to minutes are required and readout speed is not critical, the dark current becomes the main source of noise and this places greater need towards deeper cooled, high QE, low dark current camera designs such as deep cooled back-illuminated CCD cameras such as iKon series for imaging or Newton CCD and EMCCD series for spectroscopy.
  • Note that the ultrasensitive iXon EMCCD series is suited to both short exposure and long exposure experiments due to the high sensitivity, very low dark current and flexibility provided by this camera technology.

Signal to Noise Ratio Curves

The signal to noise ratio curves may be plotted on a per pixel basis or a per unit area basis. Different camera sensors will have different pixel sizes and sensor sizes so it is important to consider these parameters if comparisons between different sensors are being made.

The Andor Signal to Noise Calculator can be used to make useful comparisons between cameras or for different settings such as exposure time. An example plot for the signal to noise ratio for a Zyla 4.2 Plus sCMOS camera versus an iXon Ultra 888 EMCCD camera is shown in figure 1 (expressed per pixel).

SNR Zyla vs EMCCD

There are several points that we can take away from this example:

  • When we compare the two cameras on a per pixel basis the iXon EMCCD Ultra 888 camera has a better SNR at lower light levels. Note that if we used (2x2) binning to account for pixel size and improve signal to noise performance at the expense of spatial resolution, a similar relationship would still be seen.
  • EMCCD cameras are of course known for their sensitivity and this should translate in imaging terms to being able to use shorter exposures, and lower illumination intensities than sCMOS cameras.
  • At higher light levels the Zyla sCMOS camera can be seen to have a higher SNR than the EMCCD camera. The reason for this is the impact of EM noise of the EMCCD camera which increases with increasing incident light signal. The Zyla sCMOS camera would therefore be a better option for applications where the light is not so restricted as the sCMOS camera will also provide higher resolution and frame rates under these conditions.

SNR can be a useful tool to help compare the sensitivity of different cameras, or look at the impact of adjusting camera settings. Ultimately these theoretical comparisons should be followed up with camera demos to confirm performance is suitable for the unique parameters of any given experimental set-up.

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