Camera Noise and Temperature

Sources of Noise

Noise in a camera image is the aggregate spatial and temporal variation in the measured signal, assuming constant, uniform illumination. There are several components of noise:

• Dark Shot Noise (σ_D): Dark current is a current that flows even when no photons are incident on the camera. It is a thermal phenomenon resulting from electrons spontaneously generated within the silicon chip (valence electrons are thermally excited into the conduction band). The variation in the amount of dark electrons collected during the exposure is the dark shot noise. It is independent of the signal level but is dependent on the temperature of the sensor as shown in Table 1.
• Read Noise (σ_R): This is the noise generated in producing the electronic signal. This results from the sensor design but can also be impacted by the design of the camera electronics. It is independent of signal level and temperature of the sensor, and is larger for faster CCD pixel clock rates.
• Photon Shot Noise (σ_S): This is the statistical noise associated with the arrival of photons at the pixel. Since photon measurement obeys Poisson statistics, the photon shot noise is dependent on the signal level measured. It is independent of sensor temperature.
• Fixed Pattern Noise (σ_F): This is caused by spatial non-uniformities of the pixels and is independent of signal level and temperature of the sensor. Note that fixed pattern noise will be ignored in the discussion below; this is a valid assumption for the CCD cameras sold here but may need to be included for other non-scientific-grade sensors.

Total Effective Noise

The total effective noise per pixel is the quadrature sum of each of the noise sources listed above:

Here, σ_D is the dark shot noise, σ_R is the read noise (for sample calculations, we will use our 1.4 megapixel cameras, which use the ICX285AL sensor. Typically the read noise is less than 10 e- for scientific-grade cameras using the ICX285AL CCD; we will assume a value of 10 e- in this tutorial), and σ_S is the photon shot noise. If σ_S>>σ_D and σ_S>>σ_R, then σ_eff is approximately given by the following:

Again, fixed pattern noise is ignored, which is a good approximation for scientific-grade CCDs but may need to be considered for non-scientific-grade sensors.

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Figure 1: Plot of dark shot noise and read noise as a function of exposure for three sensor temperatures for a sample camera. This plot uses logarithmic scales for both axes.The dotted vertical line at 5 s indicates the values calculated as the example in the text.

Dark Shot Noise and Sensor Temperature

As mentioned above, the dark current is a thermal effect and can therefore be reduced by cooling the sensor. Table 1 lists typical dark current values for a sample camera with a CCD sensor. As the dark current results from spontaneously generated electrons, the dark current is measured by simply "counting" these electrons. Since counting electrons obeys Poisson statistics, the noise associated with the dark current I_D is proportional to the square root of the number of dark electrons that accumulate during the exposure. For a given exposure, the dark shot noise, σ_D, is therefore the square root of the I_D value from Table 1 (for a given sensor temperature) multiplied by the exposure time t in seconds:

Since the dark current decreases with decreasing temperature, the associated noise can be decreased by cooling the camera. For example, assuming an exposure of 5 seconds, the dark shot noise levels for the three sensor temperatures listed in the table are

Figure 1, which is a plot of the dark shot noise as a function of exposure for the three temperatures listed in Table 1, illustrates how the dark shot noise increases with increasing exposure. Figure 1 also includes a plot of the upper limit of the read noise.

If the photon shot noise is significantly larger than the dark shot noise, then cooling provides a negligible benefit in terms of the noise, and our standard package cameras will work well.

Photon Shot Noise

If S is the number of "signal" electrons generated when a photon flux of N photons/second is incident on each pixel of a sensor with a quantum efficiency QE and an exposure duration of t seconds, then

From S, the photon shot noise, σ_S, is given by:

Example Calculations (Using our 1.4 Megapixel Cameras)

If we assume that there is a sufficiently high photon flux and quantum efficiency to allow for a signal S of 10,000 e- to accumulate in a pixel with an exposure of 5 seconds, then the estimated shot noise, σ_S, would be the square root of 10,000, or 100 e-. The read noise is 10 e- (independent of exposure time). For an exposure of 5 seconds and sensor temperatures of 25, 0, and -25 °C, the dark shot noise is given in equation (4). The effective noise is:

The signal-to-noise ratio (SNR) is a useful figure of merit for image quality and is estimated as:

From Equation 7, the SNR values for the three sensor temperatures are:

As the example shows, there is a negligible benefit to using a cooled camera compared to a non-cooled camera operating at room temperature, and the photon shot noise is the dominant noise source in this example. In this case our standard package cameras should therefore work quite well.

However, if the light levels were lower such that a 100 second exposure was required to achieve 900 e- per pixel, then the shot noise would be 30 e-. The estimated dark shot noise would be 22.4 e- at 25 °C, while at -20 °C the dark shot noise would be 3.2 e-. The total effective noise would be

From Equation 8, the SNR values are

In this example, the dark shot noise is a more significant contributor to the total noise for the 25 °C sensor than for the -25 °C sensor. Depending on the application's noise budget, a cooled camera may be beneficial.

Figure 2 shows plots of the different noise components, including dark shot noise at three sensor temperatures, as a function of exposure time for three photon fluxes. The plots show that dark shot noise is not a significant contributor to total noise except for low signal (and consequently long exposure) situations. While the photon flux levels used for the calculations are given in the figure, it is not necessary to know the exact photon flux level for your application. Figure 2 suggests a general metric based on exposure time that can be used to determine whether a cooled camera is required if the exposure time can be estimated, and these results are summarized in Table 2. If you find that your dominant source of noise is due to the read noise, then we recommend running the camera at a lower CCD pixel clock rate of 20 MHz, since that will offer a lower read noise.

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(a)

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(b)

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(c)

Figure 2: Noise from all sources as a function of exposure for three different photon fluxes: (a) low, (b) medium, and (c) high. In (c) the signal and photon shot noise saturate above approximately 20 seconds because the pixel becomes saturated at the corresponding incident photon levels. A quantum efficiency of 60% was used for the calculations. Note that these plots use logarithmic scales for both axes.

Other Considerations

Thermoelectric cooling should also be considered for long exposures even where the dark shot noise is not a significant contributor to total noise because cooling also helps to reduce the effects of hot pixels. Hot pixels cause a "star field" pattern that appears under long exposures. Figure 3 shows an example of this star field pattern for images taken using cameras with and without TEC cooling with an exposure of 10 seconds.

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(b)

Figure 3: Images of the "star field" pattern that results from hot pixels using our (a) standard non-cooled camera and (b) our camera cooled to -20 °C. Both images were taken with an exposure of 10 seconds and with a gain of 32 dB (to make the hot pixels more visible). Please note that in order to show the pattern the images displayed here were cropped from the full-resolution 16 bit images. The full size 16 bit images may be downloaded here and viewed with software such as ImageJ, which is a free download.