Technical Article

# Dark Noise in CCD Image Sensors

May 21, 2020 by Robert Keim

## This article introduces the concept of image noise and discusses one noise source that plays a prominent role in the design of CCD systems.

Welcome to Part 11 of the AAC series on CCD (charge-coupled device) image sensors! Before moving on to this article on dark noise, please check out the links below to catch up on any of the topics we've covered so far:

### What Is Image Noise?

In my article on electrical noise, I defined noise as undesirable voltage or current variations that are (often) random and (usually) of relatively low amplitude. That same definition applies to noise in visual information as well.

However, there’s an interesting consideration that comes into play when we’re dealing with imagery. If I’m using a thermistor to collect temperature data, I don’t have a strong expectation for what the resulting voltage signal should “look like.” I can display the sensor signal on a scope, and I might notice some high-frequency variations that are likely to be noise, but the appearance of the waveform doesn’t really offend, so to speak, my preconceived ideas about the characteristics of this particular thermistor signal.

Image data, on the other hand, are often in direct competition with the “official” representation produced by the human vision system. I’ve looked at countless different trees on countless different occasions under a wide variety of lighting and atmospheric conditions. Thus, I have detailed and inflexible ideas regarding what trees ought to look like. If someone shows me a photograph of a tree and it contains variations in tonality or color that don’t jibe with my expectations, I will interpret these variations—especially if they are of relatively high spatial frequency—as noise.

Consider the following example:

This image certainly does not duplicate my perceived reality (there’s no color, and the background is blurred using a photographic technique that is not available to the human eye). However, I wouldn’t describe it as noisy, because it lacks high-spatial-frequency variations that conflict with my visual expectations.

If we magnify the image, though, the situation changes:

Now we have prominent variations in tonality that do not accord with my visual expectations, and I interpret these features as noise that has negatively affected the quality of the image.

The variations in this image, by the way, are due partially to film grain. This reminds us that image noise is not an inherently digital phenomenon. In fact, one CCD noise source (discussed in a future article) is a physical property of incident light and therefore exists independently of the sensor that captures the image data.

### CCD Dark Noise

The purpose of a CCD’s photodiodes (or photocapacitors) is to generate free electrons in response to incident photons. The number of free electrons is proportional to the number of photons that arrive at a given pixel location, and consequently the CCD’s two-dimensional array of electron packets becomes an electrical representation of the scene’s optical characteristics.

It follows that the electrical representation will have inaccuracies if a pixel collects electrons that were not created by the arrival of photons. This non-optical creation of pixel charge occurs continually in CCDs, because the silicon structure of the device regularly generates free electrons in response to internal temperature. We call this dark current, since the photodiode generates these charge carriers even when there is zero illumination.

#### Dark Current vs. Dark Noise

The origin of dark noise is dark current. They’re not the same thing, and it’s important to recognize the distinction between these two phenomena.

Dark current refers to the total number of thermally generated electrons. We quantify this using the unit electrons per pixel per second (e/p/s). Dark noise results from the variation in dark current. We shouldn’t think of dark current itself as noise, because a significant portion of the dark current can be eliminated by subtracting a typical value.

For example, if we know that a CCD tends to generate 100 e/p/s of dark current, we can multiply this number by the integration time and then subtract the corresponding signal amplitude from each pixel. In this case, the noise is not the 100 e/p/s dark current but rather the random variations that cause dark current to deviate from 100 e/p/s.

The behavior of dark current is bound to the discrete nature of electric charge, and consequently dark noise is a form of shot noise and follows the Poisson relationship. Thus, RMS dark noise can be calculated by taking the square root of the dark current produced during a given integration period:

$\text{dark noise} = \sqrt{\text{(dark current)}\times\text{(integration time)}}$

#### Black Pixels and Dark Current

Dark-current compensation is routinely accomplished by actually measuring the frame-by-frame dark current rather than relying on a specification found in the CCD’s datasheet. You might remember the following diagram from my article on processing CCD output signals.

##### This block diagram is from the datasheet for the AD9845B, a CCD signal processor from Analog Devices.

Optically shielded pixels included in each CCD line provide information about the amount of charge produced by dark current. This charge creates an offset in the CCD signal, and an “optical black clamp” subcircuit compensates for this offset.

### Dark Noise and Temperature

Because the amount of dark noise in pixel data is a function of temperature, it is also called thermal noise. I prefer to avoid the latter term because “thermal noise” more frequently refers to a distinct form of electrical noise influenced by temperature as well as resistance and bandwidth.

Nonetheless, the relationship between dark noise and temperature is extremely important, because it provides a straightforward way of reducing CCD noise: just make the sensor very cold! Specialized applications use thermoelectric cooling or even liquid nitrogen to reduce dark noise to negligible levels. The following plot gives you an idea of how effectively dark noise can be remedied by reducing the operating temperature of the CCD.

### Conclusion

I hope that you now understand the nature of CCD dark noise, the relationship between dark noise and dark current, and how both of these phenomena influence system design practices. We’ll continue our discussion of CCD noise in the next article.