The noise in a digital image from a camera arises from 2 sources: the camera and the light itself. Remembering that the sensor is counting the number of electrons (generated by the arrival of photons), it is easy enough to perceive that random electron activity in the sensor, the amplifiers and associated electronics will produce a level of interference with the image signal. This internally generated noise is known as "read noise" and varies between camera and sensor designs. Improvements are steadily being made as technology advances.
The amount of read noise is not proportional to the amount of light falling onto the sensor and for the sake of the argument, we will say that the read noise is generated independently from the light signal. What is important to us as photographers is the extent to which the true light signal dominates the measurements that are output to our image file. This domination of the signal over the noise is described as the Signal to Noise Ratio (SNR), which is the signal strength divided by the noise strength.
As long as the SNR is high, the noise should not be significant in our final image, on screen or in print. However, in the darkest areas of a scene where the pixels receive relatively few photons, the signal may be only slightly stronger than the noise. The digitisation process can't distinguish between what is true signal and what is noise and so the information recorded on the picture file will be corrupted. In the worst case the signal strength may drop down as low as the noise, at which point no valid measure of colour and light level can be made at all.
The second source of noise, and somewhat more interesting, is the optical “shot noise” - that is the noise within the light entering the lens. Our own eyes and brain perceive the colour and brightness of an object as unchanging when viewed under steady light. However, light is not a uniform flow of photons but a random cascade. It is easy to picture this if we think of rain; whereas on a large scale the fall of rain might be considered “steady”, if we look more closely, the arrival of each water droplet is random. The same applies to photons falling onto a pixel. If we photograph a uniform surface, there will be random variations in the number of photons falling on each pixel. So each pixel will measure the brightness of the subject slightly differently and if the differences are great enough, we will see this variation in the final image as shot noise.
Now we need to turn to mathematics. If we photograph a uniform surface and a large number of photons fall onto each pixel, the random variation between photon counts from pixel to pixel will follow a statistically “Poisson distribution”. The “shot noise” will then be the square root of the mean count of photons at the pixels. For more detail, see Wikipedia.
Noise = √S
Where S is the count of photons at a pixel.
From the discussion of read noise, we know that we are more interested in how well the true signal stands out above the noise. The Signal to Noise Ratio (SNR) is the signal divided by the noise:
Bringing this back down to Earth, we can say that the greater the number of photons a pixel collects, the more the signal will rise above the random shot noise and the cleaner our photo will look. To give some rough idea of the magnitude of the numbers here, a digital SLR might have a maximum electron count per pixel at base ISO in the tens of thousands. So, for example, the pixels in a bright area of an image at base ISO might generate 60,000 electrons, giving a healthy SNR of over 240.
Effect of ISO
We know that if we take a photo at dusk and increase our ISO to 200, 400, 800, 1600 and so on, what we are actually doing is underexposing the sensor by a factor of 2 each time we double the ISO value. At each step we halve the number of photons entering the lens and falling onto each pixel and therefore halve the signal to be measured. As the signal reduces, the Signal to Noise Ratio goes down with it - and if we continue to increase ISO and thereby reduce the signal, eventually the noise will become significant and degrade the final image.
This applies to the bright areas of our image - but consider the dark areas where the signal may already be 10 stops or more lower. In our example with an SNR of 240 in the bright areas, we would have an SNR of just 8 in the dark shadows at base ISO. Even modest increases in the ISO setting will bring out significant noise in the shadows.
Advantage of Large Pixels
We have seen how the Signal to Noise Ratio for shot noise depends on the number of photons arriving at a pixel during the exposure.
The brightness (more correctly, illuminance) of an image falling on an area of the sensor is the number of photons per square micron of area. For a given scene and exposure, the number of photons falling onto a pixel is proportional to the area of the pixel. Also, the capacity of a pixel to hold electrons (and thereby to count photons) is proportional to its surface area.
Let us compare a full-frame sensor with an APS-C sensor, both with the same number of pixels. The full frame camera has a larger sensor: 36 mm wide vs 22.4 mm wide for the APS-C. So each pixel in the full-frame sensor is 1.6 times bigger on each axis. The surface area of a full-frame pixel is therefore 2.56 times the area of an APS-C pixel. If we photograph the same scene at the same exposure, hence same illuminance on the sensor, the full frame pixels will receive 2.56 times as many photons as their APS-C counterpart. In doing so, the full-frame sensor will have benefited by an increase in signal to noise ratio of √2.56 (i.e. 1.6) and will produce the cleaner image.
Even if we compare cameras with the same size of sensor, we see that manufacturers have a trade-off to make when choosing size of pixel. On the one hand, reducing pixel size allows more pixels to be designed into the sensor, increasing spatial resolution. On the other hand, increasing pixel size offers better performance at the pixel level and a potentially cleaner image.
For example a top-of-the-range Canon 1Dx has 20 million pixels of size 6.6µm compared to a less expensive Canon 5D with 30 million pixels of 5.4µm. Similarly the Sony A7S has just 12 million pixels of 8.4µm giving much better low-light performance than its stablemate A7iii with twice as many pixels but of 6µm. Choosing larger pixels means less resolution but potentially better image quality. For marketing purposes, manufacturers tend to advertise the number of mega-pixels but we can see that this is only half the story.