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How numbers can mislead: a closer look at dynamic range, Part 2

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Photon shot noise (the random nature of light) means that captured images will always be noisy, but a small amount of noise has much more of an impact on the weak signal that makes up the shadow regions of your image than it has against the strong signals making up the highlights.

In Part One we looked at what dynamic range is, where the differences are found and why it’s not really a proxy for image quality as a whole. In this second part, we’ll look at the factors that contribute to dynamic range, and why we tend not to just quote DR numbers in our reviews.

As we discussed in Part One, the lower cutoff in dynamic range is the point at which noise overwhelms the image in the shadows. So to understand dynamic range, you need to understand noise.

What are the sources of noise?

Noise is the name given to the degree to which a signal varies from its expected value. There are many things that contribute to noise in an image but for simplicity’s sake, we’ll group them into two main categories: read noise, the combined impact of all the electronic noise sources in the camera, and photon shot noise, the variation that comes from the fact that light arrives at a surface at random intervals, as series of quantized packets.

This second source of noise the harder one to think about, because our eyes and brains have evolved to compensate for it, so it’s not very intuitive. But photon shot noise is the dominant source of noise in most of the tones of most of the photos you’ll ever take. You can read our primer on it, but the gist is that the more signal you have, the less significant the shot noise appears.

Why is the signal-to-noise ratio so important?

Counter-intuitively there will, numerically, be a greater degree of variance in your highlights than your shadows, yet it’s the shadows that we think of as being the noisy part of the image.

This is because the degree of noise isn’t the thing you perceive as noisiness, it’s the relationship between the signal and the noise that matters. A small amount of noise has much more of an impact on the tiny, weak signal that makes up the shadow regions of your image than it has against the strong signals making up the highlights.

Some examples

Let’s look at the impact of both sources of noise, electronic read noise and photon shot noise. This first graph shows the theoretical signal of a camera with the ability to retain up to 40,000 photoelectrons (blue line, left-hand scale). The right-hand scale plots the amounts of photon shot noise (orange line) and read noise (green line) we might typically expect, from the darkest recordable tone (bottom scale, 0% brightness) up to clipping (100% brightness).

A key thing to recognize is that even an imaginary camera that added no electronic noise at all to its images would still have noisy shadows. Photon shot noise (the random nature of light) means that captured images will always be noisy. But to make clear why this noise is generally seen in the shadow regions, we’re going to factor the orange line into the blue one, and see the resulting signal-to-noise ratio.

The graphs below show the signal-to-noise ratio for different lightness levels in the image. They shown how the signal-to-noise ratio increases as lightness (the signal) increases. (The axes are plotted on logarithmic scales, so that each division represents a doubling or halving of lightness or SNR. On this graph the scale along the bottom stops below the clipping point, rather than percentages. You can mouse over the ‘Normal’ scale button to see the same data plotted using a scale that matches the graph above.)

The important point is that even with no electronic read noise at all, the signal-to-noise ratio falls (noisiness increases) as you look towards the darker tones in the image, on the left of the graph. Even with a perfect sensor adding no noise, your dynamic range would eventually be limited by photon shot noise.

Electronic noise

Sensors in modern cameras aren’t perfect, though: a small amount of electronic noise is added as the light is captured and further noise can be added further down the readout process, right up until the signal is encoded into a digital number by the camera’s analog-to-digital converter.

There are a number of sources of this electronic / ‘read’ noise, including thermal noise as the sensor gets warmer. But on modern sensors, until you get to long exposures, they tend to be very well controlled.

If we add the effect of read noise onto our diagrams, you can see the effect they have on the overall SNR response curve. Even though the green line on the original graph looking trivial, you can see it has significantly changed the shape of the curve.

As you can see, read noise makes the bottom of the SNR curve drop away from the straight line we saw when we were just looking at photon shot noise. Once again, even though the total amount of read noise is relatively small, it still has a significant impact in areas where the signal is weak, i.e., the shadows. And small differences in read noise can have a big effect on how usable those deep shadows are.

In this instance we’ve assumed 5 electrons of read noise (which would be high by modern standards). This has almost no effect in the highlights (there’s a 0.04EV reduction in SNR at clipping), but it’s enough to reduce the measured engineering dynamic range from around 15.3EV to 12.3EV.

Same DR figure, different image quality

This shouldn’t come as much of a surprise, but think about what it means for DR measurements: a camera with low read noise will measure as having more dynamic range than one with high read noise. And at the extremes, this might mean a camera with excellent image quality elsewhere in the image but a high level of read noise delivers the same DR number as a lower-quality camera that has better-controlled read noise for cleaner shadows.

Here we’ve added a second camera with a lower capacity for electrons (a smaller sensor, for instance) but also with less read noise. You’ll see they cross the SNR=1 noise threshold at the same point, so would both measure as capturing around 12.3EV of dynamic range.

And yet, for most of the range, Camera 1 is producing a cleaner image with better SNR, with image quality nearly a stop better around stop 4, which would typically be used as roughly middle grey by many cameras.

This is something that we occasionally see when older Canon sensors get compared with newer, lower-read-noise chips, with people making the mistake of thinking that matching DR numbers mean the two cameras will have comparable image quality. This isn’t true.

And that’s why we generally don’t quote dynamic range numbers at because although they are a perfectly valid way to describe a single property of a sensor, we often see them discussed as if they mean more than this. Instead our dynamic range tests attempt to visually demonstrate the deep shadow response of different cameras, where the differences in dynamic range exist, while also showing you what the tones immediately above the deep shadows look like.

This isn’t to say that our DR tests are perfect, but we hope they provide a clearer impression of what the visual differences between cameras are, rather than just presenting a single number.

So is it worth caring about dynamic range at all? We’ll look to address that question in Part Three, with ramifications for the digital imaging future.

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