Ways to characterize the "dynamic range" of a camera

Doug Kerr

Well-known member
In a recent thread, there was discussion of the matter of the dynamic range of a camera, and how we might estimate what would be considered the "resolution" of the sensor, taking into account the discrete nature of the photons that constitute the light. And we use the reciprocal of that resolution as the "dynamic range" of the camera.

I called to attention that this was indeed a technically valid and useful outlook on "dynamic range", but cautioned that we often find in the discussion of camera performance a rather different measure of "dynamic range". I thought I would give a little peek into that matter here.

For those who would like a more detailed discussion, it is available in my article, "The ISO Definition of the Dynamic Range of a Digital Still Camera", available here:

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Out interest in the "dynamic range" of a camera is essentially "what range of scene luminance can the sensor system accommodate such that detail (reflected in changes in luminance) can be captured over that range."

If the digital number (DN) from our sensor has a range of 0-4095, with 0 the DN value for "no light" and 4095 the DN value for "the greatest light that has a unique DN" (duh!), then it is at first tempting to say that, since the greatest DN is 4095 and the smallest non-zero DN (and in fact the increment of the DN) is 1, the "dynamic range" of the sensor system is 4095 (often stated as 4095:1). That would be attractive if were were perhaps thinking of the dynamic range of a digital voltmeter.

But remember, we said earlier that we want detail (reflected as a change in luminance) to be recognized over the range of interest. So perhaps we need to consider the high-end "base luminance" to be that whose DN is 4094 (so we can contemplate subtle detail for which its range of DN is 4093-4095) and to consider the "low end "base luminance" to be that whose DN is 2 (so we can contemplate subtle detail for which the range of DN is 1-3). Now it might seem that the dynamic range is 2047 (4094/2).

But we are "splitting hairs" here in a very arbitrary way, and the answer we get is mightily dependent on just how. So maybe this isn't really a good outlook.

But there is another consideration that suggests against this outlook.

We probably don't want to think of light levels so low that the corresponding noise makes the "shadows" not "handsome" in the image.

So in fact the ISO standard for determining the dynamic range of a still camera takes the approach that it is the ratio of the maximum luminance that gets a distinct DN to the luminance at which the signal-to-noise ratio (SNR) is an arbitrary level, namely 1:1. Now does this mean that a survey of a zillion photographers considering a zillion scenes and intended destinations for the final image concluded that an SNR of 1:1 was the holy grail of such things? Hardly. More likely it was, "Hey, an actual survey of this would be very time consuming and costly, and I'm not sure the result would be anything magical anyway. Let's pick 1:1 and go to lunch."

But now there is a further wrinkle. In quantifying noise, a random phenomenon, we use the statistical measure "standard deviation" of the signal with noise present as the measure of the "potency" of the noise. This in fact turns out to be parallel to what we do in quantifying noise in an electrical engineering context, where we measure the root-mean-square RMS) value of the noise voltage. And guess what - the definition of the RMS value of (the variable part of) a variable is exactly that of its standard deviation!

Now, we will assume that the instantaneous value of the noise component of the signal follows the "normal distribution". Now consider a situation in which the average value of the signal (the signal with no noise present) is the same as the RMS value of the noise component - that is, we have an SNR of 1:1 (what "we" have decided will be the poster boy for our lowest luminance).

But if we look at the statistical math, we find that. for that to be so, about 16% of the time the DN - or more to the point, the instantaneous luminance that implies - would have to be negative. And of course that is physically not possible.

So we could never "measure" at what luminance was the SNR out of the sensor equal to 1:1.

So we sneak up on it. We consider a very small luminance, but not one that is as small as where the SNR would be 1:1 (considering reasonable noise performance). In fact we choose 1/100 of the luminance that corresponds to the maximum DN.

Then, with a test luminance of that value, we determine the RMS value of the variation in output due to noise.

We then say, well, that will probably be very close to the RMS metric of the noise for any luminance in this neighborhood.

Thus a base luminance whose value is numerically the same as that RMS noise figure would "no doubt" conceptually exhibit an SNR of 1:1.

And we use that luminance as the "bottom end" in determining the dynamic range of the sensor (the "top", as always, being the luminance that corresponds to the maximum available DN - the "saturation" luminance).

Nifty, wot?

Best regards,

Doug

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