ETTR — just crank up the ISO? Not so fast.

When I was in college, I learned a colloquial formulation of the laws of thermodynamics: The first law of thermodynamics says you can’t get something for nothing; the second law says you can’t even break even. Exposure in digital photography is a little like that. I’ve been talking about ETTR for a while now. You can read a summary here. In it I say that you need to get that histogram over to the right – but not too far to the right – if you want to minimize the noise in your images. One way to do that is to open up the lens wider or leave the shutter open longer. That’s a good way.

Another way to move that histogram eastward is to crank up the ISO setting. That’s usually not a good way. In fact, past a certain point, all you do when you increase the ISO is reduce your margin for overexposure error. If you’re good at this ETTR stuff, you never blow out a highlight, so there’s no harm done except for the time it takes to make the test exposure, look at the histogram, and maybe make another exposure and look at its histogram. However, sometimes the light’s a bit dim and things are moving fast. In that case, the time spent on ETTR could cost you the shot and buy you nothing.

Confusing? You bet. Let me explain by talking a bit about how your camera works. First, there are the photosites, or sensels, which are little features (usually one per pixel of the demosaiced image) on the sensor that collect photons and produce electrons. Those electrons create a voltage that can be measured by an analog-to-digital converter (ADC), and thus the output of the ADC is more-or-less proportional to the number of photons collected by the photosite. There’s an amplifier between the sensels and the ADC whose gain is controlled by the ISO setting on the back of the camera. Higher ISO means more gain.

That’s fine up to a point. With a perfect ADC and no other noise associated with reading the data out of the photosite, it doesn’t improve the signal-to-noise ratio (SNR) to crank up the gain of that amplifier past the point where one photon captured results in one least-significant-bit (LSB) change in the ADC output. If you’re a digital photography maven, you call this gain the Unity Gain. This terminology is a big step away from the way we engineers usually use the word “gain”, and it makes me cringe, but it’s the language of the art, and I will explain it here. To an engineer, gain is almost always dimensionless: volts out over volts in, or milliamps out divided by milliamps in. This Unity Gain manages to be dimensionless only if we call the units of the input counts (number of photons) and the unit of the output counts (steps in the ADC output). Unity gain occurs when one photon creates one step.

If we step away from the ideal world, it doesn’t help the signal to noise ratio to increase the gain over that that results in a two or three LSB change. That occurs at depressingly low ISOs, and there’s a way to test your camera to see what it is. Even better, there’s a test I’ve developed to figure out when turning up the ISO stops helping you increase the SNR that doesn’t even directly measure the Unity Gain point.

Here’s how you can do it. Set up the camera aimed at a white image on a monitor. Same rules as for doing the in-camera histogram calibration: camera on a tripod, normal to the monitor face, defocussed, longish shutter speed, etc. Set the camera to the highest ISO you want to consider. 3200 is plenty high. Make an exposure that places the screen on Zone VI (or meter the screen and open up a stop); don’t worry, the exposure isn’t at all critical. Trip the shutter. Turn the ISO down to half of what it was, make the shutter speed twice as fast as it was, and make another exposure. Continue until you can’t make the ISO any lower.

Bring one of the images into RawDigger. Select a square in the middle that’s a couple of hundred pixels on a side. Measure the mean and standard deviation of one of the two sets of green pixels (for extra credit, measure all four sets of pixels). Leave the selection where it is, and measure the same statistics for all the rest of the images. For each image, compute the SNR; the mean is the signal, the standard deviation is the noise. Plot the data, with the log of the SNRs as the vertical axis, and the log of the film speed as the horizontal axis.

Examine the plot. If the SNR remains constant as the ISO increases, you are in a region where photon noise dominates, and increasing the ISO can improve your SNR by a factor of two for every quadrupling. If the log (base 10) SNR falls by .15 every time you double the film speed, you are gaining no improvement in SNR at all by increasing the ISO. In between, well, you’re getting some improvement by increasing the ISO, but not as much as you’d expect in an ideal system.

Let’s look at an example. This is data from a Nikon D4. I’ve converted the ISO speeds to DIN equivalents to get the log scale for the horizontal axis. I’ve converted the SNRs to decibels to get the log scale for the vertical axis:

You can see that, after DIN 30 (ISO 800) the D4’s SNR drops very close to 1.5 dB per octave (.15 log decrease every time the ISO doubles), even though it never quite gets parallel to the 1.5 dB/o line. This means that there is a small advantage to increasing your ISO as far as 3200 on the D4, but there’s not much improvement after 800 (or even 400).  The blue line shows what the SNR would be if increasing the ISO gave you the improvement you’d expect if photon noise dominated.

For the Nikon D800E, the situation is much more clear-cut, because the greater numbers of photosites in the same area means each one can collect fewer photons than the D4, for a given light level, f-stop, and shutter speed. The D800E SNR tracks the 1.5dB/octave line almost exactly, meaning that increasing the film speed over DIN 21/ISO 100 doesn’t buy you any improvement in SNR.

With the Leica M9, you can get SNR benefits by increasing the ISO speed as far as 640 (DIN 29), but not beyond. In fact, things go bad faster than you’d expect after ISO 640.