Raw bit depth is about dynamic range, not the number of colors you get to capture
|Shooting this image in 14-bit helped retain the full dynamic range captured by the sensor. Most of the time, with most cameras, 12-bit is enough.|
Raw bit depth is often discussed as if it improves image quality and that more is better, but that's not really the case. In fact, if your camera doesn't need greater bit depth then you'll just end up using hard drive space to record noise.
In fairness, it does sound as if bit depth is about the subtlety of color you can capture. After all, a 12-bit Raw file can record each pixel brightness with 4096 steps of subtlety, whereas a 14-bit one can capture tonal information with 16,384 levels of precision. But, as it turns out, that's not really what ends up mattering. Instead, bit depth is primarily about how much of your camera's captured dynamic range can be retained.
Much of this comes down to one factor: unlike our perception of brightness, Raw files are linear, not logarithmic. Let me explain why this matters.
The human visual system (which includes the brain’s processing of the signals it gets from the eyes), interprets light in a non-linear manner: double the brightness of a light source by, say, turning on a second, identical light, and the perceptual difference isn’t that things have got twice as bright. Similarly, we’re much better as distinguishing between subtle differences in midtones than we are vast differences in bright ones. This is part of the way we’re able to cope with the high dynamic ranges in the scenes we encounter.
Digital sensors are different in this respect: double the light and you’ll get double the number of electrons released by the sensor, which results in double the value generated by the analogue-to-digital conversion process.
|This diagram shows how the linear response of a digital sensor maps to the number of EV you can potentially capture. Note how the brightest stop of light takes up 1/2 of the available values of your Raw file.|
Why does this matter? Because it means that half the values in your Raw file (the values between 2048 and 4096 in a 12-bit Raw file) are devoted to the brightest stop of light you captured. Which, with most typical tone curves, ends up translating to a series of near-indistinguishably bright tones in the final image. The next stop of light takes up the next 1024 values, and the third stop is recorded with the next 512, taking half of the remaining values each time.
In a typical out-of-camera JPEG rendering, the first ~3.5EV are captured above middle grey, and the first three of these stops of highlights have used up 7/8th of your available Raw values. The remaining Raw values are used to capture tones from just above middle grey all the way down to black.
Follow this logic onwards and you’ll see that the difference between 12 and 14-bit Raw has less to do with subtle transitions* (after all, even in the example I describe, the tones around middle brightness would be encoded using 256 levels: the same number of steps used for the entire dynamic range of the image if saved as a JPEG or viewed on most, 8-bit monitors). Instead it has much more to do with having enough Raw values left to encode shadow detail.
It's a different story for files that have been processed, either by gamma correction (eg JPEGs and TIFFs) or compressed Raw files, but for linear Raw files, that's how things work.
|By the time you've created a JPEG, the brightest stop of your image is likely to be made up from the tones in this image. Half of your Raw file was used for storing just these near-white tones.|
Since every additional 'bit' of data doubles the number of available Raw values, but the brightest stop of light takes up half of your Raw values, you can see that all of those additional values increase the capacity of your Raw file by 1EV. Which, assuming neither you nor your camera's exposure calibration are completely mad, ends up meaning an extra stop in the shadows.**
In other words, 12-bits provides enough room to encode roughly 12 stops of dynamic range, while 14 bits gives the extra space to retain up to around 14EV. Or to look at it from the opposite perspective: if your camera is overwhelmed by noise before you get to 12 stops of DR, you don’t benefit from more bit depth: all you’d be doing is capturing the shadow noise in your image in greater detail.
Bit depth in video
It's a similar story in video. Because video capture is so data intensive, it’s not usually practical to try to save all the captured data, which usually means crushing everything down to just 8 or 10 bits.
Log gamma is a way of taking the linear data captured by the sensor and reformatting it so that each stop of captured light is given the same amount of values in the smaller file. This makes more sensible use of the file space and retains as much processing flexibility as possible.
And, even if you own, say, a Sony a7S (one of the few cameras we’ve encountered that has sufficiently large/clean pixels that it doesn't have enough bit depth to encode its full dynamic range at base ISO), you need to remember that you only get the camera’s full DR at base ISO. As soon as you increase the ISO setting, you'll amplify the brightest stop of captured data beyond clipping, such that you very quickly get to the stage where you’re losing 1EV of DR for every 1EV increase in ISO.
So, even though you started with a camera whose DR outstrips its bit depth, that stops being true as soon as you hike up the ISO: instead you just go back to encoding shadow noise with tremendous precision.
Consequently, if your camera doesn’t capture more than 12 stops of DR, you probably shouldn’t clamor for 14-bit Raw: it's not going to increase the subtlety of gradation in your final images (especially not if you're viewing them as 8-bit). All those extra bits would do is increase the amount of storage you're using, with around 16% of that space being devoted to an archive of noise.
* As Emil Martinec beautifully illustrates: if the variation due to noise is greater than the steps in your sampling, the noise will dither any transition or gradient. Or, looked at the other way around: if the steps you're capturing your tonal information with are smaller than the variations caused by shot noise, there's no further gradation benefit to sampling with higher precision (you just end up perfectly describing the noise). This is exploited by some of the cleverer Raw compression methods, but that's an issue for a separate article. [Back to text]
** The best noise performance is achieved by making the most important tones in your image from as much light as possible. Which means the best thing to do if you suddenly gain an extra stop of highlight capacity is to increase your exposure by 1EV. Your highlights still clip at the same point but all your midtones and shadows receive more light and become less noisy. [Back to text]
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