Log and Linear Color

Digital video cameras are now being built to encode an image using one of two different approaches: Log (or logarithmic) color, and Linear color. These can also be referred to as Log Gamma and Linear Gamma. There are many varieties of each, but they are two distinct categories.

LINEAR

Linear color is the one we have seen most of over the past decade. Linear color refers to the way most common video cameras respond to light; the image they reproduce looks 'correct' on a display, and its colors (assuming we've white-balanced and exposed well) are good approximations of the real thing.

Linear color is premised on the ratio between f-stops. Each time we close an iris down by one stop, we cut in half the amount of light (in other words, each stop is worth twice as much light as the stop before). However, if you think about it, you'll never reach your destination if all you do is cut your distance in half each time (Xeno's Paradox), and Linear color is no different - here is a grayscale step chart shot by a Linear camera, and the resulting waveform signal:

Note how each 'stop' doubles the brightness of the previous, and how this results in a sweeping upward curve of the camera's response. In Linear color, almost three-quarters of the camera's responsiveness to light is taken up by only one-third of the dynamic range - and this preference is heavily weighted to the highlights of an image. When shooting with Linear color, we must be very careful not to overexpose the highlights, yet this challenge is heightened by the camera's low responsiveness to shadows.

LOG (Logarithmic)

Log Color, or Log Gamma, are a set of approaches to camera light reponse that use the log function to mathematically alter the camera's response to each f-stop's worth of light. Instead of halving/doubling every time the light level is one stop down or one stop up, Log color uses a set of logarithms to divide by, which has the effect of flattening the response to highlights and thereby lifting the response to shadows. (The specific logarithmic figures used differ depending on the Log Profile, and everyone has their own: Sony (SLog and SLog 2), Canon (C-Log), Blackmagic, Arri, etc etc.)

Here's the same step chart shot using Sony's SLog 2:

Here you can see that each stop, particularly in the highlights, is not twice as high as the previous one. The resulting waveform is less curved, and in fact if you count those steps, you can see there is on extra step in the Log chart - that represents an additional stop of sensitivity in the dynamic range of the image.

An image made with this Log profile, however, will look to the eye to be quite flat and 'washed out'. This is corrected in post production, by mutliplying in the same logarithmic figures that were used to flatten the range in the first place. This set of numbers is called the look-up table, or LUT, and it is applied like a pre-set in color correction software to restore the image to a 'linear' appearance, albeit while preserving the added light data that shooting Log has preserved.

When filming with a Log profile, its important to remember that what you see is NOT what you get. Depending on your specific Log profile, you may need to expose your highlights as much as 20-30% below 'full' white. Your images will look dark and a little murky, and only by viewing it through a LUT will you be able to see the final result. There are a couple of ways to do this: either offload sample shots into a software color correction platform for quick LUT application and image checking - or, some equipment and modern offboard monitoring offers live realtime LUT application to check your image while in the field.