The ‘characteristic curve’ shows the tonal response of a film. So what’s it got to do with digital imaging? Quite a lot, actually. Film does not respond to different light intensities in a linear, or proportional way so that a graph of its response doesn’t come out as a straight line.

The shadow (left) and highlight (right) ends of the graph flatten out, and this is what gives film its ‘exposure latitude’ – it holds on to detail even in very dark or very bright areas. Sensors tend to have a more linear response to light, so that extremes of light and dark tend to be ‘clipped’ instead of flattening out, and show no detail as a result.
There are other parallels. One of the properties of film, compared to digital, is its enhanced midtone contrast. Film generally looks more ‘punchy’. The way to mimic this with a digital image is to adjust the curves to produce the ‘S’ shape seen below:
The S-shape steepens the curve in the middle of the tonal range (the steeper the curve, the higher the contrast) but flattens out the shadow (left) and highlight regions (right) so that the detail in these areas is retained, albeit at lower contrast.
This is exactly how most films behave by default. The characteristic curve of a film, then, has an exact parallel in digital imaging, and it’s also a clue as to how to create that ‘film look’ from a digital original.

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