I was reading in a book about the dynamic range and several times I find the expression "responsive curve" or "image's responsive curve"?
What does the responsive curve represent? What is the responsive curve?
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A response curve is the relation between what the input and output of a sensor or even film.
As you may know, a sensor measures light by creating an electrical charge in response to photons hitting a photosite. One would expect in a perfect sensor that the amount of light falling on a photosite would be directly proportional to the charge it creates. If this were the case, the response-curve would not be a curve at all and instead it would be a line.
In practice, you have a curve. It is almost flat for most of the range but usually tapers off at the low end and, usually for film, at the high end too. This called the shoulder or roll-off.
Things get more complex as RAW data is transformed into pixels because that transformation is not at all linear either. JPEG files for example use a gamma curve which varies between cameras and converters.
Where it relates to dynamic-range is that the curve represents how various tones of the scene are mapped into an image. With a steep curve, dynamic-range would be narrower but the image would have higher contrast (and vice-versa).