Until recently this is not an aspect of digital photography that I have given much thought to, linear versus non-linear capture, although recently I am beginning to look critically at the difference between film and digital, so it is surfacing as an issue. First of all I appreciate the essential function of a sensor and the fact that it is simply counting the number of photons that arrive at each site and using a Bayer grid to bin these into red, green and blue values to construct an RGB value for each sensor site. The sensor is linear because it "counts" more photons equals more signal, film emulsion on the other hand "reacts" to light and that reaction occurs at different speeds for different light intensities. As the light intensifies this chemical reaction is relatively slower in proportion to the intensity and so is less prone to blowing out, i.e. it exhibits an non-liner response curve to light intensity, however, this will vary dramatically between different emulsions.
Clearly there are advantages to the non-linearity of film in very high light intensities, although the ability of "good" digital cameras to capture images in very low light conditions is the reverse benefit. The human eye is also a non-linear light capturing device, and in combination with the brain does a significant amount of image processing to make the world intelligible to us. Indeed when a blind person gains sight for the first time, they cannot see, as the brain does not know how to interpret the data it is receiving, a person has to learn to see, it is not instantaneous.
The implication of this exercise is that concern must be taken to compensate for this linearity, a process made easier by first understanding how the camera captures and uses the information.
I have started by selecting an image that I used in Assignment 1
Processing the image in Photoshop to achieve the type of curve in the exercise produces a very dark and pretty flat image - interesting though that this might be a more "real" view of the world, if we had linear eyes this is what things would look like!
Taking this image and reversing the process by applying a reverse curve, I arrived back at something similar to what I stated with. There is very little noise in the image, the starting image was noise free and the processing at 16 bit has not added much back in.
Looking at this again from a curves point of view. The histogram for the starting image is well distributed across the image
This is the curve I applied to return the image to a linear version
Looking at the new histogram it is pushed well to the left, i.e. most data is now in the darker tones
reversing this I applied the following curve
Which returned the histogram to pretty much where it started
An interesting exercise, I have always taken care to avoid blown highlights, but have not really understood why Digital cameras are more prone to this than Film. However, whilst Digital does suffer, a careful photographer can avoid this by judicious use of exposure compensation and checking to make sure that a frame has not blown immediately after taking. Bracketing can help.