for expander 312 for undoing approximately this compression e g darkening the mid tones of the image after processing is q f u2212 1 f 1 f 1 2 22 a better function for expander 312 may be derived as follows first consider the classic model used by photographers to characterize the response of a variety of photographic emulsions and electronics cameras proposition 0 01 the comparametric plot corresponding to the standard photographic response function 0 4 is a straight line the slope is k u03b3 and the intercept is u03b1 1 u2212 k u03b3 proof g f kg f kq u03b1 u03b2 kq u03b3 re arranging to eliminate q gives g k u03b3 u03b1 u03b2q u03b3 u03b1 1 u2212 k u03b3 so that note that the constant u03b2 does not appear in this comparametric equation thus we cannot determine u03b2 from the comparametric equation the physical intuitive interpretation is that we can only determine the nonlinear response function of a camera up to a single unknown scaler constant applying 0 5 to lighten or darken an image will be called affine correcting e g correcting by modeling the comparametric function with a straight line the special case of affine correction when the intercept is equal to.