The recovery of photographic system transfer functions from film records is invariably complicated by the presence of grain noise, which often causes these experimentally determined functions to oscillate wildly, and introduces into the calculated data a positive bias with respect to the correct transfer functions. However, by utilizing the contrast between the random behavior of grain noise and the more well behaved photographic system transfer function, we may remove a substantial amount of noise-caused error through the use of suitable smoothing techniques. To demonstrate the merit of a particular smoothing technique, which improves the signal to noise ratio in the frequency domain by convolving the raw transfer function with a variable bandwidth smoothing function, noisy photographic edge image traces were synthesized using a CDC-3300 computer, the Fourier analysis program, FRAF, and microdensitometer traces of an evenly exposed film sample. The application of the smoothing technique to the raw transfer functions produced from this edge data and the utilization of the smoothed transfer functions in the calculation of line and three-bar image cross sections serve to illustrate the effectiveness of the method.
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Elliot Blackman (1969) studied this question.