An analysis is conducted to determine the effect of random microdensitometer
positioning errors on the computed Fourier transform (FT) of measured data.
Three statistical measures of the FT are derived: the first two moments and the
mean-square error (MSE). Results show that the expected FT is multiplied by the
conjugate of the characteristic function of the position errors, whereas the
variance and the MSE are multiplied by linear combinations of the same function.
Working relationships are developed for both the continuous and discrete cases.
The continuous errors were Gaussian and uniformly distributed. A simple model of
a counter was used to develop expressions for the discrete case. These simple
equations relate the error probability density function, or counter parameters
to the relative root-mean-square error of the measured FT. An example drawn from
reflection microdensitometry suggests that continuous position error tolerances
should be about the order of 0.5 μm, with counter
failure probabilities less than 9 × 10−9, for a
10% relative rms error in the FT.
© 1982 Optical Society of America
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