An approach is explained for determining the three optical per-formance functions: The edge spread function, ES, the line spread function, LS, and the transfer function pair, MTF and PTF, from an edge trace, ET, obtained by photometric measurements at 2n + 1 points at equal intervals through the range, L, of the ET. The explanation is theoretical, but with as much consideration of the needs of the practical engineer as possible. Smoothing and normalization procedures are an integral part of this method, based on a rigid control by the method of least squares. The mean-square errors, MSE, of all individual results will be obtained. The MSE of a critical magnitude instead of Shannon's sampling theorem is used to determine the necessary and justifiable number of terms of the series applied in this case, the only assumption being the validity of the error propagation law. It will thus be possible to check the reliability or scope of applicability of the sampling theorem within this context, which differs from and goes beyond known methods.