In optical metrology, the phase-shifting technique is used to retrieve the phase information from interferograms. Such displacement can be performed by mirrors attached to electromechanical devices (such as piezoelectric or moving mounts), gratings, or polarizing components, which need to be calibrated to associate the displacement of the device with respect to the induced phase shift. For this purpose, we present a closed-form formula to calculate of the original phase step between two randomly shifted fringe patterns by extending the Gram–Schmidt orthonormalization algorithm. To demonstrate its feasibility, we perform an evaluation that consists of three cases that represent different fringe pattern conditions. First, we evaluate the accuracy of the method in the orthonormalization process by estimating the test step using synthetic normalized fringe patterns with no background, a constant amplitude, and different noise levels. Second, we evaluate the formula with a variable amplitude function on the fringe patterns and a constant background. Third, we evaluate non-normalized noisy fringe patterns in which we include the comparison of prefiltering processes such as the Gabor filters bank, Hilbert–Huang transform, and isotropic normalization process and a high-pass filter to emphasize how they affect the calculation of the phase step.