High-performance data processing algorithms for phase-shifting interferometry accommodate adjustment errors in the phase shift increment as well as harmonic distortions in the interference signal. However, a widely overlooked error source is the combination of these two imperfections. Phase shift tuning errors increase the sensitivity of phase estimation algorithms to second-order and higher harmonics present in Fizeau interference signals. I derive an analytical formula for evaluating these errors more realistically, in part to identify the characteristics of the optimal PSI algorithm. Even for advanced algorithms, it is found that multiple reflections increase the error contribution of detuning by orders of magnitude compared with the two-beam calculation and impose a practical limit of 30% in tuning error for sub-nm metrology in a 4%-4% Fizeau cavity. Consequently, a preferred approach for high precision spherical cavities is to use either wavelength tuning in place of mechanical phase shifting or an iterative solver that accommodates unknown phase shifts as a function of field position.
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