  We propose a least-squares phase-stepping algorithm (LS-PSA) consisting of
only 14 steps for high-quality optical plate testing. Optical plate testing
produces an infinite number of simultaneous fringe patterns due to multiple
reflections. However, because of the small reflection of common optical
materials, only a few simultaneous fringes have amplitudes above the measuring
noise. From these fringes, only the variations of the plate's surfaces and
thickness are of interest. To measure these plates, one must use
wavelength-stepping, which corresponds to phase-stepping in standard digital
interferometry. The designed PSA must phase-demodulate a single fringe sequence
and filter out the remaining temporal fringes. In the available literature,
researchers have adapted PSAs to the dimensions of particular plates. As a
consequence, there are as many PSAs published as different testing plate
conditions. Moreover, these PSAs are designed with too many phase-steps to
provide detuning robustness well above the required level. Instead, we
mathematically prove that a single 14-step LS-PSA can adapt to several testing
setups. As is well known, this 14-step LS-PSA has a maximum signal-to-noise
ratio (SNR) and the highest harmonics rejection among any other 14-step PSA.
Due to optical dispersion and experimental length measuring errors, the fringes
may have a slight phase detuning. Using propagation error theory, we
demonstrate that measuring distances with around 1% uncertainty produces a
small and acceptable detuning error for the proposed 14-step LS-PSA.
