  Standard phase-stepping algorithms (PSAs) estimate the measuring phase of
linear carrier temporal-fringes with respect to a linear-reference.
Linear-carrier fringes are normally obtained using feedback, closed-loop,
optical phase-shifting devices. On the other hand, open-loop, phase-shifting
devices, usually give fringe patterns with nonlinear phase-shifts. The Fourier
spectrum of linear-carrier fringes is composed by Dirac deltas only. In
contrast, nonlinear phase-shifted fringes are wideband, spread-spectrum
signals. It is well known that using linear-phase reference PSA to demodulate
nonlinear phase-shifted fringes, one obtains an spurious-piston. The problem
with this spurious-piston, is that it may wrongly be taken as a real optical
thickness. Here we mathematically find the origin of this spurious-piston and
design nonlinear phase-stepping PSAs to cope with open-loop, nonlinear
phase-shifted interferometric fringes. We give a general theory to tailor
nonlinear phase-stepping PSAs to demodulate nonlinear phase-shifted wideband
fringes.
