Application and Optimisation of the Spatial Phase Shifting ...

3.4 Spatial phase shifting 97
Since the displacement's phase gradient is constant in the test images and the histograms were generated
from an integer number of fringes (5.0), the true phase distribution is uniform as in Fig. 3.7; but
depending on the amount and type of δϕ O
, various distortions are present. For α=90°/sample, (3.57)
(upper row, right histogram) yields the most realistic phase statistics with only a small preference for
∆ϕ 0. In the centre of the lower row of Fig. 3.41, one can recognise the residual ripple in the phase map
from (3.58) by a small increase of the distribution at ∆ϕ π; generally speaking, the amount of detuning
sensitivity may be seen from the height of that peak. Finally, the Fourier method (lower row, right
histogram) suppresses this deviation as well and leads to almost uniform phase statistics.
While these effects exert a smaller influence on the measuring accuracy than the histograms may suggest,
they are characteristic of SPS. As seen above in Fig. 3.7, TPS yields perfectly uniform distributions when
the phase shift is well calibrated; but in SPS the speckle phase gradients always cause systematic
distortions. These even allow one to tell from the histogram of a sawtooth image whether it is from TPS
or SPS, and in the latter case, what type of phase-extraction formula was used.