Application and Optimisation of the Spatial Phase Shifting ...

120 Comparison of noise in phase maps from TPS and SPS
Fig. 5.6: Some examples of maps of ∆ϕ(x,y) that have been evaluated for σ d . Upper row, N x =5; lower row, N x =50;
left, SPS with d s =3 d p ; right, TPS with d s =1.5 d p .
Summarising this subsection, one can state that TPS is significantly more accurate than SPS at low fringe
densities. For SPS, the best range of d s is 2.5 to 3.5 d p , with σ d λ/15 for moderate fringe densities; for
TPS, we find d s d p to give a typical σ d of λ/20. Imperfections of the test object prevented an extension
of the TPS study towards smaller d s . It turns out that in the presence of speckle decorrelation, SPS
benefits from larger d s and spatial phase sampling, so that the advantage of TPS fades quickly with
increasing object displacement.
5.5 In-plane displacements
When carrying out in-plane displacement measurements using SPS and assessing its performance, the
reference is the ingenious symmetrical pure-in-plane TPS configuration [Lee70] with its excellent
sensitivity. A pure-in-plane SPS configuration using a double aperture has been established [Sir97a], and
we will investigate its merits, but it also seems worthwhile to modify the set-up of Fig. 5.1 for more
oblique object illumination and to gain in-plane sensitivity in this way, since this arrangement is by far
easier to handle.
Therefore we start the investigation of in-plane measurement accuracy with a set-up that has a mixed inplane/out-of-plane
sensitivity (henceforth abbreviated by "mixed sensitivity") and again offers a