Application and Optimisation of the Spatial Phase Shifting ...

5.6 Impact of light efficiency 129
The images confirm that TPS delivers good phase maps (σ ∆ϕ 25.7°) with good sensitivity. The result
from the mixed-sensitivity SPS configuration has reasonable quality in terms of σ ∆ϕ (43.0°); but on
converting to displacements, the σ d value (cf. Fig. 5.14) suffers from the relatively low in-plane
sensitivity. For the pure in-plane measurement by SPS, the σ d value is lower; but as to be seen, σ ∆ϕ has
the highest value of all the examples (64.3°). While this example does not present images that are
difficult to unwrap, it does show that the σ d figure of merit alone can be misleading when the quality of
images is to be judged. In terms of σ ∆ϕ , the mixed-sensitivity method is preferable for SPS: for N y =0 its
σ ∆ϕ is around one-half that of the pure in-plane SPS method, and it is still by some 14% better at N y =100,
which may then allow to skip some filtering before unwrapping can take place.
Moreover, the mixed-sensitivity SPS set-up has a great advantage in light efficiency over the pure inplane
SPS configuration; and in Chapter 5, we will explore methods to improve measurements with a
smooth reference wave, so that the deficiency in σ d is reduced. Finally, a 3-D SPS system with two pure
in-plane assemblies is difficult to implement, while – at the sacrifice of orthogonal sensitivity vectors – it
would not be difficult to use layouts with oblique illumination.
On the whole, the results presented here show an advantage for TPS when in-plane displacement
measurements are concerned. For moderate fringe densities, σ d λ/20 is realistic, while both of the SPS
approaches yield λ/6 to λ/7.
5.6 Impact of light efficiency
In the preceding subsections we have already mentioned the potential influence of the aperture size on the
measurement in terms of light economy. During the investigations presented thus far, it was easy to
collect sufficient object light: the laser was powerful and the image field was rather small. But it is not
unusual in practice to have very little object light available. In these cases, TPS should be in favour
because it will function with very small speckles, which in turn allows for large apertures to collect a
greater amount of the scattered light. It is even stated that under conditions difficult in this respect, the
aperture should be opened up as wide as possible [Leh97a, Leh98]. There is no way to do so in SPS: for
phase shifting to make sense, a certain minimum speckle size in the direction of the phase shift, and hence
sufficient spatial coherence over the spatial sampling window, is necessary.
This subsection presents some measurements of σ d under shortage of object light for TPS and SPS,
carried out with the out-of-plane configuration of Fig. 5.1. Aiming at getting an idea of the difference
between the methods, we simply consider d s =1 d p for TPS and d s =3 d p for SPS, although both values
could still be decreased. With this setting, the usable object wave intensity in SPS is smaller by almost an
order of magnitude than in TPS when circular apertures are used.
This can be partly circumvented by enlarging the speckles only in the direction of the spatial phase shift,
which is easy to achieve by using an elliptical or rectangular imaging aperture [Pfi93, Ped93, Sal96]. The
idea is sketched in Fig. 5.16 for the example of α x =120°/column (of course, the relevant parameter is the