Application and Optimisation of the Spatial Phase Shifting ...

Summary 177
The feasibility of combining intensity- and phase-gradient correction was demonstrated and shown to
yield the least measurement error; however the intensity-gradient correction does not recommend itself
strongly, since almost the same fringe quality can be achieved without it and at an optimised beam ratio
instead.
An important step is the extension of the phase shift to two dimensions, which allows to use the spatial
frequency plane more efficiently; thus, multiple phase measurements can be carried out and averaged for
each image pixel to make up more reliable values. The combination of this experimental modification
with the computational solutions decreases the rms of the phase-measurement error in unfiltered phase
maps to below λ/20 for moderate fringe densities, which remains valid when the speckle size is reduced to
2.5 pixels.
This accuracy is about the best that one can obtain by phase-shifting; therefore the Fourier-transform
approach to phase extraction has been tested, for which a speckle-intensity correction can also be carried
out by simple subtraction of the speckle pattern from the interferogram or, equivalently, the speckle halo
in the spatial frequency plane. It turned out that the Fourier method yields an improvement only at very
low fringe densities. For higher fringe densities, the intrinsic data smoothing property of SPS formulae
due to the spatial extent of the phase-calculation window gets apparent, and the noise introduced by
speckle decorrelation is somewhat smaller than in the Fourier transform method.
Another method of error reduction is to use a "standard" phase-shifting method and to enable it to process
only reliable data, i.e. to eliminate invalid pixels from the measurement. This has been realised by
merging valid phase data obtained from orthogonally polarised speckle patterns.
Finally, SPS has been used to implement temporal phase unwrapping, and the combination of the two
techniques has successfully been applied to deal with the practical problems of automating data storage in
long-term experiments and of measuring deformations of discontinuous objects.
On the whole, the collection of aspects of and possibilities for SPS presented in this work should prove
useful for its successful application in various ESPI measurements. It could be shown that the suspected
disadvantages of SPS constitute no serious restrictions in practice, all the less as some simple and
effective performance enhancements are possible. With its ease of use not being the least, there are good
arguments to consider SPS as an alternative also for situations where TPS is applicable, and to use it just
as confidently.