Application and Optimisation of the Spatial Phase Shifting ...

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7 Summary
This thesis work has presented a detailed investigation of various aspects that concern the application of
spatial phase shifting (SPS) in ESPI. The objective was to broaden the previously somewhat sparse
knowledge of what happens in spatial phase sampling on speckle fields, and to utilise the findings to
introduce some improvements of SPS.
The ground on which to base such an investigation is, first of all, an extensive study of the nature of
speckle fields. Fortunately, speckle statistics have been an important topic in optical research for some 40
years, so that many useful results could be collected and grouped. The theoretical studies were
accompanied by experimental validations of some results.
With respect to SPS, the one-dimensional intensity and phase gradients deserve particular interest, and it
was found that the speckle intensity is correlated with the intensity gradient and anticorrelated with the
phase gradient. This simple rule of thumb provided valuable guidance as to the assistance of speckle
statistics in improving SPS. The speckle intensity field, showing more spatial structure than the phase
field, hardly allows reasonable assumptions to be modelled in the phase calculation, but is directly
accessible in the experiment. This extra information can be used to counteract the disadvantageous
influence of speckle intensity fluctuations on the interferogram. The speckle phase field was seen to be
co-operative for interferometry: the phase gradients are low where the speckle field is bright, and those
regions of the field where the phase "leaps" or is even undefined, were seen to be rather dark anyway.
Since constant speckle phase gradients can be envisaged as linear phase-shift miscalibrations, the use of
phase-calculation formulae that are tolerant of this type of error seemed to be the most sensible decision
for effectively reducing measurement errors.
After getting familiar with the properties of the speckled object wavefront, it was necessary to turn
towards optimisation of the way to process speckle interferograms. For this purpose, digital speckle
interferometry and the phase-sampling process have been reviewed. It was found that it is always better,
in SPS and TPS, to subtract speckle phase maps than to work with correlation fringes; this has been
confirmed by experimental results.
The aspects of speckle interferometry that pertain especially to SPS have been discussed in detail. The
spatial phase shift was seen to be geometrically quasi-constant to a very high degree of accuracy; however
the spatial frequency content of speckle interferograms supersedes this theoretical result, and the subjects
of speckle size and phase-shift setting have been addressed from the viewpoint of spatial frequencies.
Since speckle phase gradients cause significant distortions in the carrier fringe pattern, its spatial
frequency spectrum will be considerably broadened. It is therefore worthwhile to examine the effect in the
spatial frequency domain. Consequently, the well-established and powerful Fourier description of phaseshifting
formulae has been used. It interprets phase extraction as a digital signal filtering process in the
spectral domain, with characteristic spectral amplitude and phase transfer functions. When using this