Application and Optimisation of the Spatial Phase Shifting ...

104 Quantification of displacement-measurement errors
grey value
224
192
160
128
96
64
32
0
raw data
9x9 median
320 370 420 470 520 570
x -position/pixel
Fig. 4.3: Deterministically distorted fringe profile due to wrong phase shift; filtering in 2D by the sine-cosine
method with 9
9-median windows.
From this, it gets clear that filtering sawtooth images to obtain reference data is always only an
approximation. This should perform well enough in most cases but seems inappropriate for us since there
are some extreme fringe densities and noise levels to be explored. And finally, the filter size cannot be
standardised, the best choice would change from image to image and still remain a matter of judgement.
4.1.2.3 Composite method
Recently it has been demonstrated that a very good filter can be implemented by using the sine-cosine
method with a small filter size together with a large number of iterations [Aebi99]; the peculiarity of this
algorithm is that the phase is always re-calculated between the iterations. Once again, the phasor
interpretation assists in understanding this qualitatively: by determining the phases and re-deriving sine
and cosine from them, the length of the phasors is re-set to unity in each iteration, which counteracts the
contrast attenuation mentioned above and preserves any phase detail in the image that survives a single
run of the filter kernel. Hence, one can in principle use arbitrarily many iterations and therefore eliminate
the speckle noise almost completely. This seems to be a promising method to generate near-ideal
reference data from whatever input fringe pattern. But still the restriction is that the filter size must be
optimised by the operator; and also, depending on the accuracy required, the number of iterations may
become very large. It was also observed that at the borders of the image and/or at phase discontinuities in
the image, the phase profile gets more and more distorted with increasing number of iterations.
4.1.2.4 Comparing unwrapped data
The problem of white-black edges in the image can also be circumvented by unwrapping the phase before
comparing raw and smoothed data. Clearly, the raw image must not be filtered before unwrapping, which
restricts the application of this method to rather good results with low to medium noise and moderate
fringe density. Even then, the result will not be a direct conversion of phase to displacement, since almost