Application and Optimisation of the Spatial Phase Shifting ...

138 Improvements on SPS
we are concerned particularly with the geometrical side-effects due to the anisotropy of the measurement.
To find out their nature and extent, we carry out the experiments with sufficient object light in an out-ofplane
configuration.
The "overall" effect of decreasing the speckle height d sy , while keeping the width d sx constant, can be
studied by a series of tilts about the y axis, giving rise to vertical sawtooth fringes. The speckle
decorrelation with increasing N x is then governed by d sx and is therefore the same for all d sy . Fig. 6.4
presents some results from these series.
0.14
σ d /λ
0.12
0.10
0.08
0.06
0.04
0.02
0.00
N x at (speckle aspect ratio)
0 (1:1) 20 (1:1) 50 (1:1) 100 (1:1)
0 (1:2) 20 (1:2) 50 (1:2) 100 (1:2)
0 (1:3) 20 (1:3) 50 (1:3) 100 (1:3)
0 (1:4) 20 (1:4) 50 (1:4) 100 (1:4)
0 2 4 6 8 d sx /d p 10
Fig. 6.4: σ d for ESPI displacement measurements by SPS with various speckle aspect ratios as a function of
speckle width d sx for out-of-plane displacements. The parameters for the curves are N x and the respective
aspect ratio, as indicated in the legend box.
This figure should be interpreted as follows: given a certain speckle width d sx , the aspect ratio d sy /d sx
indicates the respective speckle height d sy indirectly; e.g. at a speckle width d sx of 3 d p and an aspect ratio
of 1:2, the corresponding speckle height d sy is 1.5 d p . Consequently, d sx d sy in this study.
For zero displacement, σ d is virtually independent of the speckle aspect ratio. For the other curves,
corresponding to N x = 20, 50, and 100, there is indeed a very slight systematic dependence of σ d on the
aspect ratio from d sx =4 d p downwards. This corresponds to d sy 2 d p and shows that the finer phase
structure does reduce the accuracy; but compared to the performance gain that a wider aperture offers
under critical light conditions, the effect is negligible.