Application and Optimisation of the Spatial Phase Shifting ...

56 Electronic or Digital Speckle Pattern Interferometry
calculated ∆ϕ /rad
6.28
4.71
3.14
1.57
0
difference of phases
phase of differences
0 1.57 3.14 4.71 6.28
pre-set ∆ϕ /rad
measured ∆ϕ /(π/128)
256
224
192
160
128
96
64
32
0
difference of phases
phase of differences
0 100 200 300 400
x/sensor column
Fig. 3.3: Left: calculated ∆ϕ , averaged over ϕ O , vs. pre-set ∆ϕ , for the methods to be compared in this subsection.
Right: measured profiles of vertical sawtooth fringes, averaged over 200 rows.
Evidently, the phase-shifting method is not directly applicable to speckle correlation fringes. It will only
work acceptably if the individual speckle phases are suppressed, i.e. the secondary interferograms must be
smoothed to approximate the cosinusoidal envelope of (3.20) as closely as possible. This is usually done
by a low-pass filter and reduces the spatial resolution.
The left-hand part of Fig. 3.4 shows the fringe profile plotted in Fig. 3.3 on the right: surprisingly, the
image does yield direction information, although the averaged fringes do not. The reason is that for
π/4< ∆ϕ