Application and Optimisation of the Spatial Phase Shifting ...

146 Improvements on SPS
Finally, both (6.5) and (6.8) were checked for their spectral transfer properties by means of bsc(ν x ). With
the same input interferograms and averaging of the same portions of the bsc(ν x ,ν y ) maps as in 3.4.5, this
gives the plots shown in Fig. 6.10.
1.57
1.57
0.785
0.785
0
0 1 2 3 4
0
0 1 2 3 ν x /ν 0x 4
ν x /ν 0x
-1.57
-0.785
-0.785
-1.57
Fig. 6.10: Left: bsc(ν x ) for (6.5); right: bsc(ν x ) for (6.8).
By comparison with the graphs in Fig. 3.33 and Fig. 3.36, it can be seen that the noise has got higher; but
for (6.8), the region of low detuning errors is distinctly increased as compared to (6.5). However it was
found that the phase error δϕ O (∆ϕ) (cf. Fig. 5.4) produced by (6.8) has small maxima at ∆ϕ=π/2 and 3π/2
(cf. Fig. 3.39), which indicates that δϕ O due to phase-shift errors is suppressed less efficiently when the
intensity correction is used.
6.3 Modified phase shifting geometry
If we use a circular aperture with a phase shift α x only, and if the measuring points are arranged as in Fig.
3.26, we discard the phase information that would be accessible via the vertical coherence length of the
speckles. But due to the general shortage of spatial coherence in our small-speckle patterns, we should use
it as exhaustively as possible. During the comparison of different phase retrieval approaches that will be
described in this subsection, the σ d refer to just two sets of interferograms, namely a tilt series with B=3
when intensity correction is involved, and another with B=30 when it is not. In both cases, N x ∈ [0, 100]
and d sx = 3 d p .
Provided a frame-transfer or line-transfer camera with progressive scan readout is available, all image
lines can be acquired simultaneously. Then it is possible to introduce an additional vertical phase shift α y
by simply shifting the origin of the reference wave to (∆x,∆y). This results in a slant of the carrier fringes
and allows to choose any desired direction for the set of pixels to use. Examples of composite phase
shifting have been given in [Küch91, Küch97] for classical and in [Wil91] for speckle interferometry.
When the speckle shape can be fully exploited for measurement, the measurement's accuracy should
improve, since the ideal situation of Fig. 3.26, where all the used pixels are inside the same bright speckle,
is unlikely to occur. More often, speckle "boundaries" are crossed, which results in an unreliable phase
measurement. To diminish the noise, it should help to include the possibly better data of the orthogonal
direction and to establish an averaged phase value.