Application and Optimisation of the Spatial Phase Shifting ...

172 Improvements on SPS
the heater was switched on, while for the cooling period ϕ O (x, y, t i ) was stored at an ambient temperature
T 2 when the heater was switched off.
3.4 µm
-0.4 µm
-2.3 µm
1.3 µm
Fig. 6.31: Displacement phases mod 2π (left) and corresponding "temperature" height maps as delivered by
temporal unwrapping (right), for heating (top) and cooling period (bottom). Numerical values denote
maximum and minimum displacements.
While it would be very laborious to define and spatially unwrap all the regions separately, it is even
impossible to determine their relative heights from the sawtooth images on the left. When such
displacements are monitored with temporal unwrapping, the problems are overcome. Without the need to
fit data from different sub-areas together, a complete profile of the surface changes is obtained. One can,
and should, test its reliability by checking the obtained surface tilts for consistency with those following
from the number of sawtooth fringes. On removing the abovementioned "slow" pixels, Φ(x, y) from
temporal phase unwrapping did not deviate by more than 0.1 λ from Φ(x, y) as produced by spatial
unwrapping of the corresponding sawtooth images, which also justifies some confidence in the absolute
heights that are given in Fig. 6.31.
According to the height maps from temporal unwrapping on the right, the deformations that developed in
the heating period are almost reversed during cooling, apart from some remaining displacements and
deformations that are clearly emphasised by an addition of the height data from the two states, as
demonstrated in Fig. 6.32 on the right. Most of the remaining displacement is presumably caused by an
ambient temperature at the end of the cooling period that differed from T 1 .