Application and Optimisation of the Spatial Phase Shifting ...

132 Comparison of noise in phase maps from TPS and SPS
0.14
B =1000
14
0.12
12
0.10
10
σ d /λ
0.08
0.06
B =1000
08
06
0.04
0.02
0.00
N x 04
0 0
20 20
02
50 50
100 100
00
0.01 0.1 1 10 100
O I /(µW cm -2 )
N y
0 0
20 20
50 50
100 100
0.01 0.1 1 10 100
O I /(µW cm -2 )
Fig. 5.18: σ d for ESPI displacement measurements using SPS vs. TPS at low levels of O I . "Dark" black: SPS with
d sx¡d sy =3¡1 d p 2 ; "bright" white: TPS with d sx¡d sy =1¡1 d p 2 . Fringe densities N x (left) and N y (right) as
indicated in the legend boxes.
The results from TPS are distinctly better, and O I can even be lowered to 0.01 µW/cm². The improvement
by using TPS amounts to 30% for low densities of both horizontal and vertical fringes over quite a large
range of O I . This confirms that TPS is less problematic under critical illumination conditions, all the more
since d s can – and should – be further reduced in order to maximise the amount of light collected. The
occasional crossing of the curves for N y is due to the greater σσ d
for tilts about the x axis that was
described in 5.2.2.
Surprisingly little power is necessary to reach the plateau of nearly constant errors; it turns out that a
0.5-mW laser would have been powerful enough for the out-of-plane experiments. Also, this experiment
demonstrates impressively the advantage of the phase-shifting technique: even with 2-3 bits of signal
resolution, it is possible to obtain usable results [Dör82, Ker88, Vro91, Hac00]. It may also be worth
noting that both TPS and SPS reach their best performance at the same level of O I , which is 10 µW/cm²
in this case.
From the results in this subsection, it follows that the decision for or against elliptic speckle is not a
general one: it depends on the expected result of the experiment, as well as on the amount of light actually
available. We will briefly return to this issue in Chapter 6.1.3.