Application and Optimisation of the Spatial Phase Shifting ...

6.3 Modified phase shifting geometry 151
ν y /ν 0
2
ν y /ν 0
2
3
0|4
1
2
2 3 4|0 1 2 ν x /ν 0
3
0|4
1
2
2 3 4|0 1 2 ν x /ν 0
Fig. 6.14: bsc(ν x ,ν y ) for (6.16) (left) and its intensity-correcting version (right). Black lines: frequency co-ordinates
leading to correct phase calculation, bsc(ν x ,ν y )= 45°; white outlines: areas of -10°¡δϕ¡10°.
A summary of the results from (6.16) and from its intensity-correcting version is given in Fig. 6.15; note
that the ordinate is scaled to a maximum of σ d =0.1λ to make differences visible. The graphs for the
horizontal 3+3–sample averaging 90° formula are repeated from Fig. 6.9.
0.10
σ d /λ
0.08
0.06
0.04
0.02
0.00
3+3-sample averaging 90°, B=30
3+3-sample averaging 90° with intensity correction, B=3
3+3-sample averaging 90°/90°, B=30
3+3-sample averaging 90°/90° with intensity correction, B=3
0 20 40 60 80 N x 100
Fig. 6.15: Overview of σ d from ESPI displacement measurements as a function of N x , obtained with horizontal
(triangles) and averaged horizontal/vertical phase determination (squares) by a 3+3-sample averaging
formula; without intensity correction, B=30 (black symbols); with intensity correction, B=3 (black
symbols filled white). Input interferograms were the same four series as for Fig. 6.13.
In this case, the improvement obtained by switching from (α x ,0) to (α x ,α y ), with pertinent phaseevaluation
formulae, is rather small; but its remarkable property is that it lasts up to (at least) N x =100.
This is in contrast to the other improvement strategies we have discussed so far (where the σ d tended to
become more or less the same for higher N x ); it indicates that the speckle correlation remaining after
displacements that give high fringe densities is indeed more efficiently utilised by the 2-D phase retrieval.