Application and Optimisation of the Spatial Phase Shifting ...

3.4 Spatial phase shifting 85
Fig. 3.27: Sawtooth phase maps as results of deformation measurement with SPS under: stable experimental
conditions (left), vibrations (centre), and air turbulences (right).
3.4.3 Relation of speckle size and magnification
For usual imaging optics, f# = f/D is confined to a maximum of 22 or 32, which may prevent reaching the
desired d s in some cases. Considering
ds = 122 . λ ( M + 1)
f #
(3.70)
where M is the magnification (image size : object size), we can immediately see that the maximum object
size that can be imaged gets smaller when d s is to be increased, and vice versa. Fig. 3.28 gives an
overview of the necessary f-numbers when a certain magnification is required. The plots are scaled for the
pixel size of 7.5 µm of the MX12P camera.
0.01
0.1
M
1
10
100
d s= 0.5 d p
d s = 1 d p
d s = 2 d p
d s = 3 d p
d s =10
1 10 f # 100
Fig. 3.28: Double-logarithmic plot of magnification M vs. f-number for various pre-set speckle sizes.
Let us consider a practical example: with a sensor of 10241024 pixels, we would need M=0.02 in order
to image (37.5 cm) 2 on the chip; for d s =1 pixel, f#10; but for d s =3 d p , f#28, which may not be possible
with standard imaging optics. It also follows from (3.70) that the speckles tend to get very large when
M>1, even for low f# [Løk97, Aebi97]. This is the reason why SPS is applicable at no expense in
microscopic ESPI [ElJa99]: the speckles are large enough in any case.
d p