Application and Optimisation of the Spatial Phase Shifting ...

5.1 The experimental set-up 113
out-of-plane tilts. The axis of in-plane rotation coincides with the optical axis. The aluminium plate is
coated with a white chalk spray that causes complete depolarisation. Thereby an incoherent background is
present in all of the measurements, which is a realistic scenario.
A second beamsplitter BS2 together with mirror M2 guides the reference light path close to the one of the
object. The mirror M2 can be displaced by means of the piezo-electric translator PZT (PI-170) and thus
adds the possibility to use TPS. The polarisation filter PF attenuates the reference light to the extent
required. By MO2 the reference wave is coupled into a single-mode fibre that is held in place by a bent
syringe needle. The reference wavefront that leaves the fibre end (cut with blunt scissors) is very smooth.
The aperture stops A are laser-cut aluminium plates of 0.2 mm thickness with circular or elliptic holes of
various diameters to generate different speckle sizes. The distance ∆x of the fibre end relative to the centre
of the aperture stop determines the spatial phase shift α x (∆x). It is set to zero (∆x = 0) for the TPS
measurements and to the desired α x (∆x) for SPS, and calibrated by the Fourier method [Bot97]. Since the
necessary ∆x is frequently larger than the radius of the aperture, there are slits adjacent to the holes
through which the reference light can pass, which is also depicted in Fig. 5.1 as seen from the direction of
the camera. To obtain "clean" power spectra of the interferograms, the rest of the slit is covered again
once the fibre end is correctly positioned, which becomes very important for the smaller apertures. The
aperture shape for elliptical speckles is indicated by the broken line; thus the speckles will be elongated in
x direction.
For TPS, the slits are covered completely and the fibre end is brought to the centre of the aperture. The
syringe needle then obscures a part of the aperture, which becomes the more important the smaller the
aperture is. To remove the spatial phase shift, the Fourier method can assist as well: the interference
sidebands in the frequency plane are shifted into each other (see Chapter 3.3.1).
To shift the phase temporally, a control bit from the PC triggers a digital sawtooth waveform generator
(HP 33120A) that drives the PZT via an HV amplifier (built in-house). The voltage ramp is chosen so as
to generate a nominal phase shift of α t , matching α x (∆x) to obtain comparable data. While the temporal
phase shifting is in progress, a sequence of consecutive camera frames * is stored, of which the first and
the last one are subtracted. They have a nominal phase difference of 2π and should look exactly the same.
If their mean brightness difference exceeds a certain threshold, an external mechanical or thermal
disturbance is presumably present, the frames are discarded and the sequence is repeated. Otherwise the
phase shift of all recorded frames is assumed to be correct; additional tests ** confirmed α t to be accurate
* It turned out that the frame grabber was not capable of recording a full-format sequence of 1024 2 pixel frames (frame
frequency: 12.5 Hz) reliably, which is why only 1024 768 pixels were used.
** These rely on executing a temporal phase-shift sequence without removing the spatial phase shift. The global phase offsets
between the recorded interferograms can then be determined by calculating their phase maps with SPS and subtracting them. In
principle, the same was done in 5.3; see also [Lai91, Küch94, Win95].