Application and Optimisation of the Spatial Phase Shifting ...

168 Improvements on SPS
6.7.2 Long-term observation of biological object
Many industrial ESPI experiments allow to predict the number and shape of fringes with which a test
object will respond to a certain load. On the other hand, being a non-destructive examination technique,
ESPI is particularly useful for unique objects about whose properties little is known. Therefore it is in
general difficult to foresee changes in the fringe pattern, all the more when the objects are not subjected to
test sequences or cycles but left to fluctuations – or attempts of stabilisation – of ambient parameters. In
such cases, eventful periods may alternate with hours of little or no changes. A "good" experiment
requires that the object motion be adequately tracked in time, this is, neither fringe density nor speckle
decorrelation must grow too large between the capturing of consecutive interferograms; and on the other
hand, no redundant data should be produced. While there may be tasks where a human operator can make
such decisions, this is undesirable from an economical point of view. Also, some observations exclude the
presence of a person.
Temporal phase unwrapping is well suited to utilise the fringe order count n(x, y, t) to generate matched
data storage intervals ∆t: from the continuously updated values Φ(x, y, t), the extreme values Φ max and
Φ min can be extracted in every run of the temporal phase unwrapping loop. When the difference exceeds a
certain threshold Φ T , it is assumed that the corresponding sawtooth phase map ∆ϕ(x, y) = ϕ O (x, y, t f ) –
ϕ O (x, y, t i ) between the present phase distribution ϕ O (x, y, t f ) and the stored initial one, ϕ O (x, y, t i ), has
acquired m fringes with m = Φ T /2π. In that case ϕ O (x, y, t f ) is stored and re-labelled ϕ O (x, y, t i ), Φ(x, y, t)
is cleared and the procedure begins anew. This technique yields a sequence of few-fringe sawtooth images
that constitute no problem for spatial unwrapping. Note, however, that this method of fringe counting
does not limit the fringe density: when small defects generate high local phase gradients, it may possibly
come to unresolvable sawtooth fringe patterns. The phase gradient is easily accessible with the help of the
co-ordinates of Φ max and Φ min ; but this procedure was omitted for the sake of simplicity.
Of course, the most convenient data evaluation would be to accumulate Φ(x, y, t) throughout the whole
observation, whereby it may even become obsolete to save phase maps ϕ(x, y) regularly. But with the type
of filter used here (6.26), it is safer to eliminate accumulated noise or accidental errors (e.g. by abrupt
stress relaxation in the interferometer) by clearing Φ(x, y, t) when a phase map is stored. Thereby the
continuous tracking of phases Φ(x, y, t) is given up, but the propagation of errors is being limited to one
measurement of Φ(x, y, t), corresponding to only one storage interval ∆t. Nevertheless, the whole series of
k phase maps Φ k (x, y, t) may be stored and, if usable, added up later on to yield Φ(x, y, t total ) = ΣΦ k (x, y, t).
To test this approach of dynamic data storage, I examined a biological test object whose likely
deformation is not known in advance. The white spot on a fresh chestnut, as shown in Fig. 6.26, was
found to be quite co-operative for interferometry: its surface is reasonably reflective and maintains
speckle correlation over sufficient time intervals. We can expect the displacements to proceed most
rapidly at the beginning of the experiment because the object will relax in its holder. Also, the loss of
water from the surface should result in a constant shrinking, relatively fast initially and then levelling off.