Application and Optimisation of the Spatial Phase Shifting ...

76 Electronic or Digital Speckle Pattern Interferometry
whenever the integration interval is symmetrical. The static method is referred to as the step method and
the dynamically phase shifting approach is known as integrating-bucket or simply bucket method
[Wya75].
The equation system (3.12) or (3.59) is set up under the assumption that the unknowns do not change
from frame to frame, i.e. are temporally constant. While this is very likely to be correct for I b and M I , it is
difficult to assure for ϕ O , which is why vibration-isolating optical tables, phase stabilisation facilities
and/or short exposure times are very common with this method. The interferograms I n (x,y,t n ) must be
recorded as quickly as possible to diminish influences by object changes or phase fluctuations in the
interferometer, and the possibilities to carry out TPS measurements of rapidly moving objects or under
external disturbances are limited. Fig. 3.19 presents sawtooth phase maps from experiments under various
conditions. While TPS delivers good phase measurements under temporally stable conditions, a vibrating
interferometer (here: table without air cushion) can cause wrong phase shifts and thus loss of direction
information. With locally different phase shifts, as caused by turbulent air in the beam paths, also the
qualitative correctness of the image may get lost.
Fig. 3.19: Sawtooth phase maps as results of deformation measurement with TPS under: stable experimental
conditions (left), vibrations (centre), and air turbulences (right).
Much work has been done to cope with the various error sources: phase-shift miscalibrations [Moo80,
Schwi83, Che85, Joe94, Sla95, Och98], vibrations [dGro96, Dec96, Dec98, Hun98], unequal and/or
uncalibrated phase steps [Gre84, Oka91, Far94, Ryu97, Wei99], nonsinusoidal intensity profile [Hib95],
and in a wider context, variable bias intensity [Ono96, Sur97b], or variable fringe visibility [Lar96]. There
have also been attempts to reduce the data acquisition time by 2+1-frame methods [Ker90, Col92, Fac93,
Ng 96] or high-speed devices [Cog99, Hun99]. Many of these efforts are concerned with the sensitivity of
TPS to time-dependent phase fluctuations, which shows that these are indeed a major obstacle.
3.3.1 Speckle "size" in interferograms
The experimental determination of the mean speckle size is usually done by calculating the
autocorrelation function of the speckle intensity field and determining the full or half width of its central
peak. As the speckles get smaller, this digital method grows imprecise because the peak is then only a few
pixels wide and requires fitting a curve to it to estimate its width with subpixel accuracy. When dealing
with speckle interferograms however, there is a simpler method: one can conveniently determine the
speckle size from the power spectrum of an interferogram, in which the speckle size is "doubled" by