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Developments in optical technology greatly extend the
possibility of applying photogrammetric and related
measuring techniques in industry. Lasers, and the
associated imaging, recording, and measuring
techniques such as holography, provide some of the new
opportunities. Quasi-optical procedures in the X-ray
and electron microscope fields are also relevant, as
are some new departures in the use of photographic
camera systems. By way of examples, some recent work
at the National Physical Laboratory is includede
1 The principles of holographic measurement of
displacement and strain
J M Burch (1,2)
Holograms store a record of wavefronts reflected from
the surfaces of solid bodies, and since 1965 it has
been realized that two (or more) successive versions
of the wavefronts associated with a body at different
times can be "superimposed" and compared by means of
the interference effects produced. A diffusely
reflecting surface then appears to be covered by
interference fringes which map out any small changes
of shape. If both versions of the same object are
recorded on one plate, the interference pattern
appears to be "frozen" into the reconstructed image.
If only one hologram is recorded, processed, and
replaced, the interference pattern displays contin-
ously any variations in the object in "real-time",
showing departures from the stored version used as
a reference.
To measure the changes which have occurred from the
holographic record, it is necessary to determine the
vector displacement at a sufficient number of points
on the surface. Procedures can be varied to suit
special cases, but a typical basis for analysis is as
follows.
We assume that the specimen is illuminated by a
parallel laser beam whose direction of travel is
specified by the illumination unit vector ^ As
described above, two successive exposures are made,
and a deforming load is imposed before the second
exposure. The hologram is processed and re-
illuminated with the same illumination as before
but the object is removed or covered.
If the observer now looks through the hologrgm towards
a point P, on the testpiece in a direction Vi he
will see that region of the surface as having a certain
brightness somewhere between the maximum and minimum
brightness of the bands in the interference pattern,
and related to the brightness he would have seen if
only one, reconstruction had been present by a factor
2(1 + cos g.)
where Bi represents
the difference in phase of the two reconstructed
disturbances, If dj represents the small (unknown)
vector displacement of Pi between the two exposures,
the phase-angle £i will be determined by
88
^ ^
EA - GG. i) € 26 (8. V)
= X — À ces es
A A
= {M s. da where S G + V;)
X --- nn —
The "sensitivity vector" S is clearly not a unit
vector and describes how the interference fringes,
giving contours of constant dis indicate that
component of the vector displacement d; which lies in
a direction midway between the illuminating and
viewing directions.
If we can now relate the phase difference f, to some
point which does not shift (f -0), we can count
fringe contours from this datum and estimate excess
fractions, assigning & "fringe number" N; to each
point Pi, where
N. = 9i = + (s à: )
T ses Se
2T ^ —
To determine di completely (eege in terms of all three
cartersian gompgnents) three non-coplanar viewing
directions V4, Vo, V3, must be employed, and
we obtain three sets of fringe numbers N, i: Ni: Nis
The three sensitivity vectors are
S17 Xs 27 Gets or)
The cartesian components of each vector 844, 942,
$43, form the rows of the sensitivity matrix
[8j in the general relation of the fringe numbers to
the components of the displacement d
NA 4151 $12 Sq3] T enti di
Noi - x S24 S25 923 doi = x S doi
The desired three components of displacement are
obtained from the reciprocal matrix K = S” .
d \ Ea Ho 8g Ne
el Eu Kop 5 Vas Ni
d.
3i Ku m Es Nas
In practice, the determination of the values of the
"fringe numbers" N provides the greatest problems, and
some simplification is often useful. Conversely,
more automatic and rapid methods for collecting up
the experimental data are sought, and here is an