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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