DEFORMATION MEASUREMENTS BY 
PHOTOGRAMMETRIC METHODS* 
   
Bertil Hallert, Doctor of Technology, The Royal Institute of Technology, 
Stockholm, Sweden 
INTRODUCTION 
I SEVERAL sciences the measuring 
techniques have become almost a part 
of the science itself. This is particularly 
true in engineering as well as in a great 
number of other natural sciences. 
Doubtless photogrammetry has much to 
offer for solving many measuring problems 
and several successful experiments have 
been performed, but the use of such meth- 
ods for non-topographic purposes is still 
very limited in practice. Photogrammetry 
is practically unknown among those out- 
side the field, and sometimes the photo- 
grammetrists themselves have not suffi- 
ciently recognized all the possibilities of 
their science. 
Photogrammetry is especially well suited 
for some kinds of deformation measure- 
ments which are arising frequently in some 
branches of engineering. In cooperation 
with other divisions, some experiments 
concerning the use of photogrammetric 
methods for deformation measurements 
were carried out by the Division of Photo- 
grammetry at the Royal Institute of Tech- 
nology in Stockholm. A brief report on the 
principles employed and some results from 
experiments are given in this paper. 
PRINCIPLES 
The main principles of photogrammetric 
deformation measurement methods under 
different conditions are well known and are 
described in the literature. See, for in- 
stance, Lacmann: ‘“Die Photogrammetric 
in ihrer Anwendung auf nicht-topographi- 
schen Gebieten." Berlin 1950. Figure 1 
shows the very simple principle used. 
The object point P; moves into P»; by 
the deformation amount dz. The lens of the 
camera at O reproduces dz as dz’ in the 
picture. From the object distance y and 
the principal distance f we get the relation: 
dz'y 
ds = —= (1) 
f 
The scale factor y/f can be determined 
either by measuring the y and f separately 
or from corresponding distances in the 
object (parallel to the negative plane) and 
in the picture. Obviously the accuracy in 
the measurement of dz’ is of the greatest 
importance for the accuracy in dz. 
In order to measure the distances dz’ as 
accurately as possible, the following is im- 
portant: ; 
1. The definition of the image points 
must be as sharp as possible. 
2. Stereoscopic measurements of the dis- 
tances dz’ give the best possible ac- 
curacy. Consequently the distances 
dz’ must appear as horizontal paral- 
laxes. 
In order to increase the definition of the 
image points, the following suggestion by 
P. Hjelmstrom has proved to be very 
appropriate. The points in the object where 
the deformations are to be determined are 
"signalized" with small polished steel 
balls, such as are in ball bearings. The balls 
are fixed on the object with a special glue. 
For the photography an electronic flash in 
a suitable position is used. See Figure 3. 
The reflection of the flash from each ball 
gives a very distinct image point, If the 
ball should be out of sharp focus, the image 
will consist of concentric curves which can 
still be used for the measurements with 
good results, especially if stereoscopic 
methods are employed. 
«image plane 
| 
  
  
F16. 1. The principles of photogrammetric 
deformation measurements. 
* Paper read at the Twentieth Annual Meeting of the Society, Shoreham Hotel, Washington, 
D. C., January 13 to 15, 1954. 
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