Fig. 5. The sandwich hologram of Fig. 3 was tilted so that the de- 
formation of the machine head could be studied without influence 
on the fringe pattern from the deformation of the total machine. The 
fringes that have been removed from the head reappear at the refer- 
ence surface. When the number of fringes decreased at the head it 
increased on the knee indicating that head and knee tilted in different 
directions. 
Fig. 6. To study the deformation of the knee the sandwich hologram 
of Fig. 3 was tilted in a direction opposite to that of Fig. 5. The de- 
formation was, however, very small and resulted in only about one 
fringe. 
the floor to the right of the machine is the fixed refer- 
ence surface against which the motions of the machine 
could be defined. By tilting the sandwich hologram 
during reconstruction it was possible to move eliminated 
fringe patterns from any part of the milling machine to 
this surface. 
Figure 3 displays the motions of the machine in ref- 
2526 APPLIED OPTICS / Vol. 16, No. 9 / September 1977 
erence to the floor, each fringe representing a dis- 
placement of 0.32 um along the line of sight. Thus the 
motion of any part of the machine can be calculated by 
counting the number of fringes that have to be crossed 
if we trace a path from the foot of the machine to the 
studied point. Areas that have not moved in the di- 
rection of sight are fringe free (the foot of the machine, 
the reference surface). Areas covered by straight par- 
allel fringes have tilted rigidly without deformation. 
The tilt is larger when the fringes are closer. It can be 
seen that the knee has mainly tilted. The tilt angle can 
be calculated by counting the number of fringes across 
its known width from left to right. Areas of the ma- 
chine that are covered by curved fringes have been de- 
formed. (The main body has been deformed by the 
moment caused by the force acting between tool and 
table.) 
From Fig. 3 it is difficult to judge the deformation of 
the head of the milling machine because its fringe pat- 
tern is mainly caused by the large torsion of the main 
body. After the sandwich hologram has been tilted 
until the number of fringes crossing the head became 
as low as possible it was, however, easy to study the 
deformation of the head without any disturbances from 
the rest of the machine (Fig. 5). From the angles that 
the sandwich hologram had to be tilted to change the 
picture from that of Fig. 3 to that of Fig. 5 the tilt of the 
machine head could be evaluated with respect to mag- 
nitude, direction, and sign. This result corresponds to 
what could be found by counting the fringes on the head 
in Fig. 3 or the number of fringes per length on the ref- 
erence surface in Fig. 5. 
When we tried to use the same procedure for the 
study of the deformation of the knee we found that only 
one or two fringes were left (Fig. 6). Therefore we ex- 
posed a new pair of holograms with a force difference 
that was three times larger than before. We made an- 
  
Fig. 7. The load of the machine was increased so that it became three 
times larger than in Fig. 4. Without any tilt of the sandwich hologram 
the fringes on the knee were so closely spaced that they could hardly 
be counted. (The moiré patterns on the head and the knee of the 
machine did not exist on the original photo but have been caused by 
the printing process.) 
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