vertical screw. It is difficult to use Fig. 13 to study the 
deformation of the left support (just behind a small 
dial-gauge) because of the torsion and bending of the 
total upper part of the machine. From the photo in Fig. 
13 it is not possible to find the direction, sign, or am- 
plitude of deflection. 
In Fig. 14 we have during reconstruction tilted the 
sandwich hologram of Fig. 13 until the upper part of the 
machine close to the support is fringe free. By counting 
the remaining fringes (five) on the support its deflection 
in relation to the neighboring part of the machine is 
calculated (5 X 0.26 = 1.3 um). The sign of deflection 
is found by studying the sandwich tilt direction needed 
to reduce this number of fringes. That the total upper 
part of the machine could not be made fringe free in Fig. 
14 proves that it has been deformed by torsion which is 
natural the way the force was applied. The right-hand 
support has almost zero fringes which proves that it was 
almost not deflected at all. 
Even from Fig. 14 it is, however, difficult to say ex- 
actly how the deformation of the left support was dis- 
tributed over its total length. Thus, by tilting the 
sandwich hologram, we rotated the fringes close to 90° 
so that the fringe inclination became a measure of the 
tilt of the support and the curvature of the fringes a 
measure of the tilt gradient or the bending of the sup- 
port (see Ref. 4, Fig. 3). The result can be studied in 
Fig. 15 where we can see that the support was bent in the 
form of an S. This bending is however slightly less than 
one fringe, e.g., less than 0.26 um. Thus the main rea- 
son for the total deflection of 1.3 um was a tilt of the 
support because it was badly fixed to the machine in its 
upper end. This fact is further revealed by the abrupt 
change of fringe angle where the fringes pass over from 
the support to the machine. 
  
Fig. 15. The sandwich hologram of Fig. 13 was tilted so that the 
fringes at the left support were rotated 90° compared to those of Fig. 
14. That way the tilt of the support is indicated by the sharp change 
in angle as the fringes pass over from the support to the over arm. 
The curvature of the fringes on the support indicates its deformation 
from which stress and strains can be calculated. 
2530 APPLIED OPTICS / Vol. 16, No. 9 / September 1977 
  
Fig. 16. When the same procedure was performed with the right 
support, the straight, vertical fringes indicated no tilt and no 
deformation. 
When the same procedure was repeated with the right 
support (Fig. 16) it was found that it had been neither 
tilted nor deformed. Apparently the total load had 
passed through the left support. Using the methods 
described here we could with the information from one 
single sandwich hologram inspect every detail of the 
entire machine. 
VII. Vibrations 
Finally we made some vibration analysis using con- 
ventional time average holography.® An electromag- 
netic vibration generator (Goodmans type V50 Mk1) 
was clamped to the table of the milling machine and 
attached to the shaft. The direction of the forced vi- 
brations was the same as that of the static load during 
the earlier experiments. To find the resonance modes 
of the machine an electric vibration transducer was 
fixed to its upper part. We noted the lower resonance 
frequencies that had sufficient amplitudes and made 
a time average hologram at each resonance frequen- 
cy. 
To our surprise we got no image whatsoever on our 
first trials. After about 1 h of experiments we finally 
succeeded in making a first low quality hologram, and 
after some further time the quality increased. We 
concluded that the vibrations forced the machine to 
start moving on its foundation until it settled down in 
a new equilibrium. Another observation was that to get 
a high quality image a higher ratio between object and 
reference beams was needed when the time average 
holograms were made (see Ref. 7). No measurements 
were made but I would guess that by simply moving the 
reference mirror further out from the center of the il- 
luminating beam the ratio was increased from 1/10 to 
1/2. 
Figure 17 shows how the upper part of the machine 
vibrates at the lowest resonant frequency (76 Hz). The 
broad bright fringe which is slightly inclined to the 
  
Fig. 
was 
and 
vel 
the 
ifi 
pli 
bre 
toc 
in | 
in: 
WO 
no 
of 
po 
so 
su] 
an 
pos