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tudy was 
be posi- 
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he more 
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to one.) 
nsitivity 
vector will have more constant amplitude and direction 
over the object surface because illumination and ob- 
servation angles will vary less. Thus our arrangement 
resulted in these angles being approximately normal to 
the object surface, and therefore the sensitivity was 
close to 0.5A for out of plane motion and close to zero for 
in plane motion (parallel to the ellipsoids). 
(3) A third reason for using the arrangement de- 
scribed is that with illumination and observation close 
together at a large distance from the object the risk that 
contouring fringes are formed is minimized. Con- 
touring fringes represent the object intersected by a set 
of equal distant planes that are more or less normal to 
the line of sight. This type of fringe reveals the 3-D 
shape of the object, and it is, of course, important that 
they are not misinterpreted as being caused by defor- 
mation. 
Contouring fringes may be produced by a large rigid 
motion of the object if it is positioned so that the k-value 
of the holodiagram is much higher for those parts that 
are closer than for those that are further away.? In that 
case a steady rigid translation of the object forward or 
backward would, in real-time holography, result in 
fringes that are formed at a higher rate at those parts 
that are more distant. Thus the fringes accumulate 
between distant and closer parts of the object and form 
contouring fringes. With the arrangements we used for 
the study of the milling machine the error caused by this 
effect could be ruled out because the k-value over the 
total object was so constant that a rigid motion of many 
centimeters would be needed before one single fringe 
would form. 
(4) A fourth reason of using a large distance between 
the laser and the large object was simply that we did not 
need such a strong lens in the spatial filter used to di- 
verge the beam. When the illumination angle is more 
constant it is much easier to get an even illumination of 
the object. 
Two disadvantages of large distances between com- 
ponents in holographic arrangements are greater risk 
of relative motion and of turbulence and temperature 
gradients in the air along the pathlengths of the light. 
These problems are, in our experience, much smaller 
than one would think intuitively or after having studied 
the holography literature. Sometimes, however, the 
refractive index of air varies too much in any ordinary 
large room. This is particularly the case close to the 
floor and up to a height of about half a meter. For this 
reason and because we wanted to work during the whole 
day, we built a dark tent of black plastic film to shut out 
the daylight and to prevent unwanted air disturbances. 
The tent which was 15m long, 4 m wide, and about 2 m 
high was built in a few hours. It covered the whole 
machine, the lightpath, and most of the laser. The roof 
of the tent had a hatch so that the milling machine could 
be lifted and rotated with an overhead crane so that its 
deformations could be studied from all directions. 
For the experiment we used an ordinary Spectra- 
Physics He-Ne laser model 125 with an output of some 
60 mW. The exposure time was 10 sec on Agfa-Gevaert 
Scientia 10E75. As a shutter we used a small cardboard 
box which normally was placed in front of the spatial 
filter but which we removed by hand during exposure. 
We fixed to the front of the laser a Spectra-Physics 
standard spatial filter (a positive lens with a matching 
pinhole). As a stable support for the laser we used the 
table of another still heavier milling machine which 
happened to be standing in the right place. 
About half a meter from the machine which was to be 
studied we placed an upright cylinder of steel about 1 
m high and weighing some 50 kg, and on top of this we 
fixed a front surface mirror which reflected the refer- 
ence beam. No beam splitter was used, but this refer- 
ence mirror was placed directly into the divergent beam 
  
Fig. 3. The cutting force of the milling machine was simulated by 
static loading. Every fringe represents a displacement of about 0.3 
um normal to the plane of the photo. Straight fringes represent a tilt 
around an axis parallel to the fringes. Curved fringes represent de- 
formation. A fixed reference surface is seen on the lower right. 
  
Fig.4. The stable plate holder that is specially designed for sandwich 
holography. The hologram glass plates are held in position solely by 
gravity and rest against three ball points and three cylindrical pins. 
September 1977 / Vol. 16, No. 9 / APPLIED OPTICS 2523