: Reprinted from APPLIED OPTICS, Vol. 16, page 2521, September 1977 
Copyright 1977 by the Optical Society of America and reprinted by permission of the copyright owner. 
Sandwich hologram interferometry. 4: Holographic studies of 
two milling machines 
Nils Abramson 
The deformation of two milling machines was studied using real time holography, double exposure hologra- 
phy, and sandwich holography. The about 2-m high machines had a weight of about 2 tons each, and the 
experiments were made directly on the floor of ordinary machine laboratories using continuous lasers. The 
machines were deformed by static forces of the same magnitude and direction as ordinary cutting forces. 
The main advantages of sandwich holography were that it made possible detection of the signs of displace- 
ment, measurement of small deformations without influence of large rigid body motions, measurement of 
larger displacements than possible with ordinary holography, and study of local deformations of details 
down to fractions of a fringe. Some vibration measurements were also made using the conventional time 
average method. 
|l. Introduction 
Hologram interferometry! has during the last years 
become more and more accepted as a precision tool for 
measurement of mechanical deformations, displace- 
ments, dimensions, and vibrations. By studying the 
deformation caused by loading, it can be used for ho- 
lographic nondestructive testing (HNDT') where it has 
to compete with ultrasonics and x rays. It is also used 
for the study of stress and strains which have to be cal- 
culated from the observed surface displacements. In 
the latter case hologram interferometry has to compete 
with, e.g., photoelastic analysis using polarizing effects 
in comparison to which it has the great advantage that 
it can be applied directly on the actual part. In holo- 
gram interferometry there is no need to make a model 
of a material with specific optical properties that does 
not behave as the material of the original part. Pho- 
toelastic stress analysis on the other hand has the great 
advantage of producing information about the entire 
stress field inside the object, while hologram interfer- 
ometry only reveals the resulting surface displace- 
ment. 
When machine tools are designed, however, the main 
interest is the stability of the machine. The stresses 
and the strains are usually so low that they are only of 
secondary importance. The important factor is the 
static and dynamic deformation of the machine caused 
by the production forces. For these studies hologram 
interferometry is almost without competition. It pro- 
duces a 3-D image of the object covered by interference 
The author is with Royal Institute of Technology, Division of 
Production Engineering, 100 44 Stockholm 70, Sweden. 
Received 7 February 1977. 
fringes representing lines of constant displacement. 
Thus we get directly a map of the motions of the total 
machine in one single view. 
The only other way to produce a similar result would 
be to measure the machine point by point using some 
type of noncontacting sensor connected to a computer 
with a graphic display. Even then, however, we would 
run into trouble because all the measurements would 
not be made simultaneously. With these thoughts in 
mind we started studying milling machines using ho- 
logram interferometry. The first set of experiments 
was made in our own laboratory in Sweden, while the. 
second was made during one hectic week in Zurich, 
Switzerland. 
ll. Experimental Conditions 
Our first set of experiments was made directly on the 
floor of the large laboratory hall (30 m X 10 m) at the 
division of Production Engineering, Royal Institute of 
Technology in Stockholm. The test object was a 
Swedish milling machine of vertical knee type (Sajo 
type VF54 from Sandén) with a height of about 2 m and 
a weight of about 2 tons. The machine was painted 
white with ordinary diffuse paint. It stood directly on 
the ground floor (concrete covered by hard fiber board), 
which rested directly on the rock. 
We had no vibration problems whatsoever partly 
because the Swedish granite rock is very stable, and the 
Institute is situated in a park with no heavy traffic 
within 200 m. Elevators, fans for ventilation, genera- 
tors, and production machines in neighboring labora- 
tories in the same buildings were, however, running 
during some of our experiments. One reason for our 
success in making the holograms is, in my opinion, that 
the difficulties described in the literature are greatly 
September 1977 / Vol. 16, No. 9 / APPLIED OPTICS 2521