3-D LOCATION & MEASUREMENT BY COHERENT OPTICAL METHODS
wavefront. Interference between the two
waves will occur if, at every point where the
energy originated at two separate parts ofthe
orignal wavefront, the two recombining parts
are coherent. An optical system which has
been used in this way is the solid glass con-
focal element shown in Figure 3$. Part of the
light beam entering through one end is re-
flected to and fro at the confocal reflecting
end surfaces before emerging along a path
which is inverted with respect to the emerg-
ing part of the original ray, which was not
reflected.
Interference makes visible the relative in-
clination of all rays across the aperture of the
system, and the pattern is a function of the
offset of the original source point from the
axis of the system. Even a simple element
such as this can have a very high sensitivity
for "pointing" on a coherent point source.
With a 10 mm aperture a setting could be
made to about 0.5 seconds visually, and to
about 0.02 seconds with a simple photoelec-
tric system. At a working distance of, say, 100
mm this would correspond to a transverse
offset of 250 nm visually, or 5 nm photoelec-
trically.
There is one serious drawback to this sim-
ple confocal system, apart from the loss of
light at the reflecting surfaces. The two inter-
fering parts of the original wavefronts not
only have been derived from different parts
of an original wavefront, but have traversed
different lengths of optical path. It is neces-
sary, therefore, that the point source shall
emit wavefronts which not only are coherent
in the transverse aspect, but temporally coher-
ent as well.
An alternative system which avoids intro-
ducing path difference is shown in Figure 4.
This system of prisms also is much more effi-
cient, avoiding the loss of light by in-line
reflection, and has a number of alternative
possibilities for specialized measurement.
Simpler systems with the same advantage of
path compensation but using fewer compo-
nents also are possible, but with some com-
plication in forming the necessary optical sur-
faces.
COHERENT SHORT-RANGE MEASUREMENTS
The designation of the position of points in
space, and the measurement of those posi-
tions, may be similarly carried out in a
number of ways with the use of coherent re-
cording and measuring techniques. As an in-
termediate step, we may consider the exam-
ple of the recent study of a possible solution
to a problem of measuring small movements
at points within a large three-dimensional
1351
Solid glass cylinder - 2
N
Coated spherical surfaces ——/
Fıc. 3. The solid glass confocal element.
Fıc. 4. The prism system.
model subjected to complicated strain. In
order to make the problem accessible to opti-
cal measurement and photographic record-
ing, it was possible to use a transparent elastic
medium as the material of the body. It was
suggested that small reference markers could
be introduced during the molding of the
model, and that photogrammetric methods
should be used to measure changes of posi-
tion in three dimensions of each marker.
However, the severe requirements in a
number of essentials conflicted, and there
did not seem to be any possibility of adequate
photographic recording of images of the mark-
ers. The greatest difficulties occurred be-
cause of the small displacements to be meas-
ured (less than a few parts in a million), the
very large number of records required to re-
cord all the planes in the object, and the diffi-
culty of making the model well enough for
each marker in one plane to remain in focus.
The feasibility of a coherent system was
investigated. It made use of transparent
spheres embedded in the elastic medium,
each of which acted like a small lens, to pro-
duce an image of a distant point source in the
vicinity of the lens. Figure 5a shows how
each sphere, as itis moved by the straining of
the surrounding medium, produces the effect
of moving the secondary point source P. Dis-
placements of only 0.5 um would produce
easily visible effects in an inverting inter-
