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78 Part II: Metrology
Part II.B.2
This procedure may be illustrated by the use of Figure 8.2b as follows:
• The diameter of a steel ball is compared with a gage block of
known height.
• Assume a monochromatic light source with a wavelength of
0.5875 mm (23.13 min.).
• From the block, it is obvious that the difference in elevations of
positions A and B on the flat is: (4 × 0.5875)/2 = 1.175 mm ([4 × 23.13]/2
or 46.26 min.).
• By simple proportion, the difference in elevations between points
A and C is equal to (1.175 × 63.5)/12.7 = 5.875 mm ([46.26 × 2.5]/.5
= 231.3 min.).
• Thus, the diameter of the ball is 19.05 + 0.005875 = 19.055875 mm
(.750 + .0002313 = .7502313 in.).
Optical Flats. Optical flats are often used to test the flatness of surfaces. The presence
of interference bands between the flat and the surface being tested is an indication
that the surface is not parallel with the surface of the flat.
The way dimensions are measured by interferometry can be explained by
moving the optical flat of Figure 8.2a in a direction perpendicular to the face of
the workpiece or mirror. It is assumed that the mirror is rigidly attached to a base,
and the optical flat is firmly held on a true slide. As the optical flat moves, the
distance between the flat and mirror changes along the line of traverse, and
the fringes appear to glide across the face of the flat or mirror. The amount of movement
is measured by counting the number of fringes and fraction of a fringe that
pass a mark. It is difficult to precisely superimpose a real optical flat on a mirror or
the end of a piece to establish the end points of a dimension to be measured. This
difficulty is overcome in sophisticated instruments by placing the flat elsewhere
and by optical means reflecting its image in the position relative to the mirror in
Figure 8.2a. This creates interference bands that appear to lie on the face of and
move with the workpiece or mirror. The image of the optical flat can be merged
into the planes of the workpiece surfaces to establish beginning and end points of
dimensions.
Machine Tool Application. A simple interferometer for measuring movements
of a machine tool slide to micrometer (millionths of an inch) is depicted in Figure
8.2c. A strong light beam from a laser is split by a half mirror. One component
becomes the reference R and is reflected solely over the fixed machine base. The
other part M travels to a reflector on the machine side and is directed back to
merge with ray R at the second beam splitter. Their resultant is split and directed
to two photodetectors. The rays pass in and out of phase as the slide moves. The
undulations are converted to pulses by an electronic circuit; each pulse stands for
a slide movement equal to one-half the wavelength of the laser light. The signal at
one photodetector leads the other according to the direction of movement.
When measurements are made to micrometers (millionths of an inch) by an
interferometer, they are meaningful only if all causes of error are closely controlled.
Among these are temperature, humidity, air pressure, oil films, impurities, and