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A
FLASERWAVELENGTH
LASER
i
Figure
2-37.
Cosine
Error
These
wavefronts
can
be
thought
of
a s
lines
on
a
conventional
scale.
As
a
point
on
the
machine
travels
along
the
laser
beam,
the
interferometer
counts
the
number
of
wavefronts
intercepted
by
the
point
during
its
travel.
If
the
point
travels
along
the
path
P-P'
a s
shown,
the
interferometer
counts
the
number
of
wavef
ronts
intercepted
and
measures
the
distance
P-P".
In
other
words
the
interferometer
measures
the
component
of
motion
in
the
direction
of the
laser
beam.
Since
P-P"
=
P-P'
cos
8
(where
6
=
angle
of
misalignment
between
laser
beam
and
machine
axis
of
motion)
The
error
in
parts
per
million
would
be:
error
=
(1
-
cos
8)
X
106
It i s obvious from
Figure
2-37 that the measured P-P" i s shorter than the actual distance
traveled P-P'. Note that cosine error always causes the interferometer to read short of the
actual distance traveled. Table 2-3 shows some typical cosine errors for the angle 8.
Table
2-3.
Angle 8 Versus
Cosine Error
8
(deg)
(rad)
COSINE
E R R O R
.001
1.7
x
10-5
. O I
1.7
x
10-4
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