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Model
5528A
Appendix
B:
Measurement
Considerations
U-4
Abbe'
Offset
Error
Abbe' offset error
can
appear in a laser
measurement as
well as
in
a
measuremen!
made
using a
more traditiona
l
method
.
It resu lts from the
combination of-
1.
An
angular
offset
in the measurement
system,
and-
2.
A linear offsct between
the measurement
axis and
the
sca
le axis in
the mC3surement syslem.
Abbe'
offset
error will
make the indicated length eithcr shorl
er
or longer
than the
actual
length.
depending on the
direction
of
the
angu lar
o ffset.
as
show
n in
Figure
8-4.
The
amount of
measurement
error
resulting from
Abbe' offset is
-
Offset
distancc
X
tangent
(offset
ang
le)
For an
angle
of
20 degrecs
or
less,
the tangent
of
the
ansle
divided
by
the
size of
the angle in
arcseco nds
is between
5.05
X
10-
6 and
4.84
X
10-
6.
This means that
you can
get
a very
close
approximation
of
the Abbe'
offset
error by
mu ltiplying the measuremen
t
o
ffset
distance
by
-
5
X
10-
8
. .
-' - ====-
X
the
angle's
size
(m
aresec)
aresec
The units of the
crror will
be the
same as the
units
of
the measurement
(and
of the
offset
)
(centimetres,
inches,
etc. ),
since the tangent
va
lue
Is
dimension
less.
Abbc' offset
error
increases
in
proportion to the
size
of
the
angular
offset and
the distance
of the
linear offset
,
and is
really
a
question
of
"what
are
you trying to measure?"
.
for
example,
if
you
wan
t
to determine
the accuracy
of
a machinc
tool's
leadscrew
or
scale,
you
would
make your
measurement
as closcly
as
possible to the
screw
or
sca le,
which wou
ld minimize
the
results
of
Abbe
'
offset.
If,
on Ihe ot her
hand
,
you
wan
ted
to know how accu
rately
the machine positions its
cutting
1001
,
you
would make your measurement
along
the
tool 's
path
; this
would
give
you a true
picture of
the
posi
tioning
accuracy, and wou
ld include
compensation for geomctricinaccuracies
of
the measurement system
(including
those due to
Abbe'
error).
As
an
examp le of
Abbe'
offset
error, consider the
ca
liper shown in
Figure
8·4.
-
I-
r
I
.2
.3
I
SC
ALE
AXIS
...
I
c-
--
I
I
0.25
READIN
G
2
1N.
ABB
E OFFSET
I
MEASUREM
ENT AX
I
\
IU
s
_I
~S'
AN
G
ULAR OFFSET
Fiyure
8-4.
Caliper
Example of Abbe'
Error
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