Model
5528A
Appendix
B: Measurement Con
si
derations
U-4
Abbe
'
Offset
Error
Abbe'
offset error c
an
appear in a l
aser
measurement
as
well
as
in a measuremen! made using a
more
traditional
method
. It resul
ts
from the combination
of-
1. An angular offset in the measurement
sys
tem,
and-
2.
A linear offsct between the measurement
axis
and the
sca
le
axis
in the
mC3
surement sysle
m.
Abbe'
offset
error
will
make
the
indicated length e
ithcr
sho
rl
er
or
longer than the act
ua
l length.
depending
on
the
dire
c
tion
of
the angular o ff
se
t.
as
shown
in
Figure 8-4.
The amount
of
measurement
error
resulting from Abbe' offset
is
-
Offset distancc X tangent (offset angle)
For
an
angle
of
20
degrecs
or
less
, the tangent of the ansle divided by the
size
of
the angle in
ar
cseconds
is
between
5.05
X
10
-
6
and 4.
84
X 10-
6.
This means that you
can
get a very close
appro
x
imation
of
the
Abbe
' offset err
or
by mul
tip
lying the measurement off
se
t distan
ce
by -
5 X 10- 8
..
-'-====-
X the angle's si
ze
(m
aresec
)
aresec
The units
of
the
crror
will
be the same
as
the
units
of
the measurement (and of the offset)
(c
entimetres, inches, etc. ), since
the
tangent
va
lue Is dimensionle
ss.
Abbc'
offset
error
in
c
rea
ses
in
proportion
to the
size
of
the angular offset and the distance
of
the
linear offset, and
is
really a
que
s
tion
of
"w
hat are you trying to measure?" .
for
example, if you
want
to
det
ermine
the accuracy
of
a machinc tool
's
lead
sc
rew or scale, you
would
make yo
ur
meas
urement
as
clo
sc
ly
as
po
ss
ible
to the
sc
rew or
sca
le, which would minimize the results
of
Abbe' offset. If,
on
Ihe other hand, you want
ed
to
know
how
accurately the
ma
c
hine
po
sitions its
c
utting
100
1, you
would
make
yo
ur
meas
urement along the tool's path; this
would
give you a true
picture
of
the
po
si
tioning
accuracy, and
wou
ld include compensation
for
geomctricinaccuracies
of
the measurement
sys
tem (
including
those
due
to Abbe'
error
).
As
an
example
of
Abbe
' offset error, consider the
ca
liper s
hown
in Figure 8·4.
-
I-
r
I .2
.3 I SCALE AXIS
...
I
c-
--
I
I
0.25 READING
2
1N
. ABBE O
FF
SET
I
MEASUREMENT AX I
\
IU
s
_I
~S
'
ANGULAR OFFSET
Fiyure 8-4. Caliper Example
of
Abbe'
Error
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