Least Squares Fit Method - HP 5528A User Manual

Laser measurement system
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OCT
87
Model
5528A
Stra ightness
and
Squareness Conside rations
Therefore
-
V
' IOpe
=
m
, X
+
bl
-.:
8.33X
- 0.3
Ytrue
::
YLMS
-
Y,lope
X
=
0.0
0.1
0.2
0.3
0.4
0.5
0
.6
0.7
0.8
0.9
YLM
S
=
-<>.3
0.9
1.5
2.5
2.9
3.6
4.2
5.1
5.9
7.2
Y, tope
=
-<>.3
0
.5
1.4
2.2
3.0
3.9
4.7
5.5
6.4
7.2
Ytrue
-
0.0
0.4
0.1
0.3
-0.
1
-0.3
-
0.5
-<>.4 -<>.5
0.0
(microns)
Fo
r
Axis 2
-
O
ur
raw data
h.
-
YLM
S ::
-0.5,
-1
.2, -2.5,
-3.8, -4.0,
- 4.8, -5. 9,
-6.2,
-7,4,
-8.8
(microns)
x
""
0.0.
0.05,
0.1. 0.15,
0.2. 0.25, 0.3, 0.35,
0.4,
0,45 (metre
)
Number of
points =
10
Calcu
lations
for
Axis 2
-
Total distan
ce
travelled:
AX
-
0.45 metre
Slope m2
"" .!loY/
AX
-
(-8.8- (-0.5
))/(0.45-0.0)
=
-18,44
microns/metre
Intercep
t
""
b2
=
-
0.5 microns
(at
X
= 0,
you
want
Y'fUII
= 0)
Therefore
-
YSlope
=
ml
X
+
bl
""
20.67X
-
0.5
Vtrue
=
YLM
S -
YSlope
x
=
0.0 0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4 0.45
VLM
S
=
-0.5
1.2
-2.5
-
3.8
-4.0
-
4.8
-
5.9
- 6.2
-7.4
-
8.8
V
' tope
=
-0.5
- 1.42
-2.34 -
3.27
-
4.19
-
5.1
-6.03
-6.96
-7.
88
-
8.8
0.0
- 0.22
-0.16
-
0.53 0.19 0.31
0.13
0.76 0.48
0.0 (microns
)
LEAST SQUARES FIT METHOD
To
remove slope
from your measurement
data, using
the
least Squares
fit
Metho d,
you
should
a.
Determine
both
the
slope
(m)
and
the
intercept
(b)
from
ca1culmio ns
on
your
raw
data.
b.
Ide
ntify the
equation of the line of
you
r slope
-
V
,lope
=
mX
+
b,
21-3

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