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Good Practice Guide:
Straightness Orthogonality Measurements
REG2 D5.2
JRP D2.3.8
Flatness measurements of machine
reference mirrors
Workshop: Metrology for Movement and Positioning in Six
Degree of Freedom, 30th May 2016,
Gerd Ehret*, Michael Schulz*, Heiko Reinsch*, Susanne Quabis*,
Haifeng Xu**, Eberhard Manske**
* Physikalisch-Technische Bundesanstalt (PTB)
** Institute of Process Measurement and Sensor Technology, Technische Universität Ilmenau
Outline
330.05.2016
• Optical flatness metrology (interferometry / deflectometry)
• Some aspects to ageing effects and thermal behavior of flats
• Example: Zerodur cube for calibration of 6 DoF systems
• Example: Flatness measurements of a Zerodur test bed for a three-dimensional nanomeasuring and nanopositioningmachine (NPM-machine)
• Summary and conclusion
Absolute flatness measurement
4
Interferometry and small angle deflectometry in comparison:
Interferometry Small Angle Deflectometry
Measurement uncertainty: few
nanometer
Measurement uncertainty: down to
sub-nanometer
Interferometer optic limits the size of
the specimens
Scan axis allows for the measurement of
large specimens
high lateral resolution
(down to 10 µm for small specimens)
low lateral resolution (typically > 1 mm,
independent of the specimen size)
Determination of the absolute
topography by the 3 flat test
(vertical specimen with lower MU)
Straightness reference is given by the
straight light propagation
Zygo VeriFire MST 12“ Interferometer Deflectometric Flatness Reference (DFR)
30.05.2016
5 ppt-folie-vorlage
Flatness metrology: Interferometry
30.05.2016
Interferometry
6
Zygo Verifire MST, wavelength shifting,
aperture 100 mm & 300 mm
30.05.2016
Interferometry
7
Calibration typically by 3 flat test
W1 = WBinv + WC
W2 = WA + WC
W3 = WA + WCrot
W4 = WA + WB
WA = 0.5*(2W3o – W1
e + W2e + W4
e)
WC = 0.5*(W2o – W3
o + W1e + W2
e –W4e)
For example:
U. Griesmann, “Three-flat test solutions based on
simple mirror symmetry”, Appl. Opt. 45 (2006)
5856-5865
Uncertainty: single nm range
30.05.2016
8 ppt-folie-vorlage
Flatness Metrology: Small angle defelctometry
30.05.2016
Deflectometric flatness measurement
9
Deflectometric Flatness Reference (DFR)
For horizontal specimens For vertical specimens
30.05.2016
Principle of small angle deflectometry
10 ppt-folie-vorlage
Measurement of the topography in autocollimation = small angles
Different deflectometric procedures / gradient methods:
1.) Direct deflectometry2.) Difference deflectometry (ESAD: Extended Shear Angle Difference)3.) PTB procedure: Deflectometry with tilting of the specimen (EADS:
Exact Autocollimation Deflectometric Scanning)
highly accurate (< 0.01 arcsec)
30.05.2016
DFR System for horizontal specimen
1103.05.2016
12 ppt-folie-vorlage
Measurement comparison between
interferometry and deflectometry
30.05.2016
Comparison between deflectometry and interferometry
13 ppt-folie-vorlage
0 50 100 150 200 250 300-80
-60
-40
-20
0
20
x / mm
Heig
ht / nm
Interferom.
Defl.
The mean absolute difference is 1.8 nm
Measurement at a Zerodur specimen, scanlength: 290 mm
30.05.2016
14 ppt-folie-vorlage
Some aspects to ageing effects and thermal behavior of flats
with respect to topography changes
30.05.2016
Effects over time: EURAMET comparison
15
Type: EURAMET 672 - Cooperation in researchSpecimen: ZerodurParticipants: BE, CH, CZ, DE, ES, FI, GB, IT, LV, NL, PL, TR, (ZA, CN)
Design of the three support points. The black circle represents the maximum measurement area of 150 mm in diameter. To minimize the sag in this area, the support points do not coincide with the Bessel points
30.05.2016
Effects over time: EURAMET comparison
16
Weighted mean of the group of measurements with 150 mm aperture
(The measurements have been corrected for zero gravity)
PV value of the low frequency contributions of PTB’scontrol measurementsover 4 years
30.05.2016
Effects over time: EURAMET comparison
17
• Between each partner
measurement PTB measured the
topography of the specimen
• Measurements were carried out at
rather large cavity length
• Difference to mean topography is
shown
• Uncertainty (k = 2): 10 nm
PTB‘s control measurements
30.05.2016
Effects over time: EURAMET comparison
18
• High frequency residuals are partly
property of the surface
• Effects from non perfect cleaning
(see topography from 2011_01 to
2011_04)
High frequency residuals
30.05.2016
Calibration of a 150 mm flat of Zerodur
1903.05.2016
T = 21.5°C (+/- 0.3°C)
2008 2014 2016
No change of the topography during the last 8 years
Temperature effects of a 12“ transmisson flat
20
Transmission flat manufactured by INRAD Optics (US), specified /30
30.05.2016
Temperature effects of a 12“ transmisson flat
2103.05.2016
TF manufactured by INRAD Optics (US), specified /30
T = 21°C T = 24°C
22 ppt-folie-vorlage
Example: Glas cube for calibration of 6 DoF systems
30.05.2016
Example: Zerdour cube with edge length of 50 mm
23
Orthogonality better than 1 arcsec
(measured with the rotation stage of the spectrometer)
cube surface 3-4: orthogonality deviation = 0.06 arcsec
cube surface 4-1: orthogonality deviation = 0.24 arcsec
cube surface 1-2: orthogonality deviation = 0.39 arcsec
cube surface 2-3: orthogonality deviation = 0.22 arcsec
Zerdour cube with edge lengths of 50 mm produced/polished by Fa. Horst W. Kaufmann
Flatness of the cube surface better than /20
measured with the Zygo Verifire MST
30.05.2016
30.05.2016 Page 24 IND 58 6DoF REG 2 (TU-IL)
Example:
Flatness measurements of a Zerodur test bed for a three-
dimensional nanomeasuring and nanopositioning
machine (NPM-machine)
30.05.2016 Page 25 IND 58 6DoF REG 2 (TU-IL)
• Positioning range: 200 x 200 mm
• Resolution: 80 pm
• Velocity: < 30 mm/s
Laser interferometer
inner Axis
with mirror cubeouter
axis
Nanopositioning and Nanomeasuring testbed
• Moving masses:
• x-axis: 13.8 kg
• y-axis 11.4 kg
Laser interferometer
Mirror cube
Planar structure guiding system
(200 x 200 mm)
x-y-Interferometer
2-axes autocollimator
30.05.2016 Page 26 IND 58 6DoF REG 2 (TU-IL)
y
xx-laser-beam
y-laser-beammirror cube
Mirror cube of the NPM-testbed
• Overall Dimensions (L x W x H): 280 x 280 x 60 mm• Material: Zerodur® (glass ceramic with nearly zero thermal expansion)• Coating: Al• Flatness: λ/2 within the test area 200 x 25 mm (L x H)• Orthogonality error between the x-y mirror flats: < 10 arcsec• Weight: 7 Kg
Error-free laser beam mirror system:
z
probe system
touch point
(adjusted perpendicular to the mirror axis)
30.05.2016 Page 27 IND 58 6DoF REG 2 (TU-IL)
Calibrating the reference flat surface of an
interferometer by the three-flat test method
In general, the wavefront errors arising from the multi-rotation three-flat test can be calculated
using the equation from Küchel:
30.05.2016 Page 28 IND 58 6DoF REG 2 (TU-IL)
Calibrating the reference flat surface of an
interferometer by the extended three-flat test method
Flat A Flat B Flat C
Results from the extended three-flat test:
30.05.2016 Page 29 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the side
surfaces of the mirror cube using a 6-inch Fizeau interferometer
Measurement regions for subaperture data
Stitching interferometry for accurate measurement of large optical surfaces
Simulated video of the stitching process
Y
X
Z
4
6-inch Zygo GPI interferometer
motorized xy stage
30.05.2016 Page 30 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Before stitching
After stitching
4x ⌀150 mm sub-aperture, 50% diameter overlap
Stitching algorithm for subaperture stitching interferometry
30
mm
240 mm
x Mirror:
y Mirror:
28
mm
28
mm
240 mm
PV: 351.2 nm
PV: 345.3 nm
30.05.2016 Page 31 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Before stitching
After stitching
4 ⌀150 mm sub-aperture, 50% diameter overlap
Stitching algorithm for subaperture stitching interferometry
Mask size: 200 X 25 mm
30
mm
240 mm
x Mirror:
y Mirror:
PV: 315.4 nm RMS: 88.6 nm
PV: 270.3 nm RMS: 74,2
nm
200 mm
25
mm
25
mm
30.05.2016 Page 32 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Horizontal profiles
Position [mm]
He
igh
t [n
m]
- x Mirror - y Mirror
Vertical profiles
Position [mm]
He
igh
t [n
m]
- x Mirror - y Mirror
Comparison of the profiles:
Summary and conclusion
33
• Absolute flatness metrology with interferometric 3 flat test and small angle deflectometry is possible
• Within the measurement uncertainty range of flatness metrology no ageing effects for Zerodur (matured) are observed
• Temperature behavior of the specimens have to be checked
• Highly accurate Zerodur cube can be used for axis calibration of6 DoF movement systems
• Interferometric flatness measurements of a Zerodur test bed for a three-dimensional nanomeasuring and nanopositioningmachine (NPM-machine) are shown
• For transferring the accuracy of the 3 flat test to the NPMmirror cube it is proposed to use a specific transfer standard
30.05.2016
Straightness measurements at the
Nanometer Comparator
Christoph Weichert
Rainer Köning
Axel Wiegmann
Paul Köchert
Jens Flügge
Outline
30.05.2016 35 [email protected]
1. Error separation method –
Reversal technique
2. Error separation method –
Traceable Multi-Sensor method
3. Implementation at the Nanometer
Comparator
4. Calibration of a straightness
encoder system
1. Superposition with guiding errors
30.05.2016 36 [email protected]
Straightness error motion
of the slide
Straightness deviation of the
scale
Measurement result
+
=
1. Superposition with guiding errors
30.05.2016 37 [email protected]
Straightness error motion
of the slide
Straightness deviation of the
scale
Measurement result
+
=
1. Classical reversal technique
30.05.2016 38 [email protected]
Mirror topography as stable reference
Classical reversal technique is NOT
applicable for measurements of scales
0°
180°
𝑚1(𝑥𝑖) = 𝑡 𝑥𝑖 + 𝑔 𝑥𝑖𝑚2 𝑥𝑖 = 𝑡 𝑥𝑖 − 𝑔(𝑥𝑁 − 𝑥𝑖)
1. Reversal method
30.05.2016 39 [email protected]
Measurements with different relative positions of the scale
Linear equation system solved by least-squares method
Mirror topography used as reference
0°
180° with
displacement
0° with another
displacement
180° with another
displacement …
Slide
straightness
error
Topography
function
Reconstruction interspace
Sensor interspace
Measurement points
Systematic
sensor error
Yaw angle
variation
2. Traceable Multi-Sensor method
30.05.2016 40 [email protected]
Two or more sensors + angle measurement
Reconstruction of mirror topography, systematic sensor errors and horizontal
slide straightness error
Small angle approximation linear equation system
Lagrange interpolation of topography
non-equidistant sensor
interspaces
higher lateral resolution
Single measurement sufficient
Angle measurement as reference
instead of mirror topography
2. Traceable Multi-Sensor method
30.05.2016 41 [email protected]
2. Lateral resolution
30.05.2016 42 [email protected]
Two point sensors:
Lateral resolution limited
by sensor interspace
Tra
nsfe
r fu
nctio
n
Three point sensors:
First common zero point
Beams profile:
High pass filter
3. Nanometer Comparator
30.05.2016 43 [email protected]
Calibration of line scales, encoder systems and interferometer
along a range of up to
550 mm
3. Setup for straightness measurements
30.05.2016 44 [email protected]
3 heterodyne Y-interferometers
Grating scale placed inside the sample carriage with Y-mirror
Encoder head mounted at the bride as well as all reference mirrors
3. Measurement result – encoder system
30.05.2016 45 [email protected]
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
3. Measurement results – Y-interferometers
30.05.2016 46 [email protected]
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 350 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
3. Measurement results – Y-interferometers
30.05.2016 47 [email protected]
50 100 150 200 250 300 350 400 450 500-300
-200
-100
0
100
200
300
400
Position / mm
De
via
tio
n fro
m b
est-
fit lin
e / n
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 350 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 3
3. Measurement result – Yaw-interferometer
30.05.2016 48 [email protected]
50 100 150 200 250 300 350 400 450 500-50
-25
0
25
50
Position / mm
Ya
w-in
terf
ero
me
ter
/ n
rad
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 3
3. TMS method – mirror topography
30.05.2016 49 [email protected]
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-50
-25
0
25
50
Position / mm
Ya
w-in
terf
ero
me
ter
/ n
rad
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 3
50 100 150 200 250 300 350 400 450 500-20
0
20
40
60
80
100
120
140
160
180
Position / mm
Mirro
r to
po
gra
ph
y / m
m
TMS
Y-interferometers
Yaw-interferometer
3. TMS method – slide straightness error
30.05.2016 50 [email protected]
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-50
-25
0
25
50
Position / mm
Ya
w-in
terf
ero
me
ter
/ n
rad
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 2
Y-interferometer 3
50 100 150 200 250 300 350 400 450 500-300
-200
-100
0
100
200
300
400
Position / mm
Slid
e s
tra
igh
tne
ss e
rro
r / n
m
TMS
Y-interferometers
Yaw-interferometer
4. Straightness deviation of the scale
30.05.2016 51 [email protected]
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-300
-200
-100
0
100
200
300
400
Position / mm
Slid
e s
tra
igh
tne
ss e
rro
r / n
m
100 150 200 250 300 350 400 450-60
-30
0
30
60
90
120
Position / mm
Str
aig
htn
ess d
evia
tio
n o
f th
e s
ca
le / n
m
-
Encoder
Slide
straightness
4. Repeatability with TMS method
30.05.2016 52 [email protected]
100 150 200 250 300 350 400 450-200
-100
0
100
200
300
400
Position / nm
En
co
de
r va
lue
s / n
m
0
3
6
Sta
nd
ard
de
via
tio
n / n
m
100 150 200 250 300 350 400 450-200
-100
0
100
200
300
400
Position / mm
Slid
e s
tra
igh
tne
ss e
rro
r / n
m
0
3
6
Sta
nd
ard
de
via
tio
n / n
m
100 150 200 250 300 350 400 450-60
-30
0
30
60
90
120
Position / mm
Str
aig
htn
ess d
evia
tio
n / n
m
0
0.2
0.4
0.6
Sta
nd
ard
de
via
tio
n / n
m
-
Encoder
Slide
straightness
Standard deviation < 0,4 nm
4. Shifting and rotating the scale
30.05.2016 53 [email protected]
…
100 150 200 250 300 350 400 450-60
-30
0
30
60
90
120
Position / mm
Str
aig
htn
ess d
evia
tio
n / n
m
0
0.2
0.4
0.6
Sta
nd
ard
de
via
tio
n / n
m
100 150 200 250 300 350 400 450-60
-30
0
30
60
90
120
Position / mm
Str
aig
htn
ess d
evia
tio
n / n
m
0
0.2
0.4
0.6
Sta
nd
ard
de
via
tio
n / n
m
100 150 200 250 300 350 400 450-60
-30
0
30
60
90
120
Position / mmS
tra
igh
tne
ss d
evia
tio
n /
nm
0
0.2
0.4
0.6
Sta
nd
ard
de
via
tio
n / n
m
4. Reproducibility of the TMS result
30.05.2016 54 [email protected]
0 50 100 150 200 250 300-6
-4
-2
0
2
4
Position / mm
Dev
iati
on
fro
m m
ean
/ n
m
MS 1MS 2MS 3MS 4MS 5MS 6MS 7MS 8MS 9MS10MS11MS12MS13
Reproducible in the range of ±5 nm
Limited by length-proportional error of
yaw-interferometer
Standard uncertainty of single
measurement: 4.2 nm
Standard uncertainty of 13
measurements: 1.3 nm
4. Reversal method
30.05.2016 55 [email protected]
50 100 150 200 250 300 350 400 450 500-800
-600
-400
-200
0
200
Slide position / mm
En
co
de
r m
ea
su
rem
en
t va
lue
s / n
m
-200
-100
0
100
200
300
De
via
tio
n fro
m b
est-
fit lin
e / n
m
50 100 150 200 250 300 350 400 450 500-1
0
1
2
3
4
5
6
7
8
Position / mm
Y-in
terf
ero
me
ters
va
lue
s / µ
m
Y-interferometer 1
Y-interferometer 3
dSensor13
Y3
Encoder
head
Y1Y2
dSensor13
/ 2
dSensor13
/ 2
ഥ𝒚
-
…
Rotating and Shifting
Reversal
method
4. Reversal method
30.05.2016 56 [email protected]
0 50 100 150 200 250 300-60
-30
0
30
60
90
120
Position on scale / mm
Str
aig
thn
ess d
evia
tio
n / n
m
Straightness deviation reconstructed
with reversal method
Standard uncertainty: 5.2 nm
for solving equation system for
eight measurement series
Limited by variations of mirror
topography
0 100 200 300 400 500
-100
0
100
200
Position / mm
Mirro
r to
po
gra
ph
y / n
m
MS 1MS 2MS 3MS 4MS 5MS 6MS 7MS 8MS 9MS10MS11MS12MS13
4. Comparison of the results
30.05.2016 57 [email protected]
0 50 100 150 200 250 300-60
-30
0
30
60
90
120
Position on scale / mm
Str
aig
htn
ess d
evia
tio
n / n
m
-1
0
1
2
Diffe
ren
ce
/ n
m
Result of TMS method
Result of reversal method
Difference of the two results
Peak-to-peak value of scale’s
straightness deviation: 144 nm
Determined with two different error
separation methods
Peak-to-peak value of Difference:
2.5 nm
Uncertainties limited by violation of
requirements of both methods:
Stable angle measurement (TMS)
Stable mirror topography (reversal)
Summary
30.05.2016 58 [email protected]
Two error separation methods
Reversal method (stable mirror topography)
TMS method (stable angle measurement)
Implement at the Nanometer Comparator
Similar results of both methods within their uncertainties
Prove: TMS usable for straightness measurements
30.05.2016 59 [email protected]
position / mm
stra
igh
tne
ss d
evia
tion
/ nm
300 250 200 150 100 50 0
-60
-40
-20
0
20
40
60
Many thanks to HEIDENHAIN for the precision straightness reference
Physikalisch-Technische Bundesanstalt
Braunschweig und Berlin
Bundesallee 100
38116 Braunschweig
Christoph Weichert (+49 531 592 5224, [email protected])
Rainer Köning
Axel Wiegmann
Paul Köchert
Jens Flügge
Thank you for your
attention
Data acquisition
30.05.2016 61 [email protected]
Y1 Mess
Y1 Ref
Y2 Mess
Y2 Ref
Y3 Mess
Y3 Ref
Encoder
Encoder
Differential –
SingleEnded
APE
Taktsynchronisation
Startsignal
Gier
Gier
Differential –
SingleEnded
APE
X Mess
X Ref1,5MHz
1,5MHz
1,5MHz
20MHz
Homodyn Homodyn
Calibration of Yaw-interferometer
0 50 100 150 200 250-0,16
-0,14
-0,12
-0,1
-0,08
-0,06
-0,04
-0,02
0
0,02
Position / mm
An
gle
var
iati
on
/ µ
rad
yaw autocollimator
pitch autocollimator
yaw interferometer
pitch interferometer
slope: -547 nrad/m
slope: -234 nrad/m
Deformation of the mirror
30.05.2016 63 [email protected]
Temperature difference of 0.2 K between adjustment and measurement
24.04.2017 Page 64 IND 58 6DoF REG 2 (TU-IL)
Multilateration for encoder characterisation
on the base of a nanomeasuring testbed
Prof. Dr.-Ing. habil. Eberhard Manske
Institute of Process Measurement and Sensor Technology
Technische Universität Ilmenau
Workshop: Metrology for Movement and Positioning in Six Degree of Freedom
(IND 58 6DoF)
EUSPEN 2016
Nottingham, 30th May 2016
24.04.2017 Page 65 IND 58 6DoF REG 2 (TU-IL)
Overview
• Motivation
• 200 mm x 200 mm Nanomeasuring
testbed
• Squarenes of mirror cube
• Multilateration measurements
24.04.2017 Page 66 IND 58 6DoF REG 2 (TU-IL)
High Precision Measurement Technology
Kunz precision
Mask Measuring Machines
(Exposure tools)
2D-encoder
(Heidenhain)
Nanopositioning and
Nanomeasuring Machine
2D/3D CMM
24.04.2017 Page 67 IND 58 6DoF REG 2 (TU-IL)
Motivation
Verification of measurement behavior for nano measurement
applications is difficult.
Implementation of self calibration methods is important
for 2D/3D applications: straigtness, flatness and squareness:
Multilateration approach and revearsal method
24.04.2017 Page 68 IND 58 6DoF REG 2 (TU-IL)
Grid referencing method for micro measurement
technology
-20
0
20
40
60
80
100
120
140
-20 0 20 40 60 80 100 120 140
mm
0,5 µm
mm)²104.0()²4.0()2( 6 LmkU
Uncertainty influences:
- the laser interferometer (0.2 µm)
- the probing process (0.2-0.3 µm)
- the thermal expansion coefficient of the artefact
K. Wendt, J. Hirsch: Calibration of grid plates by multi-lateration. IMEKO 2005
Procedure
Results
24.04.2017 Page 69 IND 58 6DoF REG 2 (TU-IL)
Challenges
Investigation and application of self calibration methods
considering straightness and orthogonality on a precise long range
nano measuring machine
Self calibration methods have already proved their potential in the
range of micro measurement technology for the verification of
coordinate measuring machines.
Use of these methods in nano metrology with several obstacles
Extraordinary precision of the calibration of the references is necessary
Nanometre level: probe system must be able to capture the grid
points at the same level of precision, whereas the size of the grid
plate must cover the whole motion range.
24.04.2017 Page 70 IND 58 6DoF REG 2 (TU-IL)
• Positioning range: 200 x 200 mm
• Resolution: 80 pm
• Velocity: < 30 mm/s
Laser interferometers
inner Axis
with mirror cubeouter
axis
Development of a nano measuring testbed
• Moving masses:
• x-axis: 13.8 kg
• y-axis 11.4 kg
Laser interferometer
Mirror cube
Planar H-structure guiding system
(200 x 200 mm)
x-y-Interferometer
2-axes autocollimator
24.04.2017 Page 71 IND 58 6DoF REG 2 (TU-IL)
Mirror cube of the NPM-testbed
Squareness measurements under consideration of
topography errors
x-laser-beam
y-laser-beam
mirror cube
y
x
z
90o - φxy
touch point
24.04.2017 Page 72 IND 58 6DoF REG 2 (TU-IL)
Measuring orthogonality between
x and y mirrors of the mirror cube
High-resolution electronic autocollimators
Right-angle-prism as 90°angle gauge block
• Two high-resolution electronic autocollimators (resolution: 0.05 arcsec)
• High precision right-angle prism (uncertainty: < ±0.2 arcsec)
• High precision xy- linear stage (travel range: 300 mm x 300 mm)
1. Adjustment of orthogonality
24.04.2017 Page 73 IND 58 6DoF REG 2 (TU-IL)
Measuring orthogonality between
x and y mirrors of the mirror cube
Mirror cube
xy linear stage
High-resolution electronic autocollimator
Positioning aperture stop
Mounting adapter with
adjustment mechanisms
2. Measurement at mirror cube at several xy-positions
24.04.2017 Page 74 IND 58 6DoF REG 2 (TU-IL)
Measuring orthogonality between
x and y mirrors of the mirror cube
Mirror cube
XY linear stage
Positioning aperture stop
High-resolution electronic autocollimator
X1 X2 X3
Y1 -5.98" -5.07" -4.25"
Y2 -5.23" -4.30" -3.60"
Y3 -4.85" -3.77" -3.18"
2. Measurement squreness at several xy-positions
24.04.2017 Page 75 IND 58 6DoF REG 2 (TU-IL)
Local angular deviations derived from flatness of
the side surfaces of the mirror cube
Local surface flatness of the x and y mirrors:
X1 X2 X3
Y1 -1.43" -0.66" 0.12"
Y2 -0.76" 0.02" 0.79"
Y3 -0.16" 0.62" 1.39"
Squareness error between the local parts of the x and y mirrors:
reference layer
reference layer
x mirrory mirror
nx1 nx2 nx3
ny1
ny2
ny3
ni - normal vector of the surface
24.04.2017 Page 76 IND 58 6DoF REG 2 (TU-IL)
Measuring orthogonality between
x and y mirrors of the mirror cube
X1 X2 X3
Y1 -5.98" -5.07" -4.25"
Y2 -5.23" -4.30" -3.60"
Y3 -4.85" -3.77" -3.18"
Squareness error between the local parts
of the x and y mirrors (experimental results):
reference layer
reference layer
x mirrory
mirror
nx1 nx2 nx3
ny1
ny2
ny3
reference layer
reference layer
x mirror
y
mirror
nx1 nx2 nx3
ny1
ny2
ny3
Squareness error between the local parts
of the x and y mirrors (calculated results
from flatness measurements):
X1 X2 X3
Y1 -1.43" -0.66" 0.12"
Y2 -0.76" 0.02" 0.79"
Y3 -0.16" 0.62" 1.39"
x mirror reference layer
y mirror reference layer
φxy ≈ - 4.46"±0.12“
Difference between experimental and
calculated results:
X1 X2 X3
Y1 -4.55" -4.41" -4.37"
Y2 -4.47" -4.32" -4.39"
Y3 -4.69" -4.39" -4.57"
24.04.2017 Page 77 IND 58 6DoF REG 2 (TU-IL)
Heidenhain
PP281
mirror cube
xy linear stage
Integration of a Heidenhain PP281 two-coordinate
encoder into the NPM-testbed
for multilateration approach and revearsal method
cover plate of the testbed
24.04.2017 Page 78 IND 58 6DoF REG 2 (TU-IL)
Mounting Design for the PP281 Two-Coordinate Encoder
scanning head (PP28R)
mirror cube
grid plate (PP201)
rotation table
DesignTestbed with encoder
24.04.2017 Page 79 IND 58 6DoF REG 2 (TU-IL)
Structure of data processing
8 E
3 E
Motion Control
IF-X
IF-Y + IF-Y´(Tilt)
HeidenhainEIB 741
PC-Data-Processing
dSPACE Workstation
Trigger
Grating
SensorHead
SIOSSingle Beam
IF
SIOSDual Beam
IF
X-Y Motion Stage with
Mirrors
24.04.2017 Page 80 IND 58 6DoF REG 2 (TU-IL)
Measurement procedure
First measurement: 0°
24.04.2017 Page 81 IND 58 6DoF REG 2 (TU-IL)
First rotation (26.65°)
24.04.2017 Page 82 IND 58 6DoF REG 2 (TU-IL)
Second rotation (45°)
24.04.2017 Page 83 IND 58 6DoF REG 2 (TU-IL)
Third rotation (63.43°)
24.04.2017 Page 84 IND 58 6DoF REG 2 (TU-IL)
Fourth rotation (90°)
... totalling 8 rotations
24.04.2017 Page 85 IND 58 6DoF REG 2 (TU-IL)
Status
• First measurements and calculations are realized
• Proof of feasibility succesfully
• Improvement of measurement procedure
• Adaption of calculation algorithm
Outlook
• Improvement of measurement algorithm (sequence plan)
• Automatization of data aquisition
Time efficient and low drift measurement procedures
Fast scanning methods for multiple scan measurements
Nanometer uncertainty
24.04.2017 Page 86 IND 58 6DoF REG 2 (TU-IL)
Acknowledgement
Thank you for your attention!
IND 58 6DoF/ REG 2 (TU-IL):
COMPARISON OF EXTERNAL WITH SELF CALIBRATION METHODS
Thanks to
N. Vorbringer-Doroshovets, H. Xu, U. Gerhardt, M. Domhardt, A. Meister
J.Flügge, Ch. Weichert, J.Hirsch
24.04.2017 Page 87 IND 58 6DoF REG 2 (TU-IL)A1, A2, Vortragender: PD Dr. Füßl
Grenzen von Kalibrier- und Rückführstrategien für
NPM-Maschinen (A1)
Orthogonalitätsmessung der Raumspiegelecke
Konzepte zur Vermessung der 900-
Winkelabweichungen zwischen den
Spiegeln (xy-, xz- und yz-Spiegel) der
Raumspiegelecke mittels eines
Autokollimationsfernrohrs (AKF)
(a)
Spiegelecke
x
y z
(b)
Pentaprisma 2
Spiegeleckex
y
z
AKF
(Position 1)
Pentaprisma 1 Pentaprisma 1
(Position 2)
Pentaprisma 2
AKF
(Position 1)
Pentaprisma 1 Pentaprisma 1
(Position 2)
Standardabweichung bei 10 Messungen: 0,01“
24.04.2017 Page 88 IND 58 6DoF REG 2 (TU-IL)
What is the accuracy and uncertainty of flats or grids?
Precision flat-, L-shape-,cube-mirrors
(2D/(3D)-Laser interferometer)
Linear, grid scales, lithography masks
(2D-Encoder)
Flatness, straightness, squareness: sub-µm to nm
24.04.2017 Page 89 IND 58 6DoF REG 2 (TU-IL)
-100
-50
0
50
100
150
200
250
300
0 10 20 30 40 50 60 70 80
Topography
24.04.2017 Page 90 IND 58 6DoF REG 2 (TU-IL)
Straightness deviation of the 2D-Encoder
-400
-300
-200
-100
0
100
200
300
400
500
0 10 20 30 40 50 60
24.04.2017 Page 91 IND 58 6DoF REG 2 (TU-IL)
To perform time efficient and low drift measurement procedures for self
calibration, the scanning methods using these measuring systems will have
to be accelerated and the combination and sequence plan of the multiple
scan measurements will have to be worked out.
24.04.2017 Page 92 IND 58 6DoF REG 2 (TU-IL)
Encoder under test
Manufacturer specification:
• two-coordinate TITANID-phasegrid-encoder on glass (70 x 70 mm²)
• pitch= 8 µm, signal period= 4 µm
• resolution: 1 nm
• interpolation deviation < 12 nm
• αtherm = •8· 10-6 K-1
Heidenhain PP281
Requirements:
thermal stability < 0.01 K
resolution calibration interferometer: 0.1 nm
Goals:
Uncertainty < 10 nm
24.04.2017 Page 93 IND 58 6DoF REG 2 (TU-IL)
scanning head (PP28R)
mirror cube
y-interferometer
grid plate (PP201)
removable mounting adapter with manual adjustment
mechanisms (adjustment of rotation and tip/tilt )
rotation table
carrier plate
Integration of the Heidenhain PP281 two-coordinate
encoder into the NPM-testbed
24.04.2017 Page 94 IND 58 6DoF REG 2 (TU-IL)
Thanks for your attention!
Haifeng Xu
Uwe Gerhardt
Prof. Dr.-Ing. habil. Eberhard Manske
Institute of Process Measurement and Sensor Technology
Technische Universität Ilmenau
24.04.2017 Page 95 IND 58 6DoF REG 2 (TU-IL)
Design of the Nanopositioning and Nanomeasuring testbed
Planar H-structure guiding system
(200 x 200 mm)
x-y-Interferometer
2-axes autocollimator
24.04.2017 Page 96 IND 58 6DoF REG 2 (TU-IL)
Method for measuring orthogonality between
x and y mirrors of the mirror cube
Accurately align the optical axes of both electronic autocollimators orthogonal to
each other using a precision high-tolerance right-angle prism
Precision high-tolerance right-angle prism:
Material: N-BK7
Angle Tolerance (arcseconds): < ±2
Coating: Aluminum Coated Hypotenuse
Surface Flatness @ 633 nm: λ/10
Length of Hypotenuse (mm): 75
24.04.2017 Page 97 IND 58 6DoF REG 2 (TU-IL)
Method for measuring orthogonality between
x and y mirrors of the mirror cubeAccurately align the optical axes of both electronic autocollimators orthogonal to
each other using a precision high-tolerance right-angle prism
Mounting adapter with adjustment mechanisms
(high-resolution fine adjustment of tip/tilt )
High-resolution electronic autocollimators
Right-angle-prism as 90°angle gauge block
24.04.2017 Page 98 IND 58 6DoF REG 2 (TU-IL)
High-precision angle measurement of right angle
prisma unsing a Fizeau interferometer
Setting of the prism for right angle and pyramidal error determination
Right angle error:
αR = -0.97 arcsec
Pyramidal error:
αP = -0.81 arcsec
U* = 3.6 *10-4 arcsec (10 repeated measurements)
* Expanded uncertainty (k=2)
24.04.2017 Page 99 IND 58 6DoF REG 2 (TU-IL)
Mounting design for the mirror corner
• Installation on a three-point baseplate with finite stiffness
• Insert and remove components with high repeatability
• Ball and V-Groove design for precise alignment
• Increase the ability of reducing mechanical and thermal stresses in the mirror corner
24.04.2017 Page 100 IND 58 6DoF REG 2 (TU-IL)
Integration of the Heidenhain PP281 two-coordinate encoder) into the
NPM-testbed
Mounting design for the optical microscope
Three base adapters (with a V-groove, a cone and a flat) are connected
to three high-precision adjustment screws (adjustment of the tip, tilt and
translation along the vertical axis).
24.04.2017 Page 101 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Position [mm]
He
igh
t [n
m]
He
igh
t [n
m]
Horizontal profil of the y Mirror:
Position [mm]
24.04.2017 Page 102 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Position [mm]
He
igh
t [n
m]
Horizontal profil of the y Mirror:
24.04.2017 Page 103 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of
side surfaces of the mirror cube using a Fizeau interferometer
Local surface flatness of the x and y mirrors:
X1 X2 X3
Y1 -1.43" -0.66" 0.12"
Y2 -0.76" 0.02" 0.79"
Y3 -0.16" 0.62" 1.39"
Squareness error between the local parts of the x and y mirrors:
reference layer
reference layer
x mirrory mirror
nx1 nx2 nx3
ny1
ny2
ny3
ni - normal vector of the surface
24.04.2017 Page 104 IND 58 6DoF REG 2 (TU-IL)
Influence of the pyramidal error
squareness error pyramidality of faces effects of the pyramidal error
1" 15° "
5" 7° "
10" 5° "
The pyramidal error does not have much effect on angle block
measurements. Measurement error is introduced when the
autocollimator is not properly aligned to the axis formed by the side of
the angle block.
24.04.2017 Page 105 IND 58 6DoF REG 2 (TU-IL)
Question: What is the accuracy and uncertainty of
flats or grids?
24.04.2017 Page 106 IND 58 6DoF REG 2 (TU-IL)
y
xx-laser-beam
y-laser-beammirror cube
Mirror cube of the NPM-testbed
• Overall Dimensions (L x W x H): 280 x 280 x 60 mm• Material: Zerodur® (glass ceramic with thermal expansion of nearly zero)• Coating: Al/SO• Flatness: λ/2 within the test area 200 x 25 mm (L x H)• Orthogonality error between the x-y mirror flats: < 10 arcsec• Weight: 7 Kg
Error-free laser beam mirror system:
z
probe system
touch point
(adjusted perpendicular to the mirror axis)
24.04.2017 Page 107 IND 58 6DoF REG 2 (TU-IL)
thermal and dynamic:
Thermal, dynamic and gravity influence?
•Neue Kalibrierstrategien
•Hochpräzise Messung und
Korrektur: < /120
•Untersuchungen zur Messdynamik
gra: < /20
(statisch)
10 Jahre SFB 622
24.04.2017 Page 108 IND 58 6DoF REG 2 (TU-IL)
24.04.2017 Page 109 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Before stitching
After stitching
4x ⌀150 mm sub-aperture, 50% diameter overlap
Stitching algorithm for subaperture stitching interferometry
30 m
m
240 mm
x Mirror:
y Mirror:
28
mm
28 m
m
240 mm
PV: 351.2 nm
PV: 345.3 nm
24.04.2017 Page 110 IND 58 6DoF REG 2 (TU-IL)
Metrological frame: Possibility of installing a surface-sensing probe into
the NPM-testbed
Mounting design for the PP two-coordinate encoder
universal mounting adapter
with a sliding dovetail
surface-sensing probe
24.04.2017 Page 111 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the side
surfaces of the mirror cube using a 6-inch Fizeau interferometer
Measurement regions for subaperture data
Stitching interferometry for accurate measurement of large optical surfaces
Simulated video of the stitching process
Y
X
Z
4
6-inch Zygo GPI interferometer
motorized xy stage
24.04.2017 Page 112 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of the
side surfaces of the mirror cube using a Fizeau interferometer
Before stitching
After stitching
4 ⌀150 mm sub-aperture, 50% diameter overlap
Stitching algorithm for subaperture stitching interferometry
Mask size: 200 X 25 mm
30 m
m
240 mm
x Mirror:
y Mirror:
PV: 315.4 nm RMS: 88.6 nm
PV: 270.3 nm RMS: 74,2 nm200 mm
25
mm
25
mm
24.04.2017 Page 113 IND 58 6DoF REG 2 (TU-IL)
Absolute measurement of the deviations from flatness of
side surfaces of the mirror cube using a Fizeau interferometer
Horizontal profiles
Position [mm]
He
igh
t [n
m]
- x Mirror - y Mirror
Vertical profiles
Position [mm]
He
igh
t [n
m]
- x Mirror - y Mirror
Comparison of the profiles:
