Some aspects of ultra-precision
metrology
Paul Morantz
• Cranfield University
• Loxham Precision
Michael de Podesta
Robin Underwood
• NPL
10 Fields of metrology
Field
Associated measurements
Length
Wavelength, Dimension, Angle, Form, Surface quality
Temperature
Contact and non-contact thermometry, measurement of humidity
Time
Time, frequency
Vibration
Acoustics, Accelerometry, Ultrasound,
Mass
Mass, force, pressure, density, viscosity
Electricity
Current, voltage, magnetism
Flow
Gas flow, liquid flow
Photometry
Radiometry, photometry, colorimetry
Radiation
Dosimetry, calorimetry
Amount
Concentration, pH
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SI Units
quantity
unit
symbol
Length
metre
m
Mass
kilogram
kg
Time
second
s
Current
Ampere
A
Temperature
Kelvin
K
Luminous
Intensity
candela
cd
Amount
mole
mol
Definition of the
unit
National primary
standards
Reference
standards
Industrial
standards
Measurements
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Kelvin: SI Unit of Temperature
Length
Temperature
Mass
Time
Electrical Current
Luminous Intensity
Mole
1/273.16
Chosen so that 1 kelvin ≈ 1 degree Celsius
The kelvin, the unit of thermodynamic
temperature, is the fraction 1/273.16 of the
thermodynamic temperature of the triple point
of water
TTPW reproducible to ~50 mK
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Kelvin in the NEW SI Unit System
Energy
(joule)
∆𝜈
133Cs
e
A
s
Kcd
c
m
Cd
kB
kg
K
h
NA
mol
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Kelvin in the NEW SI Unit System
Energy
(joule)
133Cs
The kelvin, the unit of thermodynamic temperature,
is the fraction 1/273.16 of the thermodynamic
temperature of the triple point of water
c
m
Cd
kB
∆𝜈
e
s
A
kg
h
The kelvin, the unit of thermodynamic temperature, is such that
the Boltzmann constant has the exact value
kB= 1.380 65XX×10-23 joules per kelvin
Kcd
K
NA
mol
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Primary thermometers are based on gases
• Molecular motions are simple
• We can approach ‘ideal gas’ conditions at low pressure
• In an ideal gas the internal energy is just the kinetic
energy of the molecules
0.005
Signals / V
0.004
0.003
0.002
0.001
0
7526
7530
7534
Frequency / Hz
7538
Find mass
of molecule
𝟑𝒎
𝒌𝐁 =
𝒔𝒑𝒆𝒆𝒅 𝒐𝒇 𝒔𝒐𝒖𝒏𝒅 𝟐
𝟓𝑻
do experiment
at TTPW
Measure the
speed of sound
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Measure the Average Radius using Microwaves
100
TM11 Resonance
• In a sphere, F0 is inversely
proportional to the radius
Signal
80
60
• Requires a triaxial deformation
of the sphere to resolve these
components
40
20
0
2109
2110
2111
Frequency (MHz)
2112
• Need to measure:
• F0, F1 and F2
• Average radius ~ 62mm
• Shape ~ 31 microns
eccentricity (by design)
• And to know the
measurement uncertainties
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Dimensional measurements
CMM
Microwaves
Pycnometry
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Pycnometry (for average radius)
Fill with highly
pure water (by
evaporation)
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Pycnometry (for average radius)
And then
weigh:
infer volume
and thus
radius
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Tactile CMM Measurements
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Tactile CMM probing diamond turned copper
Even at low (< 10g) probe forces with large (8mm) stylus
tips, significant damage can occur if approach speed is not
very low
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Tactile CMM probing diamond turned copper
Even at very low approach
speeds slight damage occurs
This indentation of 50nm depth
is caused by 5 repeat
measurements in the same
location
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Metrology in support of manufacture
• The ‘spheres’ were
made at Cranfield
• Three metrology
techniques were used
in support of the
diamond turning
• On-machine
profilometery (1) was
eclipsed by:
• (2) Interferometry
• (3) CMM Scanning
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Tool position
100
Turning programming
80
mm
60
toolx'
toolz
40
20
0
-20
-10
0
10
20
30
radians
40
50
60
70
This is a tri-axial ellipsoid, non-rotationally symmetric
(freeform) turning, with sub-micron accuracy
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Interferometry
Hemisphere
Diamond
turning
tool
Interferometer
Field of view and fringe spacing
limitations require stitching
interferometry for full hemisphere
metrology
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CMM scanning metrology
Scanning measurements (as for single point
ones) will damage the surface
Final measurement is taken before final
machining pass, which removes < 2 μm
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Results
Our 2013 publication moved kB from 1.380 65XX×10-23 joules
per kelvin to 1.380 651 56 (98) with a relative standard
uncertainty of 0.71 x 10-6
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Next generation of large telescopes
39m
Hale
(1948)
Keck
(1993)
GMT
(2021)
TMT
(2022)
E-ELT
(2024)
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Process chains for ELT segments
Stage 1
<1 mm form
accuracy
Stage 3
Stage 2
Form/finish
improvement
Fixed abrasive
Grinding
>10 µm RMS
form accuracy
~300 nm RMS
form accuracy
Sub-aperture
figure correct
~10 nm RMS
form accuracy
• Differing metrology requirements after each stage
of a typical process chain, e.g.
• Grinding
• Sub-aperture polishing
• Sub-aperture broad ion-beam figuring
10.2 nm RMS residuals
after active correction (ref:
R. Geyl, Sagem)
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Surface geometry
• Sag up to ~3mm
• Departure from spherical ~ 0.15mm
Z
Non rotationally symmetric (freeform)
machining/metrology requirements
C X
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On-machine metrology
• On machine metrology is accurate, but
slow – high spatial resolution data are
not available on machine
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CMM Scanning measurement
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Areal measurements from tactile scans
Z
C X
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Complex form compensation
high (~106 points) spatial
resolution measurements
are valuable for
components unsuitable
for interferometry i.e.
non-reflective
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Ultra Precision Temperature Controllers
Thermal Control
Loxham Precision’s ultra precision
temperature
controllers are based on the most advanced
thermal management technologies offering:
o
o
o
o
o
o
o
Sub milli-Kelvin resolution control
Multiple channels
Matched performance temperature sensors
High response cooling technology
Advanced fluid heater technology
Remote heater and sensor positioning
Advanced control functions
0.1°C
1 hour
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Ultra Precision Temperature Controllers
• Modular multi-channel configurable approach
• Specific miniaturised electronic and fluid control
hardware development
• Sub milli-Kelvin operating resolution
• Specially encapsulated ultra-stable sensors
• Remote (wireless) sensor capability
• Numerous control options:
• Cascade, gain scheduling, adaptive control, alarms etc.
• Controllable:
• Pumping power
• Cooling power
• Heating power
• Tailored solutions available
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Final word on temperature
The definition of the units of
temperature (the kelvin and the
degree Celsius) is about to change.
From 2018, temperature
measurements will be fundamentally
linked to the units of energy.
Every temperature measurement
you make
is linked to our fundamental
understanding of the thermal
properties of matter - its accuracy will
have been founded on dimensional
metrology of copper components.
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