si traceable diffraction measurements on the nist parallel
TRANSCRIPT
![Page 1: SI Traceable Diffraction Measurements on the NIST Parallel](https://reader033.vdocuments.net/reader033/viewer/2022060918/629983dabf4ae762ff411cb8/html5/thumbnails/1.jpg)
Marcus H. Mendenhall, APD-IV, April, 2013
SI Traceable Diffraction Measurements on the NIST
Parallel Beam Diffractometer
Marcus H. Mendenhall, Vanderbilt University
James P. Cline, NIST Gaithersburg
Donald Windover, NIST Gaithersburg
Albert Henins, NIST Gaithersburg
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Marcus H. Mendenhall, APD-IV, April, 2013
Making XRD Traceable
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Marcus H. Mendenhall, APD-IV, April, 2013
Parallel Beam DiffractometerOverview
• Interchangeable optics and sample stages
• Vertical axes, concentrically mounted Huber 430 rotation stages
• Heidenhain RON 905 optical encoders on primary axes
• Short and long range encoder calibration
• SI-traceable reference crystals
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Marcus H. Mendenhall, APD-IV, April, 2013
PBD Schematic
Encoders
X-ray source
Isolation platform
Mirror & positioner assembly
Detector
Specimen
Nulling Autocollimator
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Marcus H. Mendenhall, APD-IV, April, 2013
Angular Measurements
• Divide angular domain into two problems:
• Short-range errors (coherent with encoder features at 100 deg-1) caused by nonlinearities in the digitizing electronics
• Long-range errors caused by scale errors in the encoder wheel, eccentricity, etc.
• Avoid use of undocumented internal angular corrections from manufacturer
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Marcus H. Mendenhall, APD-IV, April, 2013
Short-Period Compensation
• Scan a diffractometer axis at (roughly) uniform speed
• monitor encoder results as a function of time
• transform to deviations from linear as a function of angle
• these deviations include screw errors, motor speed variations, all kinds of noise
0 100 200 300 400scan time (s)
-10
-8
-6
-4
-2
0
2
4
6
offs
et fr
om u
nifo
rm (a
rcse
c)
Scan Angle deviation vs. time
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Marcus H. Mendenhall, APD-IV, April, 2013
Deviations have Periodic Structure
118.70 118.75 118.80 118.85encoder position (deg)
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
posit
ion
devi
atio
n (a
rcse
c)Angle Deviation vs. encoder position
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Marcus H. Mendenhall, APD-IV, April, 2013
Example Fourier Spectrum
0 100 200 300 400 500Frequency (deg-1)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Am
plitu
de (a
rbitr
ary
units
)
Spectrum29 deg-1 × N100 × 29 / 44 deg-1 × N102 × 29 / 44 deg-1 × N100 deg-1 × N
• Strong peaks at multiples of 100/deg
• Also at motor and gearing frequencies!
• Inset shows how a near collision of gearing and real peak is very well resolved
198 199 200 201 202Frequency (deg-1)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Am
plitu
de (a
rbitr
ary
units
)
Spectrum29 deg-1 × N100 × 29 / 44 deg-1 × N102 × 29 / 44 deg-1 × N100 deg-1 × N
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Marcus H. Mendenhall, APD-IV, April, 2013
Extracted Short-period Correction
0 45 90 135 180 225 270 315 360-5
0
5
10
15
100 deg-1 (.01 arcsec)100 deg-1 phase200 deg-1 (.01 arcsec)200 deg-1 phase300 deg-1 (.01 arcsec)300 deg-1 phase400 deg-1 (.01 arcsec)400 deg-1 phase
20130319_155838_hfcomp.datFilter bandwidth = 0.20 deg-1• Analyze as harmonic
series of encoder feature period at 100 features/deg
• Demodulated from 100/deg signal to show coefficients as a function of angle, not correction as a function of angle
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Marcus H. Mendenhall, APD-IV, April, 2013
Circle Closure Calibration
• Concept
• compare sums of angles, subject to constraints that full circle is 360°
• Two general methods
• use polygonal mirror on single stage to provide set of very stable angle offsets
• use ‘virtual polygon’ and stacked stages and solve for offsets
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Marcus H. Mendenhall, APD-IV, April, 2013
The Virtual Polygon
2θωring
θmirror = 2θ + ω + θring≣0
sample stage
2θmeas + Δ2θ + ωmeas + Δω + θring = 02θmeas + ωmeas + θring = - Δ2θ - Δω
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Marcus H. Mendenhall, APD-IV, April, 2013
Details of Virtual Polygon
• For a given ring setting θr,n measure a set of angle errors {Δ2θn,m (2θm) + Δωn,m(-2θm - θr,n)} for (typically) 36 approximately equally spaced 2θ values and corresponding ω values which null the autocollimator (n indexes ring, m indexes 2θ)
• repeat for at least 3 ring settings, to give enough degrees of freedom to solve for Δ2θ, Δω, and the θr associated with each group.
• Do least squares fit for parameters
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Marcus H. Mendenhall, APD-IV, April, 2013
Circle Closure Results
0 12 24 36time (h)
residualsring moves
0 90 180 270 360Angle (deg)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Corre
ctio
n (a
rcse
c)
detectoromega
correction function
20130320_171352_hfcomp.dat.pickle 0 020130320_171352_hfcomp.dat.pickle 0 0
Fri Mar 22 16:56:08 2013
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Marcus H. Mendenhall, APD-IV, April, 2013
Visualization of Error Sum
ω=02θ=0
1000
+erro
r (milli
arcse
c)
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Marcus H. Mendenhall, APD-IV, April, 2013
Spectrum Measurement (the future...)
• Next Step: measure spectrum through our optics, with fully traceable steps
• use ‘beam walking’ technique in combination with Dectris detector array to map out properties
• requires traceable lattice constants on diffractive optics. These optics are already fabricated.
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Marcus H. Mendenhall, APD-IV, April, 2013
Beam Walking Experiment
• Measure angular geometry of beam in non-dispersive configuration (top)
• Measure spectrum of beam in dispersive configuration (bottom)
• Depends on fully qualified angle metrology from compensation and circle closure
• Fast, using Dectris Pilatus 2-D detector array
Non-dispersive
Dispersive