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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
Marcus H. Mendenhall, APD-IV, April, 2013
Making XRD Traceable
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
Marcus H. Mendenhall, APD-IV, April, 2013
PBD Schematic
Encoders
X-ray source
Isolation platform
Mirror & positioner assembly
Detector
Specimen
Nulling Autocollimator
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
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
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
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
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
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
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
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
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
Marcus H. Mendenhall, APD-IV, April, 2013
Visualization of Error Sum
ω=02θ=0
1000
+erro
r (milli
arcse
c)
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.
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
