si traceable diffraction measurements on the nist parallel

$: SI Traceable Diffraction Measurements on the NIST Parallel$
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


Making XRD Traceable


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


PBD Schematic

Encoders

X-ray source

Isolation platform

Mirror & positioner assembly

Detector

Specimen

Nulling Autocollimator


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


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


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


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


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


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


The Virtual Polygon

2θωring

θmirror = 2θ + ω + θring≣0

sample stage

2θmeas + Δ2θ + ωmeas + Δω + θring = 02θmeas + ωmeas + θring = - Δ2θ - Δω


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


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


Visualization of Error Sum

ω=02θ=0

1000

+erro

r (milli

arcse

c)


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.


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

si traceable diffraction measurements on the nist parallel

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