An OffAxis Hartmann Sensor for Measurement of Wavefront Distortion in Interferometric Detectors

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An Off-Axis Hartmann Sensor for Measurement of
Wavefront Distortion in Interferometric Detectors

• Aidan Brooks, Peter Veitch, Jesper Munch
• Department of Physics, University of Adelaide

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Objectives

• Improve operation of advanced interferometers by
  reducing thermally induced wavefront distortion.
• Develop a sensor to measure the distortion and
  correction in the ACIGA High Optical Power Test
  Facility.

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Crux of thermal problem
Courtesy of Ryan Lawrence and David Ottaway, MIT

• Absorbed power causes thermal lensing
• Prediction of MELODY model of Advanced LIGO
• Sideband power is scattered out of TEM00
• Instrument failure at approximately 2 kW
• Adv. LIGO cannot achieve desired sensitivity
  unaided

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How to maintain cavity finesse?

• Measure distortion with wavefront sensor
• Employ active compensation system
• Sensor cannot interfere with core optics or GWI
  laser beam.

OFF-AXIS WAVEFRONT SENSOR
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Why use a Hartmann wavefront sensor?

• Interferometry
• Shack-Hartmann
• Hartmann
• Easiest to align
• Cheap
• In principle, can measure a wavefront change of
  less than l/1000

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Hartmann wavefront sensor
CCD

• Record spot positions on CCD
• Wavefront changes ? spot positions change
• Gradient of wavefront change proportional to
  displacement of spot.

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Off-Axis Bench Top Test
Hartmann plate
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Comparison of Hartmann sensor with interferometry
demonstrated accuracy

• Line - Off axis fit
• Data Interferometric fringe distortion

OPD (waves/100 at 633nm)

• Hartmann data analyzed using quasi-orthogonal
  functions.
• Lack of orthogonality results in systematic
  errors

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Determine wavefront distortion using optical
tomography
Cylinder of transparent material with internal
temperature/refractive index distribution
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Determine wavefront distortion using optical
tomography
Divide into annular volume elements (voxels)
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Determine wavefront distortion using optical
tomography
Fitting functions are off-axis projections of
voxels
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Simulation of tomography

• Temperature distribution in ITM of AdLIGO-like
  system modelled using Hello-Vinet equation
• Off-axis optical path distortion (OPD) through
  this distribution determined
• OPD used as input data for a least-squares-fit to
  voxel projections
• Internal temperature distribution reconstructed
• On-axis OPD determined from reconstruction and
  compared to OPD predicted by theory

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Simulation results
Original off-axis OPD
Best fit with voxel projections
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Tomographic analysis is accurate
input, reconstructed
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Implementation of tomography

• Hartmann sensor used to measure OPD gradient
  field
• Gradient field used to reconstruct phase
  distortion (OPD) using iterative process
• Tomographic analysis determines temperature
  distribution from reconstructed OPD
• On-axis OPD determined from reconstructed
  temperature distribution

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Initial measured precision l/120

• Measured using double snap no heating

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Conclusion
Conclusion

• Single view, off-axis Hartmann, tomographic
  wavefront sensor has sufficient accuracy to
  measure cylindrically symmetric refractive index
  distributions in advanced interferometers
• Accuracy of l/1000 (simulation).
• Current precision l/120 (measured)
• CCD noise precision limit l/500
• Can extend to non-cylindrically symmetric
  distributions use multiple views and azimuthal
  voxelation

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Interpreting Off-Axis View
Distortion interferometer sees
Distortion we see
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Analyzing distortion using functional
decomposition
r
z
n(r) ? ai fi(r)
F (x, y) ? ai gi(x, y)
F(r) C ? ai fi(r)

• gi(x, y) are path integrated fi(r)
• LSQ fit to appropriate fns gi(x, y)
• Coefficients reveal on-axis distortion
• Most appropriate functions fi(r) are elusive

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Simulated Sensitivity Test
Optical Path Difference ( l/1000 )
Radius (mm)
Radius of curvature 1570m