Hartmann Sensor for advanced gravitational wave interferometers Aidan Brooks, Peter Veitch, Jesper...
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![Page 1: Hartmann Sensor for advanced gravitational wave interferometers Aidan Brooks, Peter Veitch, Jesper Munch Department of Physics The University of Adelaide.](https://reader034.fdocuments.net/reader034/viewer/2022051019/5697c02a1a28abf838cd8093/html5/thumbnails/1.jpg)
Hartmann Sensor for advanced gravitational wave
interferometers
Aidan Brooks, Peter Veitch, Jesper Munch
Department of PhysicsThe University of Adelaide
LIGO-G060103-00-Z
LSC March 2006
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Outline of Talk
• Hartmann wavefront sensor
• Experimental validation
• Tomographic capabilities
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Objectives
• Develop versatile, robust wavefront sensor• Distortion must ultimately be corrected to /100• Sensor needs to have sensitivity << /100• Sensor should not interfere with input mirrors or
GWI laser beam.• Sensor suitable for wavefront servo
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Hartmann Wavefront Sensor:How It Works
CCD
Undistorted wavefrontDistorted wavefront
Hartmann plateUndistorted opticDistorted optic
Hartmann raysHartmann spot
pattern
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• Optimized for distortion in advanced GWIs• Spatial resolution• Sensitivity
Optimized Hartmann Plate
Hexagonal cells added to highlight arrangement
Hole size 150m
Hole spacing 430m
Distance to CCD 10mm
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Centroiding Single Hartmann Spot to Sub-Pixel Accuracy
Max
Min
• Fractional centroiding algorithm allows positioning of centroid to approximately (pixel size) / (number of grayscale levels)
• Dynamic Range of Camera 11.5 bits.
• Pixel Size = 12m
• Theoretical Accuracy of centroid 4nm
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Hartmann Wavefront Sensor:How It Works
• Spot displacement proportional to gradient of wavefront
• We can locate spots 20nm
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Sensor Has Very Low Noise
RMS noise = /1100 -2.0 -1.0 0.0 1.0 2.0 Wavefront distortion (nm)
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450m
s 450m X 400nrad
= 0.18nm
Smallest angle = 400nrad
Sensor accuracy
Smallest x = 4nm
Leve
r ar
m =
10
mmSmallest angle = 400nrad
Wavefront
Hartmann plate
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Hartmann Sensor
• Very low noise, because each pixel is
separate against a dark surround, due to the
optimization of hole size, separation and lever arm
• Superior to other sensors (eg Shack
Hartmann, Interferometers etc)• Suitable for wavefront correcting
servo system
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Hartmann Sensor
• On axis
• Off axis
• Tomography (more than one off axis view)
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Single View Optical Tomography Works for Cylindrical Symmetry
• E.g. Distortion induced by absorption of Gaussian beam heating an isolated optic
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Representation of Refractive Index Distribution in Distorted Optic
• Divide into annular volume elements (voxels)
• Cylindrical symmetry assumed
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Wavefront Distortion Analyzed with Radon Transforms
• VoxelIJ has uniform refractive index
•Radon Transform of VoxelIJ
•Fit mode to wavefront distortion
Off axis viewing angle,
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Experimental Objectives
• Demonstrate that tomographic sensor works• Validate results with independent high precision
on-axis interferometer • Experiment constructed to mimic distortion in
Advanced LIGO
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Experiment to Show Sensor Works
3W CW heating beam (1064nm)
Mach-Zehnder Interferometer object
beam, (HeNe)
Heated Glass Test Optic
Off-axis Hartmann beam, (HeNe, LED)
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Simulation of Experiment Results
Original off-axis OPD Best fit with voxel projections
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Simulation shows Tomographic Analysis is Accurate
On-axis and Reconstructed On-Axis
|1000 X Difference|
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Off axis reconstruction agrees exactly with on axis interferometer
Dashed line: 5 x absolute difference, dots: reconstruction
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ConclusionConclusion
• Hartmann sensor has accuracy and sensitivity required for advanced interferometers
• Current RMS Noise of sensor~ λ/1100• Advantageous for both on axis and off axis• Voxel analysis shown to be accurate• Initial experimental results are promising• Can extend to non-cylindrically symmetric distributions –
use multiple views and azimuthal voxelation• Ideal for active feedback servo systems