1. Thermally Deformable Mirrors: a new Adaptive Optics scheme for Advanced Gravitational Wave Interferometers
Marie Kasprzack
Laboratoire de l’Accélérateur Linéaire
European Gravitational Observatory

2. Adaptive optics: Motivation
Advanced Virgo: Dual recycling interferometer
Increase the sensitivity by a factor 10 with respect to Virgo
Gain of factor 1000 in event rate
Many improvements, in particular
increase of laser power: 125 W at the interferometer input
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

3. Adaptive optics: motivation
High laser power brings thermal effects
Optical path difference (OPD)
Consequences:
The wavefront of the beam is modified
If the substrate is not perfectly homogeneous,
the thermal lens will not be symmetric
This leads to apparition of aberrations of high spatial frequencies
After propagation, the beam will not be Gaussian any more
Opto-mechanical parameters
Temperature field
Refraction index
Thermo-optic
coefficient
Poisson
coefficient
Thermal expansion
coefficient
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

4. Matching sensitive systems
Injection: Need of 99% Matching into the ITF
Thermal effects : potentially 10% of mismatch
Potential source of noise, power losses
All effects unlikely predictable and potentially time varying
Need of adaptive optics to reach the design sensitivity
Interferometer
Pre-stabilized laser
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

5. Requirements for the corrective device
High order mode correction:
Matching control from 90-95% to better than 99%
Environment
high power laser: about 200 W
high vacuum compatible: mbar
not be a source of noise (electronic, magnetic, mechanical...)
Optics
surface roughness: lower than 0.1 nm
flatness: better than l /20
Actuation possible at long time scales: min. 10 mHz
Need of a new corrective device with
thermal actuation and high degree of actuation
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

6. Thermally deformable mirror (TDM)
TDM Actuation
Control of the optical path length via the substrate temperature
Opto-mechanical parameters
Temperature field
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

7. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Prototype
Features
Prototype
Resistor number 61
Board
PCB
Resistor type
SMD
Size (mm2)
2 resistors 0.5x1 = 1x1
Gap (mm)
~ 0.2
R Dispersion
< 5%
Substrate
Fused Silica
Animation avec l’image thermique?
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

8. Experimental Characterization
Direct observation of wavefront modification with a wavefront sensor
pupil
actuator nm
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

9. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Actuator properties
Features
Prototype
Power absorbed by the substrate
(% of dissipated power )
~ 16 %
Stroke of one actuator
~ 200 nm
Linearity:
Amplitude of response
proportional to the
dissipated power
Time response:
a few seconds
Experimental data
Linear fit
Noise level
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

10. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Zernike generation
Zernike polynomials basis:
for description of aberrations in an optical system
How well can the TDM reproduce them?
Closed-loop control : Least square algorithm with boundaries
optimization of the dynamic range nm nm nm
Sensing Noise level
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

11. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Zernike Generation
Order 2 & 3
Order 4
Order 5
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

12. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Wavefront correction
Characterization:
Efficiency: evaluation of the dynamic range
Accuracy: evaluation of the inter-mode coupling nm nm nm
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

13. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Wavefront correction
Efficiency: Highly limited above the 4th order
Accuracy: Limited coupling observed for the 5 orders
3rd order
4th order
5th order
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

14. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Wavefront correction
Efficiency: Highly limited above the 4th order
Accuracy: Limited coupling observed for the 5 orders
3rd order
4th order
5th order
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

15. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Wavefront correction
Results: the TDM is able to correct phase aberrations
Ability to reproduce the Zernike polynomials
Very good accuracy and efficiency
up to the 3rd order with 80 nm RMS
up to the 4th order with 30 nm RMS
But ideally the dynamic range must be at least 50 nm RMS for all
How to control the matching into a resonant cavity?
HG02
HG11
HG20
HG12
HG21
HG30
HG03
HG01
HG10
HG00
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

16. Suppresion of a High order mode (HOM)
TDMs only act on the phase
Small correction of the beam phase in two planes
we want this term = 0
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

17. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Suppresion of a HOM
Analytical computation of the amplitude real coefficients b1 and b2
To perform the correction of the mn HOM mode we need:
2 corrective patterns with Hmn polynomial shapes
2 corrective devices separated by z2 – z1
With the Gouy phase for the m+n order
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

18. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Mode Matching Setup
Setup with a triangular cavity
Laser frequency locked on the cavity
One TDM for creation of aberrations
Gouy phase difference ~20 deg
Mode Cleaner Cavity
F = 50
FSR = 2 GHz
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

19. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
SETUP In The calva ROOM
TDM0
TDM1
TDM2
reflection
transmission
Cavity
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

20. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Mode Matching Setup
Actuation maps: projection of the Hermite-Gauss onto the TDM basis
HG02
HG11
HG20
HG12
HG21
HG30
HG03
HG13
HG22
HG31
HG04
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

21. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Mode Matching Setup
Correction of the mode HG11:
mode reduced by a factor 3
coupling to other modes: defocus, tilt and mode 30
Mode 11
Mode 30
focus
tilt
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

22. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Mode Matching Setup
Correction of the mode HG30:
mode reduced by a factor 1.9
increase of defocus and tilt
Mode 30
focus
tilt
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

23. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Prospects
The setup is limited by the coupling to the tilt and focus
Necessary next steps:
Implementing an automatic alignement system to:
Determine the limits of the setup by systematic tests:
Determine the limits of correction for each mode
Perform simultaneous correction of several modes
Compare with simulations
Improving the sensing to keep the cavity locked:
Direct estimation of the HOM content via cameras
Reduction of the convergence time
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors

24. Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
Conclusion
The TDM is an innovative device with many advantages:
Thermal actuation
High optical quality
High order mode correction
Further steps are necessary before installation in Advanced Virgo:
End the matching characterization
Make a vacuum compatible prototype
Check the performance under vacuum
Check the noise compatibility
March 26, 2015
Moriond Marie Kasprzack - Thermally Deformable Mirrors