THERMALLY DEFORMABLE MIRRORS:A NEW ADAPTIVE OPTICS SCHEME
FOR ADVANCED GRAVITATIONAL WAVE
INTERFEROMETERS
Marie KasprzackLaboratoire de l’Accélérateur LinéaireEuropean Gravitational Observatory
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
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 2015 - 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
March 26, 2015
zzyxTnT
n d
z
d),,()1)(1( OPD0
Opto-mechanical parameters
Temperature field
Thermo-optic coefficient
Thermal expansion coefficient
Poissoncoefficient
Refraction index
Moriond 2015 - 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
March 26, 2015
Interferometer
Pre-stabilized
laser
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: 10-6 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 2015 - Marie Kasprzack - Thermally Deformable Mirrors 5
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
6
THERMALLY DEFORMABLE MIRROR (TDM)• TDM Actuation
Control of the optical path length via the substrate temperature
March 26, 2015
zzyxTnT
n d
z
d),,()1)(1( OPD0
Opto-mechanical parameters
Temperature field
PROTOTYPE
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 7
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
EXPERIMENTAL CHARACTERIZATION• Direct observation of wavefront modification with a
wavefront sensor
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 8
pupil actuator
nm
ACTUATOR PROPERTIES
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 9
• Linearity: Amplitude of response proportional to the dissipated power
• Time response: a few seconds
Features Prototype
Power absorbed by the substrate (% of dissipated power )
~ 16 %
Stroke of one actuator ~ 200 nm
Noise level
Linear fit
Experimental data
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
10
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 boundarieso optimization of the dynamic range
March 26, 2015
33Z
Sensing Noise level
nm nm nm
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 11
Order 2 & 3
ZERNIKE GENERATION
Order 4
Order 5
WAVEFRONT CORRECTION
• Characterization:
• Efficiency: evaluation of the dynamic range
• Accuracy: evaluation of the inter-mode coupling
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 12
t
TDMtt
E
1
20
1
2
i
TDMi
TDMtA
tt Z ii
TDMi Z
nm nm nm
WAVEFRONT CORRECTION• Efficiency: Highly limited above the 4th order• Accuracy: Limited coupling observed for the 5 orders
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 13
3rd order
4th order 5th order
WAVEFRONT CORRECTION• Efficiency: Highly limited above the 4th order• Accuracy: Limited coupling observed for the 5 orders
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 14
3rd order
4th order 5th order
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
15
• Results: the TDM is able to correct phase aberrations• Ability to reproduce the Zernike polynomials• Very good accuracy and efficiency
o up to the 3rd order with 80 nm RMSo 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?
March 26, 2015
WAVEFRONT CORRECTION
HG02 HG11 HG20
HG12 HG21 HG30HG03
HG01 HG10
HG00
SUPPRESION OF A HIGH ORDER MODE (HOM)
• TDMs only act on the phaseSmall correction of the beam phase in two planes
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 16
)]()[( 0000000zHaazHG mnmnz
ci ie c 1
),(
),(
22
11
2
1
yxHbz
yxHbz
mnc
mnc
)()(][
)(
2002200100
)(
20000
221
2
zzHbiaebiaea
za
mn
ii
mn
z
zzz
we want this term = 0
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 2015 - Marie Kasprzack - Thermally Deformable Mirrors 17
nmz
;0;0 002
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
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 18
Mode Cleaner Cavity
F = 50FSR = 2 GHz
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
19
SETUP IN THE CALVA ROOM
March 26, 2015
TDM0
Cavity
transmission
reflection
TDM1
TDM2
Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors
20
MODE MATCHING SETUP
March 26, 2015
HG02 HG11 HG20
HG12 HG21 HG30HG03
HG13 HG22 HG31 HG04HG04
• Actuation maps: projection of the Hermite-Gauss onto the TDM basis
MODE MATCHING SETUP
• Correction of the mode HG11:
• mode reduced by a factor 3• coupling to other modes: defocus, tilt and mode 30
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 21
focus
tilt
Mode 11 Mode
30
MODE MATCHING SETUP
• Correction of the mode HG30:
• mode reduced by a factor 1.9• increase of defocus and tilt
March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors 22
focus
tilt
Mode 30
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:
o Determine the limits of correction for each modeo 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 2015 - Marie Kasprzack - Thermally Deformable Mirrors 23
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 2015 - Marie Kasprzack - Thermally Deformable Mirrors 24