thermally deformable mirrors: a new adaptive optics scheme for advanced gravitational wave...

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


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


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


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


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


pupil actuator

nm

ACTUATOR PROPERTIES


• 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


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


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


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


3rd order

4th order 5th order


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


)]()[( 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


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


Mode Cleaner Cavity

F = 50FSR = 2 GHz


19

SETUP IN THE CALVA ROOM

March 26, 2015

TDM0

Cavity

transmission

reflection

TDM1

TDM2


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


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


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


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


thermally deformable mirrors: a new adaptive optics scheme for advanced gravitational wave...

Documents

deformable mirrors

motivation high laser

thermal actuation

environment high power

pupil actuator nm slide

substratefused silica

power losses

high degree of actuation