Albert Einstein Institute
Max Planck Institute for Gravitational Physics and
Leibniz Universität Hannover
German Aerospace
Center
European Space Agency
ESA
Centre for Quantum Engineering
and Space-Time Research
Leibniz Universität Hannover
Germany
Max Planck Society
Germany
Experimental demonstration of a two-lens imaging system for the
LISA test mass interferometer
S.Schuster¹, M.Tröbs¹, G.Wanner¹, G.Heinzel¹ and K.Danzmann¹
Max Planck Institute for Gravitational Physics
Motivation
TM
One significant noise source in the position measurement of the LISA test mass (TM) is an unintended tilting (jittering) of it.
This angular jitter results in a dithering measurement beam, which in return leads to noise in the longitudinal pathlength readout (LPS).
α
An idea to reduce this coupling between TM tilt and pathlength error, is to image the TM directly to the detector. In theory this should suppresse the remaining beam walk and reduce coupling between beam jitter and pathlength readout.
Measurement Beam
All previous experimental performance tests of imaging systems were limited by other noise sources. Therefore, it was not possible to distinguish between residual noise behind an imaging system and other noise sources, like: longitudinal movement of the tilt actuator, mismatch between wavefront curvatures, the effects of higher order modes or misalignment of the imaging system.
imaging system
rest of interferometer
Reference Beam
QPD
TM
Vanishing tilt to length coupling on a
large detector
λ/2 PBS
Mode Matching
to Cavity
Mode Matching
to Experiment
Longitudinal PZT
d1
Suppression of the longitudinal piezo movement
5e-05
0
-5e-05
-0.0001
-0.00015
-0.0002
-0.00025
-0.0003
-0.00035
-0.0004
IfoCAD
Analytical
-600
-400
-200
0
200
Beam Angle [urad]
400
600
λ/2
Tilt Locking
λ/2
Schematic
reference
QPD
PBS
Draft of the experimental setup
 Modecleaner ensures the laser beam to be a pure fundamental Gaussian mode
 Coherent filtering allows to measure the pathlength with
high accuracy
 Homodyne Mach-Zehnder setup with equal arm length
ensures a perfect wavefront curvature match of both
interfering beams equal beam parameters
 Midfringe lock for a sensitive phase readout
 Tilt QPD measures the actual beam angle
 Reference SEPD measures the longitudinal movement of
the tilt piezo
 Imaging QPD / reference QPD measure the performance
with imaging system / without imaging system
d2 = d1
λ/2
λ/4
reference
SEPD
SEPD
Tilt PZT
DPS signal for
TM-angle
measurement
2000
Pathlength Control Loop
Coherent filtering
0
Main Measurement
Imaging System
It can be analytically shown, that the coupling between
beam tilt and LPS vanishes for a singular case of two fundamental Gaussian beams with identical parameters
and complete detection of both beams without clipping.
Therefore, the reference single element photodiode
(SEPD) only sees the unintended longitudinal movement
of the tilt piezo and the remaining pathlength error after
the midfringe log.
A manuscript which describes this effect is in preparation.
λ/4
λ/2
λ/2
Pathlength [pm]
The better way of averaging
-2000
A function generator applied a symmetric ramp to the tilt piezo. The linear
piezo stabilized the pathlength via the SEPD. The DPS signal of the piezo QPD,
the sum signals of the imaging QPD, reference QPD and the reference SEPD,
the actuator signal and the error signal of the linear piezo loop were measured
with an ADC card, phase-locked to the function generator controlling the tilt
piezo. In post processing, all input data were coherently filtered with the frequency of the tilt modulation.
The sum signals were translated to the corresponding LPS and the DPS signal
was translated to the beam angle. Afterwards, the SEPD LPS signal was subtracted from imaging and reference QPD LPS.
The resulting LPS signals are plotted over the beam angle and compared to a
numerical simulation.
pathlength [pm]
Detailed experimental proceeding
-4000
-6000
-8000
-10000
D003 QPD exp
D003 QPD sim
reference QPD exp
reference QPD sim
-12000
-14000
-400
-300
-200
-100
0
100
beam angle [urad]
200
300
400
120
100
Coherent filtering is a data post-processing
technique, which allows precise measurements
in an unstable environment (without bonded
interferometers in vacuum).
The measurement is performed over several tilt
cycles of an actuation whose effects should be
investigated. The time series of the measured
data is Fourier-transformed and all bins that do
not correspond to the actuation frequency or
higher harmonics are set to zero. The inverse
transformation of the remaining bins only contains the parts which are synchronous to the
actuation.
80
Simulation
The simulation was performed with IfoCAD. Not the theoretical possible performance is simulated, but the performance for a slightly misaligned system.
The amount of misalignment is fitted to the experimental results.
The resulting misalignment parameter is a transversal offset of the first lens by
0.7 um.
pathlength slope [pm/urad]
1
60
40
20
0
-20
-40
D003 QPD exp
D003 QPD sim
reference QPD exp
reference QPD sim
-60
-80
-400
-300
-200
-100
0
100
200
300
400
We gratefully acknowledge support by the European Space Agency (ESA) (22331/09/NL/HB,
16238/10/NL/HB) and the German Aerospace
Center (DLR) (50OQ0601, 50OQ1301) and thank
the German Research Foundation for funding the
Cluster of Excellence QUEST (Centre for Quantum
Engineering and Space-Time Research).
beam angle [urad]
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