Albert Einstein Institute
Laser Frequency Stabilisation and
Interferometer Path Length
Differences on LISA Pathfinder
Sarah Paczkowski on behalf of the LISA Pathfinder
collaboration
This work has been made possible by the LISA Pathfinder mission,
which is part of the space-science program of the European Space Agency. We gratefully acknowledge support by the European Space
Agency (ESA) (22331/09/NL/HB, 16238/10/NL/HB), by Deutsches Zentrum für Luft- und Raumfahrt (DLR) with funding of the
Bundesministerium für Wirtschaft und Energie with a decision of the Deutschen Bundestag
(DLR project reference numbers FKZ OQ 0501 and FKZ 50 OQ 1601) and thank the German Research Foundation for funding the Cluster of
Excellence QUEST (Centre for Quantum Engineering and Space-Time Research).
background
interferometer
as our
measurement
stick
rewrite using
path length
difference
phase noise
frequency
fluctuations
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
2
background
phase noise
•
laser frequency noise is important because
•
•
path length
difference or
arm length
mismatch
frequency
fluctuations
with a non-zero path length difference, laser
frequency noise couples into our measurement
how to measure it: with a dedicated interferometer!
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
3
M1
M5
M5
BS10
M4
M4
PD1A
PD1A
PD12B
PD12A
PDA2
PDA2
PDRA
frequency IFO
•
•
•
•
total: 4 interferometers (IFO)
on LPF optical bench (OB)
frequency interferometer
allows us to measure the laser
frequency noise
intentional path length
difference of 0.3821m in
optical fibres before OB
input to laser frequency
control loop
Laser frequency stabilisation & IFO path length differences on LPF
PDRA
TM2
TM2
Freq.
Ref.
Testmass 1
Testmass 1
TM1
TM1
WIN1
PDA1
PDA1
PDFA
M12
M12
M11
FIOS 1
BS1
BS7
BEAM 1
BS16
BS11
FIOS 1
PDFB
BS16
BS2
BS9
BS4
BS1
BEAM 1
BS11
M6
BEAM 2
BEAM 2
FIOS 2
FIOS 2
PDRB
PDRB
M10
BS6
BS6
M14
BS5
BS9
BS4
BS5
M8
PD1B
BS8
PD1B
BS3
BS8
M15
BS3
M1
M5
M5
BS10
M4
M4
PD1A
PD12B
PD1A
PD12A
PDA2
PDRA
PDA2
PDRA
WIN2
TM2
TM2
Testmass 2
Testmass 2
Figurepicture
1.14:
Optical
showing the beampaths of th
courtesy
of ASDdiagrams
& IGR
on the LPF optical bench with the measurement beam (beam
the reference beam (beam 2) shown in blue. Picture courtes
XI LISA Symposium Zurich
4
laser frequency control loop(s)
•
nested control loop
•
implemented at 100 Hz inside data management
unit
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
5
laser frequency control loop(s)
piezo
heater
•
nested control loop
•
implemented at 100 Hz inside data management
unit
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
5
loop characterisation experiment
•
Laser frequency stabilisation & IFO path length differences on LPF
Amplitude []
10 3
10 2
10 1
10
0
10 -1
600
400
200
0
-200
-400
-600
10 -3
pr
el
im
in
ar
y
•
measured either
only at injection
frequencies (transfer
function estimate II)
or including also the
noise (transfer
function estimate I)
at all frequencies in
between injection
frequencies
model with flight
model test campaign
parameters
unity gain frequency
Hz & phase margin
Phase [deg]
•
model
transfer function estimate I
transfer function estimate II
model
transfer function estimate I
transfer function estimate II
10 -2
10 -1
10 0
10 1
Frequency [Hz]
open - loop transfer function
results from DOY 164
XI LISA Symposium Zurich
6
measured frequency noise
Req.
closed-loop freq noise DOY 116
open-loop freq noise DOY 167
frequency noise [Hz Hz -1/2]
10 6
10
5
10 4
10 3
10 2
10 1 -3
10
10 -2
10 -1
Frequency [Hz]
•
•
10 0
pr
el
im
in
ar
y
10 7
10 -11
equivalent displacement noise [m Hz-1/2]
pr
el
im
in
ar
y
derived before OB build using 1pm req. &
pessimistic 1cm mismatch assumption
path length noise
achieved with
estimated mismatch
Req.
closed-loop freq noise DOY 116
open-loop freq noise DOY 167
10 -12
10 -13
10 -14
10
-15
10 -16
10 -17
10 -18 -3
10
10 -2
10 -1
10 0
Frequency [Hz]
fulfil frequency noise requirement with stabilisation
due to small arm length difference, displacement
requirement fulfilled in both cases
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
7
pr
el
im
in
ar
y
different levels of frequency noise
•
•
observe two different levels
systematic analysis pending
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
8
10 — 11:09 — page 33 — #33
1.4 The optical metrology system
X12
TM1
PDA1
PDFA
BS7
FIOS 1
BS1
BS7
BS16
BS11
PDFB
BS2
BS9
BS4
•
M6
BEAM 2
FIOS 2
M10
PDRB
M10
BS6
14
M14
BS5
M8
PD1B
BS8
M15
BS3
M15
M1
M5
BS10
M4
PD12B
PD1A
PD12B
PD12A
PDA2
frequency
fluctuations
M11
BEAM 1
M6
difference
PDFA
M12
PDFB
Chapter 1
arm length mismatch path length
PDRA
•
TM2
Ref.courtesy of ASD & IGR
picture
Testmass 1
TM1
•
arm length mismatch: path length of
measurement and reference beam
in same interferometer is not equal
dependent on absolute TM
positions
2 x mechanical mismatch ~
optical path length difference
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
9
arm length mismatch
•
•
mismatch is interesting because
• quality assessment of LPF Core Assembly
(LCA)
• parameter is needed to estimate the frequency
noise contribution to total OMS noise
in LPF: measure frequency noise (Freq IFO) &
displacement in IFOs (o12 or o1 IFO)
deduce mismatch
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
10
arm length mismatch
two principles to calculate:
- transfer function
- noise minimisation
three ways to measure on LPF
1. arm-length mismatch experiment
2. from frequency loop characterisation experiment
3. during noise measurement
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
11
arm length mismatch experiment - design
Laser frequency stabilisation & IFO path length differences on LPF
# 10 -6
0.2
0
-0.1
-0.2
0
0.5
1
1.5
2
2.5
Origin: 2016-06-14 21:20:00.000 UTC - [s]
15
o12
10
5
Value [m]
0.1
pr
el
im
in
ar
y
DMU_OMS_FAST_FREQ_CTRL_OUT
Value [V]
steps of
experiment:
1. injection @
nominal
position
2. injection @
offset
position
3. open-loop
noise
measurement
0
3
-5
3.5
# 10 4
commanded offset: 9.576 um
TM 2 moved towards
centre of satellite
XI LISA Symposium Zurich
12
arm length mismatch experiment - results
•
•
•
the measurements are
consistent with each other
380
we know the sign of the
mismatch
expected: , measured: , agrees
within errors of of the offset
position
the error at the offset position is
larger because mismatch and
thus coherence is smaller
mismatch at nom pos
mismatch at offset pos
mismatch at nom pos during OL noise measurement
370
360
Amplitude [um]
•
350
340
330
320
•
•
•
•
mismatch during noise
measurement averaged over 5
min segments, worst case error
estimate
310
0
0.5
1
1.5
2
Origin: 2016-06-14 21:20:00.000 - Time [s]
2.5
3
# 10
4
result agrees to the estimates from the frequency characterisation experiment on
DOY164:
not inconsistent with ground measurement where OB was measured individually
well below the requirement of 1mm
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
13
arm length mismatch over time
•
•
•
•
we want: arm length mismatch estimate over noise runs
required: TM motion low, high coherence between the channels
caveat I: phase tracking is reset after every station keeping
caveat II: accordance between the different methods and their errors
check: during injection measurement:
equivalent displacement noise from
frequency noise should explain the peaks in
o12:
pr
el
im
in
ar
y
already in best case with injections, different
implementations provide different errors
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
14
contribution to total OMS noise
mismatch:
frequency noise
relevant from
max ~
@
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
15
summary
•
•
•
•
in an interferometer where the two beams
travel not the same path length, frequency
noise is relevant
on LPF, laser stabilised with nested
feedback control
deduce the arm length mismatch in o12 IFO
the integration of LCA is better than
required
Laser frequency stabilisation & IFO path length differences on LPF
XI LISA Symposium Zurich
16