Laser Frequency Stabilisation and Interferometer Path ... · Laser frequency stabilisation & IFO...

Albert Einstein Institute

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).

Laser Frequency Stabilisation and Interferometer Path Length

Differences on LISA Pathfinder

Sarah Paczkowski on behalf of the LISA Pathfinder collaboration

Laser frequency stabilisation & IFO path length differences on LPF XI LISA Symposium Zurich

background

2

interferometeras our

measurementstick

rewrite using

frequencyfluctuations

path lengthdifference

phase noise


background

3


path lengthdifference orarm lengthmismatch

phase noise

• laser frequency noise is important because

• with a non-zero path length difference, laser frequency noise couples into our measurement

• how to measure it: with a dedicated interferometer!


frequency IFO

4

• 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

“main” — 2015/3/10 — 11:09 — page 33 — #33

Chap

ter1

1.4 The optical metrology system

BS16

PDA1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1M5

BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

BS16

PDA1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1M5

BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

Testmass 1

Testmass 2

BS16

PDA1

WIN1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1

WIN2

M5BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

��

��

��

��

��

��

��

��

��

Testmass 1

Testmass 2

BS16

PDA1

WIN1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1

WIN2

M5BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

X1 X12

Freq. Ref.

TM1TM1

TM1 TM1

TM2TM2

TM2 TM2

Figure 1.14: Optical diagrams showing the beampaths of the four interferometerson the LPF optical bench with the measurement beam (beam 1) shown in red, andthe reference beam (beam 2) shown in blue. Picture courtesy of ASD and IGR.

33

picture courtesy of ASD & IGR


laser frequency control loop(s)

• nested control loop

• implemented at 100 Hz inside data management unit

5


laser frequency control loop(s)

• nested control loop

• implemented at 100 Hz inside data management unit

5

piezo

heater


loop characterisation experiment

6

• 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 open - loop transfer function

results from DOY 164

Frequency [Hz]10-3 10-2 10-1 100 101

Phas

e [d

eg]

-600

-400

-200

0

200

400

600modeltransfer function estimate Itransfer function estimate II

Am

plitu

de [

]

10-1

100

101

102

103

modeltransfer function estimate Itransfer function estimate II

prelim

inary


measured frequency noise

7

• fulfil frequency noise requirement with stabilisation• due to small arm length difference, displacement

requirement fulfilled in both cases

Frequency [Hz]10-3 10-2 10-1 100

equi

vale

nt d

ispl

acem

ent n

oise

[m H

z-1/2

]

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

Req.closed-loop freq noise DOY 116open-loop freq noise DOY 167

Frequency [Hz]10-3 10-2 10-1 100

freq

uenc

y no

ise

[Hz

Hz-1

/2]

101

102

103

104

105

106

107

Req.closed-loop freq noise DOY 116open-loop freq noise DOY 167

path length noise achieved with estimated mismatch

derived before OB build using 1pm req. & pessimistic 1cm mismatch assumption

prelim

inary

prelim

inary


different levels of frequency noise

8

• observe two different levels• systematic analysis pending

prelim

inary


arm length mismatch

• 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

9


path lengthdifference

“main” — 2015/3/10 — 11:09 — page 33 — #33

Chap

ter1

1.4 The optical metrology system

BS16

PDA1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1M5

BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

BS16

PDA1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1M5

BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

Testmass 1

Testmass 2

BS16

PDA1

WIN1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1

WIN2

M5BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

��

��

��

��

��

��

��

��

��

Testmass 1

Testmass 2

BS16

PDA1

WIN1

BS1

BS2

BS7

M11M12

M14BS5

BS8BS3

M1

WIN2

M5BS10

BS11

PDRB

BS4 BS9

M6

PDFA

PDFB

PDRA

PD1A

BS6

PDA2

PD1B

M4

M10

M8

M15

PD12B

PD12A

FIOS 1BEAM 1

FIOS 2BEAM 2

X1 X12

Freq. Ref.

TM1TM1

TM1 TM1

TM2TM2

TM2 TM2

Figure 1.14: Optical diagrams showing the beampaths of the four interferometerson the LPF optical bench with the measurement beam (beam 1) shown in red, andthe reference beam (beam 2) shown in blue. Picture courtesy of ASD and IGR.

33

picture courtesy of ASD & IGR


arm length mismatch

10

• 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


arm length mismatch

11

two principles to calculate:- transfer function - noise minimisation

three ways to measure on LPF1. arm-length mismatch experiment2. from frequency loop characterisation experiment3. during noise measurement


arm length mismatch experiment - design

12

steps of experiment:1. injection @

nominal position

2. injection @ offset position

3. open-loop noise measurement

Origin: 2016-06-14 21:20:00.000 UTC - [s] # 1040 0.5 1 1.5 2 2.5 3 3.5

Valu

e [V

]

-0.2

-0.1

0

0.1

0.2DMU_OMS_FAST_FREQ_CTRL_OUT

Valu

e [m

]

# 10-6

-5

0

5

10

15o12

commanded offset: 9.576 umTM 2 moved towards

centre of satellite

prelim

inary


arm length mismatch experiment - results

• 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

13

• the measurements are consistent with each other

• 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 during noise measurement averaged over 5 min segments, worst case error estimate

Origin: 2016-06-14 21:20:00.000 - Time [s] # 1040 0.5 1 1.5 2 2.5 3

Am

plitu

de [

um]

310

320

330

340

350

360

370

380mismatch at nom posmismatch at offset posmismatch at nom pos during OL noise measurement


arm length mismatch over time

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• 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

already in best case with injections, different implementations provide different errors

check: during injection measurement: equivalent displacement noise from frequency noise should explain the peaks in o12:

prelim

inary


contribution to total OMS noise

15

frequency noiserelevant from

max ~ @

mismatch:


summary

16

• 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 and Interferometer Path ... · Laser frequency stabilisation & IFO...

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