frequency combs for satellite formation flying combs for satellite formation flying geoff barwood...

Frequency Combs for Satellite Formation Flying

Geoff BarwoodNational Physical LaboratoryTime & Frequency Club Meeting, 3 June 2009

Monday, 22 March 2010

Introduction

• Background to this project• Introduction to FF missions (and IXO)• Introduction to femtosecond combs (in

particular, their use in distance metrology)• NPL’s possible role in missions such as IXO


HAALDM project

• High Accuracy Absolute Long Distance Measurement

• ESA study involving four partners• NPL co-authors Helen Margolis & Patrick

Gill• Final presentation at ESTEC on 2 March• Breadboarding activity could follow


Formation flying missions

• Third FF symposium at ESTEC last year

• PROBA-3 (FF testbed mission)

• Darwin (looking for earth-like planets)

• XEUS (subsumed into IXO)

• LISA?

Darwin PROBA-3


Formation flying – stages

• Launch• Free-flying• Formation acquisition (ensure

common attitude by star trackers; lateral position established via laser pointer and position sensitive detector; “local GNSS”)

• Formation flying (once this is established, use HAALDM to maintain formation)


Astronomy’s “big questions”What is “dark matter” & “dark energy”?

Was Einstein correct in his theory of general relativity?

Where do all the magnetic fields in the universe come from?

How did the universe develop in the first ~bn years after the “big bang”?


Tools at the astronomer's disposal

• Square kilometre array (to look at the H1 line at 1.42 GHz, heavily red-shifted to 100 MHz to 200 MHz)

• Planck (microwave)• Herschel (FIR)• Hubble (IR/visible/UV)• IXO (X-rays)


International X-ray Observatory

• How do super- massive black holes grow & evolve?

• How & where were the elements created & dispersed?

• How does galaxy cluster evolution constrain the nature of dark matter and dark energy?

ESA/NASA/JAXA missionAnnounced June 08Launch 2020/21


International X-ray Observatory (IXO)

Fixed Metering Structure

Deployable Metering Structure

Instrument Module

Spacecra ft Bus

Optics Module

22m

6.36m

0.89m

1.0m

12.2m

1.5m

Boom structurethat will unfoldafter launch &require on-boardmetrology

Planned focal length ~25 mMirror diameter ~3.3 mOrbit around L2 (1.5 x 106 km from earth)


IXO in schematic formz

Mirrorplane(note: thrustersalso in this plane)

Detectorplane

z = 0

z = f

x

θ

P = (r

1

1 1, θ , 0)

P = (r f

2

2 2, θ , )

y

Yaw (rotationabout z)

Roll (rotationabout x)

Pitch (rotationabout y)


IXO dimensional requirements

Parameter Uncertainty (2σ)

Focal length (z) 300 μm

x and y 170 μm

Rotation about x, y(Roll, pitch)

10 arc secs

Rotation about z (yaw)

60 arc mins


Geometrical description of rotation and displacement

• Rotations described in terms of three matrices (Rx = roll, Ry = pitch and Rz = yaw)

• General rotation matrix obtained by multiplication (R = Rz Ry Rx ; roll assumed to occur first). Inverse is RT = Rx

TRyTRz

T

• A translation x → x + h is then assumed


General points to note with the geometry

• Model as two perfectly rigid planes (no distortion) and with distances known within these planes

• Measurements from at least three points in both planes (to define them unambiguously)

• There are six parameters to determine (h, roll, pitch and yaw) and so we must need to measure (at least) six parameters (lengths)

• h, roll, pitch and yaw are expected to be “small” and so we can linearise the equations


Self-referenced optical frequency comb

Offset frequencyf0

0

I(f)

f

Maser-referenced repetition rate

frep

δ

n1 frep + f0x 2

2n1 frep + 2f0

beat = f0 if n2 = 2n1

n2 frep + f0

fprobe = m frep ±

f0 ± δ

Unknownlaser freq.


Fibre laser based femtosecond comb

Pump laser Femtosecond fibre laser EDFA Spectral

broadening

SHG Spectral broadening

EDFA

EDFA

f:2f interferometer

Spectral broadening

frep servo

f0 servo

Comb output

1000–2100 nm

Comb output

500–1000 nm

PD

PD


Femtosecond optical frequency combTime domain

Repetitive train of ultrashort pulses

Broad comb of equally spaced

optical frequencies

Frequency domain2π

f0 = Δφ

frep


Combs for distance metrology (low res.)

Laser source(from collimatedfibre)

Referencecorner-cube

Movingcorner-cube

Beamsplitter

Optics and laser source on(for example) detector plane

Moving reflectoron mirror plane

Detector

Piezo-adjustablemirror

Distance (s) between reference points (pulse overlap):

⎟⎟⎠

⎞⎜⎜⎝

⎛+Δ=

repfNtcs 2

1


Combs for distance metrology (high res.)

Laser source(from collimatedfibre)

Referencecorner-cube

Movingcorner-cube

Beamsplitter

Grating

Piezo-adjustablemirror

CCDarray

Spectral interferometry

)cos(2)( CEO212

22

1 noiseTEEEEI φφωω Δ+Δ+Δ++=


Positions of suggested reference points

1 2

34

1 2

34

s11 s22s33

s24

s12

s13

Detectorplane

Mirrorplane

LaserFibredeliveryof beams

The transformationcan be summarised as:

m = Tp

Matrix T was explicitlyderived; m is a set of 6measured parameters &p is the set of 6 parametersh, roll, pitch & yaw


Measurement “redundancy”We should measure more than theminimum number of 6 points and findthe solution via a least squares fit.

Six parameters {pj } to find, butwe measure > 6 lengths {mi }

∑ +=j

ijiji epTmMinimise the (weighted?) sum of the squares:

∑i

iiew 2


Required distance uncertainties

• Express the six parameters h, roll, pitch and yaw in terms of a linear combination of the six distances s11 , s22 , s33 , s12 , s13 and s24

• Use to calculate the uncertainties in h, roll, pitch and yaw in terms of uncertainties in the measured distances

∑∑ =i

iii

ii XVaraXaVar )()( 2


Required distance uncertaintiesParameter Uncertainty Parameter Uncertainty

s11 7 μm hx 160 μm

s22 7 μm hy 160 μm

s33 50 μm hz 30 μm

s12 5 μm Roll 7 arc secs

s13 5 μm Pitch 4 arc secs

s24 5 μm Yaw 90 arc secs

We will need dimensional measurements to ~2 parts in 107 (5 μm over 25 m).


Optical design considerations

• Diffraction → minimum beam size• Dispersion caused by optical components• Effect of temperature on silica refractive

index (1.1 x 10-5 /°C) and laser beam pointing

• Need for an on-board frequency reference (at least ten times better than the 2 x 10-7

length uncertainty)


Verification & traceability

Test lasersystemand head

x10beamexpander

Referencelaser

Up to ~30 m

"Moving"carriage

"Fixed" carriage

Polarisingbeamsplitter

ABC

Aperture &/4 plateλ


HAALDM conclusions• Optical distance metrology based on fs

combs might be used for FF missions or flexible boom satellites such as IXO

• For IXO, the required angular and linear dimensional accuracies could be obtained by monitoring a set of (at least) six distances to ~2 parts in 107

• NPL could provide the absolute traceability for these measurements

Acknowledgement:

This work was funded by the European Space Agency

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