The Laser Interferometer Gravitational-Wave Observatory ...

file: /home/coyne/Presentations/IEEE/P950017_02_IEEE_paper.fm

LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY- LIGO -

CALIFORNIA INSTITUTE OF TECHNOLOGYMASSACHUSETTS INSTITUTE OF TECHNOLOGY

The Laser Interferometer Gravitational-Wave Observatory (LIGO) Project

Document Type LIGO-P950017-02 E- 6/24/96

Dennis Coyne

Amended version of a Publication in theProceedings of the IEEE 1996

Aeropsace Applications Conference4-9 February 1996, Snowmass, CO

California Institute of TechnologyLIGO Project - MS 51-33

Pasadena CA 91125Phone (818) 395-2129Fax (818) 304-9834

E-mail: [email protected]

Massachusetts Institute of TechnologyLIGO Project - MS 20B-145

Cambridge, MA 01239Phone (617) 253-4824Fax (617) 253-7014

E-mail: [email protected]

WWW: http://www.ligo.caltech.edu/

P950017-01-E IEEE Aerospace Applications Conference (amended version) 4-9 Feb 96

CHANGE RECORD

REVISION DATE PAGES AFFECTED ITEM(S) AFFECTED

0 12/26/95 Initial Publication --

1 6/13/96 pg. 10, Table 3 For the initial interferometer, the mirror masswas changed from 12 kg to 11 kg and the mir-ror diameter was changed from 0.28 m to 0.25m. The pendulum period was also changedfrom 1 sec to 0.744 sec.

pg. 13, Figure 7 Corrected the seismic curve (crossing suspen-sion thermal at ~40 Hz rather than ~100 Hz)

pg. 17(and ref. [27] on pg. 31)

Equation for “Residual Gas” phase noise cor-rected per reference [27b]

pg. 19 changed “over 140 km of welds” to “approxi-mately 100 km of welds (depending upon beamtube skelp width)”

pg. 20 changed “worlds’s largest high performancevacuum system” to “worlds’s largest ultra-high(<10-9 torr) vacuum system”

2 6/24/96 pg. 17 Equation for “Residual Gas” phase noise cor-rected (moved L out from under the squareroot).


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The Laser Interferometer Gravitational-Wave Observatory (LIGO) Project

Dennis C. CoyneCalifornia Institute of Technology

Physics, Math and Astronomy DepartmentLIGO Project, Mail Code 51-33

Pasadena, CA 91125818-395-2034

[email protected]

Abstract—Albert Einstein’s general theory ofrelativity (and all other relativistic theories ofgravity) predict Gravitational Waves (GW). Todate gravitational waves have not beenobserved directly (unambiguously). The emis-sion mechanisms and interaction phenomenafor gravitational waves are very different thanfor electromagnetic waves. Most GW sourceswill not be seen electromagnetically and con-versely, most electromagnetic sources will notbe seen by GW detectors. Astrophysicalsources of gravitational waves include coalesc-ing binary compact systems (neutron stars andblack holes), supernovae, rotating pulsars andthe stochastic background (as a result of thebig bang and the gravitational analog to thecosmic microwave background). The LaserInterferometer Gravitational Wave Observa-tory (LIGO), a National Science Foundationsponsored project being performed jointly bythe California Institute of Technology and theMassachusetts Institute of Technology, is oneof a new class of astronomical instrumentsdesigned to probe the universe by detectinggravitational waves. Signal characteristics andexpected event rates for these sources are dis-cussed. A brief history of interferometricgravitational wave detectors and reference toongoing and collaborative internationalprojects is also provided.

LIGO will consist of two widely separatedsites at which L-shaped vacuum systems, eachwith two 4 km long arms, will house interfer-

ometers for coincident detection of gravita-tional waves. The initial LIGO detectorconsists of 3 interferometers, two at one siteand one at the other. Each interferometer mea-sures the motion of freely suspended and seis-mically isolated masses induced by a GW.Correlations among the three interferometerswill be used to eliminate events due to terres-trial noise. The LIGO facilities are designed tobe extensible with the intent to add andupgrade interferometers in the future.

Each initial LIGO interferometer is fundamen-tally a Michelson interferometer with resonantcavities in each arm designed to detect differ-ential motion at acoustic frequencies (100 Hz -> 3 Khz) between its arms as small as 10-18 mrms. The basic strategy for detecting theminute GW effect is (i) use of a very longbaseline (4 km), (ii) high laser power (≥ 6 W atthe interferometer input and > 8 kW resonantin the arms), (iii) long effective arm lengths(with light storage times of about 1 ms), (iv)geographically isolated and seismically quietsites (Hanford, WA and Livingston, LA), (v)cascaded, multi-stage seismic isolation sys-tems and pendulum suspensions for the testmasses (~10-12 transmission of ground motionat 100 Hz) and (vi) massive, suspended, high-Q test masses (to reduce thermal noise contri-butions).

Partially transmitting mirrors in each arm formresonant (Fabry-Perot) cavities with the end


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mirrors in order to increase the effective armlength (and strain sensitivity) and increase thepower. The two optics which form the Fabry-Perot resonant cavities are the suspended“test” masses used to sense the gravitationalwaves. An incident GW will cause differentialchanges in the length of the two arms of theinterferometer; The difference in length willdepend on angle of incidence and polarizationof the wave. Length change is sensed by aphotodetector (operating at a dark fringe of theinterference field) from which the effect of apassing gravitational wave is inferred. A laserbeam is used as a single-frequency, single-mode light source. Its frequency is servo-locked to the average length of the arms of theinterferometer. The principles of operation ofthe initial LIGO detector system are discussed.

A sensitivity of ~5 x 10-19 m/ (~ 1 x 10-20/ strain) has been demonstrated in a 40 m

prototype detector at the California Institute ofTechnology over a measurement band of 250Hz to 1.5 kHz, which is close to the initialLIGO target displacement sensitivity curve(minimum sensitivity of ~1 x 10-19 m/ at ~200 Hz). For future advanced interferometers,achieving a sensitivity goal of 10-24/ straincorresponding to an optical phase shift sensi-tivity of 10-11 rad/ over a measurementband of 10 Hz to 10 kHz (which will yield highevent rates for coalescing binary gravitationalwave sources) will require a thorough under-standing of the limitations of detection due to anumber of noise sources, including seismic,thermal, shot, stray light, and gravity gradi-ents. The fundamental limiting noise sourcesare quantitatively described.

Key design implementation considerations forthe facilities and design aspects of the detectorsuch as high performance optical baffling, highreflectivity (1 ppm loss) and optically flat ( /600 rms) surfaces on high mechanical Q mir-ror substrates (Qs on the order of 107) are also

described. The future of gravitational wavedetectors and some concepts for advancedoptical detectors are briefly described.

TABLE OF CONTENTS

1. INTRODUCTION

2. BACKGROUND & HISTORY

3. ASTROPHYSICALINTEREST

4. PRINCIPLES OFOPERATION

5. LIMITS TO PERFORMANCE

6. IMPLEMENTATION/DESIGN

8. CONCLUSIONS

1. INTRODUCTION

The Laser Interferometer Gravitational WaveObservatory (LIGO), a National Science Foun-dation sponsored project being performedjointly by the California Institute of Technol-ogy and the Massachusetts Institute of Tech-nology, is one of a new class of astronomicalinstruments designed to probe the universe bydetecting gravitational waves [1]. Sources ofinterest include coalescing binary compactsystems (neutron stars and black holes), super-novae, rotating pulsars and the stochastic back-ground (as a result of the big bang and thegravitational analog to the cosmic microwavebackground).

LIGO comprises two remotely located obser-vatory sites (Figure 1) where the detector sys-tem(s) and all support facilities are located andalso includes laboratories, prototype interfer-ometer facilities, research and development,and design facilities at the associated Universi-ties.

The initial detector will consist of three inde-pendent laser interferometers operating incoincidence or correlation. Interferometerswill be built on two scales, two interferometerswill have arm lengths of 4 km and the thirdwill have arm lengths of 2 km. The lengths areconstrained by considerations of site topogra-

Hz

Hz

Hz

Hz

Hz

λ


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phy and associated costs of additional earthremoval. Each interferometer is in a Michelson("L") configuration with resonant Fabry-Perotcavities in the arms.

The two LIGO observatory sites selected are(i) at the DOE Hanford Nuclear Facility inWashington State (denoted "Hanford"), and(ii) in Livingston Parish, Louisiana (denoted"Livingston"). The Hanford site will housetwo instruments in the same vacuum envelope:a full length (4 km) and the half length (2 km)interferometer. The site at Livingston willcontain a single 4 km interferometer. The ver-tex of the Hanford instrument is at geographiccoordinates 46 27 18.5 N, 119 24

27.1 W, with arms oriented toward the north-

west at a bearing N36.8 W and the southwest

at a bearing S53.2 W. The vertex of the Liv-ingston Louisiana site is at geographic coordi-nates 30 33 46.0 N, 90 46 27.3 W,with arms oriented southeast at a bearingS18 E, and southwest at a bearing S72 W.The separation of the sites is 3030 km whichcorresponds to a maximum time-of-arrival dif-ference for gravitational waves at the two sitesof approximately +/- 10 ms (i.e. the separationdistance divided by the speed of a GW, which

must equal the speed of light if, as theory pre-dicts, the graviton has zero rest mass). Theinterferometer arms at the two sites are ori-ented for maximum coincidence sensitivity fora single gravitational wave polarization. Thisis achieved by having one arm of each interfer-ometer oriented at the same angle relative tothe great circle passing through the two inter-ferometer vertices. The two arms of eachinterferometer are perpendicular and lie veryclose to the local horizontal plane at the inter-section of the arms.

The data from the detector will be analyzed forburst, chirped, periodic signals as well as forstochastic background gravitational waves (i.e.the GW analog to the cosmic microwave back-ground radiation). Accurate and precise abso-lute timing shall be provided by the GlobalPositioning System (GPS). This will permitoperating with narrow coincidence gatesamong the interferometers and also permitscorrelation of LIGO data with other detectorsystems, such as resonant bar detectors, parti-cle (neutrino) detectors, and electromagnetic(γ-ray, x-ray, visible, infrared, and radio) astro-nomical observatories. The two sites havebeen chosen to be sufficiently separated so thatenvironmental perturbations to the interferom-

° ′ ″ ° ′″

°°

° ′ ″ ° ′ ″

° °

Figure 1: LIGO Sites

3030km(+/- 10ms)CIT

MIT


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eters are expected to be independent and henceuncorrelated. The gravitational waves signalswill be correlated and this property is used inmaking the observation. At both sites an envi-ronment monitoring system is used to measurethe environmental perturbation to the interfer-ometers to reduce the singles rate in a burstsearch, to measure the background perturba-tions that could influence a periodic and sto-chastic gravitational wave measurement, andas a diagnostic for interferometer develop-ment. In addition, all relevant interferometerand system parameters that can potentiallyaffect the noise budget shall be recorded forsubsequent diagnostic studies.

The operation of a half length and a full lengthinterferometer at one site serves several func-tions: it improves the rejection of accidentalcoincidences by imposing a triple coincidencefor a valid burst event, is a diagnostic for grav-itational waves by demanding that a true signalbe in the ratio of the interferometer lengths andfinally enables a broad-band search for a sto-chastic gravitational wave background limitedby the environmental correlations at a singlesite.

The LIGO detector has the capability of mak-ing a confident detection of gravitationalwaves alone. To obtain the maximum scientificreturn, LIGO is also planned to be operated asan element of an international network of grav-itational wave detectors involving other longbaseline interferometric detectors and acousticdetectors. Long baseline interferometricdetectors are expected to be in operation by theVIRGO Project at Pisa, Italy and the GEO600project at Hannover, Germany. Plans are alsounderway to establish long baseline interfero-metric detectors in Japan and Australia. A glo-bal network of detectors (Table 1) will be ableto provide full information from the gravita-tional waves, in particular, the wave polariza-tion and the source position on the sky.Simultaneous observations in several systems

also improves the confidence of a detection.Acoustic detectors that are expected to beoperating at the inception of the LIGO are in:Frascati, Italy; Baton Rouge, Louisiana; andPerth, Australia.

2. BACKGROUND & HISTORY

The idea to use optical (laser) beam detectorsfor GW detection was first suggested in 1956by Pirani at the Imperial College. Gertsensh-tein and Pustovit explicitly suggested use of anoptical interferometer for GW detection in1962. Then in the mid-1960s J. Weber inde-pendently discovered the idea but did not pub-lish or pursue it.

The concept was independently re-discoveredby R. Weiss at MIT in 1970. Weiss carried outdetailed design and feasibility studies in 1971-72. R. Forward of Hughes Corp. constructedthe first working prototype and achieved a

strain sensitivity of 2 x 10-16 .(Required strain levels are discussed in thenext section.) This work languished due tolack of further funding. In the mid-1970s, TheMach Planck Institute at Garching pursuedWeiss’ design (a Michelson interferometerwith arm delay lines).

Concurrently, R. Drever conceived of the ideaof an arm resonant (Fabry-Perot) cavity inter-

Table 1: International Gravitational WaveInterferometer Projects

Project Country NumberLength(km)

LIGO United States 21

4.02.0

VIRGO Italy & France 1 3.0

GEO600 Germany & Britain 1 0.6

TAMA Japan 1 0.3

AIGO Australia 1 1.0

1 Hz⁄


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ferometer (the LIGO baseline design) at Glas-cow University. In 1979, Drever moved toCaltech to pursue large-scale prototyperesearch and initiated the development of theLIGO 40 m prototype interferometer. In 1983,A. Brillet initiated an interferometer design atOrsay, France which eventually lead to the on-going VIRGO project, a joint French-Italianventure. In 1985 through 1989, a collaborationbetween Caltech and MIT, promoted by theNSF, developed the basis for the current LIGOproject. More detailed background and historyon GW detection can be found in references[2], [3], [4], [5] and [6].

3. ASTROPHYSICALINTEREST

The motivation for performing gravitationalwave astrophysical observation stems from thesignificant differences between electromag-netic waves and gravitational waves, the needfor experimental confirmation of the existenceof gravitational waves and the desire to exploreGW sources.

The observations carried out by the LIGO areexpected to provide fundamental and newinformation concerning the gravitational inter-action including:• direct measurement of strong field gravity

through the observation of the gravitationalwaves from black holes. The waves willconvey information about

- the normal modes of black holes- inertial frame dragging by rotatingblack holes

• through the observation of compact stellarsystems such as neutron star/neutron star,black hole/black hole and black hole/neu-tron star binaries provide detailed informa-tion of the relativistic equations of motion.

• the direct measurement of the polarizationstates of gravitational waves (possible inconjunction with other interferometricgravitational wave detectors).

• a direct measurement of the speed of prop-

agation of gravitational waves.

The astrophysical information derived fromLIGO observations includes:• the spatial and mass distribution of neutron

star binary systems in the universe.• the spatial and mass distribution of black

holes and black hole binary systems in theuniverse.

• a new and independent method of deter-mining the Hubble expansion using com-pact binary systems as standard objects.

• the equation of state of neutron stars fromthe gravitational waveforms at the finalcoalescence of neutron star binaries.

• the internal dynamics of asymmetric super-nova explosions.

• limits to or measurements of the gravita-tional multipole moments of pulsars.

• limits or observations of the gravitationalwave background from the earliest epochof cosmic evolution.

• a new view of the universe with a highprobability of uncovering phenomena notobserved by electromagnetic astronomy.

A propagating GW (a spacetime distortion)produces time-dependent body forces [7]. Theeffect upon a body at rest (if it could be mea-sured) is a cyclical elongation and contraction,as indicated in Figure 2. Unlike the electro-magnetic wave, the GW is a tensor wave.However, the time (t) dependent propagationin free space (coordinate vector, r) is just likean electromagnetic wave (with the exceptionthat there is negligible absorption, scattering ordispersion) and is given by:

where is the wave vector and denotes thedirection of propagation,ω is the temporal fre-quency and h is the GW induced strain, analo-gous to the electric field strength, E. Like E, hcan be decomposed into two orthogonal polar-izations, hx and h+.

h t r,( ) hei k r ωt–•( )

=

k


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Gravitational waves are the result of oscilla-tions of second and higher order multipolemoments of mass and mass “current”, whereaselectromagnetic waves are the result of oscilla-tions of first and higher order electric and mag-netic multipole moments. The dominant

moment for GW emission is the mass quadra-

pole, , where M is the source’s total

mass and r is the average lengthscale of itsdeviations from spherical symmetry. The con-tributions to the two polarizations of the GWdue to the quadrapole moment are:

hx ~ h+ ~

where h is the strain amplitude. For compactrelativistic sources, the second derivative ofthe quadrapole mass moment can be approxi-

mated by Mv2 (where v is the average internalvelocity of the source) which is equal to thekinetic energy associated with internal, non-

spherical motions of the source, .

Consequently, the amplitude of the oscillationsof the GW components, hx and h+, can beexpressed as:

where Msun is the solar mass and 10 megapar-

secs (Mpc), or 30 million light years, is thedistance to the Virgo cluster of galaxies (thenearest large cluster of galaxies to our ownMilky Way galaxy). The strongest astrophysi-cal sources are likely to have masses on theorder of our sun, or even a few factors of tenlarger, internal velocities between 0.1 c and cwhere c is the speed of light, and will belocated (at the closest) at roughly the distanceto the center of the Virgo cluster. Conse-quently, the strongest GW waves arriving atthe Earth will have upper limits to their ampli-

tudes h of ~ 10-20, and will likely be much

smaller (10-22 or so). However, “local”(within our own galaxy) cataclysmic eventsalthough exceedingly rare (visible supernovaein our own galaxy occur at a rate of 3-4/cen-tury and the actual rate is believed to be ~ 10times higher), will have much greater strength.It is estimated that the supernova in 1987would have produced a burst signal-to-noiseratio (SNR) of 100 in LIGO.

An example of the expected signals is the“chirped” signal produced by the inspiral of abinary neutron star system just before the twobodies coalesce (Figure 3). The strain ampli-tude induced by this type of source varies asfollows:

Figure 2: Passage of a GW (x and +polarizations) distorts spacetime and produces

time-dependent body-forces

λGW

M2 Mr2∼

G

c4r

-------

t2

2

d

d M2

Ekineticns

hGEkinetic

ns

c4r

----------------------

1020– Ekinetic

ns

Msunc2

----------------- 10Mpc

r-----------------

∼ ∼

Figure 3: “Chirped” Strain Signal Produced bya Binary Neutron Star Inspiral

0.5 0.6 0.7 0.8 0.9 1

-1

0

1

2

T (sec)

h(t)

x 1

021


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and the frequency varies as:

The total duration of an event which is detect-able by LIGO will be seconds.

The expectation of detectability of gravita-tional-wave sources by LIGO is based prima-rily upon the best understood (theoretically) ofcandidate sources, the final, minute-longinspiral of a neutron star binary. At LIGO’slowest detection frequency, the ~10 km sizedstars are ~100 km apart and not yet tidally dis-rupting each other, so that their wave emissionis well understood [8], [9], [10], [11]. Theuncertainty in the wave amplitude reflects theuncertainty regarding the distance to the near-est such sources. Best estimates, based onextrapolations of the statistics of neutron starsin our galaxy, give 200 Mpc (650 million lightyears) for the distance to which LIGO mustlook to see three neutron inspirals per year.Analysis of the uncertainties in this data givean “ultraconservative upper limit” of 1000Mpc and an “optimistic lower limit” of 23Mpc.

The performance of the interferometer is char-acterized by its strain sensitivity spectrum,

, or noise floor, in units of 1/ . Thesignal-to-noise-ratio (SNR) for measurementof a GW burst [1] (such as from an inspiralingblack hole binary) with an amplitude of hamp, acharacteristic (mean) frequency fc and duration

of n cycles, is:

where hc is referred to as the wave’s character-istic amplitude and hrms is the interferometer’sroot mean square (rms) noise for a one-cyclelong burst at the source’s characteristic fre-

quency.

A comparison of expected sources (hc) withthe expected performance (hrms) of initial andadvanced LIGO interferometers is given inFigure 4. The GWs sweep with time from lowfrequency to high frequency. As indicated inFigure 3, the amplitude of the GW increaseswith time. However, the number of cyclesspent near each frequency decreases fasterthan the amplitude. As a consequence, thecharacteristic amplitude (which determines thesignal-to-noise ratio) decreases slightly, asshown in Figure 4. (The vertical arrows alongthe bottom inspiral source curve mark theremaining time to collision and the distancesbetween the stars.)

The lower curve of each pair in Figure 4 is therms noise hrms in each 4 km interferometer fora one-cycle burst at the source’s characteristic(mean) frequency. The upper curve in eachpair is the sensitivity to bursts [1],

, i.e. the strength hc that a burst

must have — if it arrives only rarely, from arandom direction, with a random polarizationand at a random, unpredictable time — inorder to be highly confident that it is not due toGaussian noise. (If the neutron star collisioncan be independently observed, e.g. via agamma ray detector, then the waves can beidentified with confidence at , or a

factor of 3 below the upper curves in Figure 4.)Based upon the comparison in Figure 4, oneconcludes that the initial LIGO detectors mightbe capable of detecting 3 events/yr. at the opti-mistic level and advanced interferometers willbe capable of performing comparably at the“ultraconservative” level.

4. PRINCIPLES OFOPERATION

Each initial LIGO interferometer is fundamen-tally a Michelson interferometer designed todetect differential motion between its arms as

h tcoalescence t–( )14---–

∼

f tcoalescence t–( )38---–

∼

h̃ f( ) Hz

SNRhc

hrms----------

hamp n

f ch̃ f c( )------------------------= =

hSB 11hrms=

hc hSB 3⁄=


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small as 10-18 m rms. The basic strategy fordetecting the minute GW effect is:

(1) use of a very long baseline (4 km)(2) high laser power (≥ 6 W at the inter-ferometer input and > 8 kW resonant in thearms)(3) long effective arm lengths (with lightstorage times of about 1 ms)(4) isolated seismically quiet sites (Han-ford, WA and Livingston, LA)(5) cascaded, multi-stage seismic isola-

tion systems and pendulum suspensions forthe test masses (~10-12 transmission at 100Hz) and(6) massive, suspended, high-Q testmasses (to reduce thermal noise contribu-tions).

The measurement goal of 10-18 m rms (or 10-12

of a wavelength of visible light) requires aphase shift measurement of 10-9 rad rms (asshown in the next section). Since the phasemeasurement shot noise limit (also discussed

Figure 4: Comparison of LIGO sensitivities and Estimated Wave StrengthsExpected rms noise hrms in LIGO’s initial and advanced detector systems and the characteristic amplitude hc of

gravitational wave bursts from several hypothesized sources. (NS = neutron star, BH = black hole)

Advanced D

etector System

First D

etector System

1 10 100 1000 10000

10

10

10

10

10

10

10

10 -23

-22

-21

-20

-19

-18

-17

-16

frequency, Hz

h c

NS/NS inspiral

ultraconservative

200 Mpc

1000 Mpc

1 min 100 km 20 km 1 sec

NS/NS inspiral best estimate

30 Mpc

Nonaxsmtrc Supernova,

h SB

NS/Ns inspiral, 23 Mpc

upper limit , 200 Mpc

BH/BH inspiral NS/BH inspiral , 200 Mpc

300 Mpc

Nonaxsmtrc Supernova,

h SB

h rms

h rms


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in the next section) varies inversely with thesquare root of the number of photons in themeasurement “period” (0.01 sec for a 100 Hzlower measurement band frequency) 1018

photons are required in 0.01 sec. This corre-sponds to about 20 W of power (at 1.064microns). The amplitude of vibrationalmotion of the atoms in the mirrors exceedsthe GW signal but occurs at a frequency of

~1013 Hz, far above LIGO’s GW band (~3kHz). However, thermal excitation doesexcite the normal modes of the mirrors atfrequencies of ~ 20 kHz with amplitudes on

the order of 10-16 m. The interferometeraverages this effect over many periods and issensitive only to the changes of amplitude,which are made small by giving the mirrorshigh mechanical Qs.

Two methods are employed to increase thelight power used to sense the motion of thetest mass mirrors (and thereby decrease theeffect of shot noise). The first method is toincorporate resonant (Fabry-Perot) cavities

in the Michelson arms [12]. The second methodis to “recycle” the light from the bright fringeoutput port of the Michelson (i.e. light goingback from the interferometer toward the laser)by reflecting it back into the interferometer [12],[13]. This arrangement, called a power recy-cling interferometer, can result in an additionalgain of about 30 in power.

All the optical components in the phase sensitivepart of the interferometer are suspended as pen-dula to reduce the coupling to seismic and ther-mal noise and to provide a means to control theoptical path lengths in the interferometer. Ahighly stabilized laser beam is injected into thetwo arms of the interferometer via a beamsplitterand servo-locked to the average length of thearms of the interferometer. The path lengths aremaintained by servo systems to hold the lightincident on the detector, placed at the antisym-metric port of the beam splitter, at a dark fringe.

A GW incident normal to the plane of the inter-ferometer and appropriately polarized, disturbsthis condition by inducing an antisymmetric path

.

Figure 5: Basic Configuration

Input Mirror End MirrorRecycling

Mirror

Laser

Photodetector

End Mirror

L 2

l 1

l 2

L 1


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length change (L1 - L2 in Figure 5) in the twoorthogonal Fabry - Perot cavities therebyincreasing the intensity at the photodetector.When the interferometer is operated in thismanner, the light not absorbed or scattered bythe optical components is reflected by theinterferometer and returned to the laser at thesymmetric port of the beam splitter. In the ini-tial LIGO detector a mirror is placed betweenthe laser and the interferometer to enclose theentire interferometer into an optical cavity.

The position and reflectivity of this mirror ischosen so that the light from the laser is addedconstructively with that circulating in the inter-ferometer while the light reflected by the mir-ror back to the laser is combined destructivelywith the light transmitted by this mirror fromthe interferometer. The net result is that littlelight is returned to the laser and the opticalpower circulating in the interferometer isincreased by the reciprocal of the interferome-

Table 2: LIGO Interferometer Optical ParametersOPTICAL

CHARACTERISTICSNOMINAL INITIALINTERFEROMETER

SAMPLE ENHANCEDINTERFEROMETER

Arm Length 4000 m 4000 mLaser Type &Wavelength

Nd:YAG,λ = 1.064µm

Nd:YAG,λ =1.064µm

Input Power, P 6W 100WContrast Defect,1-c 3 x 10-4 3 x 10-4

Mirror Loss, LM 1 x 10-4 1.3 x 10-5

Power RecyclingGain 30 380

Arm Cavity Stor-age Time,τArm

8.8 x 10-4 s 1.3 x 10-3s

Cavity Input MirrorTransmission, T 3 x 10-2 2 x 10-2

Total System Loss,LT = (T+A

+Scattering)4 x 10-2 3 x 10-3

Table 3: LIGO Interferometer Mechanical Parameters

MECHANICALCHARACTERISTICS

NOMINAL INITIALINTERFEROMETER

SAMPLE ENHANCEDINTERFEROMETER

Mirror Mass, MM 11 kg 40 kgMirror Diameter, DM .25 m .40 m

Mirror Internal QM 1 x 106 3 x 107

Pendulum QP(damping mechanism) 1 x 107 (material) 1 x 108 (material)

Pendulum Period, TP 0.74 s (Single) 1 s (Double)Seismic Isolation

SystemT(100 Hz) = -100

dB T(10 Hz) = -100 dB

ter optical loss. The increase in sensitivity tolength changes is equivalent to using a morepowerful laser source.

Figure 5 shows a schematic of the initialinterferometer configuration. Tables 2 and 3present the design parameters of the pres-ently planned (initial) interferometers. Alsopresented in the tables are sample parametersfor contemplated enhanced interferometers.In later phases of the LIGO more radicalchanges in the interferometer configurationsare expected such as signal recycled, reso-nant and frequency agile systems leading toadvanced detectors.

A Michelson interferometer is chosen as thebasic topology since the sensitivity of its dif-ferential length measurement to the laser fre-quency stability can be made small. Phaseinstability of the laser results in displacementnoise in an interferometer with unequal pathlengths. An analysis [14] of the spectralpower distribution in the output of a Michel-son interferometer illuminated by a lightsource with a Gaussian temporal distributionof phase noise, indicates that the displace-ment squared per unit frequency in the inter-ferometer is given by [15]:

for the case and , whereτ is thedifference in light transit time between thetwo paths in the interferometer,λ is the laserwavelength andδ is the oscillating frequencywidth of the laser. The difference in lighttravel time,τ, can be made arbitrarily smallin the Michelson, so that excessive demandsare not made on the stability of the laser,δ.In a typical case,δ might be on the order of

10 Hz andτ approximately 10-9 sec, whichgives

∆x2

f( )f∆

-----------------43---λ2δ2τ3

=

fτ 1« δτ 1«

h∆x

L f∆--------------- 10

22–1 Hz⁄( )∼=


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The arms of the interferometer, and the finesse(“bounce” factor) of the Fabry-Perot cavitiescan be made as large as is consistent with thecondition that the storage time of the light isless than one-half the period of the gravita-tional wave that is to be detected.

The interferometer is held on a fixed fringe bya servo system which maintains the opticaldelay in both arms; the output signal of theservo system is proportional to the differentialstrain in the two arms induced by the gravita-tional wave.

In the basic optical topology of Figure 5, fourresonant conditions are required for operationcorresponding to four degrees of freedom:• differential motion of the cavities (the

gravitational wave signal, or L1-L2)• common mode motion of the cavities

(L1+L2)• differential motion of the Michelson arms

formed by reflection off of the near sides ofthe corner test mass mirrors (l1-l2)

• common mode motion of the Michelsonarms (l1+l2)

It is possible to replace one of these servo con-trolled lengths with feedback control of thelaser wavelength (frequency). The servo sys-

tem signals are derived from the photodetectorby synchronous detection at the modulationfrequency.

In order to mitigate the effects of laser ampli-tude fluctuations (above shot noise), a modula-tion scheme is employed to shift themeasurement to a higher frequency [15] (about10 MHz). The basic modulation carrier fre-quency of the beam is accomplished throughthe use of electro-optical phase modulatingcrystals (Pockel-effect phase shifters).

Several methods for phase detection usingmodulated light and several control topologies[16],[17] have been, and continue to be,explored for use on the full-scale LIGO sys-tem. The frequency-shifted subcarrierapproach [18] depicted in Figure 6, is a leadingcandidate for implementation in LIGO. Tosense the lengths, phase modulation is appliedto the input light. The laser single line fre-quency is the carrier frequency; All other fre-quencies are generated by impressingsidebands on the carrier. The frequenciesused, the sensed location and the degrees offreedom to which they are sensitive are listedin Table 4.

Length change measurement is accomplished

Figure 6: Modulation and Length Sensing/Control Servo-System Topology

PM PM

PM

MODE CLEANER

PRESTABILIZEDLASER (PSL)

ADDITIONALPOWERSTABILIZATION

F

f1

f2f3

RM

+

MichelsonCommonMode(recyclingcavity)

FP Cavity Common Mode

MichelsonDifferential Mode(recycling cavity)

+

GW Signal: FP CavityDifferential Mode(to FP cavity mirrors)

f1

f1

f2

f3

optionaldegree of freedom

AO

FP = FABRY-PERTOTPM = PHASE MODULATOR (POCKEL CELL)AO = ACOUSTO-OPTIC MODULATOR


page 12 of 31

via the reflection locking technique [19]. Max-imum sensitivity to a sensed degree of freedomis achieved when the sideband field is indepen-dent of the sensed degree of freedom, so that itacts as a constant reference for interferencewith the carrier. The carrier is selected to beresonant in a sensed cavity and the sidebandsare chosen to be sufficiently outside the cavityresonance, so that only the carrier is sensitiveto changes in cavity length.

The modulation frequencies in the frequency-shifted subcarrier approach are chosen so that:• all frequencies that propagate in the inter-

ferometer are resonant in the recyclingcavity for coupling efficiency (i.e. all fre-quencies except SCSB2);

• the carrier (C) and carrier-sideband (CSB)family is used for arm cavity (Fabry-Perot)length sensing, so C is resonant in theFabry-Perot cavities, while the CSB is not;

• the frequency-shifted, subcarrier (FSSC)and its first sideband (FSSB1) are used tosense the recycling cavity length, and areselected to be anti-resonant in the Fabry-Perot cavities to ensure insensitivity to arm

cavity length; and• the second set of sidebands on the fre-

quency-shifted subcarrier (FSSB2) do notcouple into the interferometer at all, sothey are chosen to have minimal overlapwith recycling cavity modes to ensure lowcoupling to the interferometer

Optimization of the interferometer configura-tion involves a detailed, coupled many-dimen-sional study including five mirror radii ofcurvature and mirror reflectivities, fourlengths, and three families of frequency modu-lated light and their relative frequency shifts.Selection of each of these parameters canimpact the choice of another parameter and, ingeneral these parameters are subject to con-straints (physical, technical or performancerelated). Studies and experiments to refine theLIGO configuration are on-going.

5. LIMITS TO PERFORMANCE

A thorough understanding of the limitations ofdetection due to a number of noise sources,including seismic, thermal, shot, stray light,and gravity gradients, is required. The funda-mental limiting noise sources are quantita-tively described below. First, however, thetransfer function of a Fabry-Perot interferome-ter is discussed. All cases in which strainamplitudes are given, are for the 4 km baselinesystem. The ensemble of all of the sources ofnoise are given in the spectral density plots inFigures 7 and 8 for the initial and the exampleenhanced interferometers, respectively. Thelimiting noise floor envelope is the root-sum-square (rss) of all effects.

Gravitational Wave Transfer Function

The differential time delay,∆t, in light transit-ing the two evacuated arms of a single-passMichelson interferometer corresponds to ameasurable optical phase shift:

Table 4: Signals sensitive to length degrees offreedom

INTERFERING FIELDS

SIGNALLOCATION

DEGREE OFFREEDOM

C and CSB anti-symmetricport

L1-L2, differentialarm cavity length

C and CSB reflected fromrecycling mirror

L1+L2, commonmode arm cavity

length

FSSC andSCSB1

anti-symmetricport

l1-l2, differentialmode Michelson

length

FSSC andSCSB2

reflected fromrecycling mirror

l1+l2, commonmode Michelson

length

CarrierC

SubcarrierFSSC

CSBCSB SCSB1 SCSB2 SCSB1SCSB2

∆φ ω∆t2πc∆t

λ--------------- 2π∆L

λ-------------- 2πhL

λ-------------= = = =


page 13 of 31

If the time light spends in the path (the cavitystorage time) exceeds the gravitational waveperiod (due to a high cavity finesse), signalstrength is reduced; this low pass filter behav-ior of the interferometer limits the high fre-quency sensitivity:

which is the transfer function from an opticalphase shift,φ, at the output (antisymmetricport) to the strain amplitude, h, of a gravita-tional wave which causes the phase shift (atlow frequency , f < c/(4πL) and for optimalsource direction and polarization). In theabove expression, the parameter B, the“bounce factor”, is the effective number ofbounces made by light in the resonant Fabry-

Perot cavities and is completely analogous tothe number of bounces in a delay line interfer-ometer. (B is also related to the finesse or Q ofthe cavity). The bounce factor can be shown tobe , where T is the power trans-mission of the cavity input mirror. From thetransfer function it is evident that there is apole at

whereτs is the cavity storage time. Given thesystem parameters in Table 2, the light storagetime (in the Fabry-Perot cavities) is ~ 1 ms, thecavity pole is ~ 80 Hz, and the light phase shift

associated with the measurement goal of 10-18

m is 10-9 rad/s at low frequency. The com-

h f( )φ f( )----------- λ

4πBL--------------

12πfBL

c----------------

2+≈

B 4 T⁄=

f f oc

2πBL-------------- 1

4πτs-----------=≡=

Figure 7: Initial Interferometer Sensitivity

Frequency (Hz)

SHOT

SE

ISM

IC

SUSPENSION THERM

AL

RADIATION PRESSURE

TEST MASS THERMAL

RESIDUAL GASS, 10 TORR H-62

INITIAL INTERFEROMETER SENSITIVITY

1 10 100 1000 1000010

10

10

10

h(f)

[ H

z

]-1

/2∼

-25

-23

-21

-19


page 14 of 31

plete transfer function including source angu-lar dependence and polarization can be foundin reference [20].

Photon Shot Noise

The detection is dominated by photon countingstatistics (shot noise) at high frequencies. Thespectral density of the optical phase amplituderesulting from the fluctuating detector current,on the assumption of Poisson statistics (appro-priate for light in the coherent state of a single-mode laser) at the antisymmetric port (the pho-todetector port shown in Figure 5) of the inter-ferometer is given by:

where η = detector quantum efficiency,ε =

optical efficiency of the entire optical train, P =laser power, Lopt = total optical loss, GR =broad-band recycling power gain < 1/Lopt (GR= 1 for no recycling),λ = optical wavelength,and h = Planck’s constant. Basically,

,

or for λ = 1.064

microns and P = 1.8 kW. Using the DC com-ponent of the (optical phase)/(GW strain)transfer function given above, the correspond-ing shot noise equivalent strain is found to be

using B = 50, appropriate for advanced inter-φsn f( ) 2hc

ληεP 1 Lopt–( )GR----------------------------------------------

1 2⁄=

φsn f( ) hcλP-------

1 2⁄∼

φsn f( ) 1011–

rad Hz⁄∼

hsn f f o«( ) φsn f f o«( ) λ2πBL--------------

≈

Figure 8: Advanced Interferometer Sensitivity

1 10 100 1000 10000Frequency (Hz)

10-25

10-23

10-21

10-19

RESIDUAL GAS, 10 TORR H -9

2

ADVANCED INTERFEROMETER, BROADBAND RECYCLINGS

EIS

MIC

SHOT

THERMAL

STANDARD QUANTUM LIMIT, 1000 kg

h(f)

[ H

z

]-1

/2∼


page 15 of 31

ferometers, .

An optical power of 6 W @λ = 1064 nm forthe initial interferometer will result in a shot

noise equivalent strain of .

The frequency dependence of the shot noisedue to the cavity pole, can be obtained byusing the (optical phase)/(GW strain) transferfunction above. For the case with no recycling(GR=1):

where a factor of 2 has been incorporated toaccount for recovery of phase informationfrom the RF modulation techniques used in apractical interferometer. When power recy-cling is included, assuming the optimum con-dition wherein all of the optical loss in thesystem is due to loss in the cavity mirrors, thenGR = 1/Lopt = L/(4Acτs) where A = averageloss per mirror, and

Shot noise is mitigated through the use of reso-nant cavities and power recycling. Furtherreduction in the shot noise component requiresincreased laser input power (technologydriven) and/or utilization of squeezed-statelight [21].

Thermal Noise

According to the fluctuation-dissipation theo-rem of statistical mechanics [22], any dampingmechanism in a physical system is accompa-nied with thermally-driven random fluctua-tions in the system’s modes of motion. Thedamping mechanism for the LIGO suspension

system is structural (material) damping associ-ated with the flexure of the suspension wires(principally at the attachment restraints) andthe internal “drum head” modes of the mirrors[23]. The brownian motion produced by thethermal noise has kT/2 kinetic energy perdegree of freedom with a resulting rms motion:

whereωo = natural frequency, k = Boltzmannconstant, T = temperature and M = effectivemass in the degree of freedom (mode) with fre-quencyωo.

The suspension wire resonances (“violinmodes”) are excited by the thermal noise[24]. While it is desirable to place these reso-nances outside of the LIGO observation band,other considerations constrain the design. Theneed to maximize the modal quality factors,Qs, so that the thermal noise floor away fromresonance is below the LIGO detection goals,suggests minimizing the diameter of the sus-pension wires. However, strength consider-ations provide a lower limit on the smallestpractical diameter (and correspondingly thelowest frequency to ~ 500 Hz). The structuraldamping associated with the wire resonances

results in Qs > 104. In addition, the recoil

term, Mwire/Mmirror = 10-4 attenuates the effec-tive strain amplitude of wire resonance noise.

Since the suspension wire modes are withinthe measurement band for LIGO, these modeshave to have very high Q (low damping) sothat their effect is limited to narrow regions infrequency and can be filtered out of the mea-surements in post-processing. Thermal noisein the suspension wires is mitigated throughproper design of the attachment points of thewires (where bending stresses and damping ishighest), minimizing the diameter of the wire(subject to stress limitations and the effect of“excess noise” discussed below).

hsn f f o«( ) 1024–

1 Hz⁄( )≈

h 1022–

1 Hz⁄( )≈

hsn f( ) f ohλ

ηεP 1 Lopt–( )c-------------------------------------

1 2⁄

1 f f o⁄( )2+[ ]

1 2⁄

=

hsn f( )f ocA

πL------------

1 2⁄ hλ

ηεP 1 Lopt–( )c-------------------------------------

1 2⁄

1 f f o⁄( )2+[ ]

1 2⁄

=

xrmskT

Mωo2

------------ 1 2⁄

=


page 16 of 31

Thermal noise also induces brownian motionin the last stage of the seismic isolation stack.The seismic isolation system has a low Q (~ 1- 3 by viscous damping) and a low first reso-nance (~ 1 Hz) by design (for seismic isolationreasons discussed below). This results in aresidual strain of

above the resonance. The 1/f2 dependence ofthe suspension thermal noise is a result of thependulum resonance.

The mirror (test mass) with the dimensionsgiven in Table 3 has a first internal resonanceof about 10 kHz. For a monolithic fused silica

mirror the Q has been measured as > 106 andthe damping mechanism has been shown to bestructural damping (i.e. frequency indepen-dent). The resulting equivalent strain is

below the resonance. The dependenceof the test mass thermal noise is due to thenature of structural damping (whereas viscousdamping has no frequency dependence belowthe resonance, as indicated in Figure 9).

“Excess” Noise

All materials under load will creep or flow.

Glass for example is essentially a very viscousfluid at room temperature and flows understress; this is why old glass windows arethicker on the bottom than the top. Static loadson metals, especially near the yield stress, willcause diffusion of dislocation boundaries.This process is not constant in time, but rathermanifests itself as discrete (non-Gaussian),statistical events. These strain relief jumps inthe suspension system can cause suddenmechanical shocks. Experience in the 40 mprototype system suggests that if the stress inthe suspension wires is less than 1/2 of the ulti-mate stress, this phenomenon is not observ-able. Concern about this effect in the wires foradvanced interferometers and in bolted assem-blies, where the bolts may undergo strainrelief, has prompted further on-going experi-mental study [25].

Seismic Noise

The design for seismic isolation in the initialinterferometer systems is a passive stack offour mechanical low pass, critically dampedfilters topped by a single pendulum. Eachstack acts as a second order system giving a 1/

f2 roll-off above the resonance:

where fs is the stack resonance frequency, fp isthe pendulum frequency and n is the number oflayers in the seismic isolation stack andδxambient(f) is the ambient base motion distur-bance spectrum. For the parameters of the ini-tial interferometer,

based upon a conservative estimate of seismicdisturbances at the selected sites.

Gravity Gradients

Atmospheric motion, ocean tides and earthmicro-seismic motion (earth “tides”) represent

Figure 9: A comparison of viscous andstructural damping

hst f( ) 1025– 2000

f------------

21 Hz⁄( )∼

htmt f( ) 1024– 10000

f---------------

1 2⁄1 Hz⁄( )∼

1 f⁄

f/f0

1

0.1

0.01

0.001

0.0001

0.00001

X[f]

m/S

qrt[H

z]

0.001 0.01 0.1 1 100.0001

x ω[ ] ω∼ 0

x ω[ ] ω∼ 1– 2⁄

x ω[ ] ω∼ 5– 2⁄

x ω[ ] ω∼ 2–

VISCOUS

STRUCTURAL

hs f( )δxambient f( )

L-------------------------------

f s

f-----

2n f p

f------

2

1 Hz⁄( )=

hs f( ) 1025– 90

f------

121 Hz⁄( )=


page 17 of 31

low frequency sources of noise which are notattenuated by the seismic isolation system. Asthe isolation systems improve beyond the ini-tial passive design, these noise sources willrepresent a practical (though not fundamental)low frequency limitation to gravitational wavemeasurement. Based upon measurements, thefollowing is the expected frequency variationin this noise term:

Although the initial interferometer is not sensi-tive to the gravity gradient due to the motion ofa person walking in proximity of a test mass,advanced interferometers are projected to besensitive to this noise source to a distance of10 m [26].

Residual Gas

The mechanical effects of an intervening gas,such as acoustic coupling to the environmentand damping of the suspensions, are mitigatedto a negligible level in LIGO by operating at a

pressure of 10-6 torr. However, fluctuations inthe forward scattering of laser light by residualgas particles is a potentially more serious noisesource. The scattered field of individual gasmolecules causes pulses in the photodetectoras the molecules pass through the interferome-ter beam. The equivalent gravitational strainnoise derived from the average power spec-trum of the pulses produced by the moleculesresiding in the beam is [27]:

where L is the arm length (beam path length),α is the polarizability of the residual gas mole-cule at the optical frequencyν, ρn is the aver-age number density of the molecules, vo is theaverage thermal velocity of the molecule andw(z) is the beam’s Gaussian radius as a func-tion of the coordinate along the beam axis, z.

The noise due to residual gas is nearly inde-pendent of frequency within the LIGO mea-surement band and hydrogen is the dominantcontributing gas species. This gas scatteringmodel has been confirmed by experiment [28]for dependencies with respect to pressure(number density), molecular polarizabilityand molecular mass (i.e. the thermal velocityof the molecule at a given temperature).

Standard Quantum Limit

Light reflecting from the test masses impartsforces due to its momentum. Fluctuations inthe amplitude of the laser thus cause randomforces on the optics. The forces due to inten-sity fluctuations are symmetric between thetwo arms so that the effect cancels except forunintentional mechanical and optical asymme-tries.

In addition to these symmetric radiation pres-sure fluctuations, there are uncorrelated pres-sure fluctuations between the arms [29].Quantum electrodynamic vacuum fluctuationsthat enter the interferometer through the darkside of the beam splitter, superimposed withthe main beam’s electromagnetic field, are onesource of the “standard quantum limit” for thegravitational-wave detector and are a macro-scopic example of the “Heisenberg micro-scope”. Since the fluctuating radiationpressure is proportional to the correlated prod-uct of the vacuum field and the laser field, itvaries as the square root of the laser power andfluctuates on time scales of the cavity storagetime, a characteristic time for the vacuum elec-tric-field fluctuations to change phase byπ rel-ative to the laser field. There is an optimumlaser power since the radiation pressure noisevaries directly as the laser power and the sens-ing noise varies inversely with the laser power.The net pressure and sensing noise at the opti-mized laser power can be shown to be [29]:

hgg f( ) 1025– 12

f------

41 Hz⁄( )∼

hrg f( ) 4παL

----------2ρn

vo---------

e

2πfw z( )–vo

-----------------------

w z( )-------------------- zd

0

L

∫

12---

=

h f( )QL 4 π⁄ hm----

1 2⁄ 12πfL------------

1 Hz⁄( )=


page 18 of 31

The quantum noise is not a factor in the initialinterferometer designs but does set a funda-mental limit to the technique and is one of thesources of noise that argues for a long armlength.

6. IMPLEMENTATION/DESIGN

In the following subsections, the facilities, vac-uum system, and detector system design andstatus as well as supporting research anddevelopment activities are discussed.

Facilities

Each site will consist of a large corner stationbuilding complex, which includes a building tohouse the lasers and vertex interferometeroptics and vacuum equipment (the Laser andVacuum Equipment Area or LVEA) and anOperations and Support Building (OSB) tohouse the control rooms, supporting labs andoffices (Figure 10). Each site will also have

two end station buildings which house a Vac-uum Equipment Area (VEA) for the optics andvacuum equipment associated with the endmasses of the two arms, as well as supportinglabs and preparation areas. At the Hanfordsite, there will also be mid-station buildings oneach arm to house the VEAs for the 2 km longinterferometer; At the Livingston site the mid-stations will be small and simple shelters tohouse some vacuum valves and pumps. TheLVEA and VEAs are large and clean labora-tory spaces (clean room construction practices,high bay with 15m hook height) with materialhandling systems.

The vacuum enclosure between the corner,mid- and end-stations is accomplished with awelded stainless steel beam tube. Since thesteel tube is thin walled and vulnerable, it ishoused in an enclosure which permits mannedaccess. The Beam Tube Enclosure (Figure 11)is built up from 3.0 m long cast concrete sec-

Figure 10: Corner Station Site LayoutThe beam tube enclosure arms extend beyond the drawing in the upper left and right corners to the mid-station at 2

km distance and the end-station at 4 km. The X-shaped building at the vertex of the two beam tube arms is the Laserand Vacuum Equipment Area (LVEA) (~ 90 m long). The lower building in front of the LVEA is the Operations

Support Building where the control room, data storage and support laboratories are housed.


page 19 of 31

tions with an semi-elliptical cross-section hav-ing a height of 2.7 m and a width of 4.0 m. Inaddition to providing the beam tube protectionfrom the elements and stray bullets from hunt-ers, it affords some degree of passive tempera-ture control by blocking direct view of the sunand providing a significant thermal mass tomitigate temperature excursions.

Key design implementation considerations forthe facilities are:• selection of a seismically quiet site• design of the building infrastructure to

minimize vibration and acoustic noisethrough careful design of the foundationslab and the design and location of heating,ventilation and air-conditioning equipment

• proper grounding and shielding and isola-tion of EM noise sources

Both sites have been cleared and the Hanfordsite has been graded along the extent of the 4km arms and is awaiting settlement beforeconstruction activities commence. Final grad-ing of the Livingston site is currently under-way. The final design of the BTE has beenaccomplished and the process for selecting aconstruction contractor is underway. Thebuilding design has just passed the preliminarydesign review milestone, with an April 1996completion of the final design expected.Ground breaking for the construction activitiesis planned for July 1996.

Beam Tubes

The LIGO beam tubes are fabricated by thesame method used to make oil pipelines. Thetube is fabricated from rolled sheet stock byhelically winding and welding it with amachine designed expressly for this opera-tion. The characteristics of the beam tubes are:• module lengths of 2 km• tube diameter of 1.22m (1 m clear aperture

after baffling)• internally baffled to reduce scattered light

phase noise

• very low allowable air leakage rate (< 10-9

atm cc/s, He)• very low outgassing rates:

- the pressure for advanced interferometer

applications < 10-9 torr (All residualspecies)

- the outgassing rate for H2 must be

< 10-13 torr-liters/cm2/s- the outgassing rate for H2O must be

< 10-15 torr-liters/cm2/s- partial pressures for CO + CO2 +

H2NCN + higher order hydrocarbons,must be even lower

Since there will be approximately 100 km ofwelds (depending upon beam tube skelpwidth), quality control and cleanliness must bepursued diligently throughout the fabricationand integration process in order to insure lowleak rates, long lifetime and no virtual leaks.

A prototype fabrication effort has been suc-cessfully concluded with a qualification testwhich demonstrated successful cleaning pro-

cedures, leak testing procedure (< 10-11 atmcc/s), and bakeout procedures. The productioneffort for 16 km of beam tube is about to com-mence.

Concurrently, research into baffling materialoptical properties and mechanical design iscontinuing. The baffles are expandable, trun-cated conical fustrums which are friction fitted

Figure 11: Cut-away view of the Beam Tube inthe Beam Tube Enclosure


page 20 of 31

into the inner diameter of the beam tube atapproximately 300 locations per beam tubearm. The interior edge of the baffle is serratedin a random sawtooth profile in order to mini-mize diffraction effects. The surface whichfaces the test masses is coated with a materialwhich is absorptive at the laser wavelength;The most promising candidate to date is a“black glass” coating which is fired onto thestainless steel substrate. This material is usedin the household oven market and provides anaffordable, durable and highly absorptive andspecular surface. Tests to confirm its vacuumcompatibility are underway.

Vacuum System

The LIGO Vacuum System (Vacuum Equip-ment + Beam Tubes) provides:• A clear aperture for the interferometers• Very large aperture gate valves to isolate

1.22 m beam tubes• A clean environment for the precision

optics• Chambers with easy access for installation

and maintenance, repair and upgrades tothe optics

• A low pressure in order to minimize dif-

fraction and acoustic coupling• Extensive controls and monitoring equip-

ment to ensure safe and efficient operation• High pumping speeds and large volumes

— beam tube pumping is accomplishedfrom the 4 km ends

The LIGO Vacuum System will be the world’s

largest ultra-high (< 10-9 torr) vacuum system

with a pumped volume of roughly 20,000 m3.The large chambers which house the optics(depicted in Figure 12) are unique to LIGOand have been designed with maximum portaccess for external viewing and alignment sys-tems as well as large ports for easy installation.A preliminary design review of the vacuumequipment was successfully concludedrecently and final design efforts are wellunderway

Detector

The baseline detector systems employs tech-niques proven on the 40m and 5m prototypesystems at Caltech and MIT respectively.R&D experiments on optical recombinationand power recycling are being performed togain insight and confidence in the technicalapproaches to be used on the LIGO system.

.

Figure 12: Vacuum equipment layout in the Hanford corner station


page 21 of 31

The long history of prototype developmentand incremental reduction in, andimproved understanding of, the noise floorand the required precision engineeringenables the team to implement the LIGOsystem with low risk and transition from anR&D system to a “turnkey operation”required of an observatory.

Core Optics — Collaborative studies withindustry and on mirror polishing, coatingand metrology have been initiated. LIGOrequirements are for high reflectivity (1ppm loss) and optically flat ( /600 rms)surfaces over the central 15 cm diameter ofoptics as large as 25 to 30 cm in diameterand up to 10 cm thick (~ 25 kg). Therequired reflectivity has been achieved inpreliminary tests with a 34 layer dielectriccoating.

Polishing manufacturers report the capabil-ity to polish toλ/800 rms ( @λ=633 nm)using conventional pitch polishing as wellas teflon lap polishing. Since these levelsare pushing the limits of metrology, anindependent effort in establishing the per-formance of as-built optics has been initi-ated with the National I1nstitute ofStandards and Technology (NIST).

Seismic Isolation System — The baselineapproach for seismic isolation [30] is afour stage, passive, cascaded mechanicalfilter (Figure 13). In the prototype systemsbuilt and tested at MIT and employed inthe 40 m prototype at Caltech, each stage iscomprised of a monolithic stainless steelblock (with a high first vibration fre-quency). Between each layer are an arrayof elastomeric spring dampers (Figures 13and 14). The springs have been fabricatedfrom a flurocarbon elastomer (Viton). Thevisco-elastic behavior of the spring ele-ments are exploited to provide high damp-ing of the stack normal modes (Q ~ 3)

λ

while also yielding a rapid rolloff of the stacktransmission above the stack modes. Comparisonsbetween experiment and 3D finite element modelsare been used to gain an understanding and model-ing capability to enable scaling the concept for thefull scale LIGO system.

Figure 13: Passive Isolation Concept.

Figure 14: Prototype isolation stackA single circular tale is supported through springs by three

isolating legs of three mass-spring layers each. Overallheight of 68 cm and the width of 78 cm for the prototype

system.

Frequency (rad/sec)

1 Layer Stack

ω-21

10

10-1

10 -2

X1XG

ω 2o

10 100Frequency (hz)

4 Layer Stack

-1

-2

-3

-4

1

10

10

10

10

10

10-5

X1

XG f -8

Simple Model of Mark 2 Stack Isolation (vertical)

X G

X1

M

M

M

M

K

M

GX

X 1

C

ElastomericSprings

compact masselement

BASE

TOP PLATE


page 22 of 31

Tests of the degradation of the reflectivity ofmirrors exposed to the elastomer indicate < 0.3ppm/week (at the 95% confidence level) [31].While this result is close to LIGO anticipatedrequirements, improvements in the designwhich would eliminate exposure of the opticsfrom outgassing of the elastomer are beingsought. One approach under investigation is touse a metallic spring with constrained-layerdamping, such that the elastomer is sealedfrom exposure to the vacuum. Active vibrationisolation techniques have also been explored[32] and are likely candidates for advancedinterferometers.

Suspension System — Further attenuation ofthe base motion vibration is afforded by thependulum suspension of the test mass (Figure15). The test mass is suspended from a controlblock by a loop of wire sized so that it is

loaded to ~ 1/2 its breaking strength (75micron-diameter steel music wire is used in the40 m prototype). The magnetic/coil actuatorson the control block are used to damp angularmotion of the suspended test mass, on the basisof optical lever system measurements. Longi-tudinal motion, sensed by an edge detector, isdamped by a piezoelectric actuator. The largeforces required for lock acquisition (and inter-ferometer response calibration) are achievedwith magnets attached directly to the testmasses and nearby coils. A photograph of thetest mass suspension used in the 40 m proto-type interferometer, mounted on a seismic iso-lation stack in a vacuum chamber, is shown inFigure 16.

The suspension system for LIGO is designedto handle a variety of optics including the testmasses, beamsplitters and mode cleaner mir-

Figure 16:Photograph of a test mass suspension, mounted on a vibration isolation stack, inside the 40 m prototype

interferometer vacuum system


page 23 of 31

rors, ranging in size from 7.5 cm diameter to~25 cm diameter and 0.2 kg to ~ 25 kg. Thelongitudinal motion dynamic range require-

ments vary from ~ 10-5 m peak-to-peak (pp) at

0.1 Hz to ~ 10-16 m pp at 1 kHz in operation

(and to ~ 10-11 m pp at 1 kHz during lockacquisition). The experience gained with the40 m interferometer is essential to achievingthe design requirements of the suspension sys-tem. A number of improvements have beenincorporated into the design for the full scalesystem, such as a single wire-loop suspension,angular and length control through a commonset of magnet/coil actuators resulting in a lesscomplicated transfer function.

Control and Data System (CDS) — The LIGOCDS system is an advanced control and datasystem using state-of-the-art network architec-ture and hardware components. The CDS pro-vides (Figure 17):• Operator consoles in the control room of

the Operations Support Building designedto have multiple heads and to be inter-changeable,

• Local/portable consoles for use in eachbuilding

• a Rapid Array of Inexpensive Disks(RAID) used for storage of system parame-ters and data

Figure 15:Schematic of a suspended test mass and itscontrol hardware ( 40m interferometer design)

PZT

COILMAGNET &

EDGESENSOR

OPTICAL LEVER

MAGNET

COIL&

Figure 17: Control and Data System Block Diagram

Op. Console Analysis

Cus

tom

Mod

ules

RAID

19 mmTape

InterferometerDevice

Cntrl & MonCrate

Cus

tom

Mod

ules

OtherDevice

Gateway

OutsideWorld

CDS Networks

DAQCrate

Cntrl & MonCrate


page 24 of 31

• tape units for storage of archived data fromthe data acquisition system

• analysis stations to be used for preliminaryon-site data-analysis and possibly filteringand generation of triggers

• high speed, fiber-based networks for dataacquisition and lower speed for executivecontrol and monitoring

• Control and Monitoring standard VMEcrates with custom analog modules forlocal servo-control

• Data Acquisition (DAQ) Crates: standardVME crates with processors, waveformdigitizers, timing generation and commu-nications modules

Sample rates for the DAQ system range from <1 sample/sec to ~ 20 K samples/sec (the GWsignal rate). The current data rate estimate is6 Mbytes/sec per interferometer.

In addition to control and monitoring of thebasic interferometer detector, the CDS handlescontrol and monitoring of the vacuum equip-ment, remote diagnostics and physics/environ-mental monitoring (PEM). The PEM data isused for veto of erroneous GW events.

Prestabilized Laser System (PSL) — The PSLprovides a single-mode, single-frequencybeam > 4 W to the input optics subsystem.The prototype PSL servo-control system hasachieved the following stability parameters foran argon-ion laser (λ=514 nm):

• frequency stabilization∆f/f ~ 10-15/

or <1 Hz/ @ 100 Hz (achieved with a

gain of 105)• intensity (amplitude) fluctuations∆P/P ~

10-7 1/ (achieved with a gain of 103)

• beam angular jitter to < 200µrad/ @100 Hz

• polarization fluctuations in the beam to <

10-6 1/ @ 100 HzThe PSL is built around a commercially avail-

able Ar+ plasma tube laser which has beenextensively modified for stability control.(The PSL is in the process of being redesignedfor use with a Nd:YAG laser (λ=1064 nm) as aconsequence of a recent decision to switch to asolid state laser.)

A block diagram of the PSL system is given in

Hz

Hz

Hz

Hz

Hz

Figure 18: Prestabilized Laser System

Ar+ Laser

IntensityServo

PCPC

10.7MHz

AOM

ToIOO

C

light beam electrical signal

FromIOO

C

Reference

RF Mixer

PZT actuated mirror

PS

PCPC

Photodiode

FI

Cavity

Frequency Servo

PC: Pockels CellAOM: Acousto Optical Modulator

C: Optical CirculatorPS: Phase Shifter

FI: Faraday Isolator


page 25 of 31

Figure 18. Amplitude (intensity) control isaccomplished with an acousto-optic modulatorbased on feedback from sensing of the lighttransmitted through the mode cleaner. Phasenoise is controlled by phase shift control of aPockel cell modulator, where the servo-controlsignal is derived from demodulation of the out-put of a photodetector positioned to look at thereflected light from the reference cavity (i.e. a“reflection locking” technique). This reflec-tion locking signal is also used to slave thelaser cavity to the reference cavity by PZTactuation of the cavity mirrors.

The PSL frequency and intensity servo-con-trols are operational under computer control ina manner identical to what is intended forLIGO. The PSL control interface has beendeveloped with a software system, calledEPICS, developed by Los Alamos NationalLabs explicitly for control of large, complexinstrumentation. The system performs controlof the laser, the servo-controls, data monitor-ing and archival and alarm handling. Testingof the PSL prototype for noise performance,availability and environmental sensitivity(seismic noise, acoustic noise and temperaturevariations) is underway.

Alignment Sensing and Control (ASC) — TheASC subsystem provides both initial align-

ment and operational alignment of the LIGOinterferometer optical elements. The initialalignment is required to take the interferometerfrom an arbitrary misaligned state to a condi-tion where the operational length and align-ment systems are functional. The initialalignment will utilize optical referencing fromGPS-located monuments.

Automatic maintenance of alignment duringoperation as currently conceived involves threeprincipal subsystems:• An optical level system (Figure 19) will be

used to maintain angular alignment overshort time periods (10-100 sec) throughclosed loop servo-control. (The time limi-tation reflects the time scale for dimen-sional stability of the common isolatedfoundation.) The optical lever has success-fully employed in the 40 m prototype sys-tem.

• A centering system to minimize cross-coupling of angular noise to length noise.

• A wavefront sensor for use in determiningthe optimal alignment with an update rateof about 10 sec. The phase front sensorsare quadrant photodiode detectors withholes in the center. The alignment signals(proportional to the amplitude of the lightnot in the TEM00 mode) are derived from

Figure 19: Three-point optical lever

5-50 m

AUXILIARY LASER

FIDUCIAL SENSOR

LASER DRIFT CORRECTION

MIRROR ALIGNMENT CONTROL

MIRROR

MAIN LASER BEAM


page 26 of 31

the differences between opposite quadrantsof the photodiodes [18].

Length Sensing and Control (LSC) — TheLSC system performs the measurement andcontrol of the arm cavity lengths and the recy-cling cavity lengths (i.e., the 4 key lengths ofthe interferometer). The LSC must firstacquire lock (resonance) of the cavities beforetransitioning to an operational mode. The con-trol for lock acquisition is highly nonlinear[33] whereas the operations mode is in a smallsignal, linear control regime.

Research & Development

Current LIGO R&D effort is dominated bysupport to the design and development of theinitial detector system. Future efforts will beaimed at enhancements to the initial detec-tors. The R&D efforts are predominantly

related to three interferometer systems:• the 40 m interferometer: presently being

used for length control in operation andduring acquisition (nonlinear regime)

• the Phase Noise Interferometer (PNI): a 5m long interferometer used for phase noisestudies and development of photodetector/demodulation systems, and

• the Fixed Mass Interferometer (FMI), atestbed for length control configurationtests and alignment control studies basedon wavefront sensing

40 m Prototype — The 40m Interferometer(Figure 20) was recently reconfigured toinclude optical recombination (previously thesignals from the two arms were combinedelectronically) and a revised modulation andcontrol system in order to be more representa-tive of the full scale system and to test modelsfor the dynamics of length control. In the near

Figure 20: 40-m Interferometer


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future a recycling mirror will be added to com-plete the reconfiguration. The present 40 mconfiguration is shown schematically in Figure21. The two arms are 40 meter long Fabry-Perot cavities formed by mirrors suspendedwith a 1 Hz pendulum frequency from vibra-tion isolated platforms. Light from an Argonion laser operating at 514.5 nm, capable ofproducing a single mode output power up to 5W, strikes a beamsplitter illuminating bothcavities. The laser is locked in frequency to anoptical resonance of the first arm using areflection-locking technique [19]. The secondarm is held in resonance with the laser light bya servo-system which exerts forces on the endtest mass using a magnetic drive. Differentialforces on the test masses, such those producedby a gravitational wave, are sensed by record-ing the feedback force needed to keep the sec-ond arm on resonance.

The 40 m interferometer has been under devel-

test mass mirrors are a monolithic construc-tion, with the coating applied directly to thesubstrate. The measured Qs of the new test

masses range from 4.0 x 104 to 8.1 x 106, giv-ing a predicted improvement of nearly an orderof magnitude in the thermal noise contributionto the spectrum.

The new test masses also have reduced opticallosses compared with the older mirrors, result-ing in higher stored power and a reduced shotnoise component to the spectrum. The inter-ferometer is shot noise limited at frequenciesabove 1 kHz.

A comparison of the measured sensitivity ofthe 40 m interferometer with predicted perfor-mance is shown in Figure 23. The seismicnoise prediction is an empirically based pre-diction using measured base motion spectrumand the transfer function from floor motion tointerferometer output. The thermal noise pre-

Figure 21: 40 Meter Prototype Configuration

D2

DATARECORDING

AND READOUT

rf

CalibrationForce

TM

D1rfLA

SE

R P

RE

ST

AB

ILIZ

AT

ION

SY

ST

EM

TM

VacuumEnvelope

TM

TM

Key to Symbols

Pockels Cell

Faraday Isolator

Optical Circulator

Test Mass

Fixed Mirror

TM

Photodiode

Beam Splitter

Electrical Signal

Optical Signal

Amplifier

rf Mixer

rf Modulation

Gai

nω

Gai

n

ω

~

~

opment since 1982 [34], [35]. Therecent evolution of its noise spectrumas the interferometer has beenimproved is shown in Figure 22. Theimproved performance of the systemover time is the result of controllingmeasurement and control noise andincreasing the optical power deliv-ered to the cavities. The largestimprovement in the displacementsensitivity achieved to date was theresult of redesigning the seismic iso-lation stacks to give ~ 2 orders ofmagnitude lower transmission at 100Hz. At frequencies between 500 Hzand 1000 Hz, the initial (Mark I)interferometer was limited by mirrorsurface fluctuations due to thermalnoise in the test masses. The Qs ofthese mirrors (800 to 54,000) weremuch lower than expected, probablyas a consequence of bonding mirrorsto the fused silica substrate; the new


page 28 of 31

diction is theoretical, based upon measuredfrequencies and Qs for various modes. Thetheoretical shot noise curve has been con-firmed experimentally to within ~ 20%. The“line” features, or spikes, in the spectrum areeither due to wire resonances (marked “W” inFigure 23), suspension mechanical resonances(marked “S”) which will be eliminated in aplanned upgrade of the suspension system, andpowerline frequency harmonics. The disagree-ment between theory and experiment between100 Hz and 500 Hz is of unknown origin and iscurrently under investigation. The noise spec-trum of Figures 22 and 23 is the best achievedto date with the 40-m interferometer and corre-sponds to a best displacement sensitivity of 2.5

x 10-19 m/ near 450 Hz.

Phase Noise Interferometer— The intent ofthe PNI program is to demonstrate LIGO’s

required a phase sensitivity < 10-10 rad/ ,by achieving a circulating power level of 70W,approximately the same level as required in theinitial LIGO interferometer. The system willinitially be in a non-recycled Michelson con-figuration (Figure 24) with 1 W of opticalpower, then recycling will be added to increasethe power to 15 W, and finally a mode cleanerwill boost power to 70 W. The PNI will alsobe used to investigate scattered light control.The PNI system (including an active vibration

Hz

Hz

.

Figure 22: Progressive improvement in the displacement sensitivity of the 40-m interferometer

100 1000Frequency (Hz)

10-20

10-20

10-19

10-19

10-18

10-18

10-17

10-17

10-16

10-16

10-15

10-15

10-14

10-14

10-13

10-13

10-12

10-12

x (m

/Hz1/

2)

x (m/H

z1/2)

Mark I, 10/90

Mark I, 6/92

Mark II10/94

Initial LIGO Target


page 29 of 31

isolation system) has been integrated at MIT

and has achieved 8 x 10-9 rad/ to date inthe Michelson configuration. A recycling mir-ror will be added to the system soon.

Fixed Mass Interferometer— The FMI isbeing set up to perform initial tests of the fre-quency-shifted, subcarrier length sensing con-figuration. It will also be the testbed used fordevelopment of the wavefront sensor used forautomatic, optimal alignment of the interfer-ometer once lock has been achieved.

7. CONCLUSIONS

The LIGO project is intended to open the fieldof gravitational wave astrophysics by first pro-viding experimental verification of gravita-

tional waves and then operating as a long term,extensible and adaptable observatory. Thedetection technique is to measure the strainsinduced in space by gravitational waves usinglaser interferometry between nearly freemasses. The project is designed to permitphased incorporation, at later dates, ofimprovements in the technology of laser gravi-tational wave detection to further improve theinstrumental sensitivity and bandwidth. TheLIGO will be part of an international networkof long baseline interferometric detectors toestablish the polarization of the waves and thelocation of the astrophysical sources.

8. ACKNOWLEDGMENTS

I would like to acknowledge my colleagues on

Hz

Figure 23: Displacement Sensitivity of the 40 Meter Prototype Interferometer

100 1000Frequency (Hz)

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

x (m

/Hz1/

2)

data(oct28-hr.dat, 28 Oct 94)

internal thermal noise

shot + thermal noise

seismicnoise estimate

standard quantum limit

Frequency (Hz)10-19

10-18

10-17

10-16

x (m

/Hz1/

2)

SS

W

WW

W


page 30 of 31

the LIGO project, whose work has beenreported here and who have been a source ofencouragement and stimulation. I would alsolike to acknowledge the support of theNational Science Foundation for LIGO, undercooperative agreement PHY-9210038.

9. REFERENCES ANDNOTES

[1] A. Abramovici, W. Althouse, R. Drever, Y. Gur-sel, S. Kawamura, F. Raab, D. Shoemaker, L. Seivers, R.Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M.Zuker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory”,Science, v256, 325-333, April1992.

[2] Misner, Thorne, Wheeler,Gravitation, N.Y.:W.H. Freeman & Co., 1973

[3] B.F. Schutz, A First Course in General Relativity,Cambridge: Cambridge University Press, 1986

[4] Hawking & Israel, Ed.,300 Years of Gravita-tion, Cambridge: Cambridge University Press, 1990

[5] P.R. Saulson,Fundamentals of InterferometricGravitational Wave Detectors, New Jersey: World Sci-

entific, 1994.

[6] D.G.Blair, Ed., The Detection of GravitationalWaves, Cambridge: Cambridge University Press, 1991.

[7] K.S. Thorne, Gravitational Radiation: A NewWindow Onto the Universe, Cambridge: CambridgeUniv. Press, 1989.

[8] K.S. Thorne, in300 Years of Gravitation, S.W.Hawking and W. Israel, Eds., Cambridge: CambridgeUniv. Press, pp. 330-458, 1984.

[9] B.F. Schutz,Nature, 323, 310, 1986.

[10] H.D. Wahlquist,Gen. Relativ. Gravit., 19, 1101,1987.

[11] C.W. Lincoln and C.M. Will,Phys. Rev. D, 42,1123, 1990.

[12] R. Drever, “Fabry-Perot cavity gravity-wavedetectors”, inThe Detection of Gravitational Waves, ed.by D. Blair, Cambridge: Cambridge Univ. Press, 306-317, 1991.

[13] B. Meers, “Recycling in laser-interferometricgravitational-wave detectors”,Phys. Rev. D, 38, 2317-

Figure 24: PNI initial configuration

Suspension:5" x 8" footprint

Phase noise interferometer First stage, showing fiber input

l = 6 mrec

∆l =10 cm

fiber

pockels cells; f =25 MHz

isolator

output signal

laserfrequencycontrol

laseramplitude control

pre-stabilizedlaser

lp

hp

recyclingcavitycontrol

-1

MI differentialcontrol

63" dia.

39" dia.30" dia

mod


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2326, October 1988.

[14] J.A. Armstrong,J. Opt. Soc. Am., 56, 1024, 1966.

[15] R. Weiss, “Electromagnetically Coupled Broad-band Gravitational Antenna”,Q. Prog. Rep. Res. Lab.Electron. MIT 105, 54-76, 1972.

[16] J. Giaime, Studies of Laser Interferometer Designand a Vibration Isolation System for InterferometricGravitational Wave Detectors, PhD thesis, MIT, June1995.

[17] C.N. Man, D. Shoemaker, M. Pham Tu and D.Dewey, “External Modulation Technique for SensitiveInterferometric Detection of Displacements”,PhysicsLetters A, v148, n1,2, 8-16, August 1990.

[18] Y. Hefetz, N. Mavalvala, “Sensitivity of theLIGO interferometer to mirror misalignment andmethod for automatic alignment”, presented at MG7,Stanford Univ., July 1994.

[19] R. Drever et. al., Appl. Phys. B, 31, 97, 1983.

[20] R. Forward, “Wideband laser-interferometergravitational-radiation experiment”,Physical Review D,17, 2, 379-390, January 1978.

[21] J. Gea-Banacloche and G. Leuchs, “Squeezedstates for interferometric gravitational-wave detectors”,J. Modern Optics, v34, n6/7, 1987.

[22] F. Reif,Fundamentals of Statistical and ThermalPhysics, New York: McGraw Hill, 1965.

[23] A. Gillespie and F. Rabb, “Thermal excited vibra-tions of the mirrors of laser interferometer gravitational-wave detectors”,Physical Review D, 52, 2,, 577-585,July 1995.

[24] A. Gillespie and F. Rabb, “Thermal noise in thetest mass suspensions of a laser interferometer gravita-tional-wave detector prototype”,Physics Letters A, 178,357-363, May 1993

[25] V. Braginsky, Moscow State University, unpub-lished communication and continuing research.

[26] K. Thorne, “Gravity gradient noise due to humanmotion near a test mass chamber”, Caltech Report,LIGO-L950753-00-E, 21 September 1995.

[27] S. Whitcomb, “Optical pathlength fluctuations in

an interferometer due to residual gas”, Technical Report,California Institute of Technology, October 1984.andR. Weiss, “Scattering by residual gas, Technical Report,Massachusetts Institute of Technology, February 1989.

[28] M. Zuker and S. Whitcomb, “Measurement ofOptical Path Fluctuations due to Residual Gas in theLIGO 40 Meter Interferometer”, presented at MG7,Stanford Univ., July 1994.

[29] C.M. Caves,Physical Review D, 23 1693, 1981.

[30] J. Giaime, P. Saha, D. Shoemaker, L. Seivers, “Apassive vibration isolation stack for LIGO: design, mod-eling and testing”, submitted toReview of ScientificInstruments, 31 May 1994.

[31] A. Abramovici, T. Lyons, F. Raab, “Measuredlimits to contamination of optical surfaces by elastomersin vacuum”, Applied Optics, 34:1, 1 January 1995.

[32] G. Gonzalez and P. Fritschel, “Barry ControlsSTACIS isolators: performance in situ”, MassachusettsInstitute of Technology, LIGO-G952003-00-R, 26 May1995.

[33] J. Camp, L. Sievers, R. Bork, J. Heefner, “Guidedlock acquisition in a suspended Fabry-Perot cavity”,submitted toOptics Letters, August 1995.

[34] A. Abramovici et. al., to be submitted to Phys.Rev. D, 1995.

[35] F. Raab, “Development of laser interferometergravitational-wave detectors for LIGO”, Proceedings ofthe OE/LASE: Lasers and Applications Conference(SPIE), January 1995.

10. BIOGRAPHY

Dennis Coyne is the Deputy Integration andSystems Engineering Manager for the LIGOProject at the California Institute of Technol-ogy. Prior to LIGO, he worked on adaptiveoptics, pointing and tracking and servo-controlsystems, as a principal scientist for KamanSciences Corporation, and on product designat Bell Labs. He has an MSME from the Uni-versity of California at Berkeley and was aCommonwealth Scholar at the University ofMassachusetts.

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