Gravitational-wave detector

Gravitation & Cosmology, Vol. 5 (1999), No. 4 (20), pp. 351–360c© 1999 Russian Gravitational Society

GRAVITATIONAL-WAVE DETECTOR “DULKYN”:TEST EXPERIMENTS USING A PASSIVE PROTOTYPE.INTERMEDIATE RESULTS AND PERSPECTIVES1

A.B. Balakin, Z.G. Murzakhanov and A.F. Skochilov

Scientific Centre of Gravitational Wave Research “Dulkyn”,Academy of Sciences of the Republic of Tatarstan, P.O. Box 595, Kazan 420503, Russia2

Received 16 February 1999Received in final form 5 July 1999

Experimental results obtained for three years of test examinations using a passive variant of optic pentagonal two-contour interferometer “Dulkyn” are presented and generalized. Optimal ways of using the merits and advantagesof the compact two-resonator laser system in gravitational-wave experiments are discussed.

gRAWITACIONNO-WOLNOWOJ DETEKTOR “dULKYN”: TESTOWYE “KSPERIMENTY NA PASSIWNOM PROTOTI-PE. pROMEVUTOˆNYE ITOGI I PERSPEKTIWY

a.b. bALAKIN, z.g. mURZAHANOW, a.f. sKOÎLOW

pREDSTAWLENY I OBOB]ENY “KSPERIMENTALXNYE REZULXTATY, POLUÊNNYE ZA TRI GODA TESTOWYH ISPYTANIJ NA

PASSIWNOM WARIANTE OPTIÊSKOGO PENTAGONALXNOGO DWUHKONTURNOGO INTERFEROMETRA “dULKYN”. oBSUVDA@TSQ

OPTIMALXNYE PUTI ISPOLXZOWANIQ DOSTOINSTW I PREIMU]ESTW KOMPAKTNOJ DWUHREZONATORNOJ LAZERNOJ SISTEMY

W GRAWITACIONNO-WOLNOWYH “KSPERIMENTAH.

1. Introduction

In December 1995, in Kazan, there began experi-ments on a pentagonal two-contour laser interferom-eter, a passive prototype of the gravitational detec-tor “Dulkyn” [1]. The ideas underlying the detector“Dulkyn”, are related to M. Scally’s [2] ideas, but theyare realized on the basis of other engineering princi-ples.

The results of these test experiments were brieflydiscussed in Refs. [3,4]. Put together, they form aunique picture, providing significant corrections to thetactics of abatement of the disturbances and noises.They clarified the methodology of increasing the sen-sitivity of the active version of the gravitational-wave(GW) detector under construction.

That is why, not restricting ourselves to shortcommunications, we take a risk of presenting, to thereader’s attention, a review of experimental results ob-tained on the passive interferometer and an evaluationof their role for further development of the project”Dulkyn”.

1Talk presented at the 10th Russian Gravitational Confer-ence, Vladimir, June 20-27, 1999.

2e-mail: [email protected]; [email protected]

2. Passive pentagonal two-contourinterferometer

2.1. What is the difference between passiveand active pentagonal interferometers ?

The scheme of an active pentagonal interferometer wasdiscussed in Ref. [1]. Comparing Fig. 1, where the op-tical scheme of a passive pentagon is depicted, witha similar scheme of an active device, it is easy tomake sure that the internal (external) resonators ofthe active and passive interferometers are completelyidentical. The differences arise only in one substanti-nal point: in the active interferometer, a cuvette withan active medium (gas-discharge He-Ne tube withoutBrewster windows) is placed between the mirrors 10and 4; in the passive interferometer the source of elec-tromagnetic radiation is a frequency-stabilized exter-nal laser 1. In the remaining part the optical elementsdiffer by displacement and amount only. Just this cir-cumstance gives us the right to extrapolate some ofthe results obtained on a passive prototype to the caseof an active interferometer.

352 A.B. Balakin, Z.G. Murzakhanov and A.F. Skochilov

Figure 1: Optical scheme of the passive pentagonal inter-ferometer.

2.2. Construction and operation principles ofthe passive interferometer

A frequency-stabilized (∆ν/ν 10−8 ) He-Ne laser,with a generation wavelength of 0,6328 µm, withthe light polarization plane forming an angle of 45

with the figure plane (which is equivalent to a mix-ture of two beams with mutually orthogonal polar-ization asimuths, TE and TM, of equal intensity),was used as a source of electromagnetic radiation 1.In Fig. 1, the continuous line corresponds to a beamof TM-polarization, the dotted one to that of TE-polarization.

The interferometer operates as follows. The light-dividing cube 2 divides the initial laser beam into twobeams: the reflected one, playing the role of the ref-erence one, and the transmitted one, which is intro-duced to the pentagonal interferometer by means ofthe prism of complete internal reflection (CIR) 3. Inturn, the transmitted beam, having been reflected bythe mirror 4, is divided into two beams by the ac-tion of the hologram diffractional gratings 5 and 9 (thegratings’ spatial carrier frequency is 1767,8 lines/mm).

The first beam passes over the external contour of thefigure, formed by the beam path; it reflects from bothgratings in the zero order of diffraction and, due to thepolarization prism 7, contains only the TM-componentof laser radiation. The second ray diffracts to the firstorder of diffraction on the grating 5, whereupon afterpassing through the polarization prism 6 it containsonly the TE-component of laser radiation; then it isreflected from the mirrors 10, 8 and 4 and falls ontothe grating 9, at which it also diffracts to the first or-der, after which it converges with the first ray. Theoptical elements 4, 5, 8, 9 and 10 are placed in thevertices of the rectilineal pentagon. The prism CIR 11transports both rays with TE and TM polarizationsout of the pentagonal interferometer and directs themat the light-dividing cube 12, where they interfere withthe reference rays of TE and TM polarizations and arereflected from the light-dividing cube 2. Two of thefour interference patterns obtained in this way (twoper each ouput plane of the light-dividing cube 12)come immediately to the polarization prism 14, andthe other two are directed at it by the prism CIR 13.The polarization prism 14 realizes a complete spatialdivision of the interference patterns.

The photodetectors PD1k(k = 1, 2) serve forregistration of the coupled interference patterns, emerg-ing from the interference of beams with TE polariza-tion, and the photodetectors PD2k serve for registra-tion of the coupled interfernce patterns from the wavesof TM polarization. The pentagonal two-contour in-terferometer is tuned in such a way that the fringesof infinite width are observed in all four patterns. Inreality, due to divergence of laser radiation and sub-stantial difference of optical lengths in the referenceand signal branches of the interferometer, the fringesin the form of rings are observed, being characteristicof the interference of two spherical fronts with closecurvature radii.

Varying the optical path length of the light, trans-mitting it through the elements 6 and 7 (by means oftheir small, of the order of a few angular minutes, in-clination of the relative optical axis), one can set upthe initial phases in the interference patterns.

After spatial separation of all four interferencepatterns, the intensity changes Ik1 and Ik2 , causedby the phase difference variations ∆ΦTE,TM (t) =∆Φ0

TE,TM + ϕ1,2(t) in the internal and external con-tours, are registered by the photodetectors PDk1 andPDk2 . The voltages Uk1(t) = βk1Ik1 and Uk2(t) =βk2Ik2 from the outputs of the photodetectors (βk1,2

are the transformation coefficients of the photodiodes)come to the subtraction scheme, where the differ-ence voltages U1(t) = U11(t) − U12(t) and U2(t) =U21(t) − U22(t) are formed. By varying the initialphase difference ∆Φ0

TE,TM from zero to 2π the am-plitudes of oscillations Uk1(t) and Uk2(t) are deter-mined and are further used to find the normalization

Gravitational-Wave Detector “Dulkyn”: Test Experiments Using a Passive Prototype 353

coefficients. The phase variations ϕ1,2(t) in the signal(internal contour) and the reference (external contour)are calculated immediately as a result of the appro-priate interferometer tuning and the normalizationprocedure described in detail in [3].

The pentagonal interferometer, according to thescheme of Fig. 1, was mounted and adjusted on thepolished round glass plate 10 cm thick, having a di-ameter of 65 cm, the pentagon side being 30 cm. Fourseparate interference patterns with the desired tuningeither at infinitely wide fringes or at t fringes of finitewidth, were obtained in the plane of photodetectors.

2.3. Conditions of the experiments

The main experimental base of UELGOI (United Ex-perimental Laboratory of Gravitational Optical Inves-tigations) is a specialized compartment on the terri-tory of FSIC GIPO (Federal Scientific Industrial Cen-tre of State Institute of Applied Optics) provided withall necessary equipment.

The experiments were performed in a specializedchamber placed in a deepened laboratory (DL) at adepth of 12 m from the ground level, which is done forminimization of the vibrational background effect andsimplification of the temperature stabilization prob-lem. The walls and the floor of the laboratory areconfined in a whole metal chamber which rests onthe sand cushion hydroisolated from the wall sides.The laboratory has a technical underground with adepth of 2 m from the floor, which serves for installingthe foundations of the main equipment of the DL aswell as for displacing the communications and elec-tric supply systems of the main equipment. The ex-perimental chamber consists of two departments, oneinside another. In the internal chamber all the high-sensitive equipment, including the developed pentago-nal interferometer, is installed on a special foundation,which is, in turn, vibration-insulated from the roomfoundation. The foundation consists of a ferroconcreteblock of 100 ton and is vibration-insulated by means ofthe spiral car springs. The equipment is additionallyvibration-isolated by various special isolating devices.

To provide the necessary temperature conditions, athree-stage thermostabilizaton system is incorporated.The first stage is represented by a conditioner whichwarms the air flow coming as an influent ventilationto the DL and keeps the temperature within the lim-its of 0.5C (0,25C from a nominal value). Thesecond and third stages are equipped with a speciallyelaborated autonomous temperature stabilization sys-tem. The second stage keeps the temperature in theexternal room of the chamber within 0.1C from thenominal value, and the third one, working for the in-ternal room of the chamber, provides stability within0.01C .

Figure 2: Results of the SCSCD operation.

3. System of correlativeself-cancellation of disturbances(SCSCD)

In the original version of the project [1], the SCSCDwas considered as a main element in the disturbanceelimination system; the authors’ optimism was basi-cally justified by successful application of these sys-tems in radio detection and ranging. A really operat-ing SCSCD in the passive interferometer was realizedin a digital version using an IBM PC AT-486. Thephase variations ϕ1(t), ϕ2(t) in the internal and ex-ternal contours are fed to the SCSCD input. The re-sulting signal ΦΣ(t) is formed at the SCSCD output:

ΦΣ(t) = ϕ1(t)− ϕ2(t)ϕ1(t)ϕ2(t)

ϕ22(t)

, (1)

where the overline denotes time averaging (for approx-imately 1 s). For a complete correlation of the valuesϕ1(t) and ϕ2(t), i.e. for ϕ2(t) = const · ϕ1(t), theresulting signal is ΦΣ(t) = 0.

It became clear in the course of the experimentsthat the SCSCD efficiently suppressed the distur-bances caused by a simultaneous external effect onall optical elements of the interferometer (a mechani-cal shock on the interferometer basement, acoustic andseismic vibrations). Fig. 2 presents the characteristicexperimental results of the SCSCD operation. Thesecond and third tracks show phase variations in theinternal and external contours of the pentagonal inter-ferometer (ϕ1(t) and ϕ2(t)), caused by the perturba-tions of the air density in the experimental chamberdue of sudden door opening and closing, while the firsttrack presents the result of correlation processing of(ΦΣ(t)). The elaborated SCSCD allows one to reducethe correlated phase noise by one or two orders ofmagnitude depending on the type of disturbances.

The efficiency of the SCSCD operation strongly de-pends on the amplitudes ratio of the correlated anduncorrelated components of the phase disturbances inthe channels. Actually the SCSCD stops operatingwhen the uncorrelated noise level approaches that of


the correlated noise. On the average, the SCSCD pro-vides the maintanance of ΦΣ(t) at the level of theorder of 10−1 rad in the passive variant of the pentag-onal interferometer, although in separate short periods(10 to 15 seconds long) they managed to achieve thevalues 10−4 rad [3]. In other words, the experimen-tal threshold of the SCSCD efficiency was determinedwhen working on the passive interferometer. It wasfound that the SCSCD efficiently compensates roughdisturbances — the correlated phase variations in thesignal and reference channels with amplitudes vary-ing from tens to tenth of a radian, caused by exter-nal effects on the interferometer as a whole. However,stochastic independent vibrations of the interferometermirrors of smaller amplitudes result in an uncorrelatedphase noise (of the order of 10−1 rad), which is stillmuch larger than the expected amplitude of responseto a GW signal, but is still irremovable by means ofSCSCD. This experimental result gave an impetus tofurther research in the field of processing the signal ofthe pentagonal interferometer, and we turned to theidea of phase difference stabilization.

4. Phase difference stabilization andthe noise spectral characteristics inthe passive pentagonalinterferometer

4.1. Phase difference stabilizationservosystem

The development and application of the stabiliza-tion servosystem (SS) were preceded by an activediscussion of whether such a system demolishes thedesired signal together with the noise in the caseof an infra-low-frequency signal with an amplitudemuch lower than the stabilization threshold. Wehad at our disposal sufficient theoretical argumentsin favour of application of a stabilization servosystem(SS), which immediately minimizes the phase differ-ence value ∆ϕ(t) = ϕ1(t) − ϕ2(t), but there was anecessity to confirm these arguments experimentallyon the passive interferometer [4].

With this aim in view, such a SS was constructedand realized in the analogue-digital version using acomputer which controlled the stabilization processby a specially elaborated program. The polarizationprism 7, possessing the possibility of turning by smallangles around the vertical axis, controlled by a signalfrom the computer, played the role of the SS executiveelement.

The first actually working trial SS provided thepossibility of minimizing the phase difference fluctua-tions ∆ϕ(t) in the amplitude to the level of Φ0 =10−2 rad (the “stabilization threshold”). The poten-tial of the method is much greater: the stabilizationthreshold at low frequences may be fixed at a level

of Φ∗0 = 10−4 rad. However, in experiments on the

passive prototype we restricted ourselves to a higherthreshold, which is nevertheless by a factor of 10 lowerthan the SCSCD sensitivity threshold.

For theoretical estimations the phase differencevariation ∆ϕ(t) can be presented in the form

∆ϕ(t) = ϕ(t) + Φg sin(Ωgt+ βs) + ΨCC(t) , (2)

where the first term of the sum represents the non-reduced interferometer phase noise ϕ(t), which can beobserved with the SS switched off; the second term isthe inserted periodic phase variation, simulating thefriendly signal with the amplitude Φg , frequency Ωg

and initial phase βs ; the third term describes the con-trolled phase variations introduced by the executiveelement of the SS by the error signal.

Let max |ϕ(t)| be the upper threshold of the non-reduced noise in the interferometer. The stabiliza-tion system makes it possible to fix the sum ψ(t) =ϕ(t)+ΨCC(t) at a level |ψ(t)| ≤ Φ0 , the upper thresh-old for the reduced noise ψ(t) being several ordersof magnitude lower than max |ϕ(t)| . The question ofwhat are these values for an actually operating pen-tagonal interferometer was answered by a run of long-term continuous (up to 8 days) experiments performedin late 1997 — early 1998 [4]. The experimental dataprocessing allowed one to obtain the spectral charac-teristics of the reduced and non-reduced noises in thepentagonal interferometer.

4.2. Spectral density of phase noise

The spectral density of the non-reduced phase noiseSϕ(ν) = F [〈ϕ(t)ϕ(t+ τ) 〉] , where < ϕ(t)ϕ(t+ τ) > isthe autocorrelation function and F [...] is the Fourier-transform operator, is connected with the analogousfunction Sψ(ν) for the reduced noise by the relation

Sψ(ν) =Sϕ(ν)

(1 +G(ν))2(3)

(G(ν) is the amplification factor in the SS feedbackcircuit at low frequences).

The spectral densities of the amplitude of the non-reduced noise ϕ(ν) =

√Sϕ(ν) (curve 1) and that of

the reduced noise ψ(ν) =√Sψ(ν) (curve 2) vs. the

frequency ν , calculated from the experimental data,are presented in Fig. 3 [4]. As seen from the figure, thenon-reduced noise spectrum of the interferometer is acharacteristic of flicker noise and may be approximatedby the function

ϕ(ν) 5 · 102

10−5

ν

rad/

√Hz. (4)

The reduced noise in the frequency range of 10−5 Hzto 10−1 Hz is sufficiently well approximated by thewhite noise:

ψ(ν) ψ0 = 5 · 10−3 rad/√Hz. (5)


Figure 3: The spectral density of the amplitude of thephase noise: 1 — unreduced noise, 2 — reduced noise.

It follows that in this frequency range the SS operationis equivalent to the work of a whitening filter. Accord-ingly, the amplification factor G(ν) for this frequencyrange may be presented in the form

G(ν) 105

10−5

ν

, (6)

i.e., G(ν) takes values from 10 to 105 for frequenciesvarying from 10−1Hz to 10−5Hz.

4.3. Analysis of the situation

Experiments with the servosystem for phase differencestabilization have exposed two key points importantfor further investigations:

• The reduced noise spectral density is finite ev-erywhere in the infra-low-frequency range: it hasno anomaly at zero frequency, does not con-tain resonance peaks and is almost frequency-independent;

• The statistical characteristics of the reducedphase noise in the infra-low frequency range aresimilar to those of white noise: the calculatedcorrelation times and the performed stabilitytests for separate data series allow one to pre-dict the same result for long-term systematicobservations.

On the basis of these conclusions, we made thefollowing step: we modified the signal processing sys-tem, having supplemented the methodology of inter-periodic signal accumulation by the idea of intraperi-odic accumulation.

However, one more fundamental question was un-solved: it was necessary to prove that the stabilizationsystem does not demolish the desired signal itself, andthat there is an opportunity of its recognition after fin-ishing the procedure of intraperiodic and interperiodicaccumulation.

5. Extraction of a simulated periodicsignal from the noise

The GW signal simulation is considered as an im-portant point in the calibration of any GW detector.Since, for the detector “Dulkyn”, the GW field effectis associated with an efficient change in the optic pathinside the signal contour, an analogue simulation ofa periodic GW action was performed by a thin plateturning with a given frequency, introduced to the sig-nal contour. Aa actually operating executive turningmechanism provided phase variations on the level of10−4 rad. This value is by three orders greater thanthe gravitationally induced shift, so the analogue ex-periments were accomplished with digital simulation,during which the phase variation was continuously setat the levels of 10−4 , 10−5 and 10−6 radian. Therange of amplitudes in the digital simulation was re-stricted from above by the stabilization threshold andfrom below by the time sufficient for periodic signalrecognition.

5.1. Interperiodic signal accumulation

The first signal processing algorithm, used for the pen-tagonal interferometer, is based on the idea of an in-terperiodic comb accumulation filter (IPCAF) [5] andon the multichannel squeeze method [6]. The soughtfor signal period Tg = 2π/Ωg is divided into M timeintervals of duration ∆t = Tg/M . The number Mshould be no less than 20 to provide keeping informa-tion about the shape of the periodic signal by whichits amplitude and initial phase may be determined (inan actual experiment this number was equal to severalthousands). Then, during one signal period Tg , at theinstants tm = m∆t (m = 0, 1, ...,M) the phase valuesΦm = ∆ϕ(tm) are measured, numbered and recordedin definite computer storage registers. Then the pro-cedure is repeated during the following signal period,and the measurement results are added into the corre-sponding registers. One gets the following result afterN accumulation periods:

Φm =N∑

j=1

∆ϕ(tmj) , tmj =(mM

+ j − 1)Tg . (7)

We obtain at the IPCAF output

Φm = NΦg sin(2πm

M+ βs

)+Ψm (8)

where

Ψm =N∑

j=1

ψ(tmj) . (9)

The first term of the sum in Eq. (8) represents thecoherently accumulated signals whose amplitude is Ntimes greater than that of the initial signal Φg . One


should be rather careful when evaluating the secondterm of the sum Ψm .

In the case of absence of a friendly signal (Φg = 0),the value ψ(t) is a random stochastic function sincethe stabilization system “works out” the random in-herent phase noise of the interferometer ϕ(t), so thatthe second term of the sum in (8) will increase as

√N .

In the presence of the periodic signal (Φg = 0)two variants are possible: the amplitude of the signalΦg is so small that the SS does not “feel” its pres-ence, and then ψ(t) is still a random value, or, with acomparatively large signal amplitude, the SS will start“working” it “out”, and a regular component in ψ(t),responsible for the signal compensation, will appear.In this case Ψm will grow as

√N , and after a suf-

ficient number of accumulation periods the first termof the sum in (8) will exceed the second one, i.e., thefriendly signal will be found. In the first case it is im-possible to extract the friendly signal from the noise.

The performed experiments have demonstratedthat, in the two-contour pentagonal interferometer“Dulkyn”, the stabilization system does not eliminatethe friendly periodic signal if its amplitude is at leasttwo orders of magnitude smaller than “the stabiliza-tion threshold” Φ0 . Fig. 4 presents typical results ofthe IPCAF operation, using as an example a signalwith the amplitude Φg = 10−4 rad and frequencyΩg = 1, 460 · 10−2 Hz. In three diagrams of Fig. 4the values Φm (M = 3180) are marked by dots, andthe continuous line corresponds to the original signal.In the upper and middle diagrams the accumulationperiod exactly coincided with the signal period, whilein the lower diagram the accumulation period corre-sponded to the frequency Ω = 1, 461 · 10−2 Hz. Thelower diagram clearly demonstrates that it is impossi-ble to extract a steady periodic signal from the noiseif initially there is no signal at the frequency corre-sponding to the prescribed accumulation period.

When the amplitude of the signal Φg approachesthe “stabilization threshold” ”Φ0 , the friendly signal isdemolished, and the result of its accumulation be-comes similar to the lower diagram of Fig. 4. Atfriendly signal amplitudes smaller than 10−4 rad itis also unaffected by the stabilization servosystem,although a greater number of periods should be accu-mulated for its extraction from noise.

5.2. Intraperiodic signal accumulation

The infra-low-frequency signal processing by means ofthe interperiodic accumulation algorithms is compli-cated since it requires great time expenditures. How-ever, the slowness of signal changing provides a certainadvantage: the possibility of applying the algorithmsof intraperiodic accumulation. From a mathematicalpoint of view such an opportunity is given by the re-

Figure 4: Results of the BPCAF operation.

lation

〈 sin(2πmTt+ ψ

)〉 =

(sin πm

2

m

)sin (

2πmTt+ ψ),(10)

where the averaging, denoted by angular brackets,means integration of the following form:

〈 ζ(t) 〉 ≡ π

T

∫ t+ T4

t−T4

dτζ(τ). (11)

This means that a strictly periodic signal is notchanged if the averaging is performed over an intervalof exactly half-period duration, symmetrical relativeto the instant t (the case m = 1). If the period of theaveraged sinusoid is contained odd number of timesin the interval T (m = 2k + 1, k > 0), then theamplitude will decrease by a factor of m as a resultof averaging; with even m the averaging gives zero.If we deal not with the sinusoids of multiple periodsbut with random components of a signal, then theamplitude of the latter decreases proportinally to thefactor 1/

√T .


This simple fact presents an opportunity to real-ize different algorithms of intraperiodic accumulationfor all periodic signals; it is, however, obvious thatthe above-mentioned circumstances are the most use-ful and interesting in the case of infra-low-frequencysignals.

In the pentagonal interferometer, the following al-gorithm was used. After the IPCAF, the set of ac-cumulated values Φm(m = 0, 1, ...,M) comes to theinput of an intraperiodic comb accumulation filter(ICAF). If the discretization interval ∆t = τ = Tg/Mis chosen to be rather small (τ ∼ 1 s at M 3 · 103 )but still greater than the phase noise correlation time,then one can introduce another, larger-grained di-vision of the period Tg into M1 (no less than 20)intervals, each containing M/M1 values Φm , withinwhich the friendly signal changes insignificantly. TheICAF operation principle is based on obtaining a newset of values Φr(r = 1, 2, ...,M1), formed by summingthe values Φm within each of the M1 intervals. It iseasy to demonstrate that the signal-to-noise ratio willincrease in so doing by a factor of

√M/M1 (in our

case the increase was tenfold).With simultaneous application of IPCAF and ICAF,

the signal-to-noise ratio at the output of the signalprocessing unit will be

q0 = qs√N

√M

M1(12)

where qs = Φg/Φ0 ≤ 10−2 is the ratio of the GW sig-nal amplitude to the “stabilization threshold” at whichthe stabilization system does not demolish the friendlysignal. Determining from (12) the required number ofperiods N for given q0 , we obtain the following esti-mate for the accumulation time Ta ≡ NTg = NM∆t :

Ta =(q0qs

)2

M1∆t . (13)

The binary pulsar PSR J1537+1155 possesses themaximum dimensionless amplitude h+ = 2.14 · 10−22

among the sources pointed out in Fig. 5. Assummungthat qs = 10−2 for this pulsar, we obtain from Eq. (13)with M1 = 20, ∆t = 1 s the value Ta 1.8 · 106 s 20.8 days.

A digital ICAF was tested in an actual experimenton the passive version of two-contour pentagonal in-terferometer. To extract a periodic signal with the fre-quency Ωg = 1.46 · 10−2 Hz and qs = 10−2 by meansof an IPCAF it was necessary to accumulate about 104

periods (see the middle diagram in Fig. 4). The resultof ICAF operation for the same signal with N = 103

is illustrated by curve 1 in Fig. 6 (the values of Φr

(M1 = 20) are marked by circles and squares). Curve2 is calculated theoretically for the friendly signal inthe absence of noises by the algorithms of IPCAF andICAF operation. Curve 3 is obtained in the same man-ner as curve 1, but on the basis of experimental data

Figure 5: Modified pentagonal scheme of the GW detec-tor ”Dulkyn”.

Figure 6: Results of the ICAF operation.


in the absence of a friendly signal. As seen from Fig. 6,one can confidently form an opinion by the shape ofcurve 1 about the availability of a friendly sinusoidalsignal with an initial amplitude two orders of magni-tude smaller than the noise amplitude; therewith itwas necessary to accumulate only one thousand of itsperiods for this purpose. In other words, the accu-mulation time was reduced by an order of magnitudeby using the ICAF. The necessary accumulation timecan be reduced at the cost of reasonably reducing thediscretization interval ∆t .

6. Test experiments on the passiveinterferometer and concepts of GWdetector “Dulkyn” modification

The preliminary test experiments on the passive pen-tagon have resulted in a re-estimation of the efficiencyof some signal processing methods and, as a conse-quence, in a modification of the active pentagonal in-terferometer scheme itself. These modifications touchupon the principal foundations of detector operationstated in Ref. [1] and require a further discussion.

6.1. Modification scheme of the GW detector“Dulkyn”

(i) It was experimentally established that the stabi-lization system is more efficient than the disturbancecorrelation compensation system, i.e., the SS is able toperform the SCSCD functions on the signal rough pro-cessing and, at the same time, to yield a substantialimprovement in fine processing.

(ii) At SS operation the necessity of an auxiliary laser-heterodyne [1,7], which would, moreover, create an ad-ditional noise, disappears.

(iii) Experimental investigations of the reflective prop-erty of holographic gratings, operating in the passiveinterferometer, as well as a study of the balance of en-ergy circulating in the contour, have suggested a wayof obtaining and using the pentagonal scheme with alessenned number of reflections and, correspondingly,smaller energy losses.

The GW antenna scheme modified as compared to[1, 7], the phase difference stabilization system and thesignal processing unit on the basis of the friendly sig-nal between-periodic and intraperiodic accumulationsystems, are considered below.

Fig. 5 presents the modified ring pentagonal schemeof the GW antenna which, in contrast to the one con-sidered in [1,7], has smaller losses per pass-over inthe internal contour. The operation principle of theoptical resonator can be briefly formulated as follows.Along with the ordinary mirrors 3, 4, 5, the resonatorbasic elements are the hologram diffractional reflective

elements 1 and 2, which, together with the polariz-ers PTE and PTM , fulfil the function of dividing theincident light into two beams with orthogonal polar-ization azimuths. In the zeroth order of diffractionthe elements 1 and 2 work as ordinary mirrors, pro-viding TM -polarized light circulation (the electricfield vector lies in the figure plane) over the externalcontour (1-2-3-4-5-1); the radiation diffracted to thefirst order forms the internal contour (1-4-2-3-4-5-1) ofTE -polarized light circulation (the electric field vec-tor is perpendicular to the figure plane), the sectionsbetween the elements 2, 3, 4, and 1 being commonfor both contours. Here the active medium (AM) (ina gas-discharge tube without Brewster windows) issituated, providing light generation in both contours.As seen from the figure, all the basic optic elementsof the pentagonal resonator (mirrors, gratings, activemedium) belong simultaneously to the external andinternal contours of light circulation, therewith themirrors and the gratings are placed at the verticesof the regular pentagon and are rigidly fixed on thecommon basement.

The generation equations and the method of cal-culating the longitudinal eigenfrequences of the res-onators in the GW field were considered in [1]. Forthe modified scheme of the antenna the internal res-onator longitudinal eigenfrequency shift, caused by agravitational wave falling perpendicular to the pen-tagon plane, is equal to

∆ωg(t) =12Ω0

1h+ sin(Ωgt+ βg) (14)

where Ω01 is the internal resonator eigenfrequency in

the absence of GWs; h+ is the dimensionless ampli-tude of the GW first polarization in TT-gauge (thecorresponding own direction is assumed to coincidewith the direction of section 2-1 for the sake of sim-plicity); Ωg and βg are the GW frequency and initialphase. The longitudinal eigenfrequency Ω0

2 of the in-ternal resonator remains unchanged.

In operation inside the locking zone (Ω01 = Ω0

2 =ω0 ), when running waves with orthogonal linear po-larizations, counter-travelling in the active medium,are excited (one per each, internal and external, res-onator), an equation for the variable part of the phasedifference ϕ(t) has the form

dϕ

dt+Ω0ϕ = ∆ωg(t) + (B1 −B2)x(t) + ξ(t) (15)

where Ω0 is the locking zone width (see [1]), ξ(t) is arandom function due to technical and natural fluctua-tions of the difference frequency, and the coefficients

B1 = −(Ω0

1

l

)tan

π

10 −0.32

(Ω0

1

l

),

B2 = −(Ω0

2

l

)25sin

π

5 −0.24

(Ω0

2

l

)(16)


determine the shifts of the longitudinal eigenfrequencesof the internal and external resonators, equal to ∆Ω0

1,2 =B1,2x(t), if the controlled displacement of the mirror4 occurs along a normal to its surface at a given valuex(t) relative to some initial location. The coefficientsB1,2 are found by computing the internal and externalcontours’ perimeter change due to the displacement ofthe mirror 4.

Immediate integration of (15) gives an expressionfor the instant phase difference ϕ(t) which can be pre-sented in a form similar to (2):

ϕ(t) = s(t) + n(t) + f(t) , (17)

s(t) = Φg sin(Ωgt+ βs), Φg =h0ω0√Ω2

0 +Ω2g

,

βs = βg − arctanΩg

Ω0, h0 =

12h+,

n(t) = e−Ω0t

∫ξ(t) eΩ0tdt+ C0 e−Ω0t , (18)

f(t) = Be−Ω0t

∫x(t) eΩ0tdt. (19)

Here s(t) is the friendly signal, n(t) is the unreducedphase noise of the GW antenna; f(t) describes con-trolled phase variations introduced by the SS executiveelement; C0 is the integration constant, B = B1−B2 .

Since |s(t)| max |n(t)| , there is a noise mini-mization problem. This can be achieved in a defi-nite frequency range due to availability of the control-lable function x(t) inducing the preset phase varia-tions (19).

6.2. Phase difference stabilization system inthe active interferometer

The stabilization system of the phase difference of op-tical radiation generated in the two contours of thepentagonal resonator consists of the electronic unitsfor frequency autotuning (FAT) and phase autotuning(PAT) (see Fig. 5). On the back surface of the outputmirror 5, a thin phase transmitting grating is placed,which collects the beams from the external and inter-nal resonators with mutually orthogonal polarizationazimuths and provides their propagation in two di-rections (to the mirror 6 and to the semitransparentplate 8). The converged orthogonal beams, after pass-ing through the polarizers 7 where the linearly polar-ized light transmission plane forms an angle of 45

with the figure plane, get the opportunity to form aninterference field which is registrated by the photode-tectors PD1, PD2 and PD3. The PD1 output volt-age forms the error signal in the FAT, controlling thework of a piezoelement fixed on the mirror 4. Thepiezoelement provides synchronization of beams in theinternal and the external resonators. The PD2 outputvoltage forms the error signal in the PAT, controllingthe work of the specialized phase modulator PM [1,7],

maintaining the phase difference within the level setby the “stabilization threshold”.

The spectral density of the phase noise ψ(ν) willnot exceed the level of ψ0 = 10−4rad/

√Hz in the

frequency range 0 < ν < 10 (Hz) as a result of theSS operation. Let us evaluate, under these conditions,the accumulation time T required for the detection ofa low-frequency periodic GW with the characteristicparameters (see the sources of GW in Fig. 5) h0 =10−22 and Ωg/2π = 10−3 Hz. From the condition

Φg ≥ q0ψ(ν)√T, (20)

where q0 3 is the signal-to-noise ratio necessary forthe GW signal detection, using (17), we obtain

√T q0

ψ0

√Ω2

0 +Ω2g

ω0h0, (21)

whence, at the optic radiation frequency ω0/2π 1015

Hz and the locking zone width Ω0/2π 1 Hz, we getT 107s 4 months.

6.3. Interperiodic and intraperiodicaccumulation systems

The digital information about the optical radiationphase differences in the internal and the external res-onators, representing an additive mixture of a GWsignal with the reduced noise ϕ(t) = s(t) + ψ(t), isrecorded in the computer memory and comes simulta-neously (see Fig. 5) to a signal processing unit at theinput of several digital CAF after registration of theinterference pattern by the photodetector PD3 (ac-cording to methodologies described in [1]). Each CAF,tuned to a certain source of GWs (binary relativisticastrophysical objects of PSR J1537+1155-type whoseGW frequencies are known with high accuracy [8]),consists of interperiodic (IPCAF) and intraperiodic(ICAF) accumulation systems.

The IPCAF and ICAF systems in the active interfero-meter are completely similar to those in the passivepentagonal detector and are described in Sec. 6. Letus just note that a filter of the proposed scheme withthe transmission spectral band ∆ν = 2/T 2 · 10−7

Hz allows one to separate reliably the signals fromdifferent periodic GW sources. The transmission band∆ν still remains rather wide, so that one can neglectthe Doppler shift of the detected GW signal frequency(≤ 10−7 Hz) due to the Earth’s orbital motion.

7. Conclusion

Let us enumerate the main results of the test experi-ments of the passive pentagonal interferometer.

7.1. An original scheme of stabilizing the phase dif-ference of optical beams in the first and the secondpentagon contours has been created.


7.2. In the infra-low frequency range 10−5 ÷ 10 Hz(the working range for the detectors of periodic gravi-tational radiation (GR) from binary relativistic astro-physical objects), the real spectral density of the phasenoise (the stochastic component of the phase differ-ence of the first and second interferometer channels)has been studied. With this purpose a series of con-tinuous long-term measurements, with a switched-onand switched-off stabilization system, was performed.Accordingly, spectral curves of unreduced and reducednoise were obtained.

7.3. A run of experiments with analogue and digitalGW effect simulation has been performed. A periodicsignal with an amplitude of 10−4 ÷ 10−6 rad was sup-plied to the signal contour, mixed with the real distur-bance signals (with the stabilization system switchedon or off) and then was extracted from the outputsignal by means of a specially elaborated threshold al-gorithm. For the passive interferometer, relations be-tween the signal amplitude, the stabilization thresh-old and the unreduced noise level have been found,at which the “recognition criterion” for the simulatedperiodic signal is met.

Planning the nearest future, we have elaboratedthe following schedule of measures:

• to put into operation an active pentagonal laserinterferometer for travelling waves as the basicelement of a GW detector;

• to put into operation an active triangle laser in-terferometer for standing waves [9], free from in-ertial disturbances caused by the Sagnac effect;

• to create and develop the system of recognizingstationary periodic infra-low-frequency gravi-tational wave signals, incorporating a signal non-demolishing servosystem for stabilization of thephase difference of optic beams in the signal andreference contours of the active interferometer,and a modified interperiodic and intraperiodicaccumulation system;

• to perform a series of experiments in order tostudy the spectral characteristics of actual infra-low-frequency noises in the active interferometer,to classify and identify the residual noises andtheir fine filtering;

• to test the experimental data obtained on thepentagonal and triangle detectors using a coinci-dence scheme.

Acknowledgement

The authors are thankful to the government of theRepublic of Tatarstan for financial support of experi-mental works on the project “Dulkyn”.

References

[1] A.B. Balakin, Z.G. Murzakhanov and A.F. Skochilov,Grav. & Cosmol. 3, 1 (9), 71 (1997).

[2] M.O. Scully and J. Gea-Banacloche, Phys. Rev. A34, 4043–4054 (1986).

[3] A.R. Agachev, A.B. Balakin, G.N. Buinov, S.L.Buchinskaya, R.A. Daishev, G.V. Kisun’ko, V.A.Komissaruk, S.V. Mavrin, Z.G. Murzakhanov, R.A.Rafikov, A.F. Skochilov, V.A. Cheredilin and Yu.P.Chugunov, Zhurn. Tekh. Fiz. 68, No. 5, 121 (1998).

[4] A.R. Agachev, A.B. Balakin, G.V. Kisun’ko, S.V.Mavrin, Z.G. Murzakhanov, A.F. Skochilov and Yu.P.Chugunov, Pis’ma v Zhurn. Tekh. Fiz. 24, No. 22,86 (1998).

[5] V.B. Konstantinov, Z.G. Murzakhanov and A.F.Skochilov, Izvestiya VUZov, Fizika, No. 2, 26 (1999).

[6] P. Horowits and W. Hill, “The Art of Electronics”,Second Edition, Vol.3, Cambridge, New York, PortChester, Melbourne, Sydney: Cambridge UniversityPress, 1989.

[7] V.B. Konstantinov, Z.G. Murzakhanov and A.F.Skochilov, Izvestiya VUZov, Fizika, No. 2, 22, (1998).

[8] V.M. Lipunov, K.A. Postnov, Astron. Zh. 64, 438(1987).

[9] A.B. Balakin, G.V. Kisun’ko, Z.G. Murzakhanov andA.F. Skochilov, Doklady Akad. Nauk 361, No. 4, 477(1998).

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Gravitational-wave detector