Optical pulse distance-multiplying interferometry

Alexander M. Chekhovsky, Anatol N. Golubev, and Michael V. Gorbunkov

A possibility of creation of long baselines by the distance-multiplying interferometric method for acalibration distance-measuring apparatus is considered. In contrast to existing versions of this method,in which cw radiation is used, we propose using wideband picosecond continuum radiation generated bypowerful ultrashort laser pulses. In the experiment the interference pattern that is typical for whitelight, with a stable achromatic fringe, was observed. The presence of an achromatic fringe confirms apossibility of carrying out the measurements with an error of less than a wavelength of light. A possiblearrangement of a pulse interferometer free from atmospheric fluctuations to create the baselines byone-stage measurement is discussed. © 1998 Optical Society of America

OCIS codes: 140.3460, 030.1640, 120.3180, 320.5550.

1. Introduction

Increasing the instrumental accuracy of electromag-netic distance measurement requires the develop-ment of modern techniques for metrologicalverification of distance-measuring instruments.Calibration of the electromagnetic distance measure-ment apparatus is normally carried out at speciallyconstructed multisectional baselines. To achievemaximum accuracy it is necessary to create the base-lines by interferometric methods. The most widelyused method is the use of laser displacement-measuring interferometers and requires the con-struction of securely fastened, precisely aligned railguides for moving a reflector along the line to bemeasured. The measuring procedure takes rather along time, and the range does not exceed 60 m.However, the most useful length of the metrologicalbaselines is ;1 km. In principle, one can use anabsolute distance interferometer, which does not re-quire that the reflector move,1 instead of a laserdisplacement-measuring interferometer. In thecase of evacuation of the measuring arm, such aninterferometer can measure distances up to 1 km

A. M. Chekhovsky and A. N. Golubev are with Moscow StateUniversity of Geodesy and Cartography ~MIIGAIK!, Goroknovskyper. 4, 103064 Moscow, Russia. M. V. Gorbunkov is with LebedevPhysical Institute of Russian Academy of Sciences ~FIAN!, LeniskyProspect 53, 117924 Moscow, Russia.

Received 11 August 1997; revised manuscript received 9 Janu-ary 1998.

0003-6935y98y163480-04$15.00y0© 1998 Optical Society of America

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with a high accuracy, but this version is not practicalat present.2

Another method of long-baseline construction isthe interference method of optically multiplying astandard length ~Vaisala method!, in which the opti-cal path length of the measuring arm is equal to thatof the folded reference arm ~Fig. 1!. The peculiari-ties of this method are the use of a light source witha minimal time coherence for highest accuracy inequalizing the arms in the interferometer and theconstruction of the reference arm in the form of amultipath optical delay line formed by two mirrorswith the distance between them being given by thelength standard l0. Such a method ensures high ac-curacy but is extremely difficult in realization. Inthe classic version, in which a quartz bar of 1-mlength is used as the length standard, many multi-plication steps to measure a distance of 1 km arerequired. As interference appears only when thearms have been equalized with very high accuracy~2–3 mm for white light!, the arms must preliminarilybe equalized with submillimeter accuracy to facilitatea search of the interference pattern.

There are some modifications of the optical multi-plying method that enable the measurement to bemade in one step and that ease the accuracy require-ments for preliminary arm equalization. Thesegoals are attained by use of a semiconductor laserwith variable coherence length,3 a combination of thesingle-mode laser diodes,4 microwave modulation oflaser-diode radiation, and also by the measurementof the reference arm’s length by a laser displacement-measuring interferometer instead of by a mechanicallength standard.5,6 However, in these cases thebaseline length does not exceed 200–250 m.

Here we propose using an interferometer with aquasi-white-light source based on using a supercon-tinuum generated by powerful ultrashort laserpulses. Note that low-coherence interferometry isalso used in other fields such as reflectometry andoptical coherence tomography, and for these applica-tions voluminous literature exists. However, suchapplications deal with entirely different tasks thatare not associated with the long-distance measure-ments related to atmospheric routes that are the sub-ject of our consideration. Nevertheless, we assumethat interferometry by use of the supercontinuum canalso be applicable in the fields mentioned.

2. Principle

If an ultrashort laser pulse is directed to a two-beaminterferometer with reference and measuring arms,the interference pattern is observed only when a timeoverlap of the reference and measuring pulses at theoutput of the interferometer occurs, i.e., when a timedelay td in the arms does not exceed the pulse coher-ence time tc and the maximum visibility is at td 5 0.Considering that the time of existence of the inter-ference pattern is equal to the pulse duration, one canwatch not the visibility value but the resulting pulseenvelope at the interferometer output. Thus, bychanging the delay in one of the arms until the max-imum output signal occurs, we can equalize the arms’lengths with an accuracy that depends on the error infixing this maximum. However, for short pulses theproblem of preliminary arms equalization arises, as itdoes in the case of cw radiation, to catch the overlaprange of the pulses.

We consider the method that allows us to obtainultrashort pulses ~USP’s! with a superwide spectrasimilar to a white-light spectrum. Such radiation iscalled a picosecond continuum or a supercontinuum.The continuum source is, in essence, the source ofwide-band pulses with spectral bandwidths up to103–104 cm21. The continuum pulses can be ob-tained by focusing of powerful laser picosecond pulsesinto a cell with a nonlinear medium, with the sameduration and polarization of the continuum pulses.7

We assume that the changeover to quasi-white

Fig. 1. Schematic of the Vaisala interferometer: LS, lightsource; BS’s, beam splitters; M’s, mirrors; PD, photodetector.

pulses of the continuum will permit us to use twoscales of time fixing simultaneously in the opticalmultiplying method. The first, rougher, scale corre-sponds to the duration Dt of the power laser USP’sthat initiate continuum generation. ~Generallyspeaking, this scale can be achieved with USP’s with-out continuum generation.! Subject to equalizationof the arms with an accuracy of ;Dt 3 c, an inter-ference pattern will be observed that permits suffi-cient preliminary equalization of the arms to be donesimply. Indeed, if the duration of the light pulses iswithin 10–100 ps, the necessary accuracy of equal-ization lies within the range of units to tens of milli-meters.

The second scale, ideally, is defined by the coher-ence length of the quasi-white continuum pulse andallows us to reach essentially higher accuracy. Inthe case of a small detuning of the mirrors, preciseequalization of the arms must ensure observation ofan achromatic fringe bordered symmetrically with afew colored fringes. The accuracy in fixing the pointwhere optical path difference ~OPD! is zero may beexpected to be less than a wavelength of light, that is,better in comparison with the accuracy of a classicVaisala interferometer.

3. Supercontinuum Source

The principle described was verified by means of theexperimental setup shown in Fig. 2. A passivemode-locked YAG:Nd31 laser with a double-pass am-plifier was used to generate USP’s. Optical pump-ing of the YAG:Nd31 elements with 1-Hz repetitionfrequency was achieved. Dye 3274Y in an ethyl al-

Fig. 2. Experimental setup: AE’s, active elements; D, dia-phragm; GP, glass plates; M’s, dielectric mirrors; MM’s, broadbandmetallic mirrors; L’s, lenses; BSC, beam-splitter cube.

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cohol solution was used as a saturable absorber.The solution was circulated through a 0.5-mm-thickcuvette that was in optical contact with a reflectingspherical mirror of the laser cavity. The initial pass-ing of the solution was ;50%. The output mirror ofthe laser was plane wedged, with a reflection coeffi-cient of 17%. The laser cavity was 1.5 m long andwas of a semispherical type. We used the iris dia-phragm to select the lowest-order transverse mode.The linear polarization of radiation was given byplane-parallel glass plates set at the Brewster angle.By moving the active element along the cavity axis itseemed to be possible to obtain a two-threshold gen-eration regime when solitary ~within the axial inter-val! light pulses with durations of ;30 ps wereobtained at more than 95% flashes. The generationtrain consisted of four or five pulses with a total en-ergy of 3–4 mJ, which then were amplified in adouble-pass variable-gain amplifier ~maximum en-ergy might reach ;100 mJ!. For optical isolation acuvette with a solution of polymethyl dye 3955 indimethyl sulfoxide was used ~initial passing was#2%!.

The radiation of the amplified USP train was fo-cused by a lens ~ f 5 67 cm! into a cuvette with water.The length of the cuvette was 10 cm. The optimalenergy of the train ~l 5 1.064 mm! was ;50 mJ. Inthis case the supercontinuum was observed at morethan 95% flashes with no optical breakdown in water.The pulse continuum radiation was resolved byprisms into spectral components that allowed us toobserve its anti-Stokes band overlapping the entirevisible range. The temporal profile of the supercon-tinuum contained one or two USP’s. The energy ofradiation with l , 1.06 mm was 0.5 mJ.

4. Interferometric Testing

The continuum source allowed us to carry out a trialexperiment to obtain a white-light interference pat-tern and to tune a two-beam interferometer to zeroOPD with an error of less than l in the visible regionof the continuum by tracking the achromatic fringeposition. Special emphasis was laid on realization ofthese operations by the simplest and most readilyavailable means. For these purposes the continuumradiation was directed to a Twyman–Green inter-ferometer ~see Fig. 2! consisting of a beam-splittercube and two plane metallic mirrors, one of whichwas mounted upon a table with micrometric feed,permitting the OPD to be varied in 10-mm stepswithin a 1.5-cm range. At the output of the inter-ferometer we installed a frosted-glass screen to en-able us to observe and photograph the interferencepattern.

As the interference pattern was to appear onlywithin small range, we extended this range by meansof an optical filter with a bandwidth of ;50 nm and acentral wavelength of 0.5 mm. The OPD waschanged by a micrometric screw. In some positionthe interference pattern was obtained in the form ofthe equal-thickness fringes.

To facilitate preliminary equalization of the arms

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we installed a green-color filter in front of the inter-ferometer that contracted the continuum spectrumby approximately 1 order of magnitude, and the mir-rors were inclined such that the interfering wavefronts intersected at only one point. In this case theinterference pattern in high orders represented a sys-tem of one-color ~green! fringes with visibility de-creasing to zero on both sides of the central fringe.The coherence length in this case was determined asthe number of fringes observed, multiplied by themean light wavelength, and proved to be 6 mm. Af-ter removal of the filter, a picture typical for whitelight ~with an achromatic fringe in the center! wasobserved. When the OPD was changed within an;2-mm range the interference pattern disappeared:Both achromatic and colored fringes vanished.

The range resolution, ideally, is defined as r 5cyDn, where Dn is the spectral bandwidth of the ra-diation. In our experiment Dn was $20000 cm21, or,in frequency terms, Dn $ 6 3 1014 Hz, which yieldsr # 0.5 mm for the range resolution.

5. Possible Arrangement of the Pulse Interferometer

A specific peculiarity of using the interferenceschemes to implement the distance-multiplyingmethod with cw radiation sources is the application ofa multipath folded delay line as a reference arm of theinterferometer. Experience shows that it is thefolded delay line that creates the main difficulties inpractical design of an interferometer. The replace-ment of the cw radiation source by a picosecond laserallows us to use coaxial delay line ~CDL! in the ref-erence arm. A possible arrangement of such an in-terferometer is shown in Fig. 3.

The continuum radiation is collimated and directedto the two-beam interferometer where the continuumpulse is divided into two parts, one of which passes tothe distant mirror and the other to a reference armconstructed as CDL. The input mirror of the CDL is

Fig. 3. Schematic of the pulse interferometer: SPS, single-pulseselector; CCD, charge-coupled device; CDL, coaxial delay line; BS,beam splitter; M1, broadband high-reflecting mirrors; M2, broad-band mirror with a small optical transmission coefficient.

a spectrally broadband mirror with a small opticaltransmission coefficient, and the other mirror is fullyreflecting and can be moved, permitting the CDLlength to be adjusted.

The input mirror of the CDL surves also as theoutput mirror. The pulse of the continuum createsat the CDL output a sequence of decaying pulsesrepeated at equal time intervals. It is possible toadjust the interferometer such that one of thesepulses will coincide in time with the pulse comingfrom the distant mirror, and if this coincidence lieswithin the coherence time the pulses will interfere~the distant pulse must be attenuated in any suitableway to equalize the intensities of the interfering puls-es; that is a solvable technical problem!.

The optical length L of the distance to be measuredis

L 5 mln0,

where m is the number of passes of the pulse in theCDL, l is the distance between the CDL mirrors, andn0 is the refractive index of air in the CDL. The ln0value is the CDL optical length, which can be deter-mined, for instance, by a traditional displacement-measuring interferometer with a He–Ne laser ~we donot consider the technical details of this problemhere!.

6. Conclusion

A possible application of a spectral supercontinuumfor optical distance-multiplying interferometry hasbeen demonstrated. In continuum light we tuned atwo-beam interferometer to zero OPD. Visually theerror in equalizing of the interferometer arms seemedto be ;3 mm. For photoelectric detection and with a

more-precise mechanism to move the mirror, the er-ror mentioned can be decreased by more than anorder of magnitude. On the basis of the method in-vestigated, a possible scheme for a pulse distance-measuring interferometer has been suggested.

The investigations carried out encourage us to be-lieve that it should be possible to measure distancesinterferometrically by using ultrashort pulses. Thehigh energy of the supercontinuum pulses allows usto anticipate creation of extended ~1-km and more!metrological baselines of high accuracy by the opticaldistance-multiplying method in one step. The appli-cation of pulses instead of cw radiation may eliminatethe influence of atmospheric instability on the visi-bility of interference patterns.

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3. M. T. Prilepin, A. B. Sergejev, and S. E. Solodov, “A light sourcewith wide range of the coherency length tuning,” Izv. Vyssh.Uchebn. Zaved. Geod. Aerofotos’emka 3, 107–111 ~1984!.

4. B. K. Ward and K. Seta, “Quasi-monochromatic white lightfringe interferometer,” Appl. Opt. 30, 66–71 ~1991!.

5. M. T. Prilepin, A. N. Golubev, and A. S. Medovicov, “Interfero-metric methods for distance measuring in the study of recentcrustal movements,” Tectonophysics 52, 605–611 ~1979!.

6. K. Seta, S. Iwasaki, B. K. Ward, and T. O’Ishi, “Establishmentof a high accuracy baseline for EDM calibration in the NRLMtunnel,” J. Geod. Soc. Jpn. 38, 151–162 ~1992!.

7. R. R. Alfano and S. L. Shapiro, “Observation of self-phase mod-ulation and small scale filaments in liquids and glasses,” Phys.Rev. Lett. 24, 592–596 ~1970!.

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