High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser

Transcription

1 Hih-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser Kaoru Minoshima and Hirokazu Matsumoto A hih-accuracy optical distance meter with a mode-locked femtosecond laser is proposed for distance measurements in a 310-m-lon optical tunnel. We measured the phase shift of the optical beat component between lonitudinal modes of a mode-locked laser. A hih resolution of 50 m at 240-m distance was obtained without cyclic error correction. The roup refractive index of air is automatically extracted to an accuracy of 6 parts per million ppm by two-color measurement with the pulses of fundamental and second-harmonic wavelenths. Finally, an absolute mechanical distance of 240 m was obtained to within 8-ppm accuracy by use of a series of beat frequencies with the advantae of a wide rane of intermode frequency, toether with the results of the two-color measurement Optical Society of America OCIS codes: , , , Introduction Sinificant developments have been made with reard to the compactness, portability, and stability of femtosecond lasers. 1 These features are attractive for applications such as hih-accuracy distance measurements in open fields, which are necessary for many disciplines, for example, shape measurements of lare-scale structures such as buildins and parabolic antennae. An optical distance meter can be used for noncontact and hih-resolution measurements. 2,3 The phase measurement of a sinusoidally modulated cw laser has been used because a phase shift with hih resolution can be measured. Interferometric methods are not suitable for these applications because they are for displacement measurements between two points and require continuously delayed movement. Several methods have been proposed to obtain modulated waves, for example, external modulation with an electro-optic modulator, 4 direct modulation of a laser diode, or use of the internal mode beat of a He Ne laser. 5,6 Up to now, the hihest resolution, that is, several micrometers over a 100-m distance, has been realized by use The authors are with the National Research Laboratory of Metroloy, Umezono, Tsukuba, Ibaraki , Japan. The address for K. Minoshima is mino@nrlm.o.jp. Received 29 November 1999; revised manuscript received 14 July $ Optical Society of America of 28-GHz modulation with the method outlined in Ref. 4. However, with methods that use a modulator, the correction of cyclic error 2 is necessary before such hih resolution can be achieved. The main sources of cyclic error are electrical crosstalk that oriinates from the modulator and the internal optical multipath that is due to the complexity of the setup. Use of the mode beat of a laser is a method by which one can suppress the cyclic error. 5,6 Because a femtosecond mode-locked laser has a wide rane and a lare number of stable optical frequency modes, a frequency beat hiher than in the iahertz rane can be easily utilized with hih stability. Here we propose a hih-accuracy optical distance meter with a mode-locked femtosecond laser, without the necessity for cyclic error correction and with the advantaes of two-color measurement, absolute distance measurement, and use of a broad spectrum, as described in Section 2. The femtosecond distance meter is applied to distance measurements in a 310-m-lon optical tunnel. 2. Principle of the Method For the time domain we used a femtosecond modelocked optical pulse train that contains pulses with temporal widths FWHM of 180 fs and 20-ns repetition rate. In contrast, for the frequency domain, optical frequency modes appear every 50 MHz over 2 THz FWHM. The intermode beats between all possible pairs provide a wide rane of stable electric frequency components if the pulse train is detected by 5512 APPLIED OPTICS Vol. 39, No October 2000

2 Fi. 1. Stability of the repetition rate of the mode-locked fiber laser that we used for this study second-harmonic wavelenth, which was evaluated by the square root of Allan variance. a photoelectronic detector. In this case, the beat frequency covers the rane from 50 MHz to the terahertz reion when a detection method is available. For stability we used the square root of Allan variance 7 for evaluation, which has been widely used to evaluate the stability of cw lasers. Fiure 1 shows the Allan variance of the repetition frequency of the mode-locked laser that is used in this study. The 1-GHz difference of the 20th harmonic of the laser repetition frequency from a reference synthesizer with stability was enerated by a doublebalanced mixer and was measured by a frequency counter. The sinal of the Rb frequency standard was used as a reference sinal for the frequency counter. The frequencies were sampled ten times durin each ate time. By chanin the ate time from 0.01 to 1000 s, we calculated the Allan variances. We determined that stability is in the rane of 10 9 in the short term 1 s and 10 7 in the lon term 1000 s ; the latter depends on environmental stability such as temperature. In other words, a femtosecond mode-locked laser is equivalent to a series of wide-ranin and stable-modulated cw optical waves, and it is attractive for distance measurements by use of the phase of a modulated optical wave. Here we consider that a modulated optical wave propaates at a distance D and returns to the detector at its oriinal position. Then the phase of the wave is measured relative to the oriinal wave. We obtained the distance by usin the measured phase from N 2 2fn D. (1) c Here N is the inteer part of the phase, c is the speed of liht, f is the beat frequency used for measurement, and n is the roup refractive index at the optical wavelenth. The factor of 2 on the riht-hand side of Eq. 1 is necessary because the liht makes a round trip. The femtosecond distance meter has several advantaes over conventional methods that use a cw laser. First, a series of intermode beats in a wide frequency rane is available. As a result, a small amount of cyclic error is expected because the optical and electrical setups are simple. Moreover, the wide-ranin frequency components up to hih frequencies can easily be utilized for the measurements. Hih frequency is required for hih resolution because the phase resolution enerally limits the measurement and hiher frequency results in a smaller distance for the same phase value. Selectable frequency is required to determine the absolute distance, without continuous scannin, which means without ambiuity of the inteer term N in Eq. 1,as is demonstrated in Subsection 4.C. Second, hih peak power is attractive for utilization of optical nonlinear effects. For this study we performed twocolor measurements by usin the second-harmonic eneration to realize self-correction of the environmental conditions such as temperature and pressure of air Subsection 4.B. 3,8 Two-color measurement is a powerful tool because it is not subject to precise estimation of the environmental parameters of air, which is the most serious problem in lon-distance measurements because they can vary in time and space. Finally, a broad optical spectrum of the pulse, such as reater than 4 nm FWHM, has the advantae of insensitivity to sharp absorption lines of a small amount of as in air, because absorption lines can result in severe measurement errors by use of a narrow line laser when their wavelenths coincide. 3. Experimental The measurements were performed in the optical tunnel of the National Research Laboratory of Metroloy, which is a 310-m-lon semiunderround tunnel covered by soil. It has two 50-m movin carriaes and calibrated base points every 50 m up to 310 m. The temperature is stable to within 2 C year round, which makes it suitable for evaluation of the new distance meter. We performed two kinds of experiment, one-color Subsection 4.A and two-color Subsection 4.B measurements. The experimental setups are shown in Fis. 2 and 3. The liht source is a femtosecond mode-locked fiber laser Femtolite-780, IMRA America, Inc.. The dimensions of the laser head are 193 mm 109 mm 82 mm and it is equipped with a handheld electronic controller. The compactness of the laser makes it suitable for practical distance measurements in open fields. The laser enerates two coaxial beams of the fundamental and second 2 harmonic with center wavelenths of approximately 1560 and 780 nm. Both beams have 180-fs temporal width, 50-MHz repetition rate f rep, and 10-mW averae power. For the first one-color measurement experiment Fi. 2, only the 2 beam was used. The beam was divided into two: one was detected by the photodetector PD2 and the other was used as the reference. The reference beam was expanded to a diameter of 100 mm by a pair of curved mirrors CM1 and CM2, it propaated to a 240-m distance into the tunnel, was reflected by mirrors M1 and M2, 20 October 2000 Vol. 39, No. 30 APPLIED OPTICS 5513

3 Fi. 2. Experimental setup for the hih-accuracy distance meter with the intermode beats of a femtosecond mode-locked laser. The laser source enerates both fundamental and secondharmonic 2 beams. Here only 2 is used. PD, photodetector; L, lens; M, reflectin mirror; CR, corner reflector; BS, beam splitter; DM, dichroic mirror; CM, curved mirror; S, beam stopper;, phase difference between probe and reference. and then returned to the delay line. A He Ne laser beam was coaxially propaated for alinment purposes. The probe beam was detected by the photodetector PD1 after it passed the scannin optical delay line. The phase difference between the reference and the probe waves at specified electric frequency f was measured by a phasemeter vector voltmeter HP8508A. To evaluate the distance meter, we measured the phase shift by varyin the optical delay, althouh scannin was not necessary for the actual measurement. The scannin lenth was calibrated in nanometer resolution with an optical interferometer HP5500C. We carried out the main measurement near f 1 GHz, which is the 19th harmonic of f rep, and the results obtained at f rep approximately 50 MHz and 2f rep were also used for the absolute distance measurement described in Subsection 4.C. In this case, because the sinal includes a wide rane of frequency components, we selected the specified frequency components to be measured by usin the variablefrequency bandpass filters in the phasemeter. Althouh the bandpass filters do not have sharp passbands, the reference sinal selects the frequency component with the hihest intensity in the selected rane. To select a 19th harmonic component, we used a photodetector that ives a local maximum near 1 GHz for the frequency response. For measurements with f f rep and 2f rep, we used a narrow bandpass filter to select the frequencies. The frequency selection is reliable except when there is no liht. The value of the beat frequency f is extracted by the measurement of the phase for a full cycle when the optical delay is varied. In this case, the precise measurement of the cycle is not necessary because the frequency should be the harmonic of the fundamental repetition rate of the mode-locked pulse train f rep, which was measured by a hih-precision frequency counter. The stability of the beat frequency is 10 7 throuhout the measurement. Next, two-color measurement for self-correction of the roup refractive index of air was performed, as described in Subsection 4.B. The setup shown in Fi. 3 is similar to the one in Fi. 2, except that we used beams of both and 2 and took two measurements for both 0- and 240-m distances. The beams of both colors, which expand by use of CM1 and CM2, propaate up to 240 m into the tunnel, are reflected back, and are used for the 240-m distance measurement. Spatially, a part of the beam is blocked by reflective mirror M2, and reflected beams are used for the 0-m distance measurement. The other beams are blocked by beam stopper S1 or S2. For each measurement, probe beams contain both and 2 beams, which are separated by a dichroic mirror DM and are detected by PD1 and PD2. The reference detector PD3 responds only to 2. We obtained four kinds of phase difference from the references, which were measured at 0- and 240-m distances for both twocolor and 2 beams. We scanned the delay line once in advance to confirm the modulation frequency, but this scannin is not necessary for an actual measurement of the distance. 4. Results and Discussions Fi. 3. Experimental setup for two-color measurement for selfcorrection of the roup refractive index of air in the distance meter by use of the intermode beats of a femtosecond mode-locked laser. We used the pulses of two wavelenths. The abbreviations mean the same as in Fi. 2. Mirror M2 spatially reflects a portion of the beams. When the measurement is taken for 0-m propaation, the lon travelin beams are blocked by S2. In contrast, for 240-m propaation, the beam that is partially reflected by M2 is blocked by S1. A. Hih-Resolution Distance Measurement with a One-Color Setup First we measured the phase for the 240-m distance by usin the one-color setup. To evaluate the resolution, we added a small displacement to the 240-m distance by continuously scannin the optical delay line. Fiure 4 shows the result of the displacement D, which was calculated with Eq. 1 from the measured phase shift at f GHz 19th harmonic of f rep. The roup refractive index of air n is calculated by n n p np, (2) where n and n p are the roup and the phase refractive indices of air at wavelenth. Here, the 5514 APPLIED OPTICS Vol. 39, No October 2000

4 Table 1. Linear Fittin Results of the Phases by Two-Color Measurements Phase 0 de Standard Deviation of 0 Slope a.u. Standard Deviation of Slope Fi. 4. Results of the phase measurement crosses when the delay line was scanned. The displacement represents a chane from the 240-m distance. The residual nonlinearity after linear fittin is also shown solid curve. Standard deviation of the nonlinearity is 50 m without cyclic error. phase refractive index of air n p was estimated by use of Edlén formulas 9 with environmental parameters such as temperature, pressure, and humidity. Because our purpose is to evaluate the resolution, which is how a small displacement is measured when it is applied to a lon distance of 240 m, it is not necessary to determine n with as hih an accuracy as the measurement described in Subsection 4.B. The measured displacement D clearly shows a linear relationship with the applied displacement, which we measured with an optical interferometer. Because the linear chane of D is expected for linear scannin, the residual nonlinearity after a linear fit is also shown. Scannin was carried out at 500 mm, resultin in a phase chane of 3.3 cycles at the modulation frequency of 19f rep to clarify the contribution of cyclic error. Therefore, if cyclic error exists, the residual components should show a sinusoidal dependence at 19f rep or hiher harmonics. Here we did not observe a cyclic error of reater than 0.1 de standard deviation, which is the same order of nonlinearity as for the phasemeter. In conventional methods, cyclic error can reach several derees for similar measurements. This result ives a small nonlinear error in distance, that is, a 50- m standard deviation, without any correction, because of the simplicity of the setup in which there is no modulator. With our method we can achieve resolution of the 240-m distance. Moreover, when we take into account that a practical distance meter adopts time averain of the sinal, such as for 1 s, whereas each datum is taken every 10 ms, our system potentially ives very hih resolution of less than 10 m without any correction. In the experiment, because the frequency stability can reach 10 9 in1s, the resolution in distance measurement is limited by the resolution in phase measurement. Therefore, in future study, hiher resolution in distance is expected throuh the use of hiher frequency components, even with the same phase resolution. B. Two-Color Measurement for Self-Correction of the Group Refractive Index of Air Next we performed the two-color measurement with the setup described in Fi. 3. Experimentally, the four kinds of phase shift from references 0, 240, 0 2, and are measured at distances of 0 and 240 m for the two-color beams of and 2. The interestin value here is the difference amon the four phases, which is defined as (3) Durin measurement of the phases, we observed a drift of the phase value of the order of 1 de, which could have been caused by thermal instability in the phasemeter. To subtract the effect of drift, five sets of measurements of four different phases 0, 240, 0 2, and were collected with equal time intervals between each measurement. When we plotted the time for each set of five values for the same phase, four plots were obtained. Because all the plots show similar linear behavior, we performed linear fittin. Table 1 lists the results of the fittin, which includes the slopes and the intercepts 0, toether with their errors for the same units. All four plots have the same slope values; thus we concluded that the drift is of the same oriin, which supports the validity of drift cancellation by linear fittin. Finally, by usin the phase values of the intercept and Eq. 3, we obtained de standard deviation. In contrast, usin Eq. 1 yields n 2 Df c. (4) Here, n 2 is the difference in roup refractive index of air between and 2 n 2 n 2 n. Usin Eq. 4 and the measured value of de, the approximate value of mechanical distance D m and f GHz, we calculated n 2 to be Here we consider the effect of beam shift between and 2, which can be caused by imperfect beam overlap after second-harmonic eneration. The beam shift can be sinificant after lon beam propaation, which creates the path difference between the two beams in the lens in front of the de- 20 October 2000 Vol. 39, No. 30 APPLIED OPTICS 5515

5 tectors. Because the refractive-index difference of lass is , which is much larer than that of 10 5 for air, the beam shift could cause an error in the estimation of the refractive index of air in the twocolor measurement. Here, by usin the result of a preliminary measurement, we were able to estimate a beam shift of approximately 50 mm at the surface of the plano convex lens with 100-mm diameter and 300-mm focal lenth. Then the path-lenth difference in lass can be estimated as 4 mm by eometric considerations. The optical path difference of twocolor beams was obtained as mm by use of the refractive-index difference of BK7 lass. Because the total measurement lenth in air is 480 m for a round trip, the optical path difference of mm ives an error of in the measurement of n 2 of air. Finally, by addin an error of the order of , we obtained n 2 of air as by use of the two-color measurement procedure. Here we can assume that the A coefficient of the roup refractive index of air that is determined by Eq. 5 is constant because the dispersion relation of the refractive index does not chane within the practical conditions 10 : A n 2 1. (5) n 2 We estimated the variation of the A coefficient throuh calculations under different conditions of air usin Edlén s formulas for the phase refractive index of air 9 and Eq. 2. Even when the variations of temperature, pressure, and humidity are 10 K, 20 hpa, and 20%, respectively, which occur under extreme conditions, the value of A remains at 47.8 with a variation of 0.6%. Then the roup refractive index for the secondharmonic wavelenth n 2 was obtained as Eq. 6 by use of the values of n 2 and A. We simultaneously estimated n 2 with Eq. 7 and Edlén s for- mulas with the values of temperature, pressure, and humidity of air measured at specified positions in the tunnel: n 2 1 experiment , (6) n 2 1 Edlén (7) The uncertainty in Eq. 7 is estimated when the variations of temperature, pressure, and humidity are 2 K, 10 hpa, and 10%, respectively, takin into account variations of the environmental parameters in space alon the optical path and eventually durin all the measurements. The values of the refractive indices in Eqs. 6 and 7 aree with 6 ppm parts per million, which confirms the applicability of the proposed method. Here we note that the value in Eq. 6 was obtained without any assumptions with reard to environmental conditions such as temperature, pressure, or humidity, whereas it was necessary for us to assume the values to obtain the estimated value in Eq. 7. C. Absolute Mechanical Distance Measurement Finally, we obtained the absolute mechanical distance usin one-color measurements at f rep and 2f rep, toether with the results of the two-color measurements outlined in Subsection 4.B. Absolute distance is without ambiuity of inteer N in Eq. 1, and the mechanical distance is without ambiuity of the refractive index of air. The process to obtain these parameters is as follows. First, we measured the phase difference between 0 and 240 m usin a onecolor beam at f f rep and 2f rep. By mechanical measurement to within 1 m, we determined the approximate distance to be D m, and the equivalent wavelenth of the modulation optical wave at f rep is approximately 3 m for a round trip, which is reater than the uncertainty of D. Therefore the absolute distance is D and m for f f rep and 2f rep, respectively. The discrepancy oriinates from the drift of the phase of the order of 1 de, which ives an error of 0.01 m. Here the roup refractive index is used to calculate the mechanical distance, but 100-ppm accuracy is enouh to extract the distance to within an error of 0.01 m; thus, detailed information about the environmental condition is not necessary. In summary, we obtained the absolute mechanical distance of D m usin a one-color beam at f f rep and 2f rep. 240 Next, by use of the phase difference between 2 and 0 2, toether with the experimental value of n 2 Eq. 6, all of which were obtained by two-color measurement at f GHz in Subsection 4.B, we extracted the absolute mechanical distance because the equivalent wavelenth of the modulated wave is approximately 150 mm, and we determined D to within 10-mm accuracy throuh previous measurements taken with f rep and 2f rep. Finally, we obtained D m to within 8-ppm accuracy. Note that the absolute distance was obtained without continuous scannin of the entire 240- m-lon optical path because of the above-mentioned step-by-step measurements with the selectable frequency components in the mode-locked pulse laser. Moreover, by takin advantae of the two-color measurement, we were able to extract the mechanical distance without assumin environmental conditions such as temperature and pressure, which can vary temporally and even spatially alon the optical path. 5. Conclusions We have developed a hih-accuracy distance meter usin the phase measurement of intermode beat components of a femtosecond mode-locked pulse train. The instrument can be used to measure a distance of 240 m with a hih resolution of 50 m without any correction of the cyclic error. The distance measurement taken with two-color pulses self-corrects environmental conditions such as temperature and pressure of air, enablin the roup refractive index of air to be obtained to within 6-ppm accuracy. A series of mea APPLIED OPTICS Vol. 39, No October 2000

6 surements with various beat frequencies provides absolute distance measurements without the need for continuous scannin to determine the inteer part in phase. Finally, we obtained the absolute mechanical distance of 240 m with 8-ppm accuracy only by use of a series of femtosecond distance measurements. In the future, it will be possible to achieve hiher resolution by use of hiher frequency components that already exist in the laser source. One can expect micrometer resolution by usin a 10-GHz component. We thank Takeshi Yasui of Osaka University for helpin us to create Fi. 1. K. Minoshima thanks Katuo Seta and Ichiro Fujima for the informative discussions and for supplyin the experimental equipment. This research is supported by the desinated research project for Femtosecond Technoloy, Industrial Science and Technoloy Frontier Proram, Aency of Industrial Science and Technoloy, Ministry of International Trade and Industry, Japan. References 1. M. E. Fermann, A. Galvanauskas, G. Sucha, and D. Harter, Fiber lasers for ultrafast optics, J. Appl. Phys. B 65, J. Rueer, Electronic Distance Measurement Spriner-Verla, New York, P. Bender, Laser measurements of lon distances, Proc. IEEE 55, I. Fujima, S. Iwasaki, and K. Seta, Hih-resolution distance meter usin optical intensity modulation at 28 GHz, Meas. Sci. Technol. 9, K. Seta, T. Oh ishi, and S. Seino, Optical distance measurement usin inter-mode beat of laser, Jpn. J. Appl. Phys. 24, R. Balhorn, F. Lebovsky, and D. Ullrich, Untersuchunen zur Entfermunsmessun mit Stabilisierten Zweifrequenzlasern, Technical Report Physikalisch-Technischen Bundesanstalt Jahresbericht, Braunschwei, Germany, 1974, pp D. Allan, Statistics of atomic frequency standards, Proc. IEEE 54, K. E. Im, C. S. Gardner, J. B. Abshire, and J. F. McGarry, Experimental evaluation of the performance of pulsed twocolor laser-ranin systems, J. Opt. Soc. Am. A 4, R. Muijlwijk, Update of the Edlen formulae for the refractive index of air, Metroloia 25, P. Bender and J. Owens, Correction of optical distance measurements for the fluctuatin atmospheric index of refraction, J. Geophys. Res. 70, October 2000 Vol. 39, No. 30 APPLIED OPTICS 5517