Simple optical distance meter using an intermodebeat modulation of a HeNe laserand an electricalheterodyne techniqueTsutomu Araki, Shuko Yokoyama, and Norihito Suzuki Citation: Review of Scientific Instruments 65, 1883 (1994); doi: 10.1063/1.1144837 View online: http://dx.doi.org/10.1063/1.1144837 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/65/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Self-heterodyne mixing method of two inter-mode beat frequencies for frequency stabilization of a three-mode He-Ne laser AIP Advances 2, 022170 (2012); 10.1063/1.4733344 Distance measurement method using the two intermode beat frequencies of a three-longitudinal modeHe–Ne laser Rev. Sci. Instrum. 68, 4612 (1997); 10.1063/1.1148442 A very simple stabilized singlemode He–Ne laser for student laboratories and wave meters Am. J. Phys. 58, 878 (1990); 10.1119/1.16354 Method for Measuring Small Optical Losses Using a He–Ne Laser Rev. Sci. Instrum. 39, 583 (1968); 10.1063/1.1683436 Optical Crystallographic Orientation Determination Using a HeNe Gas Laser Rev. Sci. Instrum. 36, 1668 (1965); 10.1063/1.1719436

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Simple optical distance meter using an intermode-beat modulation e-Ne Baser and an electrical-heterodyne technique

Tsutomu Araki Department of Mechanical Engineering, University of Tokushitna, Jousanjima, Tokushima 770, Japan

Shuko Yokoyama IDEC Izumi Co., Mikuni Honmachi, Osaka 532, Japan

Norihito Suzuki Department of Precision Engineering, Osaka Electra Communication University, Neyagawa 572, Japan

(Received 29 November 1993; accepted for publication 24 February 1994)

A phase measurement distance meter has been devised using a frequency-stabilized intermode optical beat generated from a two-mode He-he laser (14-cm-long cavity) and a conventional phase meter. The beat frequency (1096 MHz) is stabilized to within 1 kHz fluctuation by a feedback control system. This frequency was converted to an electrical signal and reduced to 6 MHz by a rf-heterodyne technique in order to match the best frequency response range of the phase meter. Experimental results show that the total distance error of the optical distance meter due to the frequency fluctuation of the laser and the performance of the phase meter is 1 and 19 pm, respectively, for a mirror target located 1 m away from the laser source. Further improvement in the resolution is possible if a better phase meter is used.

I. INTRODUCTION

An optical distance meter based on phase-shift measure- ments of sinusoidally modulated light beam requires a light beam with good modulation waveform and high modulation frequency characteristics to obtain precise measurements. From among the various techniques aimed at generating a high-frequency modulated light beam, a method based on using an optical modulator (such as an AOM) is widely em- ployed. However, this method causes unexpected distortion of the modulation waveform, especially at high frequency near the -1 GHz range. Another method is based on direct current modulation of a laser diode. Although this method is simple and attractive, it also introduces waveform distortion and decreases the depth of modulation of the optical signal as the modulation frequency is increased.

Recently, an alternative method based on intermode op- tical beat of a gas laser has been proposed.’ Compared with the two above-mentioned methods, this approach is attractive because an optical beat signal having a modulation fre- quency of around several hundreds of MHz and a 100% depth of modulation is easily attainable. The potential of an optical distance meter utilizing the intermode beat light has been demonstrated by Seta and O’ishi.’ However, the reso- lution of this new method is limited by two factors, namely, (1) the frequency stability of the optical beat signal and (2) the frequency response of the phase meter. Although the polarization-stabilized two-frequency 1aserZe5 is commonly used as a light source to generate an optical beat signal, this laser source has an average frequency fluctuation of around 50 kHz and a typical beat frequency of about 0.6 GHz (25 cm cavity).” Assuming that an ideal phase meter is used, this frequency fluctuation introduces an -10 ,um ambiguity in the measurement for every 2~ phase change.

With regards to the phase meter, its frequency response is strongly limited to a certain frequency band range and has a cut-off frequency lower than 1 GHz. Furthermore, the ac-

curacy of the phase meter decreases as the frequency of the detected signal is increased. A typical phase meter (Hewlett Packard vector meter) has a favorable frequency response in the l-100 MHz range. These conditions entail two important points, namely, (1) the reduction of the modulation frequency to within the best frequency response range of the phase meter and (2) the stabilization of the intermode beat signal to the highest possible level, in order to realize a practical, high precision distance meter.

Previously we proposed and demonstrated a new frequency-stabilization technique for two-mode laser source6 using the frequency pulling effect. To stabilize the lasing frequency, the intermode beat frequency was “locked” at a certain value using an rf-heterodyne technique. The frequency-stability performance of this laser system is supe- rior compared with that of the polarization-stabilized two- frequency laser. Since this laser provides both stable lasing frequency and highly stable intermode beat light, the pro- posed laser system can be employed directly for optical dis- tance meter application.

In this paper, the design of an optical distance meter using this proposed frequency-stabilized two-mode laser as light source and an electrical heterodyne technique for signal processing is described. The distance error caused by the fluctuation of the laser beat frequency is only 1 pm while the error due to the phase meter is 19 ,um for the measurement of 1 m distance.

II. PRINCIPLE

A. Optical modulation of the laser beam

Suppose a laser emits two longitudinal modes at fre- quencies vI and v,, as shown in Fig. l(a), then the electric fields E of these two modes are expressed as

E,=A1 exp(2dvlt), E,=A, exp(2kv2t), (1)

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iv1 pulling :

+ w

(b) fly )v

FIG. 1. Schematic diagram of (a) the generation of an intermode optical beat synthesized from the two longitudinal modes present in the laser gain curve, (b) the effect of frequency pulling on the longitudinal modes, and (cj the curve showing the degree of the pulling (v, - u;) with respect to reso- nance frequency v~.

where A is the amplitude of the electric field of each mode. For an internal mirror He-Ne laser (h=632.8 nm), these two modes have linear polarization and are orthogonal. If a 45” polarizer is inserted into the path of the beam, El and E, interfere and generate a-modulated field (E,) given as

E,=EI cos 45”~tE, sin 45”. 0)

If the light is incident on a fast photodiode, the detected intensity is then given as

I,=E,E;=A;+A;+2A,Az cos 27r(vl- vz)t, (3)

where Ez is the complex conjugate of E,. Equation (3) clearly shows that the intensity is modulated sinusoidally at the differential frequency of the two modes. In the case when A; is equal to A,, a 100% depth of the modulation can be attained and the resultant output is expressed as

I,=R(l +cos 2n-fmt), (4)

where f,,, = vl - ~a and R = 2A 1A 2. The value of the modula- tion frequency f, is approximately given by

fm=c/2L, (5) where c is the velocity of light in the laser cavity and L is the length of the laser cavity.

B. Frequency stabilization of the optical modulation

Theoretically the resonance frequency of a laser (v,) is given by the phase condition

nc

expand t--------) shrink

CAVITY LENGTH

FIG. 2. Relation between the intermode optical beat frequency and the change in laser cavity length.

where n is the order of resonance frequency. However, in the real laser system, the actual oscillation mode frequency (VA) deviates from the resonance frequency (v,). The rela- tionship between these frequencies v,, and VA is given by

V,:=v,+(vo-V,,) 2) where tiv,) is the laser gain curve, v. is the center frequency of the gain curve, and Av is the half width value of the gain curve. As illustrated in Fig. l(b), the two resonance frequen- cies vr and u, experienced a “pull” toward the center of the gain curve and lase at frequencies V; and v;. This phenom- . enon is called “frequency pulling.” The’ degree of pulling depends on the standing position’of the mode in the cavity gain curve as shown in Fig.l(c). The amount of the deviation from the resonance frequency decreases as the oscillation mode gets closer to the center of the gain curve. This curve of the deviation (v, - VA) corresponds to the dispersion. This pulling effect leads to an optical beat frequency (f,) that changes periodically through every X/2 cavity length expan- sion of a two-mode laser. However, this simple periodic re- lation between the intermode-beat frequency and the cavity length is not observed due to an isotope effect. Such distor- tion causes extraordinary pullings that complicate the rela- tion between the beat frequency (f,) and the cavity length as shown in Fig. 2. Nevertheless, using the smooth slope por- tion of this curve, the optical beat frequency can be locked at a certain value through the control of the cavity length of the laser with an appropriate servo-control system.

C. Heterodyne signal processing for frequency reduction

The reduction of the beat frequency (normally near -1 GHz) is necessary due to the limited frequency response range of the phase meter. This reduction is accomplished by an electrical heterodyne technique as shown schematically in Fig. .3. Here, the objective signal [amplitude: R, frequency: f,, phase component: C/J(X)] is multiplied with a stable os- cillation signal (amplitude: K, frequency: fo) to generate a heterodyne beat signal given as

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21 LPF 1 b f#o> fm- f, 3 44x>

FIG. 3. Schematic diagram of the electrical heterodyne method used to reduce the detected beat frequency and facilitate signal processing.

{R cos[2rf,,$t 4(x)]}[K cos 2?Tf,t]

=0.5RK{cos[2mfat+ g&x)]

+co$2rfbt+ 4Cx>lI, (8) where f,=f,,,-fo, and fb=fm+fo. For our intended appli- cation, the analytical phase component 4-x) contains impor- tant information regarding the phase difference between the reference beam and the reflection beam. Equation (8) indi- cates that &z) can be retained in the heterodyned beat signal (f,) even after the high-frequency component (fb) is tlt:red out. This heterodyned beat frequency (f,) can be se at a

4 favorable value by adjusting the oscillator’s frequency? 5 o) in order to correspond to the best possible frequency response range of the phase meter.

Iii. EXPERIMENTAL

A. Frequency stabilization system of the modulated light

The basic idea of the frequency-stabilization method is to lock the intermode-beat frequency at a certain value by actively controlling the length of the laser cavity using the relation between optical beat frequency (f,) and cavity length (shown in Fig. 2). The block diagram of the frequency stabilization system is shown in Fig. 4. A two-mode He-Ne laser (X=632.8 nm) having a 14 cm cavity length is used as light source. The laser beam emitted from the front side of the cavity is used as probe beam for optical distance meter while the beam emitted from the back side is employed for

DBM I I n”dn.Y.

PL

-I ‘Jm‘J Lo’

ator I

I I

FIG. 4. Block diagram of the system for frequency stabilization of the intermode optical beat. PL, polarizer; APD, avalanche photodiode; DBM, double-balanced mixer; DPX, diplexer.

frequency stabilization. After passing through a 45” polar- izer, the electric fields of the two modes (coming from the left side of the cavity) interfered to generate the intensity modulated light signal (f, = 1096 MHz). The modulated light is then directed into an avalanche photodiode (APD, NEC NDL-1102, bandwidth=l.ti GHz) to obtain electrically the optical beat frequency. This beat signal is then amplified using a video-amplifier (Kuranishi WA-200H, gain 20 dB) before it is mixed with a local oscillator signa (frequency, fLO) using a double-balanced mixer (DBM: R&K M-13). The output from the mixer (intermediate frequency, IF) pro- vided the necessary signal to monitor the changes in the optical beat frequency.

It was necessary to select the value of the local oscillator frequency fLO to be as close as possible to the frequency f, to facilitate the.signal processing of the objective signal com- ponent (frequency: f, - fLO) of IF output. To eliminate the image signal component (frequency: f, + fLo) of IF output, the IF signal is passed through a diplexer’(DPX) which is made up of L-C ladder filters (combination of -24 dB/oct. low-pass and high-pass filters, cut:off frequency: 10 MHz). The output signal (objective frequency: f, - fm) from the DPX is compared with a reference signal (frequency: f, ; synthesized quartz oscillator) to obtain the differential signal (frequency: fd= f,,, - fLo-f,). Then, the frequency compo- nent of the differential signal is converted to a voltage level signal by a FV converter. This voltage signal is amplified and used to control the current of the heater that is wound around the laser tube. Thus, the feedback control loop is formed. The FV converter is composed of two integrators of ‘different time constant; main integrator with ,3 ms time const. and secondary integrator with 2 min time const. The change in the frequency fd is converted to voltage change by the main integrator. In order to lock fd independently of the surround- ing temperature, the secondary integrator is interpolated into the main integrator circuit. The secondary integrator func- tions after the completion of the main feedback control. This integrator shifts a bias voltage of the heater current control- ler. Thus, the cavity length is controlled continuously so that the value of fh is kept at 0 ,Hz. .This feedback control system stabilized the frequency of the intermode beat signal.

B. Distance meter

The block diagram of the optical system for distance measurement is shown in Fig. 5(a), while the electronic pro- cessing system is depicted in Fig. 5(b). The laser’ beam passes through a polarizer before it is divided by a beam splitter (BS) into a reference beam and a probe’ beam. The reference beam is directed into the photodetector’ (APD-1) while the probe beam travels toward a reflective target posi- tioned 1 m away from BS. After being reflected from’the target, the probe beam travels back toward the BS and is detected by a photodetector (APD-2).

The electrical signals from’these two photodetectors are processed by an electrical heterodyne system to extract the phase difference between the reference and the probe beams as shown in Fig. 5(b). Initially, these signals are amplified by video-amplifiers (Amp. 1: Kuranishi WA-200H, Amp. ~/KU- ranishi WA-300H, gain 30 dB) and then filtered by bandpass

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(a> PL

movement -500 0 soopm

I s ‘--c-3( ; : ; ’

t Moving Stage

APD-1 X=lm

09 Video ATT DBM

APD-1 (refere

FIG. 5. Block diagrams of (aj the optical system for distance meter and (b) the electrical components for heterodyne signal detection. BS, beam splitter; CML. collimator lerts; BPF, band-pass filter; ATT, attenuator; TP, test point.

filters to pass selectively the 1096 MHz component of the signals. After the attenuation of the objective rf signal to a favorable intensity, the rf signal is mixed with a local oscil- lator output (TDK, variable 1076-2000 MHz) using DEM. To eliminate the image signal component, the IF output is filtered by DPX in the same manner as in the frequency- stabilization control system of the laser. Finally, the phases of the two beat signals from the two DPX outputs are com- pared by a phase meter (HP-8508A vector volt meter, reso- lution of O.OlO).

The measurement distancC error (Ax) is obtained by

where X, is the wavelength of the modulation light (= c/f,) and Ap is the observed phase error (degj. The value of Ap depends on two factors, (1) instability of the modulation fre- quency and (2) that of the phase meter as

where x is the actual distance, s is instability of the modula- tion frequency, and Ar is the uncertainty of the phase meter (deg). Since the phase meter used in this experiment shows a maximum phase resolution at input frequency between l’and 100 MHz, the output frequency of the local oscillator (fLo) was set at 1090 MHz to obtain a heterodyned beat frequency of 6 MHz. At this frequency, uncertainty smaller than 0.05” is assured (manufacture catalogue, short-term value). This value corresponds to an approximate distance error of 19

- 170

- 80 $i

c- TIME 1 1 min / division ]

FIG. 6. The differential beat frequency during free-running and stabilized operations of the laser. The start of the stabilized operation is indicated by the “ON” position.

,um, since A, is 27.4 cm. Due to temperature drift in practi- cal experiment, the actual resolution may be slightly lower than the given value.

‘Itvo types of reflective target were used: (1) corner cube mirror and (2) plate reflector (“Reflexite”). These targets were set on a moving stage (positional resolution: 5 pm) 1 m away from the beam splitter. The targets were moved con- tinuously in a stepwise manner with an increment of 50 pm per step (step-to-step time interval: 10 s). With such a move- ment, the expected phase readout should change at the rate of O.l3”/step. The optics components including the laser source were placed on an air-suspended bench inside a temperature regulated room. During the whole period of measurement, the temperature drift was measured to be within 0.1 “C.

IV. RESULT AND DISCUSSION

A. Frequency stability of the laser optical beat

The stability of light modulation frequency (f,) is one important criterion of any laser source for optical distance meter application. The frequency fluctuation for free-running and stabilized operations of the proposed laser system is shown in Fig. 6, where the recording signal is picked up at output of the FV converter. This output voltage corresponds to the value of the differential frequency fd . This figure in- dicates that during free-running operation, the optical beat, frequency changes periodically within the range of O-170 kHz due to frequency pulling. The frequency fluctuation de- creases immediately after the control switch is turned on as indicated by the “ON” position in the figure. Analysis of experimental data confirms that the resultant fluctuation of the frequency f,,, is within the range of 500 HZ-l kHz (fre- quency instability: s = 1X1 Om6) which corresponds to a wavelength change of 0.15-0.3 ,um for 27 cm modulation wavelength. The actual value of the fluctuation also depends on the quality of the electrical servo system including the quartz oscillator.

To evaluate the performance of the present laser, the optical beat signals generated from a typical polarization sta- bilized two-mode laser and the present laser are compared. The beat frequency fluctuation of a polarization-stabilized

1886 Rev. Sci. Instrum., Vol. 65, No. 6, June 1994 Optical distance meter

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T I i :

: f f : ! j t

,~. ._ . . . . ;“.rs; ..I_” .“.“. a: .,- ;

I I A :

+J.@g& I’\

.” ..i, . ,j ” I-. , .p!.. .p.&

.- -1.: ;+l.i ..L. !I% -. :‘..L ! _ 1 !:I ., ;

I I I I I I I

- TIME [ 1 rnin / division]

1

:

m-

g

10

OS G

10 3 CY

I3

40

FIG. 7. Fluctuation of the heterodyned beat frequency generated from a polarization-stabilized laser system.

laser is shown in Fig. 7, indicating that the frequency changes over 50 kHz (.~=5xlO-~). This fluctuation corre- sponds to a change of the modulation wavelength by 14 ,um. Thus, the stability of the beat signal from the proposed laser system is two decades superior to that from the polarization- stabilized laser.

B. Distance measurement

In order to test the accuracy of the present distance meter, the measured phase error is plotted with respect to the target displacement, Reproducibility of the distance measure- ment was checked by programming the stage movement as

__,_ -j-i--F.“..“;--r -___._-_.. - .-...--,--.

-2 : I I I I 1 I -5Kl 0 500 0 -5co 0 XXI

Target Displacement (pm)

8 o ?z

-ii -O-l

8 E

-0.2 -500 -250 0 250 500

Target Displacement (pm)

PIG. 8. Results of distance measurement with a corner cube mirror as target. The phase measurement with respect to the movement of the target (step- wise) together with the variation of the room temperature (a), and the phase measurement error with respect to the target position (b).

22 -1 ._. _- p 0.0:~~ LY_..;.~Czp- temperature L---C.

I ‘- -.- --..-.-....-T.-l ,__. -.__ _ -._ .__ --~~--r-,--.-..-

” .-- T -.-- . _. .” t .

1 z ,_,. :.& j ‘.’ {... ..(a)~: ktr ‘_ target _-__ ____.. .LLL.L. .-C.

0 :~~~~~~~~ I .l_._XT~,, “i-+

-1 - _____, ~~~~~.-~~~L&LyLy~x” / :. i++‘.-’ -;--- _ . .-,. :-!L .G-;-, +.:*;.: *T-y .+- ,, .+!r+.h-i-. ;.-;.

-2 I I I I I -500 4 500 0 -xx)

Target Displacement (pm) 0 500

0.2 , I

0

-0.1

-0.2 -500 -230 0 250 500

Target Displacement (pm)

FIG. 9. Results of distance measurement with a plate reflector as a target. The phase measurement with respect to the movement of the target (step- wise) together with the variation of the room temperature (a) and the phase measurement error with respect to the target position (b).

FIG. 10. Spectral line profiles near 1096 MHz range measured at “TP” in Fig. 5 for the case when the target is (a) a corner cube mirror and (b) a reflection plate.

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follows; moves forward for 1000 ,um (20 steps), back for 1000 ,um, and forward again for 1000 pm as shown in Fig. 5(a). Initially the experiment is performed using a corner cube mirror as a target. The experimental result is shown in Fig. 8. As seen from Fig. B(b), the maximum deviation be- tween the experimental phase value and the ideal value is lower than 0.05” indicating that the accuracy of the measure- ment is better than 19 pm. Since the fluctuation(s) of the optical beat frequency is one part in 106, the maximum mea- surement error caused by the laser instability is calculated as 1 pm for 1 m distance measurement using Eq. (9). There- fore, the resultant measurement error of 19 ,rcm is mainly due to the phase meter uncertainty. When the target distance is extended to 100 m away, the error value is estimated to be 120 pm.

Using a plate reflector as target, the same experiment has been carried out and the results are recorded in Fig. 9. Here, the maximum deviation of the phase is 0.2” as shown in Fig. 9(b). This deviation corresponds to a distance measurement error of 80 pm. The increase in the measured error is due to lack of reflection power from the target, resulting in the de- crease of SN ratio and increase in uncertainty of the phase meter. To further investigate this situation, the spectral line output of the reflected laser signals (test point “TP” in Fig. 5) coming from the corner cube mirror and the reflection plate are measured and compared using a spectrum analyzer. The observed line signals are shown in Fig. 10. The use of the plate refiector reduces the photodetector (APD) output, enhances noise from the video-amp, and finally increases the

measurement error at the output of the DPX. If one desires to minimize this situation, a more intense laser source and/or more efficiently collimated optics should be used to increase the SN ratio.

As a conclusion, a simple optical distance meter has been devised using a frequency-stabilized intermode optical beat generated from a two-mode He-Ne laser (14-cm-long cavity),. The present resolution of the system is about 20 /*.m for a target 1 m away. The distance error caused by the fluctuation of the laser beat frequency is smaller than 1 ,um while the error due to the phase meter is 19 pm. A more accurate distance meter than the present one can be realized by using a high-resolution phase meter such as a lock-in amplifier (LIAj together with an appropriate frequency value of a local oscillator. Highly stable frequency feature of the present laser is favorable for the use of LIA, because hetero- dyned frequency can be lowered to the LIA response fre- quency (note that LIA does not respond typically in higher than 100 kHz).

ACKNOWLEDGMENT

We express our thanks to Dr. Benjamin B. Dingel for his help in the preparation of this manuscript.

1 K. Seta and T. O’ishi, Appl. Opt. 29, 354 (1990). ‘R. Balhom, H. Kunzmann, and E Lebowsky, Appl. Opt. 11, 742 (1972). “S. J. Bennett, R. E. Ward, and D. C. Wilson, Appl. Opt. 12, 1406 (1973). ‘T. Yoshino, Jpn. J. Appl. Phys. 19, 2181 (1980). ‘A. Sasaki and T. Hayashi, Jpn. J. Appl. Phys. 21, 1455 (1982). “S. Yokoyama, T. Araki, and N. Suzuki, Appl. Opt. (in press).

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