Two-longitudinal-mode He–Ne laser forheterodyne interferometers to measure displacement

Min-Seok Kim and Seung-Woo Kim

We propose a new configuration for a high-resolution heterodyne interferometer that employs a two-longitudinal-mode He–Ne laser with an intermode beat frequency of 600–1000 MHz. The high beatfrequency is downconverted to 5 MHz such that the phase change of the interferometer output is preciselymeasured with a displacement resolution of 0.1 nm. A thermal control scheme is adopted to stabilize thecavity length of the He–Ne plasma tube such that a frequency stability of 2 parts in 109 is obtained bysuppression of frequency drifts caused by the phenomena of frequency pulling and polarization anisot-ropy. This two-longitudinal-mode He–Ne laser yields a high output power of 2.0 mW, which permitsmultiple measurements of as many as 10 machine axes simultaneously. © 2002 Optical Society ofAmerica

OCIS codes: 120.3180, 120.5050, 120.3940, 140.3460, 040.2840.

1. Introduction

Various types of optical interferometer are being usedfor the measurement of translational displacementsof moving objects. Among them, heterodyne laserinterferometers are most suitable when the travel tobe covered is large, as many as a few meters, whereasthe measurement resolution should go far below thewavelength of light.1 Heterodyne laser interferom-eters use two beams of different frequencies gener-ated from a single coherent source, one as thereference beam and the other as the measurementbeam. The measurement beam undergoes a contin-uous phase change in proportion to the displacementof the object to be measured; the phase change isdetected by comparison of the measurement beamwith the reference beam that bears no optical pathlength change. The beat frequency between the twobeams is much lower than the original frequencies ofthe beams, allowing the phase change to be preciselymeasured with modern electronics. The polariza-tions of the two beams are required to be linearly

The authors are with the Department of Mechanical Engineer-ing, Billionth Uncertainty Precision Engineering (BUPE) CreativeResearch Group, Korea Advanced Institute of Science and Tech-nology, Science Town, Taejeon 305-701, South Korea. S.-W.Kim’s e-mail address is swk@kaist.ac.kr.

Received 6 October 2001; revised manuscript received 17 June2002.

0003-6935�02�285938-05$15.00�0© 2002 Optical Society of America

5938 APPLIED OPTICS � Vol. 41, No. 28 � 1 October 2002

orthogonal to each other such that they are effectivelydivided and recombined with a polarization beamsplitter.

Two distinct types of He–Ne laser, the so-calledZeeman and acousto-optical modulation types, arepopularly used as light sources for heterodyne laserinterferometers. The former applies a magneticfield by using permanent magnets to induce the Zee-man effect that generates two linearly orthogonalbeams of a beat frequency of �3 MHz.2 The latteruses acousto-optical modulators to diffract one outputbeam into two separate beams whose beat frequencyreaches 20 MHz.3 Each of the two types of He–Nesource has its own merits and disadvantages, andthese lasers are nowadays commercially availablewith a high level of frequency stability �as much aspart in 109� that is traceable to the internationallength standard. However, a common problem withboth the types of He–Ne source is their low poweroutput. The acousto-optical modulation type suffersoptical losses in acousto-optical modulation, and theZeeman type uses a short cavity length to obtainsingle-mode resonance. Their continuous outputpower is usually less than 0.5 mW, which in conse-quence limits the maximum number of interferom-eters that can be operated simultaneously from asingle source. Precision industrial machines are be-coming increasingly more complicated, with increas-ing numbers of measurement axes to be run at thesame time. For example, a lithography step-and-scan machine is equipped with eight translationalaxes whose motion is to be controlled with a high level

of synchronization by a single unified source.4 Thisclass of complex machine requires a new source thatis capable of providing more output power than iscurrently available while maintaining the same levelof frequency stability.

2. Two-Mode He–Ne Laser

Light from a normal He–Ne plasma source usuallyconsists of one or more longitudinal adjacent reso-nance modes whose frequencies are separated by afree spectral range of �� � c�2L, where c is the speedof light and L is the cavity length. The magnitude ofeach mode is eventually confined by the gain profile,which usually spans several modes, as shown in Fig.1. The two-mode laser corresponds to the particularcase in which the cavity length is 150–280 mm, suchthat only two longitudinal resonance modes exist andtheir frequency difference lies in the range 600–1000MHz. The two surviving modes are inherently lin-early polarized and orthogonal to each other as aresult of the mode-competition phenomenon. Theoutput power is usually �2 mW. Even though thetwo-mode He–Ne laser itself is a potential powersource of the two-frequency beam for heterodyne in-terferometers, we have found no reports of this typeof application in the published literature. The maindifficulty with this kind of application is that the beatfrequency is so high that one cannot easily preciselydetect the phase change of the measurement beam byheterodyning it with the reference beam by usingelectronic means.

The most noticeable use of the two-mode He–Nelaser made previously was for long range measure-ment by use of the long equivalent wavelength ob-tained simply by mixing of the two orthogonalmodes.5 The equivalent wavelength determined bythe beat frequency of the two modes is in fact ex-tended to almost half a meter. However, unlike inheterodyne interferometry, the resolution of the long-range measurement becomes rough, typically onehundredth to five hundredths of the equivalent wave-length. Another application of the two-mode laser is

for measurement of vibration motion implemented bymonitoring the Doppler shift of the beat frequencythrough real-time spectral processing.6 In this casethe measurement resolution is fine, in the range ofsubmicrometers, but the measuring range is limitedbecause the side peaks of the Doppler shift in thespectral domain are wide in proportion to the velocitydispersion of vibration motions. Besides the twomeasurement applications mentioned, a different butmuch related study found in the literature treats fre-quency stabilization of the two-mode laser, which wasaccomplished by monitoring the variation of the beatfrequency with subsequent temperature control tokeep the cavity length of a He–Ne laser tube con-stant.7

Now in this investigation a new attempt is made totest the feasibility of using the two-mode laser as ahigh-output light source for heterodyne interferom-eters, especially for simultaneous measurements ofmultiple machine axes. A technique of frequency-downconversion signal processing is adopted to lowerthe beat frequency to a level of 5 MHz, so the phasechange of the measurement beam is measured pre-cisely, with a resolution of 0.1°. In addition, ascheme for frequency stabilization is combined withthe frequency-downconversion technique to achieve astability of 4.0 � 10�6 for the beat frequency. Fi-nally, a full operating system for a heterodyne inter-ferometer is built and tested to demonstrate that atwo-mode He–Ne laser is capable of providing a highoutput power of 2.0 mW together with a measure-ment resolution of 0.1 nm and a frequency stability of2.0 � 10�9.

3. Frequency Downconversion

Figure 2 shows a schematic of the heterodyne inter-ferometer system configured in this investigationwith a two-mode He–Ne laser source. The lasersource maintains two separate resonance modeswithin the cavity, which results in two output beamsof different frequencies and orthogonal polarizations.The beat frequency depends on the cavity length; itlies in a range of 600–1000 MHz. A fraction of the

Fig. 1. Two adjacent longitudinal modes standing within the gaincurve of a He–Ne laser. Adjacent modes whose frequencies sep-arated by the free spectral range �FSR� are orthogonally polarized.

Fig. 2. Optoelectronic configuration of the high-resolution hetero-dyne interferometer with a two-mode He–Ne laser: APDs, ava-lanche photodiodes; DBMs, double-balanced mixers; LO, localoscillator; PS, power splitter; PBS, polarizing beam splitter; P’s,polarizers.

1 October 2002 � Vol. 41, No. 28 � APPLIED OPTICS 5939

output beams extracted from the back end of thecavity passes through a linear polarizer rotated by45°. Then the two beams of different polarizationsare mixed to produce a reference intensity signal,

Ir � A cos2� f1 � f2�t�, (1)

where A is the signal amplitude and f1 and f2 repre-sent the frequencies of the two polarized beams. Weuse an avalanche photodiode of 1-GHz cutoff fre-quency to obtain an electrical signal Ir. The major-ity of the output beams come out of the main exit holeat the right-hand end of cavity and passes through apolarized beam splitter. A beam of frequency f1 isdirected to the stationary corner cube and reflectedback as the reference beam. Beam f2 proceeds to themoving corner cube fixed on the target object and isreflected back as the measurement beam. The ref-erence and measurement beams are recombined bythe same polarizing beam splitter; they then interferewith each other through a linear polarizer rotated by45°. The measurement signal is then obtainedthrough an avalanche photodiode as

Im � B cos2� f1 � f2�t � ��, (2)

where � � 2�2d1� 1 � 2d2� 2�; 2d1 and 2d2 are theoptical path lengths, and 1 and 2 are the wave-lengths of the reference and the measurement beams,respectively.

The phase change � of Eq. �2� is determined by useof an electronic phasemeter that detects the phasedifference between the measurement beam and thereference beam. However, the beat frequency f1 � f2of 600–1000 MHz is too high for phase � to be pre-cisely monitored by current transistor–transistorlogic electronics technology. Frequency downcon-version is therefore applied to lower the beat fre-quency without significant loss of accuracy in phasemeasurement. We implement frequency downcon-version by mixing both the reference and the mea-surement signals with a local oscillator �LO� signalthat is artificially generated with a frequency fLO thatis close to the beat frequency. As a result, the ref-erence and measurement signals are converted intolow-frequency electrical signals such as

Ir � A cos�2fIFt�, Im � B cos�2fIFt � ��, (3)

respectively, where the new carrier frequency be-comes fIF � f1 � f2 � fLO. The LO signal is stablysynthesized to an accuracy of 0.1 part in 106 by use ofa well-known single-chip phase-locked loop circuit8

along with a temperature-compensated crystal oscil-lator. One might adjust carrier frequency fIF to anappropriate value by varying the LO signal, whosehighest limit is practically set by the dynamic band-width of the phasemeter electronics. Selecting ahigher carrier frequency increases the magnitude ofthe measurable maximum velocity of the displace-ment, but the measurement resolution deterioratesin proportion to the carrier frequency. In our con-figuration, fIF is set to 5 MHz.

4. Frequency Stabilization

The cavity length of a He–Ne plasma tube begins toexpand with rising temperature as soon as the laseris switched on. The beat frequency changes withcavity length in a complicated manner. Figure 3shows experimental observations of the typical pat-tern of beat-frequency variation with time when noaction is taken to keep the cavity length constant.The time-varying pattern may be characterized bytwo distinctive properties that repeat themselveswith every increase in the cavity length by half of themean wavelength of the two resonance modes. Oneproperty is the up-and-down disruptive fluctuation of�450-kHz amplitude, and the other is the convex-shaped smooth drift of �100-kHz amplitude. Theformer change is always accompanied by an inter-change of polarization states between the two reso-nance modes from �p, s� to �s, p�.9 This swap ofpolarization is caused by the polarization anisotropyof the reflecting mirrors, which yields different phaseshifts on reflection for different polarizations. Thelatter smooth change has no dependence on polariza-tion, and its phenomenon is explained by thefrequency-pulling effect encountered with cavity-length change.10

Another characteristic of beat-frequency variationis the long-term decrease of its magnitude that isobserved as a slope of �2 kHz� , as depicted in Fig.3. This phenomenon is readily explained by differ-entiating the well-known relationship of the freespectral range of �� � c�2L such that

d���� � �cdL2L2 . (4)

This result implies that free spectral range ��, whichis directly related to the intermode beat frequency ofthe two-mode laser, decreases as cavity length L in-creases. For example, if there is a length variationdL � for a cavity length L � 205 mm, beat fre-

Fig. 3. Variation in beat frequency with change in cavity length.The vertical axis represents beat-frequency fluctuation from thebasic longitudinal mode interval of 746 MHz.

5940 APPLIED OPTICS � Vol. 41, No. 28 � 1 October 2002

quency �� is reduced by 2.26 kHz, confirming ourexperimental observation.

Figure 4 shows a schematic of the frequency stabi-lization system that uses digital control specially con-figured in this investigation. The basic principle offrequency stabilization is to control the cavity lengthsuch that carrier frequency fIF that is decreased byfrequency down-conversion is locked on a designatedvalue. Cavity length is controlled by heating of theplasma tube by radiation heating.11 Two 20-W halo-gen lamps are used, and their average ON duty isvaried in a pulse-width-modulation mode. The des-ignated value at which the beat frequency is locked isselected to correspond to a particular point where thevariation of beat frequency with cavity length yieldshigh sensitivity as a result of the frequency-pullingeffect, as depicted in Fig. 4. Any deviation of theactual beat frequency from the designated value de-pends on a digital proportional, integral, and differ-ential control that is supervised by a microprocessor�Micom 80C196KC�, which changes the duty of thepulse-width-modulation signal of the halogen lampsthrough high-power operational amplifiers. Figure5 shows a test result of frequency stabilization, which

demonstrates that the frequency fluctuation is re-duced to a level of 3 kHz. This result is equivalent toa stability of 4.0 � 10�6 in terms of beat frequency.

5. Performance Evaluations

The frequency-stabilized He–Ne laser was comparedwith a standard single-mode He–Ne laser whose fre-quency stability had previously been calibrated as1.0 � 10�9. Only the high-frequency component ofthe two-mode laser was extracted by use of a linearpolarizer and then mixed with the standard beam,while the beat frequency of the two components wasmonitored. Figure 6 reveals a typical result of a testsampled for 3 h. The maximum fluctuation of thebeat frequency between the two lasers was 1 MHz,and the standard deviation of fluctuation was 324kHz. This result indicates that our two-mode laserhas a frequency stability that is better than 2.0 �10�9. The Allan variances of the test result of Fig. 6are computed as ��10 s� � 4.0 � 10�10, ��100 s� �1.0 � 10�10, and ��1000 s� � 4.0 � 10�10. The dom-inant disturbances of the frequency stability lie above0.1 Hz and would be further suppressed if one in-creased the dynamic bandwidth of the frequency sta-bilization control by replacing the current slow-responding halogen lamps with a faster heat-exchange device such as an induction coil12 or byimproving the control scheme to achieve a smallertime delay.

Finally, we evaluated the measuring resolution ofour heterodyne interferometer, using the experimen-tal setup illustrated in Fig. 7. The measuring reso-lution is affected primarily by the precision of theelectronics that perform the frequency downconver-sion and subsequent phase measurement, whereasthe frequency stability of the laser source has theleast influence. Thus we made the experimental ap-paratus perform a long-range measurement simplyby using the equivalent wavelength generated by thebeat frequency of the two-mode laser, while we usedthe same electronics for frequency downconversionand phase measurement as those used for the origi-nal heterodyne interferometer. Because the beatfrequency of the two-mode laser is 747 MHz, theequivalent wavelength is worked out to be 412 mm.

Fig. 4. Control block diagram of the digital frequency stabiliza-tion system: INT, interrupt input of a micomputer chip; PWM,pulse-width modulation output of a micomputer chip.

Fig. 5. Beat-frequency variation before and after frequency sta-bilization. An enlarged view of the stabilized region is shown atthe right.

Fig. 6. Fluctuation of beat frequency between the stabilized two-mode laser and a standard single-mode stabilized He–Ne laser.

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This result indicates that, if the reflector is moved 1mm, the phase output should change by 1.75°. Themicrometer pushing the reflector has a movement res-olution of 10 �m, which corresponds to a phase changeof 0.0175°. This procedure permits ultraprecisiontesting of the measurement resolution of the electron-ics involved; other factors that influence heterodyneinterferometers, such as change of the refractive indexof air, nonlinearity of polarization optics, and opticalalignment errors, are completely excluded. Figure 8shows the test result that we obtained by moving thereflector of a distance �5 mm while the phase changewas measured with a precision phasemeter �StanfordResearch Systems Model SR844 rf lock-in amplifier�.The test result reveals that the discrepancy betweenthe actual phase values and the values estimated fromthe reflector movements are all within 0.1°, which is infact the practical limit of the lock-in amplifier used forphase measurement. The phase resolution of 0.1°corresponds to a displacement resolution of 0.1 nmwhen the same electronics are used in heterodyne in-terferometers.

6. Conclusion

For heterodyne laser interferometry to measure dis-placement of moving objects, the feasibility of using a

new He–Ne laser source with two longitudinal reso-nance modes has been tested. The two-mode He–Nesource has a cavity length of 205 mm and producestwo orthogonal polarization beams with a beat fre-quency of 747 MHz. A frequency-downconversionmethod integrated with a phase-locked loop tech-nique was specially devised to lower the high beatfrequency to a level of 5 MHz so the phase change ofthe measurement beam with respect to the referencebeam can be detected precisely, with a resolution of0.1°. This precision of phase detection is equiva-lent to a precision of 0.1 nm in terms of resolution ofthe displacement measurement. In addition, amicroprocessor-based control scheme for frequencystabilization is equipped to confine the beat-frequency fluctuation to a narrow range, �3.0 kHz,by suppressing the polarization anisotropy of cavitymirrors and frequency pulling. This achievementcorresponds to 4.0 � 10�6 stability in terms of beatfrequency and 2.0 � 10�9 stability in terms of theoriginal frequency of the source. A significant ad-vantage of the two-mode source compared with exist-ing types of Zeeman split and acousto-opticalmodulation is its high-output power, reaching 2.0mW, which practically permits multiple-axis mea-surements of as many 10 axes to be performed simul-taneously with a single power source.

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Fig. 7. Schematic of the experimental setup for testing of phase-measuring electronics: Ps, polarizers; CC, corner cube; LO, localoscillator; APDs, avalanche photodiodes; DBMs, double-balancedmixers; PS, power splitter.

Fig. 8. Test results of phase-measuring electronics. Two mea-surements, performed separately, are marked B and C.

5942 APPLIED OPTICS � Vol. 41, No. 28 � 1 October 2002