Pulsed heterodyne CO2 laserrangefinder and velocimeter with chirp correction

Leo H. Cohen, Alexander M. J. van Eijk, and Gerrit de Leeuw

A pulsed hybrid CO2 transversely excited atmosphere (TEA) laser has been used in a bistatic laser

rangefinder-velocimeter system with heterodyne detection. Several techniques have been applied to

improve the performance of the system. These include the stabilization of the hybrid CO2 TEA-laser and

the stabilization of the frequency offset of the local oscillator (better than +74 kHz peak to peak),phase-front matching at the detector surface resulting in a heterodyne beat efficiency of 0.4-0.6, and chirp

correction. With this system, targets at distances of up to 25 km can be detected with an accuracy of 15m. The velocity of the targets can be estimated with an accuracy of approximately ±0.5 m/s.

Key words: C02 laser, rangefinder, velocimeter, chirp correction.

Introduction

The use of pulsed CO2 lasers in rangefinders andvelocimeters offers several important advantages.First, much laser energy can be compressed in a shorttime interval, which considerably increases the rangeover that of systems based on cw lasers. A furtherincrease in range is achieved when the pulsed laser isused in combination with heterodyne detection.Heterodyne detection can be 2 orders of magnitudemore sensitive than direct detection.'

Another advantage of the CO2 laser is its eye-safewavelength of 10.6 jim. This wavelength is furtherinteresting because it is compatible with thermal-imaging systems.

Apart from detection, range, and velocity measure-ments of targets, the CO2 laser rangefinder-velocim-eter has several interesting and unique applications,such as range-resolved measurement of water vapor2

and other gaseous species3 through the use of differen-tial-absorption lidar (DIAL) techniques or the deter-mination of atmospheric extinction and backscattercoefficients at 10.6 jlm when the system is used as alidar. 4 The extinction parameters can also be ob-tained with transmissometers or by calculation ofaerosol and molecular extinctions, but these methodshave their disadvantages and are not as direct as theCO2 lidar.

The authors are with the TNO Physics and Electronics Labora-tory, P.O. Box 96864,2509 JG, The Hague, The Netherlands.

Received 8 February 1993; revised manuscript received 14

February 1994.0003-6935/94/245665-06$06.00/0.© 1994 Optical Society of America.

Another interesting application is the remote mea-surement of wind speed and wind direction.5 6 Tothis end, reflections of the aerosol are measured.Because the aerosol is transported by the wind field,the reflected signal is Doppler shifted. Determina-tion of the magnitude and direction of the Dopplershift thus yields information on the wind speed anddirection. When the information is obtained as afunction of height, crosswind corrections and detec-tion of wind shear become feasible. Particular advan-tages of the remote measurement of wind speed andwind direction are that the local wind field is notdisturbed by the measurement and that elaborateand expensive calculations on flow distortion areavoided.

A study has been made at the TNO Physics andElectronics Laboratory on the application of pulsedCO2 lasers and heterodyne detection in bistatic range-finders and velocimeters. For successful operation,two major requirements have to fulfilled: opticalalignment and frequency stabilization. For bistaticsystems, optical alignment is a more stringent require-ment than for monostatic systems. To accomplishfrequency stabilization of a pulsed laser, we have useda hybrid TEA-CO2 laser. This laser has a single,linear cavity that contains both a continuous (cw) CO2laser and a transversely excited atmospheric (TEA)pulsed CO2 laser. The frequency of the cw laser isstabilized, and the single cavity forces the TEA laserpulse to follow the cw laser frequency by the processof stimulated emission. However, even then theTEA laser exhibits a frequency drift (or chirp) duringthe laser pulse. This drift severely reduces the

20 August 1994 / Vol. 33, No. 24 / APPLIED OPTICS 5665

velocimeter performance. Therefore, the drift ismonitored and compensated for.

In this paper we report on a feasibility study, i.e.,the realization of a laboratory setup of a CO2 laserrangefinder and velocimeter. We summarize severalinternal reports, which have appeared in the course ofthe present work. We describe the system in moredetail, with emphasis on frequency stabilization.Results for both rangefinder and velocimeter applica-tions are presented.

Experimental Processes

SetupA scheme of the experimental setup is shown in Fig.1. The heart of the transmitter is an EdinburghInstruments hybrid CO2 laser Model 222. It con-sists of a cw laser and a pulsed TEA laser contained ina single cavity. The wavelength of the CO2 laser isselected by a diffraction grating, which is fine tunedby adjustments of the cavity length with a ceramicpiezoelectric transducer (PZT). Because the two la-sers are in the same cavity, the TEA laser is locked tothe wavelength of the cw laser. Table 1 presents thespecifications of this system.

The beam from the TEA laser is split by beamsplitter BS1. The main beam is expanded to adiameter of 5 cm by beam expander BE2, whichreduces the divergence to approximately 0.3 mrad.7Finally, the beam is transmitted into the atmosphereby scan mirrors. The reflected signal is collected bymeans of scan mirrors and focused onto liquid-N2-

02 R BS2 L5 S2

_ L4',S5 BSI

01 ~~~~~~~~~TEALASER

BS3

Fig. 1. Experimental setup of the CO2 laser rangefinder-velocimeters: C, camera; BE's, beam expanders; BS's, beamsplitters; D's, detectors; L's, lenses; R. A/4 retarder; 5's, mirror;SS, scan mirror; W, attenuator; *1, *2, choppers.

Table 1. Specifications of the Hybrid CO2 Lasera Characteristics

Laser Typeand Characteristic Specification

CW SectionOutput power 1-1.6 W (10P20 line)Beam diameter 9 mmBeam divergence 1.3 mradLine width 45 MHzGas pressure 17.5 mbarGas mix (in percent) C0 2 :N2:H 2 :Xe:He, 15.4:14.2:2:4:64.4Polarization Linear, vertical

TEA SectionPulse power 50 mJ (10P20 line)Pulse width (FWHM) 300 ns (above threshold)Pulse rise time 100 nsPulse repetition rate 3 Hz max. (longitud. flow)Chirp 0.7 MHz/pLs2

Gas mix C0 2:N 2:He, 1:1:4

aEdinburgh Instruments model 222.

cooled HgCdTe detector D1 through lens L1, deflec-tion mirror S3, and beam splitter BS3. The last-named component allows for mixing with the localoscillator.

A rf-excited waveguide CO2 laser (Edinburgh Instru-ments, Model WL4-GT) serves as a local oscillator.Just as for the hybrid CO2 laser, the wavelength ofthe rf laser is selected by a diffraction grating and aPZT. Specifications of the rf laser are given in Table2.

The beam of the rf laser is split by beam splitterBS4. A minor part is mixed with part of the transmit-ted TEA laser pulse at a second HgCdTe detector, D2,to control the frequency-offset stabilization of the twolaser systems. The main part of the rf laser beam isdirected to the receiver part of the rangefinder, whereit is mixed with the TEA laser pulse that is reflectedby a target. The signal of detector D1 is amplifiedand subsequently amplitude demodulated8 (for rangedetermination) or quadrature demodulated9 (for rangedetermination and velocimetry). The resulting sig-nal is digitized and fed into a computer for displaying,further processing, and storage.

Frequency Stabilization

The velocimetry measurements require a well-knownfrequency offset between the TEA laser and the localoscillator. In our setup, the TEA laser (master) is

Table 2. Specifications of the rf Laser a Characteristics

Characteristic Specification

Output power 1-1.6 W (10P20 line)Beam diameter 0.8 mmBeam divergence 5 mradLine width 150 MHzGas pressure 125 mbarsGas mix (in percent) C0 2 :N2 :H2 :Xe:He, 24.5:10.5:0.7:5.6:58.7Polarization Linear, vertical

aEdinburgh Instruments model WL4-GT.

5666 APPLIED OPTICS / Vol. 33, No. 24 / 20 August 1994

stabilized on the 10P20 laser line center by means ofan optogalvanic technique, whereas an optical tech-nique is used to keep the local oscillator (slave) at afrequency offset of 20 MHz with respect to the TEAlaser.

Figure 2 presents a schematic diagram of thefrequency stabilization.8 The cw part of the TEAlaser is stabilized on the 10P20 laser line center bymeans of a frequency stabilizer (STAB1 in Fig. 2).The stabilizer consists of a bandpass filter, a lock-inamplifier and a high-voltage dc amplifier (900 V).The output of the dc amplifier is fed into the PZTelement of the cw laser (PZT-cw). The PZT elementis modulated with a 230-Hz sine wave causing thelaser to sweep across the laser line. The servoloop ofthe cw laser is closed by an optogalvanic technique,which uses the electrical impedance of the laser gasthat peaks at the center of the laser line. Thevariations in impedance are measured with a resistorin series with the low-voltage electrode of the lasertube. The output of this circuit is fed into the laserstabilizer by means of an additional bandpass filterthat eliminates power-supply ripples. This systemacts as a hill-climbing servoloop that controls the PZTelement of the cw part of the TEA laser. Thefrequency drift of the stabilized cw laser amounts toapproximately 60 kHz in 5 min (cyclic), mainly causedby thermal drift of the cooling unit.

The local oscillator (rf laser) is kept at a frequencyoffset of 20 MHz with respect to the TEA laser. Tothis end, a small part of the rf laser beam is mixedwith the cw part of the TEA laser beam on detectorD2 (see Figs. 1 and 2). The resulting heterodynebeat signal is amplified (bandwidth 10-30 MHz),passes an electronic switch, and is subsequently fedinto a phase-locked loop (PLL) circuit. The PLLoutput signal passes a sample-and-hold circuit (SH)and is then fed into a laser stabilizer (STAB2), thatwas modified to allow its use with the PLL circuit.The modification consists of the replacement of thebandpass filter and the lock-in amplifier with anadditional servo amplifier with a proportional integrat-ing and differentiating circuit. Laser stabilizer

PLLbkbft

STAB2 controls the PZT element of the rf laser.The modulation frequency of the PZT element isobtained from the cw part of the TEA laser by meansof an adjustable phase shifter (). In this way thebeat signal resulting from the 230-Hz frequencysweep of the PZT elements can be eliminated.

The electronic switch and sample-and-hold circuitare implemented to isolate the PLL circuit from thefrequency-offset detector D2 when the TEA laser ispulsed. The inhibition starts 1 ms before the TEAlaser is fired and lasts 400 ms. During this time, thegas in the laser is refreshed. This is necessarybecause the gas is heated by the discharge of the TEAlaser, and that causes shifts in the frequency of the cwpart of up to 10 MHz, which is outside the capturerange of the PZT element.

The TEA laser is fired when the 230-Hz sweep ofthe PZT element of the cw laser passes the center ofthe laser line. Also, the modulation of the PZTelements is inhibited when the TEA laser is fired (seeFig. 2). In this case, inhibition runs from 1 msbefore to 300 jis after the laser is fired. In this way,the frequency of the local oscillator is kept constantduring the travel time of the TEA laser pulse to andfrom a target. The drift during the inhibition-timeinterval is < 0.85 kHz (based on a drift of 4MHz/min for the unstabilized rf laser).

Specifications of the frequency stabilization aresummarized in Table 3. The jitter in the frequencyoffset between the cw laser and the local oscillatoramounts to ±74 kHz peak to peak (At = 1 s). It isdifficult to compare this value with others, becauseonly few similar systems have been described. Forone system,1 0 a jitter of ± 120 kHz rms in frequencyoffset between the TEA laser pulse and the localoscillator has been reported. Since the TEA laserfrequency may not always be identical to the cw laserfrequency, the two values cannot be compared directly.However, we may safely conclude that the two jittersare of the same order of magnitude.

Results

nnriae Dptermination

The system is located at a height of 30 m in the towerof the TNO Physics and Electronics Laboratory.From this position, a free line of sight is available to

I concrete buildings at distances of up to 25 km. We

Fig. 2. Flow chart of the frequency stabilization: CW, PZT-element of hybrid TEA laser; D2 , detector; PLL, phase-locked loopcircuit; rf, PZT element of the rf laser; SH, sample-and-holdcircuit; STAB's, modified laser stabilizers; Ak, phase shift circuit.

Table 3. Specifications of the Frequency Stabilization

Parameter Value

Phase-locked loopCapture range 14-22 MHzLock range 12-27 MHzInhibit time -1 ms to +400 ms

PZT modulation inhibit range - 1 ms to +300 isFrequency offset 20 MHzJitter (At = 1 s)

Regular gas mix ±74 kHzNitrogen gas only ±25 kHz

Drift (At 5 min) 60 kHz

20 August 1994 / Vol. 33, No. 24 / APPLIED OPTICS 5667

have used these buildings as targets for testing andoptimizing our rangefinder. We have been able todetect the most distant target at 25 km with singlelaser pulses. Targets at larger ranges are not avail-able.

It is difficult to assess the maximum range of oursystem because it is determined by many factors.Two important instrumental factors are the opticalpower transmitted into the atmosphere and the opti-cal alignment of the heterodyne detection system.A measure for the latter alignment is the heterodynemixing efficiency. This quantity is defined as theratio of the actual and the theoretical amplitudes ofthe heterodyne beat signal, where the theoreticalamplitude amounts to twice the square root of thelocal oscillator power and the power of the returnpulse. The heterodyne mixing efficiency for oursystem has been determined to be 0.4-0.6.11 Thisvalue compares favorably with efficiencies reportedelsewhere,'2"13 which are typically in the range 0.2-0.5.This nonideal performance has been reported oftenand is commonly ascribed to nonperfect matching ofthe wave fronts of the received radiation and the localoscillator and to phase-front distortion of the receivedradiation caused by nonspecular reflections.'4

An important environmental factor that limitsrangefinder performance is the atmospheric extinc-tion caused by scattering and absorption by moleculesand aerosols. In fog, the extinction at'10.6 jim canbe smaller than the extinction in the visible or nearIR. In such a case, a 10.6-jim rangefinder maydetect targets which are invisible to the naked eye.An example is presented in Fig. 3, which shows thereflected signal (single shot) from a target at 3.1 km infog. The visibility at 0.55 jim as measured with anAEG point visibility meter was only 1.7 km, and thetarget could not be observed by eye. The additionalpeaks in the return signal are probably due to densityfluctuations in the fog, because their distances variedwith time.

For reasons discussed in the previous paragraphs itis not easy to specify the maximum range of our

signal strength1 _

0.5-

00 10 20 30

time [us]40 50

Fig. 3. Reflection of a target (marked by the downward-pointingarrow) at 3.1 km in fog (visibility at a wavelength of 0.55 pum = 1.7km). The measurement was made in the Netherlands.

rangefinder. The accuracy of the rangefinder is de-termined mainly by instrumental parameters such asthe jitter between the trigger pulse and the opticalpulse, the variations in the shape of the envelope ofthe optical pulse, and the sample rate of the digitizer.We find that the accuracy of our rangefinder is ± 15 min single-shot mode.7 In this mode, the digitizer istriggered by the TEA laser trigger pulse, and the peakof the return pulse (after applying a threshold) is usedfor calculating the range.

Velocimetry

The application of velocimetry is technically morecomplicated than is ranging. For the latter applica-tion it is necessary to determine only the envelope ofthe return pulse, whereas velocimetry requires theretrieval of the heterodyne beat frequency in thereturn pulse as well. To this end, quadrature de-modulation9 is used. The detector signal is split intotwo signals Sl(t) and S2(t) that are related by

arctan[S2(t)/S,(t)] = Ao(t)t + A4, (1)

where Aw(t) is the difference between the heterodynebeat frequency and the offset frequency between thetwo lasers (20 Mhz) and A4 is a phase shift. Theterm Aw(t) results from two effects: (a) the Dopplershift AwD(t), which is induced by a target with radialvelocity v as

AoD(t) = 2v(t)/X 50 kHz/(km/h), 10.6 jim,

(2)

and (b) the chirp Aow(t). For our system, the chirphas been measured as 0.7 MHz/s2 , resulting in afrequency shift of 2.5 MHz during the pulse.9 Thechirp is of the order of Doppler shifts induced bytargets moving at velocities of 50 km/h. Clearly, foraccurate velocimetry the chirp must be removed fromA)(t).

Chirp is caused by the changes in TEA laserfrequency during the laser pulse that are caused bychanges in the cavity refractive index. The twomajor causes for these changes are the time-depen-dent electron density in the decaying discharge plasmaand laser-induced perturbations in the cavity (e.g.,thermal gradients). 5 6 There are several ways toremove the chirp from Ao(t). First, chirp may beminimized by improvements in the mechanical designof the cavity.'0 Second, the chirp may be modeled byan explicit expression for Awo(t). This approach wasoriginally followed for our velocimeter.9 However,such an explicit expression is necessarily a mean-chirp correction that cannot account for pulse-to-pulse chirp variations. Unfortunately, these pulse-to-pulse variations are quite large in our system (weestimate that the actual chirp may deviate from themean chirp by as much as 1 MHz), and therefore wediscarded chirp modeling.

The large pulse-to-pulse variations forced us todevelop a system that is capable of determining theactual chirp A(t) in each pulse." Our chirp-

5668 APPLIED OPTICS / Vol. 33, No. 24 / 20 August 1994

correction system consists of the frequency-offsetdetector (D2 in Fig. 1) connected with a secondquadrature demodulator and interfaced with a secondtransient digitizer. The chirp-correction systemmonitors the heterodyne beat signal of the localoscillator and the transmitted TEA laser pulse (seeFig. 1), i.e., the TEA laser pulse that is not yetDoppler shifted. The two signals from the quadra-ture demodulator are therefore related by

arctan[S 4 (t)/S 3 (t)] = AW(t)t + i4 (3)

Combining Eqs. (1) and (3) we find that

d arctan[S 2(t) arctan[S 4(t) = AwoD(t). (4)dt k [S,(t) L3t

As an example, Fig. 4 shows arctangent curves of oneTEA laser pulse before it was transmitted into theatmosphere (lower trace) and after it was reflected bya moving target (upper trace). Note that the slope ofthe upper trace is steeper because of the presence ofthe Doppler shift. The beginning of the trace of thetransmitted pulse (lower trace) is severely distorted.This is caused by electrical interference on the detec-tor caused by the discharge during the collection ofthe first few sample points of the optically transmit-ted pulse. The distorted part of the transmittedpulse was removed, and further processing consistedof our matching the two curves in time, smoothingthe result, and applying Eq. (4).

The velocimeter with chirp correction was testedwith a rotor system 9 at a distance of 260 m. A 10cm x 10 cm sheet of sand-blasted aluminum at theend of a 1-m rotor was used as a target. A total ofnine target velocities (±8, ±4, ±2, +1, and 0 m/s)was available. The firing of the TEA laser wassynchronized with the rotor system so that it would

0 50 100 150 200 250 300 350

5.0- 1 I I I I I I - 5.0

2.5- 2.5

T 0.0 -0.0

K

-2.5- x -- 2.5

-5.0- x -5.0

-7.5 ,I,|I ,, ,I,, ,,,I, -7.50 50 100 150 200 250 300 350

sample number

Fig. 4. Arctangent curves of the transmitted and reflected TEAlaser pulse (see text).

hit the target when it was exactly perpendicular tothe laser beam.

With the rotor system locked to a specific velocity,TEA laser pulses were fired onto the target. In themajority of cases, the velocities that were measuredwith our velocimeter were in reasonable agreementwith the velocity of the rotor. In a few cases themeasured velocity was wrong by a factor of 2.Unfortunately, we do not know the reason for theseoutlyers.

Table 4 presents the results of our velocimetertests. For each target velocity, all individual mea-surements (including any outlyers) have been aver-aged by iterative residual down-weighting.'7 Table 4shows the average velocity as measured with oursystem, the standard deviation, and the number ofpulses that were averaged. The performance of ourvelocimeter depends on the target velocity. For ve-locities up to ±4 m/s the velocimeter reading istypically within 10% of the actual target velocity andhas an error of ±0.3 m/s. The overall velocity-estimate accuracy is approximately ±0.5 m/s.

We have also tested the velocimeter on targets thathave larger velocities. To this end, the velocities ofautomobiles on a nearby road were measured insingle-shot mode. We do not know the actual speedsof the individual cars, but we obtained an averagevelocity of 75 km/h (from a total of 27 pulses), whichis close to the posted speed limit of 80 km/h.

Another velocimeter has extensively been describedin the literature. 0 The major differences betweenthat system and ours are that the TEA section iscoupled to the cw laser by injection locking, theCW-TEA system is folded, and the gas flow in theTEA section is laminar. Interestingly, in that sys-tem the chirp has been minimized by considerablemodifications in the laser design. In this manner, achirp of less than 200 kHz was achieved, whichresults in a standard deviation of 0.6 m/s (for station-ary targets). This value is of the same order ofmagnitude as the standard deviations obtained withour system. Therefore, we infer that our method ofchirp correction offers a good alternative for theextensive modifications to the laser that are needed tominimize the chirp.

Table 4. Test Results of the Velocimeter with Chirp Correction

Experimental MeasurementsVelocity of

Locked Rotor (m/s) N V (m/s) or (m/s)

8.0 5 10.6 8.64.0 15 3.7 0.72.0 14 2.0 0.41.0 15 0.94 0.250.0 15 0.09 0.29

- 1.0 15 -0.90 1.2-2.0 5 -2.07 0.14-4.0 25 -4.02 0.3-8.0 5 -4.9 4.8

20 August 1994 / Vol. 33, No. 24 / APPLIED OPTICS 5669

Conclusion

We have realized a laboratory setup of a 10.6-jimC02-laser rangefinder-velocimeter with heterodynedetection. The heterodyne mixing efficiency of oursystem is 0.4-0.6. The two CO2 lasers are locked to afixed frequency difference of 20 MHz by PZT modula-tion with an accuracy of 74 kHz peak to peak. Therangefinder has detected targets at 25 km with anaccuracy of better than 15 m. The velocimeter hasbeen demonstrated to detect targets moving at 80km/h. A chirp-correction method is applied andresults in an accuracy of ± 0.5 m/s in the velocimeter.

This work has been sponsored by the NetherlandsMinistry of Defense under contracts A84KL121 andA9OK700. The authors acknowledge the participa-tion in this work of W. Knippers, J. Bloem, C. P.Spruijt, and P. A. J. van den Braken.

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