Pulsed C0 2-laser heterodyne radar for simultaneousmeasurements of range and velocity

Friedrich Malota

A C0 2-laser heterodyne system consisting of a CO2 TEA laser transmitter and a CO 2 cw laser local oscillatorwith a fast data system is used to measure simultaneously range and velocity of solid targets. The basicproperties of such a system and the accuracies for range measurements were investigated. Further, hetero-dyne experiments without oscillation of the pulses but with the full advantages of heterodyne detection werecarried out.

1. Introduction

In the literature some laser range finders with hetero-dyne detection' 2 are known. To measure simulta-neously the range and velocity of solid targets, a pulsedheterodyne technique can be used. For this case, thedifficulties are in finding the relation between the os-cillations of the outgoing and the reflected pulses.Three methods were used to get this relation andtherefore the time of flight of the pulse.

To investigate the basic properties of such a systemmany experiments were done to get the accuracy forrange measurements and the range correction factorswhen the target is moving.

An advantage of heterodyne detection over directdetection is that the signal-to-noise ratio is higher thanin direct detection. Measured values of the hetero-dyne-to-direct advantage are between 100 and 150, al-though theoretical values are much higher.3

I1. CO 2 Laser Pulsed Heterodyne System

A schematic of the CO2 laser pulsed heterodyne sys-tem is shown in Fig. 1. A CO2 TEA laser emits pulseswith 400-nsec pulse length and 30-kW peak power onthe P(20) line. The laser can be tuned under the P(20)line gain curve by translating the grating with a PZT.Another laser which radiates in a cw mode is the localoscillator (LO). This laser can also be tuned by a PZTwithin the P(20) linewidth. The range of the frequencycontrol is -30 MHz for both lasers.

A small part of the power from the laser transmitteris reflected or scattered from a thin wire DR. A wirewas chosen because the two signals, one from the wire

The author is with German Aerospace Research EstablishmentDFVLR, Institute of Optoelectronics, D-8031 Wessling/Obb., FederalRepublic of Germany.

Received 8 October 1983.0003-6935/84/193395-05$02.00/0.© 1984 Optical Society of America.

and one reflected from the target, should be equal anda semitransparent mirror gives only one constant valueof the power. It is obvious that the wire deforms thewave fronts and therefore the signal-to-noise ratio4

decreases a small amount.The radiation scattered from the wire passes through

the semitransparent mirror S 2 and is reflected by mirrorS 3 to the optics 0 and then to the detector (mixer) D.Simultaneously, radiation from the LO is directed bymirrors S1, S2, and S 3 to the detector D.

When the signals are aligned to within 0.2 mrad theymix on the HgCd Te detector and produce a heterodynepulse which is the starting signal for a counter in thecase of a range measurement. Most of the transmitterpulse power reaches a solid target, from which the targetsignal is reflected. This signal is also directed by mir-rors S2 and S 3 to detector D. The target return and theLO mix to produce a heterodyne signal, which can beused as a stop signal for the counter. This is the sim-plest form of a range measurement.

In addition to the geometric alignment within 0.2mrad the system needs an optimization of power of thetwo lasers. It is well known that heterodyne current ihis proportional to the roots of power5 6 of the signal (PS)and the power of the LO (P1 ), ih (Ps - pi)1/ 2 . Becausethe mixer element is capable of dissipating only 2 mWof power and P8 depends on the measured range andreflectivity of the target, the power of the LO has to beadjusted to get an optimum ih. This can be done byinserting filters in the beam of the LO.

Because the two lasers are free running, signals fromoutgoing pulses are also detected in heterodyne form tocontrol intermediate frequency (IF), power, and length.IF stabilities were measured four times:

(1) IF stability during pulse length of 400 nsec, de-viation from adjusted value was not measurable with aspectrum analyzer (smaller than 20 kHz).

(2) IF stability during the time of flight of pulses toa target and back (range of target 148 m) of 1 msec, de-viation from adjusted value was not measurable.

(3) IF stability during the time of flight of pulses toa target and back (range of target 2000 m) of 13.3 msec,deviation from adjusted value was not measurable.

1 October 1984 / Vol. 23, No. 19 / APPLIED OPTICS 3395

0 At SS3 TARGET

,:D'R ----- TELESKOP ----- ~OR,

LO --

:

Fig. 1. Block diagram of the pulsed heterodyne system.

(4) IF stability within a time of 10 min, after 1-hwarm-up time, deviation from adjusted value was in theregion of 2 MHz (worst case).

Outgoing and reflected pulses were recorded in heightand length (therefore the system is single pulse withoutan electronic device to sample echo pulses) so that in-fluence of atmosphere and the nature of target surfacecould be studied. For small distances (148 m) a de-crease of power smaller than 1% was measured, fordistances of 2000 m a decrease of -30-40% was mea-sured. 7

Types of target examined were: retroreflectors, flatmirrors, flat aluminum with various surface structures,various coatings, and trees (2000-m range). Retrore-flectors and flat mirrors have no influence on returnpower. Flat aluminum shows a decrease of signal powerdepending on the roughness of the surface; this is aneffect of depolarization of rough surfaces. 8 Heterodynedetection is sensitive to polarization directions of theelectromagnetic vector of radiation.9 The two lasershave radiations which are linearly polarized and the EMvectors are parallel. The rough surface depolarizes thesignal radiation and the return signals as well as themain EM directions have some power in other direc-tions. Therefore there are angles between the LO ra-diation and the return signals, and for these cases ihdecreases. Measurements have shown a decrease of-10%.1o To eliminate various target reflection coeffi-cients, measurements were taken in direct and hetero-dyne detection for each target and the ratios of thesevalues were calculated.

Further experiments were done with targets of vari-ous diameters to investigate influences of spatial co-herence on heterodyne detection.11 12 Targets werespecular flat mirrors to avoid speckle influence. Resultsare given as a proportion of heterodyne-to-direct de-tection because the influence of many components couldnot be calculated and measured. It was found thatheterodyne-to-direct detection ratios with 4-cm targetdiam. are only half of those of the 1-cm target diam.The laser pulse transmitter has a 5.7-mrad divergence(without optics); all targets were completely illumi-nated.

Distance or range from a target can be measured bytime of flight of a pulse' 3 :

R c AtR=c 2 (1)

where R = range, c = velocity of light, and At = mea-sured time delay. In the pulse system there are two

Id

Ih

1h

o -'a)

b)

c)

0 5 10 15 s 20x-0

Fig. 2. (a) Two pulses directly detected; (b) two pulses heterodynedetected; (c) first pulse with an IF = 23 MHz, second pulse with an

IF = 27 MHz.

kinds of range accuracy: the first rises in the correlationbetween oscillations of two pulses (see Fig. 2). Thisaccuracy exists only in the threshold and peak-to-peakmethod, not in the zero-crossing method. The secondis inherent in all range measurement devices and de-pends on the rise time of pulses or oscillations. Theaccuracy of the first kind is given by

AR = 2rnc,WIF

(2)

where n is a number which is given by uncertainty ofcorrelation, WIF = 2 7rvIF, IIF is the intermediate fre-quency.

Equation (2) means that the discriminator could givein the first pulse (starting pulse) the starting time withthe third oscillation and the stopping time from thereturning pulse with the fifth oscillation. For this ex-ample n = 2; n depends on the height of threshold andsignal return (see Sec. III).

For the second kind of accuracy the following formulacan be used14 :

6R c c27PIF(S/N)'/ 2

-IF(S/N)1/2

where S/N signal-to-noise ratio is defined by voltageratios of signals and noise:

S/N vnv,. (4)

Here v are the measured voltages (or currents) of sig-nals and Vn are the measured voltages of noise, whichis time-averaged. In Fig. 7 the curves of relation (3) aregiven. The vertical lines are the measured values. Theuncertainties are from fluctuations of S/N.

A moving target shifts the intermediate frequency(IF) up or down by the Doppler effect. That is, thereturned frequency differs from the frequency of theoutgoing pulse. This frequency difference is propor-

3396 APPLIED OPTICS / Vol. 23, No. 19 / 1 October 1984

(3)

1.0

0.8

A

0.6

0.4.

0.- J %

0 6.6 13.2 19.8 26.4 33.0 39.6 46.2 MHz 59.4Vjf

Fig. 3. Frequency spectrum of the two pulses from Fig. 2(c). Curve1 is the spectrum of the first pulse, curve 2 is the spectrum of the

second pulse.

tional to the velocity of the target and must be used asa correction factor for the range measurements.

The frequency shift is given by the following rela-tion:

2v 27rvWIF return = WIF out ' (5)

c

where v = velocity of target and v = frequency of ra-diation. We can measure the velocity of targets withthe spectrum analyzer (see Fig. 3) or by counting theoscillations of outgoing and reflected pulses. Whentargets are moving, the numbers of oscillations fromreturning pulses is different from that of outgoingones.

There are two correction factors for range measure-ments for moving targets: the first one is counting ofoscillations and is given by

2vckArIF ~~~~~~~(6)XIF

where k is the number of oscillations used for rangemeasurement, X = wavelength of radiation, and vIF =IF of outgoing pulses. Relation (7) is given for variousvelocities and when k = 1 in Fig. 8.

The second kind of correction factor results fromdifferences of rise times from outgoing and reflectedpulses and is given by

2c(S/N) 1 2 X22rPvF (7)

This factor is for (S/N) = 100, i.e., 0.06% smaller thanthat from (6).

The target for accurate velocity measurements wasa rotating wheel placed 148-m distance from the laserrange finder. Because we know the exact rotary ve-locity 15 and range, relation (6) was measured; someexperimental points are also given in Fig. 8. Whenrange and velocity are measured simultaneously mirrorS3 is semitransparent. The signals are directed to afurther detector, and also produce a heterodyne pulse.This pulse is given on a spectrum analyzer. The de-tector is not shown in the block diagram.

Ill. Results

In Fig. 2(a) two directly detected (not heterodyned)pulses are shown. The first pulse is outgoing (reflectedfrom the wire), the second is reflected from a target at148-m range. Figure 2(b) shows two pulses, one froma wire and one from a fixed target, detected with theheterodyne method. For moving solid targets there isa frequency shift of the IF. Figure 2(c) shows pulsesfrom the wire and from the moving target. The firstpulse has an IF of 23 MHz, the second pulse has an IFof 27 MHz. The difference in the IF values is the resultof reflection of the pulses from a rotating wheel whichserves as the moving target. Figure 3 shows the fre-quency spectrum of the two pulses from Fig. 2(c).

These measurements were made with both lasersfree-running in a passively stabilized mode. Some ideaof the stability during a pulse can be obtained from theconstancy of the IF in Fig. 2(b).

To measure the time of flight of the pulse the rela-tionship between the oscillations from the outgoingpulse and the reflected pulse must be given. When therelation is not accurate there is a failure in the rangemeasurement which depends on the IF. When IF = 23MHz the failures are ±7.4 m, ±14.8 m, and so on. In thecase of heterodyne detection in this system there are twokinds of accuracy: (1) the relation accuracy and (2) theaccuracy that depends on the rise time of one oscilla-tion.

To obtain the relation between two oscillating pulsesthree methods were tested: zero-crossing measure-ments, peak-to-peak measurements, and thresholdmeasurements. The results are given in Fig. 4. In Fig.4 N is the number of events which gives the relation forthe three methods and E indicates the measured range.All measurements were done with IF = 23 MHz. Here* indicates zero-crossing, X is peak-to-peak, and 0 isthe threshold method. It can be seen that the zero-crossing method is best, because about 60 of 100 eventsgive the correct relation and therefore the exactrange.

Figure 5 shows the number of events as a function ofthe IF. Here X has an IF = 20 MHz, has an IF = 15MHz, and * has an IF = 8 MHz.

Figure 6 shows the number of events depending onthe pulse-height difference between outgoing and re-flected pulses. When the difference lies in the regionof 2 or higher, range measurement is impossible. Thebest values are in the region of 0.8-1.2. In the experi-ments differences of pulse heights can in some casestake values of 3 and higher (influence of target and at-mosphere). These large differences cannot be used forrange measurements for technical reasons [see also Eq.(2)].

In Fig. 6, * indicates a pulse-height difference of0.8-1.2, X indicates 1.2-1.4, 0 indicates 1.6-2.0, a in-dicates 2.0-2.4, and * indicates 2.4-2.8.

Figure 7 shows the accuracy R of range measure-ments of one oscillation (pulse) depending on signal-to-noise ratio. The SNR depends on bandwidth B andtherefore in this case on the IF. Curve a shows 3R asa function of B calculated with a SNR of 100, curve b,

1 October 1984 / Vol. 23, No. 19 / APPLIED OPTICS 3397

701

60-

50-

I

40-

30-

20-

10-

133..4 140.8 146.2 155.6E - 163.0 170.4. 17I

Fig. 4. Range measurement by three methods. The number ofevents is a function of the measured range.

148.2E

155.6 163.0 170.4 m

Fig. 6. Range measurement depending on the pulse-height differ-.ence between outgoing and reflected pulses.

177.8

Fig. 5. Range measurement depending on the IF.

25, and curve c, 4. The vertical lines are the measureddata for four IF and a SNR of -100. For these mea-surements -1200 data points were selected.

Figure 8 gives the correction factors AE which mustbe applied to the range measurement values when thetarget is moving: curve a, 5-m/sec target velocity; curveb, 50-m/sec target velocity; curve c, 100-m/sec targetvelocity; and curve d, 300-m/sec target velocity.

IV. Heterodyne Detection Without Oscillations

To measure the range without oscillations under thepulse envelope while still maintaining the advantagesof the heterodyne detection, the IF must be so low thatthe reciprocal of the IF is greater than the pulse dura-tion. For 400-nsec pulse lengths the IF must be lessthan -2.5 MHz. The relation between the IF and pulselength t is shown in Fig. 9. Experiments carried out forIF values below 2.5 MHz showed that the heterodynereceiving technique is valid at these frequencies. Thisheterodyne detection without oscillations is an advan-

C

Fig. 7. Accuracy R of one oscillation as a function of bandwidth B(or in this case IF). The vertical lines are measurements.

tage for some experiments where the oscillations disturbthe data system.

Figure 10 shows the received signals with various IFvalues. The lowest signal has an IF of -2 MHz. Therise times of the low IF pulses are larger than those withhigh IF, and according to Eq. (3) the accuracy of rangemeasurement is worse. The shape of a pulse changesdramatically when measured while moving. Then the

3398 APPLIED OPTICS / Vol. 23, No. 19 / 1 October 1984

IN

160-

140-

120-

100-

N 60-

40-

20-

0133.4 140.8

us | -

u l l | | l 6 . _

: i

i

4I

I9

4I

t

I 0

^ t

1.6

1

To

0

I

z ok

I

m

200-

I

100-

a

° 0 1 20 30 MHz 50Vjf-

Fig. 8. Correction factor AE for range measurements when the targetis moving.

shape of a pulse changes from the third curve in Fig. 10to the second, for example. In Fig. 10 there are exper-imentally measured shapes; the shapes in curves oneand two are produced by reflecting a pulse with a shapeof the third curve by the rotating wheel in the range of148 m. This method of producing higher IF startingwith low IF pulses is only valid when the rotating wheelgives Doppler frequency shifts with a plus sign.

V. Conclusion

Experiments demonstrate that simultaneous rangeand velocity measurements are possible using a heter-odyne system and solid targets. With a low enough IF,it is possible to make range measurements (but not ve-locity measurements) that retain the advantages ofheterodyne detection without oscillations under thepulse envelope.

References1. T. E. Honeycutt, "FM-CW Radar Range Measurement with a

C0 2-Laser," IEEE J. Quantum Electron. QE-8, 91 (1972).2. K. F. Hulme, B. S. Collins, G. D. Constant, and J. T. Pinson, "A

CO2 Laser Rangefinder Using Heterodyne Detection and ChirpPulse Compression," Opt. Quantum Electron. 13, 33 (1981).

3. F. Malota, Impuls-Heterodynanlage zur Entfernungsund Ges-chwindigkeitsmessung von bewegten Zielen, DFVLR-FB 83-18.

4. D. L. Fried, "Optical Heterodyne Detection of an AtmosphericallyDistorted Signal Wave Front," Proc. IEEE 55, 57 (1967).

5. M. C. Teich, "Infrared Heterodyne Detection," Proc. IEEE 56,37 (1968).

6. S. C. Cohen, "Heterodyne Detection: Phase Front Alignment,Beam Spot Size, and Detector Uniformity," Appl. Opt. 14, 1553(1975).

7. M. J. Taylor et al., "Pulsed CO2 TEA Laser Rangefinder," Appl.Opt. 17, 885 (1978).

8. J. Renau, P. K. Cheo, and H. G. Cooper, "Depolarization of Lin-early Polarized EM Waves Backscattered from Rough Metals andInhomogeneous Dielectrics," J. Opt. Soc. Am. 57, 459 (1967).

9. A. J. Bahr, "The Effect of Polarisation Selectivity on OpticalMixing in Photoelectric Surfaces," Proc. IRE 53, 513 (1965).

l 50\IF I

0.5\

1d-10 16-9 16-i 10-7 s 1o6t-Fig. 9. IF as a funlction of pulse length t for which no oscillation is

seen.

1

-v/f

t

t

tFig. 10. Heterodyne signals: first curve IF = 7.7 MHz; second curve

IF = 2.7 MHz; third curve IF = 2.0 MHz.

10. F. Malota, Einflufl der Depolarisation von linear polarisierterStrahlung auf den Heterodynempfang bei Laser-E-Messer,DFVLR-FB, in press.

11. R. D. Kroeger, "Motion Sensing by Optical Heterodyne DopplerDetection from Diffuse Surfaces," Proc. IEEE (Correspondence)2, 211 (1965).

12. H. T. Yura, "Optical Heterodyne Signal Power Obtained fromFinite Sized Sources of Radiation," Appl. Opt. 13, 150 (1974).

13. M. I. Skolnik, Introduction to Radar Systems (McGraw-HillKogakusha, Tokyo, 1962), p. 2.

14. Ref. 13, p. 463.15. F. Malota, Experimentelle Untersuchungen zur Impuls-Impuls

Oberlagerung geim Heterodynempfang, DFVLR-FB, in press.

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-.- ft-