Random modulation cw lidar

N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai

A new lidar scheme using a pseudorandom code modulated cw laser as a transmitting laser source (RM-CWlidar) is proposed and a demonstration of its use for aerosol measurement is shown. A formula for estimat-ing the SNR values in RM-CW lidar was derived, and it was demonstrated that the observed SNR value wasin good agreement with the calculation.

1. Introduction

Lidar (light detection and ranging)' has two uses:range-finding to a target (usually called the rangefinder) and profile measurement of a continuousquantity. This may include not only air pollutants,cloud and fog, but also temperature, humidity, and windvectors. In this paper, lidar is used for the latter.

The lidar echo can be considered as the responsefunction to an interrogative input signal. It reflects thespatial distribution profile of medium density. Twomethods have been used to obtain the response func-tion: impulse response and pseudorandom code mod-ulation.2 The first is the usual pulse lidar technique,and the latter is the pseudorandom modulation lidar.In this paper, a new type with continuous-wave opera-tion is proposed, which is called RM-CW lidar hereafter.From the point of view of continuous operation, this isa kind of cw lidar, where a pseudorandom code is usedto obtain the spatial profile, while in the case of FM-CWlidar,3 the frequency modulation is used.

RM-CW lidar is similar to the technique of pseudo-random noise (PN) radar (range finder)4 in the micro-wave region, where the spatial profile of a quantity canbe obtained by the use of a blanking period betweentransmitting and receiving periods (interrupted cwradar).4 5 In this case, complete continuous operationcan detect only the distance to a target,6 assuming anegligible return signal from the range up to the target.However, in the case of RM-CW lidar, the characteristicof small beam divergence in the laser easily allows the

H. Baba and K. Sakurai are with University of Tokyo, Departmentof Pure & Applied Science, Komaba, Meguro-ku, Tokyo 153, Japan;the other authors are with National Institute for EnvironmentalStudies, Yatabe, Tsukuba Ibaraki 305, Japan.

Received 24 September 1982.0003-6935/83/091382-05$01.00/0.© 1983 Optical Society of America.

use of crossover effect of the laser beam and the receiverfield of view,7 8 which suppresses the return signal fromthe short distance.

Pseudorandom modulation is a technique in the timedomain. The transmitting signal is modulated by adigital pulse code, usually consisting of on and off.However, if phase switching by 180° is used as in thecase of radar,4 a true continuous-wave RM-CW lidarwill be accomplished. Therefore, in the following, weuse the notation RM-CW lidar to mean a digital-pulse-code modulated lidar. The addition of frequencymodulation (FM) technique to the RM-CW lidar (i.e.,RM-FM-CW lidar) can determine both the range andvelocity information without ambiguity.

In this paper we propose the concept of RM-CW lidarwhere the crossover effect has been introduced to thepseudorandom modulation technique and report thefirst demonstration of the RM-CW lidar, to the authors'knowledge, applied as a Mie scattering lidar. Thistechnique, however, is applicable to any kind of lidars,such as Raman lidar, fluorescence lidar, and differentialabsorption lidar (DIAL), if a suitable cw laser exists.For example, a pair of Ar-ion laser frequencies is suit-able for the DIAL measurement of NO2.9

II. Lidar Equation and Signal-to-Noise Ratio

When the input signal, the response function, and thebackground noise are x (t), g(t), and b (t), respectively,the output signal z(t) is expressed in a convolution formas

z TZ(t = f. x(t -t')g(t')dt + b(t). (1)

In the lidar case, the response function as a functionof echo return time t is given as

g(t) = i7 (c/2) Arfr(R)Tr(R) 2 Y(R)/R 2 ,R = ct/2.

(2)(3)

1382 APPLIED OPTICS / Vol. 22, No. 9 / 1 May 1983

Here, Q is the device optical efficiency, c is the lightvelocity, Ar is the receiver aperture area, fir is the dif-ferential backward scattering coefficient, Tr(R) is thetransmission coefficient to the distance R Tr (R) =exp[- fR a(r)dr], a is the absorption coefficient), andY(R) is the crossover function or geometrical formfactor7 ' 8 which is the fraction of the laser beam crosssection covered by the receiver field of view.

For the special case of a -functionlike input signal,x(t) = Pptp6(t), the output signal takes the form

z(t) = Pptpg(t) + b(t), (4)

where Pp is the pulsed laser power, and tp is the laserpulse temporal width.

For the case of RM-CW lidar, the input signal takesthe form

x(t - t') = Poa(t - t'). (5)

Here, Po is the cw laser power, and a (t) is usually gen-erated by a shift register with the exclusive OR and iscalled the maximum shift register sequence (M se-quence). The nth order M sequence is expressed in Fig.1 for n = 4. The total number N of elements with gatetime At in a period T (N = T/At) is given by N = 2n -1. Then, a(t) is expressed in a series form:

Na(t) = E ai . (t - iAt) [i (modulo N)],

i=1

ai = 1 or 0, (6)

e(t') = 1(0 _ t' < At); 0 (otherwise).

Mathematically, each element of the M sequence shouldhave an absolute value of 1. In the case of a binary Msequence, the set (1,0) is transferred to the set (1,-1) bya = 2ai - 1 (a' = 1 or -1). Then, the autocorrelationfunction a',a(j) (modulo N) is given by

NTa',a(J - _ aiai+j

11 forjO0(7I- 1N for - 0.

Cross correlation between a'(t) and a(t) is given by

Ta',a ( -) =N a ai+j

j(N+ 1)/2N 1/N forj =0 (80t0 forj 0, (8

U2ill1IMPULSE MODULATION 1-

I-

14 15 1 1 2 1 3 1 4 1 5 1 6 1 7 18 1 9 110|1 1213114115 1 2

PSEUDO-RANDOM MODULATION

H I] n. . r ----Ut -

T= NAt (N =15) d

Fig. 1. Example of M sequence (N = 15).

where G(t) is nondimensional, and all elements arecircular with modulo N. Then, Eq. (1) can be expressedas

zi = Po Fj ai jGj + bi.I.

(1')

The expectation value of A (A = zi, bi, and Gj) is re-placed by the average value A:

ME(A) =A(1/M) F A-,

m=1

where A m is the quantity in the mth succeeding inter-val. Then, the demodulated signal for the jth channelis given by the cross correlation a',z (J). The signal Sjfor the measurement time over one period T is given byN times 'a',z( ):

N NSj = N',,(j) = Fi a+jzi = 1P.Gj + a+jbi.

i=l i=1(10)

Using Eq. (10), the backscattering profile fir is obtainedfrom Gj. The variance Vj for the jth signal IP(Gj isgiven by

Vj = EI [1P. (Gj - aj)]2

= E ai-j(zi - 1)1+ E ai>i(bi - 5)

N N[= Ef(zi-;Fi) 2

] + Z E(bi -i)21 i=l i=l

(11)

where I [= (N + 1)/2] is the number of elements for a =1 within the period T. The 5-functionlike autocorre-lation feature of the M sequence permits the replace-ment of demodulation by correlation.

Now we expand the output signal, background noise,and response function in series form:

Nz(t) = L zi* e(t - it), (9a)

i=lN

b(t) = Z bi* e(t - iAt), (9b)i=l

NG(t) = g(t)At = T Gi e(t - iAt), (9c)

i=l

Since the output signal and background noise followPoisson statistics,

42E[(z - 2i)2] = tZ-i

02E[(b - 6j)2] = tbi

(12a)

(12b)

where t = At7Q/hv (Q, quantum efficiency of a de-tector, h, the Planck's constant, v, the frequency) is theconversion constant from power to photoelectronnumber.

Equation (11) can be rewritten as

V = (1/0 E 1 + Nb , (13)

1 May 1983 / Vol. 22, No. 9 / APPLIED OPTICS 1383

v

where b is the average of bi over a period T. Using Eq.(1'), Eq. (13) can be rewritten as

v | = 1/ [I (Po F _i-kGk 6 + N ]

= (1/0 (Po1 ok + 2Nb)

= (N/l)(Pol + 2b), (14)

where G = (1/N) ;k=,Gk. From Eq. (14), the signal-to-noise ratio (S/N)RM for the RM-CW lidar integratedover M-time sequential intervals is given by

(S/N)RM = VM x Sj = *V v (15)v'lP0 G + 2b

The signal-to-noise ratio of the pulsed lidar is givenby

(S/N)puise = ____Ppatp (16)VPgjp - 2b

If the energies (IV1N)P 0At and Pptp in a period T arethe same, the difference between (S/N)RM and (S/N)pulse is only the difference of G and gjtp in the de-nominators. Therefore the necessary cw power Po isgiven by Pp (/1) (tp/At) to obtain the same S/N ratioas for the pulse operation with peak power Ppand pulsewidth tp, except for the difference between G and 9jtpin the denominator.

Ill. Characteristics of RM-CW Lidar

Features of the pseudorandom modulation whenapplied to lidar are found in the response function, Eq.(2). The term range square (R2) in the denominatorbrings a tremendously large contribution from the shortrange, which hampers the detection of the weak signalfrom long distances. In the present scheme, thisshort-range contribution is eliminated by the intro-duction of the crossover function Y(R).7 8 As illus-trated in Fig. 2, the detection range Robs extends fromthe first crossing point, Rmin, to Rmax (= Rmin + cT/2).

To obtain the desired Y(R) shape, careful design isrequired. As is clear from the principle, in RM-CWlidar the signal from R + p(cT/2)(p:integer) accumu-lates on range R. Therefore, the signal at Rmax must besmaller than the error limit. At the present state of theart, the discharge electrical noise is much larger inpulsed operation than in cw operation. For a givenperformance level, the RM-CW lidar is more compact,more stable, and more reliable. The compactness andquietness of the transmitting laser is a very importantfactor to mobile or airborne lidar systems.

When a moderate distance (for example, <100 km)is considered using RM-CW lidar, the period is <1 msec,and this results in a large repetition frequency and asmaller signal level for a unit period. This releases thedetector and the fast A-D converter from the require-ment of large dynamic range.

In the case of coherent detection, a cw laser is pref-erable in frequency stability to a pulsed laser, so thatRM-CW lidar is easily extendable to coherent lidar.

J1YL2;"f H R 5 T 2

I DEMODULA1ION(CORRELATION)

.,(. gR)

F. 2 eRobs R

Fig. 2. Schematic explanation of RM-CW lidar.

Fig. 3. Block diagram of the experimental setup.

IV. Experimental Setup

A RM-CW lidar system was assembled using a 1-WAr+ laser at 514.5 nm as the transmitting laser source.An electrooptical modulator modulated the laser withbinary M-sequence code. The backscattered signal wascollected by a 15-cm diam telescope, detected by aphotomultiplier (HTV R928), amplified and discrimi-nated, and then recorded cyclically on a 1023-elementmemory. The stored signal was cross correlated withthe gradually delayed modulating code (M sequence),and the processed data were displayed on a scope as afunction of delay time. The gate time had the mini-mum value of 84 nsec and was variable. The block di-agram is shown in Fig. 3. The processing electronicswere exactly the same as those used for a molecular-beam time-of-flight experiment,l where a photoncounting technique was suitable for weak signal detec-tion. For lidar signals with moderate level, analog-mode detection using an A-D converter is more ap-propriate, and a new processing unit with an A-D con-verter is being constructed. The outline of the exper-imental setup is described in Table I.

V. Example of Aerosol Measurement

Measurement of the aerosol distribution in aboundary layer was made using the RM-CW lidar sys-tem described in the previous section. The gate timewas set at 200 nsec (spatial resolution of 30 m). Themeasurement was carried out at nighttime. The

1384 APPLIED OPTICS / Vol. 22, No. 9 / 1 May 1983

Table 1. Features of the RM-CW Lidar

Laser, Ar+ laserWavelength, 514.5 nmPower, 1 W (cw)Beam divergence, 2-mrad (FWHM)

Pseudorandom code, binary M sequenceNumber of elements, 1023Gate time, 200 nsec (min 84 nsec)

Telescope, NewtonianDiameter, 15 cmFocal length, 1.3 mField of view, 2.3-mrad (FWHM)Separation between laser and telescope, 5 m

DetectionBandwidth of interference filter, 10 nmPhotomultiplier, HTV R928

demonstrated. Although the RM-CW lidar requirescareful optical design to obtain the desired crossoverfunction, cw laser operation offers a compact, reliable,and quiet lidar system. With the development of adigital processing system, the correlation technique canbe handled easily, and a RM-CW lidar is very suitablefor either mobile or airborne systems. Continuous wavelaser operation is easily applied to coherent detectionand is also suitable in combination with the frequencymodulation (FM) technique. In RM-FM-CW lidar, thevelocity information can be separated from the spatialdistribution information without ambiguity.

The authors are grateful to T. Ueno and F. Shimizufor valuable discussions and to M. Kondo for experi-mental assistance.

background counting level was very high (107 photo-electrons/sec) due to the bright illumination from thedowntown area of Tokyo, and it was suppressed to 106photoelectrons/sec by reducing the photomultiplier gain(this is equivalent to a higher discrimination level).11

The distance between the transmitter (laser) and thereceiver (telescope) was set at 5 m in order to suppressthe contribution from a short distance. An iris 3 mmin diameter at the focus position determined the fieldof view (2.3-mrad FWHM). An example of the signif-icance of the crossover function between the transmitterand the receiver is shown in Fig. 4. In this case, the el-evation angle was about 800, and the angle between theoptical axes of the transmitter and the receiver is tiltedby 4 mrad so that the crossover function started froma shorter distance, reached a maximum value at 1.2 km,and quickly decayed to zero. The estimated Y(R)profile is shown in the figure by a dashed line, where thescale has been adjusted so that Y(R) has the same initialslope at R = 0.85 km as the observed lidar signal. Thelidar signal in Fig. 4 has a large S/N ratio (500 at R =1 km). This is in the same order as the calculated valuefor a 5-min integration period in the experimentalcondition.

Another example with good parallelism between thetransmitter and receiver optical axes is shown in Fig. 5.The crossover function is shown by a dashed line in thefigure. The lidar signal data were also integrated over5 min. In a RM-CW lidar, the denominator in the S/Ncalculation [Eq. (15)] is independent of the distance.Therefore, the photon number as a function of distanceis proportional to the S/N value in any condition (i.e.,daytime and nighttime). The calculated photonnumber is shown in Fig. 5 by a solid line (the scale wasadjusted to fit the observed data). Observed and cal-culated data show similar shapes and approximately thesame S/N values (15 at R = 3 km). In this case, theexistence of a strong echo from a cloud may deterioratethe S/N value of the aerosol echo signal by the spectraldispersion effect.1 2

VI. Summary

In this paper a new concept of pseudorandom mod-ulation cw lidar (RM-CW lidar) was proposed and

References1. E. D. Hinkley, Ed., Laser Monitoring of the Atmosphere

(Springer, New York, 1976).2. Y. E. Lee, Statistical Theory of Communication (Wiley, New

York, 1960).3. R. A. Ferguson, "Feasibility Study of a cw Lidar Technique for

-J

z

0-J

Y(R)

O0 1 2 3

DISTANCE (km)

0.5

04 5

Fig. 4. Example of RM-CW lidar measurement. Two optical axesof the transmitter and the laser crossed due to the nonparallelism of4-mrad tilting. The crossover function Y(R) is shown by a dashedline. Two curves are adjusted to have the same initial slope at R =

0.85 km.

-J

zt9(n

a:0

0

0.3

0.2

0.1

0

0 5 10 15DISTANCE (km)

Fig. 5. Example of RM-CW lidar measurement. Solid line is atheoretical fit of lidar return signal (absolute value is normalized tothe experimental data). Dashed line shows the estimated crossoverfunction Y(R), which is adjusted to have the same initial slope at R

= 2.5 km with the lidar return signal.

1 May 1983 / Vol. 22, No. 9 / APPLIED OPTICS 1385

IIIIIIIIII

IIIII

Measurement of Plume Opacity," Final Report SRI project 1979,EPA no. 650/2-73/037 (Nov. 1973).

4. M. I. Skolnik, Ed., Radar Handbook (McGraw-Hill, New York,1970), Chap. 16.

5. T. Sakamoto, Y. Taki, H. Miyakawa, T. Suzuki, H. Kobayashi,and T. Kanda, J. Inst. Electron. Commun. Eng. Jpn. 46, 155(1963), in Japanese.

6. S. E. Craig, W. Fishbein, and 0. E. Ritenbach, IRE Trans. onMilitary Electr. MIL-6, 153 (1962).

7. J. Harms, Appl. Opt. 18, 1559 (1979).8. Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, Appl. Opt..

18, 3908 (1979).

9. D. C. O'Shea and L. G. Dodge, Appl. Opt. 13, 1481 (1974).10. H. Baba, K. Sakurai, and F. Shimizu, to be published in Rev. Sci.

Instrum. April (1983).11. In the case of photon counting, a theory (Ref. 10) gives the

counting efficiency in the form P = [1 - expGiAt)]/-int, where7F is the average count of incident photons/sec and At is the unitgate time. The error limit of 10% in corresponds to nAt being0.2, which gives nT to be 106 photons/sec for At = 200 nsec. Thissituation was attained by raising the discrimination level.

12. R. C. Dixon, Spread Spectrum Systems (Wiley, New York,1976).

John Eggert Prize for image science

Invitation to apply for the 1984 prize

The prize was instituted by Prof. Dr. John Eggert, late head

of the previous Department of Photography, Swiss Federal

Institute of Technology (ETH-Z) on the occasion of his 80th

birthday and will be offered for the sixth time in 1984.

Young scientists are encouraged to submit papers from the

field of Imaging Science.

Imaging Science is meant to embrace a wide field, comprising

Optics, Photography with and without silver halides, digital

and electronic methods of Image Recording, Analysis and

Processing as well as the Physiology and Psychology of Vision.

Personal applications as well as proposals by others will be

taken into consideration. Applications with complete literature

references in duplicate with copies of most important reprints

should reach Prof. Dr. W.F. Berg, a member of the Foundation

Council, at Hellstr. 7, CH-8127 Forch, Switzerland, no later

than October 15, 1983

The Prize for 1984 consists of a sum of SFr. 7'500.-- and a

Certificate. The recipient will be asked to present his work

as a lecture at a colloquium of the Institute of Communications

Technology of the ETH-Z.

1386 APPLIED OPTICS / Vol. 22, No. 9 / 1 May 1983