Random modulation cw lidar using new random sequence

Random modulation cw lidar using new random sequence Chikao Nagasawa, Makoto Abo, Hideki Yamamoto, and Osamu Uchino

New modulation codes are presented for a random modulation cw lidar. One characteristic of these modulation codes is that for very noisy background conditions, the signal-to-noise ratio is improved by using these new sequences, and is better than for the maximum-length sequence (the M-sequence) which is commonly used as the modulation code. Another characteristic of these modulation codes is that there is no correlation between them. This fact will be useful for the simultaneous multitransmitter of the differential absorption lidar. These two characteristics of the new modulation codes were confirmed experimentally. Key words: Lidar, RM-CW lidar.

1. Introduction

The laser radar (lidar) is a useful instrument for continuous monitoring of the spatial distribution of some species suspended in the atmosphere. A high peak power pulsed laser is usually used for the lidar transmitter, and it is well known that the higher the pulse energy is, the farther away a target can be detected. On the other hand, a lidar technique which makes use of a continuous wave laser modulated with pseudorandom pulse sequences for the transmitter was presented.1 ,2 It is called the random modulation continuous wave lidar (RM-CW lidar). A feature of this technique is that average laser power is more important than peak power. This technique makes it possible for a lidar transmitter to use a low peak power laser such as a diode laser. Although diode lasers cannot produce high peak power outputs, a compact and transportable lidar compared to a pulse lidar of high peak power will be easily realized by using the RM-CW lidar technique with diode lasers with average power outputs of the order of 1 W. This lidar has high range resolution.

In this paper we propose sequences consisting of new modulation codes for a RM-CW lidar. The characteristic of these sequences is that although the autocorre-

Osamu Uchino is with Meteorological Research Institute, Nagamine, Tsukuba-shi, Ibaraki 305, Japan; the other authors are with Tokyo Metropolitan University, Department of Electrical Engineering, Fukasawa, Setagaya-ku, Tokyo 158, Japan. Received 22 June 1989. 0003-6935/90/101466-05$02.00/0. © 1990 Optical Society of America. 1466

APPLIED OPTICS / Vol. 29, No. 10 / 1 April 1990

lation function of these modulation codes are not as functionlike as the M-sequences which have been most commonly used, it is confirmed that the new codes play an important role in conditions of severe noise. Moreover, these new sequences are useful for DIAL measurements because there is no correlation between the sequences. 11. Recovery of Received Signal The notation used in this paper is the same as in Ref. 2. If an autocorrelation function of a pseudorandom code is -functionlike, the response function of the target can be recovered by taking the phase-shift crosscorrelation of the detection signal with the modulation code. The integrated detection signal yi of the RM-CW lidar is expressed as N-i

i = E xi-Gj + b

i = 0,1,2,. . . N- 1,

(1)

j=o

where x = Pai is the transmitted signal, a is the pseudorandom modulation code, P0 is the laser power, bi is the background noise, and Gj is the response function needed to obtain the spatial profile of scattering medium. The suffix i is the number for the time interval. Consider the random sequence of the sequence length N consisting of elements ai = 1 or 0. The elements of the sequence can also be expressed as a = 1 or -1 connected to ai by the relation a' = 2ai - 1. A cross-correlation function for as and ai is given by N-1

Oaa'(k) =

E aaia+k i=O

(2)

If the M-sequence is used as the code of random modulation

( - -.0)

f--qi - - -- - - .---A 00.

A A A

I., N

where b is ensemble average of bi. The response function GI is derived from Eq. (6). The SNR equation is given in terms of the expectation value to the standard deviation of Si. From the nature of the Poisson statistics, the SNR equation for Mtime sequential intervals is given as

j

Il IliI

N

(a)

SNR

=

()

JMN P.(N+ 1)G1/2 WN F/1 IP(N + 1)/2 + I

where G is the average of G over one period, t is the conversion coefficient from detected power to photoelectron number, and A is the excess noise factor of the detector. -No-- - - -- - - -

Ill.

(b)

New Modulation Codes

Only the M-sequence has been utilized because it is easily generated by several shift registers and delay elements for the RM-CW lidar. This sequence has the property that the number of ones in a sequence always exceeds the number of zeros by only one. Therefore, a term of the background noise bi cannot be disregarded completely in Eq. (5). This term is especially significant for very noisy conditions. In order to correct this defect, we propose new several modulation codes for an RM-CW lidar. If a sequence a consists of an pseudorandom code of elements (1,-1) such as the M-sequence, the first new sequence a!' (the Al-sequence) iS3 ai'= (-l)a'

i = 0,1,...,2N-1.

(8)

Similarly, a second kind of sequence ai' (the A2-sequence) is given by the following equation (o) =

Fig. 1. Cross-correlation function of (a) ai and a; (M-sequence), (b) a* and a*' (Al-sequence) and (c) a** and a*' (A2-sequence).

_

f(N +1)/2 k =0 (modN)

1

0

4~aa~k)

k ip 0 (mod N).(3

This function is plotted in Fig. 1 (a). The response function G is found from the crosscorrelation SI of the signal yi with the modulation code

a

ai(i = 4m,4m + 1)

where N is the length of the original sequence. The length of the Al-sequence is 2N and the length of the A2-sequence is 4N. The cross-correlation function of a* (=(a' + 1)/2) and a*' is given by

IN qXaa,(k) =

-1 -k

-N

N-1 SI =

k=O k = 2n = 2n k =N

(4)

E yjai-1 .

m = 0,1,...,N- 1,

l-a(i = 4m + 2,4m + 3)

-

(mod 2N) 1 (mod N) (mod N) (mod 2N) n=1,2,...,(N

(10)

-

1)/2,

i=O

Substitute Eq. (1) into Eq. (4):

{

and the cross-correlation function of a* (= (a *'+ 1)/2) and a** is given by

N-1 (-

SI = E

ijGj + bi} ai-

i=o j=o N-1

= P0

E

j=o

I)Gj +

a,bi. i=O

(5)

P.GI + ,

k k k k

l-2 t-2N

If the background noise bi is independent of the modulation code a', the expectation value of Sj(=E[S1 ]) is expressed according to Eq. (3) as E[SI = N+

k=

2

l~~a*~)=

N-i

aa'(i -

02N

(6)

(mod 4N) (mod 2N) (mod 2N) (11) (mod 2N) (mod 4N) n=1,2,...,(N-1)/2.

= 4n --2 = 2n --1 = 4n = 2N

The waveforms for these cross-correlation functions are shown, respectively, in Figs. 1(b) and 1(c). If the Al-sequence a is used as the modulation code, the cross-correlation S is 1 April 1990 / Vol. 29, No. 10 / APPLIED OPTICS

1467

2N-1

2N-1

3

=P0

=

'kawa*'( - I)Gj+

j=o

3

a"jbi.

(12)

i=O

The expectation value of S' is expressed according to Eq. (10) as E[Sfl = NP.G

and the A2-sequence of same element number, i.e., between the four-cycle M-sequence, the two-cycle Alsequence, and the one-cycle A2-sequence. The crosscorrelations of the Al-sequence and the A2-sequence are given by

- NPoL0+N

(N-1)/2

3

+P.

(G2 .-1+1 + G2f.1+1+N)

n-1

P0

(G2 .+1 + G2.++N) n-1

2N-1

+

3

(18)

Oa-*a*(k) = O.

(19)

This characteristic is useful for obtaining different response functions simultaneously using two transmitters as in DIAL measurements. If transmitter A is modulated by the Al-sequence and transmitter B is modulated by the A2-sequence, the mixed detection signal yAgi is expressed as

(N-1)/2 -

4kaa..,(k) = 0

a"1 bi

4N-1

i=O

NP.G 1.

YABi =

(13)

And if the A2-sequence ai is used as the modulation code, the cross-correlation S is 4N-1

4N-1

37a--a*'i o j=0

o=P

-

I)Gj +

3

a"bi.

(14)

i=o

The expectation value of Sj is expressed according to Eq. (11) as

4N-1

XA.i.JGAj+ j=0

3

XBi-j

+ bi,

(20)

j=o

where

XAi = PAa* and XBi = PBa**, PA and PB are the power of the transmitter A and B, and GAj and GBj are the response function for the transmitter A and B respectively. The cross-correlation SAI of the mixed signal yABi with the a*' is 4N-1

SAl =

3

YABia*-l

i=O

E[S*I] = 2NPOG, - 2NPoGI+2 N 4N-1

(N-1)12

3

+ 2Po

= PA

(G4 n- 2 +1 + G4n-2+l+2N)

+

(G4 .+1 + G4fl++2N)

3

a*'bi.

(21)

The expectation value of SAI is expressed according to Eqs. (13) and (16) as

4N-1

a**b

EISAI]

i=O

2NPGl.

(15)

The first term in each of Eqs. (13) and (15) is a recovered response function. The second term is almost negligible if the sequence length N is chosen to be long enough, because the lidar return decreases in proportion to the range squared. The third and the fourth term cancel each other as the response function should be smooth. The important characteristic of the new sequences a* and a* is that the total number of zero elements in a sequence coincides with that of the one elements, that is 2N-1

a'=

(16)

i=0 4N-1

ai = 0.

(17)

i=0

Therefore the influence of the background noise b in the last term of Eqs. (13) and (15) can be removed completely from the recovery equation. Another characteristic of these sequences is no correlation between the M-sequence, the Al-sequence, 1468

ka*-a*'(i >)G~j

j=0

i=O

n=1

3

E

)GAj + PB

4N-1

(N-1)/2

+

4N-1

'kaba*'(i 4

j=0

n=1

- 2Po (

3

APPLIED OPTICS / Vol. 29, No. 10 / 1 April 1990

2

NPAGAI-

(22)

As the cross-correlation between the Al-sequence and the A2-sequence is zero, the response function GA modulated by the Al-sequence is recovered completely. Similarly the GBI can be recovered from the crosscorrelation of the mixed signal yABi with the A2-sequence. IV. Experimental Setup

The particular features of our RM-CW lidar system4 are: (1) two transmitters for the DIAL measurements and high power measurements; (2) the ability to use arbitrary pseudorandom modulation codes; (3) design and construction enabling one person to carry and operate it. The block diagram of the system is shown in Fig. 2 and the specifications for the experimental setup are described in Table I. For light sources, we use two high power near-IR diode lasers. The wavelength is tunable to the water vapor absorption line for the DIAL measurement. The temperature of each diode laser is controlled automatically to maintain suitable wavelengths. If the two

diode lasers are operated at the same wavelength, the maximum output peak power is 100 mW. For the

I

co

ZJ -LJ

r---------------- --- ----------------- I [YJ TIIG COE IUNR

Cr CD

0 iiI

--L --RQ.CES 0QR

(a)

Fig. 2. Block diagram of the experimental setup.

I

F-

DIAL measurement, each diode laser wavelength is controlled for both the on-line and off-line frequencies. The driving currents for the diode lasers are modulated by pseudorandom codes. The modulation codes are set on code memories from a control computer so that arbitrary pseudorandom modulation codes can be used. The backscattered light from particles is collected by a 280-mm diam Schmidt-Cassegrain telescope. The telescope is mounted on a lightweight fork-type mounting of which the horizontal and elevation angles can be changed. A photomultiplier tube (PMT) sensitive to near-IR wavelengths is used as a detector. As the PMT operates in a photon counting mode, the output pulses are discriminated and fed into high-speed counters. The minimum gate time of the counters is 133.3 ns which corresponds to a 20-m range resolution. The counted data are simultaneously add-

Table I. Specifications of the experimental setup

Transmitter Diode laser Peak output Wavelength Beam divergence Receiver Telescope Aperture Effective focal length Field of view Filter bandwidth Detector Signal processor Gate time Range resolution Number of elements Accumulator accuracy Correlator accuracy Control computer unit

LT017MD (Sharp) X 2 50 mW (max) 2 815-822 nm