Optical communication between aircraft in low-visibilityatmosphere using diode lasers

Arun K. Majumdar

This paper presents an experimental and theoretical framework to determine parameters of an atmosphericoptical communication link using multiple-forward-scattered (MFS) radiation. The study itself simulates ina laboratory environment the various physical factors that are encountered in the actual atmospheric channel.Parameters that affect signal-to-noise fluctuation at the receiver channel, such as multiple scattering of thelaser beam off particles in clouds and the atmosphere, sky background, and the effects of direct illuminationby the solar flux, are evaluated. Using a GaAlAs laser diode (X = 0.8486 pum) as a source, the MFS opticalchannel parameters are evaluated. The system margin using a pulse position modulation format for thislaboratory-simulation scattering medium with a quartz-halogen background condition was determined as afunction of field of view for various data rates and background noise. For a specific optical depth of thescattering medium, values of the data rates are determined for which communications can be maintained inthe presence of direct background noise radiance whereas a negative margin for higher data rates will result inan excessive error rate. Acquisition and high rates transfer between aircraft in low-visibility atmosphereseem to be feasible providing a relatively covert system with high immunity to jamming.

1. Introduction

Laser communication systems exploiting high spa-tial resolution and the compactness of diode lasertransmitters show great potential for tactical commu-nication links. However, in a low-visibility atmo-sphere, multiple scattering due to particulates such ashaze, rain, snow, clouds, fog, dust, and smoke can seri-ously degrade the performance of the atmosphericcommunication system by limiting the percentage oftime the communication link would be available fordata transmission. Performance degradation can becompensated for somewhat by adapting the opticalreceiver to increase the field of view (FOV). Theapproach of designing atmospheric laser communica-tion systems utilizing a wide angular divergent trans-mitting beam offers several potential advantages likeeliminating the need for heavy, complex, and costlystabilization, pointing, and fine tracking systems.1Such a system will allow covert communication formilitary aircraft to transfer data to a relieving aircraft,thus increasing effectiveness in antisubmarine warfare(ASW).

The author is with Lockheed-California Company, Kelly JohnsonResearch & Development Center, P.O. Box 551, Burbank, California91520.

Received 1 July 1985.0003-6935/85/213659-07$02.00/0.© 1985 Optical Society of America.

This paper presents an experimental and theoreticalframework for quantitative performance analysis of anatmospheric optical communication link using multi-ple-forward-scattered (MFS) radiation. We haveconsidered the situation when the signal becomesmasked to a degree by the spectral component of thehigh background noise near the laser transmittingwavelength. Typical examples for this case are whenthe laser transmitter happens to be between the sunand receiver terminal, or the system has to operate inthe presence of a sudden short-duration high-intensityelectromagnetic disturbance of unknown source at ornear the laser transmitting wavelength.

For scattering in a turbid atmosphere, the phasefunction exhibits strong forward-scattering peaks withsignificant wide-angle scatter. An effective scatteringangle can be assumed beyond which the scattered pho-tons do not contribute to the received field, and thusthe true phase function can be truncated. The multi-ple-forward-scattering (MFS) approach, to be dis-cussed later, can then be applied. For a particularatmospheric particle size distribution, for example, ofhaze and cloud ranging in diameters of 0.02 to 20 ,m,the multiple-scattering parameters needed to truncatethe true phase function can be estimated.

Recently, results of a laboratory-simulation experi-ment for optical communication through low-visibilityatmosphere using a diode laser have been published.2Using some of the these results we have estimatedbeam spread/angular spread angle in terms of channelcoherence length, rms forward scatter angle, and for-

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3659

ward-scattering efficiency. These parameters areneeded to determine the available signal or power atthe receiver terminal for the multiple forward-scat-tered optical communication channel. Next, a pulse-position-modulation (PPM) format has been consid-ered. PPM is an efficient modulation scheme fordiscriminating the signal pulse from a high back-ground thus permitting relatively high data rates.The SNR needed to achieve acceptable bit error ratedetermines the required optical power for various datarates and background counts. We have been able todetermine the minimum FOV which optimizes thesystem margin for a given data rate, a low-visibilityatmospheric parameter, and background condition.

In Sec. II the MFS communication channel model,with results from a laboratory-simulation experiment,is presented. This model is used to evaluate the MFSchannel propagation parameters. The signal require-ments for various data rates and background countsare described in Sec. III. Performance of the atmo-spheric optical communication system is analyzed byevaluating the system margin as a function of receiverFOV.

11. MFS Communication Channel Model: LaboratorySimulation Results

In designing an optical communication systemwhich is able to operate in a low-visibility atmosphere,the propagation effects due to multiple scatteringmust be known. Typically, turbid atmospheres exhib-it strong forward-scattering peaks with significantwide-angle scatter and backscattered components.We can, therefore, exploit scattered radiation in addi-tion to the unscattered component to improve commu-nication through a low-visibility atmosphere which ischaracterized by the optical depth, r = FL, where / isthe atmospheric attenuation coefficient and L is thepropagation path length (r > 1).

The available signal power PA received through theentire atmospheric link is given by Eq. (1).3 Thisequation considers the optical trains at both the trans-mitter and receiver terminals and the effects of thefield stop iris in the receiver and utilizes the MFSpropagation model3 :

(1)(PA) Pt(PR/OTL) exp(-faL)[1 + (/0T)

2][1 + (00O0R)

2]

wherePt = continuous wave laser transmitter power at

wavelength X,

PR = receiver aperture radius,OT = transmitter initial beam divergence (half-cone

angle),1

3at = effective attenuation coefficient = a - As',

3 = /Ad + I% (pa being the absorption coefficientand As being the scattering coefficient),

s= Ak, , being the forward-scattering efficiency,So = 21 /2 /Kpo, where K is the wave number = 27r/X,

and the channel coherence length, PO =(3/OS'LK2OF 2)1/2,

OF = rms forward scatter angle, andOR = field-of-view half-cone angle, i.e., FOV = 2 OR.

The unscattered component of the received signal isgiven by

(PA)uns = [Pt(PR/OTL)2 ] exp(-3L), (2)

where the parameters are defined above.3 Note thatfor the multiple-scattering regime [(P0 )sc/(PA)uns >1], as will be shown from the experimental data later,where (PA),, is the scattered component of radiation.

Photodetector noise plus fluctuations and interfer-ence in the channel and the noise due to backgroundflux cause some of the demodulated information tohave errors. Thus system performance is proportionalto the probability that the message was received cor-rectly. The background radiation power for extendedsources (such as the sky background) that completelyfill the receiver FOV can be written as

pB = r2TarX2O P2N(X), (3)

where Tarr are atmospheric and receiver transmissivi-ties, AX is the input optical filter bandwidth, and N(X)is the spectral radiance of the background at wave-length .4 A typical value of daytime N(X) = 10W/m 2 - sr gzm may be assumed. 5 6

It is important to include the direct solar back-ground at this point. Consider a spherical source, e.g.,

LEN

BEAM

%' i ' MULTIPLE FOV SCATTERING SPLITTEROPTICAL RECEIVER FILTER CELL

T % 4% *A _ *A_ (I5 A } __ 0e' ',d1'"

BACKGROUNDLIGHT SIMULATOR

iSDIODE LASER |TRANSMITTER

Z

'As

Fig. 1. Experimental setup.

3660 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

the sun of diameter d, which possesses a uniformradiation pattern and a subtended solid angle Q, lessthan the receiver's FOV solid angle. Then the back-ground power from direct solar illumination can bewritten as

PB = lrTaTrAX sPN(X)

in terms of spectral radiance N(X) or

PB = 7rTaTrA pH(X)

40

30

(4)

(5)

in terms of spectral irradiance H(X).6 The solar spec-tral irradiance at the diode laser transmitter wave-length, X = 0.849 m, is about H(X) = 990 W/m2

- gm7

We obtain the following ratio of scattered-to-un-scattered power when the same transmitter and thesame propagation length are used:

(PA))scattered exp(6oflL) (6)(PA)unscattered [ 2 2 [ 3 2 ' 1

From independent measurements of scattered andunscattered received power for different values ofFOVs, the above equation was solved to determine (forward-scattering efficiency) and OF (rms forward-scattering angle). These parameters are necessary todetermine the system margin (to be discussed in thenext section) needed for communication system de-sign.

The experimental results for determining the SNRand the ratio of scattered-to-unscattered signal as afunction of the receiver FOV are described in detail inan earlier paper.2 The setup is basically the same asfor this work where further communications analysishas been presented using some of the previous results.Essentially, a diode laser transmitter (X = 0.8486 im)

with a cw power output of 7 mW and a full-angledivergent beam of 150 was used. The signal lightbeam was superimposed with background noise gener-ated by a quartz-halogen lamp (model P43t, 100 W,Philips, Germany) with a highly polished aluminumconical reflector. Both signal and noise propagatedthrough a scattering cell containing both polydisperseand monidisperse particles of polystyrene latexspheres in water suspension. (The diameters of themicrospheres ranged from 0.3 to 5.17,um.) The scat-tering medium simulated the low-visibility atmo-sphere. We were able to replicate a cloudy atmo-sphere a few kilometers thick in the laboratory using a12.7-cm long scattering cell (see Fig. 1). In this experi-mental setup, a multiple FOV optical receiver with avery narrowband interference filter (AX - 15 A) de-tects the light scattered through the medium. Fourdiscrete positions of a switch in the receiver allow theFOVs to be selected from 0.043, 0.150, 0.426, and0.945° using four individual detectors. The output ofthe receiver is fed to a CRO and an rms voltmeter.The SNR was determined from the peak-signal-to-rms-noise ratio. The optical thickness characteriz-ing the medium was determined by extrapolating to azero FOV value of the ratio of Io (intensity withoutmedium) and I (intensity with medium) using the rela-

20

:

, - 2.21

E423

MONODISPERSE(DIAMETER - 3.01pm}

0.25 0.5

FIELOOFVIEW (FOVI 2

R D0EGREE)

0.75 1.0

Fig. 2. Signal-to-noise ratio as a function of receiver FOV for amonodisperse and polydisperse medium.

IV~

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 1.0FIELD OFVIEW, 2R (DEGREEi

Fig. 3. Scattered-to-unscattered signal ratio vs FOV of receptionfor the monodisperse medium.

tion = [ln(Io/I)]Fovoo. (Note that increasing means decreasing visibility.)

Figure 2 shows the SNR in decibels as a function ofFOV for a monodisperse and polydisperse medium.From the figure, notice that increasing the FOV be-yond an optimum value, we will not gain much in SNRof the communication system. For the specific back-

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3661

10

2

:

ex

.I

n

MONODISPERSE d - 3.01 pml)

l l l l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-. 3

1n-1-

I

00

I I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ground noise, the optimum FOV for the monodispersemedium ( = 4.23) is 0.22°.

Figure 3 shows the scattered-to-unscattered signalratio vs FOV for the monodisperse medium. This hasthe unscattered (extrapolated to zero FOV) signal sub-tracted out from the data. From the figure, it is seenthat the scattered component of light can be greaterthan the unscattered component, and the ratio in-creases with increasing FOV reaching a limit or opti-mum at FOV 0.8°. The curve flattens out for largeFOV. The unscattered light is attenuated more rapid-ly than the scattered light.

The multiple-scattering parameters (forward-scattering efficiency) and OF (rms forward-scatter an-gle) for the scattering medium were estimated usingthe following procedure. We first determine r = /3L ofthe medium from the empty cell and scattering cellintensity data extrapolated to FOV 00. For a finiteFOV we also measured the scattered and the unscat-tered intensity and obtained the ratio given by Eq. (6).These measurements together with another set of in-dependent measurements of Io/I for a finite FOV cangive both OF and 0. The experiment was also conduct-ed with a polydisperse (the diameters of the micro-spheres ranging from 0.2 to 5.17 /m) medium of opticalthickness, - = 2.21. The estimated values for both themonodisperse ( = 4.23) and polydisperse ( = 2.21)media are as follows: OF (monodisperse) = 21.75 mrad;0 (monodisperse) = 0.03; OF (polydisperse) = 3.64mrad; and 0 (polydisperse) = 0.12. Note that thevalues of these multiple-scattering parameters for realatmosphere were taken to be OF = 4.58 mrad and 0 =0.6, which are of the same order as found experimental-ly in the laboratory-simulated scattering medium.3

Ill. Signal Requirements for Various Data RateCommunication Links: Spatial Filtering AgainstBackground Environments

When an airborne laser transmitter terminal passesbetween the sun and receiver terminal (which may beanother airborne system), the signal becomes maskedto a degree by the spectral component of the sun'sbackground near the laser wavelength. This back-ground radiation is an important consideration in di-rect-detection systems and depends on the area of thereceiver aperture, spectral bandwidth, and the solidangle intercepted by the detector or receiver field ofview. Generally, the receiver FOV is arbitrary and canbe varied by placing a field stop, or iris, directly in frontof the detector. This iris then controls both theamount of information signal impinging on the detec-tor and the background noise, i.e., S + N. Thus forgiven data rates and background conditions there ex-ists a minimum FOV to optimize the system margin.For the laboratory-simulation condition described inthis paper, such an optimum FOV is estimated forvarious data rates and quartz-halogen lamp back-ground.

Pulse position modulation (PPM) is considered hereto be a highly efficient modulation technique for com-munications through clouds, haze, dust, smoke, rain,

snow, etc. in which multiple scattering is involved withor without direct solar background. The advantagesof gating-out background photons with relatively sim-ple PPM implementations make it an attractive candi-date for this type of communication. The use of verynarrow time slots and very narrow pulses permit highdata rates through discrimination between the signalpulse and background noise. The power which arrivesat the detector is really S (signal) + N (noise) as op-posed to pure signal. The technique of using PPMallows one to separate the signal from the unwantednoise and thus realizes a system improvement. An acsystem records the SNR directly because it recordsonly the changes on the fluctuations around the aver-age.

The PPM format employs a synch pulse to define amajor time division often called a window. This win-dow is then divided into time slots and is defined by theparticular data value depending on which slot thepulse falls in.8 Figure 4 illustrates the PPM format.To avoid ambiguity, the pulse width must not be largecompared to the time slot. Data throughput rates forthe derived bit error rate are determined by the num-ber of bits transmitted per pulse and the pulse repeti-tion rate of the laser. The necessary SNR is derivedfrom the required bit error rate. The relationshipbetween bit error probabilities and SNR assumesthreshold detection and Gaussian statistics. We as-sume that the information pulse can occur in any one ofthirty-two time delay slots within the interpulse timeinterval. As a result, five bits can be transmitted perlaser pulse.

The following analysis is valid for high backgroundnoise and assumes no pulse stretching through thecommunication channel. Therefore, these calcula-tions are approximate. The SNR is derived from thefollowing equations 9 :

PBE = PFA + (1 PD),

_ 1 (8)PFA = - exp-t-/7Z),

PD = 1 exp(-r2/2),

whereqT

qN

SYNC -- . As DD A0D

DATA N IN

T T T PRD I

N"

(9)

s- qT

qN

H T T FT

MD "N \s AD V -l

NUMBER OF BITS PER LASER PULSE - kNUMBER OF TIME SLOTS M -2

I I I 2 1 3 1 I I * .I M 11 MII' F T MT-pi f

Fig. 4. Pulse-position-modulation format.

3662 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

The voltage signal-to-noise ratio is

(S) = t + = q, * ~(10a)qN

In the above equations,PBE = probability of bit error,PFA = probability of false alarm,PD = probability of pulse detection,qs = signal charge,

qN2 = rms noise charge, andqT = charge threshold for pulse detection.

The power SNR is determined from

SNR = [(S)]2 (lOb)

We assume that the probability of bit error PBE is 10-6.Since thirty-one slots can have a false alarm rate sothat

31 PFA + (1 -PD) = 10-6. (11)

Assuming equal probability,10

31 PFA= 1/2 X 10-6 5 x10-7,

(1-PD)= 1/2 X 106 =5 X 10-7.

Thus PD = 1-5 X 10-7, andPEA = 1.6129 X 10-8. FromEqs. (8) and (9), using these values of PD and PFA, theparameters and were solved. Here = 5.5341 and v= 4.8991 so that + = 10.4332. Thus (S/N)p =108.852 (= 20.37 dB).

We now derive an expression for the signal power Prrequired on the detector to produce a given bit errorrate. The Pr is a function of the background counts Nband the electrical SNR needed to achieve the given biterror rate. The SNR of a direct-detection optical sys-tem can be written as 11 12

SNR (2hB (12)(PB + P + PD) (2

where B21

hvPBPD

is the information bandwidth,= detector quantum efficiency,= photon energy,= background noise power, and= detector dark current power.

Note that Nb, the number of background noise photo-electron counts per bit period, is given by

( PB Nb= P I\ hvm1

where m is the bit rate.Similarly we can write

N ( Pd)

Note that the PPM coding is considered here.Bandwidth B in this case is given by B = 1/(2 X slotwidth). If M is the total number of time slots and k isthe number of bits per laser pulse, in this case M = 32

and k = 5. The slot width r is given by T = k/(Mm).Therefore, the bandwidth is written as

1 Mm2T 2k

If we now solve Eq. (12) for the optical power Pr re-quired (at the receiver) for a specified bandwidth andSNR, the result is

Pr = (hvMm \ +(SNR + )2 + 4(N + Nd) (M) (SNR)].

(13)

The system margin SM can now be determined. SM isthe ratio of the available received signal power to thesignal power required to achieve a given bit rate m.

For the multiple-scattering medium, the availablereceived signal power PA is obtained from Eq. (1) as afunction of receiver FOV. From the laboratory-simu-lation experiment, the effective absorption coeffi-cients and the multiple-scattering communicationchannel parameters were evaluated. Using these pa-rameter values, the available signal power PA was thendetermined from the measurement for a specific opti-cal depth as a function of FOV. Next the requiredsignal power Pr was determined using Eq. (13) for thePPM format with thirty-two time delay slots and fivebits per laser pulse under the experimental conditions.Using the quartz-halogen lamp as a background noisesource [with spectral radiance N(X) = 700W/m2 sr m] and assuming the dark current countNd to be due to a detector dark current of 200 pA, therequired signal power P was determined for the need-ed SNR = 108.85 determined earlier for a given biterror rate BER = 10-6. The system margin SM can beexpressed in decibels as a function of FOV as

A(0R)

(SM)dB = 10 log ~ Pr(R)

(14)

The system margin was determined for two differentconcentrations of the latex spheres suspended in wa-ter. The optical depths were = 2.21 and r = 4.23. Tostudy the effects of direct background noise due to aquartz-halogen lamp, two values of spectral radiancewere used: N = 700 W/m 2 sr Am and N(X) =7000 WM 2 sr Mm.

Figure 5 is a plot of the system margin in decibels vsFOV for an optical depth of = 2.21 and for thefollowing data rates: 4 kbps, 1.28 Mbps, 327.68 Mbps,and 655.36 Mbps and for two background noise levels(one is 10 times stronger). r Fr= 2.21, notice that thesystem margin for background on N(X) = 700W/m2 sr gm is optimum for the FOV of 0.0250 forthe data rates of 4 kbps and 1.28 Mbps, these optimumsystem margins being 52.3 and 38.7 dB, respectively.For higher data rates of 327.68 Mbps and 655.36 Mbps,the system margin flattens out to 20.5 and 18 dB forlarge FOV. With the stronger background noise, forthe data rates of 4 kbps and 1.28 Mbps, the optimumsystem margins of 48.2 and 35 dB, respectively, areachieved but at a smaller FOV of .0.17°. With thestronger background noise, for the data rates of 327.68

1 November 1985 / Vol. 24, No. 21 / APPLIED OPTICS 3663

T- 221- NIX) - 700 Wlm

2srJ m

- --- NIX) - 7000 Wlm2.sr.,n

4 Kps

- / -- - -- 4 KBps

1.2B MBps

- - - - - - - - - 1.28 MBps

- -_ … 327.68 Mp

- 0k= 655.36 MOlp

/Y

-10 -

-15

0.1 0.2 0.3 0. 05 0.6 0.7 O.B 0.9 1.0

FIELD.OF VIEW 2

R IDEGREEI

Fig. 5. System margin in decibels for low-visibility scattering medi-

um with optical depth, = 2.21, and for various data rates and two

different background noise radiances.

ED

55

50

45

40

35

M- 3030, 25

54, 20

15

10

5s

T- 4.23- NIX - 700 Wm

2.sr.Wm

-- - - NIX) - 7000 W~m2

.sr.am

4 Kps

4 Bps

1.20 MBps

[/ v _ - - - - - -- 1.2 Mp

= :_ -- 327.6B Mps

___ - - ---- 655.36 MBps

0 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0

FIELD OF VIEW, 20R (DEGREE)

Fig. 6. System margin in decibels for r = 4.23 for various data rates

and two different background noise radiances.

and 655.36 Mbps, the system margins flattens out to-18.5 and 16 dB, respectively.

Figure 6 is a plot of a system margin as a function ofFOV for r = 4.23. For = 4.23 and a backgroundradiance of N(X) = 700 W/M2 * sr m, as the FOV isincreased the system margin approaches 41.7, 28.8, 10,and 7 dB for the data rates of 4 kbps, 1.28, 327.68, and655.36 Mbps, respectively. Notice that the systemmargin is zero or negative for the ranges of FOV of0.043-0.18° for the data rate of 327.68 Mbps and forthe range of 0.043-0.27° for 655.36 Mbps. This im-plies that for the range of FOV of 0.043-0.27°, commu-nication at 4 kbps and 1.28 Mbps can be maintainedwhile the negative system margin for 327.68 Mbps (forFOV < 0.180) and 655.36 Mbps (for FOV < 0.27) willresult in excess error rate.

The deviations of system margins for N(X) = 7000W/M 2 * sr * jum from the system margins for N(X) = 700W/M2 sr Am are larger for the data rates of 4 kbpsand 1.28 Mbps than the deviations for the two back-ground noise levels for 327.68- and 655.36-Mbps datarates. Results show that as we increase the FOV start-ing from an extremely small FOV angle, the systemmargin increases and reaches a maximum for thecurves for 4 kbps and 1.28 Mbps in Fig. 5 or in othercases flattens out to some system margin. The datapresented here suggest that the limiting FOV is really aminimum FOV of -0.25 or 0.80, for example, depend-ing on the date rate. From a practical point of view,the system margin for large-angle FOV would be ofgreater interest.

IV. Summary and Conclusions

Experimental and theoretical frameworks are pre-sented for quantitative performance analysis of anoptical communication link in a turbid atmospheresuch as cloud, haze, dust, smoke, rain, and snow. Alaboratory-simulation experiment was performed toestimate multiple-scattering communication channelparameters like rms forward-scatter angle and for-ward-scattering efficiency to determine the availablesignal power for a laser communication system to oper-ate in a low-visibility atmosphere. A simulation of thecomplicated phenomenology resulting in a turbulentatmospheric channel and the study of receiver parame-ters based on such a simulation are valid within theaccuracy of the simulation model and experiment.The multiple-forward scattering (MFS) propagationmodel is applicable to provide parameter values need-ed for communication system design under most atmo-spheric conditions. A PPM format with thirty-twotime delay slots and five bits/laser pulse is consideredwhich is suitable for high background noise conditionswhere easy discrimination between the signal pulseand the background is attainable. In the PPM analy-sis, the time slot width is larger than the short durationlaser pulse width, so that all the energy of the laserpulse will be present in only one slot. In free-spaceoptical communications, there is no pulse stretchingthrough the communication channel; in low-visibilityatmospheric channels there might be some pulse

3664 APPLIED OPTICS / Vol. 24, No. 21 / 1 November 1985

. I I . I . I . I .

n I

stretching due to multiple-scattering phenomena andthe PPM analysis presented in this work can be as-sumed to be still valid as long as the fraction of theenergy of stretched laser pulse in one slot spilled overthe next slot is very small, say a few percent. 10 TheSNR was determined for the laboratory-simulationconditions with background noise levels and a given biterror rate of 10-6. Obtaining very high data rates of afew gigabits per seconds requires a high bandwidth.Present electronics for detectors are limited to -6GHz, so that to send high data rate we have to decreasethe slot number. Development of semiconductor la-sers for optical communications having multigigahertzmodulation bandwidth in excess of 10 GHz is encour-aging.13 Some coding schemes may improve high-data-rate communications.

From the plots of the system margin vs receiver fieldof view, for data rates of 4 kbps and 1.28 mbps, thereexists an optimum FOV, whereas for higher data ratesof 327.68 and 655.36 Mbps the system margin ap-proaches some limiting values as the FOV is increased.Also notice that for the denser scattering medium ( =4.23), by increasing the background noise radiance 10times, the system margin decreases slightly (0.5 dB)for higher data rates of 327.68 and 655.36 Mbps. Byincreasing data rates, the system margin becomes zeroand finally becomes negative. For the present labora-tory-simulation scattering medium and backgroundlight condition, the negative system margin for 327.68mbps (for FOV < 0.18°) and 655.36 Mbps (for FOV <0.270) will result in an excess error rate. The fact thatthere is a minimum or optimum receiver FOV for agiven low-visibility atmospheric condition, back-ground noise and a given data rate can be useful indesigning a multiple FOV optical receiver which canmaximize the system margin under most low-visibilityatmospheres in the presence of direct and indirectsolar background irradiance.

The multiple-forward-scattered radiation can thusbe utilized for the potential use of optical communica-tion between aircraft in a low-visibility atmosphere.For many reasons, this capability is highly desirable.Although in this paper optical systems with a FOV of<10 have been addressed, the MFS model also holdsup under the condition of larger FOV, and the MFSappears to represent reasonably accurately the flatten-ing evident in the data for larger FOV, e.g., 170.3 Alow-visibility atmosphere is very often accompaniedby atmospheric turbulence. This turbulence can cre-ate instability in the aircraft platform. Moreover, inthe antisubmarine warfare (ASW) scenario, it is as-sumed that the relative position of the aircraft will notbe constant. For these reasons, optical transmittersand detectors with FOVs much greater than 1 wouldbe desirable. A narrower optical filter bandwidth (ap-proximately a fraction of an angstrom) with wide FOVmay be used to suppress the direct background noise.

The laboratory simulation can be used to develop atechnique of a proposed track-on-data mode of opera-tion for maintaining positive tracking through a vari-ety of background conditions, including the case wherethe sun transits the FOV of the receiver located in oneof the aircraft.14 In this track-on-data mode, the datadetector will be optimally filtered with a spatial fieldstop, and the data spectrum is spectrally removed fromthe low-frequency jitter present in the detector duringa strong background noise condition, e.g., direct solarbackground noise.

V. Summary

Acquisition and high-rate-data transfer betweenaircraft through low-visibility atmosphere seems feasi-ble. This can provide a relatively covert system withhigh immunity to jamming, for example, for a noisejammer.

The author would like to acknowledge the helpfultechnical discussions with Raymond W. Svorec of TheAerospace Corp. In addition, the author wishes toexpress his sincere thanks to Glenn Bowie for his en-couragement in this research effort. The work report-ed in this paper was supported by the independentresearch and development program of Lockheed-Cali-fornia Co.

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(IRIA Center, Environmental Research Institute of Michiganfor the Office of Naval Research, Washington, D.C., 1978).

8. M. Katzman, "Laser Space Communication Technology Sta-tus," Proc. Soc. Photo-Opt. Instrum. Eng. 295, 2 (1981).

9. R. W. Svorec, "Parametric Performance Analysis of SpaceborneLaser Communication Systems," Proc. Soc. Photo-Opt. In-strum. Eng. 295, 66 (1981).

10. R. W. Svorec, The Aerospace Corp., El Segundo, Calif.; privatecommunication (1984).

11. Ref. 4.12. See, for example, J. R. Kerr, "Microwave-Bandwidth Optical

Receiver Systems," Proc. IEEE 55, 1686 (1967).13. K. Y. Lau, C. Harder, and A. Yariv, "Direct Modulation of

Semiconductor Lasers at f > 10 GHz by Low-TemperatureOperation," Appl. Phys. Lett. 44, 273 (1984).

14. F. E. Goodwin, Digital Signal Corp., Springfield, Va.; unpub-lished results and private communication (1983-1984).

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