REQUIREMENTS OF A COHERENT LASER PULSE-DOPPLER RADAR

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• Document Creation Date: December 20, 2016
• Document Release Date: November 6, 2002
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ntaguetiqua causes par le poutp.t;;e optirlue," fbvapt. Paul.
Sea 1. S t., Paris, vol. 252, pp. 255-256; .)ann.rrv 9, 1961.
1361 Claude Colic n-Taunoutlli, "Obser vatiott d'un deplarcutent de
rate tie reonancc ntas;uetique cause par 1'esritati i i optiquc,"
Conrpi. Rend. lead. ci, furls, vol. 252, pp. 394-306; J. tinary
16, 1951.
"Conservation partiCIlc de la colterence an tours du cycle
de pompat;t? optiquc," (mol=t. Vend. Acad. Sri., Paris, vol. 253,
pp. 2662-2664; I)cccntbc'r, 4, NO,
[371 P. L. Bender, private Ct)liiliitiilic'tlti Ill.
[381 Af. Arditi (3bl, p, 157.
1391 L. Slalling, 15Ni .1aoa..Sytnp. on Frequency Control, p. 157; 1961.
NI. Arditi 1,31, p. 1962.
1-101 J. 1', Gordon, "llypcrtlue structure in the inversion spectrum
of N''Il, by a new high-resolution oticrowave spectroutelcr,"
Plays. Rev., vol. 99, pp. 1253-1263; August 15, 1955.
J. 1'. Gordon, If, J. Zciger, antl C, It. Towvncs, "The maser-
new type of microwave amplifier, frequency standard, and
spectrometer," Plays. Rev., vol. 99, pp. 1261-1274; August 15,
1955.
J. Weber, "Aruptt6cation of microwave radiation t,y substances
of the theory of the wa er,
June 1, 1956.
1959.
T. R. Singer, "Masers," John Wiley and
N. Y.; 1959.
A. A. Vitylstcke, "Elements of Ala? -r'1how v," I)
hand Company, Inc., Princeton, N. J.; l'r,l).
[411 This idea was suggested inderrtr lent!v 4 . l'ruf. A. ;: ; , Ic e
ENS, Paris, Dr. 1'. L. slender, h,i h'.t.>luegtiut, }..?;"., ml
Prof. T. It. Carver and C. O. Alley, Jr., of 1) on ?';,Z" 1=,ity
in 1958.
[421 P. L. Bender (30], p. 110.
[431 Norman Knablc, "Maser action in optacnllg pnutpol ;;it
Bull. Am. Phys. Soc., vol. 6, p. 68; February 1, 19b1.
(441 Al. Arditi, unpublished.
Requirements of a Coherent Laser
Pulse-Doppler Radar*
G. BIRRNSONf, SENIOR MEMBER, IRE, AND R. F. LUCYf,
Summary-The use of coherent detection can theoretically allow
optical radar systems employing laser transmitters to achieve con-
siderably improved receiver sensitivity, particularly in conditions of
high background radiation. However, there are many practical fac-
tors that can limit sensitivity in coherent optical detection, which are
described. It is shown that to achieve an efficient coherent optical
radar, one would generally like a pulse width less than 10 rtsec and a
spectral line width less than 10 Mc.
1. INTRODUCTION
T IIE DEVELOPMENT of the laser, which gen-
crates a coherent: light signal, provides the poten-
tiality of practical optical radar systems. One of
'the advantages of coherent light is that it allows the
beam to be very narrow. I lowever, an even more impor-
tant advantag=e for the optical radar application is that
it allows the receiver to employ coherent detection and
thereby to achieve considerably greater sensitivity in
daylight operation. The purpose of this paper is to
describe the requirements and performance of coherent
optical detection in an optical radar application, and to
compare the performance with that achieved by non-
coherent detection.
A photodetector acts as a square-law detector, pro-
viding an elgctrical output power proportional to the
square of the input optical power. In a conventional
* Received July 2, 1962.
t Applied Research Laboratory, Sylvania Electronics System,
A Division of Sylvania Electric Products, Inc., Waltham, Mass,
optical receiver, the received optical signal is'fed alone
into the detector, and noncoherent detection is per-
formed. In a. coherent optical receiver, the received opti-
cal signal is summed with a coherent optical reference
(called the local-oscillator reference) and the sttrr.naec=
optical signal is fed to the photodetector. The squa)rin
process of the detector effectively multiplies the received
signal and the local-oscillator reference together, anti
the bandwidth narrowing of the subsequent amplifier
effectively integrates the resultant product. This com-
bination of multiplication and integration in coherent
detection performs a cross correlation,. which allows the
receiver to achieve considerably greater sensitivity than
one employing noncoherent detection.
If the local-oscillator reference is a pure sinusoid and,
its power can be made arbitrarily large, the effects of
background optical power and dark current in the de-
tector become negligible, and the optical receiver is able
to achieve detection characteristics given by
PB" QP,, ; (T)
where (P8,/P?,) is the signal-to-noise power ratio out of
the receiver, of is the receiver noise bandwidt-ls-, P,, is
the received optical power, Q is the quantum efficiency
of the detector, and lapis the energy per photon (Planck's
constant h times"optical frequency v).
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1963
Biernson and Lucy: Coherent Laser Pulse-Doppler Radar
At present, there are two optical wavelengths which
are of particular interest: 6943 A for the ruby laser and
11,500 A for the gas laser. At these wavelengths, the
energy per photon is
.hv = 2.85 X 10-" joules (Ruby, 6943 A), (2)
ltv = 1.72 X 10-" joules (Gas, 11,500 A).
It is desirable to compare the sensitivity of a coherent
optical receiver to that of a microwave receiver. For a
(1) is
t t
l
i
o
en
va
microwave radar the expression equ
P,o P.
P?o - KTaf1Af
(4)
where K is Boltzman's constant and Taff is the effective
noise temperature of the receiver. Thus, for unity quan-
to KTaff. Setting by equal to KTaff gives the following
ideal noise temperatures for optical receivers:
Teff = 20,800?K
(Ruby, 6943 A),
(5)
Tiff ? 11,500?K
(Gas, 11,500 A).
(6)
'1'lins; even if ideal detection is achieved, an optical re-
ceiver is very noisy in comparison with microwave re-
ceivers.
On the other hand, quantum efficiencies of phot.ode-
0.04 for Typc S20 Photosurface at 6943 A, (7)
The Most fundamental limitation is point 1). Points 2)
and 3) are discussed later.
I^ ig. I shows the. voltage spectrum of a signal at fre-
quency Fo modulated by a rectangular pulse of width
r. The pulse modulation smears the signal in frequency.
In order to pass a reasonable amount of the pulse power,
the receiver noise bandwidth Af should be at least equal
to 1/r:
if > 1/r. (11)
To achieve maximum sensitivity, Af should be equal
to 11r. Set Af= 1/r in (1) and solve for P,.
1', ~ (Psi l Pna) Iiv/Qr.
Fig. 1-Voltage spectrum of pulse-modulated signal
of frequency Fo and pulse width T.
(12)
This equation is not strictly correct, because it ignores
the loss of signal power through the filter. However, for
the purpose of simplicity, this small discrepancy will be
ignored. It can readily be accounted for by specifying a
somewhat larger value for the output signal-to-noise
ratio at the threshold.
'I'lie received signal energy E. is equal to P,r, which
by (12) is equal to the following for optimum detection:
E. (13)
If Q could be made unity, (13) shows that the number of
photons (of energy hv) required for detection is ideally'
equal to the signal-to-noise power ratio (P,,/P?0) re-
quired at the threshold. Since the signal-to-noise ratio
at the threshold must beat least 10 db, the system must
receive at least 10 photons in order to achieve a reason-
ably high probability of false alarm and low probability
of false dismissal, for an ideal detector. With a practical
photoemissive detector available today (Q=0.04) the
system must receive at least 250 photons at the ruby
laser frequency.
If noncolicrent detection is employed, the signal
power that can be detected is given by the following:
P,o,at = X21'?P,ca>> (14)
Q = 1.5 X 10-4 for Type S1 Photosurface at 11,500 A. (8)
,The ideal noise temperatures given in .(5) and (6) should
be divided by these quantum efficiencies to obtain the
noise temperatures now achievable with photoemissive
detectors. Dividing these resultant effective noise tem-
peratures by room temperature (291?K) gives the noise
figures NF of the practical optical receivers, which are,
These are very high, . in comparison to microwave re-
ceivcrs. Semiconductor. photodetectors promise quail-
tunr efficiencies close to unity, but now have too slow a
speed of response to be generally desirable for a coherent
laser receiver. This point will be discussed later.
To minimize the signal required to achieve a given
signal-to-noise ratio at the receiver output, (1) shows
that the receiver noise bandwidth Af should be made as
small as possible. Ilowever there are important effects
that place a lower limit on the value of Af, which are as
follows:
1) Spread of spectral lice due to pulsing,
2) Spread of spectral line due to lack of perfect coher-
Cuc e of the optical signal,
3) The elfcct of Doppler shift.
t:ectors are generally much less than unity. The best
values achieved to date for photomissive surfaces at the
wavelengths of the ruby and gas lasers are as follows:
NF _ 32.5 db (Ruby, 9643 A), (9)
NF 54.5 db (Gas, 11,500 A). (10)
where
p,, =effective optical noise power on detector,
P,(c) =signal power detectable by coherent detection,
P,(?,) =signal power detectable by noncoherent detec-
tion.
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The noise power a'? represents the power in the back-
ground radiation that falls on the detector halls the cf-
fect of the detector dark current in terms of the equiva-
lent optical power. The loss L(,) produced by nonco-
llereut detection is
I'sOr)
PR(0) Ps(r)
2 P?r
I%x(c)
where E9(,) is the signal energy required for coherent de-
tection, which was given in (13).
Eq. (15) shows that in order to minimize the loss
when noncolerent detection is performed, one should
1) make the pulse length. r as short as possible and 2)
make the optical noise P,, as small its possible. The dark
current component of noise power can be kept small by
cooling the detector in liquid nitrogen. If the detector
operates at night, the background optical power can be
kept small. If the pulse is made very short, the loss with
noncoherent detection under such conditions is small.
However, under daylight conditions, there is consider-
able loss in sensitivity with noncoherent detection.
When noncoherent detection is performed, the dark
current of the photodetector is very important. 1low-
ever, with coherent detection, the dark current can be
ignored as long as its effective power is small in compari-
son to the local-oscillator power. With coherent detec-
tion, the quantum efficiency is the parameter that is of
primary importance. It, may well be that better photo-
surfaces can be achieved in coherent-detection optical
receivers by sacrificing low dark current to achieve
higher quantum efficiency.
11. LASER RADAR DESIGN
Let us now consider what is required in terms of
equipment and equipment performance to realize an
effective coherent laser radar.
Fig. 2 gives a block diagram of a coherent laser radar.
A CW laser oscillator 1) generates a signal at optical fre-
quency F0. This is fed to it pulse-modulated amplifier 2)
which generates a pulsed optical signal of carrier fre-
quency F0. The "target echo frequency is shifted from
the transmitted frequency Fo by the Doppler shift Fd,
and so has a carrier frequency of (Fa-~-Fa).ln optical
frequency translator 3) is often needed to shift the local-
oscillator frequency from the frequency Fo of the ('
\V
laser oscillator by an offset frequency F,0. Thus the
local-oscillator signal has a frequency of (F0+F,;). The
local oscillator signal and target echo signal are summed
together optically 4) and fed to the photodetector 5).
The photodetector gives as an output a signal at the
difference between the target echo frequency (F0+P1)
and the local-oscillator frequency (F,,+F,), which is
thus at the frequency I+'(- Fxj . 'T'his signal is fed to the
receiver.
The target Doppler frequency shift F,s is given by the
following expression:
OFFSET
FREQUENCY CO CAL
FR:OC'NCV
FA TR.4FISLATCR
DET,Tnk
)5) -1 1
OPTICAL
-'
SUMN11T ION
IFD F%I
RECEIVER
(6)
Fig, 2-Block diagram of a coherent optical ra(ar.
where V is the relative closing velocity and h i ;
wavelength of the optical signal. For the rube
wavelength 6943 A, the Doppler shift is 875 l.c/fi/--s__,
(or in round numbers 1 Mc/ft/sec).
It appears that laser radar systems may be quite
fill in space vehicle applications. Relative velocitif
such applications may be ashigh as 10 miles per
which represents the relative speed between two to? ,-
altitude satellites traveling in opposite directions. "rite
Doppler shift at the ruby laser wavelength for I)d
treme condition is 50 Gc. Thus for space vehicle a t)pli!?a-
tions a coherent laser radar would have to operate over
frequencies from 0 to 50 Gc.
If a frequency translator were not used, the photo de.
tector would have to pass the Doppler frequency wne-
could be as high as 50 Gc for a space vehicle appiic,r.?io;n.
By using a frequency translator, the photodetector need
merely pass the difference between the Doppler f_e
quency F,j and the offset frequency Fs, which can be
relatively small.
The most convenient detector available today is the
photomultiplier tube. Commercial units are capable of
passing 300 Mc, but much wider bandwidths appear to
be possible. Another approach is the T\V'T phototube,
which now can pass frequencies from 2 to 4 Gc. S.nni-
conductor photodetectors promise much higher quan-
tum efficiencies but appear to be limited to much lower
bandwidths.
Although the frequency translators allow the detector
to operate with a bandwidth much less than the Doppler
shift, it is usually desirable that the detector have the
widest possible bandwidth in order that it can simul-
taneously examine the largest possible region of Doppler
frequencies during search.
The receiver that follows the photodetector will gen-
erally have a large number of parallel frequency chan-
nels to allow it to achieve a relatively narrow receiver
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1$icrusau and Lucy: Coherent Laser Pulse-Doppler Radar 205
noise bandwidth Df yet also be able to cover the full
17opp.ler frequency region passed by the photodetector.
The narrower the noise bandwidth _if, the greater nurn-
her of channels are required. Therefore, practical (--on-
siclerations place a lower limit on the allowable filter
bandwidth.
It appears that the receiver bandwidth Af may typi-
cally be between 1 Mc and 100 Mc. Since 1 Mc corre-
sponds to a speed resolution of I ft/sec, a bandwidth
below 1 Mc would lead to very difficult tracking prob-
lems, and would require an excessive number of receiver
channels during search. With a 10-Me bandwidth, 30
filters would be required to cover the 300-Me region
of the photodetector, which appears reasonable. With
an TWT phototube, which has a 2000-Me bandwidth,
a wider filter bandwidth may be desirable. On the other
hand, if the radar is used for ground tracking applica-
tions, where Doppler shifts are small, a bandwidth of
1 Me might be used.
We will thus assume a receiver bandwidth Af of 10 Mc
as a typical number. To achieve op innuu detection, the
pulse width r should be equal to I/if or 0.1 iscc. Such a
laser radar system would achieve a speed resolution of
11 ft/sec and a range resolution of 50 ft. It also would
have very high angular resolution_ Thus a laser radar is
capable of achieving very high ,resolution in speed,
range and angle. In contrast, a microwave radar has
relatively poor angular resolution; and can achieve
range resolution without speed resolution (in a pulse
radar), or speed resolution without range resolution (in
a Doppler radar).
The laser radar has much greater resolution capabil-
ity than a microwave radar, but is far inferior in search.
The poor search capability is due to 1) its high noise fig-
ure, 2) the generally, smaller capture area of its receive
aperture, 3) the low efficiency of Misers. For this reason
laser radars will probably usually be operated in con-
junction with other equipment (often microwave radar),
which will p:rform the coarse search function. The laser
radar will generally search over cooly a relatively small
region of range, speed, and angle.
It has been shown that we would like to operate with
a receiver bandwidth Af of the- order of 10 Ale with a
pulse width r of 0.1 ?sec. This gives the optin-iuin detec-
t:ion condition 7-if = 1. However, as will be shown we
can tolerate without excessive degradation a value of
TTr\f up to 100, which would allow a 10-,usec pulse width
for a 10-M e bandwidth. Let us now examine the capa-
bilities of present lasers to satisfy these requirements.
A serious problem of lasers is that they tend to oscil-
late in a number of modes to deliver a series of frequen-
cics v. i.ich are separate by the resonant frequency of the
cavity, ,,Rich is typically about 1.7 Gc. In order for
efii._icnt coherent detection to be performed, the CW
L c; cillator and pulsed laser amplifier must'be able
I proo:ci.fly be t:olerateti.
t?~_s trail io Ale, although a somewhat wider
to in a single mode. It is desirable that the line
The gas laser is able to oscillate in a single mode in a
CW fashion, but is not capable of generating short
pulses of high peak powers. Thus it cannot now satisfy
our rcquiremcnt of a pulse length shorter than 10 JAsec.
In contrast, the ruby laser can generate short pulses
of high peak powers, but is very bad from a multimode
point of view. It also tends to generate very erratic pulse
trains, and does not. oscillate readily in a CW fashion
(which is needed to satisfy the CW oscillator require-
ments). Unfortunately gas and ruby lasers cannot be
used together in a system because they operate at dif-
ferent: optical wavelengths.
Thus there are many practical problems in laser de-
sign that must be solved before the coherent laser radar
system can be realized. However, the purpose of this
paper is to concentrate on the requirements of such a
system zinc] not the means of designing a laser to satisfy
these requirements.
III. GIiNLRAI, DISCUSSION OR COIIGRENT DETECTION
A detailed analysis of coherent and noncoherent. de-
tection in a photodetector is given. in Section 1V. This
section presents a simplified analysis of the difference
between coherent and noncohcrent detection, and sum-
marizes the performance achievable by coherent detec-
tion.
A. Simplified Analysis of Coherent and Noncoherent De-
tection
In a noncoherent detector, the signal is fed into a rec-
tifying device. Since this device has no negative output,
its response can be expressed as an even infinite series,
as follows
eo = ae;2 + Lei" + ce,f -l- .. , (17)
Generally one can ignore the higher order terms and get
a good approximation of the action by assuming that
e,=ae,2, i.e., that the rectifier is a square-law detector.
A photodetector is an ideal square law device in which
the higher terms of (17) are not present.
In a square-law detector, the output signal-plus-noise
(so+no) is related as follows to the input signal-plus-
noise (s,+n,) :
so + aao = a(sj + ni)2 = a(s,2 + 2s;n, +
where a is a constant, the output signal is (s,2), and the
output noise is (2s;n,+n 2). The noise consists of two
terms: one (n,2) due to beats between the noise com-
ponents, and the other 2s,n, clue to beats between the
signal and noise. If the input signal-to-noise ratio is
much less than ciuity, n.,2 is much greater than 2s,at,, and
so the output noise and signal are approximately
sa = a.s,2, - (14)
ttp ti an;2 for (P,,/ P,,r) < 1. (20)
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