REQUIREMENTS OF A COHERENT LASER PULSE-DOPPLER RADAR
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DRnr`R1 r)r7t)rc nT' 'PTT)' r7777 7
202
January
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63
niagnetique causes par Ic pompage optique," Contpt. Rend.
Aced. Sci., Paris, vol. 252, pp. 255-256; January 9, 1961.
(36] Claude Cohen -Tannoudji, "Observation d'un deplacement de
raie de resonance magnetique cause par 1'excitatiou optigno,"
Ci,npl. Rend. Acad..Sci., Paris, vol. 252, pp. 394- 396; January
16, 1961.
"Conservation partielle de la coherence all tours du cycle
de ponipage optique," Compt. Rend. Acad. Sci., Paris, vol. 253,
pp. 2662-2664; December, 4, 1961.
137] P. L. Bender, private communication.
[381 M. Arditi [3b], p. 187.
139] L. Malting, 15th Ann, Symp. on Frequency Control, p. 157; 1961.
M. Arditi [3], p. 1962.
140] J. P. Gordon, "Ilyperline structure in the inversion spectrum
of N1411;, by a new high-resolution microwave spectrometer,"
Phys. Rev., vol. 99, pp. 1253-1263; August 15, 1955.
J. P. Gordon, II. J. Zeiger, and C. 11. Townes, "The maser-
new type of microwave amplifier, frequency standard, and
spectrometer," Phys. Rev., vol. 99, pp. 1264-1274; August 15,
1955.
J. Weber, "Amplification of microwave radiation by substances
not in thermal equilibrium, IRE TRANS. ON ELECTRON
DEvicis, vol. ED-3, pp. 1-4i June, 1953.
K. Shimoda, T. C. Wang, and C. H. Townes, "Further aspects
of the theory of the maser," Phys. Rev., vol. 102, pp. 1.308-1321;
June 1, 1956.
J. I'. Wittke, "Molecular amplification and g neratiou of
microwaves," PRoc. IRE, vol. 45, pp. 291-316; March, 1957.
G. Troup, "Masers," Methuen and Co., Ltd., London, England;
1959.
T. R. Singer, "Masers," John Wiley and Sons, Inc., New York,
N. Y.; 1959.
A. A. Vuylstcke, "Elements of Maser Theory," D. Van Nos-
trand Company, Inc., Princeton, N. J.; 1960.
[41] This idea was suggested independently by Prof. A. Kastler,
ENS, Paris, Dr. P. L. Bender, NBS, Washington, D.C., and
Prof. T. R. Carver and C. O. Alley, Jr., of Princeton University
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[42] P. L. Bender [30], 110.
[43] Norman Knable, `Maser action in optically pumped Rb87,"
Bull. Am. Phys. Soc., vol. 6, p. 68; February 1, 1961.
[44] M. Arditi, unpublished.
Requirements of a Coherent Laser
Pulse-Doppler Radar*
G. BIERNSONf, SENIOR MEMBER, IRE, AND R. F. LUCYt, MEMBER, IRE
Summary-The use of coherent detection can theoretically allow
optical radar systems employing laser transmitters to achieve con-
siderably unproven 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 s' wn that to achieve an efficient coherent optical
radar, one would generally like a pulse width less than 10 .sec and a
spectral line width less than 10 Mc.
1. INTRODUCTION
TIIE DEVELOPI4 ENT of the laser, which gen-
erates 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. IIowever, an even more impor-
tant advantage 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 electrical output power proportional to the
square of the input optical power. In a conventional
Receiv d l
euly 2. 1962.
f hlicc esearch 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 non colic rent 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 summed
optical signal is fed to the photodetector. The squaring
process of the detector effectively multiplies the received
signal and the local-oscillator reference together, and
the bandwidth narrowing of the subsequent amplifier
effectively integrates the resultant product. This coni-
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 charactcristics given by
PB" QP,
P,,a (hv)Af
where (P,."/P,0,) is the signal-to-noise power ratio out of
the receiver, Af is the receiver noise bandwidth, P, is
the received optical power, Q is the quantul,, efficiency
of the detector, and by is the energy per photoit (Planck's
constant It times optical frequency v).
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'Ai present, there are two optical wavelengths which
are of part 'ular interest: 6943 A for the ruby laser and
11,500 A for the gas laser. At these wavelengths, the
energy per photon is
by = 2.85 X 10-19 joules
(Ruby, 6943 A),
(2)
lzv = 1.72 X 10-18 joules
(Gas, 11,500 A).
(3)
It is desirable to compare the sensitivity of a coherent
optical receiver to that of a microwave receiver. For a
microwave radar the expression equivalent to (1) is
Pao P8
P-no KTeffLf
(4)
where K is Boltzman's constant and Teff is the effective
noise temperature of the receiver. Thus, for unity quan-
tum efficiency Q, the energy per photon by is equivalent
to K7-,ff. Setting lip equal to KTeff gives the following
ideal noise temperatures for optical receivers:
Teff = 20,800?K (Ruby, 6943 A), (5)
Teff = 11,500?K (Gas, 11,500 A). (6)
Thus, 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 photode-
tectors 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-
Q = 0.04 for Type S20 Photosurface at 6943 A, (7)
Q = 1.5 X 10'1 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,
NF = 32.5 db (Ruby, 9643 A),
(9)
NF = 54.5 db (Gas, 11,500 A). (10)
These are very high in comparison to microwave re-
ceivers. Semiconductor photodetectors promise quan-
tum 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 Wf should be made as
small as possible. llowever there are important effects
that place a lower limit on the value of Of, which are as
follows:
1) Spread of spectral line due to pulsing,
2) Spread of spectral line due to lack of perfect coher-
ence of the optical signal,
3) The effect of Doppler shift.
The most fundamental limitation is point 1). Points 2)
and 3) are discussed later.
Fig. 1 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:
Af ? 1/r. (11)
To achieve maximum sensitivity, Af should be equal
to 1/r. Set Af = 1/r in (1) and solve for P,.
P8 >_ (P,o/P?o)hv/Q'r. (12)
Fig. 1-Voltage spectrum of pulse-me 'ulated signal
of frequency Fo and pulse width T.
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. I t can readily be accounted for by specifying a
somewhat larger value for the output signal-to-noise
ratio P,,/P,,,, at the threshold.
The received signal energy E, is equal to P,r, which
by (12) is equal to the following for optimum detection:
E. = (Peo/Pno)(hv)/Q. (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 (P8,/P,,,) re-
quired at the threshold. Since the signal-to-noise ratio
at the threshold must be at 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 noncoherent detection is employed, the signal
power that can be detected is given by the following:
where
P~ =effective optical noise power on detector,
P4(c) =signal power detectable by coherent dett,
P,tn,ol = signal power detectable by noncoherent d,
tion.
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The noise power P? represents the power in the back-
ground radiation that falls on the detector plus the ef-
iL ct of the detector dark current in terms of the equiva-
Ic)~t optical power. The loss L(,,,,) produced by nonco-
herent detection is
P8(nc) 2P?, 2P -7
L(ne) (15)
P8(e) P3(e) Es(c)
where E8 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 noncoherent detection is performed, one should
1) make the pulse length r as short as possible and 2)
make the optical noise P,, as small as 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.
I lowever, 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. how-
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
p-rirnarN7 importance. It may well be.that better photo-
surfaces can be ache^ved in coherent-detection optical
receivers by sacrificing low dark current to achieve
higher quantum efficiency.
11. L,,SER RADAR DESIGN
Let us now consider what is required in terms of
cgnipment and egr'pment performance to realize an
effective coherent laser radar.
Fig. 2 gives a block diagram of a coherent laser radar.
A ('\V' laser oscillator 1) generates a signal at optical fre-
(Jucncy F,,. This is fed to a pulse-modulated amplifier 2)
which generates a pulsed optical signal of carrier fre-
quencv F '. The target echo frequency is shifted from
the transmitted frequency F0 by the Doppler shift Fd,
kT, and (61) becomes ap-
proximately
W(v) hv. (62)
In contrast, ? at microwave frequencids and below,
kT>>hv and (61) approximates kT:
Local-Oscillator Power: The true local-oscillator fre-
quency distribution is not clearly k.own at present.
Consequently statements about setting the local-oscil-
lator power can not be made with certainty.
However, if the local oscillator is monochromatic its
output power can be set much larger than the equiva-
lent background power P. to reduce the effect of ran-
dom noise on sensitivity. The available local oscillators,
such as the helium neon laser, have output power levels
of 1 to 10 mw. From Table I it can be seen that the
equivalent dark current power is small relative to a
milliwatt.
The radiation density from background will be inte-
grated by the optics. From Table II it is evident that
even if the collecting area is as large as several square
meters, star and moon background levels will be much
less than a milliwatt. However, direct solar background
will be severe and detection of the small signals will be
limited against the suit. Daytime operation will de-
pend upon the individual circumstances encountered.
If operation is against a source surrounded by bright
clouds, diffuse reflections the background level may be
excessively high and the field of view would have to be
narrowed to improve sensitivity.
If standard photomultipliers are used for mixing, a
limit is placed upon local oscillator strength and back-
9I3. NI. Olin>er, "Some potentialities of optical masers," I'uoc.
IRE, vol. 50, pp. 1.35 141; l ebruary, 1962,
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(54)
where R is the equivalent noise resistance of the ampli-
fier, F is the noise figure, and G is the gain of the second-
ary emission multipliers. Simplification of (54) yields the
the signal-to-noise ratio in the photocurrent.
(53)
The signal-to-noise ratio becomes
Pao QPs
Poo hvAf
Thus, to achieve the best detectability, the quantum
eflicieucv of the detector should be as large as possible.
I lowever, Table I shows that the quantum eIiicieucv of
present photoemissive surfaces is small and that the
ideal detection case cannot now be approached.
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ground levels by fatigue and burnout effects in the
multipliers due to overloading. Desirable levels will be
;)asider P? this becomes
Large Signal: When the signal power is large conpr T
pared to the background power and dark curren
equivalent power (65) becomes
Froin the noise summary of Table III,
N = 2eif[ID + PPb + PPs + PPr + PP,,,,]
Poo PPs(nc)
P?o 2e4f
and the relationship between the coherent and nonco
herent case
P8(?c) = 2P8(c). (70:
Zero Background: If there is no background the re-5111:
sidual limiting noise is due to dark current. By cooling
the photosurface the therinionic current is reduced
ideally at 0?K, to Id=O. Then signal noise again limit: Ph
detection and (69) and (70) apply to this case.
D. Photoemissive Detectors
(69The
hui
:r0
7u
Photomultipliers: High-speed photomultipliers are`h'
usable as wide-band photomixing devices. These tubes~f
contain a photoemissive 'urface and several stages of.
electron multiplication. The response time is limited byto
a time spread introduced in the signal pulse by the elec-R
tron multipliers. The spread is due to a variation rn
transit time of electrons between the photoemissivele
surface and the collector. The photomultiplier anode is
connected in series with a load resi?tor at the input of t
an amplifier following the tube. The equivalent circuit is r
a constant current generator driving the load resistor
and shunt capacity. Excluding the fundamental transit-
time spread of the multipliers, the tube response can be
limited by the time constant of the output circuit.
For efficient operation, the noise due to the photo-
multiplier should be greater than or equal to the noise
figure of the amplifier. If GIN is the mean square noise
current of the multiplier output, and FkTAf is the
amplifier noise power, then
GINR > FkT4f (71)
wl re R is the load resistor and G the multiplier gain.
hv4f
Pn