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Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology

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Review of ladar: a historic, yet emerging, sensor technology with richphenomenology
Paul F. McManamon
Review of ladar: a historic, yet emerging, sensortechnology with rich phenomenology
Paul F. McManamon
University of DaytonLadar and Optical Communications Institute300 College ParkDayton, Ohio 45469-2950E-mail: paul@excitingtechnology.com
Abstract.
Ladar is becoming more prominent due to the maturation of itscomponent technologies, especially lasers. There are many forms ofladar. There is simple two-dimensional (2-D) ladar, similar to a passiveelectro-optic sensor, but with controlled illumination and the ability tosee at night even at short wavelengths. There is three-dimensional(3-D) ladar, with angle/angle/range information. 3-D images are verypowerful because shape is an invariant. 3-D images can be easily rotatedto various perspectives. You can add gray scale or color, just like passive,or 2-D ladar, imaging. You can add precise velocity measurement, includ-ing vibrations. Ladar generates orders of magnitude higher frequencychange then microwave radar for velocity measurement, because fre-quencychange isproportional to one over thewavelength. Orders of mag-nitude higher frequency change means you can measure a given velocityorders of magnitude quicker,in many casesmaking anaccurate measure-mentpossible.Polarization canbeused.Withanactivesensoryoucontrolboth theillumination and the reception, so you can pattern theillumination.Also, because ladar can use narrow band illumination it is easier to easier to coherently combine sub-aperture images to obtain the higher resolutionof an array.
©
2012 Society of Photo-Optical Instrumentation Engineers (SPIE).
[DOI: 10.1117/1.OE.51.6.060901]
Subject terms: ladar; lidar; active imaging; laser radar; remote sensing.Paper 120004V received Jan. 1, 2012; revised manuscript received Apr. 19, 2012;accepted for publication Apr. 20, 2012; published online Jun. 5, 2012; correctedAug. 21, 2012.
1 Introduction
Ladar started shortly after the invention of the laser
1
but it is just now emerging as a widespread alternative to passiveelectro-optic (EO) sensors and microwave radar. Component technologies, especially reliable and affordable lasers, havedeveloped to the point that the extremely rich phenomenol-ogy available through ladar can be more easily accessed. Onedriving factor in component availability is the similarity of many required ladar components to laser communicationssystems, which is driven by the high bandwidth requirementsof the internet, a large and lucrative market. Inexpensive,highly capable, and very reliable active EO componentsare making ladar competitive compared to alternative sensor technologies. Ladars are being made from thevisible throughthe LWIR. Twenty years ago
COCO
22
ladar was popular inthe LWIR, but it has faded as solid state lasers have becomemore prominent. Ladar operating near 1.5
μ
m is becomingwidespread.
2 Ladar Range/Signal to Noise
Ladar range and signal to noise calculations can be dividedinto two parts. The first part is to calculate how much signalis captured by the receiver (or how many photons hit eachdetector). You can then convert these photons to electrons,based on quantum efficiency. The second part has to dowith how many photons you need in each detector to accom-plish your objectives, such as object detection, or recogni-tion, or tracking. This depends on the receiver used, andwhat your information objectives are. The discussion inSecs. 2.1 and 2.2 uses simplifying assumptions with the
objective of bringing out the key dependencies while avoid-ing the complexity of a fully general representation. The lit-erature cited in the following sections can be used as requiredto consider more complex situations.
2.1
Calculating the Received Power, or Number,of Received Photons
To calculate the number of photons returned to each detector you start with the transmitted laser power. It can have a shaped beam such as a Gaussian, or you can assume thebeam is flat topped. For the computationally simple flat top beam the radiance (
Watts
∕
cm
2
) is the laser power divided by the area of the beam footprint. This is a significant gain over radiating throughout a sphere since lasers havesmall beam divergence. Beam divergence can be smaller for large aperture transmitters and for shorter wavelengthtransmitters. We then create a fictitious area we call thecross section. This is not a physical area, but will be relatedto the physical area. For area targets if you have a flashimaging sensor, using many detectors, you can only count the cross section seen by each detector. Higher spatial reso-lution will mean each detector sees a smaller area and a smal-ler cross section. Therefore, if the target illumination area isfixed, an increased imaging resolution (e.g., increased num-ber of detector pixels) results in decreased signal to noise per detector. The signal to noise can be increased by increasingthe transmitter power. High range resolution will also reducethe effective cross section if there are scatterers at multipleranges within a detector angular sub-tense (DAS). Surfaceswith high reflectivity in the backward direction (toward the
0091-3286/2012/$25.00 © 2012 SPIE
Optical Engineering 060901-1 June 2012/Vol. 51(6)Optical Engineering 51(6), 060901 (June 2012)
ladar receiver) have higher cross section. Corner cubes havea lot higher cross section, because light reflected from a cor-ner cube is returned in a small angular cone. The accepteddefinition of cross section is different for ladars than for microwave radars. For ladar, when specifying cross sectionit is usually assumed scattering is near Lambertian, andreflected light is reflected into
π
steradians. We arrive at
π
steradians as the effective solid angle of reflected light byassuming a cosine distribution of reflected light over a hemi-sphere (
2
π
steradians). This is for a Lambertion scattering of light from a rough surface. In microwave radar the cross sec-tion definition usually involves scattering of light over
4
π
steradians from a small round gold ball. This makes sensefor radar, where often the radar wavelength is longer thanthe size of the diameter of the round gold ball. For EO it does not make as much sense because the ball would bemuch larger than the wavelength, so it would block forwardradiation. Another thing to consider is the shape of the target.A point target is smaller than the DAS. A line target, like a wire, is smaller than the DAS in one dimension, but larger inthe other dimension. Area target cross section can be limitedby the DAS or by the illuminated area. Often today we havearrays of detectors, and what we call
“
flash imaging
”
, wherean area much larger than a given DAS is illuminated so youcan see many pixels, or voxels, at one time. Once light isreflected from the object of interest some of it is capturedby the receiver aperture. Obviously a larger receiver aperturecaptures more light. We also have efficiency terms to con-sider. There are losses in the ladar system, and only somuch light makes it though the two-way atmospheric pathto and from the target. The total optical power received at the detector is given by:
P
R
¼
P
sc
A
rec
R
2
η
atm
η
sys
;
(1)
where,
R
is range,
P
sc
is the power per steradian backscat-tered by the target into the direction of the receiver and
A
rec
∕
R
2
is the solid angle of the receiver with respect tothe target.
η
atm
is the one way atmospheric transmission,and
η
sys
is the receiver systems efficiency.
A
rec
is the area of the receiver.For an area target with uniform illumination, and uniform reflectivity, in the backward direction, the power scattered bythe target is given by
P
sc
¼
ρ
π
I
t
A
t
;
(2)
where
ρ
π
is the target reflectivity per steradian in the back-ward direction,
I
t
is the intensity of the transmitted light at the target location, and
A
t
is the area of the target. In thispaper the term intensity is used to describe power per unit area. Power per unit area is often called irradiance, but that is not the convention used in this paper.Under the additional assumptions that the target is normaland its scattering is Lambertion, i.e.,
ρ
π
¼
ρ
t
∕
π
, where
ρ
t
isthe total hemispherical reflectivity, and the transmitter inten-sity is flat over the entire illuminated region of the target plane, i.e.,
I
t
¼
η
atm
P
T
∕
A
illum
, we obtain,
P
R
¼
P
T
ρ
t
A
t
A
illum
A
rec
π
R
2
η
2atm
η
sys
;
(3)
where
A
illum
is the area illuminated. If we define the target cross section as
σ
¼
ρ
t
A
t
we get
P
R
¼
P
T
σ
A
illum
A
rec
π
R
2
η
2atm
η
sys
;
(4)
where
P
R
¼
Power received
,
P
T
¼
Power transmitted
,
σ
¼
crosssectioninsquaremeters
,
A
illum
¼
Areailluminated
,
A
rec
¼
Areaof thereceiver
,
R
¼
range
,
η
atm
¼
transmissionefficiency through the atmosphere
, and
η
sys
¼
receiver system optical systems efficiency
. You can see the power received is the power transmitted times two ratios of areas, times appropriate efficiency terms. The first ratio of areas is the cross section divided by the illuminated area at the object plane. The second ratio of areas is the receiver aperture area divided by the effective average area illumi-nated by Lambertion reflection.For an area target with illumination area larger than theDAS we can assume that the cross section for a given recei-ver pixel is limited by the area of a pixel. For square receiver pixels we have:
σ
¼
ρ
t
A
p
¼
ρ
t
d
2
;
(5)
where
d
¼
cross range resolution
,
ρ
t
is the reflectance of thearea, and
A
p
is the area of the pixel at the target location,which for a square pixel is equal to
d
2
.For a point target, or line target with dimensions smaller than the pixel size at the target location, the cross section willbe smaller, due to a smaller area that is reflecting.The cross range resolution of a pixel cannot be better thanthe diffraction limit, or
d
≥
R
λ
D
rec
:
(6)
In Eq. (4) we have used the full width, half power, diffractiondefinition. Often other values are used, such has half width,or the width at zero power. For a circular aperture, we have
A
rec
¼
area of the receiver
, or
A
rec
¼
π
D
rec
2
2
;
(7)
where
D
rec
is the diameter of the receiver. Equation (7) is for a single receive aperture. If you have multiple sub-aperturesthen calculating receive area can be more complex. The area illuminated can be no smaller than the diffraction limit asgiven in Eq. (8) below:
A
illum
≈
π
λ
R
2
D
2
:
(8)
The area illuminated can be larger than given in Eq. (8) if the transmit beam is spoiled, or if the transmit beam isnot diffraction limited. We can then invert Eq. (4) to obtainthe required laser transmit power for a given ladar range
P
T
¼
π
P
R
A
illum
R
2
σ
A
rec
η
2atm
η
sys
:
(9)
Terms in Eqs. (4) or (9) can be expanded if desired. When
using these equations care must be taken to properly evaluate
Optical Engineering 060901-2 June 2012/Vol. 51(6)McManamon: Review of ladar: a historic, yet emerging, sensor technology
: : :
the cross section per detector pixel for a given target, such asarea targets, line targets, or point targets. Assuming enoughis known about the target scattering properties and its shape,calculation of the effective cross section is straightforwardbut must be done with care.
2.2
Calculating the Detection/Recognition Threshold
In order to use Eq. (9) to determine the laser power that must be transmitted,
P
T
, to achieve detection at a givenladar range, we must first determine how much opticalsignal power,
P
R
, we need to receive in order to meet the desired probability of detection and false alarm requirements.The
P
R
term in Eq. (9) is received optical power, whichconverts on hitting the detector to photons per second.Photons per second in turn convert, with some quantum efficiency, to current, depending on the detector. For heterodyne detection the conversion from received opticalpower to electronic power will be linear because of thelocal oscillator, as will be discussed later. Received opticalpower converts to current, which has to be squared for direct detection to get electronic power as used in the signal tonoise calculations.The received optical power is related to the rate of arrivalof the received photons as given by Eq. (10):
P
R
¼
Nhc
λ
T
m
;
(10)
where
T
m
¼
the period of time over
which the measure-ment is made and
N
is the number of photons per pixelreceived during that measurement time. For pulsed ladar systems
T
m
will often be the pulse width.When optical signals hit the detector they create currentsin the receiver electronics which have associated mean levelsand noise fluctuations. There are also current fluctuations inthe receiver even when the detector is not illuminated by anyoptical signals (i.e., dark noise). When the signal and noisesources are considered, the resulting electrical signal to noiseis given by:
SNR
¼h
i
2
s
i
σ
2
n
¼ h
i
2
s
i
σ
2
ns
þ
σ
2
nBK
þ
σ
2
nDK
þ
σ
2
nTH
¼
ρ
2
D
P
2
R
2
eB
½
ρ
D
P
R
þ
ρ
D
P
BK
þ
2
eBi
DK
þ
4
ktB
∕
R
TH
;
(11)
where
ρ
D
is the detector current responsivity,
e
is the electroncharge,
B
is the detection bandwidth,
P
R
is the receivedoptical power at the detector as noted in the equationsabove,
P
BK
is the received background optical power at the detector,
i
DK
is the detector dark current,
k
is Boltz-mann
’
s constant,
T
is the temperature in Kelvin, and
R
TH
is the effective load resistance that creates the same thermalnoise spectral density as the receiver electronics. The first through fourth terms in the denominator represent the signalshot noise, the background light shot noise, the dark current shot noise, and the thermal (or Johnson) noise, respectively.By using the relation between the responsivity and quantum efficiency of the detector,
ρ
D
¼
η
D
e
∕
hf
, the SNR can alsobe written as
SNR
¼
η
D
P
2
R
2
hfB
½
P
R
þ
P
BK
þ
K
2
eBi
DK
þ
K
4
kTB
∕
R
TH
¼
η
D
P
2
R
B
n
2
hf
½
P
R
þ
P
BK
þ
K
h
2
ei
DK
þ
4
kT R
TH
io
;
(12)
where
K
¼
η
D
ρ
2
D
¼
h
2
f
2
e
2
η
D
;
(13)
where
f
¼
c
∕
λ
is the frequency of the received signal and
h
¼
6.63
×
10
−
34
is Planck
’
s constant. Various books canbe used to read more about signal to noise.
2
–
4
One way people eliminate most of the noise terms indirect detection ladars is by using gain on receive. Youcan use an avalanche photodiode to amplify the signal.This is now very common, as will be discussed later.You could also use a fiber amplifier to amplify the signal.Historically people have used photo multiplier tubes.Although receiver optical or electronic avalanche gain isnot included in Eqs. (10) or (12), introduction of gain effec-
tively minimizes the some of the noise terms. In ladar, eachphoton contains much more energy than in microwave radar,making shot noise more important for ladar than it is for radar. The shot noise comes from the quantum nature of electromagnetic radiation. For a background limited direct detection receiver we have:
SNR
¼
η
D
P
2
R
2
hfBP
BK
:
(14)
In the limit where the signal-shot noise dominates theother noise terms the SNR is given by
SNR
nslimit
¼
η
D
P
R
2
hfB:
(15)
For a measurement duration, or pulse width, of
T
m
thematched filter receiver for the direct detection basebandsignal has bandwidth of
B
¼
1
∕
2
T
which yields
SNR
nslimit
¼
η
D
P
R
T
m
hf
¼
η
D
E
R
hf
¼
η
D
N;
(16)
where
E
R
is the optical energy received, and as previouslydefined,
N
is the number of received photons incident uponthe detector during the measurement time
T
m
. In the limit that the signal shot noise dominates other noise terms theSNR is directly proportional to the number of photonsreceived.For a coherent ladar, the SNR is given by:
SNR
¼h
i
2
s
i
σ
2
n
¼ h
i
2
s
i
σ
2
ns
þ
σ
2
nBK
þ
σ
2
nDK
þ
σ
2
nTH
¼
2
ρ
2
D
η
het
P
LO
P
R
2
eB
½
ρ
D
P
LO
þ
ρ
D
P
R
þ
ρ
D
P
BK
þ
2
eBi
DK
þ
4
ktB
∕
R
TH
¼
η
D
η
het
P
LO
P
R
hfB
½
P
LO
þ
P
R
þ
P
BK
þ
KeBi
DK
þ
2
KkTB
∕
R
TH
;
(17)
Optical Engineering 060901-3 June 2012/Vol. 51(6)McManamon: Review of ladar: a historic, yet emerging, sensor technology
:::
where
η
het
is the heterodyne efficiency, which depends onhow well the return signal and LO fields are matched onthe detector, and
P
LO
is the LO power. The new noiseterm in the denominator (compared to the direct detectionSNR) is due to the shot noise of the local oscillator. It shouldbe noted that this is usually referred to as CNR in the litera-ture, meaning carrier to noise ratio, referring to the meanelectrical power at the IF carrier frequency (difference fre-quency) compared to the noise power.When a coherent receiver is utilized the return signal isoptically combined with a local oscillator (LO) signal.The resulting total optical intensity (and power) has fluctua-tions near DC, at the difference and sum frequencies of thetwo fields, and at double the frequency of each of the fields.For optical frequencies, the higher frequency power oscilla-tions are well beyond the maximum frequency response of detectors, so the only power fluctuations that are detectableare those near DC and at the difference frequency. The coher-ent receiver is usually designed to isolate the differencefrequency component from fluctuations and noise at other frequencies. The rms amplitude of the optical power fluctua-tions at the difference frequency is
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
η
het
P
LO
P
R
p
, whichresults in a mean squared signal current of <
i
2
s
>
¼
2
ρ
2
D
η
het
P
LO
P
R
as seen in the equations. Therefore, the elec-trical power measured in a heterodyne receiver is linearlyproportional to the optical power received. The factor of two is eliminated from the denominator because of the factor of two in the signal times LO power mentioned above. Inaddition, the LO adds additional shot noise which isaccounted for in the denominator with the addition of the
P
LO
term.For coherent ladar the local oscillator power can beincreased to dominate other noise sources, assuming thedetector dynamic range can handle the local oscillator power. In general it is better to use AC coupling with a het-erodyne receiver to reduce the impact on the dynamic rangeresulting from having a high power local oscillator. For a well-designed heterodyne case, the main noise will beshot noise from the local oscillator power, and the resultingSNR, is given by
2
SNR
¼
η
D
η
het
P
R
hfB ;
(18)
where
B
is the bandwidth. For a measurement duration (or pulse width) of
T
m
, the matched filter receiver for the hetero-dyne detection
IF
signal at the difference frequency hasbandwidth of
B
¼
1
∕
T
m
which yields
SNR
LOsnlimit
¼
η
D
η
het
P
R
T hf
¼
η
D
η
het
E
R
hf
¼
η
D
η
het
N:
(19)
Note that except for the
η
het
efficiency factor this is iden-tical to the equation for the signal-shot-noise-limited SNRfor direct detection [Eq. (16)]. The difference is that for the well-designed heterodyne detection receiver (with suffi-cient LO power), the SNR is proportional to the number of photons received even when the signal is very weak,whereas, for the direct detection receiver the signal hittingthe detector must be strong enough so that its shot (photon)noise dominates all other noise. In direct detectionamplification is often used to enhance the received signal.If a coherent receiver is truly shot noise limited, and if the heterodyne efficiency is unity, then the coherent SNRwill always be greater than or equal to the direct detectionSNR (assuming detectors having the same quantum effi-ciency). This is not to say that the probability of detectionand probability of false alarm are always better for coherent detection, as those depend on the statistical fluctuations of the signal and noise (primarily signal).Speckle is commonly seen in narrow band laser light that is scattered from a rough surface, such as a wall, as the bright and dark regions in the scattering volume. Speckle fluctua-tions of the signal can affect the probability of detection andfalse alarm. Speckle fluctuations of the signal have the big-gest impact on narrow laser line width ladar because specklecomes from interference between reflections from variousportions of the target. Narrow band signals interfere witheach other, whereas that interference is averaged out witha broadband signal. This is why a flashlight on a walldoes not produce the same bright and dark pattern on a wall as a narrow band laser.
5,6
The net speckle interferencecan range from fully constructive to fully destructive.Speckle can be more easily mitigated in a direct detectionladar because you do not need a narrow line width laser source. Coherent ladar uses a narrow line width laser sourceso you can measure phase by beating the return signalagainst a local oscillator, and have the resulting beat fre-quency be measureable within the detector bandwidth.This is interference with the LO is the same phenomena as interference of the return portions off the wall, whichis why a narrow band signal will interfere with itself uponreflection from a rough surface. Broad band light sourcesaverage out this interference. Because of thevery high carrier frequency of light it is impractical to exactly model the inter-ference between the various reflections, as can be done in themicrowave region. Instead we treat speckle as a statisticalprocess. For a full electromagnetic code simulation this pro-cess would be deterministic, but for the foreseeable futurethat is beyond our computational abilities.The discussion above calculates the SNR. For any givenSNR you can pick an operating point that defines the prob-ability of detection and the probability of false alarm. Theradar community has worked this issue and usually usesequations derived from a 1947 report by Marcum
7
and a 1954 report by Swerling.
8
Swerling case 2 is for independent pulse to pulse variations. It is often quoted. In ladar you willhave pulse to pulse variations in return signal if you haveenough change in angle to produce a new speckle pattern.For any given measurement in order to meet a given prob-ability of detection and false alarm criteria, a certain SNR(related to the number of received photons) is must beachieved. References 1 and
9
are good summary of that addresses both direct and coherent detection ladar and per-formance for general levels of speckle averaging (specklediversity).
3 Two-Dimensional Ladar
Two-dimensional (2-D) ladar is similar to a passive imaging,but with illumination. You can use a gated framing camera tocapture photons in an array. The main benefit of this type of ladar compared to passive sensors is that it will work at night while using shorter wavelengths, therefore you can haveenhancedresolution.Figure1(a)and1(b)showsan8to10
μ
m FLIR image and a 1
μ
m gated laser image of the same object,
Optical Engineering 060901-4 June 2012/Vol. 51(6)McManamon: Review of ladar: a historic, yet emerging, sensor technology
: : :

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