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8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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TIME REVERSED PHOTONICBEAMFORMING OF ARBITRARY
WAVEFORM LADAR ARRAYS
Joseph L. Cox
U. S. Air Force
Space and Missile
Systems Center Los Angeles, CA
Henry Zmuda
Department of Electrical
and Computer
EngineeringUniversity of Florida
Gainesville, FL
Rebecca J. Bussjaeger
Reinhard K. Erdmann
Michael L. Fanto
Michael J. HaydukJohn E. Malowicki
Sensors Directorate
Air Force Research Labs
Rome, NY
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Step 1Photonic-Based Time Reversal
Laser Probe Pulse
Array
Extraneous target(s) Desired target
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Step 2Photonic-Based Time Reversal
Array
(Receive Mode)
Desired targetExtraneous target(s)
Time Reversal Processor
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Step 3Photonic-Based Time Reversal
Array
(Transmit Mode)
Extraneous target(s)
(Time gating can removeenergy to extraneous target(s))
Time Reversal Processor
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Time Lensing
Laser probe pulse is transmitted from the array:
From P1: sin(ω[t0])
Pulse arrives on target:
At PT: sin(ω[t0+t1])
Reflected pulse arrives at receiver apertures:
At P1: sin(ω[t0+t1+t1])
At P2: sin(ω[t0+t1+t2])
Received pulses are time-reversed:
From P1: sin(ω[T - t0 - t1 - t1])
From P2: sin(ω[T - t0 - t1 - t2])
Re-transmitted pulses arrive on target:From P1: sin(ω[T - t0 - t1 - t1+ t1])
From P2: sin(ω[T - t0 - t1 - t2+ t2])
All pulses are phased matched:
At PT: sin(ω[T - t0 - t1])
PT
P1 P2
t2t1
sin(ωt0)
Lensing is independent of • Physical location of apertures
• Indices of refraction
Laser Probe Pulse
Note
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Pulsed
Laser EOM
RF Input
Dispersive
Element
λmax λmin
f (t )
f (t )
Wavelengths
dispersed
in time
Beam
Expander
f (t )
λmax λmin
Optical
Amplifier
Chirped
Bragg
Grating
Output
Interrogation Pulse
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Pulsed
Laser
EOMDispersive
Element
Beam
Expander
f (t+t 1)
Chirped
Bragg
Grating
λmin λmax
Optical
Amplifier
λmin λmax
λmin λmax
f (t+t 1)
λmin
f (-t-t 1+T)
λmax
λmin
f (-t-t 1+T)
λmax
Time Reversed Pulse
Input
Output
Output
Input
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Beam
Expander
λmin
f (-t-t 1+T)
λmax
Target
Only One
Pulsed Laser isNecessary
Time Lensing
Focuses Energyon Target
Beamforming Array
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Chirped Bragg Grating
L
n0
λmax λmin
maxλ
λ ∆=∆
c
LnT o
Time Reversal
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Arbitrary Waveform Generation
Bradford Pear Bark
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavelength (nm)
R e f l e c t i v i t y
Time-Stretched Chirped Pulse
1400
1450
1500
1550
1600
1650
1700
7
1 0 1
1 9 5
2 8 9
3 8 3
4 7 7
5 7 0
6 6 4
7 5 8
8 5 2
9 4 6
Time (nsec)
W
a v e l e n g t h ( n m )
Required EOM Waveform
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
7 9 4
1 8 1
2 6 8
3 5 6
4 4 3
5 3 0
6 1 7
7 0 5
7 9 2
8 7 9
9 6 6
Time (nsec)
I n t e n s i t y
Desired spectra Source is chirped in time Necessary EOM waveform
EOM RF Input
λmaxλmin f (t )
Pulsed
Laser
Dispersive
Element
Laser Output
* J. Cox and D. Goldstein, “Spectropolarimetric properties of
vegetation,” Proceedings of SPIE, Vol. 5432, pp 53-62, Jul 2004.
*
The EOM used in UWB
array beamforming is left in
place to produce output
pulses of any conceivable
spectral characteristic
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Reflectance Transformation
( )λ ρ TARGET
Eglin Soil
0.076
0.078
0.080
0.082
0.084
0.086
0.088
0.090
0.092
1 4 1 3
1 4 3 5
1 4 5 8
1 4 8 1
1 5 0 5
1 5 3 0
1 5 5 6
1 5 8 3
1 6 1 0
1 6 3 9
1 6 6 8
Wavelength (nm
R e f l e c t i v i t y
Bradford Pear Bar
0.48
0.49
0.50
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavelength (nm
R e f l e c t i v i t y
Laser Intensit
5.20
5.40
5.60
5.80
6.00
6.20
6.40
6.60
6.80
7.00
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavelength (nm
R e l a t i v e I n t e n s i t y
* J. Cox and D. Goldstein, “Spectropolarimetric properties of
vegetation,” Proceedings of SPIE, Vol. 5432, pp 53-62, Jul 2004.
Desired spectraTarget spectra
* *
Necessary spectral output
An interesting application of this ladar is to transform the apparent target reflectance1. Assuming the reflectance of the target is well-known...
2. Divide the desired reflectance by the target reflectance...
3. Modulate the interrogator pulse to produce this output
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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RF Modulation of Laser Pulses
Sinusoidal Waveform
0.00
0.50
1.00
1.50
2.00
2.50
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavelength (nm)
R
e l a t i v e I n t e n s i t y
RF Chirp Waveform
0.00
0.50
1.00
1.50
2.00
2.50
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavele ngth (nm)
R
e l a t i v e I n t e n s i t y
Code Modulated Waveform
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 4 1 3
1 4 3 4
1 4 5 5
1 4 7 6
1 4 9 8
1 5 2 1
1 5 4 5
1 5 6 9
1 5 9 4
1 6 2 0
1 6 4 7
1 6 7 5
Wavelength (nm)
R
e l a t i v e I n t e n s i t y
5MHz CW over 1μsec
Modulation of the ladar pulses, spectrally, with RF waveforms is easily achieved1. Stretching of the pulses to 1μsec lengths enables better information content
2. Re-compression to 10fsec lengths would yield a pulse compression ratio of 108
3. Detection would occur in the time domain with the assistance of dispersive fiber
Chirp,1-50MHz, 1μsec 600-bit coded waveform
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Interpretation of Signal Timing
Beam
Expander Chirped
Bragg
Grating
f (t+t 1)
λminλmax
Optical
Amplifier
λmin λmax
λmin
f (-t-t 1+T)
λmax
Time ReversedPulse
Target
Return
Delay
PhaseConjugated
Pulse
TargetReturn
Pulse
Detectable
Signal
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Phase
Conjugated
Pulse
Cross-Mixing of Conjugated Pulses
Target
Return
Pulse
ArrayElements
DetectableSignal
Signals Are Generated
SimultaneouslyCross Mixing of Time
Reversed Pulses
Target
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Angle/Angle Detection
1
Target
ReturnPulse
Phase
ConjugatedPulse
Detectable
Signal
Pulsewidth
Time
2
1
3
4
5
3
4
2
5 1
7
6
8
9
10
10
8
9
7
6
11
A
12
12
11
B D
CA
Quad Cell Detector
x
y
Dy
Dx
( ) ( )[ ]
−+−=∠ D BC A
x
t t t t D
c x
2arcsin
( ) ( )[ ]
−+−=∠DC B A
yt t t t D
c
y 2arcsin
Equally
Spaced
Cells
1. Each cell has a counterpart equally distant
from the center of the cell, A.
2. Cell A will mix with its own signal.
3. Each mixed signal will be generated at the
same time as the signal from cell A.
4. The signals from all 25 cells will be
combined and detected by a single detector.
3N
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Expectation of Performance
22
02
2
22 2
1
4
4
4G AN
R
D
R
P S
INT
TR τ π
σρ λ π
π
π
=
243
0
228
λ π
σρτ
R
N AGS S TR=
8037.11
R
N S =
8
3
037.11 R
N S =
1m2
0.5
0.8
G 30dB
DINT 245m
A (245
m)2
P 100W
1675nm
485
233
0
223316
λ π
τ ρ σ
R
DG N PAS INT =Final expression:
Received at detector:
Time-reversed signal re-
transmitted:
Modification of scene illumination ladar equations Example system
Estimation of noise
20 fsec source 5x1013 Hz bandwidth
Detector quantum efficiency 50%
Background emittance noise level -48.5dB
Array size 2.55 cm square
Performance metrics
SNR=20dB, range=100m ~11,000 fibers
Range resolution 3μm
Angular accuracy 0.46mrad
(4.6cm at 100m range)
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Comparison of Generic Ladars• Use of phase
– Coherent – use of local oscillator
– Direct detect – no local oscillator
– Coherent beamforming, no L.O.
– Incoherent beamforming also
– Phase agnostic on detection
• Pulse-width (temporal)
properties
– Detector/electronics limitations
– Target, scene limitations – Limited by selection of source
– Time-stretch photonics enable
selectable pulse-widths
• Spectral characteristics
– Narrow line is most common
– Multiple wavelength transmitters
– Fluorescence imaging
– Super-continuum
– Arbitrary waveform – selectable
spectra
• Scene illumination methods
– Scanning: push-broom, rastor
– Scannerless: flood illumination – Only illuminate objects that
generate a return signal
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Generic Ladars (cont.)• Beamforming
– Square hat beam profiling
– Collimated TEM0,0
– Other diffractive effects
– Time reversed phase
matching
• Angle/Angle Determination
– Scanning: IFOV
– Scannerless: FPA
– Conjugated pulse combinationand timing
• Depth of field
– Single pulse detection
– Multiple pulse detection
– Detect as many voxels as are
illuminated on return pulse
• Clutter rejection
– Spectro-polarimetry
– Range gating
– Time gating
– Spectral discrimination
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Advantages of Photonic Time Reversal
• No phase shifters are needed
– No squint
– No quantization noise
• Propagation distortion is negated
– Independent of index of refraction
– Appropriate for inhomogeneous media
• Beamforming independent of array construction
– Conformal arrays are easily produced
– Distributed arrays are possible
• Ability to produce arbitrary ladar waveforms
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Questions
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c
d
dnn
c
d
dnn
cn
d
d
d
dk
v g
λ λ
ω ω
ω ω
ω ω
−=
+=
== )(
1
−=
λ λ
d
dnn
c
LT
12 λ λ λ −=∆λ
λ
λ ∆−=∆
2
2
d
nd
c
LT
2
2
λ
λ
d
nd
c D −=
Fiber Dispersion
Material Dispersion:
Fiber Dispersion
8/7/2019 Time Reversed Photonic Beam Forming of Arbitrary Waveform Ladar Arrays Final
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Ordinary Fiber
(Corning SMF28):
High Chromatic
Dispersion Fiber:
kmnm
ps D 18+≈
kmnm
ps D 100−≈
λ1 λ2 λ1 λ2
∆T
Fiber Dispersion Analysis(Corning SMF28):
Fiber Dispersion (part 2)
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Dispersive Channel
( ) ( ) ( )2
1 2
1
2o oβ ω β β ω ω β ω ω ≈ + − + −
Input:2
( , 0) cosat
o f t e t ω −= ( , ) ( , ) cos ( , )a f t z f t z t z φ =
Output:
( )
( )
( )
( ) [ ] ( )
( )( )
( )
2
1
224
22
1 1
221 2
2 12
2
1( , ) exp
1 21 2
, arg ( , )
21tan 2
2 1 2
a
o o o
t z f t z a
a z a z
t z f t z t z z z
a z a z t z
a z
β
β β
φ ω β ω β β
β β β
β
−
−= −
+ +
= = − + −
− + −+
( )
( ) ( )( )
2
212
1 2
, 4
1 2i o
d t z a z t z
d t z a z
φ β ω ω β
β β = = + −
− +
Instantaneous frequency:
Pulse Dispersion
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PulsedLaser
BPF
DispersiveElement
(Wavelengths
chirped
in time)
Dispersive
Element
(Opposite
Dispersion
Slope)
Excess
Time
Delay T
Time – Reversed Output
TIME REVERSAL MODULE
Telescope
Output
RF ModulatedOptical Chirp
f ( - t + T )
EOMSOA
RF Input f (t )
t
λmin λmax
t
λminλmax
t t
Optical Chirp
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Cross Mixing of Pulses
2
1
3
4
5
3
4
2
5 1
7
6
8
9
10
10
8
9
7
6
11
A
12
12
11
Delay
Lines
Beam
Expanders
Optical
Amplifiers
λmin λmax
Chirped
Bragg
Gratings