time reversed photonic beam forming of arbitrary waveform ladar arrays final

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




Step 1Photonic-Based Time Reversal

Laser Probe Pulse

Array

Extraneous target(s) Desired target





Array

(Receive Mode)

Desired targetExtraneous target(s)

Time Reversal Processor





Array

(Transmit Mode)

Extraneous target(s)

(Time gating can removeenergy to extraneous target(s))

Time Reversal Processor




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




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


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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



Beam

Expander

λmin

f (-t-t 1+T)

λmax

Target

Only One

Pulsed Laser isNecessary

Time Lensing

Focuses Energyon Target

Beamforming Array



Chirped Bragg Grating

L

n0

λmax λmin

maxλ

λ ∆=∆

c

LnT o

Time Reversal



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



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


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


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



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


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


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



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



Phase

Conjugated

Pulse

Cross-Mixing of Conjugated Pulses

Target

Return

Pulse

ArrayElements

DetectableSignal

Signals Are Generated

SimultaneouslyCross Mixing of Time

Reversed Pulses

Target



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



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)



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



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



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



Questions



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



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)




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




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



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

time reversed photonic beam forming of arbitrary waveform ladar arrays final

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