FMCW Differential Synthetic Aperture Ladar for

Turbulence Mitigation

18th Coherent Laser Radar Conference

June 30, 2016

Zeb Barber, Jason Dahl, Ross Blaszczyk

Outline

• Ultra-high resolution (< mm) FMCW sources

– Active stabilization of chirp rate and center frequency

• Synthetic Aperture Ladar Imaging

– Introduction

– Image based phase correction

• Differential Synthetic Aperture Ladar

– DSAL concept and receiver design

– Comparison with SAL in atmospheric turbulence

2

Ultra-high Resolution FMCW Sources

• Tunable laser sources

– Large mode-hop free tuning (10’s of nm possible)

– Trade-off between tuning bandwidth, coherence

length, and tuning speed

– External-cavity, DFB, … integrated photonics?

• Active Stabilization with improvements

– Fiber delay generates error signal on chirp rate

– PLL locks chirp rate

– “Lock around the corner” for phase coherence

– Stabilize center frequency to molecular

absorption using digital loop

ChirpOutput

DFB Laser

90/10Splitter

50/50Splitter

50/50Splitter

10m Delay

AOM90

10

InlinePolarizer

Detector

CurrentDriver Servo

DPD

DDS1

DDS2

MicroController

15MHzRef

TempController

Amplifiers

Amplifier

90/10Splitter

HCNCell

Detector

Comparator

time

freq

uen

cy τ

3

f

t

τD τc

fbeat = κτD

B

Local

Oscillator

Delayed

Signal

Metrology Applications

StabilizedChirp Laser

Transmit

Return

Local Oscillator

Focusing Lens

Reference Plate

Sample

X-Y Stage

Photodetector

Computer

0

2

4

6

8

0

2

4

6

80

100

200

mmmm

mic

ron

s

Emitter B

99.99Fiber

Splitter

Stabilized

Chirped

Laser

Source

Rx

Tx

LO

Scattering

Target

Emitter C and mirror

for the interferometerComputer controlled

translational stage

Auto-Balanced

Detector

fiber path

free path

90

A

D

C

10

to interferometer

50

50

0.01

50

50

Collimated

Emitter

/Receiver A

Unprocessed

DataPost

Processing

99.99

99.99

0.2 0.25 0.3 0.35 0.41.45

1.46

1.47

1.48

1.49

Py [m]

Px [

m]

0.2 0.25 0.3 0.35 0.4

-1

0

1

Py [m]Res

idual

s P

x [

mm

]Measurements

Savitzky-Golay smooth

4

3 2 1.2 0.85 6.35

6.35

6.35

4

x

0 0.5 1 1.5-15

-10

-5

0

5

10

15

Time (s)

Re

lativ

e D

ista

nce

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2-60

-50

-40

-30

-20

-10

0

10

Relative Range (m)

Re

lativ

e P

ow

er

(dB

)

Precision = 0.7 mm

Eight targets at 14.2 km standoff

Synthetic Aperture Imaging History

• Synthetic Aperture Radar

– Proposed in 1951, Carl Wiley

– First images in 1957

• Radar signals recorded on film, processed optically

– Digital supplanted optical processing in late 70’s

• Synthetic Aperture Ladar

– Early work in 1960’s United Aircraft (Lewis & Hutchins)

– Re-emergent interest in mid 2000’s (NRL, Aerospace Corp)

– Table-top work needs a very large bandwidth (> 100’s of GHz) chirp source

• “In fact, finding a suitable source has been one of the most challenging aspects of the SAIL

imaging problem. Generally, tunable sources are not sufficiently stable and stable sources are

not broadly tunable.”

SAR of Venus

Magellan

Bashansky et. al Beck, Buck, Buell et. al

f

t

τD τc

fbeat = κτD

B

Local

Oscillator

Delayed

Signal

5

Coherent Imaging

• Coherent Illumination

– Coherent field scattering off diffuse objects creates 3D speckle field

– Speckle field is a Fourier domain representation of object • Size of speckles inversely proportional to size of object

• Speckles move with object orientation

• Absolute phase depends on absolute roundtrip distance and laser wavelength

• Coherent Detection

– Speckle field phase required to reconstruct image • Interference with LO field captures signal field phase

• Image formed by Fourier transforms and quadratic focusing

– Provides single photon sensitivity

• Digital Holography – Spatial sampling, no temporal or frequency domain sampling

• Synthetic Aperture Ladar – Frequency/Range domain sampling in one dimension, temporal sampling of spatial degree by motion

• Combinations of above – How do you divide up your resources?

6

100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

SAL Imaging Simulation

Synthetic Aperture Scan Frequency Scan

meters

me

ters

-0.05 0 0.05

-0.05

0

0.05

200 m propagation

Tx/Rx Plane Object Plane

7

SAL Imaging Demonstrations

8

• Phase of optical field required to form image

• Motion induced piston error largest phase error source

– LMCT presented a SAL flight demonstration at CLEO 2011

• Motion compensation techniques

– Prominent Point (point target of opportunity or artificial cooperative target)

– Phase Gradient Autofocus (PGA)

– Differential Synthetic Aperture Ladar • E. A. Stappaerts and E. T. Scharlemann, "Differential synthetic aperture ladar," Opt. Lett. 30, 2385–2387 (2005).

Local

Oscillator Path

Unprocessed

Data

Shot N

N-1

Shot 1

Post-

Processing

Stabilized

Chirped Laser

Source

Balanced

Detector

ADC

HCN Ref

Computer

Controlled

Stage

Fiber

Splitter\Coupler

Range

Cro

ss

-

ran

ge

EDFA99/1

90/1050/50

Circulator

a) b)

2.32 2.34 2.36 2.38 2.4

-20

-10

0

10

20

Range [m]

Pow

er

[dB

]

0 500 1000 1500 2000

0

50

100

150

SA indexP

hase C

orr

ection [ra

d]a) b) c)

Single Range Profile Image before PGA PGA Estimate Phase Correction

1300x1300

Pixels

Table Top SAL Demos

9

Phase Gradient Autofocus

10

Step 1Input Complex Image Domain Data

Step 2Center Shift Largest Targets

Step 3Determine Window Width and Apply Window

Step 4Fourier Transform in Cross-Range Dimension

(to range-compressed domain)

Step 5Estimate Phase Error Function Across Aperture

Step 6Apply Phase Correction

Step 7Inverse Fourier Transform Back to Image Domain

RMSPhase Error <Threshold?

Algorithmic Steps in PGA

DoneYes

No

• Step 2 - center shifting chooses strongest targets

and removes the linear phase variation from

each target

• Step 3 - windowing attempts to include as much

energy from a single target in each range line

without including multiple targets

- proper choice of window affects efficiency

and final image quality

• Step 5 - phase error estimation accomplished by

averaging of all targets to bring common

mode phase error above clutter and noise

• Iteration - algorithm proceeds iteratively with

decreasing window width to converge on final

processed image

- threshold on estimated RMS phase error is

used to stop iteration

*

1

, 1 ,N

k

m g k m g k m

More Demos

11

Cross-range [mm]

Range [m

m]

5 10 15 20 25

5

10

15

20

25

30

35

40

45

50

55

(a)

(b)

(c)

computer controlled stage

rotationstage belowtarget

spri

ng-

load

ed

stag

e

(d) Spotlight Motion Controland Bistatic Geometry

monstaticTx\Rxoptics

bistaticRx optics

dθ15cm

1.4

m

(a) (b)

Fig. 3. a) SAL image of Air Force Bar Resolution Target (negative of chrome pattern on glass) with PGA applied in cross range. b) Same SAL image with PGA applied in cross range and range after CZT-PF processing. Colors inverted on both images.

(d) (e)

mic

ron

s

(f)

(d) (e)

mic

ron

s

(f)

Interferometric SAL

Range Migration Correction

• 5 photons per “on” pixel – Top: Retro phased; Bottom: PGA phased

– Left: ~ 1 photon per pixel averaged 5 times

– Right: ~5 photons per pixel no averaging

– 200 cross-range samples

Extremely Low Return Levels

Cross-Range

Range

0

1

2

3

4

5

0

5

10

15

20

25R

ange

0

1

2

3

4

5

Cross-Range

0

5

10

15

20

25

(a)

(b)

(c)

(d)

Cross-Range [cm]

Ra

ng

e [cm

]

-20 -10 0 10 20

5

10

15

20

25

30

35

40

45

12

SAL Simulation Results

Meters

Mete

rs

2 km Cn

2 = 10-14 at Aperture

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-14 at Aperture w/PGA

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-13 at Aperture

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-13 at Aperture w/PGA

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-12 at Aperture

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-12 at Aperture w/PGA

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-11 at Aperture

-1 -0.5 0 0.5 1

-0.5

0

0.5

Meters

Mete

rs

2 km Cn

2 = 10-11 at Aperture w/PGA

-1 -0.5 0 0.5 1

-0.5

0

0.5

Phase Gradient Autofocus is quite good at removing common mode phase errors

-Small aperture means turbulence needs to be very strong to not be common mode

Turbulent phase screen near the aperture plane

13

Differential SAL

• E. A. Stappaerts and E. T. Scharlemann, "Differential synthetic aperture ladar,"

Opt. Lett. 30, 2385–2387 (2005). – Patented by Stappaerts in 2005

• Use differential phase of two halves of receiver aperture

– Numerical integration across SA as phase history data

– Similar to idea behind PGA

• Phase gradient instantaneous (better for dynamic errors e.g. turbulence)

• Phase evolution estimated by integrating the differential phase

• Dynamic piston errors common mode

• Different piston errors for different range lines

14

100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Real Aperture

Synthetic Aperture

• Table-top experiment with chirp from DFB laser

– Real Aperture – ~ 50 Gaussian μm

– SA – 2 mm (200 steps); Distance – 2 m

– Chirp Rate – 83.3 GHz/ms; Chirp Time – 1 ms; 83 GHz;

– dR ~ 2 mm; dCR ~ 1.5 mm

𝑑

scatterer

𝑧

𝑥

Differential SAL Setup

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-40

-20

0

20

[rad]

Absolute Measured Phase

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-0.2

0

0.2

0.4

0.6

[rad]

Differential Phase

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-15

-10

-5

0

SA Position [mm]

[rad]

Reconstructed Phase

Single Point Target 10 um steps SA

15

𝑓1&2 = 50mm

𝑓4 = 200mm

𝑓3 = −15mm

Balanced Quad Detectors

35mm 185mm 200mm 50mm

Wollaston Prism

Chirp Laser

PBS

Tx

LO

𝝀/𝟐 Tx/Rx Aperture

Magnification = 13.5

Target

𝝀/𝟐

𝝀/𝟒

• DSAL Tx/Rx design

– Monostatic

– Balanced homodyne receiver using polarization mixing

– Auto-balanced quadarture

– Large magnification to match aperture to 1 mm detector

• Lab experiment with chirp from DFB laser – Real Aperture – ~ 50 Gaussian μm soft aperture

– SA – 2 mm (200 steps); Distance – 2 m

– Chirp Rate – 83.3 GHz/ms; Chirp Time – 1 ms; 83 GHz;

– dR ~ 2 mm; dCR ~ 1.5 mm

Comparison w/ PGA w/ turbulence

• Data collection using strip map mode ~ 2 mm SA

– 8 m range

– Turbulence introduced into path using space heater

• Process data using DSAL or SAL w/PGA

• PGA performs better with no turbulence or turbulence near Tx/Rx – Soft aperture provided by LO and not enough magnification onto detector low pass filters DSAL phase estimate

causing problems with image has larger cross-range extent

• DSAL seems to degrade more gracefully, but not immune

16

DSAL Turbulence Analysis

• E. A. Stappaerts and E. T. Scharlemann make bold statement that, “DSAL, unlike SAL, is not

affected by turbulence changes near the target.”

– SAL immune to static turbulence near the target, but dynamic turbulence messes with phase evolution of

point target

– DSAL since it is immune to overall phase changes

• 𝐸±,𝑗 = 𝑎𝑝 exp 𝑖𝜙𝑝(𝑗) exp− 𝑥𝑗−𝑥𝑝

2

𝑤𝑜exp

−𝑖𝑘 𝑥𝑗−𝑥𝑝2

2𝑅exp

−𝑘 𝑥𝑗±𝑑

4−𝑥𝑝

2

2𝑧,𝑝

– 𝑗 is aperture position, 𝑝 enumerates point scatterers

– Problem becomes that the phase angle of a sum of complex numbers is not linear in phase (i.e.

∠ 𝑎 + 𝑏 ≠ ∠𝑎 + ∠𝑏)

17 1D Simulation shows that DSAL does not provide much improvement over PGA+SAL with dynamic turbulence

near the target

-0.4 -0.2 0 0.2 0.40

0.2

0.4

0.6

0.8

1

Cross-Range [m]

Inte

nsity

1D DSAL w/ Turbulence simulation r0 = 0.2

10-1

100

101

0

0.2

0.4

0.6

0.8

1

r0 [m]

Fig

ure

of

Merit

SAL

DSAL

Average Ratio of Peak Height with Turbulence to no Turbulence

Turbulence Characterization

18

• Work performed for AFOSR YIP

– High Resolution Ladar (2 mm range resolution) 250 Hz update

– 4x4 =16 square grid retro targets ~ 5 cm transverse spacing, ~ 1 cm range

spacing

– Distance 8 m

– Turbulence generated using space heater

• Ladar processing

– Capture 2000 chirps (4 seconds, every 40 seconds)

– Resolve peaks, extract peak amplitude, range, & phase

– Process amplitudes and phases using mutual coherence to generate

structure function and fit that to get 𝑟0 and 𝐶𝑛2

Ladar

Heater

Target

Turbulence Characterization

19

• Mutual coherence and modulus of the complex coherence factor

– Γ Δ𝑟 = 𝑈 𝑟 𝑈∗(𝑟′) = 𝑈0 𝑟 𝑈0∗ 𝑟′ exp 𝜓 𝑟 exp {𝜓∗(𝑟′)

– 𝜇 Δ𝑟 =Γ(𝑟,𝑟′)

Γ 𝑟,𝑟 Γ 𝑟′,𝑟′12

-> 𝐷 Δ𝑟 = −2 ln 𝜇(Δ𝑟)

-1 -0.5 0 0.5 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Accumulative 𝜇(Δ𝑟𝑖)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

All 𝜇(Δ𝑟𝑖)

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

Fitting of 𝐷(Δ𝑟𝑖)

0 200 400 600 800 1000 1200 140010

-13

10-12

10-11

Cn

2

time [sec]

Advantage: Insensitive to fixed

phase offsets!

Acknowledgements

• AFOSR Young Investigator Program (YIP)

– #FA9550-12-1-0421

• Bridger Photonics/Blackmore Sensors|Analytics

– Randy Reibel, Pete Roos, Brant Kaylor, Stephen Crouch

• Other Support

– DARPA/DSO InPho, NSF GOALI CMMI, AFRL SBIR, Montana

Board of Research and Commercialization

20