spaceborne radar interferometry - university of …web.eecs.umich.edu/~lep/ifsar_talk_2014.pdf ·...

IntroductionRadar Introduction

Synthetic Aperture RadarSAR Interferometry

Spaceborne Radar Interferometry

Leland E. Pierce

The Univ of Michigan, Radiation Lab

Ann Arbor, MI 48109-2122 USA

March 26, 2014

Leland E. Pierce Spaceborne Radar Interferometry



Radar Interferometry Overview

Used to measure the height variation of the Earth’s surface, towithin a few meters

Radar on a satellite in orbit: imaging from 2 slightly differentperspectives.

∆-path-length gets you the height.

Can also map heights of forests

http://uavsar.jpl.nasa.gov/cgi-bin/data.pl

https://www.asf.alaska.edu/




Outline

1. Introduction to Radar

2. Synthetic Aperture Radar (SAR)

3. SAR Interferometry

4. Application: Mapping forests nationwide




Electromagnetic Waves and Currents

Two Conducting Wires





Oscillating Current on One Wire





Radiated Field Propagates in All Directions





Field Induces Current on Second Wire





Current on Second Wire Radiates





Field Induces Current on First Wire





Field Induces Current on First Wire


EECS 230, EECS 330



Radar Block Diagram

A Radar is a system for generating such a field and measuring therefelected field:

Switch G

GFilterA/D

Tx

RxMixer

Oscillator

(digital control circuitry not shown)




Radar Block Diagram

A Radar is a system for generating such a field and measuring therefelected field:

Switch G

GFilterA/D

Tx

RxMixer

Oscillator

(digital control circuitry not shown)


EECS 411, EECS 430



Typical Sensing Scenario

Radar on an airplane or a satellite looks down upon the Earth:

IncidentPulse

ReflectedEnergy




Radar Equation

Received power:

Pr = Pt

1

(4πR2)2λ2G 2

4πσ0

targetAtarget

1

(4πR2)2is due to spreading loss.

λ2G 2

4πis due to the antenna.

σ0targetAtarget is due to the target.

σ0target is a dimensionless parameter that encapsulates the target’s

response to the field.




Radar Equation

Received power:

Pr = Pt

1

(4πR2)2λ2G 2

4πσ0

targetAtarget

1

(4πR2)2is due to spreading loss.

λ2G 2

4πis due to the antenna.

σ0targetAtarget is due to the target.

σ0target is a dimensionless parameter that encapsulates the target’s

response to the field.


EECS 632



Radar Equation

Recieved Power vs. Range for a few cases:




Target Properties

• Reflected Field is usually larger for targets that are largecompared with the wavelength.

• Metal objects have much larger induced currents, and so muchlarger reflected fields as compared with non-conducting materials.

• In the microwave spectrum (most spaceborne instruments), wetobjects reflect more than dry objects.




Target Properties

Scattering Mechanisms

(http://envisat.esa.int)Leland E. Pierce Spaceborne Radar Interferometry



Thermal Noise

Thermal Noise limits the radar’s performance:

Vrms =√

4RkTB

R - Resistance, Ohmsk - Boltzmann’s constant, Ws/KT - Temperature, KB - Bandwidth of voltmeter, Hz




Thermal Noise

Must design the radar with a high enough transmit power in orderto get a large enough backscattered power from the expectedtargets to overcome the receiver noise.

0

1

2

3

4

5

6

7

8

9

10

250 300 350

Temperature (K)

Noi

seV

olta

ge(m

icro

-Vol

ts)

B=1 MHz

R=1 KOhm


EECS 411



Speckle

Signal due to two targets:

Vtotal = V1ejφ1 + V2e

jφ2

Phase φ is related to distance from the radar.




Speckle

Two identical targets, same range:

Vtotal = 2Vejφ

−1

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0

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0 0.2 0.4 0.6 0.8 1Time

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tage

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tage

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tage




Speckle

Two identical targets, different ranges:


jφ2

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0 0.2 0.4 0.6 0.8 1Time

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tage

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tage




Speckle

Two identical targets, phases cancel:


−jφ1 = 0

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tage

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tage

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Vol

tage




Speckle

For many scatterers:

V =∑

Viejφi = Vejφ

φ is uniformly distributed [0, 2π],V is Rayleigh distributed.




Speckle

Rayleigh distribution for received voltage from many scatterers:

0

0.1

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1

0 1 2 3

Voltage

p(v

)

p(V ) =V

σ2e−V2

2σ2

V =

√

π

2σ

Variance = (2 − π

2)σ2




Speckle

Exponential distribution for received power from many scatterers:

0

0.1

0.2

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0.9

1

0 1 2 3

Power

p(P

)

p(P) =1

2σ2e−P

2σ2

P = 2σ2

Variance = P2

standard deviation = mean




Speckle

Speckle Mitigation: Add independent samples:

0

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0.9

1

0 1 2 3 4 5 6 7 8 9 10Number of independent samples averaged

relative σ

1.0

0.0

< P >=

N∑

i=1

Pi

stddev = P/√

N




Speckle

Speckle Mitigation: Example:

0

0.1

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0 10 20 30 40 50Sample Number

Rec

eive

dpow

er

average=⇒

0

0.1

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1


Rec

eive

dpow

er




Speckle

Speckle Mitigation: Example:

0

0.1

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1


Rec

eive

dpow

er

average=⇒

0

0.1

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1


Rec

eive

dpow

er


EECS 632, EECS 401



Range Resolution

Range Resolution: 2-target case:Transmitted pulse with width τand two received pulses.Define range resolution as thespacing between 2 targets suchthat the two returned pulses startto overlap:

2R1

c+ τ =

2R2

c




Range Resolution

Range Resolution: 2-target case:

range resolution =cτ

2=

c

2B

Cannot make pulse width too short, or the transmitted power willnot be enough to overcome thermal noise.




Range Resolution

Instead of transmitting a constant-frequency pulse, send afrequency-chirped pulse instead:

chirp = V (t) = cos(ωt + Ωt2)

−1

−0.8

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−0.4

−0.2

0

0.2

0.4

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1

0 0.2 0.4 0.6 0.8 1Time

Vol

tage




Range Resolution

Process the received signal with a matched filter:

processed signal =

∫

signal(t ′)chirp∗(t − t ′)dt ′

Matched filter applied to a single chirp:

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tage

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−1 0 1 2Time

Pow

er




Range Resolution

Because we processed the received signal with a matched filter:

range resolution =c

2Bwhere B is the bandwidth of the chirp.

• Independent of pulse width.• Can now choose pulse width to satisfy power, or other systemconstraints.




Azimuth Resolution

Antenna Pattern determines when targets at different anglesoverlap:




Phased Arrays

Antenna Arrays can be used to get narrower beams:

Array Pattern =(

∑

Aiejφi

)

f (θ, φ)

f (θ, φ) is the single-antenna pattern

Aiejφi is the amplitude and phase weighting for each antenna




Phased Arrays

Can design the weights to produce a very narrow main beam:

An array of 5 separate an-tennas, showing their single-antenna beams.

The composite antennabeam for the whole array.




Phased Arrays

Can design the weights to produce a very narrow main beam:

An array of 5 separate an-tennas, showing their single-antenna beams.

The composite antennabeam for the whole array.


EECS 531



Typical Sensing Scenario

Side-looking radar from an airplane or satellite:

(http://www.radartutorial.eu/)




JERS

Example Spaceborne SAR: JERS

(http://www.eorc.jaxa.jp)

Frequency: 1.25 GHzResolution: 18m range × 18m azOrbital Height: 568 KmSwath Width: 75 KmBoresite: 35 degrees




Example SAR Image

SAR image with speckle Despeckled SAR image(http://earth.esa.int)




Example SAR Image

(http://visibleearth.nasa.gov)Leland E. Pierce Spaceborne Radar Interferometry



Example SAR Image

(http://visibleearth.nasa.gov)Leland E. Pierce Spaceborne Radar Interferometry

EECS 632



SAR Phase

• Previous images showed SAR images of backscattered power.

• A SAR can also record the phase, but an image of it looks likenoise.

• If use two SAR antennas, the phase difference between the samepixels in the two images is meaningful.




IFSAR Processing: Motivation

• Start with 2 sensors looking atsame spot on the ground.• These sensors have a separation,B , and an angle α, defining theirrelative positions.• Relative to the ground, thesesensors have a height, H, abovesome reference surface.• A point on the ground is at aparticular range and incidence an-gle from each sensor.

The unknown height, h, of the point on the ground is what wewant to solve for.





Assume know both ranges, andbaseline. Solve for the look angleusing law of cosines:

(r +∆R)2 = r2+B2−2Br cos(β)

where β = α + (π/2 − θlook).

After solving for θlook we can calculate h:

h = H − r cos(θlook)





• However, we only know the range to within 5 or 10 meters.• This causes an uncertainty in the look angle.• This leads to a large uncertainty in the height:

heigh uncertainty ∝( r

B

)

∆r

• For current spaceborne SAR systems r ∈ (250Km, 800Km), whileB is 100 to 200 meters, giving r/B ≈ 5000.• Typical range resolutions are meters, and so this makes theheight error far too large.





• Solution 1: Use a large baseline.

Problem: Using large baselines violates the assumption ofnearly-equivalent scattering centers, and so the difference in rangesdoes not measure what we want.

• Solution 2: Improve our precision for ∆r :Problem: we need mm-scale precision in order to get height errorsof a few meters.Solution: Use the phase of the signal.





• Phase of an L-band SAR signal:

Precision of 1 degree equates to:

24cm(1/360) ≈ 7mm

This could work.




IFSAR Processing: Overview

(Taylor, et al., 1999, Atlantis Scientific, Inc.)




IFSAR Processing: Coregistration

• Start with two images covering the same region on the Earth.These were taken by two different overpasses of a SAR satellite.

• The images are single-look complex, with Real and Imaginaryparts.

• In order to form the phase difference for each pixel, we need thepixels to be lined up with each other: Co-Registration is required.





• Manually collect a few points that initializes the algorithm withan offset, rotation and scale between the 2 images.

(Richards, AESS, 2007)





• Then use correlation on small image patches to automaticallycollect many more points, with sub-pixel accuracy.

• Efficiently calculate correlation using Fourier Transform:

Fim1 = IM1

Fim2 = IM2

Correlation(i, j) = F−1IM1 · IM2∗

For an image patch centered at (i,j).





• For high-resolution correlation, use 10X-oversampled imagepatches.

• Resampling is best achieved using the Fourier Transform.

• Start with an N×N patch, and forward transform:

IM PATCH(N,N) = F(im patch(N,N))

• Zero-pad 10× and inverse transform:

im patch(10N, 10N) = F−1(IM PATCH(10N, 10N))

• The result is an image interpolated at a 1/10 the pixel spacing ofthe original.





• For each automatically-generated sample point we use a measureof contrast of the correlation function that is the peak/average.

Example correlation functions.(Richards, AESS, 2007)

• Threshhold this value to choose “good” points.





• Calculate a warping function from one image to the other usingthese automatically-collected tie points.• Assume a polynomial function for this:

xnew = a0 + a1xold + a2xoldyold + a3x2old + · · ·

• Similarly for ynew .• Use linear-least squares to solve for the unknown coefficients.





• Use the oversampled image and the polynomial functions toresample the second image.






• Use the oversampled image and the polynomial functions toresample the second image.



EECS 442, EECS 451



IFSAR Processing: Phase Difference

• Using the pixel-by-pixel phase difference is too noisy.

(ERDAS Field Guide, 1999)

Dark is 0 degrees, bright is 360 degrees.




IFSAR Processing: Phase Difference

• Intead, estimate using a small neighborhood:

Phase Difference = arg

N∑

i ,j=1

Im1 · Im2∗





IFSAR Processing: Baseline Estimation

• Using data from 2 different overpasses of a satellite means thatwe really don’t know what the baseline is.• One could use the orbital data to try to estimate it, but theorbits are not accurate enough.• Instead, use a few points on the ground where one knows theelevation. Like benchmarks that the USGS installed.• Using the previous equations for phase difference and a guess forthe baseline length and angle results in guessed phases for each ofthese calibration points.• Use a numerical nonlinear optimization technique to iterativelyupdate the guess until the error in the guessed phases comparedwith the measured phases is small enough.




IFSAR Processing: Phase Unwrapping

• The phase difference image has other issues that need to bedealt with before we can generate an elevation map:

1. Flattening.2. Unwrapping.3. Phase offset.




IFSAR Processing: Phase Flattening

• Since we want the elevation with respect to a reference surface,at this point we can subtract the phase difference that we expectdue to this reference surface.• This makes the phase variation more slowly-varying across theimage, which helps with the next step: Unwrapping.

Original Flattened





IFSAR Processing: Phase Wrapping

• The measured phase is wrapped between the values 0 and 2πradians. For an example hill shape, we get:






• Phase unwrapping involves adding back 2π radians where neededto get back the actual phase across the image.






• Involves finding the traces in the image where the phase resetsfrom 2π to 0.• Then add back n2π, region-by-region.• Many techniques: a starting point:Dennis C. Ghiglia, Mark D. Pritt, “Two-dimensional phaseunwrapping: theory, algorithms, and software,” Wiley, 1998.• Important issues:1. noise2. abrupt elevation changes3. shadow





• Example result of phase unwrapping

(ERDAS Field Guide, 1999)Leland E. Pierce Spaceborne Radar Interferometry



IFSAR Processing: Phase Offset

• Now the phase still has an arbitrary offset, which we can dealwith using the same calibration points we used for the baselineestimate.• Use the known position and elevation of the calibration points todetermine the offset, and perhaps even a slope, for determining thefinal phase values.• A linear-least squares formulation can be used.




IFSAR Processing: Convert to Elevation

• Last step is to convert phase to elevation in meters:

h =−λ

4π

r sin(θlook)

B cos(θlook − α)φunwrapped




SRTM

Example Spaceborne IFSAR: SRTM

(http://southport.jpl.nasa.gov)

Frequency: 5 GHzResolution: 6-30 m range and azOrbital Height: 225 KmSwath Width: 20-100 KmBoresite: 40 degrees




Forest Height Estimation

On the right: an airphoto, with forest stands outlined.On the left: SRTM elevation map: showing that the forests aretaller than the surrounding land.




Forest Height Estimation

One slice through the dataset showing the correspondence of theSRTM data and the known forest height.

Since the radar scatters fromwithin the canopy, equations thattake into account the species andforest density are used to estimatethe forest height.




Forest Height/Biomass Estimation

From Josef Kellndorfer:




Thanks for your attention

You can contact me at:[email protected]

Viewgraphs available at:http://www.eecs.umich.edu/~lep/ifsar talk 2014.pdf




Relevant EECS Courses

EECS 230 and 330: Intro. to Electromagnetics

EECS 280: Programming

EECS 373: Embedded Systems

EECS 411 and 430: Introduction to radar circuits and wireless

EECS 401: Probability

EECS 442: Computer Vision

EECS 451: Signal Processing

EECS 531: Antennas

EECS 632: Imaging radar systems and processing




References

ERDAS Field Guide, (especially Chapter 8) 1998.www.gis.usu.edu/manuals/labbook/erdas/manuals/FieldGuide.pdf

Mark A. Richards, “A Beginner’s Guide to Interferometric SARConcepts and Signal Processing.” IEEE A&E Systems MagazineVol. 22, No. 9, Sept., 2007.http://users.ece.gatech.edu/ mrichard/AESS%20IFSAR%20Tutorial.pdf




References

John Curlander, Robert McDonough, “Synthetic Aperture Radar:Systems and Signal Processing,” Wiley, 1991.

Ramon F. Hanssen, “Radar interferometry: data interpretation anderror analysis,” Kluwer Academic, 2001.

Stephen C. Taylor, Bernard Armour, William H. Hughes, AndrewKult, Chris Nizman, “Operational interferometric SAR dataprocessing for RADARSAT using a distributed computingenvironment,” Geocomputation, 1999.http://www.geocomputation.org/1999/084/gc 084.htm


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