Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805 Vol. 97 – 25

**Includes single user RadarCalc license for Windows PC, for the design of airborne & space-basedSAR. Retail price $1000.

What You Will Learn

• Basic concepts and principles of SAR.

• What are the key system parameters.

• Performance calculations using RadarCalc.

• Design and implementation tradeoffs.

• Current system performance. Emerging

systems.

What You Will Learn• How to apply SAR to the design of high-

resolution systems.• How to design and build high performance

signal processors.• Design and implementation tradeoffs using

RadarCalc.• SAR activities in DoD, NASA and commercial

applications.• Current state-of-the-art.

Synthetic Aperture Radar

Fundamentals

May 4-5, 2009Chantilly, Virginia

Instructors:

Walt McCandless & Bart Huxtable

$1290** (8:30am - 4:00pm)

$990 without RadarCalc software

Advanced

May 6-7, 2009Chantilly, Virginia

Instructor:

Bart Huxtable

$1290** (8:30am - 4:00pm)

$990 without RadarCalc software

Course Outline1. Applications Overview. A survey of important

applications and how they influence the SAR systemfrom sensor through processor. A wide number of SARdesigns and modes will be presented from thepioneering classic, single channel, strip mappingsystems to more advanced all-polarization, spotlight,and interferometric designs.

2. Applications and System Design Tradeoffsand Constraints. System design formulation will beginwith a class interactive design workshop using theRadarCalc model designed for the purpose ofdemonstrating the constraints imposed byrange/Doppler ambiguities, minimum antenna area,limitations and related radar physics and engineeringconstraints. Contemporary pacing technologies in thearea of antenna design, on-board data collection andprocessing and ground system processing and analysiswill also be presented along with a projection of SARtechnology advancements, in progress, and how theywill influence future applications.

3. Civil Applications. A review of the current NASAand foreign scientific applications of SAR.

4. Commercial Applications. The emerginginterest in commercial applications is international andis fueled by programs such as Canada’s RadarSat, theEuropean ERS series, the Russian ALMAZ systemsand the current NASA/industry LightSAR initiative. Theapplications (soil moisture, surface mapping, changedetection, resource exploration and development, etc.)driving this interest will be presented and analyzed interms of the sensor and platform space/airborne andassociated ground systems design and projected cost.

Course Outline1. SAR Review Origins. Theory, Design,

Engineering, Modes, Applications, System.2. Processing Basics. Traditional strip map

processing steps, theoretical justification, processingsystems designs, typical processing systems.

3. Advanced SAR Processing. Processingcomplexities arising from uncompensated motion andlow frequency (e.g., foliage penetrating) SARprocessing.

4. Interferometric SAR. Description of the state-of-the-art IFSAR processing techniques: complex SARimage registration, interferogram and correlogramgeneration, phase unwrapping, and digital terrainelevation data (DTED) extraction.

5. Spotlight Mode SAR. Theory andimplementation of high resolution imaging. Differencesfrom strip map SAR imaging.

6. Polarimetric SAR. Description of the imageinformation provided by polarimetry and how this canbe exploited for terrain classification, soil moisture,ATR, etc.

7. High Performance Computing Hardware.Parallel implementations, supercomputers, compactDSP systems, hybrid opto-electronic system.

8. Image Phenomenology & Interpretation.Imagery of moving targets (e.g., train off the track), layover, shadowing, slant-plane versus ground planeimagery, ocean imagery.

9. Example Systems and Applications. SIR-C,ERS-1, AirSAR, Almaz, image artifacts and causes.ATR, coherent change detection, polarimetry, along-track interferometry.

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Boost Your Skills with On-Site Courses Tailored to Your Needs The Applied Technology Institute specializes in training programs for technical professionals. Our courses keep you current in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highly competitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presented on-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our training increases effectiveness and productivity. Learn from the proven best. For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.asp For Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm

Advanced SAR ProcessingThe Need for SAR Image Processing

To Application-Specific Processing

SAR

Imag

e Fo

rmat

ion

Proc

essi

ng

Optical Data

SAR Data

ToApplication-

SpecificProcessing

Advanced SAR ProcessingSynthetic Aperture Image Formation

krange

kazimuth

Measured FourierComponents ofImaged Region

Image

Four

ier T

rans

form

Advanced SAR ProcessingBorn Approximation

• Electromagnetic scattering theory gives the following leading order approximation

⇒The scattered radar waves measure the Fourier transform of the target(dielectric inhomogeneity)

- Fourier transform wavevector is the bistatic scattering vectorkincident-kscattered

E e f er

iikr

incident( ) ~ ($ )r rk rk

⋅ +

( )f e dscatteredi incident scattered

kk k xk x x( $ ) ~ ( )− ⋅∫ ε

Advanced SAR ProcessingMatched-Filter on an Undersampled Signal

Ambiguity

Advanced SAR ProcessingRange-Doppler Algorithm

PhaseHistoryData

PhaseHistoryData Multiply by

RangeMatched-FilterCorner

Turn

RangeCurvature

Interpolation

Multiply byDoppler

Matched-Filter

SARSLC

Image

SARSLC

Image

Advanced SAR ProcessingRange-Doppler SAR Image Formation

• Doppler (or azimuth) compression- Apply azimuth (or along-track or slow-time) matched-filter to the

range-compressed phase history- Recall that the correlation of two matched chirps produces an

impulse

• Thus, the target energy has been localized to the correct (t,x) location- t = (R+y’)/(c/2)- x = x’

• Linearity generalizes this point-target discussion to formation of an extended image

( )

( ) ( )

( )'xx2/c

'yRt

d'yR

'xc

2i2exp

'yRx

c2

i2exp2/c

'yRt

d),t(d'yR

xc

2i2exp

azrg

20

20

rg

ressedrange_comp

20

−δ⎟⎠⎞

⎜⎝⎛ +−δ≅

ξ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−ξω

π⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−ξω

π−⎟⎠⎞

⎜⎝⎛ +−δ=

ξξ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−ξω

π−

∫

∫

Advanced SAR ProcessingSAROS Raw Data

Advanced SAR ProcessingRange Geometry of Motion Errors

ζ

η

H

δζ

δηR

Rnominal

Ground:

actual location

nominallocation

flatuneven

( )

( ) ( )⎪⎪⎩

⎪⎪⎨

⎧

δζ+≤δη−+δζ−−

δζ+>⎟⎠⎞

⎜⎝⎛ δη−δζ+−+−

=∆

kj2

k2

kjj

kj2

k2

k2j

2j

j

HRfor look*RR

HRfor look*HRHRR

Advanced SAR ProcessingMinimum Antenna Area Constraint

• SAR antenna is the key subsystem determining the performance of a SAR- Antenna design affects swath width, azimuth resolution, range and

azimuth ambiguity level, and clutter- and signal-to-noise ratios• Ambiguity constraints determine the minimum antenna area for a SAR

- Note that there is very little freedom to alter AMIN

- Practical designs typically are twice or more this area to suppress ambiguities

A Av Rcantenna MIN i≥ =

4 λϕtan

Advanced SAR Processing

Seismic Migration Algorithm in four elegant stepsStep 1: Fourier transform the range compressed[1] phase history data

Step 2: Interpolate the transformed phase history

This is the so-called “Stolt interpolation,” which effectively corrects for range curvature.Step 3Multiply the interpolated, transformed phase history by a phase factor

This is effectively the azimuth matched-filter.Step 4Inverse transform the Fourier transform of the image

which produces the complex image.Fine PointsRange compression may conveniently be done by multiplying D(κ,ω) by the complex conjugate of the range reference function[2] in Step 1.Windows, spectral filters, equalization factors, etc., may be multiplied onto I(kx,ky) or D(κ,ω) anywhere between the Fourier transforms in Steps 1

and 4. This enables custom shaping of the impulse response, compensation of antenna patterns, transmit pulse equalization, etc.

[1] “Range compressed” phase history data because we don’t want to mix in any phase modulation included with the transmit pulse, e.g., the quadratic phase of a chirped pulse.

[2] The range reference function is the Fourier transform of the transmitted pulse.

{ } ξττξκξωτπωκ dddiD ∫∫ +−= ),()(2exp),(

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ +=⎟

⎠⎞

⎜⎝⎛

λλ22

2,

2,' 2

2

xyxyx kkckDkckD

⎟⎠⎞

⎜⎝⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

λ−+⎟

⎠⎞

⎜⎝⎛ +λ

π−= yxy2x

2

y0yx k2c,k'Dk2kk2iR2exp)k,k(I

{ } yxyxyx dkdkkkIykxkiyxi ∫∫ ++= ),()(2exp),( π

Advanced SAR ProcessingSAR Image Geolocation

• SAR image pixel location Rpixel determined as a solution to three equations- range equation

- Doppler equation

- Earth model equation

Rslant range SAR pixel= −R R

( ) ( )fRDoppler centroid

slant rangeSAR pixel SAR pixel

pixel Earth pixel

= − • −

= ×

2λ

ω

V V R R

V R

R pixel EarthR h= +

Advanced SAR ProcessingAirSAR Layover Example

Advanced SAR ProcessingScattering Matrix Phase Calibration

• The 4 channel image data are used to construct a scattering matrix at each pixel

• A measured scattering matrix for a fully polarimetric SAR is:

where Sij is the complex amplitude for the j-transmitting i-receiving polarization and φt and φr are the phase factors for transmit and receive. (φt = φt,h- φt,v) and (φr = φr,h- φr,v)

• Two assumptions are used to calculate the difference in transmitted and received phase- hv = vh amplitudes for backscatter systems (averageing across the

image produces a φt - φr expression)- knowledge of the predicted phase difference in the hh and vv

signals in order to determine φt - φr- possibly given by a corner reflecting target

• R (with relative phase) is known after solving for φt and φr

R exp j ( +S exp j ( + S exp j

S exp j St,v r,vhh t r hv r

vh t vv=

⎛⎝⎜

⎞⎠⎟

φ φφ φ φφ

))

Advanced SAR ProcessingBaseline Decorrelation – Spectral View

csinBW 2 θ

k

c cos 2 θ∆θω

2/sink inc

ground λθ

=

θsθM

θδλ

=θω

θ=θ∆=

cosR

cos2c

csinBW2R RB

rgcriticalcritical

Advanced SAR ProcessingGround Wavenumber Filtering

Before Filtering

After Filtering

Advanced SAR ProcessingDPCA

• Doppler of ground clutter is primarily due to motion of the radar⇒ Try to “stop” the radar so it behaves like a conventional MTI radar

• Implement with a Displaced Phase Center Array

Phase Centers

R RT

Tim

e

Pulse n+1

R RT

R RTPulse n

Pulse n-1Antenna Path

Σ+-

ConventionalMTI signal

Advanced SAR ProcessingGround Moving Target Indication (GMTI)

100 kph

1 sq-kmAzimuth

Ran

ge

New

Jersey Turnpike

I-295

Boost Your Skillswith On-Site CoursesTailored to Your NeedsThe Applied Technology Institute specializes in training programs for technical

professionals. Our courses keep you current in the state-of-the-art technology that isessential to keep your company on the cutting edge in today’s highly competitivemarketplace. For 20 years, we have earned the trust of training departments nationwide,and have presented on-site training at the major Navy, Air Force and NASA centers, and for alarge number of contractors. Our training increases effectiveness and productivity. Learnfrom the proven best.

ATI’s on-site courses offer these cost-effective advantages:

• You design, control, and schedule the course.

• Since the program involves only your personnel, confidentiality is maintained. You canfreely discuss company issues and programs. Classified programs can also be arranged.

• Your employees may attend all or only the most relevant part of the course.

• Our instructors are the best in the business, averaging 25 to 35 years of practical, real-world experience. Carefully selected for both technical expertise and teaching ability, theyprovide information that is practical and ready to use immediately.

• Our on-site programs can save your facility 30% to 50%, plus additional savings byeliminating employee travel time and expenses.

• The ATI Satisfaction Guarantee: You must be completely satisfied with our program.

We suggest you look at ATI course descriptions in this catalog and on the ATI website.Visit and bookmark ATI’s website at http://www.ATIcourses.com for descriptions of allof our courses in these areas:

• Communications & Computer Programming

• Radar/EW/Combat Systems

• Signal Processing & Information Technology

• Sonar & Acoustic Engineering

• Spacecraft & Satellite Engineering

I suggest that you read through these course descriptions and then call me personally, JimJenkins, at (410) 531-6034, and I’ll explain what we can do for you, what it will cost, and whatyou can expect in results and future capabilities.

Our training helps you and your organizationremain competitive in this changing world.

Register online at www.aticourses.com or call ATI at 888.501.2100 or 410.531.6034