synthetic aperture radar - mathematics · synthetic aperture radar works by sampling at speciﬁc...

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IntroductionRadar Resolution

Synthetic Aperture Radar

Richard Spangler

University of Michigan

March 6, 2009 / Math 501

Richard Spangler Synthetic Aperture Radar

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Outline

1 Introduction

2 Radar ResolutionMotivationRange and DirectionRange ResolutionSynthetic Aperture Formation


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Radar Basics

The underlying principle of Radar (RAdio Detection AndRanging) is echolocation. A radar transmits a radio signal andto listens for a reflected signal. Objects in the path of the signalwill reflect (scatter) the radar pulse. If the signal is reflected inthe direction of the receiver, it will be recorded as a radar return.

Figure: Basic principle of radar operation. The radar transmits apulse at a given frequency, and records the time of the radar return


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Goal

Primary functions of radar: Detect targetsRangeDirection

’Target’ is a broad term: it means "whatever you’re lookingfor"

Goal of this talkShow how we can improve our knowledge of a target’sdirectionBe able to separate it from other targets (resolution)

We will show how Synthetic Aperture Radar (SAR) aids thisprocess.


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MotivationRange and DirectionRange ResolutionSynthetic Aperture Formation

Outline

1 Introduction



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Fine Resolution

SAR application: Monitoring of global sea ice conditionsUse of radar allows us to see underlying structureFine resolution provides greater insight into stability of iceshelf

Figure: Wilkin’s Ice shelf, AntarticaRichard Spangler Synthetic Aperture Radar

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Outline

1 Introduction



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Range

Radar as a timekeeping deviceDistance formula relates distance to round trip time

R =cT2

(1)

But knowing that we have a target doesn’t tell us what directionit lies in! It can be anywhere within a sphere surrounding theradar. Can we do better?


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Direction

We can limit the possible direction that contains a target by thebeam directivity that we use. Beam directivity concentrates thesignal strength in a particular direction, and is related to thedimensions of the antenna. The beam pattern for a linearantenna is approximately

P = (sinc(π(L/λ)sinθ))2 (2)

An antenna beam is expressed in terms of its half-powerbeamwidth:

θ3db∼= 0.88

λ

L(3)


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Antenna Beam Pattern


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Antenna Pattern Projection

For a square antenna ofdimension LxL, our detectedtarget is now in a region definedby the antenna orientation andits 3db beamwidth.In order to separate targetswithin the beam pattern, wefirst introduce range resolution.


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Outline

1 Introduction



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Range Resolution

Width of a transmittedpulse determines its rangeresolution

ρr =cτp

2(4)

For a single frequencywaveform, a short pulsemeans a fine rangeresolution.


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Linear FM waveform

Short pulses to reduce range resolution are not practicaldue to power requirementsFine range resolution can be achieved via linear FMwaveform

Frequency "chirps" from low to high over pulse durationFrom signal theory, we can compress a pulse of bandwidthB to a time duration of appoximately 1

B

Alternate form of range resolution

ρr =c

2B(5)

Example: if we want 5m range resolution, we need a linearwaveform with approximately 30MHz of bandwidth.


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Outline

1 Introduction



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Azimuth Resolution

If we would like to improve resolution in the azimuth direction,we could simply make the antenna larger. Using our formula forbeamwidth, we could calculate the antenna needed to producea 5m azimuth resolution:

ρa = θ3dbR =0.88λ

LR = 5m (6)

L = 0.176λR (7)

For an L-band radar with λ = 20cm, and a standoff range of25km, we would require an antenna 880m long! For airbornemapping applications, this (literally) won’t fly.If we had a longer standoff range, this problem gets evenworse. We need a better solution.


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Synthesizing an Antenna

Fortunately, one exists. If a radar is able to collect and storepulses, it can do so as it changes its position. As it collectspulses along its path, it will have sampled from points along avery long virtual antenna. These pulses can be coherentlycombined to synthesize a very long linear array.


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Synthetic Aperture Notes

Synthetic aperture radar works by sampling at specificpositions

Motion of the antenna is not core to the concept, other thangetting us to our next sample pointTime between pulses can usually be ignored (sort of)

Synthetic aperture requires the scene to be illuminated forall pulses

We need a smaller antenna to create a large enough beamProcessing

Can be done by matched filtering or backprojection, butfaster methods existMotion is part of the solution, but it is also part of theproblem


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End Result


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Digging further

Polarimetry: Use of radar polarization to analyze targetresponsesInterferometry: Coherent combination of two SAR images toform terrain mapsBistatics: Transmitter and receiver located in different location


synthetic aperture radar - mathematics · synthetic aperture radar works by sampling at speciﬁc...

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