Principles And Theory Of Radar Interferometry

Principles and Theory ofRadar Interferometry !Piyush S Agram!Jet Propulsion Laboratory!July 29, 2013UNAVCO Short Course"Disclaimer: Large parts of this talk has been derived from UNAVCO’sROI PAC short course (2012) notes by Paul Rosen, JPL.

Outline of Tutorial"MORNING SESSIONI. Fundamentals of InterferometryA. Young’s double slit experimentB. Variations to Young’s experimentC. Extension to radar interferometryII. Radar Imaging FundamentalsA. Basic Principles of Remote Sensing, Radar, and SARB. Range and Azimuth CompressionC. Doppler and its Implications

Outline of Tutorial"AFTERNOON SESSIONI. Properties of radar imagesII. Geometric Aspects of Interferometry and Interferometric PhaseA. Interferometry for Topographic MappingB. Interferometry for Deformation MappingIII. Interferometric CorrelationA. SNR and Interferometric CorrelationB. Geometric, Temporal and Volumetric DecorrelationC. Other Error Sources

What is interferometry?"Interferometry is a family of techniques in which waves, usuallyelectromagnetic, are superimposed in order to extract informationabout the relative change in wave properties. !Wave 1Reference waveInterferometerWave 2Modified waveQuantity of interestInferred from relativedifference in wavepropertiesWaves typically modified byinteraction with media, multiplereflections etc.

Wave Properties of Light" Light waves areelectromagnetic energythat propagates!kk 2πλr “Plane wave”propagatingin direction k!Energy propagates!Amplitude!E(x, y,z,t) E 0efrequency!“Phase”!jφ (x,y,z,t ) E 0e j(ωt k r ) 5

Youngʼs double slit experiment" In Youngʼs experiment, a point source illuminates two separatedvertical slits in an opaque screen. The slits are very narrow andact as line sources. For this case, the pattern of intensityvariations on the observing screen is bright/dark banding.!(Born and Wolf, 1980)Observing ScreenScreen laid flat

Interference Concept" Interference occurs when the phase of two different waves isnot aligned. The observed intensity, I, is the time average of thesum of the wave fields!E(z,t) E0 cos(2π(f t - z / λ))Intermediatephase alignmentE1IE2Phase alignedwaves addconstructivelyPhase opposed wavesadd destructively

Wave interference"Band spacing depends on1. wavelength2. Spacing between the two slits

The math" : The scientificsentence.net.2007.l d xLΔφ 2πlλPath differencePhase difference

Baseline / slit separation"Animation demonstrating the relationship betweenbaseline and phase difference.

Generalizing Young’s interferometer" Two slits ensure that the interfering waves have samewavelength (derived from one source). On the screen, we observe (amplitude) the sum of the twowaves. Individual wave information is lost. Two waves should be of similar amplitude.What if we can vary the experimental setup?

Variant 1: Hypothetical Phase detector" What if phase could be directly estimated? Can we use only one source at a time?A1 eA1 e jk r1 jk r1 A2 e( jk r2 conj A2 e jk r2) No more dependence on amplitudeOriginal interferometerIf direct phasemeasurements werepossible.

Phase difference image" ππObserving ScreenScreen laid flat Both sources operated at different times. Fringes generated by combining phase later.

Radar Interferometry- I" Radar Interferometry is a simple extension of the Youngʼsinterferometry concept! Radar has a coherent source much like a laser! The two radar (SAR) antennas act as coherent point sources! SAR image is equivalent to aphase and amplitude detector.!! Two SAR images can then beused to generate interferograms.!!

Variant 2: Topography/Deformation" What if the screen were not flat? What if the screen deformed between two images?AnimationObserved phase-Flat screen phaseas a function ofscreen topography

Radar Interferometry- II"Ocean The surface topography modulates the interference pattern.!

Variant 3: Coherent Imaging system" Practical problem!– we can’t set up phase detectors everywhere.! Possible solution!Incident wavesReceiverCoherentSourceScattered wavesCreate a 2D coherentimage of the screen.Screen /scattering surface

2D imaging system" Wavelength/ frequency needs to be constant for preserving phaseinformation!! Source and receiver combination used to create a 2D image of thescreen / scattering surface!! !Often source and receiver are co-located!Δφ ( x, y) φ1 ( x, y) φ2 ( x, y)φi source pixel pixel receiverRadar is one such coherent imaging system!

Moving on to radar fundamentals " We have used simple variants of Young’s interferometer tomotivate the use of radar as a coherent imaging system. Next section of talk will focus on fundamentals of radarimaging. Besides being a coherent imaging system, One of the mainbenefits of using radar: Remote Sensing

What is Remote Sensing?" In modern usage, Remote sensing generally refers tothe use of aerial [or satellite] sensor technologies todetect and classify objects on Earth [or other planets](both on the surface, and in the atmosphere and oceans)by means of propagated signals (e.g. electromagneticradiation emitted from aircraft or satellites).! Active! Radar, sonar, lidar ! Passive! Multi/hyperspectral, photometers, radiometers, gravity sensors,field detectors, seismometers ! Technique and sensor choice depends on what information is desiredand the required accuracy and resolution for that information.!

What do we want to measure?" Topography*! Geography*! Chemistry! Composition! Phase! Dynamics! Thermo-!Hydro*-!Geo*-!Bio*-!*Radar and Radar Interferometry can be useful!

Radar and Light Waves" Radars operate at microwavefrequencies, an invisible part of theelectromagnetic spectrum! Microwaves have wavelengths in themillimeter to meter range! Like lasers, radars are coherent andnearly a pure tone!Millimeters to meters wavelength!Positionzc fThe Electromagnetic Spectrum!Common Radar Frequency Bands!BandWavelength 52.51.20.4tiny!100’s µm!mm’s to m’s!

The Radar Concept"At light speed, c!Object scatters energyback to radar!Transmitter/!Receiver!!!!olleHHalo!! Much like sound waves,radar waves carryinformation that echoes fromdistant objects! The time delay of the echomeasures the distance tothe object! The changes of themessage in the echodetermines the objectcharacteristics !!!!olleHHallo!!!

A Note on Antennas" Antennas direct the radiation into a desiredangular region that depends on the size ofthe antenna and its wavelength. !3dB kLSmall Antennas Wide Beams"Big Antennas Narrow Beams"Antenna Gain Pattern!G 4 A2Antenna Footprint!

Radar on a Moving Platform"Small antenna -big beam Pulses are transmitted fromthe radar platform as it movesalong its flight path! Each pulse has finite extent intime, illuminating a narrowstrip of ground as it sweepsthrough the antenna beam! Some of the energy from theground is scattered back tothe radar instrument !Big antenna-small beamAntenna BeamwidthFootprint Size on Ground

Achieving resolution in range"R Rpoint targetsAntennaechoes of pulsetransmitted signal2Rc2 RcIf possible, use a narrow pulse to resolve close targets!

Achieving resolution in range"transmitted signalreceived pulsesIf pulse can’t be narrow,use a “chirped” signal!a2Rcmaximum energyb2 RcMatched filtering canrecover smeared targets!s(t) n(t)Matched filterhm(t)t

Range and Range Resolution"ctrt 2Range is the distance between theradar and an object! Range resolution would normally belimited by the length of the emitted pulse.!Better resolution is achieved bytransmitting coded waveforms. Mosttypical encoding is a chirp. !!PRIFrequency FYI!BandwidthB!0Time!c 2B

Radar Imaging Geometry"Quick detour: intro2radar.comA VISUAL INTRODUCTION TO RADAR REMOTESENSINGBy Iain H Woodhouse

Raw Signal of a Point Target"Pulse Number!Range !This “image” shows a sequence of simulated pulse echoes from asingle point target!

Range Compression of a Point Target;after Matched filtering"Pulse Number!Range !This “image” shows the simulated pulse echoes after rangecompression matched filtering!

Targets after range compression"Range !BackwardSquintPulse Number! Squint determineswhich part of therange curve issampled by thefootprint. Doppler centroid isa measure of squint.FootprintOverlapForwardSquint

Doppler Shift" Objects moving relative to aradar experience a frequencyshift called the Doppler shift.! Objects moving toward theradar have higher frequencies! Objects moving away from theradar have lower frequencies. !ˆ2 v , 2v cosfd sq

Doppler in SAR Imaging"Target at (x0,R0)x is satellite positionDropping the constant termt

Range-Doppler Coordinates"

SAR Imaging Concept"Real ApertureImagingSynthetic ApertureImagingCross-Track resolutionachieved by short or codedpulsesAlong-Track resolution limited by beamwidthAlong-Track resolution achieved by coherentlycombining echoes from multiple pulses along-track Resolution proportional to antenna length Independent of Range/FrequencyReal Along Track BeamSynthesized Along Track Beam

Targets after range compression"Pulse Number!Range !Two targets at samerange have differentrange curves.Combininginformation frommultiple pulsesallows use toresolve the targets.

Nyquist Sampling Theorem" A consequence of the Nyquist Sampling Theorem is the the radarPRF must be twice the bandwidth of the received signal in order toavoid spectral aliasing of the signal. ! Using the expression from the previous viewgraph for the azimuthbandwidth we have that !P RF2vcos azLazwhich for small squint angles, θaz smaller than 25 , is oftensimplified to !2v!! P RFLazNote that the required PRF is independent of wavelength and rangeand only depends on the platform velocity and the azimuth antennadimension. !Courtesy Scott Hensley

Azimuth Resolution from ApertureSynthesis" λR0/L Azimuth Footprint, Xill λR0/L !Target is visible for !2*Footprint at R0!Thus, length of syntheticaperture is 2 x Footprint.!Equivalent azimuthresolution (λR0/(2*Xill) (L/2) is constant !Aperture synthesisprocessing is very similarto matched filtering inrange!

Range Compression of a Point Target;after Matched filtering"Pulse Number!Range !This “image” shows the simulated pulse echoes after rangecompression matched filtering!

Point Target after Azimuth CompressionMatched filtering"Pulse Number!Range !This “image” shows the simulated pulse echoes after rangecompression matched filtering!

SEASAT – SAR in Space in 1978"SEASAT SAR image of Death Valley(USA) 1978!

Conventional SAR modes"Radar antennaStrip-mode SAR!Standard SAR mode! Send a pulse of energy; receive echo; repeat! One pulse transmit and receive at a time! Swath width limited by radar ambiguities! Wider swath low resolution SAR mode!uthzimScanSAR!A rathStripSARradar pulse sweepingacross swathction datpradar pulse in airdire RahfligRadarRangedireswathcontinuous stream of pulsesctionExecute sequence as follows:! Send a pulse of energy; receive echo; repeat 50-100 times! Repoint the beam across-track to position 2 electrically(almost instantaneous)! Send a pulse of energy; receive echo; repeat 50-100 times! Repoint the beam across-track to position 3 electrically(almost instantaneous)! Send a pulse of energy; receive echo; repeat 50-100 times! Again, one pulse transmit and receive at a time! ScanSAR trades resolution (in along-track dimension)for swath: low impact on data rate! Generally poorer ambiguity and radiometricperformance than Strip SAR!ScanSAR

Conventional SAR modes" Spotlight SAR! Steers beam to focus on smaller area! Higher resolution than Stripmap! Doppler variation along track!SPOTSAR!Copyright: radartutorial.eu TOPSSARCopyright: DLRTOPS SAR! Wider swath low resolution SAR mode! Steer the beam to cover a larger swath! Trades resolution (in along-track dimension) forswath.! Sentinel-I later this year!

In the afternoon session:I. Properties of radar imagesII. Geometric Aspects of Interferometry and Interferometric PhaseIII. Interferometric CorrelationIV. Interferometric Processing Workflow

Radar Interferometry- I" Radar Interferometry is a simple extension of the Youngʼs interferometry concept! Radar has a coherent source much like a laser! The two radar (SAR) antennas act as coherent point sources! SAR image is equivalent to a pha