Bistatic/Monostatic Snthetic Aperture Radar for Ice Sheet Measurements John Paden MS Thesis Defense April 18, 003 Committee Chairperson: Dr. Chris Allen Committee Members: Dr. Prasad Gogineni Dr. Glenn Prescott
Topics Overview EM Model Sensor Geometr Antenna Arra Position Errors Sandbox Tests
Overview Motivation Global sea level rise threatens coastal regions Contributions from an ice sheet are measured b finding the mass balance of the ice sheet. Create ice flow model to predict mass balance Basal conditions needed for ice flow model We can drill boreholes in a few places, but not all over the Arctic and Antarctic regions RADAR.
Overview Basal Scattering The bedrock is thought to be smooth with respect to wavelength. Therefore it looks like a mirror at our frequencies of operation. Tx T T R M R X Origin α D β β α z Ice Bedrock S 1 0 S x Swath
Data Collection Geometries Monostatic Arrangement Used when the surface is rough and side-looking radar techniques can be emploed Air Transmitters/Receivers z σ x x Ice Bedrock σ x Measurement Swath
Data Collection Geometries Bistatic Arrangement Used when the surface is smooth and exhibits specular (mirrorlike) characteristics New variable: separation distance between transmitter and receiver Air Transmitters Receivers z σ x x Ice Bedrock σ x Measurement Swath
Overview Sstem Model Modes of operation: monostatic and bistatic Broadband operation: nearl three octaves Geophsical Model EM Model Data SAR Processing Phsical Characteristics Air Ice Tx Sensor Geometr Rx Rough Surface Sloped Surface Liquid Water Smooth Surface Measurement Swath
EM Model Magnitude of Transfer Function TEM Horn Antenna Measurements Radar Sstem Transfer Function Spherical Spreading σ bs AR PR = PT HTηTeff DT ηre ff H R 4πR 4πR Phase of Transfer Function TEM Horn Antenna Measurements Radar Sstem Transfer Function Path length, phase velocit, and refraction T R
EM Model TEM Horn Antenna I ('3'& 'MND7 OP Q('R I "' 83 % = ' J<'D&6KL& %(' % A > A 7 7 " 3% 546 % 78 $9: ;& $< '& $= >@? 1,./0, - * + 1,./0, - * + ) :B :B 6B @B <:& CD3 ' E FG# =H>?!" $# % "'& ( )
EM Model TEM Horn Antenna 1. - + B @B @B @B 4 8 5O ' F <D&:K & % (' % 1. - + 'B 'B 4: QO F 4: % 78 $967 '& $< '& $= >6? A > A, + @B, +, @B, B @B :B @B :B @B <D& C'3 'E F # = >? ) 7 78!" $# % "'& ( )
Radar Sstem Transfer Function NA Calibration and Amp/Cable Assembl $ #!" SR PQ M)NO L JI FK G H FD E AD CA @ AB, +', 40, 4 ', 30, 3 ', 0, ',.-100,.-10 ',.-/-0,.-/- ' % ' ( ' * ' ' ' + 5 6 % & ()& * & ')& 7/8:9 ;=< >?
Radar Sstem Transfer Function Calibration and Amp/Cable!#"$&% '( )!+* *, -./ 01$ ( 3 Network Analzer Reference-Plane P1 P 1" Coax 37' Coax Amplifier 0" Coax Adapters Horn Antenna 37' Coax 0" Coax
Dielectric Half-space Model Three-dimensional geometr of refracted ra can be projected onto the plane of incidence (two-dimensional) Target, S θ 1 θ Antenna, A z n 1 n A S ( ) ( ) ( ) ( ) ( ) 0 ' ' ' ' ' 0 ' 1 1 ' 1 ' 1 3 ' 1 4 ' 1 = + + + + z z z z S S n S S n S T n S n S n n S n n ( ) ( ) ( ) ( ) ( ) x x x x x x a A S a A S a A S a A S a ˆ ˆ ˆ ˆ ˆ ' + + = ( ) ( ) ' x x S A S A + =
Sensor Geometr Find the optimal transmitter position that minimizes the cross-track aperture size, R. R' Tx T R' 1 R 1 R R M R z D φ 1 β β Ice Bedrock θ 1 θ 1 S 1 0 θ S θ φ x
Backscatter Characteristics Bistatic forward scattering characteristics are approximated with our knowledge of backscatter characteristics. Ice TX/RX Range of maximum backscatter angles Backscatter Angle Backscatter Mag. (db) ε ICE = 3. ε BEDROCK = 8.0 Ice TX Bedrock RX Forward scatter Angle Backscatter Angle (deg) Bedrock
Advantage of Separation TX A TX Swath B Swath As the transmitter moves awa from the swath, the ice surface illuminated b the forward scatter cones grows. In turn, the minimum required receiver movement decreases (i.e. B < A).
Disadvantages of Separation As the transmitter-receiver separation is increased, the angular resolution decreases. The bedrock surface subtended also increases for the same angular resolution. Ice Off-nadir Worse Resolution Bedrock Nadir Best Resolution ρ x ρ x
[ Plot of Receiver Arra Size \^] Minimum Receive Arra 13!54 β 6 Swath 487 = 150 MHz 9:".;<% = %" >?% @BA % $C % 9DFEG"!.C!H@IFJ+K % TVUXWZY!#" $ $&%('*) +" $," ).-!0/ O N M L S R PQ The minimum receive aperture occurs when the transmitter position is 1580 m from the center of the swath. The minimum receive aperture is 47 m. Across-track resolution: 100 m Ice thickness: 3 km Frequenc: 150 MHz Swatch Width: 1 km Backscatter: 7.5 deg
Results for 3000 m thick ice Frequenc (MHz) Max forwardscatter angle (deg) Tx Position (m) Min. Receiver Aperture (m) Min. Monostatic Aperture (m) 60 5 831 133 799 60 10 435 538 535 60 15 1710 11 73 60 0 0 66 3 150 5 831 115 76 150 10 435 371 498 150 15 1610 47 34 150 0 0 6 13 350 5 831 1049 748 350 10 435 307 484 350 15 1580 0 19 350 0 0 11 6
Monostatic Mode For comparison. Using a cross-track spatiall sampled monostatic arra. R 1 Tx/Rx R Mono R M R z ρ ρ x S 1 0 S Swath
51 6 4 5 01 Monostatic vs. Bistatic : 9 0 7. 48 34. 0 -./ ; <>=@?BA +CDEA ; <>=FG% +!CEA <H=F?BA + #CEA <H=*GI%J +DEA <H=F?BA + #CEA <H=*GI%J +DEA!#" $&%'( "*) " ' " " +, Minimum SAR aperture required using a bistatic configuration (also compared to monostatic).
Along-track Arra SAR Antenna Arra TX Vehicle Cross-track Rx Tx x Along-track z Along-track antenna arra Sharpens along-track beam Less frequent along-track sampling Sum antenna arra elements together SAR focusing hindered b loss of control over individual elements Rx Tx
% * *% )& & Results This plot shows the maximum SAR resolution attainable versus aperture size. One tenth of a wavelength variation across the aperture was tolerated. %. -/ +, '#( $ % 10354 6 1074 8 6 1074!#"
Position Errors The Radar will derive its position using the global positioning sstem (GPS). GPS s have errors that are a significant fraction of a wavelength Need to answer the question: How do positioning errors effect the performance of the SAR processor?
Position Errors Gaussian random process Correlated errors created b low pass filtering Topcon GPS sstem: 0.1 m standard deviation in latitude 0.1 m standard deviation in longitude 0. m standard deviation in elevation "! #%$'& "( )+*-, "! #%$'& "(
( %&' "#$ Results for σ = 0.05 m *) +, -. /10-340 /15 σ 6 87 *) 9- -+. :;/10 - <) -+. :;/10 - <) -+. :;/10 -!
( %&' "#$ Results for σ = 0.1 m ) +, -. /10-40 / 5 σ 6 7 ) 9- -+. :;/10 - <) -+. :;/10 - <) -+. :;/10 -!
( %&' "#$ Results for σ = 0.1 m (fixed aperture) 0 <: ; / + 40 /15 σ 6 87 ) 9- -+. :;/10 - <) -+. :;/10 - <) -+. :;/10 -!
Sandbox Laborator Test the EM model Test the SAR processing algorithm Abilit to determine the position of a target Abilit to accuratel determine the target s reflectance
Measurement Setup Tube is Perpendicular to Figure Tx Horn Rx Horn 0m Air Sand "! & $ % # 0.53 m Tube z 0 m 0.30 m ' () ' *+ -, ). )), / ) Left side: measurement setup Right side: simulation setup x
A-Scopes Left side: measured dataset Right side: simulated dataset + + + + # '& % $#! " + + & $ # '& % $#! " + + & $ + + + + + + +
% % SAR Processed Left side: measured dataset after SAR processing Right side: simulated dataset after SAR processing "! # $ & $ "! # $ & $
Ten Targets <>=?A@CBDEGFHI?JI FKH L!MBNH @OMNPQEGFHI?RI FKH ; : 0 1 - +/ -.,+* ( ) 8 73. 5 6 ) 4 +3/ 9 0 1 - +/ -.,+* ( ) 8 73. 6 5 ) 4 + 3 / [ Z XY WV U S T! "$# # %"'& \]! "C# #%"'&
Table of Results Target # Diameter Metal/Air Signal Power Position Error 1 1.5 cm Metal -35 db cm 10 cm Metal -38 db 5 cm 3 1.5 cm Metal -35 db cm 4 10 cm Metal -4 db 1.41 cm 5 10 cm Metal -40 db.4 cm 6 10 cm Metal -4 db 3.16 cm 7 11.5 cm Air-filled -53 db.4 cm 8 15 cm Air-filled -49 db 6.08 cm 9 11.5 cm Air-filled -5 db 1 cm 10 15 cm Air-filled -49 db 1 cm Max sidelobe is 49 db Signal to sidelobe is at least 4 db within the region of the target
Conclusions Transmitter Location (Sensor Geometr) The transmitter position has a ver large effect on the size of the bistatic arra. Depending on the tpe of scattering and thickness of the ice, the bistatic mode ma or ma not be faster than the monostatic mode. The bistatic transmitter position that minimizes the receiver crosstrack movement was found. Along-track Antenna Arra Along-track antenna arra could be helpful in expediting the bistatic measurements. For high-precision measurements (e.g. 10 m) its usefulness is limited unless each element can be controlled individuall.
Conclusions Position Errors Position errors can be ver severe at higher frequencies. Increasing aperture length does not help position errors. GPS errors need to be characterized in terms of magnitude of relative error and error correlation over time and space. Sandbox lab tests showed: First-order EM Model gives results consistent with the measured results Abilit to position targets to within a few centimeters Abilit to distinguish targets with different reflectivities (with similar targets giving consistent reflectivities)