Synthetic Aperture Radar Richard Spangler University of Michigan
March 6, 2009 / Math 501
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Outline
1
Introduction
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Radar Resolution Motivation Range and Direction Range Resolution Synthetic Aperture Formation
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Radar Basics The underlying principle of Radar (RAdio Detection And Ranging) is echolocation. A radar transmits a radio signal and to listens for a reflected signal. Objects in the path of the signal will reflect (scatter) the radar pulse. If the signal is reflected in the direction of the receiver, it will be recorded as a radar return.
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Goal Primary functions of radar: Detect targets Range Direction
’Target’ is a broad term: it means "whatever you’re looking for" Goal of this talk Show how we can improve our knowledge of a target’s direction Be able to separate it from other targets (resolution) We will show how Synthetic Aperture Radar (SAR) aids this process. Richard Spangler
Synthetic Aperture Radar
athematics
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Outline
1
Introduction
2
Radar Resolution Motivation Range and Direction Range Resolution Synthetic Aperture Formation
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Fine Resolution SAR application: Monitoring of global sea ice conditions Use of radar allows us to see underlying structure Fine resolution provides greater insight into stability of ice shelf
athematics
Figure: Wilkin’s Ice shelf, Antartica Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Outline
1
Introduction
2
Radar Resolution Motivation Range and Direction Range Resolution Synthetic Aperture Formation
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Range Radar as a timekeeping device Distance formula relates distance to round trip time cT (1) R= 2 But knowing that we have a target doesn’t tell us what direction it lies in! It can be anywhere within a sphere surrounding the radar. Can we do better?
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Direction We can limit the possible direction that contains a target by the beam directivity that we use. Beam directivity concentrates the signal strength in a particular direction, and is related to the dimensions of the antenna. The beam pattern for a linear antenna is approximately P = (sinc(π(L/λ)sinθ))2 An antenna beam is expressed in terms of its half-power beamwidth: λ θ3db ∼ = 0.88 L
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(3) athematics
Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Antenna Beam Pattern
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Antenna Pattern Projection
For a square antenna of dimension LxL, our detected target is now in a region defined by the antenna orientation and its 3db beamwidth. In order to separate targets within the beam pattern, we first introduce range resolution.
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Outline
1
Introduction
2
Radar Resolution Motivation Range and Direction Range Resolution Synthetic Aperture Formation
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Range Resolution
Width of a transmitted pulse determines its range resolution cτp (4) 2 For a single frequency waveform, a short pulse means a fine range resolution. ρr =
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Linear FM waveform Short pulses to reduce range resolution are not practical due to power requirements Fine range resolution can be achieved via linear FM waveform Frequency "chirps" from low to high over pulse duration From signal theory, we can compress a pulse of bandwidth B to a time duration of appoximately B1
Alternate form of range resolution ρr =
c 2B
Example: if we want 5m range resolution, we need a linear waveform with approximately 30MHz of bandwidth. Richard Spangler
Synthetic Aperture Radar
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athematics
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Outline
1
Introduction
2
Radar Resolution Motivation Range and Direction Range Resolution Synthetic Aperture Formation
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Azimuth Resolution If we would like to improve resolution in the azimuth direction, we could simply make the antenna larger. Using our formula for beamwidth, we could calculate the antenna needed to produce a 5m azimuth resolution: ρa = θ3db R =
0.88λ R = 5m L L = 0.176λR
For an L-band radar with λ = 20cm, and a standoff range of 25km, we would require an antenna 880m long! For airborne mapping applications, this (literally) won’t fly. If we had a longer standoff range, this problem gets even worse. We need a better solution. Richard Spangler
Synthetic Aperture Radar
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athematics
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Synthesizing an Antenna Fortunately, one exists. If a radar is able to collect and store pulses, it can do so as it changes its position. As it collects pulses along its path, it will have sampled from points along a very long virtual antenna. These pulses can be coherently combined to synthesize a very long linear array.
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Synthetic Aperture Notes Synthetic aperture radar works by sampling at specific positions Motion of the antenna is not core to the concept, other than getting us to our next sample point Time between pulses can usually be ignored (sort of)
Synthetic aperture requires the scene to be illuminated for all pulses We need a smaller antenna to create a large enough beam
Processing Can be done by matched filtering or backprojection, but faster methods exist Motion is part of the solution, but it is also part of the problem Richard Spangler
Synthetic Aperture Radar
athematics
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
End Result
athematics Richard Spangler
Synthetic Aperture Radar
Introduction Radar Resolution
Motivation Range and Direction Range Resolution Synthetic Aperture Formation
Digging further Polarimetry: Use of radar polarization to analyze target responses Interferometry: Coherent combination of two SAR images to form terrain maps Bistatics: Transmitter and receiver located in different location
