10/14/2017

Introduction to Synthetic Aperture Radar

Dr. Armin Doerry

Detailed contact information at www.doerry.us

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Major Sections • Introduction • Electromagnetic Roots • Signal Processing • Image Formation • Radar Equation (Performance)

This presentation is an informal communication intended for a limited audience comprised of attendees to the Institute for Computational and Experimental Research in Mathematics (ICERM) Semester Program on "Mathematical and Computational Challenges in Radar and Seismic Reconstruction“ (September 6 ‐ December 8, 2017).

This presentation is not intended for further distribution, dissemination, or publication, either whole or in part. 2

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Synthetic Aperture Radar ‐ Introduction

SAR is first and foremost a radar SAR allows resolving target scenes to much finer mode that allows creation of angles/locations than other real‐beam techniques; images or maps. effectively synthesizing an antenna much larger than what the platform might otherwise carry. Each pixel in a SAR image is a measure of radar energy reflected from that location in the target scene.

All the usual advantages of radar apply; penetration of weather, dust, smoke, etc.

Images are formed taking advantage of coherent processing of radar echoes from multiple pulses, or over extended observation intervals.

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Synthetic Aperture Radar ‐ Introduction

Radar frequencies from VHF SAR images can be formed from aircraft, through THz have been used for spacecraft, and ground‐based systems. SAR.

Lower frequencies offer better penetration of weather, foliage, and even the ground.

Higher frequencies offer easier processing to finer resolutions.

Pulse radars as well as CW radars can be used.

We will hereafter assume generally airborne microwave/mm‐wave pulse radars.

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Brief History • Late 19th century – Heinrich Hertz shows radio waves can be reflected by metal objects • November 1903 – Christian Hülsmeyer invents “Telemobiloscope” to detect passing ships • Reichspatent Nr. 165546, initially filed 21 November 1903. • June 1951 – SAR idea Invented by Carl A. Wiley, Goodyear Aircraft Co. • April 1960 – Revelation of first operational airborne SAR system • Airborne Subsystem – Texas Instruments AN/UPD‐1 • Ground processor – Willow Run Research Center • February 1961 – First publication describing SAR • L. J. Cutrona, W. E. Vivian, E. N. Leith, and G. O Hall, "A High‐Resolution Radar Combat‐Intelligence System," IRE Transactions on Military Electronics, pp 127–131, April 1961. • June 1978 – First orbital SAR system • SEASAT

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Select References • Synthetic Aperture Radar – Optics & Photonics News (OPN), November, 2004

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Electromagnetic Roots for Radar

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Outline (more‐or‐less) • Maxwell’s Equations • Wave Propagation Equation • Plane‐Wave Propagation • Plane‐Wave Reflection • Radar Range/Delay • Dielectrics • Point Sources and Reflections • Complicated Scattering • Born Approximation • Antenna Basics

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Maxwell’s Equations

Maxwell’s equations relate electric fields and magnetic fields. Let there be light. They underpin all electrical, optical, and radio technologies.

D  (1) Gauss’ Law E = Electric Field B 0 (2) Gauss’ Law for magnetism H = Magnetic Field  = charge density B E  (3) Faraday’s Law J = current density t  = permittivity D HJ   (4) Ampere‐Maxwell Law  = permeability t

D   E  Electric Displacement field BH   Magnetic Induction field

Everything starts here.

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Vector Calculus Identities/Formulae

AB C BC  A C A  B ABCBACCAB  AB B A A B AB   A B B A  B A  A   B  2  A 0 0 AAA   2 AB  A  B B   A A  B  B  A 

AAdS  dl Stokes theorem Sl AAdV dS Divergence theorem VS

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Free‐Space Propagation

In free‐space there are no currents or charges, We further identify and no losses. 1 c Propagation velocity Maxwell’s equations can be manipulated to  2E E   Characteristic 2   t  wave impedance

and in turn, using some identities, to In free‐space 2E 8.854 1012 F m 2E  0 t2 7 0 410Hm Similarly, for the magnetic field cc0 299,792,458 m s 0 377 ohms 2H 2H  t2 Note that these are second‐order In Cartesian coordinates, each component of the differential equations, with vectors E and H satisfy a scalar wave equation. solutions that are sinusoids. 11

Free‐Space Propagation

Taking the Inverse Fourier Transform of both Poynting’s theorem shows that the sides yields the Helmholtz equations direction and magnitude of energy flow is 22 EE0k  P EH 22 HH0k  As seen in the next few slides, Maxwell’s equations reveal that E and where we also define H are perpendicular to each other, f  Temporal frequency in Hz (cycles/sec.) and both are also perpendicular to the direction of travel. 2 f Angular frequency in radians/sec.  k Wavenumber in radians/meter The orientation of E defines the c “polarization” of the plane‐wave. We further define These ‘waves’ travel, with a free‐ c 2 space velocity of propagation   Wavelength in meters f k Solutions have phase that is a function of both time and space. 12

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Sinusoidal Plane‐Wave Propagation

A propagating wave with a planar E and H fields are related as wave‐front is a plane‐wave. kˆ  E =H The electric field of a linearly polarized plane wave is given by The Poynting vector is in the EEtt,cosrkr    0 direction of kˆ

where

ˆ E00E E Polarization vector kkk ˆ Direction of propagation rrr ˆ Field observation point

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Sinusoidal Plane‐Wave Propagation

If traveling in the direction of the z‐axis, with an electric field oriented parallel to Wave front (right travelling) the x‐axis, our field reduces to simply x E

E  Exxˆ P z with y H krzˆ ˆ ˆ ˆ E0  xˆ

and the field equation reduces to E and H fields are related as

221 zˆ EH EEx  x zct222 1 0 zˆ HE  with a solution  Etzex ,cos1  tkz  Forward/right travelling and another solution  Backward/left travelling 14 Etzex ,cos2  tkx 

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Propagation in a Dielectric

In a lossless dielectric, it remains true, but In a dielectric with different numerical values, that    r 0 1    c Propagation velocity r 0  where   Characteristic  wave impedance r  relative permittivity r  relative permeability with E and H fields still related as 1 zˆ E H and zˆ HE These relative quantities are typically  greater than one. with comparable electric field solutions

Complex values denote propagation is lossy.  Etzex ,cos1  tkz  Frequency‐dependence implies a Etze ,cos tkx “dispersive” media, where the echo may x 2   ‘not’ be a faithful reproduction of the incident signal. Note additionally that k and  are a