Introduction to Synthetic Aperture Radar Dr. Armin Doerry Detailed - PDF document

10/14/2017 Introduction to Synthetic Aperture Radar Dr. Armin Doerry Detailed contact information at www.doerry.us 1 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 1

10/14/2017 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. 3 Synthetic Aperture Radar ‐ Introduction SAR images can be formed from aircraft, Radar frequencies from VHF spacecraft, and ground‐based systems. through THz have been used for 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. 4 2

10/14/2017 Brief History Late 19 th 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 5 Select References • Synthetic Aperture Radar – Optics & Photonics News (OPN), November, 2004 6 3

10/14/2017 Electromagnetic Roots for Radar 7 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 8 4

10/14/2017 Maxwell’s Equations Maxwell’s equations relate electric fields and magnetic fields. Let there be light. They underpin all electrical, optical, and radio technologies.     E = Electric Field D (1) Gauss’ Law H = Magnetic Field   (2) Gauss’ Law for magnetism  0 B  = charge density  B     (3) Faraday’s Law J = current density E t  = permittivity  D  = permeability    H J (4) Ampere‐Maxwell Law  t    Electric Displacement field D E  Magnetic Induction field   B H Everything starts here. Everything starts here. 9 Vector Calculus Identities/Formulae         A B C B C A C A B             A B C B A C C A B            A B B A A B                     A B A B B A B A A B 2           0 A   0   2       A A A                         A B A B B A A B B A       dS  dl Stokes theorem A A S l        dS Divergence theorem A dV A V S 10 5

10/14/2017 Free‐Space Propagation In free‐space there are no currents or charges, We further identify and no losses. 1   Propagation velocity c Maxwell’s equations can be manipulated to  2   E     Characteristic E    2   t wave impedance and in turn, using some identities, to In free‐space  2 12        8.854 10 F m E 2 0   E 2   7       t 4 10 H m 0   299,792,458 m s c c Similarly, for the magnetic field 0     377 ohms 0 2   H 2   H 2  t 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 Poynting’s theorem shows that the Taking the Inverse Fourier Transform of both direction and magnitude of energy sides yields the Helmholtz equations flow is 2 2    E E 0 k   P E H 2 2    H H 0 k As seen in the next few slides, Maxwell’s equations reveal that E and where we also define H are perpendicular to each other, and both are also perpendicular to the  Temporal frequency in Hz (cycles/sec.) f direction of travel.     2 Angular frequency in radians/sec. f  The orientation of E defines the   Wavenumber in radians/meter k “polarization” of the plane‐wave. c We further define These ‘waves’ travel, with a free‐ space velocity of propagation  2 c     Wavelength in meters f k Solutions have phase that is a function of both time and space. 12 6

10/14/2017 Sinusoidal Plane‐Wave Propagation A propagating wave with a planar E and H fields are related as wave‐front is a plane‐wave. ˆ   k E = H The electric field of a linearly polarized plane wave is given by The Poynting vector is in the        , r cos k r  E E t t direction of ˆ 0 k where ˆ   Polarization vector E E E 0 0 ˆ   k k Direction of propagation k   r ˆ r r Field observation point 13 Sinusoidal Plane‐Wave Propagation If traveling in the direction of the z ‐axis, Wave front (right travelling) with an electric field oriented parallel to the x ‐axis, our field reduces to simply x E  x ˆ E E P x z with y H ˆ  ˆ  ˆ k r z ˆ  x ˆ E 0 E and H fields are related as and the field equation reduces to 2 2   ˆ    1 z E H  E E 2 x 2 2 x   1 z c t 0    z ˆ H E  with a solution         , cos E t z e t kz 1 x Forward/right travelling and another solution Backward/left travelling         , cos E t z e t kx 2 x 14 7