From instruments to raw data to images.


Howard Zebker and Paul Rosen

General Information


Salvatori Seminar Room

South Mudd Building, Third Floor

Caltech Campus

Northeast corner of California and Wilson


Oct. 23-Nov. 3, 2023


8:30-11:30 Lectures

1:00- Homework/Computer Lab

Intended audience:

This class is aimed at advanced students and radar professionals interested in the physical principles and signal processing and analysis needed to understand and work with radar remote sensing data.

Course goal:

The material presented here enables attendees to derive most properties of radar echoes from first physical principles, and to be able to design and implement processing code that generates high-resolution images from the raw measurements. In addition, you will be able to use multiple channel systems to produce higher order data products such as interferometric and polarimetric analyses. Finally, you will be able to apply these products to a diverse set of geophysical applications.

Course description:

Radar has evolved from a largely military detection system into a sophisticated three dimensional imaging tool with hundreds of applications ranging from commercial aviation to fundamental research in the earth and planetary sciences. The ability to measure and map surface topography and crustal change at unprecedented levels over large areas is fundamentally altering the way in which we can measure and model the processes, natural and man-made, that effect our environment. The interaction of EM waves with different surface types provides a basis for analyzing echoes to discern, for example, the structure of vegetation canopies or surface roughness. In this course we will investigate how radar images are formed and manipulated, as well as applications of the systems. We will be presenting radar as a signal processing problem, rather than the traditional approach as an instrumentation problem, acknowledging the importance of digital computer algorithms in modern radar systems. The first half of the course will be largely devoted to radar image formation, and topics will include system design, range and azimuth processing algorithms, and processor design. In the second half of the course we examine scattering from natural surfaces, polarimetric radars-- which are particularly suited to the study of vegetation cover--, plus the increasingly important field of radar interferometry. Interferometric radar techniques, which have formed a large part of radar-related research over the past 30 years, provide a means to characterize very small changes or motions on the Earth over large areas.

The course will be presented in a lecture/seminar style. Mornings will consistent largely of interactive lectures, while the afternoons will entail a computer exercise to give experience with implementation of the material presented in class. The afternoons will be augmented with guest lectures from senior radar scientists and engineers in order to present diverse ways to look at the problems.

Our approach will be to have students create their own codes to solve each day’s problem, building on the previous days’ exercises to create a full data flow. Lecture notes will be available online, and special handouts will also be distributed from time to time. Cooperation on the exercises is encouraged, with TA support to help with debugging problems quickly. We can grade you if you like but we want everyone to earn an A+ grade(!)

Day Topic Lectures Handouts Homework
1 Basic Concepts and Notation What is an imaging radar?

System design principles

Radar equation

Handout 0

Handout 1

Handout 2

Handout 3

Handout 5

Handout 6

Homework 1


Homework 1 P1 Solution

Homework 1 P2 + P3 Solution

2 Range Modulation Processing Radar as a signal processing problem

Range processing and matched filters

Pulse compression

System impulse response

FFT implementations

Handout 7

Handout 10

Handout 11

Handout 12

Homework 2

"ersdata" data file


Homework 2 Python Range Modulation Solution

Homework 2 Range Modulation Solution

Homework 2 Matlab Solution

3 Doppler viewpoint Image formation

Real aperture and unfocused processors

Range-Doppler system design

Handout 14

Handout 14a

Homework 3

"ersdata.hw3" data file


Azimuth Processing

Homework 3 Python Solutions

Homework 3 Python Notebook

Homework 3 MATLAB Solutions

4 SAR Processing Synthetic aperture technique

System impulse response

Azimuth correlator design

Handout 15

Handout 17

Handout 19

Handout 20

Homework 4

"ersdata.hw3" data file (same as hw 3)


Homework 4 Problem 1 Solution

Homework 4 Python Code focusProc

Homework 4 Python Solution focusproc

Homework 4 Matlab

5 Range Migration Processing Focusing and autofocus algorithms

Doppler tracking and filtering

Multilook processing

Handout 22

Handout 25

Handout 27

Homework 5

"simlband.dat" data file



Homework 5 Matlab

Homework 5 Python Solution rangeMigration

Homework 5 Python Code rangeMigration

6 Back Projection Methods Coherent summation viewpoint

Motion compensation


Handout 45

Handout 46

Handout 49

Homework 6

"alossim_1d.dat" data file


Homework 6 Advanced

"alosraw.dat" data file

"alos.position" data file

"alos.dem" data file

"alos.dem.rsc" data file

"" data file


Homework 6 Matlab Solution Backprojection 1D

Homework 6 Python Solution ALOS SAR Processor with 1d homework solution

7 Radar/Surface Interactions Scattering mechanisms and models

Kirchhoff facet models

Bragg scattering

Volume scattering

Handout 28

Handout 31

Handout 50

CEOS calval sigma0gamma0beta0

Homework 7

"hw7prog1a.txt" table

"hw7prob1b.txt" table

"hw7prob1c.txt" table


Homework 7 Scattering Solutions

8 Polarimetry Polarized radar waves

Polarizations signatures and diffuse scattering

Scattering from vegetation

Radiometric calibration

Geometric distortion

Handout 51

Homework 8

Homework 8 Hints


Homework 8 Solutions

9 Interferometry Interferometric radar

Image registration

Baseline determination

Surface topography

Surface velocities / ocean currents

Crustal deformation

Handout 32

Handout 33

Handout 34

Handout 37

Handout 38

Handout 39

Handout 40

Handout 42

Handout 43

Handout 44

Handout 52

Homework 9

"slc1.dat" data file

"slc2.dat" data file

"slc.dem" data file

"slc.baseline" data file


Homework 9 Solutions

Homework 9 ipynb

10 Application Examples Ecosystems


Solid Earth

NISAR applications community

Handout 47

Handout 48


Several books which may serve as useful references are listed below.

Bracewell, R. N., The Fourier Transform and Its Applications, McGraw-Hill, New York, 2nd edition, 1986.

Carrara, W.G., R.S. Goodman, and R.M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House, Norwood, MA, 1995.

Cook, C.E., and M. Bernfeld, Radar Signals, Academic Press, New York, 1967.

Curlander, J.C. and R.N. McDonough, Synthetic Aperture Radar, Wiley Interscience, New York, 1991.

Elachi, C., Introduction to the physics and techniques of remote sensing, Wiley, New York, 1987.

Elachi, C., Spaceborne Radar Remote Sensing: Applications and Techniques, IEEE press, New York, 1988.

Goodman, J.W., Introduction to Fourier Optics, McGraw-Hill, New York, 1968.

Kraus, J.D. Radio Astronomy, McGraw-Hill, New York, 1966. (Later editions good also)

Peebles, P.Z, Radar Principles, Wiley Interscience, New York, 1998.

Press, W.H., B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C, the Art of Scientific Computing, Cambridge University Press, New York, 1988. (Any of the Numerical Recipes series will have useful algorithm information)

Sabins, F., Remote Sensing, 3rd ed., Freeman, New York, 1996. Soumekh, M., Fourier Array Imaging, Prentice Hall, Englewood Cliffs, New Jersey, 1994.

Skolnik, M.I., Radar Handbook, McGraw-Hill, New York, 1970.