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This module discusses the data received for this project as well as its processing into an image.

Introduction and preparation of sar data

In order to simulate the processing of SAR data, we received SAR data from the ECE department at Ohio State University. The data they gave us was acquired through a computer simulated fly-by past a CAD model of a backhoe.

The data we received from OSU was in digital format, meaning the analog mixing and low pass filtering was already completed and we received digitized versions of Cθ(t). This function was shown to be equivalent to Pθ(U), the Fourier transform of our projection slices pθ(u). The matlab file that contained this information was a 512x1541 matrix iq_lin, a vector of various Pθsignals for different values ofθ, the viewing angle. There were 1541 different viewing angles, listed in az_lin, that stepped by 1/14˚for each element and varied from -10˚to 100˚, a median viewing angle of 45˚. We also received a vector of length 512 called f that contained the microwave frequencies (7-13 GHz) that were transmitted and received. By using the wideband approximation, we made the transformation from time frequency to spatial frequency via

R / c = ( / c ) f size 12{R approx 2ω/c= \( 4π/c \) f} {}

where R is the radial spatial frequency and f is the microwave frequency content. By the projection slice theorem, we have that the various Pθare arranged radially in a polar grid along the various anglesθ. We then get that our data lies on a domain

10 ° θ 100 ° size 12{ - "10"°<=θ<= "100"°} {}

R ΔR = [ ( / c ) f min , ( / c ) f max ] size 12{R inΔR= \[ \( 4π/c \) f rSub { size 8{"min"} } , \( 4π/c \) f rSub { size 8{"max"} } \] } {}

Processing of sar data

Knowing that our data is the Fourier transform of our image, after the proper preparation we want to take the inverse Fourier transform. To do this simply and efficiently (we don’t want Matlab running for hours!) we linearly interpolate the data to a Cartesian grid. This is done in our Matlab function sar_lin (code found in appendix). The idea is to find an inscribed rectangular grid inside our polar data. We chose to use the square centered at 45˚inscribed in our ribbon. To interpolate we made a Cartesian grid at this location and computed the polar representation of each point in order to find its 4 nearest polar neighbors. Once those neighbors were found, the Cartesian point’s value was determined by linearly interpolating in the R-direction for the twoθvalues and then linearly interpolating in theθ-direction. The end result of our program’s running of this is shown below.

After linearly interpolating each point in the Cartesian grid we have formed, we now have our data in a form that allows us to take the 2-d inverse DFT by the fast Fourier transform method. This is what saved us computation time (program ran in about 15 seconds) and is the reason we interpolated to Cartesian coordinates to begin with. Below is the image after taking the inverse Fourier transform.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is inorganic
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Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Tomographic processing of spotlight-mode sar. OpenStax CNX. Dec 19, 2007 Download for free at http://cnx.org/content/col10498/1.1
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