Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Data and Processing

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice University ELEC 301 Projects display tagshide tags

    This module is included inLens: Rice University ELEC 301 Project Lens
    By: Rice University ELEC 301As a part of collection: "ELEC 301 Projects Fall 2007"

    Click the "Rice University ELEC 301 Projects" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney BurrusAs a part of collection: "ELEC 301 Projects Fall 2007"

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Data and Processing

Module by: Aaron Hallquist. E-mail the author

Summary: 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.

Figure 1
Figure 1 (graphics1.png)

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 Pθ signals for different values of θ, 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 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 Pθ are arranged radially in a polar grid along the various angles θ. We then get that our data lies on a domain

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

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

Figure 2
Figure 2 (graphics2.png)

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 two θ values and then linearly interpolating in the θ-direction. The end result of our program’s running of this is shown below.

Figure 3
Figure 3 (graphics3.png)

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.

Figure 4
Figure 4 (graphics4.png)

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks