Homework 3: K-space spectra of geometries with 1 to 3 elements


 

    In this exercise, we will use a Graphical User Interface (GUI) to run a series of Field II simulations.  This will allow us to look at a series of related k-space examples in a short period of time.

    Getting started:

     To begin, start Matlab and open the GUI with the command Field_II_GUI.  This will open two figures on your desktop. One window has a series of data entry boxes, and the other is used for displaying results. Depending on your terminal, you may wish to resize one or both windows.You may also want to zoom in on the figures to look more closely at the results.  This can be done by clicking on the figure with the mouse. (A double-click zooms all the way back out.)

    In the data entry window, examine the data entry boxes and make sure they make sense to you.  In this exercise you will explore a number of simple array geometries by manipulating these parameters. In addition, the GUI has a calculation menu for choosing the type of response to calculate, and a display menu for choosing  how to plot the simulation results.

    A single-element system:

    Define a single element system with a 0.1 x 0.1 mm element.  This element will have a 7.5 MHz center frequency and 50% relative bandwidth.
  1. Calculate the transmit-receive  (TX/RX) on-axis at 3 cm range and look at the axial slice through k-space.
  2. Repeat this procedure for a 15 MHz center frequency.
  3. Return to a 7.5 MHz center frequency and set the pulse length to approximately 8 cycles.  (The GUI allows you to control relative bandwidth, which also called "fractional" bandwidth. A 100% relative bandwidth pulse is roughly one cycle long, a 50% relative bandwidth pulse is roughly 2 cycles long, etc.) Set the focus at 3 cm range and 30o off-axis.  What are the axial and lateral spatial frequencies associated with this pulse?

    4. A two-element system:

    Define a two-element system with 7.5 MHz center frequency and 5% relative bandwidth. These elements are 0.1 x 0.1 mm, and are spaced 3 mm apart. (In the GUI, this spacing is set by the kerf parameter.) Set the focus on-axis at 3 cm range.
  4. What is the axial wavelength of the transmit-only response?
  5. What is the lateral wavelength of the transmit-only response?
  6. Repeat the two previous steps for a 15 MHz center frequency.
  7. Repeat the three previous steps for the transmit-receive response.
  8. On a single set of axes, look at the k-space response of the Tx/Rx system operating at 7.5 MHz and 15 MHz.
  9. Redo for a 6 cm focus.

    10. A three-element system:

    Define a three-element system with 7.5 MHz center frequency and 5% relative bandwidth. Again, these elements are 0.1 x 0.1 mm, and are spaced 3 mm apart. (In the GUI, this spacing is set by the kerf parameter.) Set the focus on-axis at 3 cm range.
  10. Calculate the transmit-receive  (TX/RX) on-axis at 3 cm range and look at the lateral slice through k-space.  How are the amplitudes of the peaks in this slice related?
Duke University
Department of Biomedical Engineering