PROBLEM 1: Ultrasound Field II Simulation Software:

Task I [ZERO points]
Install the Field II program (http://field-ii.dk/?./downloading_8_10.html) on a
computer that you can use for extended periods of time (for example, all night
long) without interruption. This computer should have at least a Pentium III CPU
or better, it should have a fair amount of available disk space, and it should have a
working copy of Matlab with the signal processing package installed. Use
whatever operating system you like. Note that, in order to display the Field II logo
when you initialize with ‘field_init’, you might need to comment out the line with
the ‘eval’ command and replace it with ‘load logo_field’ (no quotes) in the file
‘edit field_logo.m’.

Task II [40 points]:
1. Run the calculation of synthetic color flow mapping image example (http://fieldii.
dk/?examples/cfm_example/cfm_example.html) from the Field II web site,
which involves executing the following m-files: mk_pht.m, then sim_img.m, and
cfm_bmode.m. This program should run for at least a few hours.
2. Download the m-files from the Field II website (http://fieldii.
dk/?examples/psf_example/psf_example.html ) for image evaluations of the
point spread function. Run the sample file pnt_img.m and plot the resulting
images
a. Describe the focusing method used to generate image A.
b. Describe the focusing method used to generate image B.
c. Describe the focusing method used to generate image C.
d. Describe the focusing method used to generate image D.
e. Describe the focusing method used to generate image E.
f. Describe the focusing method used to generate image F.
g. How does the resolution compare at each depth for the different
focusing methods used?
3. Download the m-files from the Field II website (http://fieldii.
dk/?examples/logo_example/logo_example.html) that compute the point spread
function for a spherically focused transducer. Run the sample file concave_logo.m
and plot the resulting images. Roughly speaking, what is the shape of the PSF?
How does this relate to the transducer geometry?
4. Start with the m-files from the Field II website (http://fieldii.
dk/?examples/logo_example/logo_example.html) that compute the point spread
function for a spherically focused transducer, and modify this routine so that
instead the point spread function for a circular (unfocused) transducer with the
same radius is plotted. How does this PSF compare to that computed in the
previous problem?
PROBLEM 2: Ultrasound Physics [20 points]:
2.a Calculate the intensity transmission coefficient I T for the following interfaces,
assuming that the ultrasound beam is exactly perpendicular to the interface:
muscle/kidney, air/muscle, and bone/muscle. Discuss briefly the implications of these
values of I T for ultrasonic imaging. Repeat the calculations above with the angle of
incidence of the ultrasound beam now being o 60 .
2.b Suppose it is known that a 5MHz transducer axis makes an angle of 30 degrees
relative to the direction of motion of blood in a vessel. If the Doppler frequency is
measured to be +500Hz, what is the velocity of the blood? Is it moving toward or
away from the transducer?
PROBLEM 3: X-ray CT [20 points]
The line spread function of an imaging system is described by a rectangular box function
of width W millimeter (mm), i.e.,

3.a What is the resolution of this imaging system in terms of FWHM (full width at half
maximum) and in terms of lines/mm.
3.b Suppose the field to be imaged contains 3 parallel bars of width W mm, spread nonuniformly,
with the darkness profile as indicated in the figure below. Determine the
darkness profile of the bars after imaging. Can you still tell all the bars apart? How bars
will you see? What will be their respective width?
Hint: the convolution of two rectangular functions of the same width becomes a triangle
function.

PROBLEM 4: Compute the time-harmonic pressure field generated by a circular
piston [20 points]

Use the expression below that defines the pressure as:
Turn in a printed copy of your working m-file, and also submit a mesh plot of the
absolute value of the computed pressure field to demonstrate the result obtained with
your m-file. The axes of your mesh plot should contain some meaningful information (i.e.,
not the default that merely represents the number of points in each direction) that
indicates either the distance from the origin or the normalized distance from the origin
(for example, relative to the piston radius a and the square of the piston radius for r and z,
respectively). Although any reasonable axes will be accepted, please note that the axes in
the posted solution will be normalized with respect to the piston radius in the lateral
direction (i.e., the r-axis will range from 0 to 2) and in the axial direction, the axes will be
normalized with respect to the far field distance d
2
/4?, where d=2a (i.e., the z-axis will
range from 0 to 1). Also note that the ‘mesh(cols, rows, abs(p))’ command in Matlab has
a strange convention in the sense that the vectors describing the axes are expected in
reverse order.
Important Note: For each computer-generated result, please submit your MATLAB
codes