bft_user_guide.html

超声仿真软件

63<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_excitation(xmt,&nbsp;excitation);</tt><br>
64<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
65<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
66<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;Set&nbsp;the&nbsp;apodization</i></tt><br>
67<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
68<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_apodization(xmt,&nbsp;0,&nbsp;ones(1,no_elements))</tt><br>
69<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_apodization(rcv,&nbsp;0,&nbsp;ones(1,no_elements))</tt><br>
70<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bft_apodization(xdc,&nbsp;0&nbsp;,&nbsp;ones(1,no_elements))</tt><br>
71<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
72<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Define&nbsp;and&nbsp;create&nbsp;the&nbsp;image</i></tt><br>
73<tt>&nbsp;&nbsp;&nbsp;</tt><tt>sector&nbsp;=&nbsp;30&nbsp;*&nbsp;pi&nbsp;/&nbsp;180;</tt><br>
74<tt>&nbsp;&nbsp;&nbsp;</tt><tt>no_lines&nbsp;=&nbsp;32;</tt><br>
75<tt>&nbsp;&nbsp;&nbsp;</tt><tt>d_theta&nbsp;=&nbsp;sector&nbsp;/&nbsp;(no_lines-1);</tt><br>
76<tt>&nbsp;&nbsp;&nbsp;</tt><tt>theta&nbsp;=&nbsp;-(no_lines-1)&nbsp;/&nbsp;2&nbsp;*&nbsp;d_theta;</tt><br>
77<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
78<tt>&nbsp;&nbsp;&nbsp;</tt><tt>Rmax&nbsp;=&nbsp;max(sqrt(pht_pos(:,1).^&nbsp;2&nbsp;+&nbsp;pht_pos(:,2).^&nbsp;2&nbsp;&nbsp;+&nbsp;pht_pos(:,3).^&nbsp;2))&nbsp;+&nbsp;15/1000;</tt><br>
79<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
80<tt>&nbsp;&nbsp;&nbsp;</tt><tt>no_rf_samples&nbsp;=&nbsp;ceil(2*Rmax/c&nbsp;*&nbsp;fs);</tt><br>
81<tt>&nbsp;&nbsp;&nbsp;</tt><tt>rf_line&nbsp;=&nbsp;zeros(no_rf_samples,&nbsp;1);</tt><br>
82<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bf_line&nbsp;=&nbsp;zeros(no_rf_samples,&nbsp;1);</tt><br>
83<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
84<tt>&nbsp;&nbsp;&nbsp;</tt><tt>env_line&nbsp;=&nbsp;zeros(no_rf_samples,&nbsp;no_lines);</tt><br>
85<tt>&nbsp;&nbsp;&nbsp;</tt><tt>env_bf&nbsp;=&nbsp;&nbsp;zeros(no_rf_samples,&nbsp;no_lines);</tt><br>
86<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
87<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
88<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xmt_r&nbsp;=&nbsp;(max(focus_r)&nbsp;+&nbsp;min(focus_r)&nbsp;)/2;</tt><br>
89<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bf&nbsp;=&nbsp;cell(no_lines,1);</tt><br>
90<tt>&nbsp;&nbsp;&nbsp;</tt><tt>for&nbsp;i&nbsp;=&nbsp;1&nbsp;:&nbsp;no_lines</tt><br>
91<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;rf_line(:)&nbsp;=&nbsp;0;&nbsp;&nbsp;</tt><br>
92<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;theta</tt><br>
93<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
94<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xmt_f&nbsp;=&nbsp;[sin(theta)*xmt_r,&nbsp;zeros(length(xmt_r),1),&nbsp;cos(theta)*xmt_r];</tt><br>
95<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_center_focus(xmt,[0&nbsp;0&nbsp;0])</tt><br>
96<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_center_focus(rcv,[0&nbsp;0&nbsp;0])</tt><br>
97<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bft_center_focus([0&nbsp;0&nbsp;0]);</tt><br>
98<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
99<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_focus(xmt,&nbsp;0,&nbsp;xmt_f);</tt><br>
100<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_dynamic_focus(rcv,&nbsp;0,&nbsp;theta,&nbsp;0);</tt><br>
101<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
102<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;<i>%&nbsp;&nbsp;Beamform&nbsp;with&nbsp;Field&nbsp;II</i></tt><br>
103<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;[rf_temp,&nbsp;t(i)]&nbsp;=&nbsp;calc_scat(xmt,rcv,&nbsp;pht_pos,&nbsp;pht_amp);</tt><br>
104<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
105<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;<i>%&nbsp;&nbsp;Beamform&nbsp;with&nbsp;BFT</i></tt><br>
106<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bft_dynamic_focus(xdc,&nbsp;theta,&nbsp;0)</tt><br>
107<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_focus_times(rcv,&nbsp;0,&nbsp;zeros(1,no_elements));</tt><br>
108<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;[rf_data,&nbsp;start_t]&nbsp;=&nbsp;calc_scat_multi(xmt,rcv,&nbsp;pht_pos,&nbsp;pht_amp);</tt><br>
109<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
110<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;rf_data&nbsp;=&nbsp;[zeros(300,no_elements);&nbsp;rf_data;&nbsp;zeros(300,no_elements)];</tt><br>
111<tt>&nbsp;&nbsp;</tt><tt></tt><br>
112<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;start_t&nbsp;=&nbsp;start_t&nbsp;-&nbsp;300&nbsp;&nbsp;/&nbsp;fs;</tt><br>
113<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bf_temp&nbsp;=&nbsp;bft_beamform(start_t,&nbsp;rf_data);</tt><br>
114<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
115<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;start_sample&nbsp;=&nbsp;t(i)*fs;&nbsp;no_temp_samples&nbsp;=&nbsp;length(rf_temp);</tt><br>
116<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
117<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;rf_line(start_sample:start_sample+no_temp_samples-1)&nbsp;=&nbsp;rf_temp(1:no_temp_samples);</tt><br>
118<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;env_line(:,i)&nbsp;=&nbsp;abs(hilbert(rf_line(:)));</tt><br>
119<tt>&nbsp;&nbsp;</tt><tt></tt><br>
120<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;start_sample&nbsp;=&nbsp;floor(start_t*fs);&nbsp;no_temp_samples&nbsp;=&nbsp;length(bf_temp);</tt><br>
121<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bfi&nbsp;=&nbsp;bf_temp;</tt><br>
122<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
123<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bf_line(start_sample:start_sample+no_temp_samples-1)&nbsp;=&nbsp;bf_temp(1:no_temp_samples);</tt><br>
124<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;env_bf(:,i)&nbsp;=&nbsp;abs(hilbert(bf_line(:)));</tt><br>
125<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;theta&nbsp;=&nbsp;theta&nbsp;+&nbsp;d_theta;</tt><br>
126<tt>&nbsp;&nbsp;</tt><tt></tt><br>
127<tt>&nbsp;&nbsp;</tt><tt>end</tt><br>
128<tt>&nbsp;&nbsp;</tt><tt></tt><br>
129<tt>&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Release&nbsp;the&nbsp;allocated&nbsp;memory</i></tt><br>
130<tt>&nbsp;&nbsp;</tt><tt></tt><br>
131<tt>&nbsp;&nbsp;</tt><tt>field_end</tt><br>
132<tt>&nbsp;&nbsp;</tt><tt>bft_end</tt><br>
133<tt>&nbsp;&nbsp;</tt><tt>env_line&nbsp;=&nbsp;env_line&nbsp;/&nbsp;max(max(abs(env_line)));</tt><br>
134<tt>&nbsp;&nbsp;</tt><tt>env_bf&nbsp;=&nbsp;env_bf&nbsp;/&nbsp;max(max(abs(env_bf)));</tt><br>
135<tt>&nbsp;&nbsp;</tt><tt></tt><br>
136<tt>&nbsp;&nbsp;</tt><tt>figure;</tt><br>
137<tt>&nbsp;&nbsp;</tt><tt>subplot(1,2,1)</tt><br>
138<tt>&nbsp;&nbsp;</tt><tt>imagesc([-sector/2&nbsp;sector/2]*180/pi,[0&nbsp;Rmax]*1000,20*log10(env_line&nbsp;+&nbsp;0.001))</tt><br>
139<tt>&nbsp;&nbsp;</tt><tt>axis('image')</tt><br>
140<tt>&nbsp;&nbsp;</tt><tt>xlabel('Angle&nbsp;[deg]');</tt><br>
141<tt>&nbsp;&nbsp;</tt><tt>ylabel('Axial&nbsp;distance&nbsp;[mm]')</tt><br>
142<tt>&nbsp;&nbsp;</tt><tt>title('Beamformed&nbsp;by&nbsp;Field&nbsp;II&nbsp;');</tt><br>
143<tt>&nbsp;&nbsp;</tt><tt></tt><br>
144<tt>&nbsp;&nbsp;</tt><tt>subplot(1,2,2)</tt><br>
145<tt>&nbsp;&nbsp;</tt><tt>imagesc([-sector/2&nbsp;sector/2]*180/pi,[0&nbsp;Rmax]*1000,20*log10(env_bf&nbsp;+&nbsp;0.001));</tt><br>
146<tt>&nbsp;&nbsp;</tt><tt>title('Beamformed&nbsp;by&nbsp;BFT');</tt><br>
147<tt>&nbsp;&nbsp;</tt><tt>xlabel('Angle&nbsp;[deg]');</tt><br>
148<tt>&nbsp;&nbsp;</tt><tt>ylabel('Axial&nbsp;distance&nbsp;[mm]')</tt><br>
149<tt>&nbsp;&nbsp;</tt><tt>axis('image')</tt><br>
150<tt>&nbsp;&nbsp;</tt><tt></tt><br>
151<tt>&nbsp;&nbsp;</tt><tt>colorbar</tt><br>
152<tt>&nbsp;&nbsp;</tt><tt>colormap(gray)</tt><br>
153<tt>&nbsp;&nbsp;</tt><tt></tt><br>
154<tt>&nbsp;&nbsp;</tt><tt>clc</tt><br>
155<tt>&nbsp;&nbsp;</tt><tt>disp(['&nbsp;'&nbsp;10&nbsp;10&nbsp;10&nbsp;10&nbsp;]);</tt><br>
156<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*****************************************************']);</tt><br>
157<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*']);</tt><br>
158<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*&nbsp;The&nbsp;image&nbsp;beamformed&nbsp;by&nbsp;Field&nbsp;II&nbsp;is&nbsp;in&nbsp;&#235;nv_line"&nbsp;*']);</tt><br>
159<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*&nbsp;The&nbsp;image&nbsp;beamformed&nbsp;by&nbsp;BFT&nbsp;is&nbsp;in&nbsp;&#235;nv_bf"&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*']);</tt><br>
160<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*'])</tt><br>
161<tt>&nbsp;&nbsp;</tt><tt>disp([9&nbsp;'*****************************************************']);</tt><br>
162<tt>&nbsp;&nbsp;</tt><tt>disp(['&nbsp;'&nbsp;10&nbsp;10&nbsp;]);</tt><br>
163<tt>&nbsp;&nbsp;</tt><tt></tt><br>
164<tt>&nbsp;&nbsp;</tt><tt></tt><br>
</font>

<p>

<title> Synthetic Aperture Focusing</title>

<br><br><br><br><br>
<p>
<hr> 

<H3>Synthetic Aperture Focusing</H3>
<hr>

  <A NAME="sar_focusing">
</A>
  <a name="sar_focusing"></a>

<p>
<font size="-2">1<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt><i>%SYNTHETIC&nbsp;Synthetic&nbsp;aperture&nbsp;beamforming&nbsp;with&nbsp;BFT</i></tt><br>
2<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;</i></tt><br>
3<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
4<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
5<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt>f0&nbsp;=&nbsp;4e6;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;Central&nbsp;frequency</i></tt><br>
6<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt>fs&nbsp;=&nbsp;100e6;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;Sampling&nbsp;frequency</i></tt><br>
7<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt>c&nbsp;=&nbsp;1540;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;Speed&nbsp;of&nbsp;sound</i></tt><br>
8<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt>no_elements&nbsp;=&nbsp;64;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;Number&nbsp;of&nbsp;elements&nbsp;in&nbsp;the&nbsp;transducer</i></tt><br>
9<tt>&nbsp;&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
10<tt>&nbsp;&nbsp;&nbsp;</tt><tt>lambda&nbsp;=&nbsp;c&nbsp;/&nbsp;f0;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;Wavelength</i></tt><br>
11<tt>&nbsp;&nbsp;&nbsp;</tt><tt>pitch&nbsp;=&nbsp;lambda&nbsp;/&nbsp;2;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;Pitch&nbsp;-&nbsp;center-to-center</i></tt><br>
12<tt>&nbsp;&nbsp;&nbsp;</tt><tt>width&nbsp;=&nbsp;.95*pitch;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;Width&nbsp;of&nbsp;the&nbsp;element</i></tt><br>
13<tt>&nbsp;&nbsp;&nbsp;</tt><tt>kerf&nbsp;=&nbsp;pitch&nbsp;-&nbsp;width;&nbsp;&nbsp;<i>%&nbsp;Inter-element&nbsp;spacing</i></tt><br>
14<tt>&nbsp;&nbsp;&nbsp;</tt><tt>height&nbsp;=&nbsp;10/1000;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;Size&nbsp;in&nbsp;the&nbsp;Y&nbsp;direction</i></tt><br>
15<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;</tt><br>
16<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;</tt><br>
17<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Define&nbsp;the&nbsp;impulse&nbsp;response&nbsp;of&nbsp;the&nbsp;transducer</i></tt><br>
18<tt>&nbsp;&nbsp;&nbsp;</tt><tt>impulse_response&nbsp;=&nbsp;sin(3*pi*f0*(0:1/fs:2/f0));</tt><br>
19<tt>&nbsp;&nbsp;&nbsp;</tt><tt>impulse_response&nbsp;=&nbsp;impulse_response.*hanning(length(impulse_response))';</tt><br>
20<tt>&nbsp;&nbsp;&nbsp;</tt><tt>excitation&nbsp;=&nbsp;sin(2*pi*f0*(0:1/fs:3/f0));</tt><br>
21<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
22<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Define&nbsp;the&nbsp;phantom</i></tt><br>
23<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
24<tt>&nbsp;&nbsp;&nbsp;</tt><tt>pht_pos&nbsp;=&nbsp;[0&nbsp;0&nbsp;40]&nbsp;/&nbsp;1000;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;The&nbsp;position&nbsp;of&nbsp;the&nbsp;phantom</i></tt><br>
25<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
26<tt>&nbsp;&nbsp;&nbsp;</tt><tt>[m&nbsp;n]&nbsp;=&nbsp;size(pht_pos);</tt><br>
27<tt>&nbsp;&nbsp;&nbsp;</tt><tt>pht_amp&nbsp;=&nbsp;20*ones(m,1);&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>%&nbsp;&nbsp;The&nbsp;amplitude&nbsp;of&nbsp;the&nbsp;back-scatter</i></tt><br>
28<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
29<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
30<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Define&nbsp;the&nbsp;focus&nbsp;</i></tt><br>
31<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
32<tt>&nbsp;&nbsp;&nbsp;</tt><tt>focus_r&nbsp;=&nbsp;[1:max(sqrt(pht_pos(:,1).^&nbsp;2&nbsp;+&nbsp;pht_pos(:,2).^&nbsp;2&nbsp;+&nbsp;pht_pos(:,3).^&nbsp;2))*1000]'&nbsp;/&nbsp;1000;</tt><br>
33<tt>&nbsp;&nbsp;&nbsp;</tt><tt>T&nbsp;=&nbsp;(focus_r-.5/1000)/c&nbsp;*2;</tt><br>
34<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
35<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
36<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
37<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Initialize&nbsp;the&nbsp;program</i></tt><br>
38<tt>&nbsp;&nbsp;&nbsp;</tt><tt>field_init(0);</tt><br>
39<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bft_init;</tt><br>
40<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
41<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Set&nbsp;some&nbsp;paramters</i></tt><br>
42<tt>&nbsp;&nbsp;&nbsp;</tt><tt>set_field('c',&nbsp;c);</tt><br>
43<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bft_param('c',&nbsp;c);</tt><br>
44<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
45<tt>&nbsp;&nbsp;&nbsp;</tt><tt>set_field('fs',&nbsp;fs);</tt><br>
46<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bft_param('fs',&nbsp;fs);</tt><br>
47<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
48<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
49<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;Create&nbsp;some&nbsp;apertures.</i></tt><br>
50<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
51<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xmt&nbsp;=&nbsp;xdc_linear_array(no_elements,width,height,kerf,1,1,[0&nbsp;0&nbsp;0]);</tt><br>
52<tt>&nbsp;&nbsp;&nbsp;</tt><tt>rcv&nbsp;=&nbsp;xdc_linear_array(no_elements,width,height,kerf,1,1,[0&nbsp;0&nbsp;0]);</tt><br>
53<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
54<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc&nbsp;=&nbsp;bft_linear_array(no_elements,&nbsp;width,&nbsp;kerf);</tt><br>
55<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
56<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
57<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;Set&nbsp;the&nbsp;impulse&nbsp;responses</i></tt><br>
58<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_impulse(rcv,&nbsp;impulse_response);</tt><br>
59<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_impulse(xmt,&nbsp;impulse_response);</tt><br>
60<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
61<tt>&nbsp;&nbsp;&nbsp;</tt><tt>xdc_excitation(xmt,&nbsp;excitation);</tt><br>
62<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
63<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
64<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Define&nbsp;and&nbsp;create&nbsp;the&nbsp;image</i></tt><br>
65<tt>&nbsp;&nbsp;&nbsp;</tt><tt>sector&nbsp;=&nbsp;60&nbsp;*&nbsp;pi&nbsp;/&nbsp;180;</tt><br>
66<tt>&nbsp;&nbsp;&nbsp;</tt><tt>no_lines&nbsp;=&nbsp;64;</tt><br>
67<tt>&nbsp;&nbsp;&nbsp;</tt><tt>d_theta&nbsp;=&nbsp;sector&nbsp;/&nbsp;(no_lines-1);</tt><br>
68<tt>&nbsp;&nbsp;&nbsp;</tt><tt>theta&nbsp;=&nbsp;-(no_lines-1)&nbsp;/&nbsp;2&nbsp;*&nbsp;d_theta;</tt><br>
69<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
70<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Set&nbsp;the&nbsp;delays&nbsp;for&nbsp;one&nbsp;whole&nbsp;image</i></tt><br>
71<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%</i></tt><br>
72<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bft_no_lines(no_lines);</tt><br>
73<tt>&nbsp;&nbsp;&nbsp;</tt><tt>for&nbsp;i&nbsp;=&nbsp;1&nbsp;:&nbsp;no_lines</tt><br>
74<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bft_apodization(xdc,0,hanning(no_elements)',i);</tt><br>
75<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;bft_sum_apodization(xdc,0,ones(1,no_elements),i);</i></tt><br>
76<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;focus&nbsp;=&nbsp;[sin(theta)*focus_r,&nbsp;zeros(length(focus_r),1),&nbsp;cos(theta)*focus_r];</tt><br>
77<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bft_center_focus([0&nbsp;0&nbsp;0],i);</tt><br>
78<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bft_focus(xdc,&nbsp;T,&nbsp;focus,i);</tt><br>
79<tt>&nbsp;&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;theta&nbsp;=&nbsp;theta&nbsp;+&nbsp;d_theta;</tt><br>
80<tt>&nbsp;&nbsp;&nbsp;</tt><tt>end</tt><br>
81<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
82<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
83<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%</i></tt><br>
84<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Allocate&nbsp;memory&nbsp;for&nbsp;the&nbsp;image</i></tt><br>
85<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%</i></tt><br>
86<tt>&nbsp;&nbsp;&nbsp;</tt><tt>Rmax&nbsp;=&nbsp;max(sqrt(pht_pos(:,1).^&nbsp;2&nbsp;+&nbsp;pht_pos(:,2).^&nbsp;2&nbsp;&nbsp;+&nbsp;pht_pos(:,3).^&nbsp;2))&nbsp;+&nbsp;10/1000;</tt><br>
87<tt>&nbsp;&nbsp;&nbsp;</tt><tt>Rmin&nbsp;=&nbsp;min(sqrt(pht_pos(:,1).^&nbsp;2&nbsp;+&nbsp;pht_pos(:,2).^&nbsp;2&nbsp;&nbsp;+&nbsp;pht_pos(:,3).^&nbsp;2))&nbsp;-&nbsp;10/1000;</tt><br>
88<tt>&nbsp;&nbsp;&nbsp;</tt><tt>if&nbsp;(Rmin&nbsp;&lt;&nbsp;0)&nbsp;Rmin&nbsp;=&nbsp;0;&nbsp;end;</tt><br>
89<tt>&nbsp;&nbsp;&nbsp;</tt><tt>Tmin&nbsp;=&nbsp;2*Rmin&nbsp;/&nbsp;c;&nbsp;Tmax&nbsp;=&nbsp;2*Rmax&nbsp;/&nbsp;c;</tt><br>
90<tt>&nbsp;&nbsp;&nbsp;</tt><tt>Smin&nbsp;=&nbsp;floor(Tmin&nbsp;*&nbsp;fs);&nbsp;Smax&nbsp;=&nbsp;ceil(Tmax&nbsp;*&nbsp;fs);</tt><br>
91<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
92<tt>&nbsp;&nbsp;&nbsp;</tt><tt>no_rf_samples&nbsp;=&nbsp;Smax&nbsp;-&nbsp;Smin&nbsp;+&nbsp;1;</tt><br>
93<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
94<tt>&nbsp;&nbsp;&nbsp;</tt><tt>bf_image&nbsp;=&nbsp;zeros(no_rf_samples,&nbsp;no_lines);</tt><br>
95<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
96<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%</i></tt><br>
97<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%&nbsp;Make&nbsp;one&nbsp;low-resolution&nbsp;image&nbsp;at&nbsp;a&nbsp;time&nbsp;and&nbsp;sum&nbsp;them</i></tt><br>
98<tt>&nbsp;&nbsp;&nbsp;</tt><tt><i>%</i></tt><br>
99<tt>&nbsp;&nbsp;&nbsp;</tt><tt></tt><br>
100<tt>&nbsp;&nbsp;</tt><tt>xdc_focus_times(xmt,0,zeros(1,no_elements));&nbsp;</tt><br>
101<tt>&nbsp;&nbsp;</tt><tt>xdc_focus_times(rcv,0,zeros(1,no_elements));</tt><br>
102<tt>&nbsp;&nbsp;</tt><tt>for&nbsp;emission_no&nbsp;=&nbsp;1:no_elements</tt><br>
103<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;disp(['emission&nbsp;no:&nbsp;'&nbsp;num2str(emission_no)]);&nbsp;&nbsp;</tt><br>
104<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;xdc_apodization(xmt,0,[zeros(1,emission_no-1)&nbsp;1&nbsp;zeros(1,&nbsp;no_elements&nbsp;-&nbsp;emission_no)]);</tt><br>
105<tt>&nbsp;&nbsp;</tt><tt></tt><br>
106<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;[scat,&nbsp;start_time]&nbsp;=&nbsp;calc_scat_multi&nbsp;(xmt,&nbsp;rcv,&nbsp;pht_pos,&nbsp;pht_amp);</tt><br>
107<tt>&nbsp;&nbsp;</tt><tt></tt><br>
108<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;start_sample&nbsp;=&nbsp;floor(start_time&nbsp;*&nbsp;fs&nbsp;+&nbsp;0.5);</tt><br>
109<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;end_sample&nbsp;=&nbsp;start_sample&nbsp;+&nbsp;max(size(scat))-1;</tt><br>
110<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;</tt><br>
111<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;scat&nbsp;=&nbsp;[zeros(start_sample&nbsp;-&nbsp;Smin,&nbsp;no_elements);&nbsp;scat;&nbsp;zeros(Smax&nbsp;-&nbsp;end_sample,no_elements)];</tt><br>
112<tt>&nbsp;&nbsp;</tt><tt>&nbsp;</tt><br>
113<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;start_time&nbsp;=&nbsp;Tmin;</tt><br>
114<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;beamformed&nbsp;=&nbsp;bft_beamform(start_time,scat);</tt><br>
115<tt>&nbsp;&nbsp;</tt><tt>&nbsp;&nbsp;bf_image&nbsp;=&nbsp;bft_add_image(bf_image,&nbsp;beamformed,&nbsp;emission_no,&nbsp;start_time);</tt><br>
116<tt>&nbsp;&nbsp;</tt><tt>end</tt><br>
117<tt>&nbsp;&nbsp;</tt><tt></tt><br>
118<tt>&nbsp;&nbsp;</tt><tt></tt><br>
119<tt>&nbsp;&nbsp;</tt><tt></tt><br>
120<tt>&nbsp;&nbsp;</tt><tt><i>%&nbsp;&nbsp;Release&nbsp;the&nbsp;allocated&nbsp;memory</i></tt><br>
121<tt>&nbsp;&nbsp;</tt><tt></tt><br>
122<