bft_user_guide.tex

超声仿真软件

136{\tt~~}{\tt field\_end}\\
137{\tt~~}{\tt bft\_end}\\
138{\tt~~}{\tt }\\
139{\tt~~}{\tt env\_line~=~env\_line~/~max(max(abs(env\_line)));}\\
140{\tt~~}{\tt env\_bf~=~env\_bf~/~max(max(abs(env\_bf)));}\\
141{\tt~~}{\tt }\\
142{\tt~~}{\tt figure;}\\
143{\tt~~}{\tt subplot(1,2,1)}\\
144{\tt~~}{\tt imagesc([-sector/2~sector/2]*180/pi,[0~Rmax]*1000,20*log10(env\_line~+~0.001))}\\
145{\tt~~}{\tt axis('image')}\\
146{\tt~~}{\tt xlabel('Angle~[deg]');}\\
147{\tt~~}{\tt ylabel('Axial~distance~[mm]')}\\
148{\tt~~}{\tt title('Beamformed~by~Field~II~');}\\
149{\tt~~}{\tt }\\
150{\tt~~}{\tt subplot(1,2,2)}\\
151{\tt~~}{\tt imagesc([-sector/2~sector/2]*180/pi,[0~Rmax]*1000,20*log10(env\_bf~+~0.001));}\\
152{\tt~~}{\tt title('Beamformed~by~BFT');}\\
153{\tt~~}{\tt xlabel('Angle~[deg]');}\\
154{\tt~~}{\tt ylabel('Axial~distance~[mm]')}\\
155{\tt~~}{\tt axis('image')}\\
156{\tt~~}{\tt }\\
157{\tt~~}{\tt colorbar}\\
158{\tt~~}{\tt colormap(gray)}\\
159{\tt~~}{\tt }\\
160{\tt~~}{\tt clc}\\
161{\tt~~}{\tt disp(['~'~10~10~10~10~]);}\\
162{\tt~~}{\tt disp([9~'*****************************************************']);}\\
163{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*']);}\\
164{\tt~~}{\tt disp([9~'*~The~image~beamformed~by~Field~II~is~in~"env\_line"~*']);}\\
165{\tt~~}{\tt disp([9~'*~The~image~beamformed~by~BFT~is~in~"env\_bf"~~~~~~~~*']);}\\
166{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*'])}\\
167{\tt~~}{\tt disp([9~'*****************************************************']);}\\
168{\tt~~}{\tt disp(['~'~10~10~]);}\\
169{\tt~~}{\tt }\\
170{\tt~~}{\tt }\\
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\headline{Dynamic focusing}
%%tth:\vspace{2cm}
%%tth:\begin{html}<hr>\end{html} 
%%tth:\subsection*{Dynamic focusing}
%%tth:\begin{html}<hr>\end{html}
\funlnk{dynamic_focusing}

{\footnotesize\noindent
1{\tt~~~~}{\tt {\sl \%PHASED\_DYN\_IMAGE~Create~a~phased-array~B-mode~image,~using~the~}}\\
2{\tt~~~~}{\tt {\sl \%~~~~commands~for~setting~a~dynamic~focusing}}\\
3{\tt~~~~}{\tt }\\
4{\tt~~~~}{\tt {\sl \%VERSION~1.0,~29~Feb~2000,~Svetoslav~Nikolov}}\\
5{\tt~~~~}{\tt }\\
6{\tt~~~~}{\tt f0~=~4e6;~~~~~~~~~~~~~~{\sl \%~~Central~frequency~~~~~~~~~~~~~~~~~~~~~~~~[Hz]}}\\
7{\tt~~~~}{\tt fs~=~100e6;~~~~~~~~~~~~{\sl \%~~Sampling~frequency~~~~~~~~~~~~~~~~~~~~~~~[Hz]}}\\
8{\tt~~~~}{\tt c~=~1540;~~~~~~~~~~~~~~{\sl \%~~Speed~of~sound~~~~~~~~~~~~~~~~~~~~~~~~~~~[m/s]}}\\
9{\tt~~~~}{\tt B~=~.35;~~~~~~~~~~~~~~~{\sl \%~~Relative~bandwith~~~~~~~~~~~~~~~~~~~~~~~~[fraction]}}\\
10{\tt~~~}{\tt no\_elements~=~64;~~~~~~{\sl \%~~Number~of~elements~in~the~transducer~~~~~}}\\
11{\tt~~~}{\tt }\\
12{\tt~~~}{\tt lambda~=~c~/~f0;~~~~~~~{\sl \%~Wavelength~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[m]}}\\
13{\tt~~~}{\tt pitch~=~lambda~/~2;~~~~{\sl \%~Pitch~-~center-to-center~~~~~~~~~~~~~~~~~~[m]}}\\
14{\tt~~~}{\tt width~=~.95*pitch;~~~~~{\sl \%~Width~of~the~element~~~~~~~~~~~~~~~~~~~~~~[m]}}\\
15{\tt~~~}{\tt kerf~=~pitch~-~width;~~{\sl \%~Inter-element~spacing~~~~~~~~~~~~~~~~~~~~~[m]}}\\
16{\tt~~~}{\tt height~=~10/1000;~~~~~~{\sl \%~Size~in~the~Y~direction~~~~~~~~~~~~~~~~~~~[m]}}\\
17{\tt~~~}{\tt ~}\\
18{\tt~~~}{\tt ~}\\
19{\tt~~~}{\tt {\sl \%~~Define~the~impulse~response~of~the~transducer}}\\
20{\tt~~~}{\tt impulse\_response~=~sin(2*pi*f0*(0:1/fs:2/f0));}\\
21{\tt~~~}{\tt impulse\_response~=~impulse\_response.*hanning(length(impulse\_response))';}\\
22{\tt~~~}{\tt excitation~=~impulse\_response;}\\
23{\tt~~~}{\tt }\\
24{\tt~~~}{\tt {\sl \%~~Define~the~phantom}}\\
25{\tt~~~}{\tt }\\
26{\tt~~~}{\tt pht\_pos~=~[0~0~20;}\\
27{\tt~~~}{\tt ~~~~~~~~~~~0~0~30;}\\
28{\tt~~~}{\tt ~~~~~~~~~~~0~0~40;}\\
29{\tt~~~}{\tt ~~~~~~~~~~~0~0~50;}\\
30{\tt~~~}{\tt ~~~~~~~~~~~0~0~60;}\\
31{\tt~~~}{\tt ~~~~~~~~~~~0~0~70;}\\
32{\tt~~~}{\tt ~~~~~~~~~~~0~0~80;]~/~1000;~~~~~~~~~{\sl \%~~The~position~of~the~phantom}}\\
33{\tt~~~}{\tt pht\_amp~=~20*ones(7,1);~~~~~~{\sl \%~~The~amplitude~of~the~back-scatter}}\\
34{\tt~~~}{\tt }\\
35{\tt~~~}{\tt {\sl \%~~Define~the~focus~}}\\
36{\tt~~~}{\tt focus\_r~=~[20;30;40;50;60;70;80;90]~/~1000;}\\
37{\tt~~~}{\tt T~=~(focus\_r-5/1000)/c~*2;}\\
38{\tt~~~}{\tt }\\
39{\tt~~~}{\tt {\sl \%~~Initialize~the~program}}\\
40{\tt~~~}{\tt field\_init(0);}\\
41{\tt~~~}{\tt bft\_init;}\\
42{\tt~~~}{\tt }\\
43{\tt~~~}{\tt {\sl \%~~Set~some~paramters}}\\
44{\tt~~~}{\tt set\_field('c',~c);}\\
45{\tt~~~}{\tt bft\_param('c',~c);}\\
46{\tt~~~}{\tt }\\
47{\tt~~~}{\tt set\_field('fs',~fs);}\\
48{\tt~~~}{\tt bft\_param('fs',~fs);}\\
49{\tt~~~}{\tt }\\
50{\tt~~~}{\tt }\\
51{\tt~~~}{\tt {\sl \%~Create~some~apertures.}}\\
52{\tt~~~}{\tt }\\
53{\tt~~~}{\tt xmt~=~xdc\_linear\_array(no\_elements,width,height,kerf,1,1,[0~0~0]);}\\
54{\tt~~~}{\tt rcv~=~xdc\_linear\_array(no\_elements,width,height,kerf,1,1,[0~0~0]);}\\
55{\tt~~~}{\tt }\\
56{\tt~~~}{\tt xdc~=~bft\_linear\_array(no\_elements,~width,~kerf);}\\
57{\tt~~~}{\tt }\\
58{\tt~~~}{\tt }\\
59{\tt~~~}{\tt {\sl \%~Set~the~impulse~responses}}\\
60{\tt~~~}{\tt xdc\_impulse(rcv,~impulse\_response);}\\
61{\tt~~~}{\tt xdc\_impulse(xmt,~impulse\_response);}\\
62{\tt~~~}{\tt }\\
63{\tt~~~}{\tt xdc\_excitation(xmt,~excitation);}\\
64{\tt~~~}{\tt }\\
65{\tt~~~}{\tt }\\
66{\tt~~~}{\tt {\sl \%~Set~the~apodization}}\\
67{\tt~~~}{\tt }\\
68{\tt~~~}{\tt xdc\_apodization(xmt,~0,~ones(1,no\_elements))}\\
69{\tt~~~}{\tt xdc\_apodization(rcv,~0,~ones(1,no\_elements))}\\
70{\tt~~~}{\tt bft\_apodization(xdc,~0~,~ones(1,no\_elements))}\\
71{\tt~~~}{\tt }\\
72{\tt~~~}{\tt {\sl \%~~Define~and~create~the~image}}\\
73{\tt~~~}{\tt sector~=~30~*~pi~/~180;}\\
74{\tt~~~}{\tt no\_lines~=~32;}\\
75{\tt~~~}{\tt d\_theta~=~sector~/~(no\_lines-1);}\\
76{\tt~~~}{\tt theta~=~-(no\_lines-1)~/~2~*~d\_theta;}\\
77{\tt~~~}{\tt }\\
78{\tt~~~}{\tt Rmax~=~max(sqrt(pht\_pos(:,1).\^~2~+~pht\_pos(:,2).\^~2~~+~pht\_pos(:,3).\^~2))~+~15/1000;}\\
79{\tt~~~}{\tt }\\
80{\tt~~~}{\tt no\_rf\_samples~=~ceil(2*Rmax/c~*~fs);}\\
81{\tt~~~}{\tt rf\_line~=~zeros(no\_rf\_samples,~1);}\\
82{\tt~~~}{\tt bf\_line~=~zeros(no\_rf\_samples,~1);}\\
83{\tt~~~}{\tt }\\
84{\tt~~~}{\tt env\_line~=~zeros(no\_rf\_samples,~no\_lines);}\\
85{\tt~~~}{\tt env\_bf~=~~zeros(no\_rf\_samples,~no\_lines);}\\
86{\tt~~~}{\tt }\\
87{\tt~~~}{\tt }\\
88{\tt~~~}{\tt xmt\_r~=~(max(focus\_r)~+~min(focus\_r)~)/2;}\\
89{\tt~~~}{\tt bf~=~cell(no\_lines,1);}\\
90{\tt~~~}{\tt for~i~=~1~:~no\_lines}\\
91{\tt~~~}{\tt ~~rf\_line(:)~=~0;~~}\\
92{\tt~~~}{\tt ~~theta}\\
93{\tt~~~}{\tt ~~}\\
94{\tt~~~}{\tt ~~xmt\_f~=~[sin(theta)*xmt\_r,~zeros(length(xmt\_r),1),~cos(theta)*xmt\_r];}\\
95{\tt~~~}{\tt ~~xdc\_center\_focus(xmt,[0~0~0])}\\
96{\tt~~~}{\tt ~~xdc\_center\_focus(rcv,[0~0~0])}\\
97{\tt~~~}{\tt ~~bft\_center\_focus([0~0~0]);}\\
98{\tt~~~}{\tt ~~}\\
99{\tt~~~}{\tt ~~xdc\_focus(xmt,~0,~xmt\_f);}\\
100{\tt~~}{\tt ~~xdc\_dynamic\_focus(rcv,~0,~theta,~0);}\\
101{\tt~~}{\tt ~~}\\
102{\tt~~}{\tt ~~{\sl \%~~Beamform~with~Field~II}}\\
103{\tt~~}{\tt ~~[rf\_temp,~t(i)]~=~calc\_scat(xmt,rcv,~pht\_pos,~pht\_amp);}\\
104{\tt~~}{\tt ~~}\\
105{\tt~~}{\tt ~~{\sl \%~~Beamform~with~BFT}}\\
106{\tt~~}{\tt ~~bft\_dynamic\_focus(xdc,~theta,~0)}\\
107{\tt~~}{\tt ~~xdc\_focus\_times(rcv,~0,~zeros(1,no\_elements));}\\
108{\tt~~}{\tt ~~[rf\_data,~start\_t]~=~calc\_scat\_multi(xmt,rcv,~pht\_pos,~pht\_amp);}\\
109{\tt~~}{\tt ~~}\\
110{\tt~~}{\tt ~~rf\_data~=~[zeros(300,no\_elements);~rf\_data;~zeros(300,no\_elements)];}\\
111{\tt~~}{\tt }\\
112{\tt~~}{\tt ~~start\_t~=~start\_t~-~300~~/~fs;}\\
113{\tt~~}{\tt ~~bf\_temp~=~bft\_beamform(start\_t,~rf\_data);}\\
114{\tt~~}{\tt ~~}\\
115{\tt~~}{\tt ~~start\_sample~=~t(i)*fs;~no\_temp\_samples~=~length(rf\_temp);}\\
116{\tt~~}{\tt ~~}\\
117{\tt~~}{\tt ~~rf\_line(start\_sample:start\_sample+no\_temp\_samples-1)~=~rf\_temp(1:no\_temp\_samples);}\\
118{\tt~~}{\tt ~~env\_line(:,i)~=~abs(hilbert(rf\_line(:)));}\\
119{\tt~~}{\tt }\\
120{\tt~~}{\tt ~~start\_sample~=~floor(start\_t*fs);~no\_temp\_samples~=~length(bf\_temp);}\\
121{\tt~~}{\tt ~~bf{i}~=~bf\_temp;}\\
122{\tt~~}{\tt ~~}\\
123{\tt~~}{\tt ~~bf\_line(start\_sample:start\_sample+no\_temp\_samples-1)~=~bf\_temp(1:no\_temp\_samples);}\\
124{\tt~~}{\tt ~~env\_bf(:,i)~=~abs(hilbert(bf\_line(:)));}\\
125{\tt~~}{\tt ~~theta~=~theta~+~d\_theta;}\\
126{\tt~~}{\tt }\\
127{\tt~~}{\tt end}\\
128{\tt~~}{\tt }\\
129{\tt~~}{\tt {\sl \%~~Release~the~allocated~memory}}\\
130{\tt~~}{\tt }\\
131{\tt~~}{\tt field\_end}\\
132{\tt~~}{\tt bft\_end}\\
133{\tt~~}{\tt env\_line~=~env\_line~/~max(max(abs(env\_line)));}\\
134{\tt~~}{\tt env\_bf~=~env\_bf~/~max(max(abs(env\_bf)));}\\
135{\tt~~}{\tt }\\
136{\tt~~}{\tt figure;}\\
137{\tt~~}{\tt subplot(1,2,1)}\\
138{\tt~~}{\tt imagesc([-sector/2~sector/2]*180/pi,[0~Rmax]*1000,20*log10(env\_line~+~0.001))}\\
139{\tt~~}{\tt axis('image')}\\
140{\tt~~}{\tt xlabel('Angle~[deg]');}\\
141{\tt~~}{\tt ylabel('Axial~distance~[mm]')}\\
142{\tt~~}{\tt title('Beamformed~by~Field~II~');}\\
143{\tt~~}{\tt }\\
144{\tt~~}{\tt subplot(1,2,2)}\\
145{\tt~~}{\tt imagesc([-sector/2~sector/2]*180/pi,[0~Rmax]*1000,20*log10(env\_bf~+~0.001));}\\
146{\tt~~}{\tt title('Beamformed~by~BFT');}\\
147{\tt~~}{\tt xlabel('Angle~[deg]');}\\
148{\tt~~}{\tt ylabel('Axial~distance~[mm]')}\\
149{\tt~~}{\tt axis('image')}\\
150{\tt~~}{\tt }\\
151{\tt~~}{\tt colorbar}\\
152{\tt~~}{\tt colormap(gray)}\\
153{\tt~~}{\tt }\\
154{\tt~~}{\tt clc}\\
155{\tt~~}{\tt disp(['~'~10~10~10~10~]);}\\
156{\tt~~}{\tt disp([9~'*****************************************************']);}\\
157{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*']);}\\
158{\tt~~}{\tt disp([9~'*~The~image~beamformed~by~Field~II~is~in~"env\_line"~*']);}\\
159{\tt~~}{\tt disp([9~'*~The~image~beamformed~by~BFT~is~in~"env\_bf"~~~~~~~~*']);}\\
160{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*'])}\\
161{\tt~~}{\tt disp([9~'*****************************************************']);}\\
162{\tt~~}{\tt disp(['~'~10~10~]);}\\
163{\tt~~}{\tt }\\
164{\tt~~}{\tt }\\
}

\headline{Synthetic Aperture Focusing}
%%tth:\vspace{2cm}
%%tth:\begin{html}<hr>\end{html} 
%%tth:\subsection*{Synthetic Aperture Focusing}
%%tth:\begin{html}<hr>\end{html}
\funlnk{sar_focusing}

{\footnotesize\noindent
1{\tt~~~~}{\tt {\sl \%SYNTHETIC~Synthetic~aperture~beamforming~with~BFT}}\\
2{\tt~~~~}{\tt {\sl \%~}}\\
3{\tt~~~~}{\tt }\\
4{\tt~~~~}{\tt }\\
5{\tt~~~~}{\tt f0~=~4e6;~~~~~~~~~~~~~~{\sl \%~~Central~frequency}}\\
6{\tt~~~~}{\tt fs~=~100e6;~~~~~~~~~~~~{\sl \%~~Sampling~frequency}}\\
7{\tt~~~~}{\tt c~=~1540;~~~~~~~~~~~~~~{\sl \%~~Speed~of~sound}}\\
8{\tt~~~~}{\tt no\_elements~=~64;~~~~~~{\sl \%~~Number~of~elements~in~the~transducer}}\\
9{\tt~~~~}{\tt }\\
10{\tt~~~}{\tt lambda~=~c~/~f0;~~~~~~~{\sl \%~Wavelength}}\\
11{\tt~~~}{\tt pitch~=~lambda~/~2;~~~~{\sl \%~Pitch~-~center-to-center}}\\
12{\tt~~~}{\tt width~=~.95*pitch;~~~~~{\sl \%~Width~of~the~element}}\\
13{\tt~~~}{\tt kerf~=~pitch~-~width;~~{\sl \%~Inter-element~spacing}}\\
14{\tt~~~}{\tt height~=~10/1000;~~~~~~{\sl \%~Size~in~the~Y~direction}}\\
15{\tt~~~}{\tt ~}\\
16{\tt~~~}{\tt ~}\\
17{\tt~~~}{\tt {\sl \%~~Define~the~impulse~response~of~the~transducer}}\\
18{\tt~~~}{\tt impulse\_response~=~sin(3*pi*f0*(0:1/fs:2/f0));}\\
19{\tt~~~}{\tt impulse\_response~=~impulse\_response.*hanning(length(impulse\_response))';}\\
20{\tt~~~}{\tt excitation~=~sin(2*pi*f0*(0:1/fs:3/f0));}\\
21{\tt~~~}{\tt }\\
22{\tt~~~}{\tt {\sl \%~~Define~the~phantom}}\\
23{\tt~~~}{\tt }\\
24{\tt~~~}{\tt pht\_pos~=~[0~0~40]~/~1000;~~~{\sl \%~~The~position~of~the~phantom}}\\
25{\tt~~~}{\tt }\\
26{\tt~~~}{\tt [m~n]~=~size(pht\_pos);}\\
27{\tt~~~}{\tt pht\_amp~=~20*ones(m,1);~~~~~~{\sl \%~~The~amplitude~of~the~back-scatter}}\\
28{\tt~~~}{\tt }\\
29{\tt~~~}{\tt }\\
30{\tt~~~}{\tt {\sl \%~~Define~the~focus~}}\\
31{\tt~~~}{\tt }\\
32{\tt~~~}{\tt focus\_r~=~[1:max(sqrt(pht\_pos(:,1).\^~2~+~pht\_pos(:,2).\^~2~+~pht\_pos(:,3).\^~2))*1000]'~/~1000;}\\
33{\tt~~~}{\tt T~=~(focus\_r-.5/1000)/c~*2;}\\
34{\tt~~~}{\tt }\\
35{\tt~~~}{\tt }\\
36{\tt~~~}{\tt }\\
37{\tt~~~}{\tt {\sl \%~~Initialize~the~program}}\\
38{\tt~~~}{\tt field\_init(0);}\\
39{\tt~~~}{\tt bft\_init;}\\
40{\tt~~~}{\tt }\\
41{\tt~~~}{\tt {\sl \%~~Set~some~paramters}}\\
42{\tt~~~}{\tt set\_field('c',~c);}\\
43{\tt~~~}{\tt bft\_param('c',~c);}\\
44{\tt~~~}{\tt }\\
45{\tt~~~}{\tt set\_field('fs',~fs);}\\
46{\tt~~~}{\tt bft\_param('fs',~fs);}\\
47{\tt~~~}{\tt }\\
48{\tt~~~}{\tt }\\
49{\tt~~~}{\tt {\sl \%~Create~some~apertures.}}\\
50{\tt~~~}{\tt }\\
51{\tt~~~}{\tt xmt~=~xdc\_linear\_array(no\_elements,width,height,kerf,1,1,[0~0~0]);}\\
52{\tt~~~}{\tt rcv~=~xdc\_linear\_array(no\_elements,width,height,kerf,1,1,[0~0~0]);}\\
53{\tt~~~}{\tt }\\
54{\tt~~~}{\tt xdc~=~bft\_linear\_array(no\_elements,~width,~kerf);}\\
55{\tt~~~}{\tt }\\
56{\tt~~~}{\tt }\\
57{\tt~~~}{\tt {\sl \%~Set~the~impulse~responses}}\\
58{\tt~~~}{\tt xdc\_impulse(rcv,~impulse\_response);}\\
59{\tt~~~}{\tt xdc\_impulse(xmt,~impulse\_response);}\\
60{\tt~~~}{\tt }\\
61{\tt~~~}{\tt xdc\_excitation(xmt,~excitation);}\\
62{\tt~~~}{\tt }\\
63{\tt~~~}{\tt }\\
64{\tt~~~}{\tt {\sl \%~~Define~and~create~the~image}}\\
65{\tt~~~}{\tt sector~=~60~*~pi~/~180;}\\
66{\tt~~~}{\tt no\_lines~=~64;}\\
67{\tt~~~}{\tt d\_theta~=~sector~/~(no\_lines-1);}\\
68{\tt~~~}{\tt theta~=~-(no\_lines-1)~/~2~*~d\_theta;}\\
69{\tt~~~}{\tt }\\
70{\tt~~~}{\tt {\sl \%~~Set~the~delays~for~one~whole~image}}\\
71{\tt~~~}{\tt {\sl \%}}\\
72{\tt~~~}{\tt bft\_no\_lines(no\_lines);}\\
73{\tt~~~}{\tt for~i~=~1~:~no\_lines}\\
74{\tt~~~}{\tt ~~bft\_apodization(xdc,0,hanning(no\_elements)',i);}\\
75{\tt~~~}{\tt {\sl \%~~bft\_sum\_apodization(xdc,0,ones(1,no\_elements),i);}}\\
76{\tt~~~}{\tt ~~focus~=~[sin(theta)*focus\_r,~zeros(length(focus\_r),1),~cos(theta)*focus\_r];}\\
77{\tt~~~}{\tt ~~bft\_center\_focus([0~0~0],i);}\\
78{\tt~~~}{\tt ~~bft\_focus(xdc,~T,~focus,i);}\\
79{\tt~~~}{\tt ~~theta~=~theta~+~d\_theta;}\\
80{\tt~~~}{\tt end}\\
81{\tt~~~}{\tt }\\
82{\tt~~~}{\tt }\\
83{\tt~~~}{\tt {\sl \%}}\\
84{\tt~~~}{\tt {\sl \%~~Allocate~memory~for~the~image}}\\
85{\tt~~~}{\tt {\sl \%}}\\
86{\tt~~~}{\tt Rmax~=~max(sqrt(pht\_pos(:,1).\^~2~+~pht\_pos(:,2).\^~2~~+~pht\_pos(:,3).\^~2))~+~10/1000;}\\
87{\tt~~~}{\tt Rmin~=~min(sqrt(pht\_pos(:,1).\^~2~+~pht\_pos(:,2).\^~2~~+~pht\_pos(:,3).\^~2))~-~10/1000;}\\
88{\tt~~~}{\tt if~(Rmin~<~0)~Rmin~=~0;~end;}\\
89{\tt~~~}{\tt Tmin~=~2*Rmin~/~c;~Tmax~=~2*Rmax~/~c;}\\
90{\tt~~~}{\tt Smin~=~floor(Tmin~*~fs);~Smax~=~ceil(Tmax~*~fs);}\\
91{\tt~~~}{\tt }\\
92{\tt~~~}{\tt no\_rf\_samples~=~Smax~-~Smin~+~1;}\\
93{\tt~~~}{\tt }\\
94{\tt~~~}{\tt bf\_image~=~zeros(no\_rf\_samples,~no\_lines);}\\
95{\tt~~~}{\tt }\\
96{\tt~~~}{\tt {\sl \%}}\\
97{\tt~~~}{\tt {\sl \%~Make~one~low-resolution~image~at~a~time~and~sum~them}}\\
98{\tt~~~}{\tt {\sl \%}}\\
99{\tt~~~}{\tt }\\
100{\tt~~}{\tt xdc\_focus\_times(xmt,0,zeros(1,no\_elements));~}\\
101{\tt~~}{\tt xdc\_focus\_times(rcv,0,zeros(1,no\_elements));}\\
102{\tt~~}{\tt for~emission\_no~=~1:no\_elements}\\
103{\tt~~}{\tt ~~disp(['emission~no:~'~num2str(emission\_no)]);~~}\\
104{\tt~~}{\tt ~~xdc\_apodization(xmt,0,[zeros(1,emission\_no-1)~1~zeros(1,~no\_elements~-~emission\_no)]);}\\
105{\tt~~}{\tt }\\
106{\tt~~}{\tt ~~[scat,~start\_time]~=~calc\_scat\_multi~(xmt,~rcv,~pht\_pos,~pht\_amp);}\\
107{\tt~~}{\tt }\\
108{\tt~~}{\tt ~~start\_sample~=~floor(start\_time~*~fs~+~0.5);}\\
109{\tt~~}{\tt ~~end\_sample~=~start\_sample~+~max(size(scat))-1;}\\
110{\tt~~}{\tt ~~}\\
111{\tt~~}{\tt ~~scat~=~[zeros(start\_sample~-~Smin,~no\_elements);~scat;~zeros(Smax~-~end\_sample,no\_elements)];}\\
112{\tt~~}{\tt ~}\\
113{\tt~~}{\tt ~~start\_time~=~Tmin;}\\
114{\tt~~}{\tt ~~beamformed~=~bft\_beamform(start\_time,scat);}\\
115{\tt~~}{\tt ~~bf\_image~=~bft\_add\_image(bf\_image,~beamformed,~emission\_no,~start\_time);}\\
116{\tt~~}{\tt end}\\
117{\tt~~}{\tt }\\
118{\tt~~}{\tt }\\
119{\tt~~}{\tt }\\
120{\tt~~}{\tt {\sl \%~~Release~the~allocated~memory}}\\
121{\tt~~}{\tt }\\
122{\tt~~}{\tt field\_end}\\
123{\tt~~}{\tt bft\_end}\\
124{\tt~~}{\tt }\\
125{\tt~~}{\tt }\\
126{\tt~~}{\tt }\\
127{\tt~~}{\tt {\sl \%}}\\
128{\tt~~}{\tt {\sl \%~~Dispplay~the~image}}\\
129{\tt~~}{\tt {\sl \%}}\\
130{\tt~~}{\tt }\\
131{\tt~~}{\tt bf\_image~=~abs(hilbert(bf\_image));~~~~~~~~~~~~~~~~~~{\sl \%~Envelope~detection}}\\
132{\tt~~}{\tt bf\_image~=~bf\_image~/~max(max(bf\_image));}\\
133{\tt~~}{\tt }\\
134{\tt~~}{\tt figure;}\\
135{\tt~~}{\tt imagesc([-sector/2~sector/2]*180/pi,[Rmin~Rmax]*1000,20*log10(bf\_image~+~0.001))}\\
136{\tt~~}{\tt axis('image')}\\
137{\tt~~}{\tt xlabel('Angle~[deg]');}\\
138{\tt~~}{\tt ylabel('Axial~distance~[mm]')}\\
139{\tt~~}{\tt title('Beamformed~by~BFT~');}\\
140{\tt~~}{\tt clc}\\
141{\tt~~}{\tt disp(['~'~10~10~10~10~]);}\\
142{\tt~~}{\tt disp([9~'*****************************************************']);}\\
143{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*']);}\\
144{\tt~~}{\tt disp([9~'*~The~image~beamformed~by~BFT~is~in~"bf\_image"~~~~~~*']);}\\
145{\tt~~}{\tt disp([9~'*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*'])}\\
146{\tt~~}{\tt disp([9~'*****************************************************']);}\\
147{\tt~~}{\tt disp(['~'~10~10~]);}\\
148{\tt~~}{\tt }\\
}


\end{document}