C. MATLAB Source Codes
C.1 The Strehl ratio as a function of aberration coefficient W 060
% --- TOPIC: Strehl ratio, S(w20,w40,w60), v.s. W060 --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 2 --- %
u1 = zeros(81,1); % Field u1 -- with ideal aperture u2 = zeros(81,1); % Field u2 – with the designed filter I1 = zeros(81,1); % Intensity I1 -- with ideal aperture I2 = zeros(81,1); % Intensity I2 -- with ideal aperture B = 7*pi; % assign parameters
Bo = 0.3*7*pi;
% implementing the integral for i = 0 : 1 : 80
for x = 0 : 0.001 : 1
y1 = x*exp(j*2*pi*(((i./10)-4)*(x^6)));
y2 = x*exp(j*2*pi*(((i./10)-4)*(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u1(i+1)= u1(i+1)+ 0.001*y1;
u2(i+1)= u2(i+1)+ 0.001*y2;
end end
I1 = u1.*conj(u1)*4*pi*pi/10;
I1 = I1/max(I1); % Normalize the intensity I2 = u2.*conj(u2)*4*pi*pi/10;
I2 = I2/max(I2); % Normalize the intensity
k = -4 : 0.1 : 4;
plot(k,I1,k,I2)
Appendix C: MATLAB Source Codes (CONTINUED) C.2: Plot of the shape of the designed pupil phase function
% --- TOPIC: The shape of the designed pupil phase function --- %
% --- Drafted by Chih-Yun Chan, 1st version, test ok --- %
% --- Used in Section 2 --- %
Th = zeros(1001,1); %Thickness as a function of the radius B = 5*pi;
Bo = 0.3*B;
for m = 1:1:1001
Th(m,1)=(Bo*((((m-501)/500)^2)^3)+B*((((m-501)/500)^2)^3)*log(((m-501)/500) +1e-8));
end
k=-1:2/1000:1 % Normalized radial coordinate
plot(k,Th);
Appendix C: MATLAB Source Codes (CONTINUED) C.3: Computed MTF with initial setting W020=0 and W040=0
% --- TOPIC: Computed MTF with initial setting W020=0 and W040=0 --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 2 --- %
Q1= zeros(201,201); % Field Q1 -- with w060=0 lambda Q2= zeros(201,201); % Field Q2 -- with w060=0.5 lambda Q3= zeros(201,201); % Field Q3 -- with w060=1 lambda Q4= zeros(201,201); % Field Q4 -- with w060=0 lambda mtf1 = zeros(80,1); % MTF1 -- with w060=0 lambda mtf2 = zeros(80,1); % MTF1 -- with w060=0 lambda mtf3 = zeros(80,1); % MTF1 -- with w060=0 lambda mtf4 = zeros(80,1); % MTF1 -- with w060=0 lambda B = 7*pi; % assign parameters
Bo = 0.3*B;
for m = 0:1:200 for n = 0:1:200
if(((m-100)*(m-100)+(n-100)*(n-100))<1600)
Q1(m,n)=exp(j*2*pi*(Bo*((((m-100)/40)^2+((n-100)/40)^2)^3)+B*((((m-100)/40)^2…
+((n-100)/40)^2)^3)*log((((m-100)/40)^2+((n-100)/40)^2)^0.5 +1e-8)));
Q2(m,n)=exp(j*2*pi*(Bo*((((m-100)/40)^2+((n-100)/40)^2)^3)+B*((((m-100)/40)^2…
+((n-100)/40)^2)^3)*log((((m-100)/40)^2+((n-100)/40)^2)^0.5 +1e-8)));
Q3(m,n)=exp(j*2*pi*(Bo*((((m-100)/40)^2+((n-100)/40)^2)^3)+B*((((m-100)/40)^2…
+((n-100)/40)^2)^3)*log((((m-100)/40)^2+((n-100)/40)^2)^0.5 +1e-8)));
Q4(m,n)=exp(j*2*pi*(Bo*((((m-100)/40)^2+((n-100)/40)^2)^3)+B*((((m-100)/40)^2…
+((n-100)/40)^2)^3)*log((((m-100)/40)^2+((n-100)/40)^2)^0.5 +1e-8)));
end end
end
for m = 0:1:200
for n = 0:1:200
if(((m-100)*(m-100)+(n-100)*(n-100))<1600)
Q1(m,n)=Q1(m,n)*exp(j*2*pi*((((m-100)/40)^2+((n-100)/40)^2)^3)*0);
Q2(m,n)=Q2(m,n)*exp(j*2*pi*((((m-100)/40)^2+((n-100)/40)^2)^3)*0.5);
Q3(m,n)=Q3(m,n)*exp(j*2*pi*((((m-100)/40)^2+((n-100)/40)^2)^3)*1);
Q4(m,n)=Q4(m,n)*exp(j*2*pi*((((m-100)/40)^2+((n-100)/40)^2)^3)*2);
end end
end
otf1=conv2(Q1,conj(Q1));
otf2=conv2(Q2,conj(Q2));
otf3=conv2(Q3,conj(Q3));
otf4=conv2(Q4,conj(Q4));
for n = 1:80
mtf1(n)=abs(otf1((n+198),199));
mtf2(n)=abs(otf2((n+198),199));
mtf3(n)=abs(otf3((n+198),199));
mtf4(n)=abs(otf4((n+198),199));
end
% Normalization mtf1= mtf1/max(mtf1);
mtf2= mtf2/max(mtf2);
mtf3= mtf3/max(mtf3);
mtf4= mtf4/max(mtf4);
x1=0:(2/80):(2-2/80);
plot(x1,mtf1,x1,mtf2,x1,mtf3,x1,mtf4)
Appendix C: MATLAB Source Codes (CONTINUED) C.4: Maximal on-axis intensity versus BB46
.
% --- TOPIC: Maximal on-axis intensity versus BB46 --- %
% --- Drafted by Chih-Yun Chan, 1st version, test ok --- %
% --- Used in Section 2 --- %
u1 = zeros(161,1); % Field I1 = zeros(161,1); % Intensity
maxi = zeros(81,1); % Max. intensity v.s. B46
for B46 = 0: 1 : 80 for B26 = 0 : 1 : 160 for x = 0 : 0.001 : 1
y1 = x*exp(j*2*pi*1*((B26./20 -4)*(x^2)+(B46./20-3.5)*(x^4)+(x^6)));
u1(B26+1)= u1(B26+1)+ 0.001*y1;
end end
I1 = u1.*conj(u1)*4*pi*pi/10;
maxi(B46+1)=max(I1);
u1 = zeros(161,1);
I1 = zeros(161,1);
end
k= -3.5:0.05:0.5;
plot(k,maxi)
Appendix C: MATLAB Source Codes (CONTINUED)
C.5: Plot of the Strehl ratio versus B26 for different aberration scaling factors f, with B46 = -1.5
% --- TOPIC: Strehl ratio versus B26 for different f, with BB46 = -1.5 --- %
% --- Drafted by Chih-Yun Chan, 1st version, test ok --- %
% --- Used in Section 2 --- %
u0 = zeros(101,1); u1 = zeros(101,1); u2 = zeros(101,1); u3 = zeros(101,1);
u4 = zeros(101,1); u5 = zeros(101,1); u6 = zeros(101,1); % field with ideal lens
u02 = zeros(101,1); u12 = zeros(101,1); u22 = zeros(101,1); u32 = zeros(101,1);
u42 = zeros(101,1); u52 = zeros(101,1); u62 = zeros(101,1); % field with the filter
I0 = zeros(101,1); I1 = zeros(101,1); I2 = zeros(101,1); I3 = zeros(101,1);
I4 = zeros(101,1); I5 = zeros(101,1); I6 = zeros(101,1); % intensity with ideal lens
I02 = zeros(101,1); I12 = zeros(101,1); I22 = zeros(101,1); I32 = zeros(101,1);
I42 = zeros(101,1); I52 = zeros(101,1); I62 = zeros(101,1); % intensity with the filter
B46=-1.5; % assign parameters B = 3.9*pi;
Bo = 0.55*B;
for B26 = 0 : 1 : 100 % doing the integration for x = 0 : 0.001 : 1
y0 = x*exp(j*2*pi*0.5*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y02 = x*exp(j*2*pi*0.5*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u0(B26+1)= u0(B26+1)+ 0.001*y0;
u02(B26+1)= u02(B26+1)+ 0.001*y02;
y1 = x*exp(j*2*pi*1*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y12 = x*exp(j*2*pi*1*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u1(B26+1)= u1(B26+1)+ 0.001*y1;
u12(B26+1)= u12(B26+1)+ 0.001*y12;
y2 = x*exp(j*2*pi*2*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y22 = x*exp(j*2*pi*2*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u2(B26+1)= u2(B26+1)+ 0.001*y2;
u22(B26+1)= u22(B26+1)+ 0.001*y22;
y3 = x*exp(j*2*pi*3*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y32 = x*exp(j*2*pi*3*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u3(B26+1)= u3(B26+1)+ 0.001*y3;
u32(B26+1)= u32(B26+1)+ 0.001*y32;
y4 = x*exp(j*2*pi*4*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y42 = x*exp(j*2*pi*4*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u4(B26+1)= u4(B26+1)+ 0.001*y4;
u42(B26+1)= u42(B26+1)+ 0.001*y42;
y5 = x*exp(j*2*pi*5*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y52 = x*exp(j*2*pi*5*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u5(B26+1)= u5(B26+1)+ 0.001*y5;
u52(B26+1)= u52(B26+1)+ 0.001*y52;
y6 = x*exp(j*2*pi*6*((B26./100)*(x^2)+B46*(x^4)+(x^6)));
y62 = x*exp(j*2*pi*6*((B26./100)*(x^2)+B46*(x^4)...
+(x^6)))*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
u6(B26+1)= u6(B26+1)+ 0.001*y6;
u62(B26+1)= u62(B26+1)+ 0.001*y62;
end end
I0 = u0.*conj(u0)*4*pi*pi/10;
I1 = u1.*conj(u1)*4*pi*pi/10;
I2 = u2.*conj(u2)*4*pi*pi/10;
I3 = u3.*conj(u3)*4*pi*pi/10;
I4 = u4.*conj(u4)*4*pi*pi/10;
I5 = u5.*conj(u5)*4*pi*pi/10;
I6 = u6.*conj(u6)*4*pi*pi/10;
I02 = u02.*conj(u02)*4*pi*pi/10;
I12 = u12.*conj(u12)*4*pi*pi/10;
I22 = u22.*conj(u22)*4*pi*pi/10;
I32 = u32.*conj(u32)*4*pi*pi/10;
I42 = u42.*conj(u42)*4*pi*pi/10;
I52 = u52.*conj(u52)*4*pi*pi/10;
I62 = u62.*conj(u62)*4*pi*pi/10;
k = 0 : 0.01 : 1.0;
plot(k,I12,k,I22,k,I32,k,I42,k,I52,k,I62)
Appendix C: MATLAB Source Codes (CONTINUED) C.6: The Strehl ratio as a function of aberration scaling factor f, with
BB26
=0.6 and B
46= -1.5.
% --- TOPIC:Strehl ratio as a function of f, with B26 =0.6 and B46 = -1.5. --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 2 --- %
u1 = zeros(101,1); % field with ideal lens u2 = zeros(101,1); % field with the phase filter I1 = zeros(101,1); % intensity with ideal lens I2 = zeros(101,1); % intensity with the phase filter
B46=-1.5; % assign parameters B = 5*pi;
Bo = 0.3*B;
for f = 0 : 1 :100 % doing the integration for x = 0 : 0.001 : 1
y1 = x*exp(j*2*pi*f/10*(0.6*(x^2)+B46*(x^4)+(x^6)))…
*[exp(j*2*pi*(Bo*(x^6)+B*(x^6)*log(x+1e-6)))];
y2 = x*exp(j*2*pi*f/10*(0.6*(x^2)+B46*(x^4)+(x^6)));
u1(f+1)= u1(f+1)+ 0.001*y1;
u2(f+1)= u2(f+1)+ 0.001*y2;
end end
I1 = u1.*conj(u1)*4*pi*pi/10;
I1= I1/max(I1); % Normalization I2 = u2.*conj(u2)*4*pi*pi/10;
I2= I2/max(I2); % Normalization
k = 0 : 0.1 : 10;
plot(k,I1,k,I2)
Appendix C: MATLAB Source Codes (CONTINUED)
C.7: 1) Relation among the transverse gain and the radius of the first zone.
2) Relation among the Strehl ratio and the radius of the first zone
-- For CD
% --- TOPIC: SR v.s. radius a; GT v.s. radius a (for CD) --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 4 --- %
double NUM; % number of points in the interval a: 0.4~0.6 double a(NUM+1); % radius of the 1st zone
double b(NUM+1); % radius of the 2nd zone double t1; % transmission of zone 1 double t2; % transmission of zone 3 double phi; % phase difference of the zones double I0(NUM+1); double a0(NUM+1); double b0(NUM+1);
double I1(NUM+1); double a1(NUM+1); double b1(NUM+1);
double I2(NUM+1); double a2(NUM+1); double b2(NUM+1);
double uF(NUM+1);
double SR(NUM+1);
double GT(NUM+1);
double GA(NUM+1);
t1= 1; % assign the parameters t2= 1;
phi=0.4 NUM = 200;
for i = 0 : NUM
a(i+1) = 0.4 + (0.2/NUM).*i;
b(i+1) = sqrt(1-a(i+1).*a(i+1));
I0(i+1) = exp(j*0*pi)*(t1.*(a(i+1).^2)) + t2.*exp(j*phi*pi)*(1-(b(i+1).^2));
a0(i+1) = real(I0(i+1));
b0(i+1) = imag(I0(i+1));
I1(i+1) = 0.5*exp(j*0*pi)*(t1.*(a(i+1).^4)) + t2.*0.5*exp(j*phi*pi)*(- (b(i+1).^4) +1);
a1(i+1) = real(I1(i+1));
b1(i+1) = imag(I1(i+1));
I2(i+1) = (1/3)*exp(j*0*pi)*(t1.*(a(i+1).^6))+ t2.*(1/3)*exp(j*phi*pi)*(- (b(i+1).^6) +1);
a2(i+1) = real(I2(i+1));
b2(i+1) = imag(I2(i+1));
% the displacement of the focus
uF(i+1) = 2*(a1(i+1).*b0(i+1)-a0(i+1).*b1(i+1))./( (a2(i+1).*a0(i+1)+b2(i+1).*b0(i+1))…
- (a1(i+1).*a1(i+1)+b1(i+1).*b1(i+1)) );
% the Strehl ratio
SR(i+1) = a0(i+1).*a0(i+1) + b0(i+1).*b0(i+1)…
- uF(i+1).*(a0(i+1).*b1(i+1)-a1(i+1).*b0(i+1));
% the transverse gain
GT(i+1) = 2*( (a1(i+1).*a0(i+1)+b0(i+1).*b1(i+1))…
- uF(i+1).*(-a2(i+1).*b0(i+1)+a0(i+1).*b2(i+1)) )./SR(i+1);
% the axial gain
GA(i+1) = 12*( (a2(i+1).*a0(i+1)+b0(i+1).*b2(i+1))…
- (a1(i+1).*a1(i+1)+b1(i+1).*b1(i+1)) )./SR(i+1);
end
m = 0.4: (0.2/NUM): 0.6;
subplot(2,1,1); plot(m,uF);
subplot(2,1,2); plot(m,SR);
Appendix C: MATLAB Source Codes (CONTINUED)
C.8: 1) Relation among the transverse gain and the radius of the first zone.
2) Relation among the Strehl ratio and the radius of the first zone
-- For DVF
% --- TOPIC: SR v.s. radius a; GT v.s. radius a (for DVD) --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 4 --- %
double NUM; % number of points in the interval a: 0.4~0.6 double a(NUM+1); % radius of the 1st zone
double b(NUM+1); % radius of the 2nd zone double t1; % transmission of zone 2 double t2; % transmission of zone 4 double phi; % phase difference of the zones double I0(NUM+1); double a0(NUM+1); double b0(NUM+1);
double I1(NUM+1); double a1(NUM+1); double b1(NUM+1);
double I2(NUM+1); double a2(NUM+1); double b2(NUM+1);
double uF(NUM+1);
double SR(NUM+1);
double GT(NUM+1);
double GA(NUM+1);
c= 0.7; % assign parameters t1=1;
t2=1;
phi=0.35;
NUM = 200;
for i = 0 : NUM
a(i+1) = 0.4 + (0.2/NUM).*i;
b(i+1) = sqrt(1-a(i+1).*a(i+1));
I0(i+1) = t1.*exp(j*0*pi)*((c.*b(i+1)).^2-(c.*a(i+1)).^2) + t2.*exp(j*phi*pi)*(1-(c).^2);
a0(i+1) = real(I0(i+1));
b0(i+1) = imag(I0(i+1));
I1(i+1) = (1/2)*(t1.*exp(j*0*pi)*((c.*b(i+1)).^4-(c.*a(i+1)).^4) + t2.*exp(j*phi*pi)*(1-(c).^4));
a1(i+1) = real(I1(i+1));
b1(i+1) = imag(I1(i+1));
I2(i+1) = (1/3)*(t1.*exp(j*0*pi)*((c.*b(i+1)).^6-(c.*a(i+1)).^6) + t2.*exp(j*phi*pi)*(1-(c).^6));
a2(i+1) = real(I2(i+1));
b2(i+1) = imag(I2(i+1));
% the displacement of the focus
uF(i+1) = 2*(a1(i+1).*b0(i+1)-a0(i+1).*b1(i+1))…
./( (a2(i+1).*a0(i+1)+b2(i+1).*b0(i+1)) - (a1(i+1).*a1(i+1)+b1(i+1).*b1(i+1)) );
% the Strehl ratio
SR(i+1) = a0(i+1).*a0(i+1) + b0(i+1).*b0(i+1) - uF(i+1).*(a0(i+1).*b1(i+1)-a1(i+1).*b0(i+1));
% the transverse gain
GT(i+1) = 2*( (a1(i+1).*a0(i+1)+b0(i+1).*b1(i+1))…
- uF(i+1).*(-a2(i+1).*b0(i+1)+a0(i+1).*b2(i+1)) )./SR(i+1);
% the axial gain
GA(i+1) = 12*( (a2(i+1).*a0(i+1)+b0(i+1).*b2(i+1)) … -(a1(i+1).*a1(i+1)+b1(i+1).*b1(i+1)) )./SR(i+1);
end
m = 0.4: (0.2/NUM): 0.6;
%subplot(2,1,1);
plot(m,uF);
%subplot(2,1,2); plot(m,SR);
Appendix C: MATLAB Source Codes (CONTINUED) C.9: The transverse intensity distributions -- For CD
% --- TOPIC: the transverse intensity distributions (for CD) --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 4 --- %
v = (0:0.01:10)'; % radius distance double a(3); % radius of the 1st zone double b(3); % radius of the 2nd zone double U(1001,3); % field with the clear aperture double Ut(1001,3); % field with the designed filter double I(1001,3); % intensity with the clear aperture double It(1001,3); % intensity with the designed filter
a(1)=0.5; a(2)=0.57; a(3)=0.6;
b(1)=sqrt(1-a(1).*a(1)); b(2)=sqrt(1-a(2).*a(2)); b(3)=sqrt(1-a(3).*a(3));
warning off;
for k = 1:3 for i = 0 : 1000
U(i+1,k) = (2./v(i+1))*besselj(1,v(i+1));
Ut(i+1,k) = (2./v(i+1))*( a(k).*besselj(1,(a(k).*v(i+1)))…
+ exp(j*0.1*pi).*( besselj(1,v(i+1)) - b(k).*besselj(1,(b(k).*v(i+1))) ) );
end end
for k= 1:3
I(1:1001,k) = U(1:1001,k).*conj(U(1:1001,k));
It(1:1001,k) = Ut(1:1001,k).*conj(Ut(1:1001,k));
end
subplot(2,1,1); plot(v,I(:,1),v,I(:,2),v,I(:,3));
subplot(2,1,2); plot(v,It(:,1),v,It(:,2),v,It(:,3));
warning on;
Appendix C: MATLAB Source Codes (CONTINUED) C.10: The transverse intensity distributions -- For DVD
% --- TOPIC: the transverse intensity distributions (for DVD) --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 4 --- %
v = (0:0.01:10)'; % radius distance double a(3); % radius of the 1st zone double b(3); % radius of the 2nd zone double U(1001,3); % field with the clear aperture double Ut(1001,3); % field with the designed filter double I(1001,3); % intensity with the clear aperture double It(1001,3); % intensity with the designed filter
a(1)=0.5; a(2)=0.57; a(3)=0.6;
b(1)=sqrt(1-a(1).*a(1)); b(2)=sqrt(1-a(2).*a(2)); b(3)=sqrt(1-a(3).*a(3));
c=0.7;
warning off;
for k = 1:3
for i = 0 : 1000
U(i+1,k) = (2./v(i+1))*besselj(1,v(i+1));
Ut(i+1,k) = (2./v(i+1))*( c.*b(k).*besselj(1,(c.*b(k).*v(i+1)))…
-c.*a(k).*besselj(1,(c.*a(k).*v(i+1)))…
+ exp(j*0.35*pi).*(besselj(1,v(i+1))-c.*besselj(1,(c.*v(i+1))) ) );
end end
for k= 1:3
I(1:1001,k) = U(1:1001,k).*conj(U(1:1001,k));
It(1:1001,k) = Ut(1:1001,k).*conj(Ut(1:1001,k));
end
subplot(2,1,1); plot(v,I(:,1),v,I(:,2),v,I(:,3));
subplot(2,1,2); plot(v,It(:,1),v,It(:,2),v,It(:,3));
warning on;
Appendix C: MATLAB Source Codes (CONTINUED) C.11: Radial intensity scans at various planes (FFT method)
% --- TOPIC: Radial intensity scans at various planes (FFT) --- %
% --- Drafted by Chih-Yun Chan, 2nd version, test ok --- %
% --- Used in Section 4 --- %
sq=zeros(1000); % field with the clear aperture sq1=zeros(1000); % field with the designed fillter double u;
u = 3;
for m = 0 : 1 : 1000 % generate the pupil function for n = 0 : 1 : 1000
if(((m-500)*(m-500)+(n-500)*(n-500))^0.5<10*0.6)
sq1((m+1),(n+1))=1*exp(-j*u*((m-500)*(m-500)+(n-500)*(n-500))/2/100) ; end
if(((m-500)*(m-500)+(n-500)*(n-500))^0.5>10*(sqrt(1-0.6*0.6))) if(((m-500)*(m-500)+(n-500)*(n-500))^0.5<10)
sq1((m+1),(n+1))=exp(j*0.35*pi)*…
exp(-j*u*((m-500)*(m-500)+(n-500)*(n-500))/2/100) ; end
end
if(((m-500)*(m-500)+(n-500)*(n-500))^0.5<10) sq((m+1),(n+1))=1 ;
end end end
sqft=fftshift(fft2(fftshift(sq)));
sqft1=fftshift(fft2(fftshift(sq1)));
I=sqft.*conj(sqft);
I1=sqft1.*conj(sqft1);
k= -500*1.22*pi/61: 1.22*pi/61 : 1.22*pi/61*499;
subplot(2,1,1); plot(k,(I(:,501)./max(I(:,501))));
subplot(2,1,2); plot(k,(I1(:,501)./max(I(:,501))));
Bibliography (Section 2)
2.1. W. T. Welford, Aberrations of Optical Systems, (Adam Hilger , New York, 1986) 2.2. V. N. Mahajan, Optical Imaging and Aberration, (SPIE Optical Engineering Press,
Bellingham, Wash., 1998)
2.3. J. Campos, J.Escalera and M. J. Yzuel, “Symmetry properties with pupil phase-filters,” Opt. Express 12, 2548-2559 (2004)
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Bibliography (Section 2 Continued)
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Bibliography (Section 3)
3.1 Wang, Z. Chen, and F. Gan, “High Focal Depth with a Pure-Phase Apodizer”, Appl. Opt. 40, 5658-5662 (2001)
3.2 X. Gao, Z Fei, W. Xu, F. Gan, “Focus splitting induced by a pure phase-shifting apodizer,” Opt. Comm. 239, 55-59(2004)”
3.3 A. R. FitzGerrell, E. R. Dowski, Jr., and W. T Cathey, “Defocus transfer function for circularly symmetric pupils,” Appl. Opt., 5796-5804 (1997)
3.4 A. Walther, The Ray and Wave Theory of Lenses, (Cambridge, 1995)
3.5 W. T. Welford, FRS, Aberrations of Optical Systems, (Adam Hilger Ltd, 1986) 3.6 V. N. Mahajan, Optical Imaging and Aberration, (SPIE Optical Engineering Press,
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3.7 V. N. Mahajan, Aberration Theory Made Simple, (SPIE, 1991)
3.8 OSLO Optics Reference (Release 6.1), pp.104-119; available from Lambda Research Corp. (can be downloaded from http://www.lambdares.com)
Bibliography (Section 4)
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Bibliography (Section 4 Continued)
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Bibliography (Section 4 Continued)
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作者簡歷
本論文作者： 詹志雲 (Chih-Yun Chan)
台灣省嘉義縣人，民國71年生。
2000 畢業於協同中學。
2004 年取得清華大學電機工程學士學位。
2005 年於交通大學光電所取得碩士學位。
研究興趣為光學系統成像品質的分析與改善。