update_date_01_25_2021_timestamp_11_11_00_PM

Chapter_3_Eight_level_phase_grating.m

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+%% 4-level 1D grating
+clear  %Clear all memory
+
+% Defining grating parameters
+N=500; % Matrix size
+P=100; % Grating period 
+A1=ones(P,N); % Size of fundamental building block of grating
+g=8; % Number of phase levels
+delphase= 2*pi/g;  %Phase step size
+
+% Constructing one n-level section of the phase grating
+sub =round(P/g)-1; 
+for count = 1:g;
+     A1((count -1)*sub+1:count*sub,:)=exp(1i*(count-1)*delphase);
+end
+
+%Constructing the full grating
+A2=repmat(A1,N/P,1); 
+
+%Observation of the diffraction pattern
+E=fftshift(fft2(A2)); %fftshift to re-order the terms to the natural order
+IN=(abs(E)/(N*N)).*(abs(E)/(N*N)); %Normalize the intensity values
+figure(1)
+colormap(gray); 
+imagesc(angle(A2))          
+figure(2)
+colormap(gray);
+imagesc(IN);

Chapter_3_Four_level_axicon.m

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+% 4-level axicon
+ clear; %Clear all memory
+
+%Defining axicon parameters
+N=480; % Matrix size
+A=zeros(N,N); 
+P=40; % Grating period
+g=4; %Define the number of phase levels in each period
+w=P/g; %Define the width of each phase levels
+delphase=2*pi/g;
+%Constructing the 8-level axicon
+    x=1:N;
+    y=1:N;
+    [X,Y]=meshgrid(x,y);
+    r=sqrt((X-N/2).*(X-N/2)+(Y-N/2).*(Y-N/2)); 
+for n=1:g;
+    A(rem(r+(n-2)*w,P)<P/g)=exp(1i*(w-(n))*delphase);
+end
+
+A(r>N/2)=0;
+
+
+%Observation of the diffraction pattern
+E=fftshift(fft2(A)); %fftshift to re-order the terms to the natural order
+I=abs(E).*abs(E);
+figure(1)
+colormap(gray); 
+imagesc(angle(A))          
+figure(2)
+colormap(gray);
+imagesc(I);
+

Chapter_3_Sixteen_level_axicon.m

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+%% 4-level axicon
+ clear; %Clear all memory
+
+%Defining axicon parameters
+N=480; % Matrix size
+A=zeros(N,N); 
+P=80; % Grating period
+g=16; %Define the number of phase levels in each period
+w=P/g; %Define the width of each phase levels
+delphase=2*pi/g;
+%Constructing the 8-level axicon
+    x=1:N;
+    y=1:N;
+    [X,Y]=meshgrid(x,y);
+    r=sqrt((X-N/2).*(X-N/2)+(Y-N/2).*(Y-N/2)); 
+for n=1:g;
+    A(rem(r+(n-2)*w,P)<P/g)=exp(1i*(w-(n))*delphase);
+end
+
+A(r>N/2)=0;
+
+
+%Observation of the diffraction pattern
+E=fftshift(fft2(A)); %fftshift to re-order the terms to the natural order
+I=abs(E).*abs(E);
+figure(1)
+colormap(gray); 
+imagesc(angle(A))          
+figure(2)
+colormap(gray);
+imagesc(I);
+

Chapter_6_Binary_Axicon_Binary_2D_phase_grating.m

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+%Multifunctional DOE – Blazed FZP and 2-d grating
+clear;%Clear all memory
+
+%Define grating and FZP parameters
+N=500;%Define Matrix size
+f=10000;
+lambda=0.632;
+Pr=50;
+Px=25;
+Py=25;
+FFr=0.5;
+FFy=0.5;
+FFx=0.5;
+A1=zeros(N,N);%Define the matrices assigning ones to all pixels
+A2=zeros(N,N);
+A3=zeros(N,N);
+
+%Grating and Axicon construction and multiplexing
+    x=1:N;
+    y=1:N;
+    [X,Y]=meshgrid(x,y);
+    r=sqrt((X-N/2).*(X-N/2)+(Y-N/2).*(Y-N/2));
+    A1(rem(r,Pr)<Pr*FFr)=1;
+    A2(rem(Y,Py)<Py*FFy)=1;
+    A3(rem(X,Px)<Px*FFx)=1;
+    A4=pi*xor(A1,xor(A2,A3));
+    B=exp(1i*A4);
+    B(r>150)=0;
+
+%Observation of diffraction pattern
+C=fftshift(fft2(B));
+D=abs(C).*abs(C);
+colormap(gray)
+imagesc(D)

Chapter_6_Blazed_Axicon_Binary_2D_phase_grating.m

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+%Multifunctional DOE – Blazed FZP and 2-d grating
+clear;%Clear all memory
+
+%Define grating and FZP parameters
+N=500;%Define Matrix size
+f=10000;
+lambda=0.632;
+Pr=50;
+Px=25;
+Py=25;
+FFr=0.5;
+FFy=0.5;
+FFx=0.5;
+A1=zeros(N,N);%Define the matrices assigning ones to all pixels
+A2=zeros(N,N);
+A3=zeros(N,N);
+
+%Grating and Axicon construction and multiplexing
+    x=1:N;
+    y=1:N;
+    [X,Y]=meshgrid(x,y);
+    r=sqrt((X-N/2).*(X-N/2)+(Y-N/2).*(Y-N/2));
+    A1=(rem(r,Pr))*(2*pi)/Pr;
+    A2(rem(Y,Py)<Py*FFy)=1;
+    A3(rem(X,Px)<Px*FFx)=1;
+    A4=pi*xor(A2,A3);
+    A=rem(A1+A4,2*pi);
+    B=exp(1i*A);
+    B(r>150)=0;
+
+%Observation of diffraction pattern
+C=fftshift(fft2(B));
+D=abs(C).*abs(C);
+colormap(gray)
+imagesc(D)

Chapter_6_Blazed_FZP_Binary_2D_phase_grating.m

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+%Multifunctional DOE – Blazed FZP and 2-d grating
+clear;%Clear all memory
+
+%Define grating and FZP parameters
+N=500;%Define Matrix size
+f=10000;
+lambda=0.632;
+P=100;
+FFy=0.5;
+FFx=0.5;
+A1=zeros(N,N);%Define the matrices assigning ones to all pixels
+A2=zeros(N,N);
+A3=zeros(N,N);
+
+%Grating and FZP construction and multiplexing
+    x=1:N;
+    y=1:N;
+    [X,Y]=meshgrid(x,y);
+    r=sqrt((X-N/2).*(X-N/2)+(Y-N/2).*(Y-N/2));
+    A1=(f-sqrt(f*f+r.*r))*(2*pi)/(0.632);
+    A1=rem(A1,2*pi);
+    A2(rem(Y,P)<P*FFy)=pi;
+    A3(rem(X,P)<P*FFx)=pi;
+    A4=pi*xor(A2,A3);
+    A=rem(A1+A4,2*pi);
+    B=exp(1i*A);
+
+%Observation of DOE
+colormap(gray)
+imagesc(angle(B))

Chapter_7_Axicon_Grating.m

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+%Grating+Axicon
+%Define parameters
+N=500;%%Define size of the matrix
+Angle1=1;%Define angle of axicon
+Angle2=1;%Define angle of grating
+V=0.5;%%Visibility controller
+lambda=0.632*1e-6;%Define wavelength 
+
+%Create sampled space 
+    del=1*1e-6;%sampling
+    x=-N/2:N/2-1;
+    y=-N/2:N/2-1;
+    [X,Y]=meshgrid(x*del,y*del); 
+    r=sqrt(X.^2+Y.^2);
+    A=V*exp(1i*(r/lambda)*tand(Angle1)*2*pi);
+    B=V*exp(1i*(Y/lambda)*tand(Angle2)*2*pi);
+    D=A+B;%Interference of the object and reference wave
+
+%%Intensity profile
+    I=abs(D).*abs(D);
+    I1=im2bw(I);
+    Grating_axicon=exp(1i*pi*I1);
+    Grating_axicon(r>100)=0;
+    E=fftshift(fft2(Grating_axicon));
+    I2=(abs(E).*abs(E));
+    colormap(gray);%%Display result
+    imagesc(I2);
+

Chapter_7_Helical_axicon.m

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+%Forked grating
+%Define parameters
+N=500;%%Define size of the matrix
+Angle=1;%Define angle of the second plane wave
+V=0.5;%%Visibility controller
+lambda=0.632*1e-6;%Define wavelength 
+L=5;
+
+%Create sampled space 
+    del=1*1e-6;%sampling
+    x=-N/2:N/2-1;
+    y=-N/2:N/2-1;
+    [X,Y]=meshgrid(x*del,y*del); 
+    r=sqrt(X.^2+Y.^2);
+    A=V*exp(1i*L*(atan2(Y,X))); 
+    B=V*exp(1i*(r/lambda)*tand(Angle)*2*pi);
+    D=A+B;%Interference of the object and reference wave
+
+%%Intensity profile
+    I=abs(D).*abs(D);
+    I1=im2bw(I);
+    Heli_axicon=exp(1i*pi*I1);
+    Heli_axicon(r>100*1e-6)=0;
+    E=fftshift(fft2(Heli_axicon));
+    I2=(abs(E).*abs(E));
+    colormap(gray);%%Display result
+    imagesc(I2);

E_5_2.m

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+%%program to calculate back transverse focal aberration
+u=5000;
+v=30000;
+l=0.632;
+na=1;
+ng=1.5;
+for n=1:1000;
+    a(n)=n*n*l*l+2*n*l*(u+v)+2*u*v;
+    r(n)=sqrt(((a(n)*a(n))-4*u*u*v*v)/(4*(a(n)+u*u+v*v)));
+    if r(n)>=500 && r(n)<=700;
+       t=3000;
+    else
+       t=1000;
+    end
+    theta(n)=atan(r(n)/u);
+    rr(n)=r(n)*((u-t)/u);
+    r1(n)=rr(n)+t*tan(asin(na/ng*(sin(atan(r(n)/u)))));
+    u1(n)=u*(r1(n)/r(n));
+    a1(n)=n*n*l*l+2*n*l*(u1(n)+v)+2*u1(n)*v;
+    rr(n)=sqrt(((a1(n)*a1(n))-4*u1(n)*u1(n)*v*v)/(4*(a1(n)+u1(n)*u1(n)+v*v)));
+    b(n)=(4*n*n*l*l+8*n*l*u1(n)-4*rr(n)*rr(n));
+    c(n)=(4*n^3*l^3+12*n*n*l*l*u1(n)+8*n*l*u1(n)*u1(n)-8*rr(n)*rr(n)*n*l-8*rr(n)*rr(n)*u1(n));
+    d(n)=(n^4*l^4+4*n*n*l*l*u1(n)*u1(n)+4*n^3*l^3*u1(n)-4*rr(n)*rr(n)*u1(n)*u1(n)-4*rr(n)*rr(n)*n*n*l*l-8*rr(n)*rr(n)*n*l*u1(n));
+    v2(n)=(-c(n)+sqrt(c(n)*c(n)-4*b(n)*d(n)))/(2*b(n));  
+    the1(n)=atan(rr(n)/v2(n));
+end
+plot(the1)

E_5_3.m

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+%%program to calculate back transverse focal aberration
+u=5000;
+v=30000;
+l=0.632;
+na=1;
+ng=1.5;
+for n=1:1000;
+    a(n)=n*n*l*l+2*n*l*(u+v)+2*u*v;
+    r(n)=sqrt(((a(n)*a(n))-4*u*u*v*v)/(4*(a(n)+u*u+v*v)));
+    t(n)=1000+(r(n)/1000)*1000;
+    theta(n)=atan(r(n)/u);
+    rr(n)=r(n)*((u-t(n))/u);
+    r1(n)=rr(n)+t(n)*tan(asin(na/ng*(sin(atan(r(n)/u)))));
+    u1(n)=u*(r1(n)/r(n));
+    a1(n)=n*n*l*l+2*n*l*(u1(n)+v)+2*u1(n)*v;
+    rr(n)=sqrt(((a1(n)*a1(n))-4*u1(n)*u1(n)*v*v)/(4*(a1(n)+u1(n)*u1(n)+v*v)));
+    b(n)=(4*n*n*l*l+8*n*l*u1(n)-4*r(n)*r(n));
+    c(n)=(4*n^3*l^3+12*n*n*l*l*u1(n)+8*n*l*u1(n)*u1(n)-8*r(n)*r(n)*n*l-8*r(n)*r(n)*u1(n));
+    d(n)=(n^4*l^4+4*n*n*l*l*u1(n)*u1(n)+4*n^3*l^3*u1(n)-4*r(n)*r(n)*u1(n)*u1(n)-4*r(n)*r(n)*n*n*l*l-8*r(n)*r(n)*n*l*u1(n));
+    v2(n)=(-c(n)+sqrt(c(n)*c(n)-4*b(n)*d(n)))/(2*b(n));  
+    the1(n)=atan(rr(n)/v2(n));
+end
+plot(rr)
+

E_6_3_Spiral_phase_plate_binary_axicon.m

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+%Spiral phase plate + axicon
+%Clear all memory
+clear;
+%Define Matrix size
+N=500;
+%Define Matrices by assigning 0 or 1 to all elements
+A1=zeros(N,N);
+A2=ones(N,N);
+r=zeros(N,N);
+%Define focal length and wavelength (in micrometers)
+P=10;
+M=(N/P)*0.5;
+L=10;
+r1=zeros(M,M);
+%Calculate the widths of the grating lines
+for n=1:M;
+    r1(n)=n*P;
+end
+%Scan element by element using two for loops 
+%Define pixels within grating lines with pi
+for n=1:2:M;
+for p=1:N;
+    for q=1:N;
+        r(p,q)=sqrt((p-N/2)*(p-N/2)+(q-N/2)*(q-N/2));
+        if r(p,q)<100;
+        if r(p,q) > r1(n) && r(p,q) < r1(n+1);
+        A1(p,q)=exp(1i*L*(atan2((q-N/2),(p-N/2))));
+        end
+        end
+    end
+end
+end
+%Observing the diffraction pattern
+E=fftshift(fft2(A1));
+I=abs(E).*abs(E);
+colormap(gray)
+imagesc(I)