plot is showing blank

I am not able to generate the plot. It is showing empty.

Please help me to solve the same

Thank you

clear all
clc
%% calculation of alpha angle
for i=1:2
alpha(i)= (pi*22)/180;
gamma(i)=0;
beta(i)= atan(cos(alpha(i))*sin(gamma(i))./(1+sin(alpha(i))*sin(gamma(i))));
end

%% calculation of thickness
R=0.4;

t(1)= R.*cos(alpha(1))./cot(alpha(1)+ beta(1));
t(2)= R.*cos(alpha(2))./cot(alpha(2)+ beta(2));


%%
n_1=1.49;
theta_1= asin(n_1.*sin(alpha(1)))-alpha(1);
%%
T=0.2;
H_1=0.1;
t(3)= (H_1-t(1)*(tan(alpha(1))-cot(theta_1)))./(cot(theta_1)-tan(alpha(2)));
t(4)= (t(2)*(tan(alpha(2))-cot(theta_1))+ T*(tan(alpha(1))-tan(alpha(2)))-H_1)./(tan(alpha(1))-cot(theta_1));
%%
h(1)=(T-t(1)-t(4))*tan(alpha(1));
h(2)=(T-t(3)-t(2))*tan(alpha(2));
%%
n_2=1.49;
lamda_min=0.004;
lamda_max=0.007;

phase= h(1)*(n_1 -1)./(lamda_min)+ h(2)*(n_2-1)./(lamda_min);

%%

T(1)=0.1;
e1= (sin(pi*((1-(phase/2*pi))))/(pi*((1-(phase/2*pi)))))^2;
e2= (sin(pi*(t(1)/T))/(pi*(t(1)/T)))^2;
e3= (sin(pi*(t(2)/T))/(pi*(t(2)/T)))^2;
e4= (sin(pi*(t(3)/T))/(pi*(t(3)/T)))^2;
e5= (sin(pi*(t(4)/T))/(pi*(t(4)/T)))^2;

%%

% R(j)=linspace(0,0.4,101);

syms x b(x)
f=0.025;
R=0.4;

b(x) = int(R-sqrt(R.^2-x.^2),0, f);
c(x) =sqrt((1/f)*b(x));
x =linspace(0,0.025,100);

e6= exp(((-4*pi*c(x))/lamda_min).^8);

effic= e1*e2*e3*e4*e5*e6;
fplot(effic,[0 0.025]);

% fplot(effic,x);
% efficline(0, 'k')
% syms lamda
% pide=int(e1*e2*e3*e4*e5*e6, lamda_min,lamda_max);
% fpide= (1/(lamda_max-lamda_min))*pide;

[Kundan Prasad]

exactly it is showing the same

[Alberto Cuadra Lara]

Hello Kundan,

If you check effic, you will see that all the values are infinitive, and this is because e6 is also infinitive. You can do the verification by transforming the symbolic variable to double

double(effic)
double(e6)

This is the reason the plot is empty.

Best,

Alberto

Answer 1

[Alberto Cuadra Lara]

Hello Kundan,

Some comments:

• H1, I could not find the value in the paper. See Ref 22. and verify the value.
• R_T is the parametric variable in case you want to reproduce Fig. 5.
• Check per steps the values of the variables and think if it make sense each value.
• Compare a case in which you have final results in order to check that this script works.

Best,

Alberto.

function nu_m_mean = matlab_answers_diffraction()
    % Function that computes the final difracction efficiency from Yang 2017

    % Initialization
    t = zeros(1, 4);
    % Constants
    alpha = (pi*22)/180 * ones(1, 2);
    gamma = zeros(1, 2);
    beta = atan((cos(alpha) .* cos(gamma)) ./ (1 + sin(alpha) .* sin(gamma)));
    n1 = 1.49; % refractive index of substrate material - top
    n2 = 1.49; % refractive index of substrate material - bottom
    T = 100; % [micrometer]
    H1 = 100; % microstructure height of double layer HDEs
    lambda_min = 0.4; % [micrometer]
    lambda_max = 0.7; % [micrometer]
    m = 1; % diffraction order
    f = 1.4; % feed rate [micrometer/r]
    N = 1000;
    R_T_vector = linspace(50, 400, N); % tool radius [micrometer]
    % Compute Mean diffraction efficiency (PIDE)
    for i = length(R_T_vector):-1:1
        R_T = R_T_vector(i);
        nu_m_mean(i) = compute_PIDE;
    end
    % Plot
    plot(R_T_vector, nu_m_mean);
    % NESTED FUNCTION
    function nu_m_mean = compute_PIDE
        % Compute Mean diffraction efficiency (PIDE)
    
        % Diffractive angle
        theta = asin(n1 * sin(alpha(1))) - alpha(1);
        % Distances
        t([1, 3]) = compute_distances_1_3(R_T, alpha([1,2]), beta([1,2]));
        t(2) = compute_distances_2(alpha, t(1), theta, H1);
        t(4) = compute_distances_4(alpha, t(3), theta, H1, T);
        % Effective microstructure heights
        h1 = compute_heights(alpha(1), T, t(1), t(4));
        h2 = compute_heights(alpha(2), T, t(2), t(3));
        % Phase delay
        phi = @(lambda) compute_phase(h1, h2, n1, n2, lambda);
        % Diffraction efficiency with a shadowing effect
        e0 = @(lambda) compute_c(m - phi(lambda)/(2*pi));
        e1 = compute_c(t(1)/T);
        e2 = compute_c(t(2)/T);
        e3 = compute_c(t(3)/T);
        e4 = compute_c(t(4)/T);
        nu_s = @(lambda) e0(lambda) * e1 * e2 * e3 * e4;
        % RMS of the elements
        diamond_tool_profile = @(x) R_T - sqrt(R_T^2 - x.^2);
        sigma = sqrt(1/f * integral(diamond_tool_profile, 0, f));
        % Mean diffraction efficiency (PIDE)
        tau = @(lambda) exp((-4*pi .* sigma ./ lambda).^2);
        nu_m = @(lambda) nu_s(lambda) .* tau(lambda).^4;
        nu_m_mean = 1/(lambda_max - lambda_min) * integral(nu_m, lambda_min, lambda_max);
    end
end

% SUB-PASS FUNCTIONS
function value = compute_distances_1_3(R_T, alpha, beta)
    % Compute distances 1 or 3 (same function)
    value = (R_T * cos(alpha)) ./ cot(alpha + beta);
end

function value = compute_distances_2(alpha, t, theta, H)
    % Compute distance 2
    value = (H - t * (tan(alpha(1)) - cot(theta))) / (cot(theta) - tan(alpha(2)));
end

function value = compute_distances_4(alpha, t, theta, H, T)
    % Compute distance 4
    value = (T * (tan(alpha(1)) - tan(alpha(2))) + t * (tan(alpha(2)) - cot(theta)) - H) / (tan(alpha(1)) - cot(theta));
end

function value = compute_heights(alpha, T, t1, t2)
    % Compute effective microstructure heights
    value = (T - t1 - t2) * tan(alpha);
end

function value = compute_phase(h1, h2, n1, n2, lambda)
    % Compute phase delay
    value = h1./lambda .* (n1 - 1) + h2./lambda .* (n2 - 1);
end

function value = compute_c(x)
    % Compute function c from argument x
    value = (sin(pi * x) / (pi * x))^2;
end

[Kundan Prasad]

Dear Sir,

I have put the value same as mention in the refrence 22.

The attached reference pdf file is given below

file:///D:/silicon/diffractive/diffractive_3_1.pdf

Still i am getting this plot. It is totally different from actual plot.

Please have a look.

Thank you

[Kundan Prasad]

Dear sir,

Still I am not able to plot same as given plot. I have tried by substituting with different value.

Please have a look once sir.

Thank you

Answer 2

[Cris LaPierre]

Your values are all Inf. Consider checking your equations.

%% calculation of alpha angle
for i=1:2
    alpha(i)= (pi*22)/180;
    gamma(i)=0;
    beta(i)= atan(cos(alpha(i))*sin(gamma(i))./(1+sin(alpha(i))*sin(gamma(i))));
end

%% calculation of thickness
R=0.4;

t(1)= R.*cos(alpha(1))./cot(alpha(1)+ beta(1));
t(2)= R.*cos(alpha(2))./cot(alpha(2)+ beta(2));

%%
n_1=1.49;
theta_1= asin(n_1.*sin(alpha(1)))-alpha(1);

%%
T=0.2;
H_1=0.1;
t(3)= (H_1-t(1)*(tan(alpha(1))-cot(theta_1)))./(cot(theta_1)-tan(alpha(2)));
t(4)= (t(2)*(tan(alpha(2))-cot(theta_1))+ T*(tan(alpha(1))-tan(alpha(2)))-H_1)./(tan(alpha(1))-cot(theta_1));

%%
h(1)=(T-t(1)-t(4))*tan(alpha(1));
h(2)=(T-t(3)-t(2))*tan(alpha(2));

%%
n_2=1.49;
lamda_min=0.004;
lamda_max=0.007;

phase= h(1)*(n_1 -1)./(lamda_min)+ h(2)*(n_2-1)./(lamda_min);

%%
T(1)=0.1;
e1= (sin(pi*((1-(phase/2*pi))))/(pi*((1-(phase/2*pi)))))^2;
e2= (sin(pi*(t(1)/T))/(pi*(t(1)/T)))^2;
e3= (sin(pi*(t(2)/T))/(pi*(t(2)/T)))^2;
e4= (sin(pi*(t(3)/T))/(pi*(t(3)/T)))^2;
e5= (sin(pi*(t(4)/T))/(pi*(t(4)/T)))^2;

%%
syms x b(x)
f=0.025;
R=0.4;

b(x) = int(R-sqrt(R.^2-x.^2),0, f);
c(x) =sqrt((1/f)*b(x));
x =linspace(0,0.025,100);

e6= exp(((-4*pi*c(x))/lamda_min).^8);

effic= e1*e2*e3*e4*e5*e6;

% View resulting values
double(subs(effic))

ans = 1×100

Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

[Kundan Prasad]

Dear Sir,

the equation used in the following code are attached below

[Kundan Prasad]

The attached pdf from where equation is taken is provided below

https://in.mathworks.com/matlabcentral/answers/uploaded_files/833770/diifractive-3.pdf

Answer 3

[Alberto Cuadra Lara]

Hello again Kundan,

I have to go and couldn't find the exact error. Some comments:

• Check the value of the constants and units, all in micrometers?
• H1 is less than h1. This cannot be, see Fig. 4.
• Try to include all constants at the beginning of the script. It would be easier for you to evaluate different cases.

I have tried to solve it from scratch, hope this helps.

function nu_m = matlab_answers_diffraction()
    % Function that computes the final difracction efficiency from Yang 2017

    % Initialization
    t = zeros(1, 4);
    % Constants
    alpha = (pi*22)/180 * ones(1, 2);
    gamma = zeros(1, 2);
    beta = atan((cos(alpha) .* cos(gamma)) ./ (1 + sin(alpha) .* sin(gamma)));
    n1 = 1.49; % refractive index of substrate material - top
    n2 = 1.49; % refractive index of substrate material - bottom
    R_T = 10; % [micrometer]
    T = 100; % [micrometer]
    H1 = 50; % microstructure height of double layer HDEs
    lambda_min = 0.004; % [micrometer]
    lambda_max = 0.007; % [micrometer]
    m = 1; 
    f = 0.5; % [micrometer/r]
    % Diffractive angle
    theta = asin(n1 * sin(alpha(1))) - alpha(1);
    % Distances
    t([1, 3]) = compute_distances_1_3(R_T, alpha([1,2]), beta([1,2]));
    t(2) = compute_distances_2(alpha, t(1), theta, H1);
    t(4) = compute_distances_4(alpha, t(3), theta, H1, T);
    % Effective microstructure heights
    h1 = compute_heights(alpha(1), T, t(1), t(4));
    h2 = compute_heights(alpha(2), T, t(2), t(3));
    % Phase delay
    phi = compute_phase(h1, h2, n1, n2, lambda_min);
    % Diffraction efficiency with a shadowing effect
    e0 = compute_c(m - phi/(2*pi));
    e1 = compute_c(t(1)/T);
    e2 = compute_c(t(2)/T);
    e3 = compute_c(t(3)/T);
    e4 = compute_c(t(4)/T);
    nu_s = e0 * e1 * e2 * e3 * e4;
    % RMS of the elements
    dummy_fun = @(x) R_T - sqrt(R_T^2 - x.^2);
    sigma = sqrt(1/f * integral(dummy_fun, 0, f));
    % Final diffraction efficiency
    tau = exp((-4*pi * sigma / lambda_min)^2);
    nu_m = nu_s * tau^4;
end

% SUB-PASS FUNCTIONS
function value = compute_distances_1_3(R_T, alpha, beta)
    % Compute distances 1 or 3 (same function)
    value = (R_T * cos(alpha)) ./ cot(alpha + beta);
end

function value = compute_distances_2(alpha, t, theta, H)
    % Compute distance 2
    value = (H - t * (tan(alpha(1)) - cot(theta))) / (cot(theta) - tan(alpha(2)));
end

function value = compute_distances_4(alpha, t, theta, H, T)
    % Compute distance 4
    value = (T * (tan(alpha(1)) - tan(alpha(2))) + t * (tan(alpha(2)) - cot(theta)) - H) / (tan(alpha(1)) - cot(theta));
end

function value = compute_heights(alpha, T, t1, t2)
    % Compute effective microstructure heights
    value = (T - t1 - t2) * tan(alpha);
end

function value = compute_phase(h1, h2, n1, n2, lambda)
    % Compute phase delay
    value = h1./lambda .* (n1 - 1) + h2./lambda .* (n2 - 1);
end

function value = compute_c(x)
    % Compute function c from argument x
    value = (sin(pi * (x)) / (pi * (x)))^2;
end

[Kundan Prasad]

Dear Sir,

I have spotted the mistake i.e instead of lambda_min = 0.004; lambda_max = 0.007; it should be

lambda_min = 0.4; lambda_max = 0.7;

I want to plot same as fig.5 but i am not able to generate it.

Please have a look once.

Thank you