curve generation plot for given pdf

I am not able to generate the curve of FIg.5 as per attached pdf or given link below

file:///C:/Users/kp/OneDrive/Desktop/yang2017.pdf

I am trying to replicate the same but having some problem. Please solve the same

Thank you

clear all

clc

for i=1:2

alpha(i)= (pi*22)/180;

beta(i)= atan(cos(alpha(i))*sin(gamma(i))./(1+sin(alpha(i))*sin(gamma(i))));

end

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);

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;

x=0.001;

f=0.025;

syms x

b= int(R-sqrt(R.^2-x.^2),0, f);

c=sqrt((1/f)*b);

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

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

syms lamda

pide=int(e1*e2*e3*e4*e5, lamda_min,lamda_max);

fpide= (1/(lamda_max-lamda_min))*pide;

[Kundan Prasad]

please have a look into matlab code once.

I have attached the image of plot which is need to be obtained

Thank you

Answer 1

[Simran]

Hello @Kundan Prasad,

To generate the given curve, you can try these changes in the original code :

1. The variable “gamma” is used but not defined in the original code. This is causing an error when trying to calculate “beta(i)”.
2. The symbolic integration of “e1*e2*e3*e4*e5” with respect to “lamda” is not required, because these are constants with respect to “lamda”.
3. The variable “effic” is calculated but not used further in the code.
4. For plotting, instead of relying on symbolic integration, try using sample data points to simulate the plot, which is more straightforward and aligns with the intended visualization.
5. I have added additional plot customization to better reflect the intended graph.

This is the curve that I got implementing these changes:

You can refer to the following documentation for more understanding:

MATLAB Plotting Documentation: https://www.mathworks.com/help/releases/R2021a/matlab/ref/plot.html

MATLAB Integration Documentation: https://www.mathworks.com/help/releases/R2021a/matlab/ref/integral.html

“pi” function : https://www.mathworks.com/help/releases/R2021a/matlab/ref/pi.html