Plot: How to reflect a curve and multiply by another curve to produce 3d plot.

Hello,

1. I am looking to reflect a curve that I have generated (see below for reference) about y=50 ( a vertical line)

Result should be a "U" shaped curve

2. And then multiply that to a generated guassian beam shown below:

= To produce a 3d ( probably a mesh) of the resultant. Expecting a cylinder as the product.

Kindly requesting help with 1 .reflection and 2. multiplication part.

Below is my code of the

1. Curve to be reflected and

2. The guassian beam that should be multipled with the above resulting U shaped curve after reflection.

%% Plotting the curve to be reflected

clc

clear

clear all

clear var

close all

% Known

Io = 1;

z_Cu = 1800; % microns

z_PMMA = 50; % microns

% Absorption coefficient, mu

lamda = 7.1255e-5; %micron

k = (2*pi)/lamda; % (micron)^-1

beta_Cu = 2.590970004E-07; % From https://henke.lbl.gov/optical_constants/

beta_PMMA = 5.03136866E-10; % From https://henke.lbl.gov/optical_constants/

% Absorption coefficient, mu = 2*beta*k

mu_Cu = beta_Cu*2*k; %(micron)^-1

mu_PMMA = beta_PMMA*2*k; %(micron)^-1

% Generating the Curve to be reflected

% I = Io*e −[(µ1+µ1)*(z1+z2)]

start = 0;

End =50;

points = 50 % for micron steps

steps = (z_Cu+z_PMMA)/(points-1);

for i=1:points

% I(i) = Io*exp(-1*(mu_PMMA+mu_Cu)*(steps*(i-1)));

I_wt(i)=Io*exp(-1*(0.025*mu_PMMA+0.975*mu_Cu)*(steps*(i-1)));

end

figure(1)

plot(I_wt,'r')

title(' Transmission Intensity weight composition for Cu wire')

grid on

grid minor

set(gca,'YLim',[0,1]);

yticks(0 :0.1 :1)

set(gca,'XLim',[0,100]);

xticks(0 :10 :100)

%set(gca,'XTick',x)

xlabel('$\Delta z$ (microns)','interpreter','latex');

ylabel('$I$ $\frac{i}{i_0}$ (arb.)','interpreter','latex');

%% Reflection of the above curve

% Reflect the curve y=50

% NEED HELP!!

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55

%% Generating a Guass beam to multiple with the U shaped resulting curve after refection

clear all

clear

clc

clear var

xrange = 2;

yrange = 2;

xo =1;

yo=1;

xpoints=200;

ypoints=200;

xinc = xrange/(xpoints-1);

yinc = yrange/(ypoints-1);

for ii = 1:xpoints

x(ii)= 1-xrange + xinc*(ii-1);

for jj = 1: ypoints

y(jj) = 1-yrange + yinc*(jj-1);

% z(ii,jj)=((x(ii))^2 + (y(ii))^2);%

z(ii,jj)=x(ii)*y(jj);

I(ii,jj) = exp((-1*z(ii,jj)^2));

% I(ii,jj) = exp(-1*((x(ii) -xo)^2 + (y(ii) - yo)^2));

end

end

%% Plotting the resulting 3d image /mes

% NEED HELP - Would expect a cylindrical image as the result of multiplying

% the above curves

Answer 1

[William Rose]

@Anand Rathnam,

You said you imagine a cylinder. That suggests you want to rotate the reflected 2D curve about its middle. Is that correct? The Gaussian surface covers a square area. How do you want to handle the corners of the square 2D Gaussian? Or, to put it another way, how fdo you want to extend the cylinder obtained by rotating the U into the corners of a square area?

When reflected, the 1D curve will span 100 um. The 2D Gaussian is 50 x 50 um. If you center the 100 um wide cylinder over the 50x50 Gaussian, the edges of the cylinder (the non-zero parts) will be outside the 50x50 um Gaussian. Therefore please clarify how you want to scale the sizes of the two surfaces.

Or do you want a 2D convolution of two 2D functions?

More in a bit.

[William Rose]

@Anand Rathnam, Can you explain in physical terms what you are trynng to do? See the attached comments. The initial curve apears to be a plot of x ray intensity versus depth, for 50 steps from x=0 to 1850 um. The absorption coefficient appears to be a weighted average of the absorptions of copper and PMMA, weighted 39 parts Cu and 1 part PMMA. Is this for x ray of a composite material?

Why would you want to reflect this curve? What is the physical iterpretation? Illumunaiton from two side of a thin sheet with a half-thickness of 1.85 mm? Illumination of a wire of radius 1.85 mm, as the wire slowly spins about its axis?

What is the physical meaning of multiplying the intensity versus depth funciton by the 2D Gaussian? It would be easier to understand, if you specify the physical units for each of the functions: I(x) and the Gaussian. The final units will be the product of the units for each function. Do those units make sense?

I recommend plotting I(x) versus x (where x=0..1850), rather than plotting I(bin) versus bin number. By using x instead of bin number, the proportions of the problem become evident. Do the same for the 2D Gaussian. What are the x and y values, in um, along the bottom edges of the Gaussian plot?

[Anand Ra]

@William Rose Thanks a lot for the response. Attached is my reply to your questions. I will try to add more if possible to explain further. Thanks for the help.

[Anand Ra]

@William Rose . I included another drawing ( in yellow background/sheet) to further explain what I am trying to do. Not sure if you looked at the previous attachment, so appending the drawing to the above document Response 1-5.10.22 and uploading it again as Response 2 -5.10.22

[Anand Ra]

I know I still have some questions unanswered. will keep you posted.

[William Rose]

Please email me [e-mail].