function start_elevation

% This code enables the analysis of nanolens menisus formed around the
% nanoparticle. A theoretical framework is provided in the following paper
% "Toward giga-pixel nanoscopy on a chip: a computational widefield look at
% the nano-scale without the use of lenses" and written by Ozcan et
% al. This paper can be found under the following link:
% https://doi.org/10.1039/c3lc50222h

% The results from this code are presented and analysed in the following paper "Holographic Detection
% of Nanoparticles using Acoustically Actuated Nanolenses" and written by
% Aniruddha Ray, Muhammad Arslan Khalid, Andriejus Demcenko, Mustafa
% Daloglu, Derek Tseng, Julien Reboud, Jonathan Cooper, and Aydogan Ozcan,
% see Nature Communications 2019.

% The code is developed and implemented by M.A. Khalid and A. Demcenko 2017. The last check
% of this code was performed using Matlab R2018a on the 2nd December 2019.
% To run the code in Matlab, please, type start_dispersion_analysis and press Enter.  


clear all;
j=0;
i=0;

%Radius of the particle range
RawRp = [10e-9:100e-9:510e-9];

%Contact angle range
thetapRaw = [50, 25, 25, 50, 50];
thetasRaw = [10, 2.5, 5, 2.5, 5 ];

for j=1:size(thetapRaw,2)
   
for i=1:size(RawRp,2)
  
    Rp = RawRp(i);

andri = Rp/1000;
thetap=thetapRaw(j)*pi/180;
thetas=thetasRaw(j)*pi/180;


z00=1e-12;
for p=1:1001
    z=Rp-p*andri+andri; 
    Z(p)=z;
    Z0(p)=fsolve(@(z0) elevation(z0,Rp,thetap,thetas),z00);
    z0=Z0(p);
    
    % r(z)
    a=-asinh(cot(thetas));
    beta=(Rp-z0)/sqrt(Rp^2-(Rp-z0)^2);
    b=1/z0*(1/a*asinh((beta*cos(thetap)-sin(thetap))/(beta*sin(thetap)+cos(thetap)))-1);
    r=1/(a*b)*cosh(a*(b*z+1));
    R(p)=r;
    
       
    p;

end
maxR(i) = max(R)+Rp;

    figure(101); hold on;
    plot(R*1e+6,Z*1e6);
    xlabel('\itr\rm [\mum]');
    ylabel('\itz\rm [\mum]');


end
figure(102); hold on;
plot(RawRp*1e+6,maxR*1e6); %drawnow;
xlabel('\itRp \rm [\mum]');
ylabel('\itz\rm [\mum]');
legend(num2str(thetasRaw(j)))
end