I try to extract optical constants (complex refractive index) from the spetral reflectance data - R(omiga), the common method is using Kramers-Kronig relations to calculate the Phase information of the reflection - Psi(omiga), then according to the normal reflection coefficients, the complex refractive index can be extracted. But in the practice, I found the results didn't look appropriate, so i guess the phase angle-Phi(omiga) may be calculated uncorrectly, and can not find the mistake for a long time. So, indeed need your expert advice and help, if you have the right tool, can you calculate the results for me? thank you.(adsbygoogle = window.adsbygoogle || []).push({});

Reply for me also can mail to : shayu296@gmail.com , I will be appriciate for your advice.

the main calculate formation as listed below:

The reflectance data is from 200nm to 2500nm measured by spectrophotometer, as listed below.

View attachment Reflectance data.xls

Why the calculated phase angle have positive and negtive values both? that is also the reason why k have positve and negtive values both. I thought maybe the wavelength region is not wide enough, but from some refrences it should can be calculated. Is there something Wrong in my code? but i think it is right ... I am confused by the Kramers-Kronig calculation...

Matlab code:

Code (Text):function[Phi temp]=refphase2(R)

% %2011-07-20

% Phase angle calculation using Kramers-Kronig relation.

% R - measured reflectance data, column 1 is wavelength, column 2 is reflectance

% Phi is the phase angle

% Ref: Kramers-Kronig Transform and Applications.pdf

% Stern, F. 1963. Elementary Optical Properties of Solids. Solid State Phys. vol15:327-340.

% google books: Frederick Seitz,Solid State Physics: Advances in Research and Applications, P337

tic;

wavlen0=length(R); %length of wavelength

wav0=1e7./R(:,1); %wavelength->wavenumber nm -> cm-1

ref0=R(:,2); %reflectance

%interplation

wav=[wav0(1):2*sign(wav0(end)-wav0(1)):wav0(end)]'; %new interval 0.25cm-1

ref=interp1(wav0,ref0,wav,'spline'); %reflectance interplation

wavlen=length(ref);

Phi=zeros(wavlen0,1); %phase angle initialization

temp=[];

for i=1:wavlen0-1

% integration using discrete summing

intsum=0;

g=i

for j=1:wavlen-1

%%%%% if 'wav(j)=wav0(g)' then 'wav(j+1)' replace 'wav(j)', to aviod 'log(0)=-inf'

if wav(j)==wav0(g)

temp(j,i)=(log(ref(j+1))-log(ref(j)))*log(abs((wav(j+1)-wav0(g))/(wav(j)+wav0(g))));

else

temp(j,i)=(log(ref(j+1))-log(ref(j)))*log(abs((wav(j)-wav0(g))/(wav(j)+wav0(g))));

end

intsum=intsum+temp(j,i);

end

Phi(i)=(1/2*pi)*intsum;

end

Phi(wavlen0)=Phi(wavlen0-1);

Phi(1)=2*Phi(2)-Phi(3);

toc

end

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# How extract phase angle from reflectance using Kramers-Kronig

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