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#ifndef MATERIALSTRUCT_H
#define MATERIALSTRUCT_H
#include <vector>
#include <ostream>
#include <iostream>
#include <fstream>
#include <complex>
#include <algorithm>
#include <sstream>
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#include "rts/math/complex.h"
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#include "rts/math/function.h"
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#define PI 3.14159f
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namespace rts{
enum field_type {field_microns, field_wavenumber, field_n, field_k, field_A, field_ignore};
//conversion functions
//convert wavenumber to lambda
template <class T>
static T _wn(T inverse_cm)
{
return (T)10000.0/inverse_cm;
}
template <class T>
static T _2wn(T lambda)
{
return (T)10000.0/lambda;
}
//convert absorbance to k
template <class T>
static T _A(T absorbance, T lambda)
{
return (absorbance * lambda) / (4 * PI);
}
template <class T>
static T _2A(T k, T lambda)
{
return (4 * PI * k)/lambda;
}
//define the dispersion as a single wavelength/refractive index pair
template <class T>
struct refIndex
{
//wavelength (in microns)
T lambda;
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complex<T> n;
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};
template <class T>
struct entryType
{
//list of value types per entry
std::vector<field_type> valueList;
entryType(std::string format)
{
//location of the end of a parameter
size_t e;
//string storing a token
std::string token;
do
{
//find the end of the first parameter
e = format.find_first_of(',');
//get the substring up to the comma
token = format.substr(0, e);
//turn the token into a val_type
if(token == "microns")
valueList.push_back(field_microns);
else if(token == "wavenumber")
valueList.push_back(field_wavenumber);
else if(token == "n")
valueList.push_back(field_n);
else if(token == "k")
valueList.push_back(field_k);
else if(token == "A")
valueList.push_back(field_A);
else
valueList.push_back(field_ignore);
//remove the first token from the format string
format = format.substr(e+1, format.length()-1);
}while(e != std::string::npos);
}
void addValue(field_type value)
{
valueList.push_back(value);
}
refIndex<T> inputEntry(std::string line, T scaleA = 1.0)
{
T val;
std::stringstream ss(line);
//create a new refractive index
refIndex<T> newRI;
//read the entry from an input string
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for(unsigned int i=0; i<valueList.size(); i++)
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{
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while(ss.peek() < '0' || ss.peek() > '9')
{
//cout<<"bad char"<<endl;
ss.ignore();
}
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//retrieve the value
ss>>val;
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//cout<<val<<endl;
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//store the value in the appropriate location
switch(valueList[i])
{
case field_microns:
newRI.lambda = val;
break;
case field_wavenumber:
newRI.lambda = _wn(val);
break;
case field_n:
newRI.n.real(val);
break;
case field_k:
newRI.n.imag(val);
break;
case field_A:
newRI.n.imag(_A(val * scaleA, newRI.lambda));
break;
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default:
break;
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}
}
//return the refractive index associated with the entry
return newRI;
}
std::string outputEntry(refIndex<T> material)
{
//std::string result;
std::stringstream ss;
//for each field in the entry
for(int i=0; i<valueList.size(); i++)
{
if(i > 0)
ss<<"\t";
//store the value in the appropriate location
switch(valueList[i])
{
case field_microns:
ss<<material.lambda;
break;
case field_wavenumber:
ss<<_2wn(material.lambda);
break;
case field_n:
ss<<material.n.real();
break;
case field_k:
ss<<material.n.imag();
break;
case field_A:
ss<<_2A(material.n.imag(), material.lambda);
break;
}
}
return ss.str();
}
};
//a material is a list of refractive index values
template <class T>
class material
{
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std::string name;
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//dispersion (refractive index as a function of wavelength)
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//std::vector< refIndex<T> > dispersion;
function< T, complex<T> > dispersion;
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//average refractive index (approximately 1.4)
T n0;
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/*void add(refIndex<T> ri)
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{
//refIndex<T> converted = convert(ri, measurement);
dispersion.push_back(ri);
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}*/
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//comparison function for sorting
static bool compare(refIndex<T> a, refIndex<T> b)
{
return (a.lambda < b.lambda);
}
//comparison function for searching lambda
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/*static bool findCeiling(refIndex<T> a, refIndex<T> b)
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{
return (a.lambda > b.lambda);
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}*/
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public:
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void add(T lambda, complex<T> n)
{
dispersion.insert(lambda, n);
}
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std::string getName()
{
return name;
}
void setName(std::string n)
{
name = n;
}
T getN0()
{
return n0;
}
void setN0(T n)
{
n0 = n;
}
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void setM(function< T, complex<T> > m)
{
dispersion = m;
}
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unsigned int nSamples()
{
return dispersion.size();
}
material<T> computeN(T _n0, unsigned int n_samples = 0, T pf = 2)
{
/* This function computes the real part of the refractive index
from the imaginary part. The Hilbert transform is required. I
use an FFT in order to simplify this, so either the FFTW or CUFFT
packages are required. CUFFT is used if this file is passed through
a CUDA compiler. Otherwise, FFTW is used if available.
*/
n0 = _n0;
int N;
if(n_samples)
N = n_samples;
else
N = dispersion.size();
#ifdef FFTW_AVAILABLE
//allocate memory for the FFT
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complex<T>* Chi2 = (complex<T>*)fftw_malloc(sizeof(complex<T>) * N * pf);
complex<T>* Chi2FFT = (complex<T>*)fftw_malloc(sizeof(complex<T>) * N * pf);
complex<T>* Chi1 = (complex<T>*)fftw_malloc(sizeof(complex<T>) * N * pf);
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//create an FFT plan for the forward and inverse transforms
fftw_plan planForward, planInverse;
planForward = fftw_plan_dft_1d(N*pf, (fftw_complex*)Chi2, (fftw_complex*)Chi2FFT, FFTW_FORWARD, FFTW_ESTIMATE);
planInverse = fftw_plan_dft_1d(N*pf, (fftw_complex*)Chi2FFT, (fftw_complex*)Chi1, FFTW_BACKWARD, FFTW_ESTIMATE);
float k, alpha;
T chi_temp;
//the spectrum will be re-sampled in uniform values of wavenumber
T nuMin = _2wn(dispersion.back().lambda);
T nuMax = _2wn(dispersion.front().lambda);
T dnu = (nuMax - nuMin)/(N-1);
T lambda, tlambda;
for(int i=0; i<N; i++)
{
//go from back-to-front (wavenumber is the inverse of wavelength)
lambda = _wn(nuMax - i * dnu);
//compute the frequency
k = 2 * PI / (lambda);
//get the absorbance
alpha = getN(lambda).imag() * (2 * k);
//compute chi2
Chi2[i] = -alpha * (n0 / k);
}
//use linear interpolation between the start and end points to pad the spectrum
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//complex<T> nMin = dispersion.back();
//complex<T> nMax = dispersion.front();
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T a;
for(int i=N; i<N*pf; i++)
{
//a = (T)(i-N)/(T)(N*pf - N);
//Chi2[i] = a * Chi2[0] + ((T)1 - a) * Chi2[N-1];
Chi2[i] = 0.0;//Chi2[N-1];
}
//perform the FFT
fftw_execute(planForward);
//perform the Hilbert transform in the Fourier domain
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complex<T> j(0, 1);
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for(int i=0; i<N*pf; i++)
{
//if w = 0, set the DC component to zero
if(i == 0)
Chi2FFT[i] *= (T)0.0;
//if w <0, multiply by i
else if(i < N*pf/2.0)
Chi2FFT[i] *= j;
//if i > N/2, multiply by -i
else
Chi2FFT[i] *= -j;
}
//execute the inverse Fourier transform (completing the Hilbert transform)
fftw_execute(planInverse);
//divide the Chi1 values by N
for(int i=0; i<N*pf; i++)
Chi1[i] /= (T)(N*pf);
//create a new material
material<T> newM;
newM.dispersion.clear();
refIndex<T> ri;
for(int i=0; i<N; i++)
{
ri.lambda = _wn(nuMax - i * dnu);
ri.n.real(Chi1[i].real() / (2 * n0) + n0);
ri.n.imag(getN(ri.lambda).imag());
newM.dispersion.push_back(ri);
}
//dispersion[i].n.real(Chi1[i].real() / (2 * n0) + n0);
/*//output the Absorbance value
ofstream outOrig("origN.txt");
for(int i=0; i<N; i++)
outOrig<<dispersion[i].lambda<<" "<<dispersion[i].n.real()<<endl;
//output the Chi2 value
ofstream outChi2("chi2.txt");
for(int i=0; i<N; i++)
outChi2<<dispersion[i].lambda<<" "<<Chi2[i].real()<<endl;
//output the Fourier transform
ofstream outFFT("chi2_FFT.txt");
for(int i=0; i<N; i++)
{
float mag = std::sqrt( std::pow(Chi2FFT[i].real(), 2.0) + std::pow(Chi2FFT[i].imag(), 2.0));
outFFT<<dispersion[i].lambda<<" "<<mag<<endl;
}
//output the computed Chi1 value
ofstream outChi1("chi1.txt");
for(int i=0; i<N; i++)
{
outChi1<<dispersion[i].lambda<<" "<<Chi1[i].real()<<" "<<Chi1[i].imag()<<endl;
}
ofstream outN("n.txt");
for(int i=0; i<N; i++)
outN<<dispersion[i].lambda<<" "<<Chi1[i].real() / (2 * n0) + n0<<endl;*/
//de-allocate memory
fftw_destroy_plan(planForward);
fftw_destroy_plan(planInverse);
fftw_free(Chi2);
fftw_free(Chi2FFT);
fftw_free(Chi1);
return newM;
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#else
std::cout<<"MATERIAL Error: Must have FFTW in order to compute Kramers-Kronig."<<std::endl;
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return material<T>();
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#endif
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}
material(T lambda = 1.0, T n = 1.4, T k = 0.0)
{
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dispersion.insert(lambda, complex<T>(0.0, k));
/*//create a default refractive index
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refIndex<T> def;
def.lambda = lambda;
def.n.real(n);
def.n.imag(k);
add(def);
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*/
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//set n0
n0 = n;
}
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material(std::string filename, std::string format = "", T scaleA = 1.0)
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{
fromFile(filename, format);
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n0 = 0;
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}
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void fromFile(std::string filename, std::string format = "", T scaleA = 1.0)
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{
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name = filename;
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//clear any previous values
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dispersion = rts::function< T, complex<T> >();
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//load the file into a string
std::ifstream ifs(filename.c_str());
std::string line;
if(!ifs.is_open())
{
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std::cout<<"Material Error -- file not found: "<<filename<<std::endl;
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exit(1);
}
//process the file as a string
std::string instr((std::istreambuf_iterator<char>(ifs)), std::istreambuf_iterator<char>());
fromStr(instr, format, scaleA);
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}
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void fromStr(std::string str, std::string format = "", T scaleA = 1.0)
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{
//create a string stream to process the input data
std::stringstream ss(str);
//this string will be read line-by-line (where each line is an entry)
std::string line;
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//if the format is not provided, see if it is in the file, otherwise use a default
if(format == "")
{
//set a default format of "lambda,n,k"
format = "microns,n,k";
//see if the first line is a comment
char c = ss.peek();
if(c == '#')
{
//get the first line
getline(ss, line);
//look for a bracket, denoting the start of a format string
int istart = line.find('[');
if(istart != std::string::npos)
{
//look for a bracket terminating the format string
int iend = line.find(']');
if(iend != std::string::npos)
{
//read the string between the brackets
format = line.substr(istart+1, iend - istart - 1);
}
}
}
}
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entryType<T> entry(format);
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//std::cout<<"Loading material with format: "<<format<<std::endl;
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while(!ss.eof())
{
//read a line from the string
getline(ss, line);
//if the line is not a comment, process it
if(line[0] != '#')
{
//load the entry and add it to the dispersion list
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add(entry.inputEntry(line, scaleA).lambda, entry.inputEntry(line, scaleA).n);
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}
//generally have to peek to trigger the eof flag
ss.peek();
}
//sort the vector by lambda
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//sort(dispersion.begin(), dispersion.end(), &material<T>::compare);
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}
//convert the material to a string
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std::string toStr(std::string format = "microns,n,k", bool reverse_order = false)
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{
std::stringstream ss;
entryType<T> entry(format);
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if(reverse_order)
{
for(int l=dispersion.size() - 1; l>=0; l--)
{
if(l < dispersion.size() - 1) ss<<std::endl;
ss<<entry.outputEntry(dispersion[l]);
}
}
else
{
for(unsigned int l=0; l<dispersion.size(); l++)
{
if(l > 0) ss<<std::endl;
ss<<entry.outputEntry(dispersion[l]);
}
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}
return ss.str();
}
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void save(std::string filename, std::string format = "microns,n,k", bool reverse_order = false)
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{
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std::ofstream outfile(filename.c_str());
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outfile<<"#material file saved as [" + format + "]"<<std::endl;
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outfile<<toStr(format, reverse_order)<<std::endl;
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}
//convert between wavelength and wavenumber
/*void nu2lambda(T s = (T)1)
{
for(int i=0; i<dispersion.size(); i++)
dispersion[i].lambda = s/dispersion[i].lambda;
}
void lambda2nu(T s = (T)1)
{
for(int i=0; i<dispersion.size(); i++)
dispersion[i].lambda = s/dispersion[i].lambda;
}*/
refIndex<T>& operator[](unsigned int i)
{
return dispersion[i];
}
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complex<T> getN(T l)
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{
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//return complex<T>(1.0, 0.0);
complex<T> ri = dispersion.linear(l) + n0;
return ri;
}
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function<T, complex<T> > getF()
{
return dispersion + complex<T>(n0, 0.0);
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}
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//returns the scattering efficiency at wavelength l
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complex<T> eta(T l)
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{
//get the refractive index
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complex<T> ri = getN(l);
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//convert the refractive index to scattering efficiency
return ri*ri - 1.0;
}
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//interpolate the given lambda value and return the index of refraction
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complex<T> operator()(T l)
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{
return getN(l);
}
};
} //end namespace rts
template <typename T>
std::ostream& operator<<(std::ostream& os, rts::material<T> m)
{
os<<m.toStr();
return os;
}
#endif
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