///
/// @file nmie.cc
/// @author Ladutenko Konstantin <kostyfisik at gmail (.) com>
/// @date Tue Sep 3 00:38:27 2013
/// @copyright 2013 Ladutenko Konstantin
///
/// nmie is free software: you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation, either version 3 of the License, or
/// (at your option) any later version.
///
/// nmie-wrapper is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with nmie-wrapper. If not, see <http://www.gnu.org/licenses/>.
///
/// nmie uses nmie.c from scattnlay by Ovidio Pena
/// <ovidio@bytesfall.com> . He has an additional condition to
/// his library:
// The only additional condition is that we expect that all publications //
// describing work using this software , or all commercial products //
// using it, cite the following reference: //
// [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
// a multilayered sphere," Computer Physics Communications, //
// vol. 180, Nov. 2009, pp. 2348-2354. //
///
/// @brief Wrapper class around nMie function for ease of use
///
#include "nmie-wrapper.h"
#include <array>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <stdexcept>
#include <vector>
namespace nmie {
//helpers
template<class T> inline T pow2(const T value) {return value*value;}
//#define round(x) ((x) >= 0 ? (int)((x) + 0.5):(int)((x) - 0.5))
int round(double x) {
return x >= 0 ? (int)(x + 0.5):(int)(x - 0.5);
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
//emulate C call.
int nMie_wrapper(int L, const std::vector<double>& x, const std::vector<std::complex<double> >& m,
int nTheta, const std::vector<double>& Theta,
double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo,
std::vector<std::complex<double> >& S1, std::vector<std::complex<double> >& S2) {
if (x.size() != L || m.size() != L)
throw std::invalid_argument("Declared number of layers do not fit x and m!");
if (Theta.size() != nTheta)
throw std::invalid_argument("Declared number of sample for Theta is not correct!");
try {
MultiLayerMie multi_layer_mie;
multi_layer_mie.SetWidthSP(x);
multi_layer_mie.SetIndexSP(m);
multi_layer_mie.SetAngles(Theta);
multi_layer_mie.RunMieCalculations();
*Qext = multi_layer_mie.GetQext();
*Qsca = multi_layer_mie.GetQsca();
*Qabs = multi_layer_mie.GetQabs();
*Qbk = multi_layer_mie.GetQbk();
*Qpr = multi_layer_mie.GetQpr();
*g = multi_layer_mie.GetAsymmetryFactor();
*Albedo = multi_layer_mie.GetAlbedo();
S1 = multi_layer_mie.GetS1();
S2 = multi_layer_mie.GetS2();
//multi_layer_mie.GetFailed();
} catch( const std::invalid_argument& ia ) {
// Will catch if multi_layer_mie fails or other errors.
std::cerr << "Invalid argument: " << ia.what() << std::endl;
throw std::invalid_argument(ia);
return -1;
}
return 0;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::GetFailed() {
double faild_x = 9.42477796076938;
//double faild_x = 9.42477796076937;
std::complex<double> z(faild_x, 0.0);
std::vector<int> nmax_local_array = {20, 100, 500, 2500};
for (auto nmax_local : nmax_local_array) {
std::vector<std::complex<double> > D1_failed(nmax_local +1);
// Downward recurrence for D1 - equations (16a) and (16b)
D1_failed[nmax_local] = std::complex<double>(0.0, 0.0);
const std::complex<double> zinv = std::complex<double>(1.0, 0.0)/z;
for (int n = nmax_local; n > 0; n--) {
D1_failed[n - 1] = double(n)*zinv - 1.0/(D1_failed[n] + double(n)*zinv);
}
printf("Faild D1[0] from reccurence (z = %16.14f, nmax = %d): %g\n",
faild_x, nmax_local, D1_failed[0].real());
}
printf("Faild D1[0] from continued fraction (z = %16.14f): %g\n", faild_x,
calcD1confra(0,z).real());
//D1[nmax_] = calcD1confra(nmax_, z);
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetQext() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qext_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetQabs() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qabs_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<double> MultiLayerMie::GetQabs_channel() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qabs_ch_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<double> MultiLayerMie::GetQabs_channel_normalized() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
// std::vector<double> NACS(nmax_-1, 0.0);
// double x2 = pow2(size_parameter_.back());
// for (int i = 0; i < nmax_ - 1; ++i) {
// const int n = i+1;
// NACS[i] = Qabs_ch_[i]*x2/(2.0*(2.0*static_cast<double>(n)+1));
// // if (NACS[i] > 0.250000001)
// // throw std::invalid_argument("Unexpected normalized absorption cross-section value!");
// }
//return NACS;
return Qabs_ch_norm_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetQsca() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qsca_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<double> MultiLayerMie::GetQsca_channel() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qsca_ch_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<double> MultiLayerMie::GetQsca_channel_normalized() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
// std::vector<double> NACS(nmax_-1, 0.0);
// double x2 = pow2(size_parameter_.back());
// for (int i = 0; i < nmax_ - 1; ++i) {
// const int n = i+1;
// NACS[i] = Qsca_ch_[i]*x2/(2.0*(2.0*static_cast<double>(n)+1.0));
// }
// return NACS;
return Qsca_ch_norm_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetQbk() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qbk_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetQpr() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return Qpr_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetAsymmetryFactor() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return asymmetry_factor_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetAlbedo() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return albedo_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<std::complex<double> > MultiLayerMie::GetS1() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return S1_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector<std::complex<double> > MultiLayerMie::GetS2() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
return S2_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::AddTargetLayer(double width, std::complex<double> layer_index) {
isMieCalculated_ = false;
if (width <= 0)
throw std::invalid_argument("Layer width should be positive!");
target_width_.push_back(width);
target_index_.push_back(layer_index);
} // end of void MultiLayerMie::AddTargetLayer(...)
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetTargetPEC(double radius) {
isMieCalculated_ = false;
if (target_width_.size() != 0 || target_index_.size() != 0)
throw std::invalid_argument("Error! Define PEC target radius before any other layers!");
// Add layer of any index...
AddTargetLayer(radius, std::complex<double>(0.0, 0.0));
// ... and mark it as PEC
SetPEC(0.0);
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetCoatingIndex(std::vector<std::complex<double> > index) {
isMieCalculated_ = false;
coating_index_.clear();
for (auto value : index) coating_index_.push_back(value);
} // end of void MultiLayerMie::SetCoatingIndex(std::vector<complex> index);
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetAngles(const std::vector<double>& angles) {
isMieCalculated_ = false;
theta_ = angles;
// theta_.clear();
// for (auto value : angles) theta_.push_back(value);
} // end of SetAngles()
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetCoatingWidth(std::vector<double> width) {
isMieCalculated_ = false;
coating_width_.clear();
for (auto w : width)
if (w <= 0)
throw std::invalid_argument("Coating width should be positive!");
else coating_width_.push_back(w);
}
// end of void MultiLayerMie::SetCoatingWidth(...);
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetWidthSP(const std::vector<double>& size_parameter) {
isMieCalculated_ = false;
size_parameter_.clear();
double prev_size_parameter = 0.0;
for (auto layer_size_parameter : size_parameter) {
if (layer_size_parameter <= 0.0)
throw std::invalid_argument("Size parameter should be positive!");
if (prev_size_parameter > layer_size_parameter)
throw std::invalid_argument
("Size parameter for next layer should be larger than the previous one!");
prev_size_parameter = layer_size_parameter;
size_parameter_.push_back(layer_size_parameter);
}
}
// end of void MultiLayerMie::SetWidthSP(...);
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetIndexSP(const std::vector< std::complex<double> >& index) {
isMieCalculated_ = false;
//index_.clear();
index_ = index;
// for (auto value : index) index_.push_back(value);
} // end of void MultiLayerMie::SetIndexSP(...);
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetPEC(int layer_position) {
isMieCalculated_ = false;
if (layer_position < 0)
throw std::invalid_argument("Error! Layers are numbered from 0!");
PEC_layer_position_ = layer_position;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::SetMaxTermsNumber(int nmax) {
isMieCalculated_ = false;
nmax_preset_ = nmax;
//debug
printf("Setting max terms: %d\n", nmax_preset_);
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::GenerateSizeParameter() {
isMieCalculated_ = false;
size_parameter_.clear();
double radius = 0.0;
for (auto width : target_width_) {
radius += width;
size_parameter_.push_back(2*PI*radius / wavelength_);
}
for (auto width : coating_width_) {
radius += width;
size_parameter_.push_back(2*PI*radius / wavelength_);
}
total_radius_ = radius;
} // end of void MultiLayerMie::GenerateSizeParameter();
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::GenerateIndex() {
isMieCalculated_ = false;
index_.clear();
for (auto index : target_index_) index_.push_back(index);
for (auto index : coating_index_) index_.push_back(index);
} // end of void MultiLayerMie::GenerateIndex();
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
double MultiLayerMie::GetTotalRadius() {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
if (total_radius_ == 0) GenerateSizeParameter();
return total_radius_;
} // end of double MultiLayerMie::GetTotalRadius();
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
std::vector< std::vector<double> >
MultiLayerMie::GetSpectra(double from_WL, double to_WL, int samples) {
if (!isMieCalculated_)
throw std::invalid_argument("You should run calculations before result request!");
std::vector< std::vector<double> > spectra;
double step_WL = (to_WL - from_WL)/ static_cast<double>(samples);
double wavelength_backup = wavelength_;
long fails = 0;
for (double WL = from_WL; WL < to_WL; WL += step_WL) {
wavelength_ = WL;
try {
RunMieCalculations();
} catch( const std::invalid_argument& ia ) {
fails++;
continue;
}
//printf("%3.1f ",WL);
spectra.push_back(std::vector<double>({wavelength_, Qext_, Qsca_, Qabs_, Qbk_}));
} // end of for each WL in spectra
printf("Spectrum has %li fails\n",fails);
wavelength_ = wavelength_backup;
return spectra;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::ClearTarget() {
isMieCalculated_ = false;
target_width_.clear();
target_index_.clear();
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::ClearCoating() {
isMieCalculated_ = false;
coating_width_.clear();
coating_index_.clear();
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::ClearLayers() {
isMieCalculated_ = false;
ClearTarget();
ClearCoating();
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::ClearAllDesign() {
isMieCalculated_ = false;
ClearLayers();
size_parameter_.clear();
index_.clear();
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Computational core
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Calculate Nstop - equation (17)
//
void MultiLayerMie::Nstop() {
const double& xL = size_parameter_.back();
if (xL <= 8) {
nmax_ = round(xL + 4.0*pow(xL, 1.0/3.0) + 1);
} else if (xL <= 4200) {
nmax_ = round(xL + 4.05*pow(xL, 1.0/3.0) + 2);
} else {
nmax_ = round(xL + 4.0*pow(xL, 1.0/3.0) + 2);
}
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::Nmax(int first_layer) {
int ri, riM1;
const std::vector<double>& x = size_parameter_;
const std::vector<std::complex<double> >& m = index_;
Nstop(); // Set initial nmax_ value
for (int i = first_layer; i < x.size(); i++) {
if (i > PEC_layer_position_)
ri = round(std::abs(x[i]*m[i]));
else
ri = 0;
nmax_ = std::max(nmax_, ri);
// first layer is pec, if pec is present
if ((i > first_layer) && ((i - 1) > PEC_layer_position_))
riM1 = round(std::abs(x[i - 1]* m[i]));
else
riM1 = 0;
nmax_ = std::max(nmax_, riM1);
}
nmax_ += 15; // Final nmax_ value
}
//**********************************************************************************//
// This function calculates the spherical Bessel (jn) and Hankel (h1n) functions //
// and their derivatives for a given complex value z. See pag. 87 B&H. //
// //
// Input parameters: //
// z: Real argument to evaluate jn and h1n //
// nmax_: Maximum number of terms to calculate jn and h1n //
// //
// Output parameters: //
// jn, h1n: Spherical Bessel and Hankel functions //
// jnp, h1np: Derivatives of the spherical Bessel and Hankel functions //
// //
// The implementation follows the algorithm by I.J. Thompson and A.R. Barnett, //
// Comp. Phys. Comm. 47 (1987) 245-257. //
// //
// Complex spherical Bessel functions from n=0..nmax_-1 for z in the upper half //
// plane (Im(z) > -3). //
// //
// j[n] = j/n(z) Regular solution: j[0]=sin(z)/z //
// j'[n] = d[j/n(z)]/dz //
// h1[n] = h[0]/n(z) Irregular Hankel function: //
// h1'[n] = d[h[0]/n(z)]/dz h1[0] = j0(z) + i*y0(z) //
// = (sin(z)-i*cos(z))/z //
// = -i*exp(i*z)/z //
// Using complex CF1, and trigonometric forms for n=0 solutions. //
//**********************************************************************************//
void MultiLayerMie::sbesjh(std::complex<double> z,
std::vector<std::complex<double> >& jn,
std::vector<std::complex<double> >& jnp,
std::vector<std::complex<double> >& h1n,
std::vector<std::complex<double> >& h1np) {
const int limit = 20000;
const double accur = 1.0e-12;
const double tm30 = 1e-30;
double absc;
std::complex<double> zi, w;
std::complex<double> pl, f, b, d, c, del, jn0, jndb, h1nldb, h1nbdb;
absc = std::abs(std::real(z)) + std::abs(std::imag(z));
if ((absc < accur) || (std::imag(z) < -3.0)) {
throw std::invalid_argument("TODO add error description for condition if ((absc < accur) || (std::imag(z) < -3.0))");
}
zi = 1.0/z;
w = zi + zi;
pl = double(nmax_)*zi;
f = pl + zi;
b = f + f + zi;
d = 0.0;
c = f;
for (int n = 0; n < limit; n++) {
d = b - d;
c = b - 1.0/c;
absc = std::abs(std::real(d)) + std::abs(std::imag(d));
if (absc < tm30) {
d = tm30;
}
absc = std::abs(std::real(c)) + std::abs(std::imag(c));
if (absc < tm30) {
c = tm30;
}
d = 1.0/d;
del = d*c;
f = f*del;
b += w;
absc = std::abs(std::real(del - 1.0)) + std::abs(std::imag(del - 1.0));
if (absc < accur) {
// We have obtained the desired accuracy
break;
}
}
if (absc > accur) {
throw std::invalid_argument("We were not able to obtain the desired accuracy");
}
jn[nmax_ - 1] = tm30;
jnp[nmax_ - 1] = f*jn[nmax_ - 1];
// Downward recursion to n=0 (N.B. Coulomb Functions)
for (int n = nmax_ - 2; n >= 0; n--) {
jn[n] = pl*jn[n + 1] + jnp[n + 1];
jnp[n] = pl*jn[n] - jn[n + 1];
pl = pl - zi;
}
// Calculate the n=0 Bessel Functions
jn0 = zi*std::sin(z);
h1n[0] = std::exp(std::complex<double>(0.0, 1.0)*z)*zi*(-std::complex<double>(0.0, 1.0));
h1np[0] = h1n[0]*(std::complex<double>(0.0, 1.0) - zi);
// Rescale j[n], j'[n], converting to spherical Bessel functions.
// Recur h1[n], h1'[n] as spherical Bessel functions.
w = 1.0/jn[0];
pl = zi;
for (int n = 0; n < nmax_; n++) {
jn[n] = jn0*(w*jn[n]);
jnp[n] = jn0*(w*jnp[n]) - zi*jn[n];
if (n != 0) {
h1n[n] = (pl - zi)*h1n[n - 1] - h1np[n - 1];
// check if hankel is increasing (upward stable)
if (std::abs(h1n[n]) < std::abs(h1n[n - 1])) {
jndb = z;
h1nldb = h1n[n];
h1nbdb = h1n[n - 1];
}
pl += zi;
h1np[n] = -(pl*h1n[n]) + h1n[n - 1];
}
}
}
//**********************************************************************************//
// This function calculates the spherical Bessel functions (bj and by) and the //
// logarithmic derivative (bd) for a given complex value z. See pag. 87 B&H. //
// //
// Input parameters: //
// z: Complex argument to evaluate bj, by and bd //
// nmax_: Maximum number of terms to calculate bj, by and bd //
// //
// Output parameters: //
// bj, by: Spherical Bessel functions //
// bd: Logarithmic derivative //
//**********************************************************************************//
void MultiLayerMie::sphericalBessel(std::complex<double> z,
std::vector<std::complex<double> >& bj,
std::vector<std::complex<double> >& by,
std::vector<std::complex<double> >& bd) {
std::vector<std::complex<double> > jn(nmax_), jnp(nmax_), h1n(nmax_), h1np(nmax_);
sbesjh(z, jn, jnp, h1n, h1np);
for (int n = 0; n < nmax_; n++) {
bj[n] = jn[n];
by[n] = (h1n[n] - jn[n])/std::complex<double>(0.0, 1.0);
bd[n] = jnp[n]/jn[n] + 1.0/z;
}
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Calculate an - equation (5)
std::complex<double> MultiLayerMie::calc_an(int n, double XL, std::complex<double> Ha, std::complex<double> mL,
std::complex<double> PsiXL, std::complex<double> ZetaXL,
std::complex<double> PsiXLM1, std::complex<double> ZetaXLM1) {
std::complex<double> Num = (Ha/mL + n/XL)*PsiXL - PsiXLM1;
std::complex<double> Denom = (Ha/mL + n/XL)*ZetaXL - ZetaXLM1;
return Num/Denom;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Calculate bn - equation (6)
std::complex<double> MultiLayerMie::calc_bn(int n, double XL, std::complex<double> Hb, std::complex<double> mL,
std::complex<double> PsiXL, std::complex<double> ZetaXL,
std::complex<double> PsiXLM1, std::complex<double> ZetaXLM1) {
std::complex<double> Num = (mL*Hb + n/XL)*PsiXL - PsiXLM1;
std::complex<double> Denom = (mL*Hb + n/XL)*ZetaXL - ZetaXLM1;
return Num/Denom;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Calculates S1 - equation (25a)
std::complex<double> MultiLayerMie::calc_S1(int n, std::complex<double> an, std::complex<double> bn,
double Pi, double Tau) {
return double(n + n + 1)*(Pi*an + Tau*bn)/double(n*n + n);
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// Calculates S2 - equation (25b) (it's the same as (25a), just switches Pi and Tau)
std::complex<double> MultiLayerMie::calc_S2(int n, std::complex<double> an, std::complex<double> bn,
double Pi, double Tau) {
return calc_S1(n, an, bn, Tau, Pi);
}
//**********************************************************************************//
// This function calculates the Riccati-Bessel functions (Psi and Zeta) for a //
// real argument (x). //
// Equations (20a) - (21b) //
// //
// Input parameters: //
// x: Real argument to evaluate Psi and Zeta //
// nmax: Maximum number of terms to calculate Psi and Zeta //
// //
// Output parameters: //
// Psi, Zeta: Riccati-Bessel functions //
//**********************************************************************************//
void MultiLayerMie::calcPsiZeta(double x,
std::vector<std::complex<double> > D1,
std::vector<std::complex<double> > D3,
std::vector<std::complex<double> >& Psi,
std::vector<std::complex<double> >& Zeta) {
//Upward recurrence for Psi and Zeta - equations (20a) - (21b)
Psi[0] = std::complex<double>(sin(x), 0);
Zeta[0] = std::complex<double>(sin(x), -cos(x));
for (int n = 1; n <= nmax_; n++) {
Psi[n] = Psi[n - 1]*(n/x - D1[n - 1]);
Zeta[n] = Zeta[n - 1]*(n/x - D3[n - 1]);
}
}
//**********************************************************************************//
// Function CONFRA ported from MIEV0.f (Wiscombe,1979)
// Ref. to NCAR Technical Notes, Wiscombe, 1979
/*
c Compute Bessel function ratio A-sub-N from its
c continued fraction using Lentz method
c ZINV = Reciprocal of argument of A
c I N T E R N A L V A R I A B L E S
c ------------------------------------
c CAK Term in continued fraction expansion of A (Eq. R25)
c a_k
c CAPT Factor used in Lentz iteration for A (Eq. R27)
c T_k
c CNUMER Numerator in capT ( Eq. R28A )
c N_k
c CDENOM Denominator in capT ( Eq. R28B )
c D_k
c CDTD Product of two successive denominators of capT factors
c ( Eq. R34C )
c xi_1
c CNTN Product of two successive numerators of capT factors
c ( Eq. R34B )
c xi_2
c EPS1 Ill-conditioning criterion
c EPS2 Convergence criterion
c KK Subscript k of cAk ( Eq. R25B )
c k
c KOUNT Iteration counter ( used to prevent infinite looping )
c MAXIT Max. allowed no. of iterations
c MM + 1 and - 1, alternately
*/
std::complex<double> MultiLayerMie::calcD1confra(const int N, const std::complex<double> z) {
// NTMR -> nmax_ -1 \\TODO nmax_ ?
//int N = nmax_ - 1;
int KK, KOUNT, MAXIT = 10000, MM;
// double EPS1=1.0e-2;
double EPS2=1.0e-8;
std::complex<double> CAK, CAPT, CDENOM, CDTD, CNTN, CNUMER;
std::complex<double> one = std::complex<double>(1.0,0.0);
std::complex<double> ZINV = one/z;
// c ** Eq. R25a
std::complex<double> CONFRA = static_cast<std::complex<double> >(N+1)*ZINV; //debug ZINV
MM = -1;
KK = 2*N +3; //debug 3
// c ** Eq. R25b, k=2
CAK = static_cast<std::complex<double> >(MM*KK) * ZINV; //debug -3 ZINV
CDENOM = CAK;
CNUMER = CDENOM + one / CONFRA; //-3zinv+z
KOUNT = 1;
//10 CONTINUE
do { ++KOUNT;
if (KOUNT > MAXIT) {
printf("re(%g):im(%g)\t\n", CONFRA.real(), CONFRA.imag());
throw std::invalid_argument("ConFra--Iteration failed to converge!\n");
}
MM *= -1; KK += 2; //debug mm=1 kk=5
CAK = static_cast<std::complex<double> >(MM*KK) * ZINV; // ** Eq. R25b //debug 5zinv
// //c ** Eq. R32 Ill-conditioned case -- stride two terms instead of one
// if (std::abs( CNUMER / CAK ) >= EPS1 || std::abs( CDENOM / CAK ) >= EPS1) {
// //c ** Eq. R34
// CNTN = CAK * CNUMER + 1.0;
// CDTD = CAK * CDENOM + 1.0;
// CONFRA = ( CNTN / CDTD ) * CONFRA; // ** Eq. R33
// MM *= -1; KK += 2;
// CAK = static_cast<std::complex<double> >(MM*KK) * ZINV; // ** Eq. R25b
// //c ** Eq. R35
// CNUMER = CAK + CNUMER / CNTN;
// CDENOM = CAK + CDENOM / CDTD;
// ++KOUNT;
// //GO TO 10
// continue;
// } else { //c *** Well-conditioned case
{
CAPT = CNUMER / CDENOM; // ** Eq. R27 //debug (-3zinv + z)/(-3zinv)
// printf("re(%g):im(%g)**\t", CAPT.real(), CAPT.imag());
CONFRA = CAPT * CONFRA; // ** Eq. R26
//if (N == 0) {output=true;printf(" re:");prn(CONFRA.real());printf(" im:"); prn(CONFRA.imag());output=false;};
//c ** Check for convergence; Eq. R31
if ( std::abs(CAPT.real() - 1.0) >= EPS2 || std::abs(CAPT.imag()) >= EPS2 ) {
//c ** Eq. R30
CNUMER = CAK + one/CNUMER;
CDENOM = CAK + one/CDENOM;
continue;
//GO TO 10
} // end of if < eps2
}
break;
} while(1);
//if (N == 0) printf(" return confra for z=(%g,%g)\n", ZINV.real(), ZINV.imag());
return CONFRA;
}
//**********************************************************************************//
// This function calculates the logarithmic derivatives of the Riccati-Bessel //
// functions (D1 and D3) for a complex argument (z). //
// Equations (16a), (16b) and (18a) - (18d) //
// //
// Input parameters: //
// z: Complex argument to evaluate D1 and D3 //
// nmax_: Maximum number of terms to calculate D1 and D3 //
// //
// Output parameters: //
// D1, D3: Logarithmic derivatives of the Riccati-Bessel functions //
//**********************************************************************************//
void MultiLayerMie::calcD1D3(const std::complex<double> z,
std::vector<std::complex<double> >& D1,
std::vector<std::complex<double> >& D3) {
// Downward recurrence for D1 - equations (16a) and (16b)
D1[nmax_] = std::complex<double>(0.0, 0.0);
//D1[nmax_] = calcD1confra(nmax_, z);
const std::complex<double> zinv = std::complex<double>(1.0, 0.0)/z;
// printf(" D:");prn((D1[nmax_]).real()); printf("\t diff:");
// prn((D1[nmax_] + double(nmax_)*zinv).real());
for (int n = nmax_; n > 0; n--) {
D1[n - 1] = double(n)*zinv - 1.0/(D1[n] + double(n)*zinv);
//D1[n-1] = calcD1confra(n-1, z);
// printf(" D:");prn((D1[n-1]).real()); printf("\t diff:");
// prn((D1[n] + double(n)*zinv).real());
}
// printf("\n\n"); iformat=0;
if (std::abs(D1[0]) > 100000.0 )
throw std::invalid_argument
("Unstable D1! Please, try to change input parameters!\n");
// Upward recurrence for PsiZeta and D3 - equations (18a) - (18d)
PsiZeta_[0] = 0.5*(1.0 - std::complex<double>(cos(2.0*z.real()), sin(2.0*z.real()))
*exp(-2.0*z.imag()));
D3[0] = std::complex<double>(0.0, 1.0);
for (int n = 1; n <= nmax_; n++) {
PsiZeta_[n] = PsiZeta_[n - 1]*(static_cast<double>(n)*zinv - D1[n - 1])
*(static_cast<double>(n)*zinv- D3[n - 1]);
D3[n] = D1[n] + std::complex<double>(0.0, 1.0)/PsiZeta_[n];
}
}
//**********************************************************************************//
// This function calculates Pi and Tau for all values of Theta. //
// Equations (26a) - (26c) //
// //
// Input parameters: //
// nmax_: Maximum number of terms to calculate Pi and Tau //
// nTheta: Number of scattering angles //
// Theta: Array containing all the scattering angles where the scattering //
// amplitudes will be calculated //
// //
// Output parameters: //
// Pi, Tau: Angular functions Pi and Tau, as defined in equations (26a) - (26c) //
//**********************************************************************************//
void MultiLayerMie::calcPiTau(std::vector< std::vector<double> >& Pi,
std::vector< std::vector<double> >& Tau) {
//****************************************************//
// Equations (26a) - (26c) //
//****************************************************//
std::vector<double> costheta(theta_.size(), 0.0);
for (int t = 0; t < theta_.size(); t++) {
costheta[t] = cos(theta_[t]);
}
for (int n = 0; n < nmax_; n++) {
for (int t = 0; t < theta_.size(); t++) {
if (n == 0) {
// Initialize Pi and Tau
Pi[n][t] = 1.0;
Tau[n][t] = (n + 1)*costheta[t];
} else {
// Calculate the actual values
Pi[n][t] = ((n == 1) ? ((n + n + 1)*costheta[t]*Pi[n - 1][t]/n)
: (((n + n + 1)*costheta[t]*Pi[n - 1][t]
- (n + 1)*Pi[n - 2][t])/n));
Tau[n][t] = (n + 1)*costheta[t]*Pi[n][t] - (n + 2)*Pi[n - 1][t];
}
}
}
} // end of void MultiLayerMie::calcPiTau(...)
//**********************************************************************************//
// This function calculates the scattering coefficients required to calculate //
// both the near- and far-field parameters. //
// //
// Input parameters: //
// L: Number of layers //
// pl: Index of PEC layer. If there is none just send -1 //
// x: Array containing the size parameters of the layers [0..L-1] //
// m: Array containing the relative refractive indexes of the layers [0..L-1] //
// nmax: Maximum number of multipolar expansion terms to be used for the //
// calculations. Only use it if you know what you are doing, otherwise //
// set this parameter to -1 and the function will calculate it. //
// //
// Output parameters: //
// an, bn: Complex scattering amplitudes //
// //
// Return value: //
// Number of multipolar expansion terms used for the calculations //
//**********************************************************************************//
void MultiLayerMie::ScattCoeffs(std::vector<std::complex<double> >& an,
std::vector<std::complex<double> >& bn) {
const std::vector<double>& x = size_parameter_;
const std::vector<std::complex<double> >& m = index_;
const int& pl = PEC_layer_position_;
const int L = index_.size();
//************************************************************************//
// Calculate the index of the first layer. It can be either 0
// (default) // or the index of the outermost PEC layer. In the
// latter case all layers // below the PEC are discarded. //
// ************************************************************************//
// TODO, is it possible for PEC to have a zero index? If yes than
// is should be:
// int fl = (pl > -1) ? pl : 0;
// This will give the same result, however, it corresponds the
// logic - if there is PEC, than first layer is PEC.
int fl = (pl > 0) ? pl : 0;
if (nmax_ <= 0) Nmax(fl);
std::complex<double> z1, z2;
//**************************************************************************//
// Note that since Fri, Nov 14, 2014 all arrays start from 0 (zero), which //
// means that index = layer number - 1 or index = n - 1. The only exception //
// are the arrays for representing D1, D3 and Q because they need a value //
// for the index 0 (zero), hence it is important to consider this shift //
// between different arrays. The change was done to optimize memory usage. //
//**************************************************************************//
// Allocate memory to the arrays
std::vector<std::complex<double> > D1_mlxl(nmax_ + 1), D1_mlxlM1(nmax_ + 1),
D3_mlxl(nmax_ + 1), D3_mlxlM1(nmax_ + 1);
std::vector<std::vector<std::complex<double> > > Q(L), Ha(L), Hb(L);
for (int l = 0; l < L; l++) {
// D1_mlxl[l].resize(nmax_ + 1);
// D1_mlxlM1[l].resize(nmax_ + 1);
// D3_mlxl[l].resize(nmax_ + 1);
// D3_mlxlM1[l].resize(nmax_ + 1);
Q[l].resize(nmax_ + 1);
Ha[l].resize(nmax_);
Hb[l].resize(nmax_);
}
an.resize(nmax_);
bn.resize(nmax_);
PsiZeta_.resize(nmax_ + 1);
std::vector<std::complex<double> > D1XL(nmax_ + 1), D3XL(nmax_ + 1),
PsiXL(nmax_ + 1), ZetaXL(nmax_ + 1);
//*************************************************//
// Calculate D1 and D3 for z1 in the first layer //
//*************************************************//
if (fl == pl) { // PEC layer
for (int n = 0; n <= nmax_; n++) {
D1_mlxl[n] = std::complex<double>(0.0, -1.0);
D3_mlxl[n] = std::complex<double>(0.0, 1.0);
}
} else { // Regular layer
z1 = x[fl]* m[fl];
// Calculate D1 and D3
calcD1D3(z1, D1_mlxl, D3_mlxl);
}
// do { \
// ++iformat;\
// if (iformat%5 == 0) printf("%24.16e",z1.real()); \
// } while (false);
//******************************************************************//
// Calculate Ha and Hb in the first layer - equations (7a) and (8a) //
//******************************************************************//
for (int n = 0; n < nmax_; n++) {
Ha[fl][n] = D1_mlxl[n + 1];
Hb[fl][n] = D1_mlxl[n + 1];
}
//*****************************************************//
// Iteration from the second layer to the last one (L) //
//*****************************************************//
std::complex<double> Temp, Num, Denom;
std::complex<double> G1, G2;
for (int l = fl + 1; l < L; l++) {
//************************************************************//
//Calculate D1 and D3 for z1 and z2 in the layers fl+1..L //
//************************************************************//
z1 = x[l]*m[l];
z2 = x[l - 1]*m[l];
//Calculate D1 and D3 for z1
calcD1D3(z1, D1_mlxl, D3_mlxl);
//Calculate D1 and D3 for z2
calcD1D3(z2, D1_mlxlM1, D3_mlxlM1);
// prn(z1.real());
// for ( auto i : D1_mlxl) { prn(i.real());
// // prn(i.imag());
// } printf("\n");
//*********************************************//
//Calculate Q, Ha and Hb in the layers fl+1..L //
//*********************************************//
// Upward recurrence for Q - equations (19a) and (19b)
Num = exp(-2.0*(z1.imag() - z2.imag()))
* std::complex<double>(cos(-2.0*z2.real()) - exp(-2.0*z2.imag()), sin(-2.0*z2.real()));
Denom = std::complex<double>(cos(-2.0*z1.real()) - exp(-2.0*z1.imag()), sin(-2.0*z1.real()));
Q[l][0] = Num/Denom;
for (int n = 1; n <= nmax_; n++) {
Num = (z1*D1_mlxl[n] + double(n))*(double(n) - z1*D3_mlxl[n - 1]);
Denom = (z2*D1_mlxlM1[n] + double(n))*(double(n) - z2*D3_mlxlM1[n - 1]);
Q[l][n] = ((pow2(x[l - 1]/x[l])* Q[l][n - 1])*Num)/Denom;
}
// Upward recurrence for Ha and Hb - equations (7b), (8b) and (12) - (15)
for (int n = 1; n <= nmax_; n++) {
//Ha
if ((l - 1) == pl) { // The layer below the current one is a PEC layer
G1 = -D1_mlxlM1[n];
G2 = -D3_mlxlM1[n];
} else {
G1 = (m[l]*Ha[l - 1][n - 1]) - (m[l - 1]*D1_mlxlM1[n]);
G2 = (m[l]*Ha[l - 1][n - 1]) - (m[l - 1]*D3_mlxlM1[n]);
} // end of if PEC
Temp = Q[l][n]*G1;
Num = (G2*D1_mlxl[n]) - (Temp*D3_mlxl[n]);
Denom = G2 - Temp;
Ha[l][n - 1] = Num/Denom;
//Hb
if ((l - 1) == pl) { // The layer below the current one is a PEC layer
G1 = Hb[l - 1][n - 1];
G2 = Hb[l - 1][n - 1];
} else {
G1 = (m[l - 1]*Hb[l - 1][n - 1]) - (m[l]*D1_mlxlM1[n]);
G2 = (m[l - 1]*Hb[l - 1][n - 1]) - (m[l]*D3_mlxlM1[n]);
} // end of if PEC
Temp = Q[l][n]*G1;
Num = (G2*D1_mlxl[n]) - (Temp* D3_mlxl[n]);
Denom = (G2- Temp);
Hb[l][n - 1] = (Num/ Denom);
} // end of for Ha and Hb terms
} // end of for layers iteration
//**************************************//
//Calculate D1, D3, Psi and Zeta for XL //
//**************************************//
// Calculate D1XL and D3XL
calcD1D3(x[L - 1], D1XL, D3XL);
//printf("%5.20f\n",Ha[L-1][0].real());
// Calculate PsiXL and ZetaXL
calcPsiZeta(x[L - 1], D1XL, D3XL, PsiXL, ZetaXL);
//*********************************************************************//
// Finally, we calculate the scattering coefficients (an and bn) and //
// the angular functions (Pi and Tau). Note that for these arrays the //
// first layer is 0 (zero), in future versions all arrays will follow //
// this convention to save memory. (13 Nov, 2014) //
//*********************************************************************//
for (int n = 0; n < nmax_; n++) {
//********************************************************************//
//Expressions for calculating an and bn coefficients are not valid if //
//there is only one PEC layer (ie, for a simple PEC sphere). //
//********************************************************************//
if (pl < (L - 1)) {
an[n] = calc_an(n + 1, x[L - 1], Ha[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
bn[n] = calc_bn(n + 1, x[L - 1], Hb[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
} else {
an[n] = calc_an(n + 1, x[L - 1], std::complex<double>(0.0, 0.0), std::complex<double>(1.0, 0.0), PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
bn[n] = PsiXL[n + 1]/ZetaXL[n + 1];
}
} // end of for an and bn terms
} // end of void MultiLayerMie::ScattCoeffs(...)
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::InitMieCalculations() {
isMieCalculated_ = false;
// Initialize the scattering parameters
Qext_ = 0;
Qsca_ = 0;
Qabs_ = 0;
Qbk_ = 0;
Qpr_ = 0;
asymmetry_factor_ = 0;
albedo_ = 0;
Qsca_ch_.clear();
Qext_ch_.clear();
Qabs_ch_.clear();
Qbk_ch_.clear();
Qpr_ch_.clear();
Qsca_ch_.resize(nmax_-1);
Qext_ch_.resize(nmax_-1);
Qabs_ch_.resize(nmax_-1);
Qbk_ch_.resize(nmax_-1);
Qpr_ch_.resize(nmax_-1);
Qsca_ch_norm_.resize(nmax_-1);
Qext_ch_norm_.resize(nmax_-1);
Qabs_ch_norm_.resize(nmax_-1);
Qbk_ch_norm_.resize(nmax_-1);
Qpr_ch_norm_.resize(nmax_-1);
// Initialize the scattering amplitudes
std::vector<std::complex<double> > tmp1(theta_.size(),std::complex<double>(0.0, 0.0));
S1_.swap(tmp1);
S2_ = S1_;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
void MultiLayerMie::ConvertToSP() {
isMieCalculated_ = false;
if (target_width_.size() + coating_width_.size() == 0)
return; // Nothing to convert, we suppose that SP was set directly
GenerateSizeParameter();
GenerateIndex();
if (size_parameter_.size() != index_.size())
throw std::invalid_argument("Ivalid conversion of width to size parameter units!/n");
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
//**********************************************************************************//
// This function calculates the actual scattering parameters and amplitudes //
// //
// Input parameters: //
// L: Number of layers //
// pl: Index of PEC layer. If there is none just send -1 //
// x: Array containing the size parameters of the layers [0..L-1] //
// m: Array containing the relative refractive indexes of the layers [0..L-1] //
// nTheta: Number of scattering angles //
// Theta: Array containing all the scattering angles where the scattering //
// amplitudes will be calculated //
// nmax_: Maximum number of multipolar expansion terms to be used for the //
// calculations. Only use it if you know what you are doing, otherwise //
// set this parameter to -1 and the function will calculate it //
// //
// Output parameters: //
// Qext: Efficiency factor for extinction //
// Qsca: Efficiency factor for scattering //
// Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca) //
// Qbk: Efficiency factor for backscattering //
// Qpr: Efficiency factor for the radiation pressure //
// g: Asymmetry factor (g = (Qext-Qpr)/Qsca) //
// Albedo: Single scattering albedo (Albedo = Qsca/Qext) //
// S1, S2: Complex scattering amplitudes //
// //
// Return value: //
// Number of multipolar expansion terms used for the calculations //
//**********************************************************************************//
void MultiLayerMie::RunMieCalculations() {
isMieCalculated_ = false;
ConvertToSP();
nmax_ = nmax_preset_;
if (size_parameter_.size() != index_.size())
throw std::invalid_argument("Each size parameter should have only one index!");
if (size_parameter_.size() == 0)
throw std::invalid_argument("Initialize model first!");
std::vector<std::complex<double> > an, bn;
const std::vector<double>& x = size_parameter_;
// Calculate scattering coefficients
ScattCoeffs(an, bn);
// std::vector< std::vector<double> > Pi(nmax_), Tau(nmax_);
std::vector< std::vector<double> > Pi, Tau;
Pi.resize(nmax_);
Tau.resize(nmax_);
for (int i =0; i< nmax_; ++i) {
Pi[i].resize(theta_.size());
Tau[i].resize(theta_.size());
}
calcPiTau(Pi, Tau);
InitMieCalculations(); //
std::complex<double> Qbktmp(0.0, 0.0);
std::vector< std::complex<double> > Qbktmp_ch(nmax_ - 1, Qbktmp);
// By using downward recurrence we avoid loss of precision due to float rounding errors
// See: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
// http://en.wikipedia.org/wiki/Loss_of_significance
for (int i = nmax_ - 2; i >= 0; i--) {
const int n = i + 1;
// Equation (27)
Qext_ch_norm_[i] = (an[i].real() + bn[i].real());
Qext_ch_[i] = (n + n + 1.0)*Qext_ch_norm_[i];
//Qext_ch_[i] = (n + n + 1)*(an[i].real() + bn[i].real());
Qext_ += Qext_ch_[i];
// Equation (28)
Qsca_ch_norm_[i] = (an[i].real()*an[i].real() + an[i].imag()*an[i].imag()
+ bn[i].real()*bn[i].real() + bn[i].imag()*bn[i].imag());
Qsca_ch_[i] = (n + n + 1.0)*Qsca_ch_norm_[i];
Qsca_ += Qsca_ch_[i];
// Qsca_ch_[i] += (n + n + 1)*(an[i].real()*an[i].real() + an[i].imag()*an[i].imag()
// + bn[i].real()*bn[i].real() + bn[i].imag()*bn[i].imag());
// Equation (29) TODO We must check carefully this equation. If we
// remove the typecast to double then the result changes. Which is
// the correct one??? Ovidio (2014/12/10) With cast ratio will
// give double, without cast (n + n + 1)/(n*(n + 1)) will be
// rounded to integer. Tig (2015/02/24)
Qpr_ch_[i]=((n*(n + 2)/(n + 1))*((an[i]*std::conj(an[n]) + bn[i]*std::conj(bn[n])).real())
+ ((double)(n + n + 1)/(n*(n + 1)))*(an[i]*std::conj(bn[i])).real());
Qpr_ += Qpr_ch_[i];
// Equation (33)
Qbktmp_ch[i] = (double)(n + n + 1)*(1 - 2*(n % 2))*(an[i]- bn[i]);
Qbktmp += Qbktmp_ch[i];
// Calculate the scattering amplitudes (S1 and S2) //
// Equations (25a) - (25b) //
for (int t = 0; t < theta_.size(); t++) {
S1_[t] += calc_S1(n, an[i], bn[i], Pi[i][t], Tau[i][t]);
S2_[t] += calc_S2(n, an[i], bn[i], Pi[i][t], Tau[i][t]);
}
}
double x2 = pow2(x.back());
Qext_ = 2.0*(Qext_)/x2; // Equation (27)
for (double& Q : Qext_ch_) Q = 2.0*Q/x2;
Qsca_ = 2.0*(Qsca_)/x2; // Equation (28)
for (double& Q : Qsca_ch_) Q = 2.0*Q/x2;
//for (double& Q : Qsca_ch_norm_) Q = 2.0*Q/x2;
Qpr_ = Qext_ - 4.0*(Qpr_)/x2; // Equation (29)
for (int i = 0; i < nmax_ - 1; ++i) Qpr_ch_[i] = Qext_ch_[i] - 4.0*Qpr_ch_[i]/x2;
Qabs_ = Qext_ - Qsca_; // Equation (30)
for (int i = 0; i < nmax_ - 1; ++i) {
Qabs_ch_[i] = Qext_ch_[i] - Qsca_ch_[i];
Qabs_ch_norm_[i] = Qext_ch_norm_[i] - Qsca_ch_norm_[i];
}
albedo_ = Qsca_ / Qext_; // Equation (31)
asymmetry_factor_ = (Qext_ - Qpr_) / Qsca_; // Equation (32)
Qbk_ = (Qbktmp.real()*Qbktmp.real() + Qbktmp.imag()*Qbktmp.imag())/x2; // Equation (33)
isMieCalculated_ = true;
nmax_used_ = nmax_;
//return nmax;
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
// external scattering field = incident + scattered
// BH p.92 (4.37), 94 (4.45), 95 (4.50)
// assume: medium is non-absorbing; refim = 0; Uabs = 0
void MultiLayerMie::fieldExt(double Rho, double Phi, double Theta, std::vector<double> Pi, std::vector<double> Tau,
std::vector<std::complex<double> > an, std::vector<std::complex<double> > bn,
std::vector<std::complex<double> >& E, std::vector<std::complex<double> >& H) {
double rn = 0.0;
std::complex<double> zn, xxip, encap;
std::vector<std::complex<double> > vm3o1n, vm3e1n, vn3o1n, vn3e1n;
vm3o1n.resize(3);
vm3e1n.resize(3);
vn3o1n.resize(3);
vn3e1n.resize(3);
std::vector<std::complex<double> > Ei, Hi, Es, Hs;
Ei.resize(3);
Hi.resize(3);
Es.resize(3);
Hs.resize(3);
for (int i = 0; i < 3; i++) {
Ei[i] = std::complex<double>(0.0, 0.0);
Hi[i] = std::complex<double>(0.0, 0.0);
Es[i] = std::complex<double>(0.0, 0.0);
Hs[i] = std::complex<double>(0.0, 0.0);
}
std::vector<std::complex<double> > bj, by, bd;
bj.resize(nmax_);
by.resize(nmax_);
bd.resize(nmax_);
// Calculate spherical Bessel and Hankel functions
sphericalBessel(Rho, bj, by, bd);
for (int n = 0; n < nmax_; n++) {
rn = double(n + 1);
zn = bj[n] + std::complex<double>(0.0, 1.0)*by[n];
xxip = Rho*(bj[n] + std::complex<double>(0.0, 1.0)*by[n]) - rn*zn;
vm3o1n[0] = std::complex<double>(0.0, 0.0);
vm3o1n[1] = std::cos(Phi)*Pi[n]*zn;
vm3o1n[2] = -(std::sin(Phi)*Tau[n]*zn);
vm3e1n[0] = std::complex<double>(0.0, 0.0);
vm3e1n[1] = -(std::sin(Phi)*Pi[n]*zn);
vm3e1n[2] = -(std::cos(Phi)*Tau[n]*zn);
vn3o1n[0] = std::sin(Phi)*rn*(rn + 1.0)*std::sin(Theta)*Pi[n]*zn/Rho;
vn3o1n[1] = std::sin(Phi)*Tau[n]*xxip/Rho;
vn3o1n[2] = std::cos(Phi)*Pi[n]*xxip/Rho;
vn3e1n[0] = std::cos(Phi)*rn*(rn + 1.0)*std::sin(Theta)*Pi[n]*zn/Rho;
vn3e1n[1] = std::cos(Phi)*Tau[n]*xxip/Rho;
vn3e1n[2] = -(std::sin(Phi)*Pi[n]*xxip/Rho);
// scattered field: BH p.94 (4.45)
encap = std::pow(std::complex<double>(0.0, 1.0), rn)*(2.0*rn + 1.0)/(rn*(rn + 1.0));
for (int i = 0; i < 3; i++) {
Es[i] = Es[i] + encap*(std::complex<double>(0.0, 1.0)*an[n]*vn3e1n[i] - bn[n]*vm3o1n[i]);
Hs[i] = Hs[i] + encap*(std::complex<double>(0.0, 1.0)*bn[n]*vn3o1n[i] + an[n]*vm3e1n[i]);
}
}
// incident E field: BH p.89 (4.21); cf. p.92 (4.37), p.93 (4.38)
// basis unit vectors = er, etheta, ephi
std::complex<double> eifac = std::exp(std::complex<double>(0.0, 1.0)*Rho*std::cos(Theta));
Ei[0] = eifac*std::sin(Theta)*std::cos(Phi);
Ei[1] = eifac*std::cos(Theta)*std::cos(Phi);
Ei[2] = -(eifac*std::sin(Phi));
// magnetic field
double hffact = 1.0/(cc*mu);
for (int i = 0; i < 3; i++) {
Hs[i] = hffact*Hs[i];
}
// incident H field: BH p.26 (2.43), p.89 (4.21)
std::complex<double> hffacta = hffact;
std::complex<double> hifac = eifac*hffacta;
Hi[0] = hifac*std::sin(Theta)*std::sin(Phi);
Hi[1] = hifac*std::cos(Theta)*std::sin(Phi);
Hi[2] = hifac*std::cos(Phi);
for (int i = 0; i < 3; i++) {
// electric field E [V m-1] = EF*E0
E[i] = Ei[i] + Es[i];
H[i] = Hi[i] + Hs[i];
}
}
// ********************************************************************** //
// ********************************************************************** //
// ********************************************************************** //
//**********************************************************************************//
// This function calculates complex electric and magnetic field in the surroundings //
// and inside (TODO) the particle. //
// //
// Input parameters: //
// L: Number of layers //
// pl: Index of PEC layer. If there is none just send 0 (zero) //
// x: Array containing the size parameters of the layers [0..L-1] //
// m: Array containing the relative refractive indexes of the layers [0..L-1] //
// nmax: Maximum number of multipolar expansion terms to be used for the //
// calculations. Only use it if you know what you are doing, otherwise //
// set this parameter to 0 (zero) and the function will calculate it. //
// ncoord: Number of coordinate points //
// Coords: Array containing all coordinates where the complex electric and //
// magnetic fields will be calculated //
// //
// Output parameters: //
// E, H: Complex electric and magnetic field at the provided coordinates //
// //
// Return value: //
// Number of multipolar expansion terms used for the calculations //
//**********************************************************************************//
// int MultiLayerMie::nField(int L, int pl, std::vector<double> x, std::vector<std::complex<double> > m, int nmax,
// int ncoord, std::vector<double> Xp, std::vector<double> Yp, std::vector<double> Zp,
// std::vector<std::vector<std::complex<double> > >& E, std::vector<std::vector<std::complex<double> > >& H) {
// double Rho, Phi, Theta;
// std::vector<std::complex<double> > an, bn;
// // This array contains the fields in spherical coordinates
// std::vector<std::complex<double> > Es, Hs;
// Es.resize(3);
// Hs.resize(3);
// // Calculate scattering coefficients
// ScattCoeffs(L, pl, an, bn);
// std::vector<double> Pi, Tau;
// Pi.resize(nmax_);
// Tau.resize(nmax_);
// for (int c = 0; c < ncoord; c++) {
// // Convert to spherical coordinates
// Rho = sqrt(Xp[c]*Xp[c] + Yp[c]*Yp[c] + Zp[c]*Zp[c]);
// if (Rho < 1e-3) {
// // Avoid convergence problems
// Rho = 1e-3;
// }
// Phi = acos(Xp[c]/sqrt(Xp[c]*Xp[c] + Yp[c]*Yp[c]));
// Theta = acos(Xp[c]/Rho);
// calcPiTau(Theta, Pi, Tau);
// //*******************************************************//
// // external scattering field = incident + scattered //
// // BH p.92 (4.37), 94 (4.45), 95 (4.50) //
// // assume: medium is non-absorbing; refim = 0; Uabs = 0 //
// //*******************************************************//
// // Firstly the easiest case: the field outside the particle
// if (Rho >= x[L - 1]) {
// fieldExt(Rho, Phi, Theta, Pi, Tau, an, bn, Es, Hs);
// } else {
// // TODO, for now just set all the fields to zero
// for (int i = 0; i < 3; i++) {
// Es[i] = std::complex<double>(0.0, 0.0);
// Hs[i] = std::complex<double>(0.0, 0.0);
// }
// }
// //Now, convert the fields back to cartesian coordinates
// E[c][0] = std::sin(Theta)*std::cos(Phi)*Es[0] + std::cos(Theta)*std::cos(Phi)*Es[1] - std::sin(Phi)*Es[2];
// E[c][1] = std::sin(Theta)*std::sin(Phi)*Es[0] + std::cos(Theta)*std::sin(Phi)*Es[1] + std::cos(Phi)*Es[2];
// E[c][2] = std::cos(Theta)*Es[0] - std::sin(Theta)*Es[1];
// H[c][0] = std::sin(Theta)*std::cos(Phi)*Hs[0] + std::cos(Theta)*std::cos(Phi)*Hs[1] - std::sin(Phi)*Hs[2];
// H[c][1] = std::sin(Theta)*std::sin(Phi)*Hs[0] + std::cos(Theta)*std::sin(Phi)*Hs[1] + std::cos(Phi)*Hs[2];
// H[c][2] = std::cos(Theta)*Hs[0] - std::sin(Theta)*Hs[1];
// }
// return nmax;
// } // end of int nField()
} // end of namespace nmie