|
|
@@ -0,0 +1,1165 @@
|
|
|
+#ifndef SRC_NMIE_IMPL_H_
|
|
|
+#define SRC_NMIE_IMPL_H_
|
|
|
+//**********************************************************************************//
|
|
|
+// Copyright (C) 2009-2016 Ovidio Pena <ovidio@bytesfall.com> //
|
|
|
+// Copyright (C) 2013-2016 Konstantin Ladutenko <kostyfisik@gmail.com> //
|
|
|
+// //
|
|
|
+// This file is part of scattnlay //
|
|
|
+// //
|
|
|
+// This program 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. //
|
|
|
+// //
|
|
|
+// This program 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. //
|
|
|
+// //
|
|
|
+// The only additional remark 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. //
|
|
|
+// //
|
|
|
+// You should have received a copy of the GNU General Public License //
|
|
|
+// along with this program. If not, see <http://www.gnu.org/licenses/>. //
|
|
|
+//**********************************************************************************//
|
|
|
+
|
|
|
+//**********************************************************************************//
|
|
|
+// This class implements the algorithm for a multilayered sphere described by: //
|
|
|
+// [1] W. Yang, "Improved recursive algorithm for light scattering by a //
|
|
|
+// multilayered sphere,” Applied Optics, vol. 42, Mar. 2003, pp. 1710-1720. //
|
|
|
+// //
|
|
|
+// You can find the description of all the used equations in: //
|
|
|
+// [2] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
|
|
|
+// a multilayered sphere," Computer Physics Communications, //
|
|
|
+// vol. 180, Nov. 2009, pp. 2348-2354. //
|
|
|
+// //
|
|
|
+// Hereinafter all equations numbers refer to [2] //
|
|
|
+//**********************************************************************************//
|
|
|
+#include "nmie.hpp"
|
|
|
+#include <array>
|
|
|
+#include <algorithm>
|
|
|
+#include <cstdio>
|
|
|
+#include <cstdlib>
|
|
|
+#include <iostream>
|
|
|
+#include <iomanip>
|
|
|
+#include <stdexcept>
|
|
|
+#include <vector>
|
|
|
+#include <boost/multiprecision/cpp_int.hpp>
|
|
|
+#include <boost/multiprecision/cpp_bin_float.hpp>
|
|
|
+#include <boost/multiprecision/cpp_dec_float.hpp>
|
|
|
+#include <boost/multiprecision/number.hpp>
|
|
|
+
|
|
|
+namespace nmie {
|
|
|
+ //helpers
|
|
|
+
|
|
|
+ //namespace nmm = std;
|
|
|
+ namespace nmm = boost::multiprecision;
|
|
|
+
|
|
|
+
|
|
|
+ template<class T> inline T pow2(const T value) {return value*value;}
|
|
|
+
|
|
|
+ template<class T> inline T cabs(const std::complex<T> value)
|
|
|
+ {return nmm::sqrt(pow2(value.real()) + pow2(value.imag()));}
|
|
|
+
|
|
|
+ template <typename FloatType>
|
|
|
+ int newround(FloatType x) {
|
|
|
+ return x >= 0 ? static_cast<int>(x + 0.5):static_cast<int>(x - 0.5);
|
|
|
+ //return x >= 0 ? (x + 0.5).convert_to<int>():(x - 0.5).convert_to<int>();
|
|
|
+ }
|
|
|
+ template<typename T>
|
|
|
+ inline std::complex<T> my_exp(const std::complex<T>& x) {
|
|
|
+ using std::exp; // use ADL
|
|
|
+ T const& r = exp(x.real());
|
|
|
+ return std::polar(r, x.imag());
|
|
|
+ }
|
|
|
+
|
|
|
+ template <typename ToFloatType, typename FromFloatType>
|
|
|
+ std::vector<ToFloatType> ConvertVector(std::vector<FromFloatType> x) {
|
|
|
+ std::vector<ToFloatType> new_x;
|
|
|
+ for (auto element : x) {
|
|
|
+ new_x.push_back(static_cast<ToFloatType>(element));
|
|
|
+ }
|
|
|
+ return new_x;
|
|
|
+ }
|
|
|
+
|
|
|
+ template <typename ToFloatType, typename FromFloatType>
|
|
|
+ std::vector<std::complex<ToFloatType> > ConvertComplexVector(std::vector<std::complex<FromFloatType> > x) {
|
|
|
+ std::vector<std::complex<ToFloatType> > new_x;
|
|
|
+ for (auto element : x) {
|
|
|
+ new_x.push_back(std::complex<ToFloatType>(static_cast<ToFloatType>(element.real()),
|
|
|
+ static_cast<ToFloatType>(element.imag())
|
|
|
+ )
|
|
|
+ );
|
|
|
+ }
|
|
|
+ return new_x;
|
|
|
+ }
|
|
|
+
|
|
|
+ template <typename ToFloatType, typename FromFloatType>
|
|
|
+ std::vector<std::vector<std::complex<ToFloatType> > > ConvertComplexVectorVector(std::vector<std::vector<std::complex<FromFloatType> > > x) {
|
|
|
+ std::vector<std::vector<std::complex<ToFloatType> > > new_x;
|
|
|
+ std::vector<std::complex<ToFloatType> > new_y;
|
|
|
+ for (auto y : x) {
|
|
|
+ new_y.clear();
|
|
|
+ for (auto element : y) {
|
|
|
+ new_y.push_back(std::complex<ToFloatType>(static_cast<ToFloatType>(element.real()),
|
|
|
+ static_cast<ToFloatType>(element.imag())
|
|
|
+ )
|
|
|
+ );
|
|
|
+ }
|
|
|
+ new_x.push_back(new_y);
|
|
|
+ }
|
|
|
+ return new_x;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Qext //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetQext() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return Qext_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Qabs //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetQabs() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return Qabs_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Qsca //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetQsca() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return Qsca_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Qbk //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetQbk() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return Qbk_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Qpr //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetQpr() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return Qpr_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated assymetry factor //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetAsymmetryFactor() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return asymmetry_factor_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated Albedo //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetAlbedo() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return albedo_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated S1 //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::vector<std::complex<FloatType> > MultiLayerMie<FloatType>::GetS1() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return S1_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Returns previously calculated S2 //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::vector<std::complex<FloatType> > MultiLayerMie<FloatType>::GetS2() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ return S2_;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Modify scattering (theta) angles //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetAngles(const std::vector<FloatType>& angles) {
|
|
|
+ MarkUncalculated();
|
|
|
+ theta_ = angles;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Modify size of all layers //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetLayersSize(const std::vector<FloatType>& layer_size) {
|
|
|
+ MarkUncalculated();
|
|
|
+ size_param_.clear();
|
|
|
+ FloatType prev_layer_size = 0.0;
|
|
|
+ for (auto curr_layer_size : layer_size) {
|
|
|
+ if (curr_layer_size <= 0.0)
|
|
|
+ throw std::invalid_argument("Size parameter should be positive!");
|
|
|
+ if (prev_layer_size > curr_layer_size)
|
|
|
+ throw std::invalid_argument
|
|
|
+ ("Size parameter for next layer should be larger than the previous one!");
|
|
|
+ prev_layer_size = curr_layer_size;
|
|
|
+ size_param_.push_back(curr_layer_size);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Modify refractive index of all layers //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetLayersIndex(const std::vector< std::complex<FloatType> >& index) {
|
|
|
+ MarkUncalculated();
|
|
|
+ refractive_index_ = index;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Modify coordinates for field calculation //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetFieldCoords(const std::vector< std::vector<FloatType> >& coords) {
|
|
|
+ if (coords.size() != 3)
|
|
|
+ throw std::invalid_argument("Error! Wrong dimension of field monitor points!");
|
|
|
+ if (coords[0].size() != coords[1].size() || coords[0].size() != coords[2].size())
|
|
|
+ throw std::invalid_argument("Error! Missing coordinates for field monitor points!");
|
|
|
+ coords_ = coords;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Modify index of PEC layer //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetPECLayer(int layer_position) {
|
|
|
+ MarkUncalculated();
|
|
|
+ if (layer_position < 0 && layer_position != -1)
|
|
|
+ throw std::invalid_argument("Error! Layers are numbered from 0!");
|
|
|
+ PEC_layer_position_ = layer_position;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Set maximun number of terms to be used //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::SetMaxTerms(int nmax) {
|
|
|
+ MarkUncalculated();
|
|
|
+ nmax_preset_ = nmax;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Get total size parameter of particle //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ FloatType MultiLayerMie<FloatType>::GetSizeParameter() {
|
|
|
+ if (size_param_.size() > 0)
|
|
|
+ return size_param_.back();
|
|
|
+ else
|
|
|
+ return 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Mark uncalculated //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::MarkUncalculated() {
|
|
|
+ isExpCoeffsCalc_ = false;
|
|
|
+ isScaCoeffsCalc_ = false;
|
|
|
+
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ }
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Clear layer information //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::ClearLayers() {
|
|
|
+ MarkUncalculated();
|
|
|
+ size_param_.clear();
|
|
|
+ refractive_index_.clear();
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Computational core
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate calcNstop - equation (17) //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcNstop() {
|
|
|
+ const FloatType& xL = size_param_.back();
|
|
|
+ if (xL <= 8) {
|
|
|
+ nmax_ = newround(xL + 4.0*pow(xL, 1.0/3.0) + 1);
|
|
|
+ } else if (xL <= 4200) {
|
|
|
+ nmax_ = newround(xL + 4.05*pow(xL, 1.0/3.0) + 2);
|
|
|
+ } else {
|
|
|
+ nmax_ = newround(xL + 4.0*pow(xL, 1.0/3.0) + 2);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Maximum number of terms required for the calculation //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcNmax(unsigned int first_layer) {
|
|
|
+ int ri, riM1;
|
|
|
+ const std::vector<FloatType>& x = size_param_;
|
|
|
+ const std::vector<std::complex<FloatType> >& m = refractive_index_;
|
|
|
+ calcNstop(); // Set initial nmax_ value
|
|
|
+ for (unsigned int i = first_layer; i < x.size(); i++) {
|
|
|
+ if (static_cast<int>(i) > PEC_layer_position_) // static_cast used to avoid warning
|
|
|
+ ri = newround(cabs(x[i]*m[i]));
|
|
|
+ else
|
|
|
+ ri = 0;
|
|
|
+ nmax_ = std::max(nmax_, ri);
|
|
|
+ // first layer is pec, if pec is present
|
|
|
+ if ((i > first_layer) && (static_cast<int>(i - 1) > PEC_layer_position_))
|
|
|
+ riM1 = newround(cabs(x[i - 1]* m[i]));
|
|
|
+ else
|
|
|
+ riM1 = 0;
|
|
|
+ nmax_ = std::max(nmax_, riM1);
|
|
|
+ }
|
|
|
+ nmax_ += 15; // Final nmax_ value
|
|
|
+ // nmax_ *= nmax_;
|
|
|
+ // printf("using nmax %i\n", nmax_);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate an - equation (5) //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::complex<FloatType> MultiLayerMie<FloatType>::calc_an(int n, FloatType XL, std::complex<FloatType> Ha, std::complex<FloatType> mL,
|
|
|
+ std::complex<FloatType> PsiXL, std::complex<FloatType> ZetaXL,
|
|
|
+ std::complex<FloatType> PsiXLM1, std::complex<FloatType> ZetaXLM1) {
|
|
|
+
|
|
|
+ std::complex<FloatType> Num = (Ha/mL + n/XL)*PsiXL - PsiXLM1;
|
|
|
+ std::complex<FloatType> Denom = (Ha/mL + n/XL)*ZetaXL - ZetaXLM1;
|
|
|
+ // std::cout<< std::setprecision(100)
|
|
|
+ // << "Ql " << PsiXL
|
|
|
+ // <<std::endl;
|
|
|
+
|
|
|
+
|
|
|
+ return Num/Denom;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate bn - equation (6) //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::complex<FloatType> MultiLayerMie<FloatType>::calc_bn(int n, FloatType XL, std::complex<FloatType> Hb, std::complex<FloatType> mL,
|
|
|
+ std::complex<FloatType> PsiXL, std::complex<FloatType> ZetaXL,
|
|
|
+ std::complex<FloatType> PsiXLM1, std::complex<FloatType> ZetaXLM1) {
|
|
|
+
|
|
|
+ std::complex<FloatType> Num = (mL*Hb + n/XL)*PsiXL - PsiXLM1;
|
|
|
+ std::complex<FloatType> Denom = (mL*Hb + n/XL)*ZetaXL - ZetaXLM1;
|
|
|
+
|
|
|
+ return Num/Denom;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculates S1 - equation (25a) //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::complex<FloatType> MultiLayerMie<FloatType>::calc_S1(int n, std::complex<FloatType> an, std::complex<FloatType> bn,
|
|
|
+ FloatType Pi, FloatType Tau) {
|
|
|
+ return FloatType(n + n + 1)*(Pi*an + Tau*bn)/FloatType(n*n + n);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculates S2 - equation (25b) (it's the same as (25a), just switches //
|
|
|
+ // Pi and Tau) //
|
|
|
+ // ********************************************************************** //
|
|
|
+ template <typename FloatType>
|
|
|
+ std::complex<FloatType> MultiLayerMie<FloatType>::calc_S2(int n, std::complex<FloatType> an, std::complex<FloatType> bn,
|
|
|
+ FloatType Pi, FloatType Tau) {
|
|
|
+ return calc_S1(n, an, bn, Tau, Pi);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // 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 //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcD1D3(const std::complex<FloatType> z,
|
|
|
+ std::vector<std::complex<FloatType> >& D1,
|
|
|
+ std::vector<std::complex<FloatType> >& D3) {
|
|
|
+
|
|
|
+ // Downward recurrence for D1 - equations (16a) and (16b)
|
|
|
+ D1[nmax_] = std::complex<FloatType>(0.0, 0.0);
|
|
|
+ std::complex<FloatType> c_one(1.0, 0.0);
|
|
|
+ const std::complex<FloatType> zinv = std::complex<FloatType>(1.0, 0.0)/z;
|
|
|
+ for (int n = nmax_; n > 0; n--) {
|
|
|
+ D1[n - 1] = static_cast<FloatType>(n)*zinv - c_one/(D1[n] + static_cast<FloatType>(n)*zinv);
|
|
|
+ }
|
|
|
+ // TODO: Do we need this check?
|
|
|
+ // if (cabs(D1[0]) > 1.0e15) {
|
|
|
+ // throw std::invalid_argument("Unstable D1! Please, try to change input parameters!\n");
|
|
|
+ // //printf("Warning: Potentially unstable D1! Please, try to change input parameters!\n");
|
|
|
+ // }
|
|
|
+
|
|
|
+ // Upward recurrence for PsiZeta and D3 - equations (18a) - (18d)
|
|
|
+ PsiZeta_[0] = static_cast<FloatType>(0.5)*(static_cast<FloatType>(1.0) - std::complex<FloatType>(nmm::cos(2.0*z.real()), nmm::sin(2.0*z.real()))
|
|
|
+ *static_cast<FloatType>(nmm::exp(-2.0*z.imag())));
|
|
|
+ D3[0] = std::complex<FloatType>(0.0, 1.0);
|
|
|
+
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ PsiZeta_[n] = PsiZeta_[n - 1]*(static_cast<FloatType>(n)*zinv - D1[n - 1])
|
|
|
+ *(static_cast<FloatType>(n)*zinv - D3[n - 1]);
|
|
|
+ D3[n] = D1[n] + std::complex<FloatType>(0.0, 1.0)/PsiZeta_[n];
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the Riccati-Bessel functions (Psi and Zeta) for a //
|
|
|
+ // complex argument (z). //
|
|
|
+ // Equations (20a) - (21b) //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // z: Complex argument to evaluate Psi and Zeta //
|
|
|
+ // nmax: Maximum number of terms to calculate Psi and Zeta //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // Psi, Zeta: Riccati-Bessel functions //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcPsiZeta(std::complex<FloatType> z,
|
|
|
+ std::vector<std::complex<FloatType> >& Psi,
|
|
|
+ std::vector<std::complex<FloatType> >& Zeta) {
|
|
|
+
|
|
|
+ std::complex<FloatType> c_i(0.0, 1.0);
|
|
|
+ std::vector<std::complex<FloatType> > D1(nmax_ + 1), D3(nmax_ + 1);
|
|
|
+
|
|
|
+ // First, calculate the logarithmic derivatives
|
|
|
+ calcD1D3(z, D1, D3);
|
|
|
+
|
|
|
+ // Now, use the upward recurrence to calculate Psi and Zeta - equations (20a) - (21b)
|
|
|
+ Psi[0] = std::sin(z);
|
|
|
+ Zeta[0] = std::sin(z) - c_i*std::cos(z);
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ Psi[n] = Psi[n - 1]*(std::complex<FloatType>(n,0.0)/z - D1[n - 1]);
|
|
|
+ Zeta[n] = Zeta[n - 1]*(std::complex<FloatType>(n,0.0)/z - D3[n - 1]);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates Pi and Tau for a given value of cos(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) //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcPiTau(const FloatType& costheta,
|
|
|
+ std::vector<FloatType>& Pi, std::vector<FloatType>& Tau) {
|
|
|
+
|
|
|
+ int i;
|
|
|
+ //****************************************************//
|
|
|
+ // Equations (26a) - (26c) //
|
|
|
+ //****************************************************//
|
|
|
+ // Initialize Pi and Tau
|
|
|
+ Pi[0] = 1.0; // n=1
|
|
|
+ Tau[0] = costheta;
|
|
|
+ // Calculate the actual values
|
|
|
+ if (nmax_ > 1) {
|
|
|
+ Pi[1] = 3*costheta*Pi[0]; //n=2
|
|
|
+ Tau[1] = 2*costheta*Pi[1] - 3*Pi[0];
|
|
|
+ for (i = 2; i < nmax_; i++) { //n=[3..nmax_]
|
|
|
+ Pi[i] = ((i + i + 1)*costheta*Pi[i - 1] - (i + 1)*Pi[i - 2])/i;
|
|
|
+ Tau[i] = (i + 1)*costheta*Pi[i] - (i + 2)*Pi[i - 1];
|
|
|
+ }
|
|
|
+ }
|
|
|
+ } // end of MultiLayerMie::calcPiTau(...)
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates vector spherical harmonics (eq. 4.50, p. 95 BH), //
|
|
|
+ // required to calculate the near-field parameters. //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // Rho: Radial distance //
|
|
|
+ // Phi: Azimuthal angle //
|
|
|
+ // Theta: Polar angle //
|
|
|
+ // rn: Either the spherical Ricatti-Bessel function of first or third kind //
|
|
|
+ // Dn: Logarithmic derivative of rn //
|
|
|
+ // Pi, Tau: Angular functions Pi and Tau //
|
|
|
+ // n: Order of vector spherical harmonics //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // Mo1n, Me1n, No1n, Ne1n: Complex vector spherical harmonics //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcSpherHarm(const std::complex<FloatType> Rho, const FloatType Theta, const FloatType Phi,
|
|
|
+ const std::complex<FloatType>& rn, const std::complex<FloatType>& Dn,
|
|
|
+ const FloatType& Pi, const FloatType& Tau, const FloatType& n,
|
|
|
+ std::vector<std::complex<FloatType> >& Mo1n, std::vector<std::complex<FloatType> >& Me1n,
|
|
|
+ std::vector<std::complex<FloatType> >& No1n, std::vector<std::complex<FloatType> >& Ne1n) {
|
|
|
+
|
|
|
+ // using eq 4.50 in BH
|
|
|
+ std::complex<FloatType> c_zero(0.0, 0.0);
|
|
|
+
|
|
|
+ using nmm::sin;
|
|
|
+ using nmm::cos;
|
|
|
+ Mo1n[0] = c_zero;
|
|
|
+ Mo1n[1] = cos(Phi)*Pi*rn/Rho;
|
|
|
+ Mo1n[2] = -sin(Phi)*Tau*rn/Rho;
|
|
|
+ Me1n[0] = c_zero;
|
|
|
+ Me1n[1] = -sin(Phi)*Pi*rn/Rho;
|
|
|
+ Me1n[2] = -cos(Phi)*Tau*rn/Rho;
|
|
|
+ No1n[0] = sin(Phi)*(n*n + n)*sin(Theta)*Pi*rn/Rho/Rho;
|
|
|
+ No1n[1] = sin(Phi)*Tau*Dn*rn/Rho;
|
|
|
+ No1n[2] = cos(Phi)*Pi*Dn*rn/Rho;
|
|
|
+ Ne1n[0] = cos(Phi)*(n*n + n)*sin(Theta)*Pi*rn/Rho/Rho;
|
|
|
+ Ne1n[1] = cos(Phi)*Tau*Dn*rn/Rho;
|
|
|
+ Ne1n[2] = -sin(Phi)*Pi*Dn*rn/Rho;
|
|
|
+ } // end of MultiLayerMie::calcSpherHarm(...)
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // 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 //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcScattCoeffs() {
|
|
|
+
|
|
|
+ isScaCoeffsCalc_ = false;
|
|
|
+
|
|
|
+ const std::vector<FloatType>& x = size_param_;
|
|
|
+ const std::vector<std::complex<FloatType> >& m = refractive_index_;
|
|
|
+ const int& pl = PEC_layer_position_;
|
|
|
+ const int L = refractive_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. //
|
|
|
+ // ***********************************************************************//
|
|
|
+ int fl = (pl > 0) ? pl : 0;
|
|
|
+ if (nmax_preset_ <= 0) calcNmax(fl);
|
|
|
+ else nmax_ = nmax_preset_;
|
|
|
+
|
|
|
+ std::complex<FloatType> 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<FloatType> > D1_mlxl(nmax_ + 1), D1_mlxlM1(nmax_ + 1),
|
|
|
+ D3_mlxl(nmax_ + 1), D3_mlxlM1(nmax_ + 1);
|
|
|
+
|
|
|
+ std::vector<std::vector<std::complex<FloatType> > > Q(L), Ha(L), Hb(L);
|
|
|
+
|
|
|
+ for (int l = 0; l < L; l++) {
|
|
|
+ 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<FloatType> > 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<FloatType>(0.0, - 1.0);
|
|
|
+ D3_mlxl[n] = std::complex<FloatType>(0.0, 1.0);
|
|
|
+ }
|
|
|
+ } else { // Regular layer
|
|
|
+ z1 = x[fl]* m[fl];
|
|
|
+ // Calculate D1 and D3
|
|
|
+ calcD1D3(z1, D1_mlxl, D3_mlxl);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //******************************************************************//
|
|
|
+ // 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<FloatType> Temp, Num, Denom;
|
|
|
+ std::complex<FloatType> 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);
|
|
|
+
|
|
|
+ //*************************************************//
|
|
|
+ //Calculate Q, Ha and Hb in the layers fl + 1..L //
|
|
|
+ //*************************************************//
|
|
|
+ // Upward recurrence for Q - equations (19a) and (19b)
|
|
|
+ Num = std::complex<FloatType>(nmm::exp(-2.0*(z1.imag() - z2.imag())), 0.0)
|
|
|
+ *std::complex<FloatType>(nmm::cos(-2.0*z2.real()) - nmm::exp(-2.0*z2.imag()), nmm::sin(-2.0*z2.real()));
|
|
|
+ Denom = std::complex<FloatType>(nmm::cos(-2.0*z1.real()) - nmm::exp(-2.0*z1.imag()), nmm::sin(-2.0*z1.real()));
|
|
|
+ Q[l][0] = Num/Denom;
|
|
|
+
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ Num = (z1*D1_mlxl[n] + FloatType(n))*(FloatType(n) - z1*D3_mlxl[n - 1]);
|
|
|
+ Denom = (z2*D1_mlxlM1[n] + FloatType(n))*(FloatType(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 Psi and Zeta for XL //
|
|
|
+ //**************************************//
|
|
|
+ // Calculate PsiXL and ZetaXL
|
|
|
+ calcPsiZeta(std::complex<FloatType>(x[L - 1],0.0), 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<FloatType>(0.0, 0.0), std::complex<FloatType>(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
|
|
|
+ isScaCoeffsCalc_ = true;
|
|
|
+ } // end of MultiLayerMie::calcScattCoeffs()
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // 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 //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::RunMieCalculation() {
|
|
|
+ if (size_param_.size() != refractive_index_.size())
|
|
|
+ throw std::invalid_argument("Each size parameter should have only one index!");
|
|
|
+ if (size_param_.size() == 0)
|
|
|
+ throw std::invalid_argument("Initialize model first!");
|
|
|
+
|
|
|
+ const std::vector<FloatType>& x = size_param_;
|
|
|
+
|
|
|
+ MarkUncalculated();
|
|
|
+
|
|
|
+ // Calculate scattering coefficients
|
|
|
+ calcScattCoeffs();
|
|
|
+
|
|
|
+ // Initialize the scattering parameters
|
|
|
+ Qext_ = 0.0;
|
|
|
+ Qsca_ = 0.0;
|
|
|
+ Qabs_ = 0.0;
|
|
|
+ Qbk_ = 0.0;
|
|
|
+ Qpr_ = 0.0;
|
|
|
+
|
|
|
+ asymmetry_factor_ = 0.0;
|
|
|
+ albedo_ = 0.0;
|
|
|
+
|
|
|
+ // Initialize the scattering amplitudes
|
|
|
+ std::vector<std::complex<FloatType> > tmp1(theta_.size(),std::complex<FloatType>(0.0, 0.0));
|
|
|
+ S1_.swap(tmp1);
|
|
|
+ S2_ = S1_;
|
|
|
+
|
|
|
+ std::vector<FloatType> Pi(nmax_), Tau(nmax_);
|
|
|
+
|
|
|
+ std::complex<FloatType> Qbktmp(0.0, 0.0);
|
|
|
+ std::vector< std::complex<FloatType> > 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_ += (n + n + 1.0)*(an_[i].real() + bn_[i].real());
|
|
|
+ // Equation (28)
|
|
|
+ Qsca_ += (n + n + 1.0)*(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)
|
|
|
+ Qpr_ += ((n*(n + 2)/(n + 1))*((an_[i]*std::conj(an_[n]) + bn_[i]*std::conj(bn_[n])).real())
|
|
|
+ + ((FloatType)(n + n + 1)/(n*(n + 1)))*(an_[i]*std::conj(bn_[i])).real());
|
|
|
+ // Equation (33)
|
|
|
+ Qbktmp += (FloatType)(n + n + 1)*(1 - 2*(n % 2))*(an_[i]- bn_[i]);
|
|
|
+ // Calculate the scattering amplitudes (S1 and S2) //
|
|
|
+ // Precalculate cos(theta) - gives about 5% speed up.
|
|
|
+ std::vector<FloatType> costheta(theta_.size(), 0.0);
|
|
|
+ for (int t = 0; t < theta_.size(); t++) {
|
|
|
+ costheta[t] = nmm::cos(theta_[t]);
|
|
|
+ }
|
|
|
+ // Equations (25a) - (25b) //
|
|
|
+ for (unsigned int t = 0; t < theta_.size(); t++) {
|
|
|
+ calcPiTau(costheta[t], Pi, Tau);
|
|
|
+
|
|
|
+ S1_[t] += calc_S1(n, an_[i], bn_[i], Pi[i], Tau[i]);
|
|
|
+ S2_[t] += calc_S2(n, an_[i], bn_[i], Pi[i], Tau[i]);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ FloatType x2 = pow2(x.back());
|
|
|
+ Qext_ = 2.0*(Qext_)/x2; // Equation (27)
|
|
|
+ Qsca_ = 2.0*(Qsca_)/x2; // Equation (28)
|
|
|
+ Qpr_ = Qext_ - 4.0*(Qpr_)/x2; // Equation (29)
|
|
|
+ Qabs_ = Qext_ - Qsca_; // Equation (30)
|
|
|
+ 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;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the expansion coefficients inside the particle, //
|
|
|
+ // required to calculate the near-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: //
|
|
|
+ // aln, bln, cln, dln: Complex scattering amplitudes inside the particle //
|
|
|
+ // //
|
|
|
+ // Return value: //
|
|
|
+ // Number of multipolar expansion terms used for the calculations //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcExpanCoeffs() {
|
|
|
+ if (!isScaCoeffsCalc_)
|
|
|
+ throw std::invalid_argument("(calcExpanCoeffs) You should calculate external coefficients first!");
|
|
|
+
|
|
|
+ isExpCoeffsCalc_ = false;
|
|
|
+
|
|
|
+ std::complex<FloatType> c_one(1.0, 0.0), c_zero(0.0, 0.0);
|
|
|
+
|
|
|
+ const int L = refractive_index_.size();
|
|
|
+
|
|
|
+ aln_.resize(L + 1);
|
|
|
+ bln_.resize(L + 1);
|
|
|
+ cln_.resize(L + 1);
|
|
|
+ dln_.resize(L + 1);
|
|
|
+ for (int l = 0; l <= L; l++) {
|
|
|
+ aln_[l].resize(nmax_);
|
|
|
+ bln_[l].resize(nmax_);
|
|
|
+ cln_[l].resize(nmax_);
|
|
|
+ dln_[l].resize(nmax_);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Yang, paragraph under eq. A3
|
|
|
+ // a^(L + 1)_n = a_n, d^(L + 1) = 1 ...
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ aln_[L][n] = an_[n];
|
|
|
+ bln_[L][n] = bn_[n];
|
|
|
+ cln_[L][n] = c_one;
|
|
|
+ dln_[L][n] = c_one;
|
|
|
+ }
|
|
|
+
|
|
|
+ std::vector<std::complex<FloatType> > D1z(nmax_ + 1), D1z1(nmax_ + 1), D3z(nmax_ + 1), D3z1(nmax_ + 1);
|
|
|
+ std::vector<std::complex<FloatType> > Psiz(nmax_ + 1), Psiz1(nmax_ + 1), Zetaz(nmax_ + 1), Zetaz1(nmax_ + 1);
|
|
|
+ std::complex<FloatType> denomZeta, denomPsi, T1, T2, T3, T4;
|
|
|
+
|
|
|
+ auto& m = refractive_index_;
|
|
|
+ std::vector< std::complex<FloatType> > m1(L);
|
|
|
+
|
|
|
+ for (int l = 0; l < L - 1; l++) m1[l] = m[l + 1];
|
|
|
+ m1[L - 1] = std::complex<FloatType> (1.0, 0.0);
|
|
|
+
|
|
|
+ std::complex<FloatType> z, z1;
|
|
|
+ for (int l = L - 1; l >= 0; l--) {
|
|
|
+ if (l <= PEC_layer_position_) { // We are inside a PEC. All coefficients must be zero!!!
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ // aln
|
|
|
+ aln_[l][n] = c_zero;
|
|
|
+ // bln
|
|
|
+ bln_[l][n] = c_zero;
|
|
|
+ // cln
|
|
|
+ cln_[l][n] = c_zero;
|
|
|
+ // dln
|
|
|
+ dln_[l][n] = c_zero;
|
|
|
+ }
|
|
|
+ } else { // Regular material, just do the calculation
|
|
|
+ z = size_param_[l]*m[l];
|
|
|
+ z1 = size_param_[l]*m1[l];
|
|
|
+
|
|
|
+ calcD1D3(z, D1z, D3z);
|
|
|
+ calcD1D3(z1, D1z1, D3z1);
|
|
|
+ calcPsiZeta(z, Psiz, Zetaz);
|
|
|
+ calcPsiZeta(z1, Psiz1, Zetaz1);
|
|
|
+
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ int n1 = n + 1;
|
|
|
+
|
|
|
+ denomZeta = Zetaz[n1]*(D1z[n1] - D3z[n1]);
|
|
|
+ denomPsi = Psiz[n1]*(D1z[n1] - D3z[n1]);
|
|
|
+
|
|
|
+ T1 = aln_[l + 1][n]*Zetaz1[n1] - dln_[l + 1][n]*Psiz1[n1];
|
|
|
+ T2 = (bln_[l + 1][n]*Zetaz1[n1] - cln_[l + 1][n]*Psiz1[n1])*m[l]/m1[l];
|
|
|
+
|
|
|
+ T3 = (dln_[l + 1][n]*D1z1[n1]*Psiz1[n1] - aln_[l + 1][n]*D3z1[n1]*Zetaz1[n1])*m[l]/m1[l];
|
|
|
+ T4 = cln_[l + 1][n]*D1z1[n1]*Psiz1[n1] - bln_[l + 1][n]*D3z1[n1]*Zetaz1[n1];
|
|
|
+
|
|
|
+ // aln
|
|
|
+ aln_[l][n] = (D1z[n1]*T1 + T3)/denomZeta;
|
|
|
+ // bln
|
|
|
+ bln_[l][n] = (D1z[n1]*T2 + T4)/denomZeta;
|
|
|
+ // cln
|
|
|
+ cln_[l][n] = (D3z[n1]*T2 + T4)/denomPsi;
|
|
|
+ // dln
|
|
|
+ dln_[l][n] = (D3z[n1]*T1 + T3)/denomPsi;
|
|
|
+ } // end of all n
|
|
|
+ } // end PEC condition
|
|
|
+ } // end of all l
|
|
|
+
|
|
|
+ // Check the result and change aln_[0][n] and aln_[0][n] for exact zero
|
|
|
+ for (int n = 0; n < nmax_; ++n) {
|
|
|
+ if (cabs(aln_[0][n]) < 1e-10) aln_[0][n] = 0.0;
|
|
|
+ else {
|
|
|
+ //throw std::invalid_argument("Unstable calculation of aln_[0][n]!");
|
|
|
+ std::cout<< std::setprecision(100)
|
|
|
+ << "Warning: Potentially unstable calculation of aln[0]["
|
|
|
+ << n << "] = "<< aln_[0][n] <<std::endl;
|
|
|
+ aln_[0][n] = 0.0;
|
|
|
+ }
|
|
|
+ if (cabs(bln_[0][n]) < 1e-10) bln_[0][n] = 0.0;
|
|
|
+ else {
|
|
|
+ //throw std::invalid_argument("Unstable calculation of bln_[0][n]!");
|
|
|
+ std::cout<< std::setprecision(100)
|
|
|
+ << "Warning: Potentially unstable calculation of bln[0]["
|
|
|
+ << n << "] = "<< bln_[0][n] <<std::endl;
|
|
|
+ bln_[0][n] = 0.0;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ isExpCoeffsCalc_ = true;
|
|
|
+ } // end of void MultiLayerMie::calcExpanCoeffs()
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the electric (E) and magnetic (H) fields inside and //
|
|
|
+ // around the particle. //
|
|
|
+ // //
|
|
|
+ // Input parameters (coordinates of the point): //
|
|
|
+ // Rho: Radial distance //
|
|
|
+ // Phi: Azimuthal angle //
|
|
|
+ // Theta: Polar angle //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // E, H: Complex electric and magnetic fields //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::calcField(const FloatType Rho, const FloatType Theta, const FloatType Phi,
|
|
|
+ std::vector<std::complex<FloatType> >& E, std::vector<std::complex<FloatType> >& H) {
|
|
|
+
|
|
|
+ std::complex<FloatType> c_zero(0.0, 0.0), c_i(0.0, 1.0), c_one(1.0, 0.0);
|
|
|
+ std::vector<std::complex<FloatType> > ipow = {c_one, c_i, -c_one, -c_i}; // Vector containing precomputed integer powers of i to avoid computation
|
|
|
+ std::vector<std::complex<FloatType> > M3o1n(3), M3e1n(3), N3o1n(3), N3e1n(3);
|
|
|
+ std::vector<std::complex<FloatType> > M1o1n(3), M1e1n(3), N1o1n(3), N1e1n(3);
|
|
|
+ std::vector<std::complex<FloatType> > Psi(nmax_ + 1), D1n(nmax_ + 1), Zeta(nmax_ + 1), D3n(nmax_ + 1);
|
|
|
+ std::vector<FloatType> Pi(nmax_), Tau(nmax_);
|
|
|
+
|
|
|
+ int l = 0; // Layer number
|
|
|
+ std::complex<FloatType> ml;
|
|
|
+
|
|
|
+ // Initialize E and H
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ E[i] = c_zero;
|
|
|
+ H[i] = c_zero;
|
|
|
+ }
|
|
|
+
|
|
|
+ if (Rho > size_param_.back()) {
|
|
|
+ l = size_param_.size();
|
|
|
+ ml = c_one;
|
|
|
+ } else {
|
|
|
+ for (int i = size_param_.size() - 1; i >= 0 ; i--) {
|
|
|
+ if (Rho <= size_param_[i]) {
|
|
|
+ l = i;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ ml = refractive_index_[l];
|
|
|
+ }
|
|
|
+
|
|
|
+ // Calculate logarithmic derivative of the Ricatti-Bessel functions
|
|
|
+ calcD1D3(Rho*ml, D1n, D3n);
|
|
|
+ // Calculate Ricatti-Bessel functions
|
|
|
+ calcPsiZeta(Rho*ml, Psi, Zeta);
|
|
|
+
|
|
|
+ // Calculate angular functions Pi and Tau
|
|
|
+ calcPiTau(nmm::cos(Theta), Pi, Tau);
|
|
|
+
|
|
|
+ for (int n = nmax_ - 2; n >= 0; n--) {
|
|
|
+ int n1 = n + 1;
|
|
|
+ FloatType rn = static_cast<FloatType>(n1);
|
|
|
+
|
|
|
+ // using BH 4.12 and 4.50
|
|
|
+ calcSpherHarm(Rho*ml, Theta, Phi, Psi[n1], D1n[n1], Pi[n], Tau[n], rn, M1o1n, M1e1n, N1o1n, N1e1n);
|
|
|
+ calcSpherHarm(Rho*ml, Theta, Phi, Zeta[n1], D3n[n1], Pi[n], Tau[n], rn, M3o1n, M3e1n, N3o1n, N3e1n);
|
|
|
+
|
|
|
+ // Total field in the lth layer: eqs. (1) and (2) in Yang, Appl. Opt., 42 (2003) 1710-1720
|
|
|
+ std::complex<FloatType> En = ipow[n1 % 4]
|
|
|
+ *static_cast<FloatType>((rn + rn + 1.0)/(rn*rn + rn));
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ // electric field E [V m - 1] = EF*E0
|
|
|
+ E[i] += En*(cln_[l][n]*M1o1n[i] - c_i*dln_[l][n]*N1e1n[i]
|
|
|
+ + c_i*aln_[l][n]*N3e1n[i] - bln_[l][n]*M3o1n[i]);
|
|
|
+
|
|
|
+ H[i] += En*(-dln_[l][n]*M1e1n[i] - c_i*cln_[l][n]*N1o1n[i]
|
|
|
+ + c_i*bln_[l][n]*N3o1n[i] + aln_[l][n]*M3e1n[i]);
|
|
|
+ }
|
|
|
+ } // end of for all n
|
|
|
+
|
|
|
+ // magnetic field
|
|
|
+ std::complex<FloatType> hffact = ml/static_cast<FloatType>(cc_*mu_);
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ H[i] = hffact*H[i];
|
|
|
+ }
|
|
|
+ } // end of MultiLayerMie::calcField(...)
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates complex electric and magnetic field in the surroundings //
|
|
|
+ // and inside 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 //
|
|
|
+ //**********************************************************************************//
|
|
|
+ template <typename FloatType>
|
|
|
+ void MultiLayerMie<FloatType>::RunFieldCalculation() {
|
|
|
+ FloatType Rho, Theta, Phi;
|
|
|
+
|
|
|
+ // Calculate scattering coefficients an_ and bn_
|
|
|
+ calcScattCoeffs();
|
|
|
+
|
|
|
+ // Calculate expansion coefficients aln_, bln_, cln_, and dln_
|
|
|
+ calcExpanCoeffs();
|
|
|
+
|
|
|
+ long total_points = coords_[0].size();
|
|
|
+ E_.resize(total_points);
|
|
|
+ H_.resize(total_points);
|
|
|
+ for (auto& f : E_) f.resize(3);
|
|
|
+ for (auto& f : H_) f.resize(3);
|
|
|
+
|
|
|
+ for (int point = 0; point < total_points; point++) {
|
|
|
+ const FloatType& Xp = coords_[0][point];
|
|
|
+ const FloatType& Yp = coords_[1][point];
|
|
|
+ const FloatType& Zp = coords_[2][point];
|
|
|
+
|
|
|
+ // Convert to spherical coordinates
|
|
|
+ Rho = nmm::sqrt(pow2(Xp) + pow2(Yp) + pow2(Zp));
|
|
|
+
|
|
|
+ // If Rho=0 then Theta is undefined. Just set it to zero to avoid problems
|
|
|
+ Theta = (Rho > 0.0) ? nmm::acos(Zp/Rho) : 0.0;
|
|
|
+
|
|
|
+ // If Xp=Yp=0 then Phi is undefined. Just set it to zero to avoid problems
|
|
|
+ if (Xp == 0.0)
|
|
|
+ Phi = (Yp != 0.0) ? nmm::asin(Yp/nmm::sqrt(pow2(Xp) + pow2(Yp))) : 0.0;
|
|
|
+ else
|
|
|
+ Phi = nmm::acos(Xp/nmm::sqrt(pow2(Xp) + pow2(Yp)));
|
|
|
+
|
|
|
+ // Avoid convergence problems due to Rho too small
|
|
|
+ if (Rho < 1e-5) Rho = 1e-5;
|
|
|
+
|
|
|
+ //*******************************************************//
|
|
|
+ // 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 //
|
|
|
+ //*******************************************************//
|
|
|
+
|
|
|
+ // This array contains the fields in spherical coordinates
|
|
|
+ std::vector<std::complex<FloatType> > Es(3), Hs(3);
|
|
|
+
|
|
|
+ // Do the actual calculation of electric and magnetic field
|
|
|
+ calcField(Rho, Theta, Phi, Es, Hs);
|
|
|
+
|
|
|
+ { //Now, convert the fields back to cartesian coordinates
|
|
|
+ using nmm::sin;
|
|
|
+ using nmm::cos;
|
|
|
+ E_[point][0] = sin(Theta)*cos(Phi)*Es[0] + cos(Theta)*cos(Phi)*Es[1] - sin(Phi)*Es[2];
|
|
|
+ E_[point][1] = sin(Theta)*sin(Phi)*Es[0] + cos(Theta)*sin(Phi)*Es[1] + cos(Phi)*Es[2];
|
|
|
+ E_[point][2] = cos(Theta)*Es[0] - sin(Theta)*Es[1];
|
|
|
+
|
|
|
+ H_[point][0] = sin(Theta)*cos(Phi)*Hs[0] + cos(Theta)*cos(Phi)*Hs[1] - sin(Phi)*Hs[2];
|
|
|
+ H_[point][1] = sin(Theta)*sin(Phi)*Hs[0] + cos(Theta)*sin(Phi)*Hs[1] + cos(Phi)*Hs[2];
|
|
|
+ H_[point][2] = cos(Theta)*Hs[0] - sin(Theta)*Hs[1];
|
|
|
+ }
|
|
|
+ } // end of for all field coordinates
|
|
|
+ } // end of MultiLayerMie::RunFieldCalculation()
|
|
|
+} // end of namespace nmie
|
|
|
+#endif // SRC_NMIE_IMPL_H_
|
