8e4f8364
 David Mayerich
started a new opt...
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#ifndef RTS_BEAM
#define RTS_BEAM
#include "../math/vec3.h"
#include "../optics/scalarwave.h"
#include "../math/bessel.h"
#include <vector>
//Boost
//#include <boost/math/special_functions/bessel.hpp>
//#include <boost/math/special_functions/legendre.hpp>
namespace stim{
/// Function returns the value of the scalar field produced by a beam with the specified parameters
template<typename T>
std::vector< stim::vec3<T> > generate_focusing_vectors(size_t N, stim::vec3<T> d, T NA, T NA_in = 0){
std::vector< stim::vec3<T> > dirs(N); //allocate an array to store the focusing vectors
///compute the rotation operator to transform (0, 0, 1) to k
T cos_angle = d.dot(vec3<T>(0, 0, 1));
stim::matrix<T, 3> rotation;
//if the cosine of the angle is -1, the rotation is just a flip across the z axis
if(cos_angle == -1){
rotation(2, 2) = -1;
}
else if(cos_angle != 1.0)
{
vec3<T> r_axis = vec3<T>(0, 0, 1).cross(d).norm(); //compute the axis of rotation
T angle = acos(cos_angle); //compute the angle of rotation
quaternion<T> quat; //create a quaternion describing the rotation
quat.CreateRotation(angle, r_axis);
rotation = quat.toMatrix3(); //compute the rotation matrix
}
//find the phi values associated with the cassegrain ring
T PHI[2];
PHI[0] = (T)asin(NA);
PHI[1] = (T)asin(NA_in);
//calculate the z-axis cylinder coordinates associated with these angles
T Z[2];
Z[0] = cos(PHI[0]);
Z[1] = cos(PHI[1]);
T range = Z[0] - Z[1];
//draw a distribution of random phi, z values
T z, phi, theta;
//T kmag = stim::TAU / lambda;
for(int i=0; i<N; i++){ //for each sample
z = (T)((double)rand() / (double)RAND_MAX) * range + Z[1]; //find a random position on the surface of a cylinder
theta = (T)(((double)rand() / (double)RAND_MAX) * stim::TAU);
phi = acos(z); //project onto the sphere, computing phi in spherical coordinates
//compute and store cartesian coordinates
vec3<T> spherical(1, theta, phi); //convert from spherical to cartesian coordinates
vec3<T> cart = spherical.sph2cart();
dirs[i] = rotation * cart; //create a sample vector
}
return dirs;
}
/// Class stim::beam represents a beam of light focused at a point and composed of several plane waves
template<typename T>
class scalarbeam
{
public:
//enum beam_type {Uniform, Bartlett, Hamming, Hanning};
private:
T NA[2]; //numerical aperature of the focusing optics
vec3<T> f; //focal point
vec3<T> d; //propagation direction
stim::complex<T> A; //beam amplitude
T lambda; //beam wavelength
public:
///constructor: build a default beam (NA=1.0)
scalarbeam(T wavelength = 1, stim::complex<T> amplitude = 1, vec3<T> focal_point = vec3<T>(0, 0, 0), vec3<T> direction = vec3<T>(0, 0, 1), T numerical_aperture = 1, T center_obsc = 0){
lambda = wavelength;
A = amplitude;
f = focal_point;
d = direction.norm(); //make sure that the direction vector is normalized (makes calculations more efficient later on)
NA[0] = numerical_aperture;
NA[1] = center_obsc;
}
///Numerical Aperature functions
void setNA(T na)
{
NA[0] = (T)0;
NA[1] = na;
}
void setNA(T na0, T na1)
{
NA[0] = na0;
NA[1] = na1;
}
//Monte-Carlo decomposition into plane waves
std::vector< scalarwave<T> > mc(size_t N = 100000) const{
std::vector< stim::vec3<T> > dirs = generate_focusing_vectors(N, d, NA[0], NA[1]); //generate a random set of N vectors forming a focus
std::vector< scalarwave<T> > samples(N); //create a vector of plane waves
T kmag = (T)stim::TAU / lambda; //calculate the wavenumber
stim::complex<T> apw; //allocate space for the amplitude at the focal point
stim::vec3<T> kpw; //declare the new k-vector based on the focused plane wave direction
for(size_t i=0; i<N; i++){ //for each sample
kpw = dirs[i] * kmag; //calculate the k-vector for the new plane wave
apw = exp(stim::complex<T>(0, kpw.dot(-f))); //calculate the amplitude for the new plane wave
samples[i] = scalarwave<T>(kpw, apw); //create a plane wave based on the direction
}
return samples;
}
/// Calculate the field at a given point
/// @param x is the x-coordinate of the field point
/// @O is the approximation accuracy
stim::complex<T> field(T x, T y, T z, size_t O){
std::vector< scalarwave<T> > W = mc(O);
T result = 0; //initialize the result to zero (0)
for(size_t i = 0; i < O; i++){ //for each plane wave
result += W[i].pos(x, y, z);
}
return result;
}
/// Calculate the field at a set of positions
/*void field(stim::complex<T>* F, T* x, T* y, T* z, size_t N, size_t O){
memset(F, 0, N * sizeof(stim::complex<T>));
std::vector< scalarwave<T> > W = mc(O); //get a random set of plane waves representing the beam
size_t o, n;
T px, py, pz;
for(n = 0; n < N; n++){ //for each point in the field
(x == NULL) ? px = 0 : px = x[n]; // test for NULL values
(y == NULL) ? py = 0 : py = y[n];
(z == NULL) ? pz = 0 : pz = z[n];
for(o = 0; o < O; o++){ //for each plane wave
F[n] += W[o].pos(px, py, pz);
}
}
}*/
std::string str()
{
std::stringstream ss;
ss<<"Beam:"<<std::endl;
//ss<<" Central Plane Wave: "<<beam::E0<<" e^i ( "<<beam::k<<" . r )"<<std::endl;
ss<<" Beam Direction: "<<d<<std::endl;
if(NA[0] == 0)
ss<<" NA: "<<NA[1];
else
ss<<" NA: "<<NA[0]<<" -- "<<NA[1];
return ss.str();
}
}; //end beam
template<typename T>
void cpu_scalar_psf(stim::complex<T>* F, size_t N, T* x, T* y, T* z, T lambda, T A, stim::vec3<T> f, T NA, T NA_in, int Nl){
memset(F, 0, N * sizeof(stim::complex<T>));
T k = stim::TAU / lambda;
T jl, Pl, C, kr, cos_phi;
T cos_alpha_1 = cos(asin(NA_in));
T cos_alpha_2 = cos(asin(NA));
stim::vec3<T> p, ps;
/*double vm;
size_t table_bytes = (Nl + 1) * sizeof(double);
double* jv = (double*) malloc( table_bytes );
double* yv = (double*) malloc( table_bytes );
double* djv= (double*) malloc( table_bytes );
double* dyv= (double*) malloc( table_bytes );
*/
T vm;
size_t table_bytes = (Nl + 1) * sizeof(T);
T* jv = (T*) malloc( table_bytes );
T* yv = (T*) malloc( table_bytes );
T* djv= (T*) malloc( table_bytes );
T* dyv= (T*) malloc( table_bytes );
for(size_t n = 0; n < N; n++){
(x == NULL) ? p[0] = 0 : p[0] = x[n]; // test for NULL values and set positions
(y == NULL) ? p[1] = 0 : p[1] = y[n];
(z == NULL) ? p[2] = 0 : p[2] = z[n];
ps = p.cart2sph(); //convert this point to spherical coordinates
kr = k * ps[0];
cos_phi = std::cos(ps[2]);
stim::bessjyv_sph<T>(Nl, kr, vm, jv, yv, djv, dyv);
for(int l = 0; l <= Nl; l++){
//jl = boost::math::sph_bessel<T>(l, kr);
//jl = stim::bessjyv(l, kr
jl = (T)jv[l];
Pl = 1;//boost::math::legendre_p<T>(l, cos_phi);
C = 1;//boost::math::legendre_p<T>(l+1, cos_alpha_1) - boost::math::legendre_p<T>(l + 1, cos_alpha_2) - boost::math::legendre_p<T>(l - 1, cos_alpha_1) + boost::math::legendre_p<T>(l - 1, cos_alpha_2);
F[n] += pow(complex<T>(0, 1), l) * jl * Pl * C;
}
F[n] *= A * stim::TAU;
}
}
} //end namespace stim
#endif
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