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StokesMuller.c
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StokesMuller.c
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/* File: StokesMuller.c
Sprout 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.
Sprout 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 Sprout. If not, see <http://www.gnu.org/licenses/>.
Copyright 2013, Michihiro Takami, Hyosun Kim, Jennifer Karr
All rights reserved.
Contact: Jennifer Karr (jkarr@asiaa.sinica.edu.tw)
*/
#include <stdlib.h>
#include <math.h>
#include "mt19937ar.h"
const double pi, rad2deg;
double g, albedo, S11[181], S12[181], S33[181], S34[181], probability_func[201], PSI;
void VectorRotate(double new_xyz[3], double xyz[3], double xyz0[3]);
double scatterAngle_HG() {
/* WARNING : check if 0 < g < 1 */
/* WARNING : check if 0 < g < 1 */
/* WARNING : check if 0 < g < 1 */
/* WARNING : check if 0 < g < 1 */
/* */
/* DESCRIPTION */
/* phase function P(theta;g) */
/* the Henyey-Greenstein phase function for 0.15 < g <= 1 */
/* the Rayleigh scattering phase function for 0 <= g < 0.15 */
/* INPUTS */
/* (g as a global variable) */
/* (P as a random number) */
/* OUTPUT */
/* cos(theta) */
/* */
/* 2011-08-24 Hyosun Kim */
double g2,A,B,C,D,cosT,P;
P=genrand_real2();
if (g > 0.15) {/* Henyey-Greenstein phase function for 0.15 < g <= 1 */
g2 = g*g;
A = 1.0 + g2;
B = 1.0 - g2;
C = 1.0 - g + 2.0*g*P;
D = B / C;
cosT = ( A - D*D ) / ( 2.0 * g );
} else { /* Rayleigh scattering phase function for 0 <= g < 0.15 */
B = 1.0 - 2.0*P;
C = pow(sqrt(4.*B*B+1.)-2.*B , 1./3.);
cosT = C - 1.0/C;
}
return cosT;
}
double scatterAngle_table_lookup(){
/* */
/* DESCRIPTION */
/* phase function P(theta;g) */
/* the table-lookup method */
/* INPUTS */
/* (probability_func[201]) */
/* (P as a random number) */
/* OUTPUT */
/* cos(theta) */
/* */
/* 2011-09-17 Hiro Takami */
/* */
/* Note: check completed on 9/19/2011 */
double cosT,P,i,i_residual;
int i_int;
P = genrand_real2();
i = P*200; // number of elements - 1 for "probability func"
i_int = i;
i_residual = i-i_int*1.;
cosT = probability_func[i_int]*(1.-i_residual)+probability_func[i_int+1]*i_residual;
return cosT;
}
double calVelo(double new_vel[3],double vel[3],double cosPSI,double IQUV[4]) {
/* */
/* DESCRIPTION */
/* */
/* INPUTS */
/* vel[3] */
/* cosPSI */
/* IQUV[4] */
/* (S11[181], S12[181]) */
/* (2 random numbers for PHI) */
/* OUTPUTS */
/* new_vel[3] */
/* PHI */
/* 2011-08-24 Hyosun Kim */
double CRIT, A,B,C, dx_norm, dy_norm, dz_norm;
double PHI, sinPHI, cosPHI;
//double PSI, sinPSI;
double sinPSI;
int intPSI;
dx_norm=vel[0]; dy_norm=vel[1]; dz_norm=vel[2];
PHI = genrand_real2();
PHI = pi * (PHI + (PHI>0.5)*0.5);
/* if (PHI < 0.5) { */
/* PHI = pi * PHI; */
/* } else { */
/* PHI = pi * (PHI + 0.5); */
/* } */
PSI = acos(cosPSI); if (PSI > pi) PSI = 0.0;
intPSI = (int) (PSI * rad2deg);
CRIT = (IQUV[1]*cos(2.*PHI)+IQUV[2]*sin(2.*PHI))/IQUV[0];
CRIT = (1.+S12[intPSI]/S11[intPSI]*CRIT)*0.5;
if (genrand_real2() > CRIT) PHI = PHI + pi*0.5;
sinPSI = sqrt(1.-cosPSI*cosPSI);
sinPHI = sin(PHI);
cosPHI = cos(PHI);
A = sinPSI * cosPHI;
B = sinPSI * sinPHI;
C = sqrt(1.-dz_norm*dz_norm);
if (abs(dz_norm) == 1) {
new_vel[0] = A;
new_vel[1] = B;
new_vel[2] = cosPSI*dz_norm;
} else {
new_vel[0] = ( A*dz_norm*dx_norm - B*dy_norm ) / C + cosPSI*dx_norm;
new_vel[1] = ( A*dz_norm*dy_norm + B*dx_norm ) / C + cosPSI*dy_norm;
new_vel[2] = -A*C + cosPSI*dz_norm;
}
return PHI;
}
void StokesMuller(double new_IQUV[4], double new_vel[3],
double IQUV[4], double vel[3]) {
/* WARNING : check what do W and W2 mean */
/* WARNING : check what do W and W2 mean */
/* WARNING : check what do W and W2 mean */
/* WARNING : check what do W and W2 mean */
/* */
/* DESCRIPTION */
/* RPO * XMUL * ROP */
/* = | 1 0 0 0 | * | s11 s12 0 0 | * | 1 0 0 0 | */
/* | 0 cosW sinW 0 | | s12 s11 0 0 | | 0 cosW2 sinW2 0 | */
/* | 0 -sinW cosW 0 | | 0 0 s33 -s34 | | 0 -sinW2 cosW2 0 | */
/* | 0 0 0 1 | | 0 0 s34 s33 | | 0 0 0 1 | */
/* */
/* IQUV_out = (RPO * XMUL * ROP) * IQUV_in */
/* IQUV_out *= I_in / I_out * albedo */
/* */
/* INPUTS */
/* IQUV[4] */
/* vel[3] */
/* (S11[181], S12[181], S33[181], S34[181], albedo) */
/* OUTPUTS */
/* new_IQUV[4] */
/* new_vel[3] */
/* */
/* 2011-08-30 Hyosun Kim */
int i, ANGDIFF;
double W, W2, cosW,sinW,cosW2,sinW2, cosPSI, vel_modified[3];
double I1,Q1,U1,V1, I2,Q2,U2,V2, s11,s12,s33,s34, scale;
/* cosPSI */
/* The probability function is replaced on 9/19/2011 */
//cosPSI = scatterAngle_HG();
cosPSI = scatterAngle_table_lookup();
/* W2 (= 2 PHI) */
W2 = 2. * calVelo(new_vel, vel, cosPSI, IQUV); /* get new_vel */
/* W (= 2 THETA) */
VectorRotate(vel_modified, vel, new_vel); /* get vel_modified */
scale = sqrt(pow(vel_modified[1],2) + pow(vel_modified[2],2));
if (scale == 0.) {
W = 0.;
} else {
W = 2. * acos(-vel_modified[1] / scale);
}
if (W > 2.*pi) W = 0.;
if (vel_modified[2] < 0.) W = -W;
/* cosW, sinW, cosW2, sinW2 */
cosW = cos(W); cosW2 = cos(W2);
sinW = sin(W); sinW2 = sin(W2);
/* s11, s12, s33, s34 */
ANGDIFF=(int) (acos(cosPSI)*rad2deg + 0.5); if (ANGDIFF>180) ANGDIFF=180;
s11=S11[ANGDIFF]; s12=S12[ANGDIFF]; s33=S33[ANGDIFF]; s34=S34[ANGDIFF];
/* new_IQUV via. matrix calculation */
I1 = IQUV[0];
Q1 = IQUV[1] * cosW2 + IQUV[2] * sinW2;
U1 =-IQUV[1] * sinW2 + IQUV[2] * cosW2;
V1 = IQUV[3];
I2 = s11 * I1 + s12 * Q1;
Q2 = s12 * I1 + s11 * Q1;
U2 = s33 * U1 - s34 * V1;
V2 = s34 * U1 + s33 * V1;
new_IQUV[0] = I2;
new_IQUV[1] = Q2 * cosW + U2 * sinW;
new_IQUV[2] =-Q2 * sinW + U2 * cosW;
new_IQUV[3] = V2;
scale = I1 / I2 * albedo;
for (i=0; i<4; i++) {
new_IQUV[i] *= scale;
}
}