Remove PartialExtinction codes from Bobbert_Vlieger_BRDF_Model, Subsu…

…rface_Bobbert_Vlieger_BRDF_Model, Axisymmetric_Particle_BRDF_Model, and Subsurface_Axisymmetric_Particle and replace them with Specular(theta).

Add 90 degree phase to Bobbert_Vlieger_BRDF_Model, Subsurface_Bobbert_Vlieger_BRDF_Model, Axisymmetric_Particle_BRDF_Model, and Subsurface_Axisymmetric_Particle, so that the optical theorem works the same as for free space scatterers.

Correct JonesMatrix::hermitian() and add JonesMatrix::conj().

code/axipart.h

@@ -47,8 +47,10 @@ namespace SCATMECH {
         public:
             Axisymmetric_Particle_BRDF_Model();
 
-            COMPLEX PartialExtinctionS(double theta);
-            COMPLEX PartialExtinctionP(double theta);
+            MuellerMatrix Specular(double theta);
+
+            //COMPLEX PartialExtinctionS(double theta);
+            //COMPLEX PartialExtinctionP(double theta);
 
         protected:
             void setup();
@@ -114,7 +116,6 @@ namespace SCATMECH {
             void    calculate_Z(double thetas);
             void    calculate_eIP(double phis);
 
-            COMPLEX	PartialExtinction(double theta,int pol);
 
             void    iterative_improvement(ScatterTMatrix& Ainv, ScatterTMatrix& A,
                                           std::vector<COMPLEX>& b,std::vector<COMPLEX>& x);

code/axipart1.cpp

@@ -581,112 +581,78 @@ namespace SCATMECH {
         MMAX = 0;
     }
 
-    COMPLEX
+    MuellerMatrix
     Axisymmetric_Particle_BRDF_Model::
-    PartialExtinctionS(double theta)
-    {
-        return PartialExtinction(theta,1);
-    }
-
-    COMPLEX
-    Axisymmetric_Particle_BRDF_Model::
-    PartialExtinctionP(double theta)
-    {
-        return PartialExtinction(theta,0);
-    }
-
-    COMPLEX
-    Axisymmetric_Particle_BRDF_Model::
-    PartialExtinction(double theta,int pol)
+    Specular(double theta)
     {
         SETUP();
 
-        // This function returns the partial extinction cross section for
-        // an incident angle of theta and polarization pol, where the "partial"
-        // means the following: when type=0 or type=2, the reflectance changes
-        // by a factor exp(-sigma*density/cos(theta)) and for type=1 or type=3, the
-        // transmittance changes by a factor exp(-sigma*density/cos(theta). The total
-        // extinction cross section is the sum of these values for type=0 and type=1,
-        // for light incident downward, or the sum of these values for type=2 and type=3,
-        // for light incident upward. The value of the partial extinction cross
-        // section can be negative, which is an indication that the reflectance
-        // or transmittance is increased by the presence of the particle.
-        //
-
-        pol = pol ? 1 : 0;
-        vector<COMPLEX>& W = pol ? Ws : Wp;
-        vector<COMPLEX>& Z = pol ? Zs : Zp;
+        // This function returns the Mueller matrix specular reflectance (for type==0 or 
+        // type==2) or the regular transmittance (for type==1 or type==3) for an incident 
+        // angle of theta (in radians). The result is derived from the optical theorem 
+        // and is only valid when density is suffiently low that multiple scattering 
+        // between spheres can be neglected.
 
         switch (type) {
-            case 0:
-            {
-                set_geometry(theta,theta,0.);
-                COMPLEX e = E(W,Z);
-                COMPLEX r = stack->r12(theta,lambda,vacuum,substrate)[pol];
-                r *= exp(2.*cI*qq*cos(theta));
-                double R = norm(r);
-                return 4.*pi/k*COMPLEX(0.,-1.)*(e/r)*R;
-            }
-            break;
-            case 1:
-            {
-                double index = substrate.n(lambda);
-                double sint = sin(theta)/index;
-                if (sint>=1. || substrate.k(lambda)!=0) return 0.;
-                double thetat = asin(sint);
-                set_geometry(theta,thetat,0.);
-                COMPLEX e = E(W,Z);
-                COMPLEX phase =  exp(cI*qq*(cos(theta)-index*cos(thetat)));
-                double factor = cos(thetat)/cos(theta);
-                e /= phase;
-                COMPLEX t = stack->t12(theta,lambda,vacuum,substrate)[pol];
-                double T = norm(t)*factor*index;
-                return 4.*pi/k/sqrt(cube(index))/factor*COMPLEX(0.,-1.)*(e/t)*T;
-            }
-            break;
-            case 2:
-            {
-                set_geometry(theta,theta,0.);
-                COMPLEX e = E(W,Z);
-                double index = substrate.n(lambda);
-
-                COMPLEX sint = sin(theta)*index;
-                COMPLEX cost = sqrt(1.-sqr(sint));
-                if (imag(cost)<0) cost = -cost;
-
-                COMPLEX r = stack->r21i(theta,lambda,substrate,vacuum)[pol];
-                double R = norm(r);
-
-                r *= exp(-2.*cI*qq*index*cos(theta));
-
-                return 4.*pi/k/index*COMPLEX(0.,-1.)*(e/r)*R;
-            }
-            break;
-            case 3:
-            {
-                double index = substrate.n(lambda);
-                double sint = sin(theta)*index;
-                COMPLEX cost = sqrt(1.-sqr(sint));
-                if (imag(cost)<0) cost = -cost;
-                if (sint>=1.) return 0.;
-                double thetat = asin(sint);
-
-                set_geometry(theta,thetat,0.);
-                COMPLEX e = E(W,Z);
-
-                double factor = cos(theta)/real(cost);
-                COMPLEX phase = exp(cI*qq*(cost-index*cos(theta)));
-
-                e /= phase;
-                COMPLEX t = stack->t21i(theta,lambda,substrate,vacuum)[pol];
-                double T = norm(t)/index/factor;
-                return 4.*pi/k*sqrt(index)*factor*COMPLEX(0.,-1.)*(e/t)*T;
-            }
-            break;
-            default:
-                error("Invalid type = " + to_string(type));
+        case 0:
+        {
+            JonesMatrix X = JonesDSC(theta, theta, 0., 0.);
+            JonesMatrix r = stack->r12(theta, lambda, vacuum, substrate);
+            r *= exp(2. * cI * qq * cos(theta));
+            MuellerMatrix sigma = (4. * pi / k) * ReCrossMueller(X, r);
+
+            return MuellerMatrix(r) - sigma * (density / cos(theta));
+        }
+        break;
+        case 1:
+        {
+            double index = substrate.n(lambda);
+            double sint = sin(theta) / index;
+            if (sint >= 1. || substrate.k(lambda) != 0) return MuellerZero();
+            double thetat = asin(sint);
+            JonesMatrix X = JonesDSC(theta, thetat, 0., 0.);
+            COMPLEX phase = exp(cI * qq * (cos(theta) - index * cos(thetat)));
+            //double factor = cos(thetat)/cos(theta);
+            JonesMatrix t = stack->t12(theta, lambda, vacuum, substrate);
+            t *= phase;
+            MuellerMatrix sigma = (4. * pi / k / sqrt(index)) * ReCrossMueller(X, t);
+
+            return MuellerMatrix(t) * (cos(thetat) / cos(theta) * index) - sigma * (density / cos(theta));
+        }
+        break;
+        case 2:
+        {
+            double index = substrate.n(lambda);
+            JonesMatrix X = JonesDSC(theta, theta, 0., 0.);
+            JonesMatrix r = stack->r21i(theta, lambda, substrate, vacuum);
+            r *= exp(-2. * cI * index * qq * cos(theta));
+            MuellerMatrix sigma = (4. * pi / k / index) * ReCrossMueller(X, r);
+
+            return MuellerMatrix(r) - sigma * (density / cos(theta));
+        }
+        break;
+        case 3:
+        {
+            double index = substrate.n(lambda);
+            double sint = sin(theta) * index;
+            COMPLEX cost = sqrt(1. - sqr(sint));
+            if (imag(cost) < 0) cost = -cost;
+            if (sint >= 1.) return MuellerZero();
+            double thetat = asin(sint);
+            JonesMatrix X = JonesDSC(theta, thetat, 0., 0.);
+            COMPLEX phase = exp(cI * qq * (cost - index * cos(theta)));
+            //double factor = cos(thetat)/cos(theta);
+            JonesMatrix t = stack->t21i(theta, lambda, substrate, vacuum);
+            t *= phase;
+            MuellerMatrix sigma = (4. * pi / k / sqrt(index)) * ReCrossMueller(X, t);
+
+            return MuellerMatrix(t) * (cos(theta) / index / cos(thetat)) - sigma * (density / cos(theta));
+        }
+        break;
+        default:
+            error("Invalid type = " + to_string(type));
         }
-        return 0;
+        return MuellerZero();
     }
 
     DEFINE_MODEL(Axisymmetric_Particle_BRDF_Model,Local_BRDF_Model,

code/axipart2.cpp

@@ -474,7 +474,7 @@ namespace SCATMECH {
             }
         }
 
-        return E;
+        return COMPLEX(0, -1) * E;
     }
 
 

code/bobvlieg.h

@@ -59,17 +59,9 @@ namespace SCATMECH {
 
         public:
             Bobbert_Vlieger_BRDF_Model();
-
-            // The real part of the following are the partial extinction cross
-            // sections for S or P polarization, respectively, where the "partial"
-            // means that when type=0, the downward reflectance is reduced by the
-            // result, when type=1, the downward transmittance is reduced by the result,
-            // when type=2, the upward reflectance is reduced by the result, and
-            // when type=3, the upward transmittance is reduced by the result.
-            // The total extinction cross section can be obtained by summing these
-            // values for type=0 and type=1 or for type=2 and type=3.
-            COMPLEX PartialExtinctionS(double theta);
-            COMPLEX PartialExtinctionP(double theta);
+
+            // The Mueller matrix specular reflectance or regular transmittance...
+            MuellerMatrix Specular(double theta);
 
         protected:
             void setup();
@@ -135,8 +127,6 @@ namespace SCATMECH {
             void    calculate_Z(double thetas);
             void    calculate_eIP(double phis);
 
-            COMPLEX	PartialExtinction(double theta,int pol);
-
             void    iterative_improvement(ScatterTMatrix& Ainv, ScatterTMatrix& A,
                                           std::vector<COMPLEX>& b,std::vector<COMPLEX>& x);
     };