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scatmat_amp2stokes

PURPOSE ^

SCATMAT_AMP2STOKES Conversion of scattering matrices

SYNOPSIS ^

function F = scatmat_amp2stokes(S1,S2,varargin)

DESCRIPTION ^

 SCATMAT_AMP2STOKES   Conversion of scattering matrices

    Converts amplitude scattering functions to a scattering matrix
    for Stokes vectors.

    The input specifies the matrix describing the effect of a scattering
    event:
       [E1b,E2b]' = [S2,S3;S4,S1]*[E1a,E2a]'
    where E1a is one of the ortoghonal components of the incoming radiation
    etc. This function return the corresponding matrix to use for
    Stokes vactors:
       Ib = F*Ia
    where Ia is the incoming Stokes vector.

    See further polarisation theory chapter in ARTS user guide.

 FORMAT   F = scatmat_amp2stokes(S1,S2,S3,S4)
        
 OUT   F   Stokes scattering matrix.
 IN    S1  Amplitude scattering function.
       S2  Amplitude scattering function.
 OPT   S3  Amplitude scattering function. Default is 0.
       S4  Amplitude scattering function. Default is 0.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SUBFUNCTIONS ^

DOWNLOAD ^

scatmat_amp2stokes.m

SOURCE CODE ^

0001 % SCATMAT_AMP2STOKES   Conversion of scattering matrices
0002 %
0003 %    Converts amplitude scattering functions to a scattering matrix
0004 %    for Stokes vectors.
0005 %
0006 %    The input specifies the matrix describing the effect of a scattering
0007 %    event:
0008 %       [E1b,E2b]' = [S2,S3;S4,S1]*[E1a,E2a]'
0009 %    where E1a is one of the ortoghonal components of the incoming radiation
0010 %    etc. This function return the corresponding matrix to use for
0011 %    Stokes vactors:
0012 %       Ib = F*Ia
0013 %    where Ia is the incoming Stokes vector.
0014 %
0015 %    See further polarisation theory chapter in ARTS user guide.
0016 %
0017 % FORMAT   F = scatmat_amp2stokes(S1,S2,S3,S4)
0018 %
0019 % OUT   F   Stokes scattering matrix.
0020 % IN    S1  Amplitude scattering function.
0021 %       S2  Amplitude scattering function.
0022 % OPT   S3  Amplitude scattering function. Default is 0.
0023 %       S4  Amplitude scattering function. Default is 0.
0024 
0025 % 2004-05-20   Created by Patrick Eriksson.
0026 
0027 
0028 function F = scatmat_amp2stokes(S1,S2,varargin)
0029 %
0030 [S3,S4] = optargs( varargin, { 0, 0 } );
0031 
0032 
0033 F = [
0034 (Mfun(S2)+Mfun(S3)+Mfun(S4)+Mfun(S1))/2, ...
0035 (Mfun(S2)-Mfun(S3)+Mfun(S4)-Mfun(S1))/2, ...
0036 Sfun(S2,S3)+Sfun(S4,S1), ...
0037 -Dfun(S2,S3)-Dfun(S4,S1); ...
0038 (Mfun(S2)+Mfun(S3)-Mfun(S4)-Mfun(S1))/2, ...
0039 (Mfun(S2)-Mfun(S3)-Mfun(S4)+Mfun(S1))/2, ...
0040 Sfun(S2,S3)-Sfun(S4,S1), ...
0041 -Dfun(S2,S3)+Dfun(S4,S1); ...
0042 Sfun(S2,S4)+Sfun(S3,S1), ...
0043 Sfun(S2,S4)-Sfun(S3,S1), ...
0044 Sfun(S2,S1)+Sfun(S3,S4), ...
0045 -Dfun(S2,S1)+Dfun(S3,S4); ...
0046 Dfun(S2,S4)+Dfun(S3,S1), ...
0047 Dfun(S2,S4)-Dfun(S3,S1), ...
0048 Dfun(S2,S1)+Dfun(S3,S4), ...
0049 Sfun(S2,S1)-Sfun(S3,S4) ];
0050 
0051 
0052 
0053 function a = Mfun(Sk)
0054   %
0055   a = abs(Sk)^2;
0056   %
0057 return
0058 
0059 
0060 function a = Sfun(Sk,Sj)
0061   %
0062   a = (Sj*conj(Sk)+Sk*conj(Sj))/2;
0063   %
0064 return
0065 
0066 
0067 function a = Dfun(Sk,Sj)
0068   %
0069   a = -j*(Sj*conj(Sk)-Sk*conj(Sj))/2;
0070   %
0071 return

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