first draft of spherical transformation algorithm

misc_functions/associatedLegendre.m

@@ -0,0 +1,18 @@
+function [P] = associatedLegendre(n,x)
+%ASSOCIATEDLEGENDRE
+% Modified associated legendre function to duplicate negative m values
+%
+%   Input Arguments:
+%       
+%           n       Degree
+%           x       Argument
+%
+%   Output Arguments
+%
+%           P       Polynomial Value
+
+p = legendre(n,x);
+P = [flipud(p(2:end,:));p]' ;
+
+end
+

misc_functions/associatedLegendreDerivative.m

@@ -0,0 +1,41 @@
+function [dP] = associatedLegendreDerivative(n,x)
+%ASSOCIATEDLEGENDREDERIVATIVE
+% First derivative of associated legendre function using recursion formula
+% and boundary conditions
+%
+
+m = -n:n;
+M = repmat(m,length(x),1);
+X = repmat(x,1,length(m));
+Pnm = associatedLegendre(n,x);
+
+DP1 = Pnm;
+
+% Handle m=0
+i = find(m==0);
+DP2 = [Pnm(:,i)./sqrt(1-x.^2) Pnm(:,i+1:end)];
+DP2 = [fliplr(DP2(:,2:end)) DP2];
+
+dP = 1./(1-X.^2) .* (n*x.*DP1 -(n+M).*(n-M+1).*sqrt(1-X.^2).*DP2);
+
+% Handle boundaries at x = +/-1
+i1 = find(abs(x+1)<0.0000001);
+i2 = find(abs(x-1)<0.0000001);
+
+k0 = find(abs(m)==0);
+k1 = find(abs(m)==1);
+k2 = find(abs(m)==2);
+k3 = find(abs(m)>=3);
+
+dP(i1,k0) = n*(n+1)/2;
+dP(i1,k1) = Inf;
+dP(i1,k2) = -(n-1)*n*(n+1)*(n+2)/4;
+dP(i1,k3) = 0;
+
+dP(i2,k0) = (-1)^(n+1)*n*(n+1)/2;
+dP(i2,k1) = (-1)^n*Inf;
+dP(i2,k2) = (-1)^n*(n-1)*n*(n+1)*(n+2)/4;
+dP(i2,k3) = 0;
+
+end
+

misc_functions/rotateSphericalNFData.m

@@ -0,0 +1,31 @@
+function [data_nf_rotated] = rotateSphericalNFData(data_nf)
+
+% Create Results Table
+p = length(data_nf.E);
+data_nf_rotated = table(zeros(p,1),zeros(p,1),zeros(p,1),zeros(p,1),zeros(p,1),zeros(p,1),zeros(p,3),zeros(p,1));
+data_nf_rotated.Properties.VariableNames = {'x','y','z','r','theta','phi','E','Eabs'};
+
+data_nf_rotated.x = data_nf.x;
+data_nf_rotated.y = data_nf.y;
+data_nf_rotated.z = data_nf.z;
+
+r = sqrt(data_nf.x.^2 + data_nf.y.^2 + data_nf.z.^2);
+theta = acos(data_nf.z./r);
+phi = atan2(data_nf.y,data_nf.x);
+for i =1:length(data_nf.E)
+    R = [sin(theta(i))*cos(phi(i)) sin(theta(i))*sin(phi(i)) cos(theta(i));...
+         cos(theta(i))*cos(phi(i)) cos(theta(i))*sin(phi(i)) -sin(theta(i));...
+         -sin(phi(i)) cos(phi(i)) 0];
+
+    %E(1)-> Radial,E(2)->Theta,E(3)->Phi
+    data_nf_rotated.E(i,:) = (R*data_nf.E(i,:)')';
+    data_nf_rotated.r(i) = r(i);
+    data_nf_rotated.theta(i) = theta(i);
+    if phi(i) <0
+        data_nf_rotated.phi(i) = pi - phi(i);
+    else
+        data_nf_rotated.phi(i) = phi(i);
+    end
+    data_nf_rotated.Eabs(i) = data_nf.Eabs(i);
+end
+

misc_functions/sphericalVectorWaveFunction.m

@@ -0,0 +1,60 @@
+function [fr,ftheta,fphi, Y] = sphericalVectorWaveFunction(s,m,n,A,theta,phi,k)
+%SPHERICALVECTORWAVEFUNCTION
+%
+% Input Arguments:
+%
+%       s       Parity
+%       m,n     Iterators over 
+%       A       Radius
+%       theta   Theta angle
+%       phi     Phi angle
+%       k       Wavenumber at given frequency
+%
+% Output Arguments:
+%
+%       fr      Radial Component of Spherical wave function
+%
+%       ftheta  Theta Component of Spherical wave function
+%
+%       fphi    Phi Component of Spherical wave function
+%
+%       Y       Factor that shows up when solving for the spherical wave
+%               expansion coefficients
+%
+
+% Helper Functions
+z =@(n,r) sqrt(pi/(2*r)).* besselh(n+0.5,r);
+dz = @(n,r) z(n-1,r) - (n+1)/r * z(n,r); % CHECK IF THIS IS CORRECT!!
+delta = @(s,sigma) 0.5*(1+(-1)^(s+sigma));
+
+
+%%%% Note %%%
+% R,T and P provide values for each |m| to speed up the process
+% This means the f output will be a matrix with m columns
+
+% Radial Function
+R = @(s,n,r) delta(s,1).*z(n,k*r) + delta(s,2).*1/(k*r).* dz(n,k*r);
+% Theta Function
+T = @(s,m,n,theta) delta(s,1)*1j*m./sin(theta) .* associatedLegendre(n,cos(theta))...
+                   + delta(s,2) .* associatedLegendreDerivative(n,cos(theta)); % Add derivative of Associated Legendre Function;
+
+% Phi Function
+P = @(m,phi) exp(1j*m.*repmat(phi,1,size(m,2)));
+
+
+
+% Radial Component
+fr = delta(s,2)*n*(n+1)/(k*A) *z(n,k*A) * associatedLegendre(n,cos(theta)).*P(m,theta);
+% Theta Component
+ftheta = repmat(R(s,n,A),1,size(m,2)).*T(s,m,n,theta).*P(m,phi);
+% Phi Component
+fphi = (-1)^s.*repmat(R(s,n,A),1,size(m,2)).*T(s+1,m,n,theta).*P(m,theta);
+
+
+
+% Additional Factor that shows up when solving for the spherical wave
+% expansion coefficients.
+Y = 4*pi/(2*n + 1) *factorial(n+abs(m(1,:)))./factorial(n-abs(m(1,:))) *n*(n+1)*R(s,n,A).^2;
+
+end
+

misc_functions/sphericalVectorWaveFunctionFarField.m

@@ -0,0 +1,49 @@
+function [xtheta,xphi] = sphericalVectorWaveFunctionFarField(s,m,n,A,theta,phi,k)
+%SPHERICALVECTORWAVEFUNCTION
+% Far-Field approximation of the spherical vector wave function
+%
+% Input Arguments:
+%
+%       s       Parity
+%       m,n     Iterators over 
+%       A       Radius
+%       theta   Theta angle
+%       phi     Phi angle
+%       k       Wavenumber at given frequency
+%
+% Output Arguments:
+%
+%       xtheta  Theta Component of Spherical wave function
+%
+%       xphi    Phi Component of Spherical wave function
+%
+
+
+% Helper Functions
+delta = @(s,sigma) 0.5*(1+(-1)^(s+sigma));
+
+
+%%%% Note %%%
+% T and P provide values for each |m| to speed up the process
+% This means the f output will be a matrix with m columns
+
+% Theta Function
+T = @(s,m,n,theta) delta(s,1)*1j*m./sin(theta) .* associatedLegendre(n,cos(theta))...
+                   + delta(s,2).*associatedLegendreDerivative(n,cos(theta));
+% Phi Function
+P = @(m,phi) exp(1j*m.*repmat(phi,1,size(m,2)));
+
+
+
+
+C = 1/(k*A) * (-1j)^(n+delta(s,1)) * exp(1j*k*A) *P(m,phi);
+% Theta Component
+xtheta = C .* T(s,m,n,theta);
+% Phi Component
+xphi = C .* (-1)^s .* T(s+1,m,n,theta);
+
+
+
+
+end
+

nf2ff_spherical.m

@@ -0,0 +1,125 @@
+% 
+% NF2FF Conversion using Spherical Scanner
+%
+clear 
+close all
+clc
+
+disp('************************************************')
+disp('          Near-To-Far-Field Conversion')
+disp('          Spherical Scanner')
+disp('************************************************')
+
+addpath('misc_functions')
+addpath('plot_functions')
+addpath('transformation_functions')
+%% Load Data
+disp('Load Data...')
+f = 5e9;
+
+setup = '../measurement/SphericalScan_HornAntenna/';
+
+
+data_ff = readtable([setup 'Farfield/farfield (f=' num2str(f*1e-9) ') [1].txt']);
+
+scans = dir(setup);
+scan_names = {scans.name};
+scan_names(ismember(scan_names,{'.','..','Farfield','Scan-NTheta-NPhi.txt'})) = [];
+
+data_nf= cellfun(@(scan_names) readtable([setup,scan_names,'/NearFieldProbeResults' num2str(f*1e-9) 'GHz.txt']),scan_names,'UniformOutput',false);
+
+% Rearrange farfield table
+data_ff = table(data_ff.Var1*pi/180,data_ff.Var2*pi/180,data_ff.Var3,data_ff.Var4,data_ff.Var6);
+data_ff.Properties.VariableNames = {'theta' 'phi' 'Eabs' 'Ethetaabs' 'Ephiabs'};
+
+% Rearrange nearfield table
+data_nf = cellfun(@rearrangeTables,data_nf,'UniformOutput',false);
+data_nf = cellfun(@rotateSphericalNFData,data_nf,'UniformOutput',false);
+
+% Select measurements to process
+data_nf = data_nf([2]);
+scan_names = scan_names([2]);
+
+disp('Done!')
+%% NF2FF transformation
+disp('NF2FF Transformation...')
+delta_theta=1;
+theta_range = (0:delta_theta:180)*pi/180;
+delta_phi = 1;
+phi_range = (0:delta_phi:360)*pi/180;
+
+
+data_nf2ff = cellfun(@(data_nf) nf2ff_spherical_manual(data_nf,f,theta_range,phi_range),data_nf,'Uniformoutput',false);
+
+disp('Done!')
+%% Plots
+disp('Plotting...')
+close all
+
+normalized = true;
+logarithmic = true;
+
+% Phi=0 cut
+figure('name','Far-Field Cuts,Phi=0°','numbertitle','off',...
+        'units','normalized','outerposition',[0 0 1 1]);
+plotFFPhiCut(data_ff,0,normalized,logarithmic)
+cellfun(@(data_nf2ff) plotNFPhiCutCylindrical(data_nf2ff,0,normalized,logarithmic),data_nf2ff)
+grid on
+xlabel('Theta [°]')
+if logarithmic == true
+    ylim([-50 0])
+    ylabel('E-Field Pattern [dB]')
+elseif normalized == true
+    ylim([0 1])
+    ylabel('E-Field Pattern [-]')
+end
+ylabel('E-Field Pattern [-]')
+title('Far-Field Cut Phi=0°')
+legend(['Far-Field',scan_names])
+
+
+figure('name','Far-Field Error,Phi=0°','numbertitle','off',...
+        'units','normalized','outerposition',[0 0 1 1]);
+cellfun(@(data_nf2ff) plotDiffPhiCutCylindrical(data_nf2ff,data_ff,0,theta_range),data_nf2ff)
+grid on
+xlabel('Theta [°]')
+ylabel('Difference to Reference Far-Field [dB]')
+title('Difference to Reference Far-Field, Phi=0°')
+legend(scan_names)
+
+
+% Theta=90 cut
+figure('name','Far-Field Cuts,Theta=90°','numbertitle','off',...
+        'units','normalized','outerposition',[0 0 1 1]);
+plotFFThetaCut(data_ff,pi/2,normalized,logarithmic)
+cellfun(@(data_nf2ff) plotNFThetaCutCylindrical(data_nf2ff,pi/2,normalized,logarithmic),data_nf2ff)
+grid on
+xlabel('Phi [°]')
+if logarithmic == true
+    ylim([-50 0])
+    ylabel('E-Field Pattern [dB]')
+elseif normalized == true
+    ylim([0 1])
+    ylabel('E-Field Pattern [-]')
+end
+ylabel('E-Field Pattern [-]')
+title('Far-Field Cut Theta=90°')
+legend(['Far-Field',scan_names])
+
+
+figure('name','Far-Field Error,Theta=90°','numbertitle','off',...
+        'units','normalized','outerposition',[0 0 1 1]);
+cellfun(@(data_nf2ff) plotDiffThetaCutCylindrical(data_nf2ff,data_ff,pi/2),data_nf2ff)
+grid on
+xlabel('Phi [°]')
+ylabel('Difference to Reference Far-Field [dB]')
+title('Difference to Reference Far-Field, Theta=90°')
+legend(scan_names)
+
+
+disp('Done!')
+
+
+
+
+