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OR_fitting.m
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OR_fitting.m
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% maximize the completeness to derive orientation expressed by quaternion
function Err2Sum=OR_fitting(x, x_representation, ...
proj_bin_bw,pos,rot_angles,S,B,Ahkl,nrhkl,hklnumber,hkl_square,RotDet, ...
thetamax,lambda_min,lambda_max, ...
Lsam2sou,Lsam2det,minEucDis,dety00,detz00,P0y,P0z,RotAxisOffset, ...
pixelysize,pixelzsize,dety0,detz0,detysize,detzsize,BeamStopY,BeamStopZ)
L=Lsam2sou+Lsam2det; % [mm]
if strcmp(x_representation,'quaternion')
% x is represented by the last three quantities of the quaternions (a, b, c, d)
% Extract the values from Q
q0 = sqrt(1-(x(1)^2+x(2)^2+x(3)^2));
q1 = x(1);
q2 = x(2);
q3 = x(3);
% First row of the rotation matrix
r00 = 2 * (q0 * q0 + q1 * q1) - 1;
r01 = 2 * (q1 * q2 - q0 * q3);
r02 = 2 * (q1 * q3 + q0 * q2);
% Second row of the rotation matrix
r10 = 2 * (q1 * q2 + q0 * q3);
r11 = 2 * (q0 * q0 + q2 * q2) - 1;
r12 = 2 * (q2 * q3 - q0 * q1);
% Third row of the rotation matrix
r20 = 2 * (q1 * q3 - q0 * q2);
r21 = 2 * (q2 * q3 + q0 * q1);
r22 = 2 * (q0 * q0 + q3 * q3) - 1;
% 3x3 rotation matrix
U = [r00 r01 r02;r10 r11 r12;r20 r21 r22];
elseif strcmp(x_representation,'euler_angle')
U=euler2u(x(1)*pi/180,x(2)*pi/180,x(3)*pi/180);
else
U=euler2u(x(1)*pi/180,x(2)*pi/180,x(3)*pi/180);
end
Nr_simu=0;
Nr_intersect=0;
Err2=[];
hkl = [Ahkl(1:nrhkl,1) Ahkl(1:nrhkl,2) Ahkl(1:nrhkl,3)]';
Gw = S*U*B*hkl;
pos(:,2)=pos(:,2)-RotAxisOffset;
for i=1:length(rot_angles)
omega=rot_angles(i)*pi/180; % [rad]
Omega(:,:,i)=[cos(omega) -sin(omega) 0;sin(omega) cos(omega) 0;0 0 1];
SamposW=Omega(:,:,i)*S*pos';
center = [L, (SamposW(2)-P0y+RotAxisOffset)*L/(Lsam2sou+SamposW(1)), ...
(SamposW(3)-P0z)*L/(Lsam2sou+SamposW(1))]; % sample center projected to the position of the detector
alpha = atan(sqrt((SamposW(2)-P0y+RotAxisOffset)^2+(SamposW(3)-P0z)^2)/(Lsam2sou+SamposW(1)));
grainpos = [Lsam2sou+SamposW(1) SamposW(2)-P0y+RotAxisOffset SamposW(3)-P0z];
Gt=Omega(:,:,i)*Gw;
v1 = [zeros(1,size(hkl,2));Gt(2,:);Gt(3,:)];
Glen = (Gt(1,:).^2 + Gt(2,:).^2 + Gt(3,:).^2).^0.5;
beta = acos(dot((ones(size(hkl))'.*grainpos/norm(grainpos))',Gt./Glen)); % [rad]
% select1=find(beta > pi/2 & beta < (90+thetamax*4)/180*pi);
theta = beta-pi/2;
sintth = sin(2*theta);
costth = cos(2*theta);
d = 1./Glen*2*pi;
lambdahkl = 2 * d .*sin(theta);
Energy_hkl=12.398./lambdahkl; % [keV]
% select2=find(lambdahkl > lambda_min & lambdahkl < lambda_max);
phix = acos(dot(v1./sqrt(v1(1,:).^2+v1(2,:).^2+v1(3,:).^2),(ones(size(hkl))'.*center/norm(center))'));
phiy = phix-2*theta;
L2 = (Lsam2det-SamposW(1))/cos(alpha);
diffvec = L2*sintth./sin(phiy); % [mm]
konst=sqrt(Gt(2,:).^2+Gt(3,:).^2);
dety22 = (center(2)+ (diffvec.*Gt(2,:)./konst)); % dety [mm]
detz22 = (center(3)+ (diffvec.*Gt(3,:)./konst)); % detz [mm]
K_out_unit = ([ones(1,size(hkl,2))*Lsam2det;dety22;detz22]-ones(1,size(hkl,2)).*SamposW) ...
./((Lsam2det-SamposW(1)).^2+(dety22-SamposW(2)).^2+(detz22-SamposW(3)).^2).^(1/2);
t = (RotDet(1,1)*(Lsam2det-SamposW(1))+RotDet(2,1)*(dety00-RotAxisOffset-SamposW(2))+RotDet(3,1)*(detz00-SamposW(3)))./ ...
(RotDet(1,1)*K_out_unit(1,:)+RotDet(2,1)*K_out_unit(2,:)+RotDet(3,1)*K_out_unit(3,:));
dety22 = [RotDet(1,2) RotDet(2,2) RotDet(3,2)]*(t.*K_out_unit+[SamposW(1)-Lsam2det SamposW(2)-dety00+RotAxisOffset SamposW(3)-detz00]');
detz22 = [RotDet(1,3) RotDet(2,3) RotDet(3,3)]*(t.*K_out_unit+[SamposW(1)-Lsam2det SamposW(2)-dety00+RotAxisOffset SamposW(3)-detz00]');
% dety = -round(dety22/pixelysize-0.5)+dety0; % [pixel]
% detz = -round(detz22/pixelzsize-0.5)+detz0; % [pixel]
dety = round(-dety22/pixelysize+dety0); % [pixel]
detz = round(-detz22/pixelzsize+detz0); % [pixel]
select3=find(beta > pi/2 & ...
lambdahkl > lambda_min & lambdahkl < lambda_max & ...
dety>=1 & dety<=detysize & detz>=1 & detz<=detzsize & ...
~(dety>=BeamStopY(1) & dety<=BeamStopY(2) & ...
detz>=BeamStopZ(1) & detz<=BeamStopZ(2)));
if ~isempty(select3)
Nr_simu=Nr_simu+length(select3);
for j=1:length(select3)
dis = proj_bin_bw(detz(select3(j)),dety(select3(j)),i); % euclidian [pixel]
if dis <= minEucDis/mean([pixelysize pixelzsize])
Nr_intersect=Nr_intersect+1;
end
Err2=[Err2;dis]; % [mm]
end
end
end
% Err2Sum=median(Err2); % minimize the Euclidian distance [mm]
Err2Sum=1-Nr_intersect/Nr_simu; % 1 - completeness, this is shown to be better
%{
Nr_simu=0;
Nr_intersect=0;
Err2=[];
for i=1:length(rot_angles)
omega=rot_angles(i); % [rad]
Omega=[cos(omega) -sin(omega) 0;sin(omega) cos(omega) 0;0 0 1];
for j=1:nrhkl
% for j=find(Ahkl(:,1)==-1 & Ahkl(:,2)==1 & Ahkl(:,3)==3)
if (Ahkl(j,1)^2+Ahkl(j,2)^2+Ahkl(j,3)^2)<=hkl_square(hklnumber)
hkl = [Ahkl(j,1) Ahkl(j,2) Ahkl(j,3)]';
% dhkl=sqrt(1./sum(hkl(1:3)'.^2./cell(1:3).^2)); % for orthogonal [angstrom]
SamposW=Omega*S*pos';
center = [L, (SamposW(2)-P0y)*L/(Lsam2sou+SamposW(1)), ...
(SamposW(3)-P0z)*L/(Lsam2sou+SamposW(1))]; % sample center projected to the position of the detector
alpha = atan(sqrt((SamposW(2)-P0y)^2+(SamposW(3)-P0z)^2)/(Lsam2sou+SamposW(1)));
grainpos = [Lsam2sou+SamposW(1) SamposW(2)-P0y SamposW(3)-P0z];
Gw = S*U*B*hkl;
Gt=Omega*Gw;
v1 = [0 Gt(2) Gt(3)];
Glen = (Gt(1)^2 + Gt(2)^2 + Gt(3)^2)^0.5;
beta = acos(dot(grainpos/norm(grainpos),Gt/Glen)); % [rad]
if beta > pi/2 %&& beta < (90+thetamax*4)/180*pi
theta = beta-pi/2;
sintth = sin(2*theta);
costth = cos(2*theta);
d = 1/Glen*2*pi;
lambdahkl = 2 * d *sin(theta);
Energy_hkl=12.398/lambdahkl; % [keV]
if lambdahkl > lambda_min && lambdahkl < lambda_max
phix = acos(dot(v1/norm(v1),center/norm(center)));
phiy = phix-2*theta;
L2 = (Lsam2det-SamposW(1))/cos(alpha);
diffvec = L2*sintth/sin(phiy); % [mm]
konst = norm([0 Gt(2) Gt(3)]);
dety22 = (center(2)+ (diffvec*Gt(2)/konst)); % dety [mm]
detz22 = (center(3)+ (diffvec*Gt(3)/konst)); % detz [mm]
%%% include detector tilt and center offset
K_out_unit = ([Lsam2det dety22 detz22]'-SamposW)./norm([Lsam2det dety22 detz22]'-SamposW);
t = (RotDet(1,1)*(Lsam2det-SamposW(1))-RotDet(2,1)*(dety00-SamposW(2))-RotDet(3,1)*(detz00-SamposW(3)))./ ...
(RotDet(1,1)*K_out_unit(1)+RotDet(2,1)*K_out_unit(2)+RotDet(3,1)*K_out_unit(3));
dety22 = [RotDet(1,2) RotDet(2,2) RotDet(3,2)]*(t*K_out_unit+[SamposW(1)-Lsam2det SamposW(2)-dety00 SamposW(3)-detz00]');
detz22 = [RotDet(1,3) RotDet(2,3) RotDet(3,3)]*(t*K_out_unit+[SamposW(1)-Lsam2det SamposW(2)-dety00 SamposW(3)-detz00]');
dety = -round(dety22/pixelysize+0.5)+dety0; % [pixel]
detz = -round(detz22/pixelzsize+0.5)+detz0; % [pixel]
% if (dety22>=-(detysize-dety0)*pixelysize && dety22<=(detysize-dety0)*pixelysize) && ...
% (detz22>=-(detzsize-detz0)*pixelzsize && detz22<=(detzsize-detz0)*pixelzsize) && ...
% ~((dety22>=(BeamStopY(1)-dety0)*pixelysize && dety22<=(BeamStopY(2)-dety0)*pixelysize) && ...
% (detz22>=(BeamStopZ(1)-detz0)*pixelzsize && detz22<=(BeamStopZ(2)-detz0)*pixelzsize))
if (dety>=1 && dety<=detysize && detz>=1 && detz<=detzsize) ...
&& ~(dety>=dety0-BeamStopY(1) && dety<=dety0+BeamStopY(2) && ...
detz>=detz0-BeamStopZ(1) && detz<=detz0+BeamStopZ(2))
Nr_simu=Nr_simu+1;
dis = proj_bin_bw(detz,dety,i); % euclidian [pixel]
if dis <= minEucDis/mean([pixelysize pixelzsize])
Nr_intersect=Nr_intersect+1;
end
Err2=[Err2;dis]; % [mm]
end
end
end
end
end % end of nrhkl
end
% Err2Sum=median(Err2); % minimize the Euclidian distance [mm]
Err2Sum=1-Nr_intersect/Nr_simu; % 1 - completeness, this is shown to be better
%}