磁束検出コイルの種類と波形

球中心を[0,0,0]、電流双極子を半径7cmの円上に[0,0,1]nAのモーメントで回転させます。 センサーは[0.1,0,0]m上にあるとします。 式はSarvas式を使います。

Contents

Sarvas式

functionからreturnまでの%を削除してreturnまでをコピーしてhns_Sarvas.mという名前で保存してください。 QはNq個×[x,y,z,qx,qy,qz]の電流双極子です。 sは[x,y,z,zx,zy,zz]のセンサー位置と単位ベクトル化した法線方向です。 pは[x,y,z]にある仮想球の中心座標です。

% function Bz=hns_Sarvas(Q,s,p)
% Nq=size(Q,1);
% R=ones(Nq,1)*(s(1:3)-p);
% R0=Q(:,1:3)-ones(Nq,1)*p;
% A=R-R0;
% r =sqrt(sum(R.^2,2));
% a =sqrt(sum(A.^2,2));
% ar=sum(A.*R,2);
% F=(a.*(r.*a+ar))*ones(1,3);
% n=a+2*r+ar./a;
% nn=(a.^2)./r+a+n;
% n=n*ones(1,3);
% nn=nn*ones(1,3);
% nablaF=nn.*R-n.*R0;
% Q=Q(:,4:6);
% QR0=[Q(:,2).*R0(:,3)-Q(:,3).*R0(:,2),...
%      Q(:,3).*R0(:,1)-Q(:,1).*R0(:,3),...
%      Q(:,1).*R0(:,2)-Q(:,2).*R0(:,1)];
% QR0R=sum(QR0.*R,2)*ones(1,3);
% B=QR0-(QR0R.*nablaF)./F;
% B=B./F*(1e-7)*(1e+15);% fT
% Bz=s(4)*B(:,1)+s(5)*B(:,2)+s(6)*B(:,3);
% return;

magnetometer detecting flux normal to Dewar aspect

Dewar面と法線方向の磁束を検出する通常のmagnetometerです。

t=linspace(0,2*pi,361);
t([1:3,359:361])=[];
p=[cos(t);sin(t);t*0];
pp=p(:,1);pp(3,1)=2;
p=[pp,p];
pp=p(:,end);pp(3,1)=2;
p=[p,pp];
figure('color',[1,1,1]);
subplot(121);
plot3(p(1,:),p(2,:),p(3,:),'r');hold on;
h=quiver3(0,0,0,0,0,1);
set(h,'color',[0,0,1],'maxheadsize',6,'linewidth',3,'ShowArrowHead','off');
set(h,'ShowArrowHead','on');
daspect([1,1,1]);axis tight;axis off;
subplot(122);
t=linspace(-pi,pi,361);
r=0.04:0.01:0.07;
map=jet(length(r));
sensor=[0.1,0,0,1,0,0];
centroid=[0,0,0];
for n=1:length(r)
    Q=[cos(t)*r(n);sin(t)*r(n);0*t;0*t;0*t;ones(1,361)*1e-9]';
    Bz(:,n)=hns_Sarvas(Q,sensor,centroid);
end;
plot(t,Bz);
set(gca,'xlim',[min(t),max(t)]);
xlabel('[rad]');ylabel('[fT]');
grid on;

axial gradiometer detecting flux normal to Dewar aspect

Dewar面と法線方向の磁束を検出する通常の軸型gradioemterです。 simulationではbaselineを5cmとしています。

t=linspace(0,2*pi,361);
t([1:3,359:361])=[];
p=[cos(t);sin(t);t*0];
pp=p(:,1);pp(3,1)=4;
p=[pp,p];
t=linspace(0,2*pi,361);
t=fliplr(t);
t([1:3,353:361])=[];
pp=[cos(t);sin(t);t*0];
pp(3,:)=2;
p=[p,pp];
pp=p(:,end);
pp(3,:)=4;
p=[p,pp];

figure('color',[1,1,1]);
subplot(121);
plot3(p(1,:),p(2,:),p(3,:),'r');hold on;
h(1)=quiver3(0,0,0,0,0,1.5);
h(2)=quiver3(0,0,2,0,0,1);
set(h,'color',[0,0,1],'maxheadsize',6,'linewidth',3,'ShowArrowHead','off');
set(h,'ShowArrowHead','on');
daspect([1,1,1]);axis tight;axis off;

subplot(122);
t=linspace(-pi,pi,361);
sensor1=[0.1,0,0,1,0,0];
sensor2=[0.15,0,0,1,0,0];
centroid=[0,0,0];
r=0.04:0.01:0.07;
for n=1:length(r)
    Q=[cos(t)*r(n);sin(t)*r(n);0*t;0*t;0*t;ones(1,361)*1e-9]';
    Bz1=hns_Sarvas(Q,sensor1,centroid);
    Bz2=hns_Sarvas(Q,sensor2,centroid);
    Bz(:,n)=Bz1-Bz2;
end;
plot(t,Bz);
set(gca,'xlim',[min(t),max(t)]);
xlabel('[rad]');ylabel('[fT]');
grid on;

planar gradiometer detecting flux normal to Dewar aspect

Neuromagの脳磁計のように、Dewar面の法線方向の磁束を検出する平面型gradiometerです。 simulationではbaselineは16.8mmとします。

t=linspace(0,pi/2,91);
tt=0.05;
p=[cos(t)+tt;sin(t);t*0];
p(:,1:2)=[];
pp=p(:,1);pp(3,1)=2;
p=[pp,p];
pp=[1,-1;1,-1;0,0]*tt;
p=[p,pp];
t=linspace(pi/2,3/2*pi,181);
pp=[cos(t)-tt;-sin(t);t*0];
p=[p,pp];
pp=[-1,1;1,-1;0,0]*tt;
p=[p,pp];
t=linspace(3/2*pi,2*pi,91);
pp=[cos(t)+tt;sin(t);t*0];
pp(:,90:91)=[];
pp(:,89)=pp(:,88);
pp(3,89)=2;
p=[p,pp];
figure('color',[1,1,1]);
subplot(121);
plot3(p(1,:),p(2,:),p(3,:),'r');hold on;
h(1)=quiver3(0.5,0,0,0,0,1.5);
h(2)=quiver3(-0.5,0,0,0,0,1);
set(h,'color',[0,0,1],'maxheadsize',6,'linewidth',3,'ShowArrowHead','off');
set(h,'ShowArrowHead','on');
daspect([1,1,1]);axis tight;axis off;

subplot(122);
t=linspace(-pi,pi,361);
r=0.04:0.01:0.07;
sensor1=[0.1,-0.0084,0.0003,1,0,0];
sensor2=[0.1,0.0084,0.0003,1,0,0];
centroid=[0,0,0];
for n=1:length(r)
    Q=[cos(t)*r(n);sin(t)*r(n);0*t;0*t;0*t;ones(1,361)*1e-9]';
    Bz1=hns_Sarvas(Q,sensor1,centroid);
    Bz2=hns_Sarvas(Q,sensor2,centroid);
    Bz(:,n)=Bz1-Bz2;
end;
plot(t,Bz);
set(gca,'xlim',[min(t),max(t)]);
xlabel('[rad]');ylabel('[fT]');
grid on;

magnetometer detecting flux tangential to Dewar aspect

Dewar面と接平面方向の磁束を検出するmagnetometerです。

t=linspace(0,2*pi,361);
t([1:3,359:361])=[];
p=[t*0;sin(t);cos(t)];
pp=p(:,1);pp(3,1)=2;
p=[pp,p];
pp=p(:,end);pp(3,1)=2;
p=[p,pp];
figure('color',[1,1,1]);
subplot(121);
plot3(p(1,:),p(2,:),p(3,:),'r');hold on;
h=quiver3(0,0,0,-1,0,0);
set(h,'color',[0,0,1],'maxheadsize',6,'linewidth',3,'ShowArrowHead','off');
set(h,'ShowArrowHead','on');
daspect([1,1,1]);axis tight;axis off;

subplot(122);
t=linspace(-pi,pi,361);
r=0.04:0.01:0.07;
sensor=[0.1,0,0,0,1,0];
centroid=[0,0,0];
for n=1:length(r)
    Q=[cos(t)*r(n);sin(t)*r(n);0*t;0*t;0*t;ones(1,361)*1e-9]';
    Bz(:,n)=hns_Sarvas(Q,sensor,centroid);
end;
plot(t,Bz);
set(gca,'xlim',[min(t),max(t)]);
xlabel('[rad]');ylabel('[fT]');
grid on;

planar gradiometer detecting flux tangential to Dewar aspect

Dewar面と接平面方向の磁束を検出する通常の平面型gradioemterです。横河の脳磁計で採用されています。 simulationではbaselineを5cmとしています。

t=linspace(0,pi,181);
t([1:5,176:181])=[];
p=[t*0;sin(t);cos(t)+4];
pp=p(:,1);pp(3,1)=6;
p=[pp,p];
pp=[0,0;1,-1;1,-1]*p(2,end);
pp(3,:)=pp(3,:)+2;
p=[p,pp];
t=linspace(0,2*pi,361);
t([1:5,356:361])=[];
t=fliplr(t);
pp=[t*0;sin(t);cos(t)];
p=[p,pp];
pp=[0,0;1,-1;-1,1]*p(2,end);
pp(3,:)=pp(3,:)+2;
p=[p,pp];
t=linspace(pi,2*pi,181);
t([1:5,176:181])=[];
pp=[t*0;sin(t);cos(t)+4];
p=[p,pp];
pp=p(:,end);
pp(3,1)=6;
p=[p,pp];

figure('color',[1,1,1]);
subplot(121);
plot3(p(1,:),p(2,:),p(3,:),'r');hold on;
h(1)=quiver3(0,0,0,-1.5,0,0);
h(2)=quiver3(0,0,4,-1,0,0);
set(h,'color',[0,0,1],'maxheadsize',6,'linewidth',3,'ShowArrowHead','off');
set(h,'ShowArrowHead','on');
daspect([1,1,1]);axis tight;axis off;

subplot(122);
t=linspace(-pi,pi,361);
r=0.04:0.01:0.07;
sensor1=[0.1,0,0,0,1,0];
sensor2=[0.15,0,0,0,1,0];
centroid=[0,0,0];
for n=1:length(r)
    Q=[cos(t)*r(n);sin(t)*r(n);0*t;0*t;0*t;ones(1,361)*1e-9]';
    Bz1=hns_Sarvas(Q,sensor1,centroid);
    Bz2=hns_Sarvas(Q,sensor2,centroid);
    Bz(:,n)=Bz1-Bz2;
end;
plot(t,Bz);
set(gca,'xlim',[min(t),max(t)]);
xlabel('[rad]');ylabel('[fT]');
grid on;

Neuromag社の脳磁計

ChInformは102個のセンサーの[x,y,z]座標,差分方向の単位ベクトルEx[Ex_x,Ex_y,Ex_z], それと直交する接平面方向の単位ベクトルEy[Ey_x,Ey_y,Ey_z],法線方向Ez[Ez_x,Ez_y,Ez_z]です。 2つの直交する平面型グラジオメータとマグネトメーターは同一センサー平面上にあります。 真ん中の黄色は半径7cmの仮想球面です。

ChInform=[...
-0.10610000,0.04600000,-0.06040000, -0.01360000,0.00590000,-0.99989003,  -0.19429800,-0.98088998,-0.00320000, -0.98080099, 0.19423300, 0.01448600;...
-0.10170000,0.06260000,-0.02500000, 0.01420000,0.00100000,-0.99988902,  -0.27549699,-0.96129000,-0.00480000, -0.96118897, 0.27553499, -0.01337500;...
-0.10800000,0.02990000,-0.02660000, 0.00800000,0.00170000,-0.99998403,  -0.09489800,-0.99548399,-0.00250000, -0.99547201, 0.09491700, -0.00780200;...
-0.10940000,0.01270000,-0.06270000, -0.01669900,0.00190000,-0.99985898,  -0.02739900,-0.99955899,-0.00140000, -0.99941999, 0.02737200, 0.01674400;...
-0.10660000,0.03300000,0.00790000, -0.05920100,0.00850000,-0.99821001,  -0.10530100,-0.99440998,-0.00220000, -0.99264902, 0.10498200, 0.05976500;...
-0.09840000,0.04030000,0.04110000, -0.34060699,0.05930100,-0.93842000,  -0.16360401,-0.98652202,-0.00300000, -0.92594999, 0.15250701, 0.34571901;...
-0.10070000,0.00440000,0.04050000, -0.34880501,0.00880000,-0.93711400,  0.03980100,-0.99891502,-0.02420000, -0.93630999, -0.04573900, 0.34807599;...
-0.10750000,-0.00050000,0.00710000, -0.07250100,-0.01080000,-0.99730998,  0.07910100,-0.99690998,0.00510000, -0.99428302, -0.07851800, 0.07313100;...
-0.08530000,0.09840000,0.00900000, -0.04160000,0.12169900,-0.99169499,  -0.48579699,-0.86979598,-0.08640000, -0.87308699, 0.47816899, 0.09530500;...
-0.08830000,0.07560000,0.04090000, -0.34660500,0.11680200,-0.93071502,  -0.37140599,-0.92821503,0.02180000, -0.86135697, 0.35322899, 0.36510500;...
-0.06970000,0.07530000,0.07010000, -0.59129900,0.22750001,-0.77369899,  -0.38819900,-0.92119801,0.02570000, -0.70688301, 0.31554601, 0.63301897;...
-0.09940000,0.06620000,0.00850000, -0.07289800,0.02679900,-0.99697900,  -0.29259399,-0.95617998,-0.00430000, -0.95340699, 0.29139701, 0.07754500;...
-0.08030000,0.04120000,0.07140000, -0.63980198,0.04860000,-0.76700199,  -0.13450000,-0.98970300,0.04950000, -0.75669801, 0.13483199, 0.63975000;...
-0.05250000,0.04060000,0.09470000, -0.87236398,-0.02049900,-0.48838001,  -0.05539800,-0.98855901,0.14029400, -0.48566800, 0.14944300, 0.86124700;...
-0.05350000,0.00580000,0.09640000, -0.86706901,-0.01759900,-0.49778199,  0.03069900,-0.99936497,-0.01809900, -0.49714801, -0.03097500, 0.86705899;...
-0.08240000,0.00630000,0.07210000, -0.64428502,0.00230000,-0.76478201,  0.04479900,-0.99817699,-0.04079900, -0.76348102, -0.06054800, 0.64300698;...
-0.06290000,0.12460000,0.01340000, 0.01340000,0.22440100,-0.97440499,  -0.79030401,-0.59470302,-0.14780100, -0.61264801, 0.77205598, 0.16937600;...
-0.03290000,0.13890000,0.01720000, 0.00960000,0.22200000,-0.97499901,  -0.95699900,-0.28070000,-0.07330000, -0.28995499, 0.93377799, 0.20975900;...
-0.03350000,0.12700000,0.04840000, -0.05180100,0.46841300,-0.88202500,  -0.96202701,-0.26040700,-0.08180200, -0.26800299, 0.84429502, 0.46411601;...
-0.06680000,0.10860000,0.04420000, -0.17039099,0.37697899,-0.91035002,  -0.71006101,-0.68756199,-0.15189201, -0.68318301, 0.62052399, 0.38483301;...
-0.03550000,0.10410000,0.07440000, -0.00940000,0.77057499,-0.63727999,  -0.95656902,-0.19259401,-0.21889301, -0.29141000, 0.60754502, 0.73891902;...
0.00010000,0.07730000,0.09630000, 0.00020000,0.91630000,-0.40050000,  -1.00000000,0.00040000,0.00030000, 0.00043500, 0.40050000, 0.91630000;...
-0.01830000,0.04390000,0.10550000, 0.00680000,0.98358899,-0.18029800,  -0.99128801,-0.01710000,-0.13089800, -0.13183300, 0.17961700, 0.97490400;...
-0.03690000,0.07490000,0.09180000, -0.02540000,0.89688998,-0.44149500,  -0.95049000,-0.15849800,-0.26729700, -0.30971199, 0.41284701, 0.85651100;...
-0.01840000,0.01050000,0.10880000, -0.98930103,-0.01190000,-0.14540000,  0.01420000,-0.99980098,-0.01500000, -0.14519300, -0.01690400, 0.98927402;...
0.01860000,0.01020000,0.10880000, 0.98855400,-0.00720000,-0.15069300,  0.00170000,0.99935400,-0.03669800, 0.15086000, 0.03602200, 0.98792797;...
0.01840000,-0.02330000,0.10500000, -0.03689800,-0.96985102,-0.24088800,  0.98745000,0.00160000,-0.15749200, 0.15312900, -0.24367601, 0.95762098;...
-0.01850000,-0.02310000,0.10500000, 0.03920100,-0.97012800,-0.23940700,  0.99212801,0.00920000,0.12510400, -0.11916400, -0.24242599, 0.96285200;...
0.00010000,0.14360000,0.01840000, -0.00030000,0.25461099,-0.96704298,  -0.99994498,-0.00800000,-0.00180000, -0.00819500, 0.96698999, 0.25459999;...
0.00010000,0.13110000,0.04980000, 0.00070000,0.49630001,-0.86809897,  -0.99999899,0.00110000,-0.00010000, 0.00090500, 0.86809897, 0.49630001;...
0.03290000,0.13900000,0.01710000, -0.00430000,0.24020299,-0.97071302,  -0.96411300,0.25660300,0.06780100, 0.26537400, 0.93616903, 0.23048000;...
0.06310000,0.12440000,0.01330000, -0.01740000,0.22379600,-0.97448099,  -0.78578502,0.59958798,0.15179700, 0.61825901, 0.76837301, 0.16542201;...
0.06680000,0.10860000,0.04410000, 0.17240299,0.37460700,-0.91101599,  -0.70991302,0.68841201,0.14870299, 0.68286002, 0.62110502, 0.38462201;...
0.03360000,0.12700000,0.04820000, 0.05469800,0.46608499,-0.88297200,  -0.96156901,0.26289201,0.07919700, 0.26903901, 0.84470701, 0.46255299;...
0.00010000,0.10890000,0.07650000, 0.00090000,0.75779301,-0.65249401,  -0.99969101,-0.01400000,-0.01760000, -0.02247200, 0.65230799, 0.75754601;...
0.03540000,0.10410000,0.07440000, 0.00600000,0.76645899,-0.64226502,  -0.96184802,0.17979001,0.20558900, 0.27304900, 0.61652899, 0.73829597;...
0.03670000,0.07500000,0.09190000, 0.02940000,0.89631301,-0.44250599,  -0.95061398,0.16190200,0.26480401, 0.30899000, 0.41286701, 0.85680801;...
0.01860000,0.04410000,0.10530000, -0.01390000,0.97940999,-0.20140199,  -0.99181002,0.01210000,0.12700100, 0.12682299, 0.20151800, 0.97122103;...
0.05230000,0.04050000,0.09480000, 0.87324101,-0.01840100,-0.48692301,  -0.05680300,0.98864698,-0.13910700, 0.48395500, 0.14913200, 0.86228198;...
0.08020000,0.04110000,0.07150000, 0.64160401,0.05150000,-0.76530498,  -0.17140099,0.98210597,-0.07760100, 0.74761498, 0.18096299, 0.63895100;...
0.08220000,0.00600000,0.07220000, 0.64210999,0.00070000,-0.76661199,  0.01130000,0.99991602,0.01040000, 0.76655501, -0.01534100, 0.64204800;...
0.05340000,0.00610000,0.09650000, 0.86810398,-0.01810000,-0.49610201,  0.03030000,0.99940503,0.01650000, 0.49550799, -0.02935600, 0.86813599;...
0.08550000,0.09810000,0.00870000, 0.05440000,0.12470000,-0.99070197,  -0.50440103,0.85970199,0.08040000, 0.86173397, 0.49533701, 0.10966700;...
0.09960000,0.06570000,0.00810000, 0.07160100,0.02900000,-0.99701202,  -0.31310400,0.94971102,0.00520000, 0.94702399, 0.31179601, 0.07708000;...
0.08830000,0.07560000,0.04090000, 0.34709999,0.11710000,-0.93049902,  -0.37120000,0.92829901,-0.02170000, 0.86124098, 0.35293299, 0.36568001;...
0.06950000,0.07540000,0.07020000, 0.61337101,0.23868901,-0.75286400,  -0.42748001,0.90185702,-0.06239700, 0.66408199, 0.36010599, 0.65520698;...
0.09840000,0.04030000,0.04110000, 0.34030700,0.06010100,-0.93841898,  -0.16420300,0.98641998,0.00360000, 0.92589200, 0.15286601, 0.34555399;...
0.10660000,0.03280000,0.00810000, 0.06960000,0.01230000,-0.99749899,  -0.12850000,0.99169898,0.00330000, 0.98926002, 0.12794900, 0.07060300;...
0.10760000,-0.00080000,0.00670000, 0.05650000,-0.00260000,-0.99839902,  0.06420000,0.99789900,0.00100000, 0.99629903, -0.06415400, 0.05654800;...
0.10060000,0.00440000,0.04060000, 0.34980401,0.00790000,-0.93681097,  0.04030000,0.99891102,0.02350000, 0.93597603, -0.04597400, 0.34910500;...
0.10170000,0.06260000,-0.02540000, -0.01450000,0.00350000,-0.99987501,  -0.27479300,0.96147603,0.00730000, 0.96138102, 0.27486399, -0.01297900;...
0.10600000,0.04670000,-0.06000000, 0.01500000,0.00010000,-0.99988699,  -0.17129800,0.98518801,-0.00240000, 0.98507702, 0.17131500, 0.01479500;...
0.10930000,0.01300000,-0.06220000, 0.01450000,0.00440000,-0.99988502,  -0.00340000,0.99998498,0.00430000, 0.99988902, 0.00333700, 0.01451500;...
0.10800000,0.02980000,-0.02610000, -0.00830000,0.00430000,-0.99999303,  -0.09469900,0.99549299,0.00510000, 0.99550802, 0.09474100, -0.00785500;...
-0.10830000,-0.00350000,-0.02840000, 0.01840000,0.00060000,-0.99979103,  0.08249900,-0.99659097,0.00090000, -0.99638200, -0.08249900, -0.01838700;...
-0.10130000,-0.03610000,-0.02790000, 0.02590000,0.00200000,-0.99970001,  0.34330001,-0.93919998,0.00700000, -0.93890399, -0.34337801, -0.02501200;...
-0.09470000,-0.05190000,-0.06240000, -0.01750100,-0.00090000,-0.99984598,  0.45202100,-0.89204103,-0.00710000, -0.89189798, -0.45207599, 0.01601800;...
-0.10620000,-0.02060000,-0.06250000, -0.01709900,0.00100000,-0.99985301,  0.19109100,-0.98155397,-0.00430000, -0.98141497, -0.19113700, 0.01659300;...
-0.10110000,-0.03340000,0.00560000, -0.07030000,-0.03230000,-0.99700302,  0.33160099,-0.94340301,0.00720000, -0.94080800, -0.33010101, 0.07703200;...
-0.09470000,-0.03070000,0.03890000, -0.32199901,-0.05730000,-0.94499701,  0.30949900,-0.94969702,-0.04780000, -0.89472300, -0.30786699, 0.32353601;...
-0.07780000,-0.06260000,0.03910000, -0.25939399,-0.19959500,-0.94487703,  0.59678602,-0.80238098,0.00570000, -0.75928903, -0.56241101, 0.32724801;...
-0.08620000,-0.06330000,0.00530000, -0.06230200,-0.04950100,-0.99682897,  0.56421602,-0.82562399,0.00570000, -0.82328802, -0.56207198, 0.07936700;...
-0.07530000,-0.07920000,-0.06210000, -0.00110000,-0.01629900,-0.99986702,  0.66877800,-0.74327499,0.01140000, -0.74336201, -0.66867602, 0.01171800;...
-0.08580000,-0.06580000,-0.02820000, 0.02069900,0.00790000,-0.99976999,  0.57108301,-0.82087499,0.00530000, -0.82064497, -0.57106102, -0.02150300;...
-0.06270000,-0.08990000,-0.02770000, 0.02370000,0.03380000,-0.99908698,  0.80718899,-0.59029198,-0.00090000, -0.58978301, -0.80643100, -0.04127200;...
-0.04860000,-0.09880000,-0.06210000, -0.00990000,-0.01170000,-0.99988300,  0.88818502,-0.45939201,-0.00340000, -0.45929801, -0.88811398, 0.01493900;...
-0.07790000,-0.02850000,0.06900000, -0.61656600,-0.04059800,-0.78625602,  0.24968600,-0.95704699,-0.14639200, -0.74654102, -0.28657699, 0.60021901;...
-0.05170000,-0.02800000,0.09210000, -0.85628599,0.02680000,-0.51579100,  0.11099800,-0.96578401,-0.23439600, -0.50442499, -0.25796199, 0.82401198;...
-0.01810000,-0.05400000,0.09180000, 0.07110200,-0.83921897,-0.53921199,  0.98892200,-0.01130000,0.14800300, -0.13030000, -0.54376203, 0.82911903;...
-0.05470000,-0.06200000,0.07000000, -0.38340399,-0.49910501,-0.77710700,  0.77940702,-0.62620598,0.01770000, -0.49546400, -0.59889698, 0.62909597;...
-0.05110000,-0.08570000,0.03950000, -0.15409400,-0.30038801,-0.94126099,  0.87996399,-0.47498000,0.00760000, -0.44936299, -0.82710397, 0.33752200;...
-0.03330000,-0.10240000,0.00610000, -0.04479800,-0.14269300,-0.98875302,  0.95795399,-0.28688601,-0.00200000, -0.28337401, -0.94726902, 0.14954500;...
-0.03300000,-0.10480000,-0.02780000, 0.00710000,0.01980000,-0.99979001,  0.95129001,-0.30829701,0.00060000, -0.30822000, -0.95109397, -0.02102400;...
-0.06330000,-0.08750000,0.00590000, -0.06580100,-0.08830200,-0.99391800,  0.80071503,-0.59911102,0.00030000, -0.59549397, -0.79582500, 0.11012700;...
-0.01860000,-0.07950000,0.06840000, -0.00150000,-0.62351102,-0.78181303,  0.99261701,-0.09620200,0.07470100, -0.12178900, -0.77592897, 0.61905199;...
0.01840000,-0.07950000,0.06850000, 0.00020000,-0.62000102,-0.78460097,  0.98710102,0.12560000,-0.09890000, 0.15986399, -0.77446097, 0.61202902;...
0.01690000,-0.09680000,0.03950000, -0.00050000,-0.37198400,-0.92815900,  0.98985702,0.13169400,-0.05329800, 0.14205900, -0.91877103, 0.36814499;...
-0.01690000,-0.09670000,0.03960000, -0.00020000,-0.37219399,-0.92818499,  0.98978400,-0.13239799,0.05289900, -0.14257801, -0.91869199, 0.36841801;...
-0.00010000,-0.10770000,0.00680000, -0.00010000,-0.16710700,-0.98593903,  0.99993902,0.01150000,-0.00210000, 0.01169000, -0.98587900, 0.16709501;...
0.00000000,-0.11020000,-0.02740000, 0.00000000,0.03660000,-0.99930000,  1.00000000,-0.00040000,0.00000000, -0.00040000, -0.99930000, -0.03660000;...
0.01690000,-0.10910000,-0.06190000, 0.00950000,-0.01230000,-0.99987900,  0.98807901,0.15369700,0.00750000, 0.15358600, -0.98803103, 0.01361300;...
-0.01700000,-0.10910000,-0.06190000, -0.00650000,-0.01380000,-0.99988401,  0.98038399,-0.19689700,-0.00370000, -0.19682300, -0.98029399, 0.01480900;...
0.05160000,-0.02790000,0.09220000, 0.85719198,0.02850000,-0.51419502,  0.10849900,0.96609098,0.23429801, 0.50343698, -0.25662801, 0.82503402;...
0.07800000,-0.02830000,0.06920000, 0.62779897,-0.04280000,-0.77719802,  0.22579999,0.96559799,0.12930000, 0.74492699, -0.25666499, 0.61586499;...
0.05470000,-0.06220000,0.06980000, 0.37639499,-0.49189401,-0.78509003,  0.76659101,0.64129198,-0.03430000, 0.52034402, -0.58893299, 0.61846101;...
0.01820000,-0.05400000,0.09170000, -0.07050000,-0.83909798,-0.53939801,  0.98889703,0.01220000,-0.14810000, 0.13085100, -0.54385102, 0.82892102;...
0.05110000,-0.08580000,0.03950000, 0.15249699,-0.30129400,-0.94118202,  0.88048297,0.47399101,-0.00910000, 0.44885299, -0.82730699, 0.33756599;...
0.06310000,-0.08770000,0.00610000, 0.05720200,-0.07230300,-0.99574101,  0.80593300,0.59202403,0.00330000, 0.58926398, -0.80268902, 0.09213700;...
0.03290000,-0.10480000,-0.02770000, -0.00410000,0.02080000,-0.99978101,  0.95148200,0.30769399,0.00250000, 0.30767900, -0.95126402, -0.02105200;...
0.03300000,-0.10260000,0.00620000, 0.04110000,-0.12189900,-0.99169099,  0.94969201,0.31319699,0.00080000, 0.31049699, -0.94183397, 0.12863900;...
0.09480000,-0.03040000,0.03900000, 0.32109901,-0.06260000,-0.94499600,  0.30939901,0.94999599,0.04220000, 0.89510000, -0.30593100, 0.32440999;...
0.10100000,-0.03360000,0.00580000, 0.06840200,-0.02910100,-0.99723297,  0.32151100,0.94693202,-0.00550000, 0.94447201, -0.32024500, 0.07412900;...
0.08590000,-0.06350000,0.00550000, 0.06170300,-0.04580200,-0.99704301,  0.55552399,0.83153600,-0.00390000, 0.82925600, -0.55364102, 0.07675200;...
0.07780000,-0.06260000,0.03910000, 0.25730100,-0.20190100,-0.94500297,  0.59820199,0.80130202,-0.00830000, 0.75890899, -0.56316698, 0.32695299;...
0.06260000,-0.09000000,-0.02760000, -0.02120100,0.03560100,-0.99912602,  0.80782098,0.58941501,0.00390000, 0.58903903, -0.80703199, -0.04125500;...
0.08580000,-0.06570000,-0.02800000, -0.01910000,0.01020000,-0.99978799,  0.57079297,0.82108998,-0.00260000, 0.82088900, -0.57072097, -0.02150500;...
0.07520000,-0.07930000,-0.06200000, 0.01590000,-0.00240000,-0.99987102,  0.70427901,0.70987898,0.00950000, 0.70976502, -0.70433903, 0.01297700;...
0.04850000,-0.09890000,-0.06210000, 0.01200000,-0.00890000,-0.99988800,  0.90819001,0.41859499,0.00710000, 0.41848499, -0.90817302, 0.01310600;...
0.10830000,-0.00350000,-0.02790000, -0.01820000,0.00320000,-0.99978203,  0.08259800,0.99658197,0.00170000, 0.99636900, -0.08254900, -0.01840200;...
0.10620000,-0.02050000,-0.06210000, 0.01470000,0.00420000,-0.99988300,  0.22869600,0.97348398,0.00740000, 0.97340101, -0.22877800, 0.01334900;...
0.09450000,-0.05220000,-0.06200000, 0.01649900,0.00260000,-0.99986100,  0.48578101,0.87396598,0.01030000, 0.87387002, -0.48588300, 0.01315700;...
0.10130000,-0.03610000,-0.02770000, -0.02500000,0.00430000,-0.99969798,  0.34279901,0.93939799,-0.00450000, 0.93909502, -0.34280801, -0.02495900;...
]';
figure('color',[1,1,1]);
[x,y,z]=sphere(36);
k=0.07;
x=k*x;y=k*y;z=k*z-0.04;
h=surface(x,y,z);
set(h,'facecolor',[1,1,0.5]);hold on;
w=0.014;z=0.0003;
t=zeros(1,17);
for n=1:102
    pp=ChInform(1:3,n);
    ex=ChInform(4:6,n);
    ey=ChInform(7:9,n);
    ez=ChInform(10:12,n);
    O=[0,0,0]';
    pp=pp+z*ez;
    CC=w*[O,ex,ex+ey,ey,O,ex,ex-ey,-ey,O,-ex,-ex-ey,-ey,O,-ex,-ex+ey,ey,O];
    h=fill3(CC(1,:)+pp(1,1),CC(2,:)+pp(2,1),CC(3,:)+pp(3,1),t);
    set(h,'facecolor',[0,0,1],'edgecolor',[1,0,0]);
end;
axis tight;grid on;
daspect([1,1,1]);
view([-120,30]);

横河電機社製脳磁計

ChInformは210個の軸型グラジオメーターと190個の平面型グラジオメーターで、 Dewar表面のセンサーの[x,y,z]座標,Dewarから離れたセンサー[x,y,z], センサー面の法線方向の方位角と仰角[theta,phi], センサーコイルの直径[diameter]です。 赤は軸型グラジオメータ、青は平面型グラジオメーターです。 真ん中の黄色は半径7cmの仮想球面です。

横河の脳磁計のデータはATRのVBMEG http://vbmeg.atr.jp/ のサンプルデータを使用しました。

ChInform=[...
0.08187300,0.09824700,-0.06880100, 0.10383636,0.14313943,-0.06729099,  1.54059162,1.11579033,0.0155;...
0.06003600,0.10851100,-0.06558200, 0.07776551,0.15524572,-0.06434479,  1.54604963,1.20820433,0.0155;...
0.03703800,0.11505200,-0.06719600, 0.04187150,0.16475368,-0.06467001,  1.52025498,1.47385098,0.0155;...
0.08457000,0.09624900,-0.04465700, 0.11082264,0.13877619,-0.04316141,  1.54087997,1.01774299,0.0155;...
0.06334900,0.10600800,-0.01296900, 0.08292413,0.15195914,-0.01066530,  1.52470599,1.16807998,0.0155;...
0.03927800,0.11367500,-0.04218400, 0.04787470,0.16288311,-0.04002570,  1.52761699,1.39784099,0.0155;...
0.08548000,0.09339600,-0.01797200, 0.11258910,0.13540853,-0.01776213,  1.56659898,0.99775899,0.0155;...
0.03941100,0.11212300,-0.01597000, 0.04778667,0.16139009,-0.01435686,  1.53852798,1.40240097,0.0155;...
0.08634600,0.09196200,0.00713000, 0.11555418,0.13235460,0.01104406,  1.49243497,0.94472999,0.0155;...
0.06478100,0.10336000,0.01035600, 0.08458951,0.14871848,0.01744337,  1.42856999,1.15904898,0.0155;...
0.04221700,0.11064500,0.00984500, 0.05172099,0.15936110,0.01587952,  1.44981098,1.37812699,0.0155;...
0.08092100,0.09021200,0.02898300, 0.10811588,0.12989455,0.04261141,  1.29473498,0.96999698,0.0155;...
0.03678600,0.10766300,0.03050200, 0.04301452,0.15522848,0.04459918,  1.28497698,1.44059098,0.0155;...
0.07102200,0.08678400,0.04974700, 0.09443781,0.12475414,0.07232948,  1.10218298,1.01819498,0.0155;...
0.04921900,0.09630800,0.04913700, 0.06286292,0.13876479,0.07174816,  1.10153998,1.25985999,0.0155;...
0.02488400,0.10086300,0.05004100, 0.02788372,0.14522894,0.07290287,  1.09590999,1.50328598,0.0155;...
0.01264800,0.11530600,-0.06836400, 0.01013898,0.16523448,-0.06744137,  1.55234263,1.62100633,0.0155;...
-0.01455900,0.11276400,-0.06839300, -0.01735938,0.16267198,-0.06723032,  1.54754063,1.62684833,0.0155;...
-0.03841600,0.10934500,-0.07122600, -0.04981806,0.15802699,-0.07098742,  1.56602463,1.80086432,0.0155;...
0.01374400,0.11515700,-0.04266400, 0.01124326,0.16505144,-0.04059248,  1.52935397,1.62087497,0.0155;...
-0.01309500,0.11345300,-0.04223600, -0.01586696,0.16336880,-0.04138187,  1.55371297,1.62627198,0.0155;...
-0.03864400,0.10841600,-0.04235100, -0.05221607,0.15652139,-0.04105873,  1.54494798,1.84578098,0.0155;...
-0.01241500,0.11327300,-0.01562200, -0.01655840,0.16301283,-0.01265872,  1.51149597,1.65390597,0.0155;...
-0.03750600,0.10980400,-0.01662300, -0.04984950,0.15824557,-0.01559725,  1.55027998,1.82029898,0.0155;...
0.01788000,0.11340300,0.00899800, 0.01706739,0.16317345,0.01371410,  1.47633398,1.58712198,0.0155;...
-0.00968500,0.11335500,0.00843600, -0.01248347,0.16291045,0.01447141,  1.44979298,1.62720797,0.0155;...
-0.04051500,0.10338200,0.02931600, -0.05393842,0.14946454,0.04332355,  1.28684498,1.85424398,0.0155;...
0.01088400,0.10896600,0.03109100, 0.00874815,0.15704490,0.04465041,  1.29616898,1.61519098,0.0155;...
-0.01703900,0.10782500,0.02880700, -0.02119062,0.15585788,0.04205866,  1.30255798,1.65701498,0.0155;...
-0.00048200,0.10092000,0.04854200, -0.00298116,0.14546003,0.07112385,  1.10219698,1.62684798,0.0155;...
-0.02725100,0.09933300,0.04799200, -0.03403610,0.14365276,0.07012165,  1.11230798,1.72271097,0.0155;...
-0.04983700,0.09131100,0.04993000, -0.06607567,0.13257013,0.07303822,  1.09036199,1.94575398,0.0155;...
0.08277400,0.10330200,-0.06989900, 0.09937575,0.15041737,-0.07202591,  0.53366400,2.73069085,0.0120;...
0.08659000,0.10271700,-0.06922100, 0.11265237,0.14537607,-0.07019896,  2.10080629,2.60462670,0.0120;...
0.03713300,0.11822100,-0.06808600, 0.04333001,0.16782465,-0.06704917,  1.53801878,6.15821865,0.0120;...
0.03517600,0.11934000,-0.06844100, 0.03396740,0.16931293,-0.06732514,  3.10897477,2.41236137,0.0120;...
0.08842900,0.09675100,-0.01762600, 0.11548279,0.13879731,-0.01717888,  2.46823370,5.72265420,0.0120;...
0.08928500,0.09844100,-0.01613600, 0.11459823,0.14120938,-0.01064909,  2.24922288,2.51806287,0.0120;...
0.06115800,0.11361400,-0.04280200, 0.06771578,0.16254642,-0.03488911,  0.63854799,5.93232461,0.0120;...
0.03952500,0.11998400,-0.01565200, 0.04023648,0.16973126,-0.01068168,  0.35039354,5.99201405,0.0120;...
0.06723000,0.11008300,0.01000700, 0.07973825,0.15772348,0.01860517,  0.34682225,5.52237183,0.0120;...
0.06803200,0.10801700,0.00888400, 0.08860494,0.15355580,0.01060786,  1.26175424,2.72828431,0.0120;...
0.06401400,0.11122600,-0.04456000, 0.07980192,0.15863040,-0.04644798,  2.17033183,5.93586363,0.0120;...
0.08443900,0.09567800,0.03167800, 0.10625469,0.13751349,0.04822695,  0.47310436,5.04761111,0.0120;...
0.03784800,0.11363800,0.03073400, 0.04251119,0.16249646,0.04027890,  1.88771410,6.25185635,0.0120;...
0.03737800,0.11237000,0.03224000, 0.04094819,0.16008071,0.04676385,  0.40973636,5.43456722,0.0120;...
0.05061500,0.10099100,0.05189700, 0.06312409,0.14381286,0.07447599,  1.16309897,5.77860142,0.0120;...
0.05124200,0.10075000,0.05125900, 0.06691697,0.14234014,0.07416217,  2.52066620,0.44394155,0.0120;...
-0.01686900,0.11854200,-0.06911500, -0.02579154,0.16771490,-0.06756126,  3.01569088,0.42766909,0.0120;...
-0.01576200,0.12095700,-0.06619200, -0.01886866,0.16971639,-0.05556794,  1.42602036,0.03192005,0.0120;...
0.01175500,0.11999600,-0.04333600, 0.00308942,0.16910661,-0.03972270,  2.75417246,3.13773008,0.0120;...
0.01314800,0.11865600,-0.04439300, 0.00968112,0.16835989,-0.04857678,  1.95874776,0.03531576,0.0120;...
-0.03861300,0.11116700,-0.04326100, -0.05086198,0.15963216,-0.04430555,  2.20535143,0.23217171,0.0120;...
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]';

figure('color',[1,1,1]);
[x,y,z]=sphere(36);
k=0.07;
x=k*x;y=k*y;z=k*z-0.04;
h=surface(x,y,z);
set(h,'facecolor',[1,1,0.5]);hold on;
t=linspace(0,2*pi,17);
C=[cos(t);sin(t);t*0];
h=zeros(1,2);
for n=1:size(ChInform,2)
    pp=[ChInform(1:3,n),ChInform(4:6,n)]';
    phi=ChInform(7,n);
    theta=ChInform(8,n);
    coil=ChInform(9,n);
    Theta=[cos(theta),-sin(theta),0;sin(theta),cos(theta),0;0,0,1];
    Phi=[cos(phi),0,sin(phi);0,1,0;-sin(phi),0,cos(phi)];
    CC=Theta*Phi*C*coil/2;
    if coil==0.0155;
        color=[1,0,0];
    else
        color=[0,0,1];
    end;
    plot3(pp(:,1),pp(:,2),pp(:,3),'color',color,'linewidth',2);
    h(1)=fill3(CC(1,:)+pp(1,1),CC(2,:)+pp(1,2),CC(3,:)+pp(1,3),t*0);
    h(2)=fill3(CC(1,:)+pp(2,1),CC(2,:)+pp(2,2),CC(3,:)+pp(2,3),t*0);
    set(h,'facecolor',color);
end;
axis tight;grid on;
daspect([1,1,1]);
view([150,30]);