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Author SHA1 Message Date
Thomas Dehaeze
f549fc5313 Add analysis of errors based on ray-tracing 2022-06-02 18:06:51 +02:00
Thomas Dehaeze
f17ceca29d Working ray tracing with dz/dry/drx 2022-06-02 10:59:32 +02:00
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@ -13,12 +13,10 @@
#+BIND: org-latex-image-default-option "scale=1"
#+BIND: org-latex-image-default-width ""
#+LATEX_CLASS: scrreprt
#+LATEX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
#+LATEX_HEADER_EXTRA: \input{preamble.tex}
#+bibliography: dcm-metrology.bib
#+cite_export: csl ~/.local/data/csl-styles/elsevier-harvard.csl
#+LaTeX_CLASS: scrreprt
#+LaTeX_CLASS_OPTIONS: [a4paper, 10pt, DIV=12, parskip=full]
#+LaTeX_HEADER_EXTRA: \input{preamble.tex}
#+LATEX_HEADER_EXTRA: \bibliography{ref}
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
@ -186,68 +184,12 @@ In this section, the impact of an error in the relative pose between the first a
This is very important in order to:
- link a measurement of the x-ray beam position to a default in the crystal position
- understand which pose default will have large impact on the output beam position/orientation
- calibrate the deformations of the metrology frame using and external metrology measuring the x-ray beam position/orientation
- calibrate the deformations of the metrology frame using an external metrology measuring the x-ray beam position/orientation
In order to simplify the problem, the first crystal is supposed to be fixed (i.e. ideally positioned), and only the motion of the second crystal is studied.
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
In order to easily study that, "ray tracing" techniques are used.
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab
bragg = pi/180*linspace(5,75,100);
#+end_src
** Axial motion of second crystal
Let's consider the relation between the $[y, z]$ motion of the beam and the motion of the second crystal $[z^\prime, R_{y^\prime}, R_{x^\prime}]$.
#+name: fig:relation_dz_output_beam
#+caption: Relation between $d_{z^\prime}$ motion of the second crystal and vertical motion of the beam
[[file:figs/relation_dz_output_beam.png]]
\begin{equation}
d_z = d_{z^\prime} 2 \cos \theta
\end{equation}
#+begin_src matlab :exports none :results none
%% Relation between vertical motion of the second crystal and vertical motion of the output beam
figure;
hold on;
plot(180/pi*bragg, 2*cos(bragg))
xlabel('Bragg [deg]'); ylabel('Motion amplification');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/relation_vert_motion_crystal_beam.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:relation_vert_motion_crystal_beam
#+caption: Relation between vertical motion of the second crystal and vertical motion of the output beam
#+RESULTS:
[[file:figs/relation_vert_motion_crystal_beam.png]]
** Ry motion of second crystal
\begin{equation}
d_z = D_{\text{vlm}} d_{R_y^\prime}
\end{equation}
with $D_{\text{vlm}} \approx 10\,m$.
** Rx motion of second crystal
\begin{equation}
d_y = 2 D_{\text{vlm}} \sin \theta \cdot d_{R_x^\prime}
\end{equation}
* Ray Tracing
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
@ -278,147 +220,438 @@ d_y = 2 D_{\text{vlm}} \sin \theta \cdot d_{R_x^\prime}
| reflected beam | =x2,y2,z2= | =s2= |
| secondary mirror | =xs,ys,zz= | =ns= |
| output beam | =x3,y3,z3= | =s3= |
| Dectector | =xd,yd,zd= | =nd= |
#+begin_src matlab
theta = 5*pi/180; % [rad]
#+end_src
- [ ] Add schematic
#+begin_src matlab
%% Secondary crystal defaults
drx = 5*pi/180; % [rad]
dry = 0*pi/180; % [rad]
dz = 0; % [m]
Notations for the pose of the output beam: =d_b_y=, =d_b_z=, =r_b_y=, =r_b_z=.
% Rotation matrix for drx
udrx = [cos(theta), 0, -sin(theta)];
Rdrx = cos(drx)*eye(3)+sin(drx)*[0, -udrx(3), udrx(2); udrx(3), 0, -udrx(1); -udrx(2), udrx(1), 0] + (1-cos(drx))*(udrx'*udrx);
$d_{b,y}, d_{b,z}, r_{b,y}, r_{b,z}$
% Rotation matrix for dry
Rdry = [ cos(dry), 0, sin(dry); ...
0, 1, 0; ...
-sin(dry), 0, cos(dry)];
#+end_src
The xy position of the beam is taken in the $x=0$ plane.
#+begin_src matlab
%% Input Beam
p1 = [-0.1, 0, 0]; % [m]
s1 = [ 1, 0, 0];
** Effect of an error in crystal's distance
<<sec:ray_tracing_dz>>
%% Primary Mirror
pp = [0, 0, 0]; % [m]
np = [cos(pi/2-theta), 0, sin(pi/2-theta)];
In Figure [[fig:ray_tracing_error_dz_overview]] is shown the light path for three bragg angles (5, 55 and 85 degrees) when there is an error in the =dz= position of 1mm.
%% Reflected beam
[p2, s2] = get_plane_reflection(p1, s1, pp, np);
Visually, it is clear that this induce a =z= offset of the output beam.
%% Secondary Mirror
ps = pp ...
+ 0.07*[cos(theta), 0, -sin(theta)] ... % x offset (does not matter a lot)
- np*10e-3./(2*cos(theta)) ... % Theoretical offset
+ np*dz; % Add error in distance
ns = [Rdry*Rdrx*[cos(pi/2-theta), 0, sin(pi/2-theta)]']'; % Normal
%% Output Beam
[p3, s3] = get_plane_reflection(p2, s2, ps, ns);
#+end_src
#+begin_src matlab
%% Primary crystal plane
z = np;
y = [0,1,0];
x = cross(y,z);
xtal1_rectangle = [pp + 0.02*y + 0.07*x;
pp - 0.02*y + 0.07*x;
pp - 0.02*y - 0.07*x;
pp + 0.02*y - 0.07*x];
%% Secondary crystal plane
z = ns;
y = [0,cos(drx),sin(drx)];
x = cross(y,z);
xtal2_rectangle = [ps + 0.02*y + 0.07*x;
ps - 0.02*y + 0.07*x;
ps - 0.02*y - 0.07*x;
ps + 0.02*y - 0.07*x];
#+end_src
#+begin_src matlab
#+begin_src matlab :exports none :results none
%% Visual Effect of an error in dz
figure;
tiledlayout(2, 1, 'TileSpacing', 'Compact', 'Padding', 'None');
ax1 = nexttile();
hold on;
plot3([p1(1), p2(1)],[p1(2), p2(2)], [p1(3), p2(3)])
plot3([p2(1), p3(1)],[p2(2), p3(2)], [p2(3), p3(3)])
plot3([p3(1), p3(1)+0.3*s3(1)],[p3(2), p3(2)+0.3*s3(2)], [p3(3), p3(3)+0.3*s3(3)])
patch(xtal1_rectangle(:,1), xtal1_rectangle(:,2), xtal1_rectangle(:,3), 'k')
patch(xtal2_rectangle(:,1), xtal2_rectangle(:,2), xtal2_rectangle(:,3), 'k')
for theta = [5, 55, 85]
results = getBeamPath(theta*pi/180, 'dz', 1e-3);
set(gca,'ColorOrderIndex',1)
plotBeamPath(results);
plotCrystals(results);
end
hold off;
view(0,0)
axis equal
xlim([-0.1, 0.15])
zlim([-0.02, 0.01])
xlim([-10, 15])
zlim([-4, 2])
grid off;
xlabel('X')
ylabel('Y')
zlabel('Z')
axis equal
xlabel('X [cm]')
ylabel('Y [cm]')
zlabel('Z [cm]')
#+end_src
ax2 = nexttile();
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/ray_tracing_error_dz_overview.pdf', 'width', 'full', 'height', 'normal');
#+end_src
#+name: fig:ray_tracing_error_dz_overview
#+caption: Visual Effect of an error in =dz= (1mm). Side view.
#+RESULTS:
[[file:figs/ray_tracing_error_dz_overview.png]]
The motion of the output beam is displayed as a function of the Bragg angle in Figure [[fig:motion_beam_dz_error]].
It is clear that an error in the distance =dz= between the crystals only induce a =z= offset of the output beam.
This offset decreases with the Bragg angle.
This is indeed equal to:
\begin{equation}
\boxed{d_{b,z} = 2 d_z \cos \theta}
\end{equation}
#+begin_src matlab :exports none
%% Effect of dz
thetas = 1:1:85;
Dy = zeros(length(thetas), 1); % [m]
Dz = zeros(length(thetas), 1); % [m]
Ry = zeros(length(thetas), 1); % [rad]
Rz = zeros(length(thetas), 1); % [rad]
for i = 1:length(thetas)
results = getBeamPath(thetas(i)*pi/180, 'dz', 1e-9);
Ry(i) = atan2(results.s3(3), results.s3(1));
Rz(i) = atan2(results.s3(2), results.s3(1));
Dy(i) = results.p4(2)-tan(Rz(i));
Dz(i) = results.p4(3)+tan(Ry(i));
end
#+end_src
#+begin_src matlab :exports none :results none
%% Motion of the output beam with dZ error
figure;
hold on;
plot3([p1(1), p2(1)],[p1(2), p2(2)], [p1(3), p2(3)])
plot3([p2(1), p3(1)],[p2(2), p3(2)], [p2(3), p3(3)])
plot3([p3(1), p3(1)+0.3*s3(1)],[p3(2), p3(2)+0.3*s3(2)], [p3(3), p3(3)+0.3*s3(3)])
patch(xtal1_rectangle(:,1), xtal1_rectangle(:,2), xtal1_rectangle(:,3), 'k')
patch(xtal2_rectangle(:,1), xtal2_rectangle(:,2), xtal2_rectangle(:,3), 'k')
plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy');
plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz');
plot(thetas, 1e9*Ry, 'DisplayName', 'Ry');
plot(thetas, 1e9*Rz, 'DisplayName', 'Rz');
hold off;
xlabel('Bragg [deg]'); ylabel('Offset [m/m] Tilt [rad/m]')
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
xlim([0, 85]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/motion_beam_dz_error.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:motion_beam_dz_error
#+caption: Motion of the output beam with dZ error
#+RESULTS:
[[file:figs/motion_beam_dz_error.png]]
** Effect of an error in crystal's x parallelism
<<sec:ray_tracing_rx>>
The effect of an error in =rx= crystal parallelism on the output beam is visually shown in Figure [[fig:ray_tracing_error_drx_overview]] for three bragg angles (5, 55 and 85 degrees).
The error is set to one degree, and the top view is shown.
It is clear that the output beam experiences some rotation around a vertical axis.
The amount of rotation depends on the bragg angle.
#+begin_src matlab :exports none :results none
%% Visual Effect of an error in drx
figure;
hold on;
for theta = [5, 55, 85]
results = getBeamPath(theta*pi/180, 'drx', -1*pi/180);
set(gca,'ColorOrderIndex',1)
plotBeamPath(results);
% plotCrystals(results);
end
hold off;
view(0,90)
axis equal
xlim([-0.1, 0.15])
zlim([-0.02, 0.01])
xlim([-10, 15])
ylim([-1, 1])
grid off;
xlabel('X')
ylabel('Y')
zlabel('Z')
xlabel('X [cm]');
ylabel('Y [cm]');
zlabel('Z [cm]');
#+end_src
#+begin_src matlab
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/ray_tracing_error_drx_overview.pdf', 'width', 'full', 'height', 'normal');
#+end_src
#+name: fig:ray_tracing_error_drx_overview
#+caption: Visual Effect of an error in =drx= (1 degree). Top View.
#+RESULTS:
[[file:figs/ray_tracing_error_drx_overview.png]]
The effect of =drx= as a function of the Bragg angle on the output beam pose is computed and shown in Figure [[fig:motion_beam_drx_error]].
It induces a rotation of the output beam in the =z= direction that depends on the Bragg Angle.
It is starting at zero for small bragg angles, and it increases with the bragg angle up to 2 times =drx=.
This is indeed equal to:
\begin{equation}
\boxed{r_{b,z} = 2 r_x \cos \theta}
\end{equation}
If also induces a small $y$ shift of the beam.
This shift is due to the fact that the rotation point (around which the second crystal is moved) is changing as a function of bragg.
We can note that the $y$ shift is equal to zero for a bragg angle of 45 degrees, at which point the center of rotation of the second crystal is at $x = 0$;
#+begin_src matlab :exports none
%% Effect of drx
thetas = 1:1:85;
Dy = zeros(length(thetas), 1);
Dz = zeros(length(thetas), 1);
Ry = zeros(length(thetas), 1);
Rz = zeros(length(thetas), 1);
for i = 1:length(thetas)
results = getBeamPath(thetas(i)*pi/180, 'drx', 1e-9);
Ry(i) = atan2(results.s3(3), results.s3(1));
Rz(i) = atan2(results.s3(2), results.s3(1));
Dy(i) = results.p4(2)-tan(Rz(i));
Dz(i) = results.p4(3)+tan(Ry(i));
end
#+end_src
#+begin_src matlab :exports none :results none
%% Motion of the output beam with drx error
figure;
hold on;
plot3([p1(1), p2(1)],[p1(2), p2(2)], [p1(3), p2(3)])
plot3([p2(1), p3(1)],[p2(2), p3(2)], [p2(3), p3(3)])
plot3([p3(1), p3(1)+0.3*s3(1)],[p3(2), p3(2)+0.3*s3(2)], [p3(3), p3(3)+0.3*s3(3)])
surf(xtal1_x, xtal1_y, xtal1_z)
patch(xtal2_rectangle(:,1), xtal2_rectangle(:,2), xtal2_rectangle(:,3), 'k')
plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy');
plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz');
plot(thetas, 1e9*Ry, 'DisplayName', 'Ry');
plot(thetas, 1e9*Rz, 'DisplayName', 'Rz');
hold off;
xlabel('Bragg [deg]'); ylabel('Offset [m/rad] Tilt [rad/rad]')
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
xlim([0, 85]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/motion_beam_drx_error.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:motion_beam_drx_error
#+caption: Motion of the output beam with drx error
#+RESULTS:
[[file:figs/motion_beam_drx_error.png]]
** Effect of an error in crystal's y parallelism
<<sec:ray_tracing_ry>>
The effect of an error in =ry= crystal parallelism on the output beam is visually shown in Figure [[fig:ray_tracing_error_dry_overview]] for three bragg angles (5, 55 and 85 degrees).
#+begin_src matlab :exports none :results none
%% Visual Effect of an error in dry
figure;
hold on;
for theta = [5, 55, 85]
results = getBeamPath(theta*pi/180, 'dry', -1*pi/180);
set(gca,'ColorOrderIndex',1)
plotBeamPath(results);
plotCrystals(results);
end
hold off;
view(0,0)
axis equal
xlim([-0.1, 0.15])
zlim([-0.02, 0.01])
xlim([-10, 15])
zlim([-4, 2])
grid off;
xlabel('X [cm]')
ylabel('Y [cm]')
zlabel('Z [cm]')
#+end_src
#+begin_src matlab
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/ray_tracing_error_dry_overview.pdf', 'width', 'full', 'height', 'normal');
#+end_src
#+name: fig:ray_tracing_error_dry_overview
#+caption: Visual Effect of an error in =dry= (1 degree). Side view.
#+RESULTS:
[[file:figs/ray_tracing_error_dry_overview.png]]
The effect of =dry= as a function of the Bragg angle on the output beam pose is computed and shown in Figure [[fig:motion_beam_dry_error]].
It is clear that this induces a rotation of the output beam in the =y= direction equals to 2 times =dry=:
\begin{equation}
\boxed{r_{b,z} = 2 r_z}
\end{equation}
It also induces a small vertical motion of the beam (at the $x=0$ location) which is simply due to the fact that the $x$ coordinate of the impact point on the second crystal changes with the Bragg angle.
#+begin_src matlab :exports none
%% Effect of dry
thetas = 1:1:85;
Dy = zeros(length(thetas), 1);
Dz = zeros(length(thetas), 1);
Ry = zeros(length(thetas), 1);
Rz = zeros(length(thetas), 1);
for i = 1:length(thetas)
results = getBeamPath(thetas(i)*pi/180, 'dry', 1e-9);
Ry(i) = atan2(results.s3(3), results.s3(1));
Rz(i) = atan2(results.s3(2), results.s3(1));
Dy(i) = results.p4(2)-tan(Rz(i));
Dz(i) = results.p4(3)-tan(Ry(i));
end
#+end_src
#+begin_src matlab :exports none :results none
%% Motion of the output beam with dry error
figure;
hold on;
plot3([p1(1), p2(1)],[p1(2), p2(2)], [p1(3), p2(3)])
plot3([p2(1), p3(1)],[p2(2), p3(2)], [p2(3), p3(3)])
plot3([p3(1), p3(1)+0.3*s3(1)],[p3(2), p3(2)+0.3*s3(2)], [p3(3), p3(3)+0.3*s3(3)])
surf(xtal1_x, xtal1_y, xtal1_z)
patch(xtal2_rectangle(:,1), xtal2_rectangle(:,2), xtal2_rectangle(:,3), 'k')
plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy');
plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz');
plot(thetas, 1e9*Ry, 'DisplayName', 'Ry');
plot(thetas, 1e9*Rz, 'DisplayName', 'Rz');
hold off;
view(90,90)
axis equal
xlim([-0.1, 0.15])
zlim([-0.02, 0.01])
grid off;
xlabel('Bragg [deg]'); ylabel('Offset [m/rad] Tilt [rad/rad]')
legend('location', 'east', 'FontSize', 8, 'NumColumns', 2);
xlim([0, 85]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/motion_beam_dry_error.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:motion_beam_dry_error
#+caption: Motion of the output beam with dry error
#+RESULTS:
[[file:figs/motion_beam_dry_error.png]]
** Summary
Effects of crystal's pose errors on the output beam are summarized in Table [[tab:crystal_pose_beam_pose]].
Note that the three pose errors are well decoupled regarding their effects on the output beam.
Also note that the effect of an error in crystal's distance does not depend on the Bragg angle.
#+name: tab:crystal_pose_beam_pose
#+caption: Summary of the effects of the errors in second crystal's pose on the output beam
#+attr_latex: :environment tabularx :width 0.65\linewidth :align X|ccc
#+attr_latex: :center t :booktabs t
| *Beam Motion* | *Crystal* $d_z$ | *Crystal* $r_x$ | *Crystal* $r_y$ |
|---------------+--------------------------------+--------------------------------------+--------------------|
| $d_{b,y}$ | 0 | $\approx 0$ | 0 |
| $d_{b,z}$ | $\boxed{d_{z} 2 \cos(\theta)}$ | 0 | $\approx 0$ |
| $r_{b,y}$ | 0 | 0 | $\boxed{2 r_{y}}$ |
| $r_{b,z}$ | 0 | $\boxed{- r_x 2 \sin(\theta)}$ | 0 |
** "Channel cut" Scan
A "channel cut" scan is a Bragg scan where the distance between the crystals is fixed.
This is visually shown in Figure [[fig:ray_tracing_channel_cut]] where it is clear that the output beam experiences some vertical motion.
#+begin_src matlab :exports none :results none
%% Visual Effect of a channel cut scan
figure;
hold on;
for theta = [30, 40, 50]
results = getBeamPath(theta*pi/180, 'dz', 10e-3/(2*cos(pi/180*theta))-10e-3/(2*cos(pi/180*theta_fixed)));
set(gca,'ColorOrderIndex',1)
plotBeamPath(results);
plotCrystals(results);
end
hold off;
view(0,0)
axis equal
xlim([-10, 15])
zlim([-4, 2])
grid off;
xlabel('X [cm]')
ylabel('Y [cm]')
zlabel('Z [cm]')
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/ray_tracing_channel_cut.pdf', 'width', 'full', 'height', 'normal');
#+end_src
#+name: fig:ray_tracing_channel_cut
#+caption: Visual Effect of a channel cut scan
#+RESULTS:
[[file:figs/ray_tracing_channel_cut.png]]
The $z$ offset of the beam for several channel cut scans are shown in Figure [[fig:channel_cut_scan]].
#+begin_src matlab :exports none
%% Computation of Z motion of the beam during "channel cut" scans
thetas = 5:1:84;
Dz = zeros(length(thetas), 1);
for i = 1:length(thetas)
results = getBeamPath(thetas(i)*pi/180, 'dz', 10e-3/(2*cos(pi/180*thetas(i)))-10e-3/(2*cos(pi/180*(10*fix((5+thetas(i))/10)))));
Dz(i) = results.p4(3);
end
#+end_src
#+begin_src matlab :exports none :results none
%% Dz motion of the beam during "channel cut" scans
figure;
hold on;
for i = 1:8
plot(thetas((i-1)*10+1:i*10), 1e3*(Dz((i-1)*10+1:i*10)+10e-3), '-', 'DisplayName', sprintf('$%i^o$: $%.0f\\,\\mu$m/deg', (10*fix((5+thetas((i-1)*10+5))/10)), 1e6*(Dz((i-1)*10+6)-Dz((i-1)*10+5))));
end
hold off;
xlabel('Bragg [deg]'); ylabel('Dz Offset [mm]')
xlim([0, 90]); ylim([-4, 4]);
xticks([0:10:90]);
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/channel_cut_scan.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:channel_cut_scan
#+caption: Z motion of the beam during "channel cut" scans
#+RESULTS:
[[file:figs/channel_cut_scan.png]]
* Determining relative pose between the crystals using the X-ray
** Introduction :ignore:
As Interferometers are only measuring /relative/ displacement, it is mandatory to initialize them correctly.
They should be initialize in such a way that:
- $r_x = 0$ and $r_y = 0$ when the two crystallographic planes are parallel
- measured $d_z$ is equal to the distance between the crystallographic planes
In order to do that, an external metrology using the x-ray is used.
** Determine the $y$ parallelism - "Rocking Curve"
** Determine the $x$ parallelism - Bragg Scan
** Determine the $z$ distance - Bragg Scan
** Use Channel cut scan to determine crystal =dry= parallelism
Now, let's suppose we want to determine the =dry= angle between the crystals.
#+begin_src matlab
dry = 1e-6; % [rad]
#+end_src
#+begin_src matlab :exports none
%% Computation of Z motion of the beam during "channel cut" scans
thetas = 5:1:84;
Dz_expected = zeros(length(thetas), 1);
Dz_obtained = zeros(length(thetas), 1);
for i = 1:length(thetas)
results = getBeamPath(thetas(i)*pi/180, 'dz', 10e-3/(2*cos(pi/180*thetas(i)))-10e-3/(2*cos(pi/180*(10*fix((5+thetas(i))/10)))));
Dz_expected(i) = results.p4(3);
results = getBeamPath(thetas(i)*pi/180, 'dz', 10e-3/(2*cos(pi/180*thetas(i)))-10e-3/(2*cos(pi/180*(10*fix((5+thetas(i))/10)))), 'dry', dry);
Dz_obtained(i) = results.p4(3);
end
#+end_src
The error is
\begin{equation}
\boxed{d_{b,z} = -2 d_z \cos()}
\end{equation}
#+begin_src matlab :exports none :results none
%% Dz motion of the beam during "channel cut" scans
figure;
hold on;
plot(thetas, 1e6*(Dz_expected-Dz_obtained), '-');
hold off;
xlabel('Bragg [deg]'); ylabel('Dz Offset [$\mu$m]')
xlim([0, 90]);
xticks([0:10:90]);
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
#+end_src
#+begin_src matlab :exports none :results none
%% Dz motion of the beam during "channel cut" scans
figure;
hold on;
plot(thetas, 1e3*Dz_expected, '-');
plot(thetas, 1e3*Dz_obtained, '-');
hold off;
xlabel('Bragg [deg]'); ylabel('Dz Offset [mm]')
xlim([0, 90]);
xticks([0:10:90]);
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
#+end_src
** Effect of an error on Bragg angle
* Deformations of the Metrology Frame
<<sec:frame_deformations>>
** Introduction :ignore:
The transformation matrix in Table [[tab:transformation_matrix]] is valid only if the metrology frames are solid bodies.
The transformation matrices are valid only if the metrology frames are solid bodies.
The metrology frame itself is experiencing some deformations due to the gravity.
When the bragg axis is scanned, the effect of gravity on the metrology frame is changing and this introduce some measurement errors.
@ -1147,16 +1380,16 @@ freqs = logspace(1, 3, 1000);
** Intersection between Ray and Plane
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/get_plane_reflection.m
:header-args:matlab+: :tangle matlab/src/getPlaneReflection.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:get_plane_reflection>>
<<sec:getPlaneReflection>>
#+begin_src matlab
function [p_reflect, s_reflect] = get_plane_reflection(p_in, s_in, p_plane, n_plane)
% get_plane_reflection -
function [p_reflect, s_reflect] = getPlaneReflection(p_in, s_in, p_plane, n_plane)
% getPlaneReflection -
%
% Syntax: [p_reflect, s_reflect] = get_plane_reflection(p_in, s_in, p_plane, n_plane)
% Syntax: [p_reflect, s_reflect] = getPlaneReflection(p_in, s_in, p_plane, n_plane)
%
% Inputs:
% - p_in, s_in, p_plane, n_plane -
@ -1175,9 +1408,176 @@ s_reflect = s_reflect./norm(s_reflect);
end
#+end_src
* Bibliography
** Get Beam Path
:PROPERTIES:
:UNNUMBERED: t
:header-args:matlab+: :tangle matlab/src/getBeamPath.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:getBeamPath>>
#+print_bibliography:
#+begin_src matlab
function [results] = getBeamPath(theta, args)
% getBeamPath -
%
% Syntax: [in_data] = getBeamPath(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
#+end_src
#+begin_src matlab
arguments
theta
args.drx (1,1) double {mustBeNumeric} = 0 % [rad]
args.dry (1,1) double {mustBeNumeric} = 0 % [rad]
args.dz (1,1) double {mustBeNumeric} = 0 % [m]
end
#+end_src
#+begin_src matlab
% Rotation matrix for drx
udrx = [cos(theta), 0, -sin(theta)];
Rdrx = cos(args.drx)*eye(3)+sin(args.drx)*[0, -udrx(3), udrx(2); udrx(3), 0, -udrx(1); -udrx(2), udrx(1), 0] + (1-cos(args.drx))*(udrx'*udrx);
% Rotation matrix for dry
Rdry = [ cos(args.dry), 0, sin(args.dry); ...
0, 1, 0; ...
-sin(args.dry), 0, cos(args.dry)];
#+end_src
#+begin_src matlab
%% Input Beam
p1 = [-0.1, 0, 0]; % [m]
s1 = [ 1, 0, 0];
%% Primary Mirror
pp = [0, 0, 0]; % [m]
np = [cos(pi/2-theta), 0, sin(pi/2-theta)];
%% Reflected beam
[p2, s2] = getPlaneReflection(p1, s1, pp, np);
%% Secondary Mirror
ps = pp ...
+ 0.032*[cos(theta), 0, -sin(theta)] ... % x offset (does not matter a lot)
- np*10e-3./(2*cos(theta)) ... % Theoretical offset
+ np*args.dz; % Add error in distance
ns = [Rdry*Rdrx*[cos(pi/2-theta), 0, sin(pi/2-theta)]']'; % Normal
%% Output Beam
[p3, s3] = getPlaneReflection(p2, s2, ps, ns);
%% Detector
pd = [1, 0, 0]; % [m]
nd = [-1, 0, 0];
%% Get beam position on the decector
p4 = getPlaneReflection(p3, s3, pd, nd);
#+end_src
#+begin_src matlab
results = struct();
% Beam position and orientations
results.p1 = p1;
results.s1 = s1;
results.p2 = p2;
results.s2 = s2;
results.p3 = p3;
results.s3 = s3;
results.p4 = p4;
% Mirrors/detector positions and orientations
results.pp = pp;
results.np = np;
results.ps = ps;
results.ns = ns;
results.pd = pd;
results.nd = nd;
#+end_src
** Plot Beam Path
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/plotBeamPath.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:plotBeamPath>>
#+begin_src matlab
function [] = plotBeamPath(results)
% plotBeamPath -
%
% Syntax: [in_data] = plotBeamPath(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
#+end_src
#+begin_src matlab
plot3(100*[results.p1(1), results.p2(1)],100*[results.p1(2), results.p2(2)], 100*[results.p1(3), results.p2(3)], 'linewidth', 0.5)
plot3(100*[results.p2(1), results.p3(1)],100*[results.p2(2), results.p3(2)], 100*[results.p2(3), results.p3(3)], 'linewidth', 0.5)
plot3(100*[results.p3(1), results.p4(1)],100*[results.p3(2), results.p4(2)], 100*[results.p3(3), results.p4(3)], 'linewidth', 0.5)
#+end_src
** Plot Crystal
:PROPERTIES:
:header-args:matlab+: :tangle matlab/src/plotCrystals.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:plotCrystals>>
#+begin_src matlab
function [] = plotCrystals(results, args)
% plotCrystals -
%
% Syntax: [in_data] = plotCrystals(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
#+end_src
#+begin_src matlab
arguments
results
args.color (3,1) double {mustBeNumeric} = [1;1;1]
args.alpha (1,1) double {mustBeNumeric} = 1
end
#+end_src
#+begin_src matlab
z = results.np;
y = [0,1,0];
x = cross(y,z);
xtal1_rectangle = [results.pp + 0.02/2*y + 0.035/2*x;
results.pp - 0.02/2*y + 0.035/2*x;
results.pp - 0.02/2*y - 0.035/2*x;
results.pp + 0.02/2*y - 0.035/2*x];
#+end_src
#+begin_src matlab
patch(100*xtal1_rectangle(:,1), 100*xtal1_rectangle(:,2), 100*xtal1_rectangle(:,3), 'k-')
#+end_src
#+begin_src matlab
z = results.ns;
% y = [0,cos(drx),sin(drx)];
y = [0,1,0];
x = cross(y,z);
xtal2_rectangle = [results.ps + 0.02/2*y + 0.07/2*x;
results.ps - 0.02/2*y + 0.07/2*x;
results.ps - 0.02/2*y - 0.07/2*x;
results.ps + 0.02/2*y - 0.07/2*x];
#+end_src
#+begin_src matlab
patch(100*xtal2_rectangle(:,1), 100*xtal2_rectangle(:,2), 100*xtal2_rectangle(:,3), 'k-')
#+end_src

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19.04 6.066 29.758 33.3 5.5537 0.1180 0.5170 24.8737 0.5074 0.5075 0.118 24.874 5.554 1.320e-05 3188.0 675.083 916.581 2139.9032 -4222.2674 5553292.6038 118356.9332 510621.2267 -30427418.2201 120421.6405 506332.6670 24874134.3053 -70.0988 -65.5562 8.6829 -0.0000 -0.0000 -0.0000 0.1328 -0.6779 752.793 883.153 14787.9314 -2106.8303 5553233.9685 118386.4586 510597.5147 -30427420.4625 133092.0619 508436.1824 24874194.9789 -73.2521 -64.3678 8.7921 30.5088 -68.9274 -19.2093 0.5094 -0.8231 768.124 893.376 17299.2297 -2798.1393 5553320.9449 118329.4346 510643.6800 -30427419.6266 135561.2373 507787.8423 24874107.6164 -71.2252 -62.4499 8.6950 -46.3131 -145.7494 57.6127 -4.6922 752.109 894.469 14718.9556 -2858.2384 5553321.5937 118341.2660 510650.6062 -30427420.7145 132979.3323 507734.6034 24874107.5773 -73.0835 -61.6967 8.6868 134.3375 -553.8859 -56.1303 0.0250 29 173008
20.05 5.770 28.494 33.1 5.5888 0.1180 0.5170 24.8386 0.5072 0.5072 0.118 24.839 5.589 1.287e-05 3257.8 667.941 906.061 2379.4074 -3652.2583 5588404.4306 118237.8676 509713.6462 -30427415.5094 120549.1371 505997.9397 24839018.5725 -71.6710 -60.1910 8.0257 -0.0000 -0.0000 -0.0000 0.1334 -0.7521 752.600 870.783 15565.9864 -1389.3999 5588356.2781 118298.7743 509667.1289 -30427416.4969 133796.0832 508216.7045 24839068.5560 -71.5565 -62.7106 8.6389 33.8477 -76.4708 -21.3115 0.5081 -0.6454 767.847 893.421 17924.1889 -2861.8894 5588437.8065 118258.0319 509715.8934 -30427416.7346 136096.7467 506799.4062 24838987.0211 -70.7544 -62.1622 8.1580 -26.3900 -136.7085 38.9262 -4.5147 751.961 894.291 15536.0852 -2927.5485 5588437.9351 118236.7028 509737.7707 -30427416.9389 133696.9984 506743.2288 24838987.0960 -72.5373 -60.9475 8.2416 142.9329 -519.2528 -67.6845 0.0250 43 173242
21.07 5.503 27.477 33.0 5.6262 0.1180 0.5170 24.8012 0.5079 0.5079 0.118 24.801 5.626 1.109e-05 3204.6 653.788 901.918 1630.0857 -3391.2413 5625400.9308 118171.4826 508778.6987 -30427413.0208 119726.2507 505334.5413 24802020.2237 -76.7317 -55.5379 8.1954 -0.0000 -0.0000 -0.0000 0.1353 -0.7708 752.821 866.417 16351.7091 -1200.3811 5625345.5067 118113.2127 508809.1022 -30427411.7785 134394.5728 507546.6080 24802074.6766 -75.7298 -59.6244 8.2067 34.6861 -78.3648 -21.8394 0.5086 -0.6341 768.403 893.501 18605.6815 -2900.6683 5625392.0568 118132.3103 508822.3467 -30427413.0050 136655.0997 505868.3342 24802027.7594 -75.0672 -62.9989 7.8065 -24.5033 -137.5542 37.3500 -4.5196 752.075 894.294 16212.3318 -2954.3124 5625392.7593 118128.9652 508827.1751 -30427412.9061 134268.5952 505819.5625 24802027.7912 -73.1829 -57.1331 8.0850 144.2045 -518.7088 -68.8734 0.0250 57 173509
22.09 5.262 26.581 32.9 5.6658 0.1180 0.5170 24.7616 0.5064 0.5064 0.118 24.762 5.666 1.002e-05 3146.0 634.008 924.726 78.0122 -4996.8948 5664672.4363 118155.5807 507932.8391 -30427407.0523 118156.0363 502887.4793 24762741.9683 -81.5736 -52.4288 7.6538 -0.0000 -0.0000 -0.0000 0.1373 -1.0405 752.753 886.666 16911.1568 -2637.9321 5664643.7807 118146.8810 507952.3129 -30427407.1380 134975.3429 505252.2098 24762771.0784 -82.4641 -56.6925 7.9788 46.8261 -105.7922 -29.4831 0.5085 -0.6647 769.601 893.515 19156.4765 -3050.9355 5664664.5813 118153.7674 507952.4800 -30427406.8217 137222.0928 504836.8955 24762750.1935 -82.7944 -55.2637 7.7280 -15.2201 -167.8385 32.5631 -4.7569 751.880 894.269 16767.1766 -3105.9065 5664663.8473 118149.3770 507967.1574 -30427407.2409 134835.8059 504804.0379 24762751.3478 -81.2584 -58.1363 7.6463 152.0228 -545.6836 -72.7380 0.0250 71 173723
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32.00 3.734 21.406 35.0 6.1907 0.1180 0.5170 24.2367 0.4988 0.4988 0.118 24.237 6.191 8.188e-06 3447.4 555.898 896.515 -445.6390 -4336.9013 6189403.0098 117955.9818 500573.8454 -30427328.0232 117418.5429 496319.3623 24237909.2600 -93.2262 85.9123 -15.7031 -0.0000 -0.0000 -0.0000 0.1409 -0.7847 752.577 848.165 19261.6130 -1349.1507 6189439.1913 118000.4148 500504.5725 -30427328.2082 137173.7259 499239.1831 24237872.7516 -94.4389 89.2086 -15.6943 35.3113 -79.7773 -22.2330 0.4990 -0.5635 778.345 893.510 21703.8248 -4199.3337 6189457.4197 118013.4538 500522.7271 -30427328.4850 139616.8960 496413.2741 24237855.3313 -96.9316 84.0616 -15.7100 -17.2859 -132.3745 30.3642 -4.8522 751.689 894.349 19111.9537 -4249.1102 6189457.5281 118004.3914 500522.6596 -30427328.6593 137022.3829 496354.3831 24237855.3601 -95.9538 82.3936 -15.2493 165.7625 -545.9284 -84.8886 0.0250 603 200327
31.00 3.842 21.764 34.9 6.1248 0.1180 0.5170 24.3026 0.4994 0.4994 0.118 24.303 6.125 8.694e-06 3446.4 549.365 908.848 -1887.6138 -5065.7438 6123436.1801 117983.1519 501390.8978 -30427343.2208 116003.6949 496407.8889 24303893.0321 -93.0555 75.7235 -14.2164 -0.0000 -0.0000 -0.0000 0.1414 -1.3035 752.963 855.866 19155.1864 -1787.2698 6123436.4797 117957.2319 501335.9965 -30427341.6250 137021.1925 499625.5968 24303891.5693 -93.2021 71.6928 -14.1790 58.6604 -132.5291 -36.9344 0.5004 -0.7845 777.625 893.533 21574.6911 -4121.0123 6123427.4283 117959.2543 501311.1111 -30427341.9474 139441.1221 497266.2350 24303900.0326 -95.1316 78.4748 -14.2164 -14.5640 -205.7535 36.2900 -5.2730 751.680 894.536 19016.3387 -4174.9639 6123427.7141 117961.1615 501316.0711 -30427342.4387 136872.0597 497207.7115 24303900.9705 -96.6566 72.3483 -14.6278 164.0724 -609.3394 -76.1847 0.0250 617 200551
30.00 3.957 22.141 34.7 6.0622 0.1180 0.5170 24.3652 0.5004 0.5004 0.118 24.365 6.062 9.311e-06 3043.8 543.837 907.619 -3121.1813 -4821.6617 6060511.7444 117893.7268 502130.3325 -30427357.1123 114675.7973 497394.6062 24366831.3779 -93.1107 69.8213 -13.6404 -0.0000 -0.0000 -0.0000 0.1438 -0.4579 753.115 869.415 19054.9317 -2493.3083 6060653.5260 117880.1887 502082.1085 -30427355.2088 136842.1888 499653.8647 24366688.3554 -92.3196 65.6350 -13.3722 20.6082 -46.5593 -12.9755 0.5023 -0.9586 779.706 893.298 21790.3090 -3994.4320 6060667.7268 117877.9956 502071.1787 -30427355.3724 139586.2059 498137.3353 24366674.2107 -89.8440 66.0285 -13.0228 -68.8692 -136.0367 76.5019 -4.9804 751.567 894.586 18913.1519 -4065.2591 6060669.3339 117867.8666 502082.7982 -30427356.0058 136700.8811 498080.1742 24366673.8536 -90.1220 68.3769 -12.8633 134.6536 -595.8476 -51.6421 0.0125 631 200813
29.00 4.081 22.540 34.5 6.0026 0.1180 0.5170 24.4248 0.5015 0.5015 0.118 24.425 6.003 9.983e-06 3451.2 548.230 918.461 -3644.4772 -5399.3063 6000870.5409 117911.3610 502900.6685 -30427365.8059 114163.8315 497561.5785 24426483.3409 -87.2799 63.6409 -12.3589 -0.0000 -0.0000 -0.0000 0.1437 -0.2970 752.665 875.245 18806.8885 -2755.2989 6001011.7326 117897.9423 502868.5796 -30427365.9223 136618.3680 500170.6135 24426341.5648 -90.6360 65.3272 -12.4551 13.3647 -30.1942 -8.4148 0.5040 -0.9383 775.628 893.557 21217.5462 -3881.5695 6000951.9555 117898.3604 502850.6205 -30427365.7814 139022.3019 499030.2688 24426400.8040 -93.9400 61.2305 -12.6955 -74.2105 -117.7694 79.1604 -4.2615 752.136 894.464 18707.0729 -3940.9909 6000952.7065 117901.4538 502854.6205 -30427365.4654 136518.7413 498985.2183 24426399.9863 -93.5976 64.1287 -12.8083 104.2020 -520.8496 -33.1734 0.0250 645 201034
28.00 4.214 22.985 34.4 5.9460 0.1180 0.5170 24.4814 0.5033 0.5033 0.118 24.481 5.946 1.045e-05 3425.2 562.140 912.953 -3009.1077 -5006.7404 5944291.9027 117970.0106 503739.7867 -30427376.3866 114871.4197 498789.4057 24483072.2095 -89.7526 57.9254 -12.0353 -0.0000 -0.0000 -0.0000 0.1422 -0.8049 752.833 863.865 18581.5734 -1982.6658 5944331.5060 117957.4538 503693.0951 -30427375.6377 136444.5824 501773.1131 24483032.0979 -86.9597 62.8372 -11.8507 36.2230 -81.8371 -22.8071 0.5045 -0.5363 776.331 893.609 21157.7592 -3829.3655 5944339.1364 117960.4106 503682.7271 -30427374.8884 139031.1168 499912.0645 24483024.3517 -87.4737 61.1867 -11.6939 -13.8377 -131.8979 27.2537 -5.0261 751.610 894.408 18462.0936 -3880.0241 5944339.3009 117964.1354 503684.3129 -30427375.4587 136341.9563 499857.7614 24483024.6892 -86.1816 57.2692 -11.5180 176.1234 -561.0693 -92.3515 0.0250 659 201259
27.00 4.358 23.473 34.2 5.8922 0.1180 0.5170 24.5352 0.5043 0.5044 0.118 24.535 5.892 1.070e-05 3455.4 563.386 910.532 -3818.3008 -4778.3837 5890355.3182 118021.4836 504562.2294 -30427384.9859 114124.3520 499849.2768 24537018.1276 -83.0645 54.8136 -11.0551 -0.0000 -0.0000 -0.0000 0.1436 -0.6264 752.770 868.322 18318.7326 -2190.3862 5890470.8324 118029.5775 504519.4880 -30427384.1431 136265.2117 502381.9451 24536903.3636 -86.7910 51.9404 -10.5135 28.1872 -63.6822 -17.7475 0.5061 -0.5292 775.551 893.455 20887.9186 -3737.5518 5890434.2173 118029.5647 504510.8942 -30427384.6569 138839.4197 500811.3394 24536939.2010 -85.6586 44.4072 -11.2095 -21.2077 -113.0770 31.6474 -4.9015 752.015 894.352 18173.8839 -3789.3311 5890434.4560 118031.3311 504511.3814 -30427385.1870 136122.6667 500770.2277 24536939.8518 -88.3812 46.7732 -10.9556 171.1827 -547.7367 -89.4873 0.0250 673 201521
26.00 4.513 23.980 34.0 5.8412 0.1180 0.5170 24.5862 0.5047 0.5047 0.118 24.586 5.841 1.113e-05 3438.2 577.196 915.244 -3239.1632 -4996.0924 5839433.2566 118035.5039 505374.4249 -30427393.4402 114711.4027 500431.4830 24587950.1000 -79.5839 45.6131 -10.2086 -0.0000 -0.0000 -0.0000 0.1427 -0.5909 752.730 863.002 18059.7223 -1754.8012 5839502.1987 118051.4143 505326.4427 -30427393.8489 136028.2240 503610.9207 24587881.9551 -83.7030 40.9950 -9.7341 26.5916 -60.0774 -16.7429 0.5058 -0.7881 773.826 893.610 20509.2688 -3649.1713 5839507.2505 118052.8223 505309.8667 -30427394.0556 138474.5131 501705.5493 24587877.5157 -85.2781 38.3131 -9.7169 -46.9725 -133.6415 56.8212 -4.6522 751.841 894.498 17945.1298 -3712.3007 5839508.7332 118045.2660 505323.8258 -30427394.3735 135889.2672 501651.1182 24587876.4580 -84.9900 40.5012 -9.5230 135.7968 -546.5647 -58.2557 0.0250 687 201744
25.00 4.682 24.534 33.9 5.7927 0.1180 0.5170 24.6347 0.5048 0.5048 0.118 24.635 5.793 1.132e-05 3439.6 585.074 912.322 -3303.5439 -4697.1312 5791031.8357 118032.5727 506161.6498 -30427400.2536 114646.5323 501501.8299 24636359.8209 -80.3238 37.3598 -8.9552 -0.0000 -0.0000 -0.0000 0.1419 -0.2699 752.826 873.409 17791.6571 -2288.7575 5791088.2285 118042.5780 506106.4676 -30427399.9290 135748.1984 503862.6254 24636302.9940 -80.5737 38.5637 -8.7776 12.1454 -27.4397 -7.6471 0.5066 -0.6597 773.937 893.417 20406.9597 -3537.6503 5791102.0630 118038.3583 506099.0542 -30427400.0868 138365.8581 502604.3927 24636289.1555 -81.1851 40.6616 -8.7850 -49.4275 -89.0126 53.9259 -4.5627 752.353 894.272 17681.4450 -3586.1096 5791102.5412 118042.3178 506102.0765 -30427400.3440 135649.6853 502550.4974 24636288.6912 -76.9928 39.1309 -9.0010 143.7566 -525.4657 -67.7086 0.0250 701 202009
24.00 4.864 25.160 33.7 5.7468 0.1180 0.5170 24.6806 0.5067 0.5067 0.118 24.681 5.747 1.102e-05 3371.8 604.513 897.109 -1875.7137 -3660.0616 5745324.5400 118042.5780 506964.6969 -30427407.7523 116084.2155 503347.0597 24682075.4186 -74.4880 38.1770 -8.5527 -0.0000 -0.0000 -0.0000 0.1404 -0.3357 752.604 857.658 17529.8500 -1208.1651 5745333.4918 118052.4084 506917.3689 -30427408.3360 135494.7797 505741.0089 24682067.0685 -76.3201 35.5833 -8.4482 15.1070 -34.1307 -9.5118 0.5075 -0.5621 775.076 893.506 20329.8344 -3432.6363 5745378.3676 118061.6244 506900.6934 -30427408.8235 138325.7429 503499.8240 24682022.2064 -71.1630 34.8544 -8.0889 -37.3613 -86.5990 42.9565 -4.9484 752.105 894.345 17402.7712 -3491.0166 5745379.0398 118053.7055 506914.0231 -30427409.5964 135392.8320 503456.7282 24682022.2033 -74.5683 34.3148 -7.9098 170.2213 -555.5817 -87.7436 0.0250 715 202232
23.00 5.064 25.869 33.5 5.7034 0.1180 0.5170 24.7240 0.5084 0.5084 0.118 24.724 5.703 1.049e-05 3268.2 613.001 911.138 -1906.0942 -4434.4120 5701757.5347 118110.3498 507789.6818 -30427416.1699 116120.4395 503388.0069 24725651.7285 -78.0619 28.9011 -7.3900 -0.0000 -0.0000 -0.0000 0.1400 -0.2910 752.617 875.063 17125.3080 -2178.9262 5701808.3757 118132.4084 507730.5885 -30427415.9330 135173.5893 505581.1296 24725599.7516 -76.9687 27.0154 -7.2842 13.0972 -29.5901 -8.2464 0.5106 -0.9635 771.478 893.567 19583.5599 -3326.9900 5701812.5675 118138.4714 507722.7805 -30427416.0203 137640.4907 504433.3189 24725596.1627 -73.5985 28.9199 -7.2484 -76.8368 -119.5241 81.6876 -4.3365 752.143 894.435 17008.5505 -3377.4371 5701813.8643 118141.5434 507721.9378 -30427416.7257 135088.8491 504377.7833 24725595.3828 -72.0464 29.6084 -7.0949 105.2190 -530.8353 -32.9401 0.0250 729 202458
22.00 5.282 26.654 33.4 5.6623 0.1180 0.5170 24.7651 0.5081 0.5081 0.118 24.765 5.662 1.066e-05 3154.0 633.947 900.842 -5.0574 -3839.3999 5660978.9015 118103.8431 508570.8836 -30427421.2976 118021.9392 504750.9765 24766435.6859 -70.1259 26.5775 -6.6215 -0.0000 -0.0000 -0.0000 0.1386 0.1885 752.687 867.085 16914.0809 -1749.5048 5660981.2319 118099.2991 508539.8045 -30427420.2264 134941.6363 506809.0683 24766432.2760 -68.8590 19.5907 -6.7220 -8.4835 19.1665 5.3415 0.5096 -1.0321 771.096 893.597 19415.4126 -3407.9436 5661002.8402 118110.0383 508540.5120 -30427421.1838 137456.0384 505153.4322 24766411.3082 -70.7855 22.1406 -6.1755 -104.8160 -77.1659 101.6740 -3.9750 752.188 894.455 16777.6564 -3451.9793 5661003.3745 118117.6543 508542.5636 -30427420.8754 134826.4576 505109.4277 24766411.3839 -70.1099 18.0527 -6.3923 82.5507 -500.4760 -16.2977 0.0250 743 202719
21.00 5.521 27.544 33.2 5.6235 0.1180 0.5170 24.8039 0.5080 0.5080 0.118 24.804 5.624 1.156e-05 3241.0 651.499 904.707 1228.6080 -3896.3146 5622556.7360 118148.1012 509464.5014 -30427423.1430 119307.3536 505577.0098 24804861.7071 -65.7579 17.0125 -5.6153 -0.0000 -0.0000 -0.0000 0.1359 -0.5399 752.474 870.118 16224.3961 -1677.2121 5622564.1421 118226.5908 509353.8098 -30427424.5857 134382.8608 507698.5184 24804855.6612 -68.6090 17.8169 -5.5469 24.2980 -54.8955 -15.2987 0.5095 -0.8479 769.320 893.572 18670.0922 -3149.1603 5622617.6991 118208.3124 509356.1458 -30427424.1985 136807.2405 506222.4608 24804801.3387 -70.7775 15.5466 -5.3888 -54.8390 -134.0325 63.8382 -4.4430 752.123 894.337 16200.1002 -3213.7626 5622618.5479 118198.1151 509370.4782 -30427424.2682 134338.3893 506166.0603 24804800.3551 -68.2255 15.8821 -5.1930 120.8102 -530.8695 -46.7557 0.0250 757 202944
20.00 5.785 28.556 33.1 5.5869 0.1180 0.5170 24.8405 0.5082 0.5081 0.118 24.840 5.587 1.301e-05 3265.0 665.753 896.569 2092.4510 -3270.9379 5586361.3386 118339.8196 510240.4978 -30427428.5496 120354.6539 506971.9538 24841062.3524 -66.3361 15.9515 -4.6636 -0.0000 -0.0000 -0.0000 0.1348 -0.5949 752.613 856.589 15801.6386 -835.6408 5586331.7081 118259.6490 510264.3840 -30427426.7424 133992.7125 509435.1547 24841091.1188 -66.4094 13.0237 -4.8761 26.7730 -60.4871 -16.8571 0.5088 -0.5708 770.773 893.426 18460.9658 -3132.7183 5586365.1683 118294.5332 510254.9085 -30427427.2162 136690.9611 507134.0366 24841057.7384 -66.9997 14.3751 -4.6212 -26.5080 -113.7681 36.4239 -5.0111 751.972 894.309 15620.5792 -3169.7594 5586364.3881 118310.2858 510245.1485 -30427428.4325 133862.6133 507091.1273 24841058.9711 -68.9072 9.7199 -4.6028 172.2315 -562.7722 -88.7084 0.0250 771 203207
19.00 6.077 29.806 32.9 5.5525 0.1180 0.5170 24.8749 0.5074 0.5074 0.118 24.875 5.553 1.320e-05 3218.0 671.548 914.796 1763.0641 -4290.6467 5551902.5957 118399.8260 511080.3342 -30427433.8558 120091.8485 506803.0432 24875526.9398 -65.0983 9.7172 -4.2039 -0.0000 -0.0000 -0.0000 0.1347 -0.6019 752.602 877.510 15121.7730 -2029.5533 5551898.7838 118311.2415 511110.2187 -30427432.0078 133370.8032 509085.1534 24875529.1186 -64.2600 10.7311 -3.8978 27.0889 -61.2008 -17.0559 0.5093 -0.6029 768.517 893.550 17596.4263 -2989.5559 5551934.1802 118354.3775 511070.8765 -30427432.7317 135880.9216 508081.5913 24875494.2513 -65.8502 7.3425 -3.7354 -29.1822 -117.4718 39.2151 -4.7266 752.296 894.303 14962.5765 -3039.2142 5551933.6992 118342.6826 511073.6640 -30427432.9010 133243.5925 508044.6688 24875495.6445 -63.3655 10.3148 -3.8854 156.4375 -536.8349 -77.6565 0.0250 785 203431
18.00 6.403 31.350 32.8 5.5202 0.1180 0.5170 24.9072 0.5094 0.5094 0.118 24.907 5.520 1.290e-05 3105.2 682.656 908.714 2178.6430 -3789.1566 5519885.8250 118480.2570 511888.1778 -30427435.7913 120594.0651 508109.5959 24907546.3721 -61.1810 5.8031 -3.3645 -0.0000 -0.0000 -0.0000 0.1327 -0.9510 752.765 862.355 14358.1459 -968.0686 5519880.2721 118398.6698 511923.5449 -30427434.3418 132707.0976 510965.7239 24907551.6428 -62.0644 7.2650 -2.8861 42.7969 -96.6894 -26.9462 0.5103 -0.8630 766.473 893.489 16583.1587 -2872.0409 5519895.6814 118439.2970 511890.6276 -30427434.4249 134963.2939 509021.9726 24907535.1952 -65.8231 -0.7680 -2.9502 -37.7517 -177.2380 53.6024 -4.7621 752.150 894.502 14159.0446 -2925.6579 5519897.2039 118444.5834 511880.5689 -30427434.1185 132537.8048 508958.7205 24907534.8436 -67.0158 1.7799 -2.6954 133.7588 -564.7247 -54.3857 0.0250 799 203657
17.00 6.767 33.386 32.6 5.4899 0.1180 0.5170 24.9375 0.5101 0.5101 0.118 24.938 5.490 1.104e-05 3286.2 692.023 906.597 2366.4201 -3577.3492 5489709.4253 118440.6580 512800.9636 -30427437.7661 120745.8731 509219.7125 24937726.0370 -60.9149 0.1125 -2.4401 -0.0000 -0.0000 -0.0000 0.1320 -0.9304 752.483 861.648 13361.3487 -696.0657 5489689.3672 118536.8415 512685.1485 -30427437.9263 131849.2800 511990.4846 24937746.1012 -60.1891 -1.8991 -2.2415 41.8699 -94.5949 -26.3625 0.5106 -0.5575 766.289 893.550 15682.9006 -2714.0755 5489738.5430 118525.2319 512704.3947 -30427437.8298 134150.9291 509988.4439 24937696.9731 -60.4843 -0.0768 -1.8673 -10.1635 -146.6282 25.6708 -4.7998 751.996 894.362 13224.5629 -2767.4609 5489738.1213 118522.0020 512709.0596 -30427437.6595 131680.3371 509937.2311 24937696.8442 -57.6050 -2.2656 -2.3014 163.9668 -540.0336 -83.9667 0.0500 813 203920
16.00 7.178 36.369 32.5 5.4616 0.1180 0.5170 24.9658 0.5101 0.5101 0.118 24.966 5.462 8.806e-06 3092.2 696.133 910.392 1423.0462 -3714.3573 5461393.1775 118573.1167 513681.7387 -30427438.3205 119937.6171 509971.3851 24966043.9361 -53.3695 1.5872 -1.7183 -0.0000 -0.0000 -0.0000 0.1324 -0.6456 752.313 871.025 12310.4221 -1158.9633 5461380.2363 118650.2580 513544.8249 -30427439.9644 130893.3077 512392.2235 24966056.5492 -53.0482 -0.0189 -1.8196 29.0536 -65.6395 -18.2930 0.5118 -0.9902 765.310 893.554 14687.8913 -2548.6115 5461380.7405 118664.0138 513533.5538 -30427438.6035 133288.6912 510984.8690 24966056.5649 -56.8922 -3.3974 -1.5014 -63.3736 -158.0667 74.1342 -4.5774 752.344 894.370 12207.3520 -2614.7572 5461381.4851 118646.5930 513549.8347 -30427438.6938 130797.5637 510922.9335 24966055.8062 -57.1523 -4.1546 -1.4036 113.5664 -557.8201 -37.2725 0.0500 827 204148
15.00 7.645 17.258 32.3 5.4352 0.1180 0.5170 24.9922 0.5115 0.5115 0.118 24.992 5.435 1.137e-05 3102.4 700.771 906.875 233.0220 -3170.5120 5435092.1483 118748.8607 514433.7494 -30427441.1859 118923.2384 511270.8357 24992348.1972 -57.4193 -5.2433 -0.6559 -0.0000 -0.0000 -0.0000 0.1306 -0.9443 752.461 856.410 11078.2206 -103.1162 5435068.1544 118651.0388 514475.1431 -30427438.9506 129678.7883 514361.8875 24992369.5454 -53.4920 -2.0763 -1.0665 42.4952 -96.0077 -26.7562 0.5121 -0.8337 765.948 893.488 13601.6519 -2359.8965 5435116.4259 118726.6442 514420.0000 -30427440.1057 132278.9504 512056.8837 24992322.4474 -51.8636 -11.1340 -1.0703 -35.3231 -173.8260 51.0621 -5.2243 752.375 894.506 10847.8521 -2426.7478 5435117.5635 118744.1162 514426.4462 -30427440.4716 129534.6731 511990.3675 24992322.0598 -55.0631 -10.3175 -0.7092 157.2860 -608.9799 -70.2103 0.0250 841 204416
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11.00 10.369 20.520 31.7 5.3483 0.1180 0.5170 25.0791 0.5168 0.5168 0.118 25.079 5.348 6.733e-06 2784.0 737.757 893.594 -568.5636 -1660.9363 5348172.1088 119161.5540 518066.6489 -30427450.5939 118554.6923 516387.0267 25079280.6282 -45.5871 -18.5600 1.7805 -0.0000 -0.0000 -0.0000 0.1254 -0.5178 752.471 852.563 3608.5988 892.2012 5348174.9791 119168.6623 518033.8098 -30427450.4435 122738.3851 518906.2734 25079276.8073 -46.7978 -18.5189 1.9521 23.3036 -52.6489 -14.6726 0.5170 -0.4448 761.938 893.512 6000.9346 -1658.8501 5348215.4606 119220.5578 518043.7120 -30427450.8376 125161.2843 516350.8997 25079237.5665 -45.7447 -20.1236 2.0731 -18.2115 -94.1639 26.8424 -4.5755 752.388 894.175 3433.5345 -1688.7346 5348216.1014 119211.6404 518032.5867 -30427450.9965 122596.3136 516317.2009 25079237.1386 -46.6241 -26.5984 1.7225 164.3919 -506.7122 -88.1300 0.0500 897 205408
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10.00 11.394 21.663 31.8 5.3310 0.1227 0.5194 25.0964 0.5168 0.5168 0.123 25.096 5.331 3.768e-06 1722.0 762.632 929.152 3413.4907 -3671.4085 5330897.3522 119411.5295 518947.5342 -30427451.6947 122779.3152 515249.3847 25096557.6227 -48.9924 -33.0658 3.5943 -0.0000 -0.0000 -0.0000 0.1226 -0.7066 752.353 887.931 605.9006 -1093.7926 5330904.7671 119401.5498 518919.2498 -30427450.1997 119959.8592 517793.7467 25096547.9197 -49.1249 -33.9463 3.2909 31.8006 -71.8459 -20.0226 0.5193 -0.6555 760.840 893.460 3085.2042 -1424.5972 5330915.6388 119397.8207 518899.5129 -30427449.9017 122432.3797 517439.2361 25096537.4339 -50.2694 -33.8836 3.7625 -29.3857 -133.0323 41.1637 -4.8034 752.024 894.254 457.2798 -1485.0133 5330916.1871 119400.7050 518906.9156 -30427450.4412 119813.7941 517397.2247 25096538.0858 -50.3657 -30.8520 4.2173 154.9778 -549.5573 -74.9170 0.4000 925 210005
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12.00 9.516 19.541 34.9 5.3673 0.1227 0.5194 25.0601 0.5147 0.5147 0.123 25.060 5.367 9.133e-06 3233.2 742.550 894.272 3306.2682 -1890.9837 5367314.6429 119177.4132 516992.2702 -30427446.0210 122432.1408 515062.2304 25060134.6036 -51.9851 -36.5898 4.1056 -0.0000 -0.0000 -0.0000 0.1279 -0.0666 752.356 856.222 5866.7720 461.2495 5367303.5221 119169.9594 516997.7138 -30427445.7083 124989.3035 517426.6939 25060146.2893 -50.4531 -33.8836 4.3505 2.9952 -6.7669 -1.8859 0.5151 -0.4740 762.783 893.590 8303.5962 -1842.0459 5367322.5671 119159.2586 516971.4667 -30427445.6846 127407.7440 515102.4078 25060128.2851 -53.7640 -34.8106 4.7277 -41.2427 -51.0048 42.3520 -4.2357 752.058 894.181 5663.5692 -1890.5436 5367321.8960 119176.2612 516976.5760 -30427446.2116 124790.6091 515067.1401 25060128.4518 -50.8175 -32.0909 4.5667 146.3772 -474.8868 -75.7790 0.0500 29 210551
13.00 8.795 18.691 34.7 5.3881 0.1227 0.5194 25.0393 0.5132 0.5132 0.123 25.039 5.388 1.167e-05 3439.0 742.576 900.849 4723.0595 -2343.4835 5388156.9726 119073.3407 516011.6694 -30427441.9846 123740.7659 513634.4416 25039290.3309 -53.7028 -36.8492 4.8900 -0.0000 -0.0000 -0.0000 0.1288 -0.4922 752.945 863.580 7720.9448 -115.4221 5388124.4930 119060.1268 516004.7360 -30427441.1049 126725.0944 515858.5751 25039321.1889 -53.2932 -40.0835 4.8329 22.1500 -50.0426 -13.9463 0.5140 -0.4935 763.925 893.546 10220.7267 -2003.5767 5388181.9688 119087.7791 516011.9609 -30427440.8204 129252.8939 513952.6624 25039264.0324 -56.8420 -38.8312 4.9971 -23.9126 -96.1051 32.1163 -4.6644 752.296 894.205 7574.0821 -2057.3695 5388181.9231 119082.1514 516021.7920 -30427441.5303 126599.5392 513929.3134 25039264.5572 -54.3674 -39.7683 5.1829 163.8477 -520.3043 -86.1032 0.0500 43 210815
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17.00 6.767 33.380 34.0 5.4899 0.1227 0.5194 24.9375 0.5094 0.5094 0.123 24.938 5.490 1.138e-05 3239.2 717.843 904.708 6663.6204 -3330.2351 5489803.5044 118577.4772 512368.7574 -30427430.7534 125181.5637 508993.2658 24937631.8791 -66.4947 -43.8616 5.5401 -0.0000 -0.0000 -0.0000 0.1317 -1.0608 752.592 869.272 12934.9799 -1083.4507 5489758.1731 118627.0346 512329.9734 -30427431.2174 131493.4443 511212.3835 24937678.7523 -65.1224 -36.3796 5.3987 47.7392 -107.8552 -30.0580 0.5102 -0.6348 764.518 893.516 15050.5349 -2619.3758 5489810.5454 118583.8431 512358.5600 -30427430.3319 133565.3547 509700.3397 24937626.0148 -68.0478 -43.4877 5.5228 -11.5123 -167.1066 29.1934 -4.4785 752.222 894.226 12881.5364 -2680.4886 5489811.2479 118576.7775 512377.7814 -30427431.8672 131395.9680 509660.8937 24937625.7805 -65.9466 -40.3530 5.5364 142.2901 -514.5860 -67.6451 0.0500 99 211803
18.00 6.403 31.348 33.9 5.5202 0.1227 0.5194 24.9072 0.5086 0.5086 0.123 24.907 5.520 1.312e-05 3133.6 711.322 911.349 6739.2457 -3784.5847 5519958.2228 118585.4218 511411.0045 -30427429.7270 125255.2235 507578.3611 24907476.2342 -69.5487 -40.5410 5.0860 -0.0000 -0.0000 -0.0000 0.1321 -0.8517 752.805 873.795 13928.7159 -1504.2747 5519920.7992 118494.3711 511478.4356 -30427428.6997 132350.7541 509937.2000 24907512.8437 -68.6692 -40.1940 4.8847 38.3273 -86.5913 -24.1320 0.5098 -0.8643 765.207 893.500 16013.1359 -2721.6051 5519964.7860 118525.3471 511469.8596 -30427429.3501 134474.1248 508714.5623 24907469.6785 -68.5287 -38.4856 5.0220 -42.3430 -167.2615 56.5382 -4.3618 752.443 894.345 13772.8069 -2763.9438 5519966.4212 118548.6132 511464.1671 -30427429.8497 132245.9563 508654.9033 24907468.6838 -68.1843 -38.6250 5.2095 115.6208 -524.1424 -42.9204 0.0250 113 212032
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21.00 5.521 27.538 33.4 5.6235 0.1227 0.5194 24.8039 0.5071 0.5071 0.123 24.804 5.624 1.148e-05 3220.6 686.199 909.755 6299.4014 -3980.4289 5622644.7715 118245.0740 508865.1236 -30427418.4019 124470.5536 504851.6137 24804779.7349 -81.0386 -38.1514 4.6723 -0.0000 -0.0000 -0.0000 0.1355 -0.6403 752.741 883.137 16158.9286 -2294.4416 5622620.9869 118277.9615 508842.6560 -30427419.3184 134364.6720 506511.3787 24804802.9837 -82.2222 -44.8829 4.9615 28.8157 -65.1022 -18.1432 0.5091 -1.0159 767.044 893.527 18231.8585 -2966.8151 5622690.5829 118267.7514 508867.8471 -30427420.2647 136420.5525 505862.7918 24804734.4536 -81.9612 -39.5614 5.1780 -66.0036 -159.9216 76.6761 -3.9699 752.118 894.327 16143.7504 -3023.4390 5622691.4819 118245.3130 508886.2187 -30427420.5630 134320.3285 505815.8670 24804733.9077 -80.7876 -35.9741 5.0481 83.8339 -498.4433 -17.6660 0.0250 155 212746
22.00 5.282 26.655 33.2 5.6623 0.1227 0.5194 24.7651 0.5074 0.5073 0.123 24.765 5.662 1.028e-05 3261.8 664.391 902.827 4302.7925 -3784.9390 5661065.5351 118289.8783 508030.0267 -30427416.9625 122507.8784 504209.8674 24766355.9564 -85.6195 -37.5774 4.3837 -0.0000 -0.0000 -0.0000 0.1387 -0.3516 752.453 876.564 16867.0911 -2180.3768 5661055.8713 118268.7156 508056.7005 -30427418.7031 135037.0603 505840.1595 24766366.8449 -88.2829 -34.3714 4.5850 15.8218 -35.7455 -9.9619 0.5091 -1.0322 770.184 893.537 19260.3746 -3224.9027 5661102.1498 118256.3594 508050.7947 -30427418.4439 137428.3008 504795.0871 24766320.8694 -87.3231 -35.6898 4.7809 -80.5241 -132.0914 86.3840 -4.2696 752.385 894.499 16777.3415 -3276.3845 5661104.1617 118260.0842 508056.1209 -30427419.2041 134946.5643 504755.6466 24766319.7183 -87.5871 -36.4712 4.4394 95.7941 -530.4400 -24.6312 0.0250 169 213011
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26.00 4.513 23.981 32.6 5.8412 0.1227 0.5194 24.5862 0.5031 0.5031 0.123 24.586 5.841 1.040e-05 3349.0 611.985 910.972 987.5926 -4518.3105 5839688.7435 118146.4884 504738.4249 -30427385.7939 119042.1589 500181.7915 24587700.4389 -101.6009 -27.6359 3.3656 -0.0000 -0.0000 -0.0000 0.1425 -0.7981 752.631 873.975 18089.5057 -2244.4777 5839718.1632 118133.1167 504764.9422 -30427386.8249 136119.1979 502492.7529 24587672.2310 -103.5174 -29.0297 3.3262 35.9182 -81.1484 -22.6151 0.5045 -0.9503 770.838 893.536 20186.6297 -3467.0375 5839730.2963 118135.6767 504772.3342 -30427386.2891 138214.6389 501290.7799 24587659.1500 -101.5165 -25.1917 3.3587 -52.7825 -169.8491 66.0855 -4.3203 752.186 894.367 17955.0461 -3516.1940 5839731.2309 118130.6164 504786.4782 -30427386.5397 135996.4459 501239.8359 24587657.9531 -103.5645 -32.0310 3.3177 105.7234 -527.9550 -33.7145 0.0250 225 213941
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58.50 2.320 16.352 34.2 10.0479 0.1190 0.5194 20.3795 0.4952 0.4952 0.119 20.380 10.048 2.053e-06 3032.0 436.648 947.068 -3551.2186 -9371.8110 10044572.3884 120550.7978 482227.8614 -30426794.9040 116944.8448 473254.5211 20382164.6452 -59.2203 391.1330 -58.4143 -0.0000 -0.0000 -0.0000 0.1411 -1.3412 752.886 896.463 16140.7271 -6266.8348 10044577.1418 120552.8074 482179.4631 -30426794.5799 136630.2976 476300.4677 20382159.4288 -54.2178 391.8585 -57.9820 60.3564 -136.3608 -38.0022 0.4986 -0.6067 786.757 893.571 18236.7033 -6097.2781 10044537.5876 120537.1530 482181.3974 -30426795.0636 138712.7637 476483.2443 20382198.6653 -58.0096 392.3981 -58.4152 3.7305 -192.9867 18.6237 -4.7362 751.654 894.285 16074.0408 -6140.8892 10044538.8340 120531.5978 482184.9316 -30426795.2019 136552.9856 476435.7435 20382197.7875 -58.9724 393.6707 -58.3789 156.5120 -538.1596 -77.5720 0.0500 225 001637
57.50 2.346 16.455 34.0 9.7711 0.1190 0.5194 20.6563 0.4967 0.4967 0.119 20.656 9.771 2.065e-06 3040.6 449.674 912.454 -2621.6000 -7151.8828 9767622.8728 120392.2399 482801.7565 -30426815.7266 117725.1584 476041.3079 20659134.4129 -56.4324 383.7474 -57.5175 -0.0000 -0.0000 -0.0000 0.1415 -0.8207 752.874 868.604 16471.0442 -4496.1777 9767718.8267 120397.5178 482757.5574 -30426814.7410 136814.9120 478651.6064 20659038.1733 -56.0590 386.5896 -57.3401 36.9354 -83.4466 -23.2556 0.4983 -0.5439 796.228 893.569 19090.2405 -6032.0995 9767713.1913 120392.1546 482730.8196 -30426814.1538 139429.3077 477080.7173 20659043.4682 -54.5702 383.4732 -57.3864 -13.8276 -134.2095 27.5074 -5.1334 751.450 894.538 16342.3641 -6078.6225 9767714.6644 120387.8324 482732.2845 -30426814.2937 136687.5776 477040.8306 20659042.5091 -54.5481 384.1752 -57.0952 180.2525 -572.6868 -94.6912 0.0500 239 001859
56.50 2.373 16.566 33.9 9.5120 0.1190 0.5194 20.9154 0.4948 0.4948 0.119 20.915 9.512 2.146e-06 3072.2 544.340 919.304 3399.8180 -7633.6971 9509360.0614 120286.2858 483479.9609 -30426837.4649 123642.8629 476209.7906 20917421.7746 -50.3637 374.5893 -56.1959 -0.0000 -0.0000 -0.0000 0.1347 -1.0531 752.661 868.797 16696.2651 -4530.5640 9509421.9924 120312.4831 483415.0151 -30426837.4442 136942.9632 479233.2750 20917360.2447 -52.1316 376.2722 -56.4945 47.3902 -107.0668 -29.8383 0.4964 -0.5450 794.049 893.576 19187.4448 -6069.8157 9509444.7573 120306.0660 483409.0738 -30426837.1559 139433.7877 477717.1351 20917336.3286 -49.4080 375.7979 -56.0642 -3.4773 -157.9344 21.0293 -5.1746 751.512 894.530 16568.7324 -6130.0479 9509445.6828 120294.4308 483418.3040 -30426838.4090 136810.8459 477654.7314 20917335.8100 -52.7079 375.9892 -56.4812 182.0018 -576.9799 -95.7539 0.0500 253 002123
55.50 2.401 16.681 33.7 9.2690 0.1190 0.5194 21.1584 0.4951 0.4951 0.119 21.158 9.269 2.163e-06 3095.6 522.896 899.765 2069.6294 -6355.8878 9266609.4650 120199.1604 484119.7867 -30426866.9454 122228.2240 478126.9600 21160201.9056 -50.4993 362.9790 -55.4458 -0.0000 -0.0000 -0.0000 0.1366 -1.1269 752.673 847.172 16953.1805 -3145.6609 9266617.8008 120189.8463 484087.0898 -30426866.6384 137095.2576 481300.3653 21160193.5254 -50.8145 362.4697 -55.3384 50.7123 -114.5723 -31.9300 0.4954 -0.6759 786.280 893.549 19012.7464 -6020.0812 9266549.5577 120185.6010 484079.0009 -30426866.8019 139141.2267 478421.6361 21160262.1362 -53.1878 363.8184 -55.4047 -12.3755 -177.6601 31.1579 -4.6012 751.544 894.438 16811.4957 -6065.8410 9266550.6924 120186.3775 484081.3511 -30426867.5822 136935.1893 478377.0427 21160261.3779 -52.9779 363.1030 -55.4906 143.9779 -530.9031 -67.2869 0.0500 267 002348
54.50 2.430 16.793 33.6 9.0408 0.1190 0.5194 21.3866 0.4926 0.4926 0.119 21.387 9.041 2.327e-06 3140.2 424.067 919.122 -4183.4215 -7485.2830 9037737.0851 119898.2666 484823.7654 -30426907.8505 115663.5947 477698.0905 21389116.7351 -46.9544 355.0006 -54.2420 -0.0000 -0.0000 -0.0000 0.1438 -0.4661 752.990 879.440 17262.0406 -5074.9936 9037857.9498 119907.2436 484784.3520 -30426907.7401 137114.6368 480074.7104 21388996.0501 -48.0708 353.9597 -54.0237 20.9774 -47.3934 -13.2080 0.4952 -0.7273 792.784 893.505 19766.5309 -5959.0547 9037793.9805 119891.8538 484786.9014 -30426908.6620 139602.5984 479174.1883 21389060.4150 -49.7533 349.6232 -54.1211 -46.9075 -115.2783 54.6769 -4.6280 751.773 894.507 17157.1798 -5997.9709 9037796.5560 119869.1892 484782.3111 -30426910.3769 136981.4485 479125.7367 21389059.7649 -49.4953 348.6794 -54.2836 140.3861 -538.4230 -63.2487 0.0500 281 002611
53.50 2.461 16.915 33.4 8.8262 0.1190 0.5194 21.6012 0.4925 0.4926 0.119 21.601 8.826 2.443e-06 3144.4 448.126 941.890 -2602.4545 -8892.0637 8823089.0862 119739.1284 485521.8134 -30426934.7323 117099.3877 476972.7273 21603792.3920 -46.7275 344.7929 -53.3465 -0.0000 -0.0000 -0.0000 0.1421 -0.6431 752.924 907.201 17482.8599 -6752.8170 8823102.7453 119777.0207 485453.4791 -30426933.9358 137222.0544 479041.5054 21603778.3167 -49.5807 344.7761 -53.3790 28.9426 -65.3887 -18.2231 0.4962 -0.8383 789.357 893.516 19876.9340 -5902.9339 8823116.5003 119728.9226 485442.0587 -30426934.2530 139547.0293 479880.8032 21603765.3666 -46.3882 343.0521 -53.1087 -49.3042 -143.6355 60.0237 -4.4518 751.569 894.440 17479.0417 -5951.8303 8823116.1385 119701.5263 485443.6622 -30426935.2712 137137.4208 479835.6631 21603765.3044 -47.3419 345.0759 -53.2015 122.0959 -530.8728 -47.8949 0.0500 295 002835
52.50 2.494 17.038 33.3 8.6241 0.1190 0.5194 21.8033 0.4920 0.4920 0.119 21.803 8.624 2.544e-06 3177.6 541.205 923.334 3513.7640 -7685.3098 8621566.8533 119659.1668 486077.1769 -30426956.4697 123129.8347 478729.6608 21805336.7467 -44.0792 334.1581 -52.3211 -0.0000 -0.0000 -0.0000 0.1359 -0.4920 752.697 878.978 17736.2657 -4969.9293 8621559.7349 119632.9524 486052.2880 -30426955.5733 137325.7344 481419.5735 21805343.4139 -44.2579 331.7046 -52.1556 22.1391 -50.0180 -13.9395 0.4941 -0.9085 793.416 893.512 20354.9707 -5868.7920 8621577.2634 119641.7503 486037.3796 -30426955.2687 139947.7077 480498.2642 21805326.1665 -44.9677 332.0677 -52.1095 -62.6564 -134.8136 70.8561 -4.7715 751.657 894.515 17614.4952 -5935.7416 8621576.8066 119639.4420 486052.5867 -30426956.5028 137214.4299 480444.3214 21805327.0997 -44.5420 331.5059 -52.0903 129.9338 -569.9248 -50.4044 0.0500 309 003057

132
matlab/mat/itf_polynom.csv Normal file
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@ -0,0 +1,132 @@
theta,itf2rx2,itf4ry2,itf2rx1,itf4ry1
10,129268.1233,516205.9655,132663.358,505443.6737
10.5,130661.9623,515907.0507,132643.1895,504958.7422
11,130618.63,514979.9943,132615.5884,504495.3075
11.5,132056.2919,514783.9257,132599.8401,504075.3608
12,132441.2177,513942.8999,132581.7281,503629.2346
12.5,132874.8007,513612.0491,132546.8908,503250.447
13,132946.7281,512848.2055,132497.9351,502825.1386
13.5,133527.3489,512561.5513,132563.5223,502377.9742
14,134121.4481,511861.4114,132491.6076,501969.3946
14.5,134087.3831,511565.8942,132410.6433,501543.3146
15,135032.326,510932.296,132333.5745,501113.4159
15.5,136498.4551,510185.6519,132245.2588,500654.2586
16,135547.9015,510008.0153,132122.2721,500163.5599
16.5,135175.1527,509391.6898,132037.1905,499678.1839
17,134874.1905,508707.5609,131910.1633,499183.0764
17.5,134421.6465,508298.5351,131819.1127,498650.7599
18,134677.0919,507861.3803,131675.8636,498194.8239
18.5,135180.3495,507412.488,131609.2865,497699.1617
19,134806.1927,506790.9456,131522.6348,497248.9608
19.5,136084.2513,506247.8709,131498.75,496764.9999
20,136228.5543,505784.8181,131420.1452,496311.6559
20.5,136335.5324,505397.5541,131403.3175,495870.0915
21,136543.8012,505064.1086,131350.1249,495433.3626
21.5,137080.7612,504602.3723,131311.7079,494942.9519
22,137342.9607,504173.5778,131210.2636,494580.7084
22.5,137687.7927,503787.411,131169.2183,494079.0764
23,137657.2689,503269.4169,131145.2055,493634.2479
23.5,138087.2764,502767.2363,131125.4039,493161.9564
24,138126.4401,502133.9582,131048.9281,492790.3937
24.5,138405.9623,501694.8286,130995.6801,492424.4666
25,138516.9937,501340.744,131080.9153,491989.2559
25.5,138236.7377,500982.4336,131072.9409,491600.4773
26,137739.7607,500416.6645,131079.7079,491217.2275
26.5,137813.1473,499839.6789,131079.742,490867.983
27,137928.9233,499495.5051,131089.9948,490476.2035
27.5,137617.3201,499144.2293,131052.926,490185.1137
28,137719.1185,498328.0482,131042.6689,489816.8506
28.5,138223.5111,498121.9975,131097.2908,489376.5413
29,137660.9255,497746.3705,130988.7169,489074.7493
29.5,138302.0817,497112.0281,131056.0961,488614.3155
30,137586.9543,496833.5513,130970.4001,488267.6097
30.5,138142.7473,496295.3077,131007.1276,487856.3599
31,137780.2044,495980.7294,131013.886,487486.5217
31.5,137640.0913,494929.5733,131024.1687,487158.4044
32,138463.8652,494887.4923,131127.1703,486749.3555
32.5,138064.0231,494626.5936,131190.9185,486392.8826
33,137922.8945,494099.2793,131239.4689,486068.1857
33.5,138162.5148,493655.5454,131322.5153,485719.7093
34,138523.4193,493132.8939,131340.5847,485387.3359
34.5,138837.3991,492688.9131,131373.6428,485055.7804
35,138961.2945,492410.8441,131344.8855,484704.5946
35.5,139011.8759,491945.6683,131347.0828,484305.7999
36,139162.4465,491522.1017,131298.9804,483878.8382
36.5,139243.6924,491078.2672,131227.6332,483486.3404
37,138928.3644,490537.1637,131191.9169,483037.0035
37.5,138605.8983,490392.136,131098.9164,482592.9999
38,138633.5591,489872.8437,130992.2839,482162.7848
38.5,138628.038,489428.2741,130996.0172,481761.5475
39,138938.7623,489088.5291,130951.4689,481363.055
39.5,138671.2551,488798.0697,130904.9708,480940.3564
40,139014.0433,488245.1938,130921.1073,480545.2488
40.5,138589.6081,488001.3045,130927.55,480193.2417
41,138770.4167,487463.5161,130940.9815,479793.6328
41.5,139248.7313,486925.8119,130900.798,479407.8159
42,138863.1868,486539.1239,130946.6177,479014.4044
42.5,138777.2689,486179.6761,130911.7975,478666.6995
43,138864.518,485817.6098,131014.3041,478237.2382
43.5,138862.1372,485239.4558,131082.6689,477886.4222
44,138924.1532,484895.8142,131304.766,477500.815
44.5,138982.7431,484501.4407,131369.1116,477245.6542
45,139019.7991,484282.8533,131473.3463,476871.2862
45.5,139695.3959,483714.8843,131553.3207,476620.1928
46,138922.5831,483400.9954,131643.4711,476322.2693
46.5,139164.7889,483096.3499,131769.2567,475998.831
47,138783.6007,482763.1147,131833.5681,475732.0008
47.5,139531.3809,482296.1872,131892.0001,475422.3688
48,138831.5025,482186.6558,131989.5105,475054.1164
48.5,138858.0455,481657.341,131997.9415,474782.191
49,138705.6231,481208.7669,132081.1244,474411.1795
49.5,138744.6417,480929.1746,132175.2556,474101.6364
50,138967.9036,480440.9003,132330.2465,473738.0133
50.5,139060.9553,479937.5751,132437.2204,473472.5555
51,138740.358,479585.9609,132570.7244,473230.4862
51.5,138886.2225,479258.1986,132644.7639,472961.199
52,138900.5244,478998.9163,132671.0721,472704.0613
52.5,138561.6188,478687.0699,132776.3521,472456.8364
53,138446.0988,478522.9173,132825.8284,472198.7457
53.5,138620.6908,478142.483,132894.1079,471956.2639
54,138791.7457,477608.1909,132917.8049,471664.0684
54.5,138331.0268,477302.4464,132934.398,471338.1697
55,138858.7495,476807.2894,132949.6727,470785.1422
55.5,139017.8449,476604.3637,132853.5788,470294.8204
56,138932.166,476163.0197,132861.9244,469928.8435
56.5,138643.4876,475697.4526,132836.2348,469574.0168
57,138181.0449,475494.5525,132843.6076,469235.8479
57.5,138521.5591,474977.9152,132868.6273,468881.4195
58,138158.9052,474609.2971,132873.4785,468581.5333
58.5,138333.2412,474364.7349,132925.8647,468308.1075
59,138274.9969,473945.981,133060.9985,467957.903
59.5,137748.0167,473827.5902,133097.3847,467526.4435
60,137578.9031,473409.5915,133113.1244,467231.2079
60.5,137479.7372,473037.0823,133164.99,466986.5893
61,138029.2369,472697.7415,133296.7617,466789.8959
61.5,137216.646,472512.8985,133378.7884,466527.6275
62,137313.8236,471935.3113,133613.7409,466200.8328
62.5,137784.4796,471642.3157,133733.7793,466001.7039
63,137323.4705,471293.9783,133889.2695,465665.359
63.5,137168.582,470930.4016,133881.9009,465452.0933
64,136934.3463,470545.4745,133914.7585,465174.0773
64.5,137238.2609,470096.0482,134111.7249,464797.7893
65,136723.3895,470109.4736,134181.8689,464473.8355
65.5,136658.0113,469491.9285,134223.9127,464119.2684
66,136609.9004,469054.5269,134191.2343,463802.2302
66.5,136355.3681,468726.5653,134324.5548,463624.3279
67,136154.3484,468450.8331,134370.1228,463383.4213
67.5,135887.1441,468124.0181,134488.7105,463088.655
68,136190.0049,467697.3611,134541.118,462828.8648
68.5,135852.3879,467342.4738,134624.2583,462394.4079
69,136011.2828,466776.4981,134614.2828,462130.0524
69.5,136023.2977,466567.6587,134632.0321,461902.0382
70,135692.87,466021.6729,134464.4503,461179.5848
70.5,135009.2903,465635.4219,134430.0951,460812.9004
71,134767.2935,465199.2071,134530.8225,460352.9395
71.5,134398.6492,464892.5227,134622.9057,459865.3697
72,134501.8556,464351.4357,134553.5852,459516.527
72.5,133453.3607,463913.1527,134253.822,458867.2577
73,133572.6268,463630.5781,134221.182,458640.5448
73.5,132994.6855,463103.5106,134255.6524,457926.5004
74,133058.5105,462389.6747,134241.9905,457545.487
74.5,132387.7607,461906.9099,134116.99,457110.4364
75,132187.4321,461429.2871,134257.0647,456640.0257
1 theta itf2rx2 itf4ry2 itf2rx1 itf4ry1
2 10 129268.1233 516205.9655 132663.358 505443.6737
3 10.5 130661.9623 515907.0507 132643.1895 504958.7422
4 11 130618.63 514979.9943 132615.5884 504495.3075
5 11.5 132056.2919 514783.9257 132599.8401 504075.3608
6 12 132441.2177 513942.8999 132581.7281 503629.2346
7 12.5 132874.8007 513612.0491 132546.8908 503250.447
8 13 132946.7281 512848.2055 132497.9351 502825.1386
9 13.5 133527.3489 512561.5513 132563.5223 502377.9742
10 14 134121.4481 511861.4114 132491.6076 501969.3946
11 14.5 134087.3831 511565.8942 132410.6433 501543.3146
12 15 135032.326 510932.296 132333.5745 501113.4159
13 15.5 136498.4551 510185.6519 132245.2588 500654.2586
14 16 135547.9015 510008.0153 132122.2721 500163.5599
15 16.5 135175.1527 509391.6898 132037.1905 499678.1839
16 17 134874.1905 508707.5609 131910.1633 499183.0764
17 17.5 134421.6465 508298.5351 131819.1127 498650.7599
18 18 134677.0919 507861.3803 131675.8636 498194.8239
19 18.5 135180.3495 507412.488 131609.2865 497699.1617
20 19 134806.1927 506790.9456 131522.6348 497248.9608
21 19.5 136084.2513 506247.8709 131498.75 496764.9999
22 20 136228.5543 505784.8181 131420.1452 496311.6559
23 20.5 136335.5324 505397.5541 131403.3175 495870.0915
24 21 136543.8012 505064.1086 131350.1249 495433.3626
25 21.5 137080.7612 504602.3723 131311.7079 494942.9519
26 22 137342.9607 504173.5778 131210.2636 494580.7084
27 22.5 137687.7927 503787.411 131169.2183 494079.0764
28 23 137657.2689 503269.4169 131145.2055 493634.2479
29 23.5 138087.2764 502767.2363 131125.4039 493161.9564
30 24 138126.4401 502133.9582 131048.9281 492790.3937
31 24.5 138405.9623 501694.8286 130995.6801 492424.4666
32 25 138516.9937 501340.744 131080.9153 491989.2559
33 25.5 138236.7377 500982.4336 131072.9409 491600.4773
34 26 137739.7607 500416.6645 131079.7079 491217.2275
35 26.5 137813.1473 499839.6789 131079.742 490867.983
36 27 137928.9233 499495.5051 131089.9948 490476.2035
37 27.5 137617.3201 499144.2293 131052.926 490185.1137
38 28 137719.1185 498328.0482 131042.6689 489816.8506
39 28.5 138223.5111 498121.9975 131097.2908 489376.5413
40 29 137660.9255 497746.3705 130988.7169 489074.7493
41 29.5 138302.0817 497112.0281 131056.0961 488614.3155
42 30 137586.9543 496833.5513 130970.4001 488267.6097
43 30.5 138142.7473 496295.3077 131007.1276 487856.3599
44 31 137780.2044 495980.7294 131013.886 487486.5217
45 31.5 137640.0913 494929.5733 131024.1687 487158.4044
46 32 138463.8652 494887.4923 131127.1703 486749.3555
47 32.5 138064.0231 494626.5936 131190.9185 486392.8826
48 33 137922.8945 494099.2793 131239.4689 486068.1857
49 33.5 138162.5148 493655.5454 131322.5153 485719.7093
50 34 138523.4193 493132.8939 131340.5847 485387.3359
51 34.5 138837.3991 492688.9131 131373.6428 485055.7804
52 35 138961.2945 492410.8441 131344.8855 484704.5946
53 35.5 139011.8759 491945.6683 131347.0828 484305.7999
54 36 139162.4465 491522.1017 131298.9804 483878.8382
55 36.5 139243.6924 491078.2672 131227.6332 483486.3404
56 37 138928.3644 490537.1637 131191.9169 483037.0035
57 37.5 138605.8983 490392.136 131098.9164 482592.9999
58 38 138633.5591 489872.8437 130992.2839 482162.7848
59 38.5 138628.038 489428.2741 130996.0172 481761.5475
60 39 138938.7623 489088.5291 130951.4689 481363.055
61 39.5 138671.2551 488798.0697 130904.9708 480940.3564
62 40 139014.0433 488245.1938 130921.1073 480545.2488
63 40.5 138589.6081 488001.3045 130927.55 480193.2417
64 41 138770.4167 487463.5161 130940.9815 479793.6328
65 41.5 139248.7313 486925.8119 130900.798 479407.8159
66 42 138863.1868 486539.1239 130946.6177 479014.4044
67 42.5 138777.2689 486179.6761 130911.7975 478666.6995
68 43 138864.518 485817.6098 131014.3041 478237.2382
69 43.5 138862.1372 485239.4558 131082.6689 477886.4222
70 44 138924.1532 484895.8142 131304.766 477500.815
71 44.5 138982.7431 484501.4407 131369.1116 477245.6542
72 45 139019.7991 484282.8533 131473.3463 476871.2862
73 45.5 139695.3959 483714.8843 131553.3207 476620.1928
74 46 138922.5831 483400.9954 131643.4711 476322.2693
75 46.5 139164.7889 483096.3499 131769.2567 475998.831
76 47 138783.6007 482763.1147 131833.5681 475732.0008
77 47.5 139531.3809 482296.1872 131892.0001 475422.3688
78 48 138831.5025 482186.6558 131989.5105 475054.1164
79 48.5 138858.0455 481657.341 131997.9415 474782.191
80 49 138705.6231 481208.7669 132081.1244 474411.1795
81 49.5 138744.6417 480929.1746 132175.2556 474101.6364
82 50 138967.9036 480440.9003 132330.2465 473738.0133
83 50.5 139060.9553 479937.5751 132437.2204 473472.5555
84 51 138740.358 479585.9609 132570.7244 473230.4862
85 51.5 138886.2225 479258.1986 132644.7639 472961.199
86 52 138900.5244 478998.9163 132671.0721 472704.0613
87 52.5 138561.6188 478687.0699 132776.3521 472456.8364
88 53 138446.0988 478522.9173 132825.8284 472198.7457
89 53.5 138620.6908 478142.483 132894.1079 471956.2639
90 54 138791.7457 477608.1909 132917.8049 471664.0684
91 54.5 138331.0268 477302.4464 132934.398 471338.1697
92 55 138858.7495 476807.2894 132949.6727 470785.1422
93 55.5 139017.8449 476604.3637 132853.5788 470294.8204
94 56 138932.166 476163.0197 132861.9244 469928.8435
95 56.5 138643.4876 475697.4526 132836.2348 469574.0168
96 57 138181.0449 475494.5525 132843.6076 469235.8479
97 57.5 138521.5591 474977.9152 132868.6273 468881.4195
98 58 138158.9052 474609.2971 132873.4785 468581.5333
99 58.5 138333.2412 474364.7349 132925.8647 468308.1075
100 59 138274.9969 473945.981 133060.9985 467957.903
101 59.5 137748.0167 473827.5902 133097.3847 467526.4435
102 60 137578.9031 473409.5915 133113.1244 467231.2079
103 60.5 137479.7372 473037.0823 133164.99 466986.5893
104 61 138029.2369 472697.7415 133296.7617 466789.8959
105 61.5 137216.646 472512.8985 133378.7884 466527.6275
106 62 137313.8236 471935.3113 133613.7409 466200.8328
107 62.5 137784.4796 471642.3157 133733.7793 466001.7039
108 63 137323.4705 471293.9783 133889.2695 465665.359
109 63.5 137168.582 470930.4016 133881.9009 465452.0933
110 64 136934.3463 470545.4745 133914.7585 465174.0773
111 64.5 137238.2609 470096.0482 134111.7249 464797.7893
112 65 136723.3895 470109.4736 134181.8689 464473.8355
113 65.5 136658.0113 469491.9285 134223.9127 464119.2684
114 66 136609.9004 469054.5269 134191.2343 463802.2302
115 66.5 136355.3681 468726.5653 134324.5548 463624.3279
116 67 136154.3484 468450.8331 134370.1228 463383.4213
117 67.5 135887.1441 468124.0181 134488.7105 463088.655
118 68 136190.0049 467697.3611 134541.118 462828.8648
119 68.5 135852.3879 467342.4738 134624.2583 462394.4079
120 69 136011.2828 466776.4981 134614.2828 462130.0524
121 69.5 136023.2977 466567.6587 134632.0321 461902.0382
122 70 135692.87 466021.6729 134464.4503 461179.5848
123 70.5 135009.2903 465635.4219 134430.0951 460812.9004
124 71 134767.2935 465199.2071 134530.8225 460352.9395
125 71.5 134398.6492 464892.5227 134622.9057 459865.3697
126 72 134501.8556 464351.4357 134553.5852 459516.527
127 72.5 133453.3607 463913.1527 134253.822 458867.2577
128 73 133572.6268 463630.5781 134221.182 458640.5448
129 73.5 132994.6855 463103.5106 134255.6524 457926.5004
130 74 133058.5105 462389.6747 134241.9905 457545.487
131 74.5 132387.7607 461906.9099 134116.99 457110.4364
132 75 132187.4321 461429.2871 134257.0647 456640.0257

72
matlab/src/getBeamPath.m Normal file
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@ -0,0 +1,72 @@
function [results] = getBeamPath(theta, args)
% getBeamPath -
%
% Syntax: [in_data] = getBeamPath(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
arguments
theta
args.drx (1,1) double {mustBeNumeric} = 0 % [rad]
args.dry (1,1) double {mustBeNumeric} = 0 % [rad]
args.dz (1,1) double {mustBeNumeric} = 0 % [m]
end
% Rotation matrix for drx
udrx = [cos(theta), 0, -sin(theta)];
Rdrx = cos(args.drx)*eye(3)+sin(args.drx)*[0, -udrx(3), udrx(2); udrx(3), 0, -udrx(1); -udrx(2), udrx(1), 0] + (1-cos(args.drx))*(udrx'*udrx);
% Rotation matrix for dry
Rdry = [ cos(args.dry), 0, sin(args.dry); ...
0, 1, 0; ...
-sin(args.dry), 0, cos(args.dry)];
%% Input Beam
p1 = [-0.1, 0, 0]; % [m]
s1 = [ 1, 0, 0];
%% Primary Mirror
pp = [0, 0, 0]; % [m]
np = [cos(pi/2-theta), 0, sin(pi/2-theta)];
%% Reflected beam
[p2, s2] = getPlaneReflection(p1, s1, pp, np);
%% Secondary Mirror
ps = pp ...
+ 0.032*[cos(theta), 0, -sin(theta)] ... % x offset (does not matter a lot)
- np*10e-3./(2*cos(theta)) ... % Theoretical offset
+ np*args.dz; % Add error in distance
ns = [Rdry*Rdrx*[cos(pi/2-theta), 0, sin(pi/2-theta)]']'; % Normal
%% Output Beam
[p3, s3] = getPlaneReflection(p2, s2, ps, ns);
%% Detector
pd = [1, 0, 0]; % [m]
nd = [-1, 0, 0];
%% Get beam position on the decector
p4 = getPlaneReflection(p3, s3, pd, nd);
results = struct();
% Beam position and orientations
results.p1 = p1;
results.s1 = s1;
results.p2 = p2;
results.s2 = s2;
results.p3 = p3;
results.s3 = s3;
results.p4 = p4;
% Mirrors/detector positions and orientations
results.pp = pp;
results.np = np;
results.ps = ps;
results.ns = ns;
results.pd = pd;
results.nd = nd;

16
matlab/src/getPlaneReflection.m Normal file
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@ -0,0 +1,16 @@
function [p_reflect, s_reflect] = getPlaneReflection(p_in, s_in, p_plane, n_plane)
% getPlaneReflection -
%
% Syntax: [p_reflect, s_reflect] = getPlaneReflection(p_in, s_in, p_plane, n_plane)
%
% Inputs:
% - p_in, s_in, p_plane, n_plane -
%
% Outputs:
% - p_reflect, s_reflect -
p_reflect = p_in + s_in*dot(p_plane - p_in, n_plane)/dot(s_in, n_plane);
s_reflect = s_in-2*n_plane*dot(s_in, n_plane);
s_reflect = s_reflect./norm(s_reflect);
end

14
matlab/src/plotBeamPath.m Normal file
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@ -0,0 +1,14 @@
function [] = plotBeamPath(results)
% plotBeamPath -
%
% Syntax: [in_data] = plotBeamPath(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
plot3(100*[results.p1(1), results.p2(1)],100*[results.p1(2), results.p2(2)], 100*[results.p1(3), results.p2(3)], 'linewidth', 0.5)
plot3(100*[results.p2(1), results.p3(1)],100*[results.p2(2), results.p3(2)], 100*[results.p2(3), results.p3(3)], 'linewidth', 0.5)
plot3(100*[results.p3(1), results.p4(1)],100*[results.p3(2), results.p4(2)], 100*[results.p3(3), results.p4(3)], 'linewidth', 0.5)

37
matlab/src/plotCrystals.m Normal file
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@ -0,0 +1,37 @@
function [] = plotCrystals(results, args)
% plotCrystals -
%
% Syntax: [in_data] = plotCrystals(drx, dry, dz, theta, )
%
% Inputs:
% - drx, dry, dz, theta, -
%
% Outputs:
% - in_data -
arguments
results
args.color (3,1) double {mustBeNumeric} = [1;1;1]
args.alpha (1,1) double {mustBeNumeric} = 1
end
z = results.np;
y = [0,1,0];
x = cross(y,z);
xtal1_rectangle = [results.pp + 0.02/2*y + 0.035/2*x;
results.pp - 0.02/2*y + 0.035/2*x;
results.pp - 0.02/2*y - 0.035/2*x;
results.pp + 0.02/2*y - 0.035/2*x];
patch(100*xtal1_rectangle(:,1), 100*xtal1_rectangle(:,2), 100*xtal1_rectangle(:,3), 'k-')
z = results.ns;
% y = [0,cos(drx),sin(drx)];
y = [0,1,0];
x = cross(y,z);
xtal2_rectangle = [results.ps + 0.02/2*y + 0.07/2*x;
results.ps - 0.02/2*y + 0.07/2*x;
results.ps - 0.02/2*y - 0.07/2*x;
results.ps + 0.02/2*y - 0.07/2*x];
patch(100*xtal2_rectangle(:,1), 100*xtal2_rectangle(:,2), 100*xtal2_rectangle(:,3), 'k-')