From f17ceca29d82c32d0de3cd92b0a6f2b80b36e769 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 2 Jun 2022 10:59:32 +0200 Subject: [PATCH] Working ray tracing with dz/dry/drx --- dcm-metrology.org | 387 ++++++++++- dcm-metrology.pdf | Bin 450631 -> 703400 bytes figs/metrology_schematic.pdf | Bin 27523 -> 19600 bytes figs/metrology_schematic.png | Bin 63892 -> 87538 bytes figs/metrology_schematic.svg | 810 ++++++++++++------------ figs/motion_beam_drx_error.pdf | Bin 0 -> 16016 bytes figs/motion_beam_drx_error.png | Bin 0 -> 25444 bytes figs/motion_beam_dry_error.pdf | Bin 0 -> 15348 bytes figs/motion_beam_dry_error.png | Bin 0 -> 17330 bytes figs/motion_beam_dz_error.pdf | Bin 0 -> 15093 bytes figs/motion_beam_dz_error.png | Bin 0 -> 19925 bytes matlab/mat/correctInterf-vlm-220201.dat | 185 ++++++ matlab/mat/itf_polynom.csv | 132 ++++ matlab/src/getBeamPath.m | 72 +++ matlab/src/get_plane_reflection.m | 16 + matlab/src/plotBeamPath.m | 14 + 16 files changed, 1212 insertions(+), 404 deletions(-) create mode 100644 figs/motion_beam_drx_error.pdf create mode 100644 figs/motion_beam_drx_error.png create mode 100644 figs/motion_beam_dry_error.pdf create mode 100644 figs/motion_beam_dry_error.png create mode 100644 figs/motion_beam_dz_error.pdf create mode 100644 figs/motion_beam_dz_error.png create mode 100644 matlab/mat/correctInterf-vlm-220201.dat create mode 100644 matlab/mat/itf_polynom.csv create mode 100644 matlab/src/getBeamPath.m create mode 100644 matlab/src/get_plane_reflection.m create mode 100644 matlab/src/plotBeamPath.m diff --git a/dcm-metrology.org b/dcm-metrology.org index ebb337e..5569e59 100644 --- a/dcm-metrology.org +++ b/dcm-metrology.org @@ -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 @@ -248,6 +246,8 @@ d_y = 2 D_{\text{vlm}} \sin \theta \cdot d_{R_x^\prime} * Ray Tracing +** Introduction :ignore: + ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) <> @@ -278,16 +278,30 @@ 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] +theta = 85*pi/180; % [rad] +#+end_src + +#+begin_src matlab +thetas = pi/180*[5:1:85]; +#+end_src + +#+begin_src matlab +yz = zeros(2, length(thetas)); +#+end_src + +#+begin_src matlab +for i = 1:length(thetas) + theta = thetas(i); #+end_src #+begin_src matlab %% Secondary crystal defaults -drx = 5*pi/180; % [rad] -dry = 0*pi/180; % [rad] -dz = 0; % [m] +drx = 0; % [rad] +dry = 0; % [rad] +dz = 1e-9; % [m] % Rotation matrix for drx udrx = [cos(theta), 0, -sin(theta)]; @@ -321,6 +335,29 @@ ns = [Rdry*Rdrx*[cos(pi/2-theta), 0, sin(pi/2-theta)]']'; % Normal %% Output Beam [p3, s3] = get_plane_reflection(p2, s2, ps, ns); + +%% Detector +pd = [1, 0, 0]; % [m] +nd = [-1, 0, 0]; + +%% Get beam position on the decector +p4 = get_plane_reflection(p3, s3, pd, nd); +yz(:,i) = p4(2:3); +end +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*thetas, 1e9*(yz(2,:) + 10e-3)); +xlabel('Bragg Angle [deg]'); ylabel('Z position [nm/m/nrad]'); +#+end_src + +#+begin_src matlab +figure; +hold on; +plot(180/pi*thetas, 1e9*yz(1,:)); +xlabel('Bragg Angle [deg]'); ylabel('Y position [nm/m/nrad]'); #+end_src #+begin_src matlab @@ -414,11 +451,223 @@ zlim([-0.02, 0.01]) grid off; #+end_src +** Effect of =dry= +#+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); + Dy(i) = results.p4(2); + Dz(i) = results.p4(3); + Ry(i) = atan2(results.s3(3), results.s3(1)); + Rz(i) = atan2(results.s3(2), results.s3(1)); +end +#+end_src + +#+begin_src matlab :exports none :results none +%% Motion of the output beam with dry error +figure; +hold on; +plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz'); +plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy'); +plot(thetas, 1e9*Rz, 'DisplayName', 'Rz'); +plot(thetas, 1e9*Ry, 'DisplayName', 'Ry'); +hold off; +xlabel('Bragg [deg]'); ylabel('Offset [nm/m], Tilt [nrad]') +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_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]] + +** Effect of =drx= +#+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); + Dy(i) = results.p4(2); + Dz(i) = results.p4(3); + Ry(i) = atan2(results.s3(3), results.s3(1)); + Rz(i) = atan2(results.s3(2), results.s3(1)); +end +#+end_src + +#+begin_src matlab :exports none :results none +%% Motion of the output beam with drx error +figure; +hold on; +plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz'); +plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy'); +plot(thetas, 1e9*Rz, 'DisplayName', 'Rz'); +plot(thetas, 1e9*Ry, 'DisplayName', 'Ry'); +hold off; +xlabel('Bragg [deg]'); ylabel('Offset [nm/m], Tilt [nrad]') +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 =dz= +#+begin_src matlab :exports none +%% Effect of dz +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, 'dz', 1e-9); + Dy(i) = results.p4(2); + Dz(i) = results.p4(3); + Ry(i) = atan2(results.s3(3), results.s3(1)); + Rz(i) = atan2(results.s3(2), results.s3(1)); +end +#+end_src + +#+begin_src matlab :exports none :results none +%% Motion of the output beam with dZ error +figure; +hold on; +plot(thetas, 1e9*(Dz+10e-3), '--', 'DisplayName', 'Dz'); +plot(thetas, 1e9*Dy, '--', 'DisplayName', 'Dy'); +plot(thetas, 1e9*Rz, 'DisplayName', 'Rz'); +plot(thetas, 1e9*Ry, 'DisplayName', 'Ry'); +hold off; +xlabel('Bragg [deg]'); ylabel('Offset [nm/m], Tilt [nrad]') +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]] + +** Test :noexport: +#+begin_src matlab +figure; +plot(thetas, 1e9*yz(:,1)); +xlabel('Bragg [deg]'); ylabel('Y Displacement [nm/m/nrad]') +#+end_src + +#+begin_src matlab +figure; +plot(thetas, 1e9*yz(:,1)); +xlabel('Bragg [deg]'); ylabel('Y Displacement [nm/m/nrad]') +#+end_src + +#+begin_src matlab +%% Effect of dry +thetas = 1:1:85; +yz = zeros(length(thetas), 2); +for i = 1:length(thetas) + results = getBeamPath(thetas(i)*pi/180, 'dry', 1e-9); + yz(i,:) = results.p4(2:3); +end +#+end_src + +#+begin_src matlab +figure; +plot(thetas, 1e9*(yz(:,2) + 10e-3)); +xlabel('Bragg [deg]'); ylabel('Z Displacement [nm/m/nrad]') +#+end_src + +#+begin_src matlab +%% Effect of dz +thetas = 1:1:85; +yz = zeros(length(thetas), 2); +for i = 1:length(thetas) + results = getBeamPath(thetas(i)*pi/180, 'dz', 1e-9); + yz(i,:) = results.p4(2:3); +end +#+end_src + +#+begin_src matlab +figure; +plot(thetas, 1e9*(yz(:,2) + 10e-3)); +xlabel('Bragg [deg]'); ylabel('Z Displacement [nm/m/nm]') +#+end_src + + + +#+begin_src matlab +figure; +hold on; +for theta = 5:5:85 + set(gca,'ColorOrderIndex',1) + plotBeamPath(getBeamPath(theta*pi/180, 'dz', 1e-3)) +end +hold off; +view(0,0) +axis equal +xlim([-0.1, 0.15]) +zlim([-0.02, 0.01]) +grid off; +#+end_src + +#+begin_src matlab +figure; +hold on; +for theta = 5:5:85 + set(gca,'ColorOrderIndex',1) + plotBeamPath(getBeamPath(theta*pi/180, 'dry', 1*pi/180)) +end +hold off; +view(0,0) +axis equal +xlim([-0.1, 0.15]) +zlim([-0.02, 0.01]) +grid off; +#+end_src + +#+begin_src matlab +figure; +hold on; +for theta = 5:5:85 + set(gca,'ColorOrderIndex',1) + plotBeamPath(getBeamPath(theta*pi/180, 'drx', 1*pi/180)) +end +hold off; +view(0,90) +axis equal +xlim([-0.1, 0.15]) +zlim([-0.02, 0.01]) +grid off; +#+end_src + * Deformations of the Metrology Frame <> ** 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. @@ -1175,9 +1424,119 @@ 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: +<> + +#+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] = get_plane_reflection(p1, s1, pp, np); + +%% 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*args.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); + +%% Detector +pd = [1, 0, 0]; % [m] +nd = [-1, 0, 0]; + +%% Get beam position on the decector +p4 = get_plane_reflection(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: +<> + +#+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([results.p1(1), results.p2(1)],[results.p1(2), results.p2(2)], [results.p1(3), results.p2(3)]) +plot3([results.p2(1), results.p3(1)],[results.p2(2), results.p3(2)], [results.p2(3), results.p3(3)]) +plot3([results.p3(1), results.p4(1)],[results.p3(2), results.p4(2)], 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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] = get_plane_reflection(p1, s1, pp, np); + +%% 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*args.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); + +%% Detector +pd = [1, 0, 0]; % [m] +nd = [-1, 0, 0]; + +%% Get beam position on the decector +p4 = get_plane_reflection(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; diff --git a/matlab/src/get_plane_reflection.m b/matlab/src/get_plane_reflection.m new file mode 100644 index 0000000..b65c203 --- /dev/null +++ b/matlab/src/get_plane_reflection.m @@ -0,0 +1,16 @@ +function [p_reflect, s_reflect] = get_plane_reflection(p_in, s_in, p_plane, n_plane) +% get_plane_reflection - +% +% Syntax: [p_reflect, s_reflect] = get_plane_reflection(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 diff --git a/matlab/src/plotBeamPath.m b/matlab/src/plotBeamPath.m new file mode 100644 index 0000000..066468b --- /dev/null +++ b/matlab/src/plotBeamPath.m @@ -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([results.p1(1), results.p2(1)],[results.p1(2), results.p2(2)], [results.p1(3), results.p2(3)]) +plot3([results.p2(1), results.p3(1)],[results.p2(2), results.p3(2)], [results.p2(3), results.p3(3)]) +plot3([results.p3(1), results.p4(1)],[results.p3(2), results.p4(2)], [results.p3(3), results.p4(3)])

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