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matlab/test_id31_1_metrology.m

@@ -1,5 +1,3 @@
-% Matlab Init                                              :noexport:ignore:
-
 %% test_id31_1_metrology.m
 
 %% Clear Workspace and Close figures
@@ -34,51 +32,6 @@ specs_dz_rms = 15; % [nm RMS]
 specs_dy_rms = 30; % [nm RMS]
 specs_ry_rms = 0.25; % [urad RMS]
 
-% Metrology Kinematics
-% <<ssec:test_id31_metrology_kinematics>>
-
-% The proposed short-stroke metrology system is schematized in Figure ref:fig:test_id31_metrology_kinematics.
-% The point of interest is indicated by the blue frame $\{B\}$, which is located $H = 150\,mm$ above the nano-hexapod's top platform.
-% The spheres have a diameter $d = 25.4\,mm$, and the indicated dimensions are $l_1 = 60\,mm$ and $l_2 = 16.2\,mm$.
-% To compute the pose of the $\{B\}$ frame with respect to the granite (i.e. with respect to the fixed interferometer heads), the measured (small) displacements $[d_1,\ d_2,\ d_3,\ d_4,\ d_5]$ by the interferometers are first written as a function of the (small) linear and angular motion of the $\{B\}$ frame $[D_x,\ D_y,\ D_z,\ R_x,\ R_y]$ eqref:eq:test_id31_metrology_kinematics.
-
-% \begin{equation}\label{eq:test_id31_metrology_kinematics}
-% d_1 = D_y - l_2 R_x, \quad d_2 = D_y + l_1 R_x, \quad d_3 = -D_x - l_2 R_y, \quad d_4 = -D_x + l_1 R_y, \quad d_5 = -D_z
-% \end{equation}
-
-% #+attr_latex: :options [b]{0.48\linewidth}
-% #+begin_minipage
-% #+name: fig:test_id31_metrology_kinematics
-% #+caption: Schematic of the measurement system. The measured distances are indicated by red arrows.
-% #+attr_latex: :scale 1 :float nil
-% [[file:figs/test_id31_metrology_kinematics.png]]
-% #+end_minipage
-% \hfill
-% #+attr_latex: :options [b]{0.48\linewidth}
-% #+begin_minipage
-% #+name: fig:test_id31_align_top_sphere_comparators
-% #+attr_latex: :width \linewidth :float nil
-% #+caption: The top sphere is aligned with the rotation axis of the spindle using two probes.
-% [[file:figs/test_id31_align_top_sphere_comparators.jpg]]
-% #+end_minipage
-
-% The five equations eqref:eq:test_id31_metrology_kinematics can be written in matrix form, and then inverted to have the pose of the $\{B\}$ frame as a linear combination of the measured five distances by the interferometers eqref:eq:test_id31_metrology_kinematics_inverse.
-
-% \begin{equation}\label{eq:test_id31_metrology_kinematics_inverse}
-% \begin{bmatrix}
-%    D_x \\ D_y \\ D_z \\ R_x \\ R_y
-% \end{bmatrix} = {\underbrace{\begin{bmatrix}
-%    0 &  1 &  0 & -l_2 &  0   \\
-%    0 &  1 &  0 &  l_1 &  0   \\
-%   -1 &  0 &  0 &  0   & -l_2 \\
-%   -1 &  0 &  0 &  0   &  l_1 \\
-%    0 &  0 & -1 &  0   &  0
-% \end{bmatrix}}_{\bm{J_d}}}^{-1} \cdot \begin{bmatrix}
-%   d_1 \\ d_2 \\ d_3 \\ d_4 \\ d_5
-% \end{bmatrix}
-% \end{equation}
-
-
 %% Geometrical parameters of the metrology system
 H = 150e-3;
 l1 = (150-48-42)*1e-3;
@@ -91,21 +44,6 @@ Hm = [ 0  1  0 -l2  0;
       -1  0  0  0   l1;
        0  0 -1  0   0];
 
-% Fine Alignment of reference spheres using interferometers
-% <<ssec:test_id31_metrology_sphere_fine_alignment>>
-
-% Thanks to the first alignment of the two reference spheres with the spindle axis (Section ref:ssec:test_id31_metrology_sphere_rought_alignment) and to the fine adjustment of the interferometer orientations (Section ref:ssec:test_id31_metrology_alignment), the spindle can perform complete rotations while still having interference for all five interferometers.
-% Therefore, this metrology can be used to better align the axis defined by the centers of the two spheres with the spindle axis.
-
-% The alignment process requires few iterations.
-% First, the spindle is scanned, and alignment errors are recorded.
-% From the errors, the motion of the micro-hexapod to better align the spheres with the spindle axis is computed and the micro-hexapod is positioned accordingly.
-% Then, the spindle is scanned again, and new alignment errors are recorded.
-
-% This iterative process is first performed for angular errors (Figure ref:fig:test_id31_metrology_align_rx_ry) and then for lateral errors (Figure ref:fig:test_id31_metrology_align_dx_dy).
-% The remaining errors after alignment are in the order of $\pm5\,\mu\text{rad}$ in $R_x$ and $R_y$ orientations, $\pm 1\,\mu m$ in $D_x$ and $D_y$ directions, and less than $0.1\,\mu m$ vertically.
-
-
 %% Angular alignment
 % Load Data
 data_it0 = h5scan(data_dir, 'alignment', 'h1rx_h1ry', 1);
@@ -168,16 +106,6 @@ legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
 xlim([-1, 21]);
 ylim([-8, 14]);
 
-% Estimated measurement volume
-% <<ssec:test_id31_metrology_acceptance>>
-
-% Because the interferometers point to spheres and not flat surfaces, the lateral acceptance is limited.
-% To estimate the metrology acceptance, the micro-hexapod was used to perform three accurate scans of $\pm 1\,mm$, respectively along the $x$, $y$ and $z$ axes.
-% During these scans, the 5 interferometers are recorded individually, and the ranges in which each interferometer had enough coupling efficiency to be able to measure the displacement were estimated.
-% Results are summarized in Table ref:tab:test_id31_metrology_acceptance.
-% The obtained lateral acceptance for pure displacements in any direction is estimated to be around $+/-0.5\,mm$, which is enough for the current application as it is well above the micro-station errors to be actively corrected by the NASS.
-
-
 %% Estimated acceptance of the metrology
 % This is estimated by moving the spheres using the micro-hexapod
 
@@ -229,30 +157,6 @@ for i = [1:size(dz_acceptance, 1)]
     end
 end
 
-% Estimated measurement errors
-% <<ssec:test_id31_metrology_errors>>
-
-% When using the NASS, the accuracy of the sample positioning is determined by the accuracy of the external metrology.
-% However, the validation of the nano-hexapod, the associated instrumentation, and the control architecture is independent of the accuracy of the metrology system.
-% Only the bandwidth and noise characteristics of the external metrology are important.
-% However, some elements that affect the accuracy of the metrology system are discussed here.
-
-% First, the "metrology kinematics" (discussed in Section ref:ssec:test_id31_metrology_kinematics) is only approximate (i.e. valid for small displacements).
-% This can be easily seen when performing lateral $[D_x,\,D_y]$ scans using the micro-hexapod while recording the vertical interferometer (Figure ref:fig:test_id31_xy_map_sphere).
-% As the top interferometer points to a sphere and not to a plane, lateral motion of the sphere is seen as a vertical motion by the top interferometer.
-
-% Then, the reference spheres have some deviations relative to an ideal sphere [fn:test_id31_6].
-% These sphere are originally intended for use with capacitive sensors that integrate shape errors over large surfaces.
-% When using interferometers, the size of the "light spot" on the sphere surface is a circle with a diameter approximately equal to $50\,\mu m$, and therefore the measurement is more sensitive to shape errors with small features.
-
-% As the light from the interferometer travels through air (as opposed to being in vacuum), the measured distance is sensitive to any variation in the refractive index of the air.
-% Therefore, any variation in air temperature, pressure or humidity will induce measurement errors.
-% For instance, for a measurement length of $40\,mm$, a temperature variation of $0.1\,{}^oC$ (which is typical for the ID31 experimental hutch) induces errors in the distance measurement of $\approx 4\,nm$.
-
-% Interferometers are also affected by noise [[cite:&watchi18_review_compac_inter]].
-% The effect of noise on the translation and rotation measurements is estimated in Figure ref:fig:test_id31_interf_noise.
-
-
 %% Interferometer noise estimation
 data = load("test_id31_interf_noise.mat");