Add matlab file names

matlab/test_id31_1_metrology.m

@@ -1,3 +1,7 @@
+% Matlab Init                                              :noexport:ignore:
+
+%% test_id31_1_metrology.m
+
 %% Clear Workspace and Close figures
 clear; close all; clc;
 
@@ -33,10 +37,10 @@ specs_ry_rms = 0.25; % [urad RMS]
 % Metrology Kinematics
 % <<ssec:test_id31_metrology_kinematics>>
 
-% The developed short-stroke metrology system is schematically shown in Figure ref:fig: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 indicated dimensions are $l_1 = 60\,mm$ and $l_2 = 16.2\,mm$.
-% In order 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.
+% 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
@@ -45,7 +49,7 @@ specs_ry_rms = 0.25; % [urad RMS]
 % #+attr_latex: :options [b]{0.48\linewidth}
 % #+begin_minipage
 % #+name: fig:test_id31_metrology_kinematics
-% #+caption: Schematic of the measurement system. Measured distances are indicated by red arrows.
+% #+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
@@ -58,7 +62,7 @@ specs_ry_rms = 0.25; % [urad RMS]
 % [[file:figs/test_id31_align_top_sphere_comparators.jpg]]
 % #+end_minipage
 
-% The five equations eqref:eq:test_id31_metrology_kinematics can be written in a 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.
+% 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}
@@ -90,16 +94,16 @@ Hm = [ 0  1  0 -l2  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 interferometers orientations (Section ref:ssec:test_id31_metrology_alignment), the spindle can perform complete rotations while still having interference for all five interferometers.
-% This metrology can therefore be used to better align the axis defined by the two spheres' center with the spindle axis.
+% 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 is made by few iterations.
-% First, the spindle is scanned and the alignment errors are recorded.
+% 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 the new alignment errors are recorded.
+% 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 is 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.
+% 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
@@ -167,9 +171,9 @@ ylim([-8, 14]);
 % Estimated measurement volume
 % <<ssec:test_id31_metrology_acceptance>>
 
-% Because the interferometers are pointing to spheres and not flat surfaces, the lateral acceptance is limited.
-% In order to estimate the metrology acceptance, the micro-hexapod is 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 has enough coupling efficiency to be able to measure the displacement are estimated.
+% 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.
 
@@ -228,25 +232,25 @@ end
 % Estimated measurement errors
 % <<ssec:test_id31_metrology_errors>>
 
-% When using the NASS, the accuracy of the sample's 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.
+% 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.
-% Yet, some elements effecting the accuracy of the metrology are discussed here.
+% 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 very small displacements).
+% 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 interferometer is pointing to a sphere and not to a plane, lateral motion of the sphere is seen as a vertical motion by the top interferometer.
+% 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 with respect to an ideal sphere [fn:6].
-% They are initially meant to be used with capacitive sensors which are integrating the shape errors over large surfaces.
+% 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 is travelling 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 of 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 an errors in the distance measurement of $\approx 4\,nm$.
+% 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 the noise on the translation and rotation measurements is estimated in Figure ref:fig:test_id31_interf_noise.
+% The effect of noise on the translation and rotation measurements is estimated in Figure ref:fig:test_id31_interf_noise.
 
 
 %% Interferometer noise estimation