Rename footnotes

test-bench-id31.org

@@ -507,7 +507,7 @@ As the long-stroke ($\approx 1 \,cm^3$) metrology system was not developed yet,
 
 A first considered option was to use the "Spindle error analyzer" shown in Figure ref:fig:test_id31_lion.
 This system comprises 5 capacitive sensors which are facing two reference spheres.
-But as the gap between the capacitive sensors and the spheres is very small[fn:1], the risk of damaging the spheres and the capacitive sensors is too high.
+But as the gap between the capacitive sensors and the spheres is very small[fn:test_id31_1], the risk of damaging the spheres and the capacitive sensors is too high.
 
 #+name: fig:test_id31_short_stroke_metrology
 #+caption: Short stroke metrology system used to measure the sample position with respect to the granite in 5DoF. The system is based on a "Spindle error analyzer" (\subref{fig:test_id31_lion}), but the capacitive sensors are replaced with fibered interferometers (\subref{fig:test_id31_interf}). Interferometer heads are shown in (\subref{fig:test_id31_interf_head})
@@ -534,7 +534,7 @@ But as the gap between the capacitive sensors and the spheres is very small[fn:1
 #+end_figure
 
 Instead of using capacitive sensors, 5 fibered interferometers were used in a similar way (Figure ref:fig:test_id31_interf).
-At the end of each fiber, a sensor head[fn:2] (Figure ref:fig:test_id31_interf_head) is used, which consists of a lens precisely positioned with respect to the fiber's end.
+At the end of each fiber, a sensor head[fn:test_id31_2] (Figure ref:fig:test_id31_interf_head) is used, which consists of a lens precisely positioned with respect to the fiber's end.
 The lens is focusing the light on the surface of the sphere, such that the reflected light comes back into the fiber and produces an interference.
 This way, the gap between the head and the reference sphere is much larger (here around $40\,mm$), removing the risk of collision.
 
@@ -860,7 +860,7 @@ First, the "metrology kinematics" (discussed in Section ref:ssec:test_id31_metro
 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.
 
-Then, the reference spheres have some deviations with respect to an ideal sphere [fn:6].
+Then, the reference spheres have some deviations with respect to an ideal sphere [fn:test_id31_6].
 They are initially meant to be used with capacitive sensors which are integrating the 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.
 
@@ -1081,7 +1081,7 @@ A good match can be observed for the diagonal dynamics (except the high frequenc
 However, the coupling for the transfer function from command signals $\bm{u}$ to the estimated strut motion from the external metrology $\bm{\epsilon\mathcal{L}}$ is larger than expected (Figure ref:fig:test_id31_first_id_int).
 
 The experimental time delay estimated from the FRF (Figure ref:fig:test_id31_first_id_int) is larger than expected.
-After investigation, it was found that the additional delay was due to a digital processing unit[fn:3] that was used to get the interferometers' signals in the Speedgoat.
+After investigation, it was found that the additional delay was due to a digital processing unit[fn:test_id31_3] that was used to get the interferometers' signals in the Speedgoat.
 This issue was later solved.
 
 #+begin_src matlab
@@ -3218,7 +3218,7 @@ exportFig('figs/test_id31_hac_characteristic_loci.pdf', 'width', 'half', 'height
 ** Performance estimation with simulation of Tomography scans
 <<ssec:test_id31_iff_hac_perf>>
 
-To estimate the performances that can be expected with this HAC-LAC architecture and the designed controller, simulations of tomography experiments were performed[fn:4].
+To estimate the performances that can be expected with this HAC-LAC architecture and the designed controller, simulations of tomography experiments were performed[fn:test_id31_4].
 The rotational velocity was set to $180\,\text{deg/s}$, and no payload was added on top of the nano-hexapod.
 An open-loop simulation and a closed-loop simulation were performed and compared in Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim.
 The obtained closed-loop positioning accuracy was found to comply with the requirements as it succeeded to keep the point of interest on the beam (Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim_yz).
@@ -3815,7 +3815,7 @@ data_tomo_m3_Wz6.Ry_rms_ol = rms(data_tomo_m3_Wz6.Ry_int(1:i_m3) - (y0 + R*sin(d
 
 **** Fast Tomography scans
 
-A tomography experiment was then performed with the highest rotational velocity of the Spindle: $180\,\text{deg/s}$[fn:7].
+A tomography experiment was then performed with the highest rotational velocity of the Spindle: $180\,\text{deg/s}$[fn:test_id31_7].
 The trajectory of the point of interest during this fast tomography scan is shown in Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_exp.
 While the experimental results closely mirror the simulation results (Figure ref:fig:test_id31_tomo_m0_30rpm_robust_hac_iff_sim), the actual performance are slightly lower than predicted.
 Nevertheless, even with this robust (conservative) HAC implementation, the system performance approaches the specified requirements.
@@ -4455,7 +4455,7 @@ exportFig('figs/test_id31_dz_scan_10ums_ry.pdf', 'width', 'third', 'height', 'no
 #+end_subfigure
 #+end_figure
 
-A subsequent scan at $100,\mu m/s$ - the maximum velocity for high-precision $D_z$ scans[fn:8] - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure ref:fig:test_id31_dz_scan_100ums).
+A subsequent scan at $100,\mu m/s$ - the maximum velocity for high-precision $D_z$ scans[fn:test_id31_8] - maintains positioning errors within specifications during the constant velocity phase, with deviations occurring only during acceleration and deceleration phases (Figure ref:fig:test_id31_dz_scan_100ums).
 Since detectors typically operate only during the constant velocity phase, these transient deviations do not compromise measurement quality.
 Yet, performance during acceleration phases could potentially be enhanced through the implementation of feedforward control.
 
@@ -4555,7 +4555,7 @@ exportFig('figs/test_id31_dz_scan_100ums_ry.pdf', 'width', 'third', 'height', 'n
 **** Introduction                                                  :ignore:
 
 Lateral scans are executed using the $T_y$ stage.
-The stepper motor controller[fn:5] generates a setpoint that is transmitted to the Speedgoat.
+The stepper motor controller[fn:test_id31_5] generates a setpoint that is transmitted to the Speedgoat.
 Within the Speedgoat, the system computes the positioning error by comparing the measured $D_y$ sample position against the received setpoint, and the Nano-Hexapod compensates for positioning errors introduced during $T_y$ stage scanning.
 The scanning range is constrained $\pm 100\,\mu m$ due to the limited acceptance of the metrology system.
 
@@ -7599,11 +7599,11 @@ function [stewart] = initializeStewartPlatform()
 
 * Footnotes
 
-[fn:8]Such scan could corresponding to a 1ms integration time (which is typically the smallest integration time) and 100nm "resolution" (equal to the vertical beam size).
-[fn:7]The highest rotational velocity of $360\,\text{deg/s}$ could not be tested due to an issue in the Spindle's controller.
-[fn:6]The roundness of the spheres is specified at $50\,nm$.
-[fn:5]The "IcePAP" [[cite:&janvier13_icepap]]  which is developed at the ESRF.
-[fn:4]Note that the eccentricity of the "point of interest" with respect to the Spindle rotation axis has been tuned based on measurements.
-[fn:3]The "PEPU" [[cite:&hino18_posit_encod_proces_unit]] was used for digital protocol conversion between the interferometers and the Speedgoat.
-[fn:2]M12/F40 model from Attocube.
-[fn:1]Depending on the measuring range, gap can range from $\approx 1\,\mu m$ to $\approx 100\,\mu m$.
+[fn:test_id31_8]Such scan could corresponding to a 1ms integration time (which is typically the smallest integration time) and 100nm "resolution" (equal to the vertical beam size).
+[fn:test_id31_7]The highest rotational velocity of $360\,\text{deg/s}$ could not be tested due to an issue in the Spindle's controller.
+[fn:test_id31_6]The roundness of the spheres is specified at $50\,nm$.
+[fn:test_id31_5]The "IcePAP" [[cite:&janvier13_icepap]]  which is developed at the ESRF.
+[fn:test_id31_4]Note that the eccentricity of the "point of interest" with respect to the Spindle rotation axis has been tuned based on measurements.
+[fn:test_id31_3]The "PEPU" [[cite:&hino18_posit_encod_proces_unit]] was used for digital protocol conversion between the interferometers and the Speedgoat.
+[fn:test_id31_2]M12/F40 model from Attocube.
+[fn:test_id31_1]Depending on the measuring range, gap can range from $\approx 1\,\mu m$ to $\approx 100\,\mu m$.