From 155c95845a8983e33f91b1495e8a28dfa9d815b2 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Sat, 1 Feb 2025 09:45:01 +0100 Subject: [PATCH] Rework metrology section --- test-bench-id31.org | 147 +++++++++++++------------ test-bench-id31.pdf | Bin 23171464 -> 23192807 bytes test-bench-id31.tex | 255 +++++++++++++++++++++++--------------------- 3 files changed, 204 insertions(+), 198 deletions(-) diff --git a/test-bench-id31.org b/test-bench-id31.org index d678f8e..9e26e6b 100644 --- a/test-bench-id31.org +++ b/test-bench-id31.org @@ -181,6 +181,10 @@ CLOSED: [2025-01-30 Thu 11:16] - RMS errors (/ by 6.6) gives 30nmRMS in Dy and 15nmRMS in Dz. - Ry error <1.7urad, 250nrad RMS +** TODO [#A] Maybe should only put experimental results in last section +Some Tomography experiments are presented in ref:sec:test_id31_iff_hac +Maybe it should only be simulations, and put everything in the last "experimental" section. + ** TODO [#A] Ask Veijo to give me a short summary (5 lines) for each experiment type with references - Tomography @@ -423,18 +427,17 @@ CLOSED: [2024-11-12 Tue 16:03] * Introduction :ignore: -Now that the nano-hexapod is mounted and that a good multi-body model of the nano-hexapod -The system is validated on the ID31 beamline. +Now that the nano-hexapod is mounted and that the the multi-body model of the nano-hexapod could be validated based on dynamics measurements, the complete NASS is mounted as shown in Figure ref:fig:test_id31_micro_station_nano_hexapod and the performances are evaluated on the ID31 beamline. At the beginning of the project, it was planned to develop a long stroke 5-DoF metrology system to measure the pose of the sample with respect to the granite. The development of such system was complex, and was not completed at the time of the experimental tests on ID31. -To still validate the developed nano active platform and the associated instrumentation and control architecture, a 5-DoF short stroke metrology system was developed (Section ref:sec:test_id31_metrology). +To still be able to validate the developed nano active platform and the associated instrumentation and control architecture, a 5-DoF short stroke metrology system is developed and presented in Section ref:sec:test_id31_metrology. -The identify dynamics of the nano-hexapod fixed on top of the micro-station was identified for different experimental conditions (payload masses, rotational velocities) and compared with the model (Section ref:sec:test_id31_open_loop_plant). +The identify dynamics of the nano-hexapod fixed on top of the micro-station is identified for different experimental conditions (payload masses, rotational velocities) and compared with the multi-body model in Section ref:sec:test_id31_open_loop_plant. -Decentralized Integral Force Feedback is then applied to actively damp the plant in a robust way (Section ref:sec:test_id31_iff). +In order to apply the developed HAC-LAC architecture, decentralized Integral Force Feedback is first applied to actively damp the plant in a robust way (Section ref:sec:test_id31_iff), and the high authority controller is then implemented (Section ref:sec:test_id31_hac). -High authority control is then applied (Section ref:sec:test_id31_iff_hac). +Finally, the positioning accuracy of the NASS is evaluated by performing scans corresponding to several scientific experiments (Section ref:sec:test_id31_experiments) #+name: fig:test_id31_micro_station_nano_hexapod #+caption: Picture of the micro-station without the nano-hexapod (\subref{fig:test_id31_micro_station_cables}) and with the nano-hexapod (\subref{fig:test_id31_fixed_nano_hexapod}) @@ -466,7 +469,7 @@ 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. -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 high. +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. #+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}) @@ -494,10 +497,11 @@ As the gap between the capacitive sensors and the spheres is very small[fn:1], t 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. -The lens is focusing the light on the surface of the sphere, such that it comes back to the fiber and produces an interference. -This way, the gap between the sensor and the reference sphere is much larger (here around $40\,mm$), removing the risk of collision. +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. -Nevertheless, the metrology system still has limited measurement range, as when the spheres are moving perpendicularly to the beam axis, the reflected light does not coincide with the incident light, and for some perpendicular displacement, the interference is too small to be detected. +Nevertheless, the metrology system still has limited measurement range due to limited angular acceptance of the fibered interferometers. +Indeed, when the spheres are moving perpendicularly to the beam axis, the reflected light does not coincide with the incident light, and above some perpendicular displacement, the reflected light does not comes back into the fiber, and no interference is produced. ** Matlab Init :noexport:ignore: #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) @@ -526,7 +530,7 @@ Nevertheless, the metrology system still has limited measurement range, as when The developed short-stroke metrology system is schematically shown 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. +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. \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 @@ -548,18 +552,18 @@ 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, \qua [[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 $\{B\}$ 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 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. \begin{equation}\label{eq:test_id31_metrology_kinematics_inverse} \begin{bmatrix} D_x \\ D_y \\ D_z \\ R_x \\ R_y -\end{bmatrix} = \begin{bmatrix} +\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}^{-1} \cdot \begin{bmatrix} +\end{bmatrix}}_{\bm{J_d}}}^{-1} \cdot \begin{bmatrix} d_1 \\ d_2 \\ d_3 \\ d_4 \\ d_5 \end{bmatrix} \end{equation} @@ -585,43 +589,49 @@ The two reference spheres are aligned with the rotation axis of the spindle. To do so, two measuring probes are used as shown in Figure ref:fig:align_top_sphere_comparators. To not damage the sensitive sphere surface, the probes are instead positioned on the cylinder on which the sphere is mounted. -First, the probes are fixed to the bottom (fixed) cylinder to align its axis with the spindle axis. +First, the probes are fixed to the bottom (fixed) cylinder to align the first sphere with the spindle axis. Then, the probes are fixed to the top (adjustable) cylinder, and the same alignment is performed. -With this setup, the precision of the alignment of both sphere better with the spindle axis is expected to limited to $\approx 10\,\mu m$. -This is probably limited due to the poor coaxiality between the cylinders and the spheres. -However, the alignment precision should be enough to stay in the acceptance of the interferometers. +With this setup, the alignment accuracy of both spheres with the spindle axis is expected to around $10\,\mu m$. +The accuracy is probably limited due to the poor coaxiality between the cylinders and the spheres. +However, this first alignment should permit to position the two sphere within the acceptance of the interferometers. ** Tip-Tilt adjustment of the interferometers <> -The short stroke metrology system is placed on top of the main granite using a gantry made of granite blocs to have good vibration and thermal stability (Figure ref:fig:short_stroke_metrology_overview). +The short-stroke metrology system is placed on top of the main granite using a gantry made of granite blocs (Figure ref:fig:short_stroke_metrology_overview). +Granite is used to have good vibration and thermal stability. #+name: fig:short_stroke_metrology_overview #+caption: Granite gantry used to fix the short-stroke metrology system #+attr_latex: :width 0.8\linewidth [[file:figs/test_id31_short_stroke_metrology_overview.jpg]] -The interferometers need to be aligned with respect to the two reference spheres to approach as much as possible the ideal case shown in Figure ref:fig:test_id31_metrology_kinematics. -The vertical position of the spheres is adjusted using the micro-hexapod to match the height of the interferometers. +The interferometer beams need to be position with respect to the two reference spheres as close as possible to the ideal case shown in Figure ref:fig:test_id31_metrology_kinematics. +This means that their positions and angles needs to be well adjusted with respect to the two spheres. +First, the vertical position of the spheres is adjusted using the micro-hexapod to match the height of the interferometers. Then, the horizontal position of the gantry is adjusted such that the coupling efficiency (i.e. the intensity of the light reflected back in the fiber) of the top interferometer is maximized. -This is equivalent as to optimize the perpendicularity between the interferometer beam and the sphere surface (i.e. the concentricity between the beam and the sphere center). +This is equivalent as to optimize the perpendicularity between the interferometer beam and the sphere surface (i.e. the concentricity between the top beam and the sphere center). -The lateral sensor heads (i.e. all except the top one), which are each fixed to a custom tip-tilt adjustment mechanism, are individually oriented such that the coupling efficient is maximized. +The lateral sensor heads (i.e. all except the top one) are each fixed to a custom tip-tilt adjustment mechanism. +This allow to individually orient them such that they all point to the spheres' center (i.e. perpendicular to the sphere surface). +This is done by maximizing the coupling efficiency of each interferometer. + +After the alignment procedure, the top interferometer should coincide with with spindle axis, and the lateral interferometers should all be in the horizontal plane and intersect the spheres' center. ** Fine Alignment of reference spheres using interferometers <> -Thanks to the good alignment of the two reference spheres with the spindle axis and to the fine adjustment of the interferometers orientations, the interferometer measurement is made possible during complete spindle rotation. -This metrology and 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 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. The alignment process is made by few iterations. First, the spindle is scanned and the alignment errors are recorded. -From the errors, the motion of the micro-hexapod to better align the spheres is determined and the micro-hexapod is moved. +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. -This iterative process is first perform 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). -Remaining error after alignment is in the order of $\pm5\,\mu\text{rad}$ for angular errors, $\pm 1\,\mu m$ laterally and less than $0.1\,\mu m$ vertically. +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. #+begin_src matlab %% Angular alignment @@ -725,9 +735,9 @@ exportFig('figs/test_id31_metrology_align_dx_dy.pdf', 'width', 'half', 'height', 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 the $x$, $y$ and $z$ axes. -During these scans, the 5 interferometers are recorded, and the ranges in which each interferometer has enough coupling efficiency for measurement are estimated. +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. 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. +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. #+begin_src matlab %% Estimated acceptance of the metrology @@ -803,24 +813,24 @@ end ** Estimated measurement errors <> -When using the NASS, the accuracy of the sample's positioning is linked to the accuracy of the external metrology. -However, to validate the nano-hexapod with the associated instrumentation and control architecture, the accuracy of the metrology is not an issue. +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. Only the bandwidth and noise characteristics of the external metrology are important. Yet, some elements effecting the accuracy of the metrology 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). -This can be 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). +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. -They are 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 $\approx 50\,\mu m$, therefore the system is more sensitive to shape errors with small features. +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. +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 interferometer light is travelling in air, the measured distance is sensitive to any variation in the refractive index of the air. +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 a measurement length of $40\,mm$, a temperature variation of $0.1\,{}^oC$ induces an errors in the distance measurement of $\approx 4\,nm$. +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 $\approx 4\,nm$. -Finally, even in vacuum and in the absence of target motion, the interferometers are affected by noise [[cite:&watchi18_review_compac_inter]]. +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. #+begin_src matlab @@ -859,7 +869,6 @@ leg.ItemTokenSize(1) = 15; exportFig('figs/test_id31_interf_noise.pdf', 'width', 'half', 'height', 'normal'); #+end_src - #+begin_src matlab %% X-Y scan with the micro-hexapod, and record of the vertical interferometer data = h5scan(data_dir, 'metrology_acceptance', 'after_int_align_meshXY', 1); @@ -917,6 +926,8 @@ exportFig('figs/test_id31_xy_map_sphere.pdf', 'width', 'half', 'height', 'normal <> ** Introduction :ignore: + + - Force sensors: $\bm{V}_s = [V_{s1},\ V_{s2},\ V_{s3},\ V_{s4},\ V_{s5},\ V_{s6}]$ - Encoders: $\bm{d}_e = [d_{e1},\ d_{e2},\ d_{e3},\ d_{e4},\ d_{e5},\ d_{e6}]$ - Interferometers: $\bm{d} = [d_{1},\ d_{2},\ d_{3},\ d_{4},\ d_{5}]$ @@ -2498,7 +2509,7 @@ exportFig('figs/test_id31_comp_ol_iff_plant_model.pdf', 'width', 'wide', 'height :PROPERTIES: :header-args:matlab+: :tangle matlab/test_id31_4_hac.m :END: -<> +<> ** Introduction :ignore: The position of the sample is actively stabilized by implementing a High-Authority-Controller as shown in Figure ref:fig:test_id31_iff_hac_schematic. @@ -2733,7 +2744,7 @@ exportFig('figs/test_id31_comp_simscape_hac.pdf', 'width', 'full', 'height', 700 The six direct terms for all four payload conditions are compared with the model in Figure ref:fig:test_id31_hac_plant_effect_mass. It is shown that the model accurately represents the dynamics for all payloads. -In Section ref:sec:test_id31_iff_hac, a High Authority Controller is tuned to be robust to the change of dynamics due to different payloads used. +In Section ref:sec:test_id31_iff, a High Authority Controller is tuned to be robust to the change of dynamics due to different payloads used. Without decentralized IFF being applied, the controller would have had to be robust to all the undamped dynamics shown in Figure ref:fig:test_id31_comp_all_undamped_damped_plants, which is a very complex control problem. With the applied decentralized IFF, the HAC instead had to be be robust to all the damped dynamics shown in Figure ref:fig:test_id31_comp_all_undamped_damped_plants, which is easier from a control perspective. This is one of the key benefit of using the HAC-LAC strategy. @@ -3660,14 +3671,9 @@ data2orgtable([1e9*data_tomo_m0_Wz6.Dx_rms_cl, 1e9*data_tomo_m0_Wz6.Dy_rms_cl, 1 {'$m_0$', '$m_1$', '$m_2$', '$m_3$'}, {'$D_x$ [nm]', '$D_y$ [nm]', '$D_z$ [nm]', '$R_x$ [nrad]', '$R_y$ [nrad]'}, ' %.0f '); #+end_src -** Conclusion -:PROPERTIES: -:UNNUMBERED: t -:END: - -* Dynamic Error Budgeting -<> -** Introduction :ignore: +** Dynamic Error Budgeting +<> +**** Introduction :ignore: In this section, the noise budget is performed. The vibrations of the sample is measured in different conditions using the external metrology. @@ -3685,28 +3691,7 @@ The vibrations of the sample is measured in different conditions using the exter | peak 2 peak | | 200nm | 100nm | | 1.7 urad | | | RMS | | 30nm | 15nm | | 250 nrad | | -** Matlab Init :noexport:ignore: -#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) -<> -#+end_src - -#+begin_src matlab :exports none :results silent :noweb yes -<> -#+end_src - -#+begin_src matlab :tangle no :noweb yes -<> -#+end_src - -#+begin_src matlab :eval no :noweb yes -<> -#+end_src - -#+begin_src matlab :noweb yes -<> -#+end_src - -** Open-Loop Noise Budget +**** Open-Loop Noise Budget - Effect of rotation. - Comparison with measurement noise: should be higher @@ -3827,7 +3812,7 @@ linkaxes([ax1,ax2,ax3],'xy'); xlim([0.1, 5e2]); ylim([1e-10, 3e-5]); #+end_src -** Effect of LAC +**** Effect of LAC - [ ] Maybe merge this with the HAC-LAC #+begin_src matlab @@ -3896,7 +3881,7 @@ linkaxes([ax1,ax2,ax3],'xy'); xlim([0.1, 5e2]); ylim([1e-10, 3e-5]); #+end_src -** Effect of HAC +**** Effect of HAC #+begin_src matlab %% Effect of HAC @@ -4006,12 +3991,24 @@ linkaxes([ax1,ax2,ax3],'xy'); xlim([0.1, 5e2]); ylim([1e-10, 3e-5]); #+end_src + + +** Conclusion +:PROPERTIES: +:UNNUMBERED: t +:END: + * Validation with Scientific experiments +:PROPERTIES: +:header-args:matlab+: :tangle matlab/test_id31_5_experiments.m +:END: +<> ** Introduction :ignore: # - [ ] Where are different experiment explained? # - [ ] Explain which controller was used here: robust one that works for all payloads! # - [ ] All results are not filtered (i.e. 10kHz) +# - [ ] For ramp scans, a higher performance controller was used with two integrators The online metrology prototype does not allow samples to be placed on top of the nano-hexapod while being illuminated by the x-ray beam. However, in order to fully validate the NASS, typical motion performed during scientific experiments can be mimicked, and the positioning performances can be evaluated. @@ -8481,6 +8478,8 @@ Otherwise, when the limbs' lengths derived yield complex numbers, then the posit #+end_src * Footnotes + +[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 from the measurements. [fn:3]The "PEPU" [[cite:&hino18_posit_encod_proces_unit]] was used for digital protocol conversion between the interferometers and the Speedgoat diff --git a/test-bench-id31.pdf b/test-bench-id31.pdf index 5f7beb9918759a42ce4bc46cd4bd241d4d851952..e8576c874b7cb46d19df6c6673f12e962c16e4f1 100644 GIT binary patch delta 240957 zcmX`Sb97|E+P59swr$(CGqH_{t&Z(v(!s>GZQIGjP9~bzesj+EooB7S{oH zApa&Zshbstq?Ouu{`orN6n=|(K_#LF0aL!`#52kr!F}6ec-XBY(G}3EySX_MrWJ01 zWwm{_J(T5jqd=d3&ooXOG4d z64rZ&uxxy{dth%PLm^{WOhqUGs)*&h5d&?`Dy1ATXpxGV*&H@J+X}?8ZQU&**Z)iq zgm+Yr8{dJANsjCGdoQ=Xl@Qr=ya67UJ3S>Q)>IjuHMdY-emL&&a#)~- zMFnd6)cutVwoAeayAQ8^TAC+z#M<_ymrjI%8a+&l-4we?PQFNt>TPwdiFgaJ*3?=K zAG0lss<%8QT=f)bK;j2FKk34e)o*BSoYWv07@Ojz1!H(w_=8OqcN$SWVgXL-mJLcf z83}c9`f%B00m34OqQ832Z9|PIP@f$ra-cD6KVtmi&iE?ngyt7JK-sUON_Nmi=NIlT z1=*24A}GzE%uD*uKhxsZ@n$jue9dPHanC)Hg~5eJkZ3X*ezlP*KZOg=_rHxG6YLrSld8$Y(7+q+OWK1IsA2W~k@M?_J9WZmj^ZpjM zvM1jZHibZw^^!Anh64?7`;fs0QcM-4D`Xx>wRSb~WfLza#7q}Z7 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