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\input{preamble.tex}
\input{preamble_extra.tex}
\bibliography{nass-introduction.bib}
\author{Dehaeze Thomas}
\date{\today}
\title{Nano Active Stabilization System - Introduction}
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 pdftitle={Nano Active Stabilization System - Introduction},
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\begin{document}

\maketitle
\tableofcontents

\clearpage
\chapter{Context of this thesis}
\section*{Synchrotron Radiation Facilities}
\subsubsection*{Accelerating electrons to produce intense X-ray}

\begin{itemize}
\item Explain what is a Synchrotron:
\begin{itemize}
\item A particle (electrons) accelerator light source
\item Electrons produce very bright light, called synchrotron light
\item This very intense light, in the X-ray regime, is then used to study matter.
\end{itemize}
\item There are around 70 Synchrotron light sources in the world
Some of the main ones are shown in Figure \ref{fig:introduction_synchrotrons}.
This shows how useful the produced light is for the scientific community.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=\linewidth]{figs/introduction_synchrotrons.png}
\caption{\label{fig:introduction_synchrotrons}Major synchrotron radiation facilities in the world. 3rd generation Synchrotrons are shown in blue. Planned upgrades to 4th generation are shown in green, and 4th generation Synchrotrons in operation are shown in red.}
\end{figure}

There are two main parts in the Synchrotron:
\begin{itemize}
\item The accelerator where electrons are accelerated close to the speed of light
The generation of the synchrotron light is made by placing magnetic fields on the electron beam path.
These are called Insertion device or Bending magnet.
\item The beamlines where the intense X-ray beam is used to study matter
\end{itemize}
\subsubsection*{The European Synchrotron Radiation Facility}

European Synchrotron Radiation Facility (ESRF):
\begin{itemize}
\item Joint research facility situated in Grenoble, France
\item supported by 19 countries
\item Opened for user operation in 1994: World's first third generation synchrotron (i.e. integrating )
\end{itemize}

Accelerator (Schematically shown in Figure \ref{fig:introduction_esrf_schematic}):
\begin{itemize}
\item The Linear accelerator: where the electrons are
\item Booster: electrons are accelerated closed to the speed of light
\item Storage Ring: where the electrons are stored. Circumference of 844m.
\end{itemize}

Then, there are over 40 beamlines all around the storage ring:
\begin{itemize}
\item Large diversity in terms of instrumentation and science
\item Science that can be performed: structural biology, structure of materials, matter at extreme, \ldots{}
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_esrf_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_esrf_schematic} Schematic of the ESRF. The linear accelerator is shown in blue, the booster synchrotron in purple and the storage ring in green. There are over 40 beamlines, the ID31 beamline is highlighted in red}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_esrf_picture.jpg}
\end{center}
\subcaption{\label{fig:introduction_esrf_picture} European Synchrotron Radiation Facility}
\end{subfigure}
\caption{\label{fig:instroduction_esrf}Schematic (\subref{fig:introduction_esrf_schematic}) and picture (\subref{fig:introduction_esrf_picture}) of the European Synchrotron Radiation Facility}
\end{figure}
\subsubsection*{3rd and 4th Generation Light Sources}

ESRF–EBS (Extremely Brilliant Source): \cite{raimondi21_commis_hybrid_multib_achrom_lattic}
\begin{itemize}
\item In August 2020, after a 20-month shutdown, the ESRF is the first fourth-generation
\item It uses a new storage ring concept that allows increased brilliance and coherence of the X-ray beams
The brilliance (also called brightness) is figure of merit for Synchrotron.
It corresponds to \ldots{}
100x increase with the EBS
\item This new beam offers many new scientific opportunities, but also creates many engineering challenges.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_moore_law_brillance.png}
\caption{\label{fig:introduction_moore_law_brillance}Evolution of the peak brilliance (expressed in \(\text{photons}/s/mm^2/mrad^2/0.1\%BW\)) of synchrotron radiation facilities. Note the vertical logarithmic scale.}
\end{figure}
\section*{The ID31 ESRF Beamline}
\subsubsection*{Beamline Layout}

Beamline ``layout'' refers to the series of elements located in between the ``light source'' and the sample.
\begin{itemize}
\item Each beamline start with a ``white'' beam, which is just generated by the insertion device (i.e. the ``source'').
This beam has very high power (typically above kW), and is typically not directly used on the sample.
\item Instead, the beam goes through a series of optical elements (absorbers, mirrors, slits, monochromators, etc.) to filter and ``shape'' the x-ray beam as wanted.
These elements are located in several Optical Hutches as shown in Figure Figure \ref{fig:introduction_id31_oh}
\item Then, there is the Experimental Hutch (Figure \ref{fig:introduction_id31_cad}).
For some experiments (that are especially of interest here), focusing optics are used.
The sample is located on the sample stage (also called ``end-station''), as is used to position the sample with respect to the x-ray.
Detectors are used to capture the image formed by the x-ray going through the sample
\item Explain the XYZ frame for all the thesis (ESRF convention: X: x-ray, Z gravity up)
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_id31_oh1.png}
\end{center}
\subcaption{\label{fig:introduction_id31_oh1}OH1}
\end{subfigure}

\bigskip
\begin{subfigure}{\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_id31_oh2.png}
\end{center}
\subcaption{\label{fig:introduction_id31_oh2}OH2}
\end{subfigure}
\caption{\label{fig:introduction_id31_oh}Schematic of the two ID31 optical hutches: OH1 (\subref{fig:introduction_id31_oh1}) and OH2 (\subref{fig:introduction_id31_oh2}). Distance from the source (the insertion device) is indicated in meters.}
\end{figure}
\subsubsection*{Positioning End Station: The Micro-Station}

The end station on the ID31 beamline is called the ``micro-station'':
\begin{itemize}
\item It is composed of several stacked stages, shown in Figure \ref{fig:introduction_micro_station_dof}:
\begin{itemize}
\item A translation stage (blue)
\item Tilt stage (red)
\item Spindle (yellow) for continuous rotation
\item Micro hexapod (purple)
\item The sample (cyan), which can weight up to 50kg
Typically the samples are fixed inside a sample environment, to provide special environment: high pressure, low or high temperatures, high magnetic field, etc.
\end{itemize}
\end{itemize}

Presentation of the Micro-Station in details:
\begin{itemize}
\item Goal of each stage (e.g. micro-hexapod: static positioning, Ty and Rz: scans, \ldots{})
\item Stroke
\item Initial design objectives: as stiff as possible, smallest errors as possible
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.52\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_id31_station_detector.png}
\end{center}
\subcaption{\label{fig:introduction_id31_cad} Experimental Hutch}
\end{subfigure}
\begin{subfigure}{0.44\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_micro_station_dof.png}
\end{center}
\subcaption{\label{fig:introduction_micro_station_dof} Micro-Station}
\end{subfigure}
\caption{\label{fig:introduction_micro_station}CAD view of the ID31 Experimal Hutch (\subref{fig:introduction_id31_cad}). There are typically four main elements: the focusing optics in yellow, the sample stage in green, the sample itself in purple and the detector in blue. All these elements are fixed to the same granite. CAD view of the The micro-station with the associated degrees of freedom (\subref{fig:introduction_micro_station_dof}).}
\end{figure}
\subsubsection*{Example of Scientific experiments performed on ID31}

Such end station, being composed of several stacked stages, has an high mobility and allow for various scientific experiments (i.e. imaging techniques).

Two examples are here given to showcase the possibility offers by


Tomography experiment:
\begin{itemize}
\item Experimental setup illustrated in Figure \ref{fig:introduction_tomography_schematic}.
\item A sample is place on the X-ray beam, and its vertical angle is controlled using a rotation stage.
\item The detector images are captures for many different rotation angles.
\item A 3D image of the sample, such as the one shown in Figure \ref{fig:introduction_tomography_results} (taken from \cite{schoeppler17_shapin_highl_regul_glass_archit}), can then be reconstructed if the sample's point of interest stays on the beam while it is being rotated.
\end{itemize}


Mapping/Scanning experiments:
\begin{itemize}
\item Experimental setup illustrated in Figure \ref{fig:introduction_scanning_schematic}
\item Optics are used to focus the X-ray beam on the sample.
\item Then, the sample is moved perpendicularly to the beam (i.e. in the Y and Z directions)
\item Example of obtained imagine in Figure \ref{fig:introduction_scanning_results}, the position of the sample is scanned with 20nm step increments \cite{sanchez-cano17_synch_x_ray_fluor_nanop}
\item The quality/accuracy of the obtained image is directly linked to the beam size and the positioning accuracy of the sample with respect to the focused X-ray beam.
Any vibrations and drifts would blur and deforms the obtained image.
\end{itemize}


Other imaging techniques used on ID31 include reflectivity, diffraction tomography, small and wide angle X-ray scattering.

\begin{figure}[htbp]
\begin{subfigure}{0.65\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_tomography_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_tomography_schematic} Experimental setup}
\end{subfigure}
\begin{subfigure}{0.34\textwidth}
\begin{center}
\includegraphics[scale=1,height=4.5cm]{figs/introduction_tomography_picture.png}
\end{center}
\subcaption{\label{fig:introduction_tomography_results} Obtained image \cite{schoeppler17_shapin_highl_regul_glass_archit}}
\end{subfigure}
\caption{\label{fig:introduction_tomography}Exemple of a tomography experiment. The sample is rotated and images are taken at several angles (\subref{fig:introduction_tomography_schematic}). Example of one 3D image obtained after tomography (\subref{fig:introduction_tomography_results}).}
\end{figure}

\begin{figure}[htbp]
\begin{subfigure}{0.65\textwidth}
\begin{center}
\includegraphics[scale=1,scale=0.9]{figs/introduction_scanning_schematic.png}
\end{center}
\subcaption{\label{fig:introduction_scanning_schematic} Experimental setup}
\end{subfigure}
\begin{subfigure}{0.34\textwidth}
\begin{center}
\includegraphics[scale=1,height=4.5cm]{figs/introduction_scanning_picture.png}
\end{center}
\subcaption{\label{fig:introduction_scanning_results} Obtained image \cite{sanchez-cano17_synch_x_ray_fluor_nanop}}
\end{subfigure}
\caption{\label{fig:introduction_scanning}Exemple of a scanning experiment. The sample is scanned in the Y-Z plane (\subref{fig:introduction_scanning_schematic}). Example of one 2D image obtained after scanning with a step size of 20nm (\subref{fig:introduction_scanning_results}).}
\end{figure}
\section*{Need of Accurate Positioning End-Stations with High Dynamics}
\subsubsection*{A push towards brighter and smaller beams}

Thanks to the improvement of both the light source and the instrumentation, smaller and more stable beams are available.

First, the EBS upgrade allowed for a smaller source (especially in the horizontal direction) as illustrated in Figure \ref{fig:introduction_beam_3rd_4th_gen}.

\begin{figure}[htbp]
\begin{subfigure}{0.69\textwidth}
\begin{center}
\includegraphics[scale=1,height=1.6cm]{figs/introduction_beam_3rd_gen.png}
\end{center}
\subcaption{\label{fig:introduction_beam_3rd_gen}$3^{rd}$ generation}
\end{subfigure}
\begin{subfigure}{0.29\textwidth}
\begin{center}
\includegraphics[scale=1,height=1.6cm]{figs/introduction_beam_4th_gen.png}
\end{center}
\subcaption{\label{fig:introduction_beam_4th_gen}$4^{th}$ generation}
\end{subfigure}
\caption{\label{fig:introduction_beam_3rd_4th_gen}View of the ESRF X-ray beam before the EBS upgrade (\subref{fig:introduction_beam_3rd_gen}) and after the EBS upgrade (\subref{fig:introduction_beam_4th_gen}). The brilliance is increased, whereas the horizontal size and emittance are reduced.}
\end{figure}

\begin{itemize}
\item At the start of the ESRF, spot sizes for micro-focusing were in the order to \(10\,\mu m\) \cite{riekel89_microf_works_at_esrf}.
\item Since then, lots of developments were perform to decrease the spot size, whether using Zone plates, Mirrors or Refractive lenses \cite{barrett16_reflec_optic_hard_x_ray}.
\item Each with their advantages and drawbacks.
\item Such evolution is illustrated in Figure \ref{fig:introduction_moore_law_focus}
\item Today, spot size in the order of 10 to 20nm FWHM are common for specialized nano-focusing beamline.
\end{itemize}

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_moore_law_focus.png}
\caption{\label{fig:introduction_moore_law_focus}Evolution of the measured spot size for different hard x-ray focusing elements. CRL, KB, FZP, MLL. Adapated from~\cite{barrett24_x_optic_accel_based_light_sourc}}
\end{figure}
\subsubsection*{New Dynamical Positioning Needs}

\begin{itemize}
\item Higher brilliance / flux density => ``Radiation damage''.
\item This is especially true for high energy beamlines such as ID31.
\item This means that the focused beam should not be kept on the sample for long period of time with the risk of damaging the sample.
\end{itemize}

Two solutions:
\begin{itemize}
\item Traditional way of performing experiments, illustrated in Figure \ref{fig:introduction_scan_step}.
The sample is positioned as wanted, the detector acquisition (i.e. ``photon integration'') starts, and then a beam shutter is opened for a short period of time to avoid radiation damage.
Then it goes to the next position, and this process is repeated.
This process can takes of lot of time when high resolution is wanted.
\item An alternative is to perform what is called \emph{fly-scan} of \emph{continuous-scan}, \cite{xu23_high_nsls_ii}.
This is illustrated in Figure \ref{fig:introduction_scan_fly}.
As the sample undergoes continuous movement, the detector is triggered either based on the measured position of the sample of based on the time elapsed since the start of the motion.
This allows to perform experiments much faster \cite{huang15_fly_scan_ptych} (i.e. better use of the beam time), and have potentially smaller pixel size.
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.55\textwidth}
\begin{center}
\includegraphics[scale=1,height=6cm]{figs/introduction_scan_step.png}
\end{center}
\subcaption{\label{fig:introduction_scan_step} Step by step scan}
\end{subfigure}
\begin{subfigure}{0.44\textwidth}
\begin{center}
\includegraphics[scale=1,height=6cm]{figs/introduction_scan_fly.png}
\end{center}
\subcaption{\label{fig:introduction_scan_fly} Fly scan}
\end{subfigure}
\caption{\label{fig:introduction_scan_mode}Two acquisition modes. In step-by-step mode (\subref{fig:introduction_scan_step}), the motor moves at the wanted imaged position, the detector acquisition is started, the shutter is openned briefly to have the wanted exposition, the detector acquisition is stopped, and the motor can move to a new position. In \emph{fly-scan} mode (\subref{fig:introduction_scan_fly}), the shutter is openned while the sample is in motion, and the detector is acquired only at the wanted positions, on the \emph{fly}.}
\end{figure}


Recent detector developments:
\begin{itemize}
\item Better spatial resolution, lower noise and higher frame rates \cite{hatsui15_x_ray_imagin_detec_synch_xfel_sourc}.
\item For typical scanning/tomography experiments: the detector integration time was in the order to 0.1s to 1s
\item This long integration time (i.e. averaging) effectively ``filters'' out high frequency vibration in the beam position or of the sample's position, resulting in a apparent stable beam (but having bigger apparent size)
\item With higher x-ray beam flux and lower noise in the detector, the integration time can be reduced.
Typical integration time can be in the over of 1ms, with frame rate in the order of 100Hz or more.
\end{itemize}

This has two main implications related to positioning requirements:
\begin{itemize}
\item First: need for faster scans. For a same ``pixel size'', having an integration time reduced means that the scanning velocity is increased by the same amount.
\item Second: the measurement is more sensitive to high frequency vibration.
This means that there is a need to control the position up to higher frequency, typically in the kHz range.
When performing dynamic error budgeting, the vibration needs to be integrated up to higher frequencies.
Not only the sample position need to be stable (i.e. free of drifts) with respect to the x-ray beam, it also need to be vibration-less
Combined with \emph{fly-scan} mode, this means that the position needs to be well controlled, even during scans.
\end{itemize}
\section*{Existing Nano Positioning End-Stations}
In order to highlight the specificity of the developed system:
\begin{itemize}
\item Options to tackle the need of higher accuracy and better dynamical characteristics of end-station is briefly discussed.
\item The goal is to extract specific characteristics of the developed system that puts it apart from currently developed end-station.
\end{itemize}
\subsubsection*{End-Station with Stacked Stages}

Distinction between serial and parallel kinematics: Example of an end-station with 3DoF (Dx, Dy, Rz): Figure \ref{fig:introduction_kinematics}
\begin{itemize}
\item Stack stages (serial kinematics): Figure \ref{fig:introduction_serial_kinematics}
Each DoF is decoupled and positioned by only one actuator.
This usually lead to higher mobility.
But positioning errors / guiding errors of different stages are combined, and the overall positioning accuracy may be poor.
Similarly, the stiffness (i.e dynamical performances) of the overall end-station depends on the stiffness of the individual stages in all DoF, requiring extremely stiff stages.
When too many stages are stacked up, the overall stiffness is usually poor, and dynamical performances are not great.
\item Parallel architecture: Figure \ref{fig:introduction_parallel_kinematics}
Motion induced by several actuator are combined to obtain the wanted DoF.
Theoretically, the controlled DoF are the same as the stacked stages architecture.
But in practice, motion are limited to very small strokes.
However, this has the advantage of having much higher stiffness, and therefore better dynamical performances.
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_serial_kinematics.png}
\end{center}
\subcaption{\label{fig:introduction_serial_kinematics} Serial Kinematics}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_parallel_kinematics.png}
\end{center}
\subcaption{\label{fig:introduction_parallel_kinematics} Parallel Kinematics}
\end{subfigure}
\caption{\label{fig:introduction_kinematics}Two positioning platforms with \(D_x/D_y/R_z\) degrees of freedom. One is using serial kinematics (\subref{fig:introduction_serial_kinematics}), while the other uses parallel kinematics (\subref{fig:introduction_parallel_kinematics})}
\end{figure}

Most of end-station, because of the wanted high mobility, are composed of stacked stages.
In such case, their positioning performance solely depends on the accuracy of each of the individual stages.

To have acceptable performance / stability:
\begin{itemize}
\item A limited number of high performances stages, such as air bearing spindles, are used \cite{riekel10_progr_micro_nano_diffr_at}
\item Extremely stable hutch temperature, while wanted stability usually reached only after several days without intervention in the hutch \cite{leake19_nanod_beaml_id01}
\end{itemize}

Two examples of such end-stations are shown in Figure \ref{fig:introduction_passive_stations}.
\begin{itemize}
\item ID16b \cite{martinez-criado16_id16b}: uses a limited number of stacked stages, and uses extremely accurate air bearing spindle for tomography experiments
\item ID11 \cite{wright20_new_oppor_at_mater_scien}: Spindle, XYZ stage for scanning purposes and small hexapod used for pre-positioning
\end{itemize}

But when many degrees of freedom are wanted, the overall accuracy and stability usually does not allow (or maybe is making working with nano-focused beam very difficult) for experiments with a nano-beam.

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_endstation_id16b.png}
\end{center}
\subcaption{\label{fig:introduction_endstation_id16b}ID16b}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_endstation_id11.png}
\end{center}
\subcaption{\label{fig:introduction_endstation_id11}ID11}
\end{subfigure}
\caption{\label{fig:introduction_passive_stations}Example of two nano end-stations without online metrology: (\subref{fig:introduction_endstation_id16b}) \cite{martinez-criado16_id16b} and (\subref{fig:introduction_endstation_id11}) \cite{wright20_new_oppor_at_mater_scien}}
\end{figure}
\subsubsection*{Online Metrology}

The idea of having an external metrology to correct for errors is not new.

Ideally, the relative position between the sample and the x-ray beam is measured.
In practice, it is not possible, but instead the position of the sample is measured with respect to the focusing optics and/or slits, providing an indirect measurement.

Several strategies:
\begin{itemize}
\item Used for know the relative position of the sample with respect to the x-ray beam.
Used during the post processing of the obtained data
\item For calibration purposes. In that way repeatable errors can be compensated.
\item For real time positioning control
For some applications, it is not only important to know the relative position of the sample with respect to the X-ray, but it is equality important to precisely control this position.
For instance, in order to keep a nano-particle on the beam while a tomography experiment is performed.
\end{itemize}

Several Sensors have been used, but mainly two types:
\begin{itemize}
\item Capacitive: \cite{schroer17_ptynam,villar18_nanop_esrf_id16a_nano_imagin_beaml,schropp20_ptynam}
\item Fiber Interferometers Interferometers: more and more used
\begin{itemize}
\item Attocube FPS3010 Fabry-Pérot interferometers: \cite{nazaretski15_pushin_limit,stankevic17_inter_charac_rotat_stages_x_ray_nanot,engblom18_nanop_resul,nazaretski22_new_kirkp_baez_based_scann}
\item Attocube IDS3010 Fabry-Pérot interferometers: \cite{holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,kelly22_delta_robot_long_travel_nano}
\item PicoScale SmarAct Michelson interferometers: \cite{schroer17_ptynam,schropp20_ptynam,xu23_high_nsls_ii,geraldes23_sapot_carnaub_sirius_lnls}
\end{itemize}
\end{itemize}

Two examples are shown in Figure \ref{fig:introduction_metrology_stations}, in which metrology systems are used ot monitor the sample's position:
\begin{itemize}
\item Figure \ref{fig:introduction_stages_wang}: X8C beamline at National Synchrotron Light Source (NSLS). Capacitive sensors are used to calibrate the errors of the rotation stage, and are used during the alignment of different images captures during a tomography experiment \cite{wang12_autom_marker_full_field_hard}.
\item Figure \ref{fig:introduction_stages_schroer}: PtiNAMi microscope at P06 beamline at DESY. Three interferometers are pointed at a ball lens (1cm in diameter) located just below the sample. The spheres allows the sample to be rotated to perform tomography experiments.
Interferometers were reported to be used for monitoring, and is planned to be further used in a feedback loop with the piezoelectric stage located just below the sample \cite{schropp20_ptynam}.
\end{itemize}

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_wang.png}
\end{center}
\subcaption{\label{fig:introduction_stages_wang} Wang}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_schroer.png}
\end{center}
\subcaption{\label{fig:introduction_stages_schroer} Schroer}
\end{subfigure}
\caption{\label{fig:introduction_metrology_stations}Two examples of end-station with integrated online metrology. (\subref{fig:introduction_stages_wang}) \cite{wang12_autom_marker_full_field_hard} and (\subref{fig:introduction_stages_schroer}) \cite{schroer17_ptynam}}
\end{figure}
\subsubsection*{Active Control of Positioning Errors}

For some applications (especially when using a nano-beam), the sample's position has not only to be measured, but to be controlled using feedback loops.

In that case, mainly three actuator types are used:
\begin{itemize}
\item Piezoelectric: \cite{nazaretski15_pushin_limit,holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,villar18_nanop_esrf_id16a_nano_imagin_beaml,nazaretski22_new_kirkp_baez_based_scann}
\item 3-phase linear motor: \cite{stankevic17_inter_charac_rotat_stages_x_ray_nanot,engblom18_nanop_resul}
\item Voice Coil: \cite{kelly22_delta_robot_long_travel_nano,geraldes23_sapot_carnaub_sirius_lnls}
\end{itemize}

In the literature, the feedback bandwidth for such end-station is rarely specificity.
It is usually slow (in the order of 1Hz), so that only (thermal) drifts are compensated.
Only recently, high bandwidth (100Hz) have been reported with the use of voice coil actuators \cite{kelly22_delta_robot_long_travel_nano,geraldes23_sapot_carnaub_sirius_lnls}.

Two examples of end-station integrating online-metrology and feedback loops are shown in Figure \ref{fig:introduction_active_stations}:
\begin{itemize}
\item Figure \ref{fig:introduction_stages_villar}: ID16a beamline at ESRF (short stroke) Piezoelectric hexapod, rotation stage, Online metrology using many capacitive sensors.
The feedback loop (between the capacitive sensors and the piezoelectric hexapod) is used to compensate for errors of the rotation stage, and also to perform accurate scans with the hexapod.
\item Figure \ref{fig:introduction_stages_nazaretski}: interferometers are used to measure the position of the sample. multi-layer Laue lenses (MLLs) are used to focus the beam down
Feedback control is used to compensate for drifts of the positioning stages.
\end{itemize}

More extensive review of end-station with feedback loops based on online metrology will be given in section [\ldots{}].
\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stages_villar.jpg}
\end{center}
\subcaption{\label{fig:introduction_stages_villar} ID16a. =KB= is the focusing optics, =S= the sample, =C= the capacitive sensors and =LM= is the light microscope}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,scale=1]{figs/introduction_stages_nazaretski.png}
\end{center}
\subcaption{\label{fig:introduction_stages_nazaretski} 1 and 2 are stage to position the focusing optics. 3 is the sample location, 4 the sample stage and 5 the interferometers}
\end{subfigure}
\caption{\label{fig:introduction_active_stations}Example of two end-stations with real-time position feedback based on an online metrology. (\subref{fig:introduction_stages_villar}) \cite{villar18_nanop_esrf_id16a_nano_imagin_beaml}. (\subref{fig:introduction_stages_nazaretski}) \cite{nazaretski17_desig_perfor_x_ray_scann,nazaretski15_pushin_limit}}
\end{figure}

For tomography experiments, correcting for guiding errors of the rotation stage is of primary concern.
Two approaches can be used:
\begin{itemize}
\item Having the stage used for correcting the errors below the Spindle. \cite{stankevic17_inter_charac_rotat_stages_x_ray_nanot,holler17_omny_pin_versat_sampl_holder,holler18_omny_tomog_nano_cryo_stage,villar18_nanop_esrf_id16a_nano_imagin_beaml,engblom18_nanop_resul,nazaretski22_new_kirkp_baez_based_scann,xu23_high_nsls_ii}
\item Having the stage correcting the errors above the Spindle: \cite{wang12_autom_marker_full_field_hard,schroer17_ptynam,schropp20_ptynam,geraldes23_sapot_carnaub_sirius_lnls}
In all these cases, only XYZ stages are used to compensate for the guiding errors of the spindle.
\end{itemize}

In terms of payload capabilities:
\begin{itemize}
\item All are only supported calibrated, micron scale samples
\item Higher sample masses to up to 500g have been reported in \cite{nazaretski22_new_kirkp_baez_based_scann,kelly22_delta_robot_long_travel_nano}
\end{itemize}

100 times heavier payload capabilities than previous stations with similar performances.
\subsubsection*{Long Stroke - Short Stroke architecture}

As shown in the previous examples, end-stations integrating online-metrology for nano-positioning are typically limited to only few degrees of freedom with only short stroke capabilities (in the order of \(100\,\mu m\)).

An other strategy, illustrated in Figure \ref{fig:introduction_two_stage_schematic}, is to use two stacked stages for a single DoF:
\begin{itemize}
\item A long stroke, with limited accuracy is combined with short stroke stage with good dynamical properties.
The short stroke stage is used to position the sample based on the metrology measurement, while the long stroke is performing large motion.
\end{itemize}

Such strategy is typically limited to few degrees of freedom:
\begin{itemize}
\item 1DoF as shown in Figure \ref{fig:introduction_two_stage_control_example}
\item 3DoF as shown in Figure \ref{fig:introduction_two_stage_control_h_bridge}
\end{itemize}

With such strategy, it is possible to obtain an overall stage with long stroke capability and with good accuracy and dynamical properties (brought by the short stroke stage).

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_two_stage_schematic.png}
\caption{\label{fig:introduction_two_stage_schematic}Typical Long Stroke - Short Stroke architecture. The long stroke stage is \ldots{}}
\end{figure}

\begin{figure}[htbp]
\begin{subfigure}{0.59\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_two_stage_control_example.png}
\end{center}
\subcaption{\label{fig:introduction_two_stage_control_example} Two stage control with classical stage and voice coil}
\end{subfigure}
\begin{subfigure}{0.39\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_two_stage_control_h_bridge.png}
\end{center}
\subcaption{\label{fig:introduction_two_stage_control_h_bridge} H-bridge. $y_1$, $y_2$ and $x$ are 3-phase linear motors. Short stroke actuators are voice coils.}
\end{subfigure}
\caption{\label{fig:introduction_two_stage_example}(\subref{fig:introduction_two_stage_control_example}) \cite{shinno11_newly_devel_long_range_posit}, (\subref{fig:introduction_two_stage_control_h_bridge}) \cite{schmidt20_desig_high_perfor_mechat_third_revis_edition}}
\end{figure}
\chapter{Challenge definition}
Based on the positioning requirements brought by the 4th light sources, improved focusing optics and development in detector technology, there are several challenges that need to be addressed.


Smallest beam-size foreseen to be used on ID31 is around 200nm x 100nm
\begin{itemize}
\item During the experiments, the goal is therefore to keep to point of interest of the sample on the beam
\item Therefore, the peak to peak positioning errors should be below 200nm in Dy and 100nm in Dz
\item RMS errors (/ by 6.6) gives 30nmRMS in Dy and 15nmRMS in Dz.
\item Also the tilt angle Ry error should be below <1.7urad, 250nrad RMS
\end{itemize}


As high frame rate detectors can be used, the specified position errors of the sample should hold even when taking into account high frequency vibrations.


Combined with the specificity of ID31:
\begin{itemize}
\item Build on top of the existing micro-station
\item High required mobility to be able to perform many different experiments
\item Handle large payloads (up to 50kg)
\end{itemize}


The current micro-station, while being composed of high performance positioning stages, the positioning accuracy is still limited by several effects:
\begin{itemize}
\item Backlash, play, thermal expansion, guiding imperfections, \ldots{}
\item Give some numbers: straightness of the Ty stage for instance, change of \(0.1^oC\) with steel gives x nm of motion
\item Vibrations
\item Possibility to have linear/rotary encoders that correct the motion in the considered DoF, but does not change anything to the other 5DoF
\end{itemize}

Typically, the final position accuracy is around 10um and 10urad.

The goal of this project is therefore to increase the positioning accuracy of the micro-station to fully exploit the new beam and detectors.
\subsubsection{The Nano Active Stabilization System Concept}

In order to address the new positioning requirements, the concept of the Nano Active Stabilization System (further referred to as the ``NASS'') is proposed.

It is composed of mainly four elements (Figure \ref{fig:introduction_nass_concept_schematic}):
\begin{itemize}
\item The micro station (in yellow)
\item A 5 degrees of freedom metrology system (in red)
\item A 5 or 6 degrees of freedom stabilization platform (in blue)
\item Control system and associated instrumentation (in purple)
\end{itemize}

It therefore corresponds to a 5 DoF vibration control platform on top of a complex positioning platform that correct positioning errors based on an external metrology.
That way, the goal is to improve the positioning accuracy of the micro-station from \textasciitilde{}10um to less than 100nm, while keeping the same mobility and payload capabilities.

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_nass_concept_schematic.png}
\caption{\label{fig:introduction_nass_concept_schematic}The Nano Active Stabilization System concept}
\end{figure}
\subsubsection{Online Metrology system}

As the position of the sample is actively controlled based on the measured position, the accuracy of the NASS depends on the accuracy of the metrology system.

Such metrology system should:
\begin{itemize}
\item Measure the sample's position along 5 DoF (only the rotation along the vertical axis is not measured)
\item Ideally measure the position with respect to the focusing optics
\item Long stroke, as the micro-station as high mobility, compatible with the spindle continuous rotation
\item Have an accuracy compatible with the positioning requirements
\item High bandwidth
\end{itemize}

Initial Concept:
\begin{itemize}
\item A spherical reflector with flat bottom is fixed just under the sample
\item The center of the sphere coincide with the focused point of the X-ray
\item Fiber interferometers are pointed both on spherical surface and on the bottom flat surface.
\item A tracking system (tip-tilt mechanism) is used to keep the beam perpendicular to the mirror surface: Spherical mirror with center at the point of interest => No Abbe errors
\end{itemize}

In that case:
\begin{itemize}
\item XYZ positions can be measured from at least 3 interferometers pointing at the spherical surface
\item Rx/Ry angles are measured from at least 3 interferometers pointing at the bottom flat surface
\end{itemize}

Such metrology system is a complex mechatronics system on its own.
This metrology system is not further discussed in this thesis as it is still under active development.
In the following of this thesis, it is supposed that the metrology system is accurate, and high bandwidth.

\begin{figure}[htbp]
\centering
\includegraphics[scale=1]{figs/introduction_nass_metrology.png}
\caption{\label{fig:introduction_nass_metrology}2D representation of the NASS metrology system.}
\end{figure}
\subsubsection{Active Stabilization Platform}

The Active stabilization platform, located in between the sample and the micro-station should:
\begin{itemize}
\item Be able to move the sample in 5 DoF (the vertical rotation is not controlled)
\item Have good dynamical properties such that the sample's position can be controlled up to high frequency
\item Be capable to control the position down to nanometers.
It should therefore be free of play, backlash.
Low level of vibration should be induced by the active parts of the platform (such as actuator noise).
\item It should accept payloads up to 50kg.
\end{itemize}

A good candidate for the active platform is the Stewart platform:
\begin{itemize}
\item Parallel architecture, capable of controlling the motion in 6DoF
\item Very popular for positioning and vibration control applications
\item Many different designs, in terms of geometry, actuators, sensors and control strategies
Figure \ref{fig:introduction_stewart_platform_piezo}
\end{itemize}

\textbf{Challenge}: Optimally designing such active platform

\begin{figure}[htbp]
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stewart_du14.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_du14}PZT based, for positioning purposes}
\end{subfigure}
\begin{subfigure}{0.49\textwidth}
\begin{center}
\includegraphics[scale=1,width=0.95\linewidth]{figs/introduction_stewart_hauge04.png}
\end{center}
\subcaption{\label{fig:introduction_stewart_hauge04}Voice coil based, Cubic architecture, for vibration isolation}
\end{subfigure}
\caption{\label{fig:introduction_stewart_platform_piezo}Example of Stewart platforms. (\subref{fig:introduction_stewart_du14}) \cite{du14_piezo_actuat_high_precis_flexib} and (\subref{fig:introduction_stewart_hauge04}) \cite{hauge04_sensor_contr_space_based_six}}
\end{figure}
\subsubsection{MIMO robust control strategies}

The NASS also includes feedback control:
\begin{itemize}
\item from the measured position of the sample using the online metrology
\item from the wanted position of the sample (based on the wanted motion of each of the micro-station stages)
\item the active platform is controlled in real time to stabilize the sample's position, compensating for all the errors of the micro-station stages, thermal drifts, etc.
\end{itemize}

When feedback control is being used, attention should be made on the stability of the feedback loop.
This is especially important in the context of a beamline application, as the instrument should be able to 24/7 with minimum intervention.
That is why most of end-stations are based on well-proven design (stepper motors, linear guides, ball bearing, \ldots{}).

This need for robust feedback control is there made difficult due to:
\begin{itemize}
\item Many different configurations (tomography, Ty scans, slow fast, \ldots{})
\item Rotation aspect, gyroscopic effects, actuators are rotating with respect to the sensors
\item The variety of payloads that will be used, with masses ranging from 1kg to 50kg.
Typically, high performance position feedback controllers are working with calibrated payloads (lithography machines, AFM, \ldots{})
Being robust to change of payload inertia means larger stability margins and therefore less performance.
\item For most of end-stations, the top stages (for small stroke scans) as well as the sample are quite light compared to the long stroke stages.
This way, the short stroke stage dynamics is not coupled to the dynamics of the stages bellow.
In the NASS case, the payload's mass may be one order of magnitude heavier than the mass of the long stroke top platform.
This induce a high coupling between the active platform and the micro-station.
This there may lead to a MIMO system with more complex dynamics and more coupling.
\item This translates in change on the plant dynamics.
The feedback controller therefore need to be robust against plant uncertainty, while providing the wanted level of performance.
\end{itemize}
\subsubsection{Predictive Design / Mechatronics approach}

\begin{itemize}
\item The performances of the system will depend on many factors:
\begin{itemize}
\item sensors
\item actuators
\item mechanical design
\item achievable bandwidth
\end{itemize}
\item Need to evaluate the different concepts, and predict the performances to guide the design
\item The goal is to design, built and test this system such that it work as expected the first time.
Very costly system, so must be correct.
\item \textbf{Challenge}:
\begin{itemize}
\item Proper design methodology
\item Have accurate models to be able to compare different concepts
\item Converge to a solution that gives the wanted level of performance
\end{itemize}
\end{itemize}
\chapter{Original Contributions}
In order to address the challenges associated with the development of the Nano Active Stabilization Systems, this thesis proposes several original contributions in the fields of Control, Mechatronics Design and Experimental validation.
\subsubsection{6DoF vibration control of a rotating platform}

Long stroke / short stroke architectures are usually limited to 1DoF or 2DoF.
It is here extended to 6DoF.

The active platform will not only compensate for errors of the rotation stage, but also of all other stages.

To the author's knowledge, the use of a continuously rotating stewart platform for vibration control has not been proved in the literature.
\subsubsection{Mechatronics design approach}

For the design of the NASS, a rigorous mechatronics design approach was conducted.

\cite{dehaeze18_sampl_stabil_for_tomog_exper,dehaeze21_mechat_approac_devel_nano_activ_stabil_system}

While not new, this approach is here applied from start to finish:
\begin{itemize}
\item From first concepts using basic models, to concept validation using mode accurate models
\item Detailed design phase: models were used to optimize each individual components
\item Experimental phase: models were still found to have great use.
For instance to better understand the observed behavior, and also to optimize the implemented control strategy.
\end{itemize}

The use of dynamical models were used all along the development.

This document, being written chronologically:
\begin{itemize}
\item Make clear how each models can be useful during different parts of the project
\item Clearly show how each design decision are based on facts / clear conclusions extracted from the models
\item While the developed system is quite specific for the presented application, it shows the effectiveness of this design approach
\end{itemize}

I hope this document can make a small contribution in the adoption of the mechatronics approach for the design of future end-station and synchrotron instrumentation.
\subsubsection{Multi-body simulations with reduced order flexible bodies obtained by FEA}

One of the key tool that were used

Combined multi-body / FEA techniques and experimental validation on a Stewart platform containing amplified piezoelectric actuators
Super-element of amplified piezoelectric actuator / combined multibody-FEA technique, experimental validation on an amplified piezoelectric actuator and further validated on a complete stewart platform

While not new:
\begin{itemize}
\item Experimentally validated with both an amplified piezoelectric actuator as well as a flexible joint
\item It proved to be a very useful tool for the design/optimisation of components that have to be integrated in a larger system
\item Believed to be quite useful for the development of future mechatronics instrumentation
\end{itemize}

Subject of one publication \cite{brumund21_multib_simul_reduc_order_flexib_bodies_fea}
Further detailed in Section [\ldots{}].
\subsubsection{Control Robustness by design}

One of the main challenge is to design a system that is robust for all the experimental conditions:
\begin{itemize}
\item various rotational velocities used
\item payload used can weight up to 50kg
\end{itemize}

Instead of relying on complex controller synthesis (such as \(\mathcal{H}_\infty\) synthesis or \(\mu\text{-synthesis}\)) to guarantee the robustness and performance, the approach was to:
\begin{itemize}
\item Choose an adequate architecture (mechanics, sensors, actuators) such that controllers are robust by nature
\item An example is the use of collocated actuator/sensor pairs, such that controller stability can be guaranteed using passivity principles
\item To make informed choices on the chosen architecture:
\begin{itemize}
\item different ways to combine sensors (HAC-LAC, sensors fusion, two sensor control) were evaluated
\item different decoupling strategy were compared
\end{itemize}
Such discussion, presented in Section [\ldots{}] ,were found to be lacking in the literature.
\end{itemize}
\subsubsection{Active Damping of rotating mechanical systems using Integral Force Feedback}

During the conceptual design, it was found the guaranteed stability of the active damping technique called ``Integral Force Feedback'' (IFF), is lost for rotating platforms as is the case for the NASS.

To overcome this issue, two modifications of the classical IFF control scheme are proposed.
The first consists of slightly modifying the control law while the second consists of adding springs in parallel with the force sensors.
Conditions for stability and optimal parameters are derived.

\cite{dehaeze20_activ_dampin_rotat_platf_integ_force_feedb,dehaeze21_activ_dampin_rotat_platf_using}
\subsubsection{Design of complementary filters using \(\mathcal{H}_\infty\) Synthesis}

One way to combine sensors is to use ``sensor fusion''.
In such case, complementary filters are used to filter and combine the sensors.

A method for designing such filter is proposed \cite{dehaeze19_compl_filter_shapin_using_synth}, that allows to shape the complementary filters norm, which allows to guarantee the performance of the fusion.
This was latter applied for optimal sensor fusion in gravitational wave detectors \cite{tsang22_optim_sensor_fusion_method_activ}.
The design strategy is discussed in Section [\ldots{}].
The use of such complementary filters for feedback control can also lead to interesting control architecture, as discussed in \cite{verma20_virtual_sensor_fusion_high_precis_contr} and further developed in Section [\ldots{}].
\subsubsection{Experimental validation of the Nano Active Stabilization System}

The positioning performances of the Nano Active Stabilization System is experimentally evaluated/demonstrated on the ID31 beamline.

The positioning accuracy of the micro-station is effectively improved from the \textasciitilde{}10um down to \textasciitilde{}100nm while performing experiments.
Robustness to sample's mass, and different experimental conditions are also verified.

This therefore lead to a very versatile end-station, with high payload capabilities and nano-meter accuracy, allowing for full exploitation of the x-ray beam and associated instrumentation.

To the author's knowledge, this is the first time such active platform is used to improve the accuracy of a positioning stage in 5DoF.
\chapter{Thesis Outline - Mechatronics Design Approach}
This thesis is organized:
\begin{itemize}
\item to follow the mechatronics development approach, i.e. it is chronologically written.
\end{itemize}

The three chapters corresponds to the three mains parts of the proposed mechatronics approach.
A brief overview of these three chapters is given bellow.
\subsubsection{Conceptual design development}

\begin{itemize}
\item Talk about dynamic error budgeting
\item Talk about used model
\end{itemize}

The goal of this first chapter is to find a concept:
\begin{itemize}
\item that will provide the wanted performances with high level of confidence
\item As such system is costly, a mechatronics design approach is used \cite{monkhorst04_dynam_error_budget} to be able to design the system ``right the first time'':
\begin{itemize}
\item When the system is finally build, its performance level should satisfy the specifications.
\item No significant changes are allowed in the post design phase.
\item Because of this, the designer wants to be able to predict the performance of the system a-priori and gain insight in the performance limiting factors of the system.
\end{itemize}
\end{itemize}

To do so:
\begin{itemize}
\item Dynamical models are used, with included disturbances, feedback architecture, etc..
These models can be used to perform simulations, evaluate performances
\item General idea is to start with very simple models, that can easily be understood (mass-spring-damper uniaxial model)
\item Increase the model complexity if important physical phenomenon are to be modelled (cf the rotating model)
\item Only when better understanding of the physical effects in play, and only if required, go for higher model complexity (here multi-body model)
\end{itemize}

To better understand the performance limitations, for different models, \emph{dynamic error budgeting} \cite{monkhorst04_dynam_error_budget,okyay16_mechat_desig_dynam_contr_metrol} are performed.
It consists of:
\begin{itemize}
\item Disturbance and noise signals are modeled by their spectral content, i.e. by their power spectral density (PSD)
\item The effect of each error sources on the final error, while the feedback control is active, can be easily estimated
\item Therefore, the effect that have the greatest impact on the achievable performance can be easily spotted and improved
\item Different concepts can be compared
\item This tool is therefore key in better understanding the main limitations, and guide the determination of the best concept, early in the project.
\end{itemize}

This chapter concludes with accurate time domain simulations of a tomography experiment, validating the developed concept.
\subsubsection{Detailed design}

\begin{itemize}
\item In the second chapter, the chosen concept can be design in more details.
\item First, the architecture and geometry of the active platform is optimized.
\item Then, key components of the active platform, such as the flexible joints and the actuators, are optimized using the combined multi-body / FEA design approach.
\item This allowed to optimize the components using very accurate models (thanks to FEA), while still being able to integrate these components in the complete multi-body model of the NASS for time domain simulations.
\item Different aspects of the control of the NASS, such as the optimal use of multiple sensors integrated in the active platform, the best adapted decoupling strategy and the design of the robust controller, are then discussed.
\item The requirements for all the associated instrumentation (digital to analog converters, analog to digital converters, voltage amplifiers, relative motion sensors) are chosen based on dynamic error budgeting.
Using such approach, it was made sure that none of these instrumentation will limit the overall performance of the system.
\item This chapter concludes with a presentation of the final design of the active platform.
\end{itemize}
\subsubsection{Experimental validation}

After converging to a detailed design that give acceptable performance based on the models, the different parts were ordered and the experimental phase began.

Instead of directly assembling the active platform and testing it on the ID31 micro-station, a systematic approach was followed to characterize individual components.
\begin{itemize}
\item Therefore, actuators and flexible joints were individual characterized.
This allowed to update the model of these components, and obtained a more accurate model of the active platform
Systematic validation/refinement of models with experimental measurements
\item Actuators and flexible joints were combined to form the active ``struts'' of the active platform.
These struts are also characterized
\item Once the active platform were assembled, its dynamical model were found to over a very good match with the measured dynamics.
\item This chapter conclude with the experimental tests on the ID31 micro-station of the complete NASS.
\item Various scientific experiments are performed, such as tomography, and with various payload masses, to access the performances of the final system.
\end{itemize}
\printbibliography[heading=bibintoc,title={Bibliography}]
\end{document}
