Jiaqiang Huang

Xile Han

Fu Liu

Charlotte Gervillié

Laura Albero Blanquer

Tuan Guo
email: tuanguo@jnu.edu.cn

Jean-Marie Tarascon
email: jean-marie.tarascon@college-de-france.fr

Monitoring battery electrolyte chemistry via in-operando tilted fiber Bragg grating sensors

Introduction

Batteries are essential energy storage devices in the transition from fossil fuel towards sustainable energy 1 . Their rapid market growth driven by the increasing popularity of electric vehicles raises concerns about their sustainability. Besides securing recycling 2 , extending the lifetime of batteries and ensuring their second life become increasingly critical for enhancing their greenness. To meet such objectives, accurate monitoring of their state of health becomes a must 3 .

Considerable efforts have been placed in the quest for new diagnostic techniques 4 beyond the use of current and voltage or the positioning of a few thermal probes in the latest electric vehicles. Generic lithium-and sodium-ion batteries consist of two electrodes immersed in a liquid electrolyte. Nowadays, numerous techniques can operando track batteries in real working conditions by monitoring heat flow via the isothermal calorimetry 5 or follow the electrode cracking by either acoustic 6 or optic 7 means. In contrast, only a few can operando monitor the electrochemical stability of liquid electrolyte that mainly governs the nucleation and growth of solid electrolyte interphase (SEI), 8,9 which largely influences the lifetime of batteries [8][9][10] . Methods such as infrared spectroscopy 11 , mass spectrometry 11 , and nuclear magnetic resonance 12 provide valuable information about electrolyte decomposition. However, such techniques usually required post-mortem analysis or specific cell designs that take us away from battery operation in the real world. Recently, Dahn et al. showed that differential thermal analysis (DTA) is useful to examine the composition of electrolytes 13 but also reported how acoustic transmission mapping can in situ probe the electrolyte depletion 14,15 . Nevertheless, to be implemented in electric vehicles, these two methods still need to overcome a few challenges, such as the cumbersome DTA apparatus or the liquid coupling agent for acoustics 15 . Recently, we have been witnessing the ingress of optical fiber sensors, because of their low-invasiveness, smallness, electromagnetic immunity, and insulator nature, as promising candidates to study electrolyte degradation by exploiting the interaction of the light carried by the fiber with its surrounding chemical environment.

We previously demonstrated the use of fiber Bragg grating (FBG) sensors, inscribed either in single-mode fiber (SMF) or in microstructured fiber (MOF) that was placed inside a battery, to monitor changes in multiple parameters such as temperature (T) and pressure (P) in real-world conditions 4,16 with high sensitivity and space resolution 17 . However, in such a configuration, the fiber acts as a true waveguide with the traveling light being fully transparent to the fiber-surrounding environment. Nonetheless, this limitation can be bypassed by modifying the structure of the fibers to obtain either claddingetched fibers for optic evanescent wave spectroscopy 18 or hollow-core fibers with pumped electrolyte for Raman spectroscopy 19 . Besides, increasing the grating period (~500 nm to ~500 µm) and tilting the grating plane of FBGs leads to two other types of sensors called LPG for long-period grating sensing and TFBG for tilted fiber Bragg grating, respectively. Both This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins provide the advantage of coupling the core mode and the cladding modes 20,21 . Bearing in mind that the light of cladding modes is penetrating the fiber environment, LPG and TFBG are sensitive to the surrounding refractive index (RI), hence enabling their real applications in (bio-)chemical sensing [21][22][23] and their onset within the field of electrochemistry 24 such as supercapacitors 25 .

Progress in this direction is illustrated by a recent study dealing with RI measurements conducted in pouch cells via the use of an FBG sensor inscribed into the etched cladding of an optical fiber 26 . However, with this approach, several intertwined parameters (T, RI, and ε) are measured at once, hence rendering the quantification infeasible 26 . To contour this complexity and explicitly link the RI with the underlying chemistries, we decided to implement the injection of TFBGs into cylindrical cells 4 to remove the sensibility to ε. Unlike the solely peak pertaining to FBG and LPG detection, the rich features in TFBG's spectra facilitate the decoupling of multiple parameters such as T and RI. In addition, inscribed in commercial SMFs, TFBG gets rid of the intricate processes of hydrofluoric acid etching 18,26 or microstructural fiber fabrication 19 .

Herein, we explore the application of TFBG for monitoring in operando mode the electrolyte degradations of batteries. We first introduce the working principle of TFBG and its spectral characteristics in response to perturbations (RI, T, ε, and P). For proof of concept, we select studying the Na3V2(PO4)2F3/hard carbon (NVPF/HC) Na-ion electrochemistry in 18650 cells containing various electrolyte combinations. We demonstrate the capability of a single TFBG to operando monitor T and RI simultaneously inside the battery. By exploiting the timeresolved RI signals, we illustrate the feasibility of tracking electrolyte deterioration while accessing the turbidity of electrolytes as well. Lastly, we prove that TFBG-based observables are not only helpful in verifying the proposed mechanisms of SEI formation but also correlated to the cell capacity loss, thus offering additional metrics to monitor the state of health of batteries.

Results

From an experimental standpoint, the use of optical sensing and namely TFBGs is novel within the battery community; hence we decided at first to briefly recall the fundamental science beyond it together with means to calibrate, collect, read, and exploit optical signals to access various observables, prior to moving to the implementation of TFBG's sensors for in operando battery inspection. Sensing theory of TFBG Fig. 1a andb show the schematics of a FBG and a TFBG, respectively. Differing from FBG, the TFBGs' grating plane is rotated around an axis perpendicular to the fiber axis by an angle, which ensures the coupling between the single forwardpropagating core mode and a larger number of backward propagating cladding modes (dips in Fig. 1b and2a) through the phase matching relation 21,27 :

𝜆 𝑐𝑙𝑎𝑑 (𝑖) = (𝑛 𝑒𝑓𝑓 (𝑖) + 𝑛 𝑒𝑓𝑓,𝑐𝑙𝑎𝑑 (𝑖)) 𝛬/cos𝜃
(1) where 𝜆 𝑐𝑙𝑎𝑑 (𝑖) is the corresponding wavelength of the 𝑖 th order cladding mode, 𝑛 𝑒𝑓𝑓 (𝑖) is the effective refractive index of the core mode at 𝜆 𝑐𝑙𝑎𝑑 (𝑖) , 𝑛 𝑒𝑓𝑓,𝑐𝑙𝑎𝑑 (𝑖) is the 𝑖 th order cladding mode's effective refractive index, 𝛬 is the period of the interference pattern creating the grating, and 𝜃 is the tilting angle of grating planes relative to the cross section of the fiber. Upon any perturbation in the external medium's refractive index (or permittivity), these discrete cladding mode resonances shift in wavelength and/or amplitude, because the evanescent field of the cladding modes (purple arrows in Fig. 1b) can penetrate and interact with the surrounding (i.e., "Electrolyte" in Fig. 1b), enabling spatial monitoring. Meanwhile, the Bragg resonance exists for both FBG and TFBG as shown by the peak in Fig. 1a and2a, whose wavelength (𝜆 𝐵 ) is defined by

𝜆 𝐵 = 2𝑛 𝑒𝑓𝑓 𝛬/𝑐𝑜𝑠𝜃 (2)
where 𝑛 𝑒𝑓𝑓 is the effective refractive index of the core at 𝜆 𝐵 . Since the effective refractive indices ( 𝑛 𝑒𝑓𝑓 (𝑖) , 𝑛 𝑒𝑓𝑓,𝑐𝑙𝑎𝑑 (𝑖) , 𝑛 𝑒𝑓𝑓 ) of core and cladding modes together with the grating period ( 𝛬 ) are strongly dependent on T, ε, and P, the 𝜆 𝐵 is sensitive to these perturbations.

Sensitivities of TFBG to RI, T, ε, and P

A thin gold layer was coated on one end of TFBG by magnetron sputtering to obtain a sensing probe working in the reflection mode (Fig. 1b) for the read-out of an optical interrogator (si255, LUNA). To decouple the multiple perturbations sensed by TFBG, The incident light with wavelength ranging from 1,500 to 1,600 nm was injected into FBG and TFBG (black arrows in a and b). As for FBG in (a), the light was largely confined inside the fiber core, and the backward coupled core mode gives rise to a peak and a dip in reflected and transmitted spectra, respectively 21 . Turning to TFBG in (b), the light from the propagating core mode couples with the backward cladding modes (purple arrows), exhibiting numerous resonances (dips) in the collected spectrum, see the enlarged one in Fig. 2a. The evanescent field of these cladding modes can penetrate and interact with the surrounding (i.e., "Electrolyte" in b), rendering the sensitivity to surrounding refractive index.

Reflected spectrum θ

Please do not adjust margins Please do not adjust margins we firstly measured its spectrum response to a single variable parameter.

Starting from RI, the TFBG was thoroughly immersed in series of sucrose aqueous solutions ranging from 0 to 50 wt.%, and the reflection spectra were collected at 2 wt.% intervals. The refractive indices of the solutions were benchmarked by a commercial refractometer (AR200, Reichert Technologies; resolution: ±0.0001 refractive index unit (RIU)), revealing RI increases with the concentration of sucrose (Fig. S1). Fig. 2a shows spectra for a TFBG sensor in 10 wt.% sucrose solution (top) and greater sucrose contents (bottom). They all display a low-amplitude Bragg peak at the longest wavelength (Fig. 2a, red-shaded region) and tens of high-amplitude dips at shorter wavelengths. These dips are further classified into the leaky mode (Fig. 2a, grey-shaded region) and guided cladding mode (Fig. 2a, yellow-shaded region) resonances 21 , between which is the so-called "cut-off" mode 21 (~1,526 nm in Fig. 2a). The leaky modes are distinguished from the guided cladding modes by the sharp decreases in the resonance amplitudes, because their 𝑛 𝑒𝑓𝑓,𝑐𝑙𝑎𝑑 (𝑖) is lower than the surrounding refractive index so that the total internal reflection is lost 21 . As expected, by increasing the sucrose concentration (i.e., RI) in Fig. 2a (bottom), more and more resonances at shorter wavelengths are suppressed in amplitude, namely, become leaky. To Please do not adjust margins Please do not adjust margins examine the wavelength shifts, we selected two sucrose concentrations (14 and 30 wt.%) and zoomed in one dip at ~1,550 nm together with the Bragg resonance in Fig. 2b. The dip shifts its wavelength by 213 pm, because the evanescent field penetration of the cladding mode (into the surrounding media) goes up from 14 to 30 wt.% sucrose concentration, leading to the increase of 𝑛 𝑒𝑓𝑓,𝑐𝑙𝑎𝑑 (𝑖) and 𝜆 𝑐𝑙𝑎𝑑 (𝑖) in eqn (1). On the contrary, the Bragg resonance remains invariant with RI in Fig. 2b and thus can be used as a stable power and wavelength reference 19 . Therefore, we use the wavelength separation (Fig. 2b andc) between the cladding and Bragg resonances 27 to monitor RI rather than the solely cladding wavelength. Fig. 2c further shows wavelength separations of three different resonances in response to RI. Interestingly, the wavelength separations vary with RI (in response range, shaded regions in Fig. 2c) and remain constant after a specified RI (unshaded data in Fig. 2c). The constancy of wavelength separations is associated with the transition from the guided to leaky mode, as discussed in Fig. 2a.

An immediate question is how to select the appropriate resonance for RI measurement. Two criteria matter: the working range and the sensitivity. For example, in one measurement, the RI of electrolyte varies between 1.38 and 1.39 RIU, that is, the working range (dashed rectangle in Fig. 2c).

To have a response within the working range, we can directly exclude the 1,540-nm resonance in Fig. 2c because of its response range below 1.38 RIU. Next to select the proper resonance from the remaining ones in Fig. 2c, we examined their sensitivities in the working range via dividing the shift in wavelength separation by the RI change, namely, -18.0 (-0.180/0.01) and -6.5 (-0.065/0.01) nm RIU -1 for 1,550-and 1,560-nm resonances, respectively. For better sensitivity, the 1,550-nm resonance was eventually chosen. In this case, given the 1-pm accuracy of the interrogator, we expected a RI resolution of |(1 pm) / (-18 nm RIU -1 )|, namely, 6×10 -5 RIU.

To interrogate the TFBG's response to T, a TFBG was placed into an oven, and the temperature was changed from 10 to 60 o C with a step of 10 o C and a rest time of 4 hours in each step. The collected spectra, once thermal equilibrium was achieved, are shown in Fig. S2. They show a redshift of the resonances with temperature (Fig. S2b). Moreover, the thermal sensitivity (kT) linearly increases with the wavelength in the range of 9.2 and 10.1 pm o C -1 (Fig. S2d). Though usually ignored 27 , the wavelength separation grows slightly and linearly with the temperature (Fig. 2d, <1 pm o C -1 ), which we will consider in this work.

We also examined the responses of TFBG to ε and P (Fig. S3 andS4), see details in Methods. The wavelengths redshift and blueshift in response to ε and P, respectively. Among these two perturbations, the rate constant response of ε (kε) increases with wavelength (Fig. S3d), leading to the increase of wavelength separation with ε (Fig. S3e). On the contrary, we could not spot a clear trend of the rate constant response to P (kP) as a function of wavelength (Fig. S4d) within the 20-bar range (the limit of the safety device of 18650 cells); hence the effect of P will be excluded from our data analysis.

T and RI dynamics in 18650 cells unravelled by TFBG

We inserted the TFBG sensor into the central void of the jelly roll of NVPF/HC 18650 cells 4 (Fig. 3a), thus removing the sensibility to ε. Consequently, having excluded the effect of both ε and P, changes in the collected spectra will be from now on ascribed to variations of T and RI. For proof of concept, we started with the simplest electrolyte formula, 1 M NaPF6 in dimethyl carbonate (denoted as "NaPF6/DMC"), which was injected through the same hole that for the sensor (Fig. 3a). Fig. 3b shows the voltage profile (top) and the TFBG spectrum evolution (middle and bottom) during the first charge at C/10. Distinguishable amplitude and wavelength changes are seen in the enlarged contour (Fig. 3b, bottom). For example, towards the end of charge, the resonance amplitude at 1538.8 nm decreases together with the wavelength redshift at 1541 nm. To further visualize the spectrum evolution, we evenly selected five points (Fig. 3b, scatters) and presented their spectra in Fig. 3c andd. Amplitude changes of leaky modes together with the wavelength shifts of guided cladding modes are clearly seen, implying the RI variation of electrolyte upon the charging process.

To decrypt the information hidden in the signals, we firstly calculated T (Fig. 3e, top) from the Bragg wavelength shifts (∆λB) by T = T0 + ∆λB/kT (with T0 being the oven temperature (25 o C) and kT being the thermal sensitivity in Fig. S2c, black), because the Bragg resonance is immune to RI change (Fig. 2b). For decoding RI, we then selected a cladding mode according to two criteria (the working range and the sensitivity) as discussed previously. The wavelength separations of the cladding were measured as done in Fig. 2b. To avoid the possible drifts of TFBG (Fig. S5a), we mimicked the procedure of the commercial refractometer (i.e., calibration against distilled water before measurements) and corrected the TFBG against the RI of pristine electrolyte. Namely, the wavelength separations were corrected to ensure the measured RI by the TFBG before charging is equal to the electrolyte's RI given by the commercial refractometer. This correction method is described in detail and tested in Fig. S5. We thus obtained the corrected wavelength separation (Fig. 3e, middle). We further removed the minor variation of wavelength separation due to temperature (Fig. 2d) and calculated the RI (Fig. 3e, bottom, black line) according to the established calibration curves as shown in Fig. 2c. However, besides the intrinsic temperature dependence of TFBG, the RI itself is also influenced by temperature 28,[START_REF] Snyder | Refractive indices and densities of aqueous solutions of invert sugar[END_REF] , pressure 28 , and composition of the electrolyte [START_REF] Snyder | Refractive indices and densities of aqueous solutions of invert sugar[END_REF] . To gain the desired composition information of electrolyte, we thus measured the temperature coefficient of RI (dRI/dT) of the electrolyte (Fig. S6, see details in Methods), namely, -6.85×10 -4 RIU o C -1 for NaPF6/DMC, and removed the T-induced RI change (Fig. 3e, bottom, purple line) by RI' = RI -(T -T0)*dRI/dT. Regarding the pressure, we cannot experimentally measure the pressure coefficient of RI (dRI/dP) of the electrolyte but found that the dRI/dP of liquids (benzene, carbon tetrachloride, and water) 28 ranges typically from 1×10 -5 to 5×10 -5 RIU bar -1 . Considering the pressure of <5 bar inside the cell 4 , we neglected the dRI/dP afterward. Consequently, the changes of RI' (Fig. 3e, bottom, Please do not adjust margins Please do not adjust margins purple line) stems mostly from the electrolyte composition evolution.

We further examined the repeatability of TFBG measurements in the first two formation cycles (Fig. 3f, shadings for error bars). While the time-resolved voltage and T profiles deliver negligible error bars (Fig. 3f, top and middle, shadings), the RI' results manifest considerate error bars in the first charge (Fig. 3f, bottom, shading). Surprisingly, the significant error bars of RI' immediately decrease after the cell resting period, implying that its origin is most likely nested in kinetics-or diffusion-driven issues rather than in an experimental artefact, and this is confirmed by the negligible error bars of RI' as seen in other electrolyte combinations (Fig. 5a). To challenge further the capability of TFBG, we performed Probing degradation and turbidity of electrolyte via TFBG Fig. 4a shows the temporal voltage profile and the TFBG spectra during the GITT test. Surprisingly, the cell's voltage could not go above 3.25 V (Fig. 4a, top) when resting steps of 4 hours were used, while we can reach 4.25 V in galvanostatic cycling (Fig. 3f, top). Such a difference is the result of copious electrochemically driven decompositions previously reported 8 . This is

Please do not adjust margins

Please do not adjust margins accompanied by a dramatic change in the TFBG spectrum contours after ~30 hours (Fig. 4a, bottom). Looking into the spectra every 10 hours (Fig. 4b andc), the amplitudes of most of the cladding resonances simultaneously decrease after ~30 hours. This response is different from the gradual RI change in liquid solutions (Fig. 2a, 3c, 3d, and S7) but rather similar to the presence of particles on the cladding [START_REF] Liu | [END_REF] , for example, by taking a TFBG from a sucrose solution to air with some sucrose remains (Fig. S7). Therefore, the dramatic amplitude changes in Fig. 4b and c likely pertain to the excessive depletion of dimethyl carbonate (DMC) and the subsequent precipitation of solid particles such as by-products, which could then enter the evanescent field of TFBG or even be deposited on the cladding.

To verify this hypothesis, we utilized the scanning electron microscope (SEM) together with energy-dispersive X-ray spectroscopy (EDX) mapping for the fibers before and after the GITT test. Visibly, some materials, which were rich in Na, P, F, and O, etc., were deposited on the fiber after the test (Fig. S8). This motivates us to find a measurable that reflects the turbidity of electrolytes via the particulates near the TFBG's cladding while being transparent to the change in RI. We found that the peak-to-peak amplitude of a guided cladding mode (A, Fig. 4d ande) meets this RI-immune condition (Fig. S9). Thus, A that solely manifests the photonic energy loss due to the scattering or absorption of particles was taken as the metric reflecting the turbidity of electrolytes. However, for easier comparison, A is further normalized to the pristine amplitude (A0, before electrochemical tests) as A A0 -1 .

Bearing this in mind, we collected the TFBG spectra from two cells and extracted the time-resolved T, RI', and A A0 -1 (Fig. 4f). The periodic voltage patterns are spotted at ~3.1 V (dash rectangle), indicating repeated redox processes. Meanwhile, the peaks in temperature suggest intense exothermic chemical reactions as expected when cells are activated. Besides, the A A0 -1 rapidly approaches zero upon these repeated redox processes, implying the severe saturation of solid particles in the electrolyte. Interestingly, the patterns are absent in the galvanostatic charge in Fig. 3f, implying the critical role of the 4hour rest with respect to the SEI, in agreement with our previous study reporting soluble SEI in NaPF6/DMC electrolyte 8 . We thus inferred that with the additional 4-hour rest, the severe dissolution of SEI could not prevent the continuous degradation of the electrolyte, hence by the same token, the formation of solid particles was detected by TFBG.

To further understand the decomposition mechanism of DMC, we recalled the proposed reduction pathways of DMC 8 in Fig. 4g and prepared the DMC-based solutions saturated with by-products (sodium methoxide, sodium methyl carbonate, and dimethyl oxalate). We measured their RI (Table S1) and found that the additions of saturated sodium methoxide or sodium methyl carbonate slightly decreased the RI by <2×10 -4 RIU, while it is increased by ~1.9×10 -2 RIU with dimethyl oxalate. These results suggest the possible formation of dimethyl oxalate (and sodium methoxide) through Route I (Fig. 4g) when RI increases, for example, after the 2 nd -4 th titrations between 3.0 and 3.2 V in Fig. 4f. To further explore whether the monitoring of RI can help to determine the occurring reaction pathway, we mimicked the two reaction routes in Fig. 4g. Namely, we prepared artificially "degraded" electrolyte solutions by replacing DMC with the required amount of either sodium methoxide + dimethyl oxalate or sodium methyl carbonate + sodium carbonate that are formed in GITT cells after each step assuming that all the passed electrons are used for electrolyte decomposition through Route I and Route II, respectively (Note S1 and Fig. S10). Interestingly, the as-prepared "degraded" electrolytes give RIs of ~1.3750 and ~1.3650 RIU at 25 o C, corresponding to Routes I and II (Fig. 4g), respectively, which indicates that among the previously reported electrolyte decomposition pathways, Route I is most likely because we measured an RI of 1.3739 RIU for our electrochemical cells. The Route I is further confirmed by the ex situ FT-IR spectra showing the formation of sodium methoxide and dimethyl oxalate (Fig. S11). Besides, it is worth mentioning that the visualized turbidity of the "degraded" electrolytes (Fig. 4g andS10) is consistent with the suppressed resonance amplitudes in Fig. 4b and the vastly reduced A A0 -1 after the test in Fig. 4f.

Generalization to other electrolytes and implication for capacity loss

TFBG's sensors were next injected in various 18650 Na-ion cells filled with other electrolyte formulae, including 1 M NaPF6 in ethylene carbonate (EC) and DMC (v.:v. = 1:1) with 3 wt.% vinylene carbonate (VC) (denoted as "NP30+VC") and 1 M NaPF6 in EC:DMC:propylene carbonate (PC) (1:1:1 in volume) with 3 wt.% VC, 3 wt.% succinonitrile (SN), 0.5 wt.% sodium (oxalate) difluoro borate (NaODFB), and 0.2 wt.% tris(trimethylsilyl) phosphite (TMSPi) (denoted as "Magic C"). Fig. 5a shows the time-resolved voltage, T, and ∆RI' (relative to the pristine RI of the electrolytes, rather than RI' for easier comparison) of two 18650 NVPF/HC cells for each electrolyte during the 1 st cycle at C/10. The slight voltage shifts in the time scale between different electrolytes (Fig. 5a, top, arrow) manifest the presence of copious side reactions 8 . This is accompanied by the decrease in temperature signals from NaPF6/DMC to NP30+VC and Magic C (Fig. 5a, middle), implying the suppression of parasitic reactions with proper co-solvent and additives as confirmed by exploiting the dV/dQ plot in Fig. S12. Interestingly, NP30+VC and Magic C also give less ∆RI' change than NaPF6/DMC (Fig. 5a, bottom), confirming the positive attributes of additives against electrolyte degradation. At this stage, the RI' information may be further combined with the optical calorimetry 4 and the theoretical calculations of dielectric constant 31 (square of RI) to investigate the chemistries of SEI formation, but it is beyond the scope of this paper.

To further access the benefit of TFBG for cell monitoring, we plotted the charge capacity (or capacity retention), ∆RI', and A A0 -1 against the cycle number in Fig. 5b andc. During the formation cycles (Fig. 5b), as expected, NaPF6/DMC delivers the highest 1 st charge capacity and the fastest decay due to the worst SEI formation 8 . Meanwhile, from TFBG data we can deduce a dramatic increase in ∆RI' and a decrease in A A0 -1 , pertaining to the severe degradation and particle saturation in the electrolyte, respectively. Such changes in ∆RI' and A A0 -1 are reduced in NP30+VC and Magic C, which show nearly the same This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins capacities. Turning to capacity retention (Fig. 5c), NaPF6/DMC immediately loses ~15% capacity after 10 cycles, and this is accompanied by a considerable increase in ∆RI' and a decrease in A A0 -1 . The capacity retentions are similar among the other two electrolytes; however, the information from TFBG is quite different. The ∆RI' and A A0 -1 remain nearly unchanged in Magic C, while the ∆RI' of NP30+VC increases concomitantly with a gradual decrease of A A0 -1 to ~0.8, meaning the deterioration of electrolytes involving particle nucleation (i.e., the increased turbidity).

Furthermore, to know whether TFBG's observables enable to track capacity retention, we plotted independently the Please do not adjust margins Please do not adjust margins capacity loss per cycle against the changes in ∆RI' and A A0 -1 during both formation (squares) and cycling (circles) tests (Fig. 5d ande). We further exploited the data by calculating the Pearson correlation coefficient (r), see the equation in the reference [START_REF] David Freedman | Statistics[END_REF] . Remarkably, we found r of 0.97 for the ∆RI', indicating a strong correlation between the capacity loss and ∆RI'. This contrasts with the moderate relationship (r = 0.73) between the capacity loss and A A0 -1 , most likely due to the turbidity inhomogeneity. Additionally, we computed the r of cycling data from 5 th to 123 rd cycles of NP30+VC and Magic C (Fig. 5d and e, insets). We found r of 1.00 and 0.85 for ∆RI' and A A0 -1 , respectively, which according to statistical criteria [START_REF] Taylor | [END_REF] indicate that these metrics are strongly correlated to the capacity loss. Altogether, these two TFBG metrics spot different aspects, namely, electrolyte deterioration via changes in RI (Fig. 5f) and turbidity (Fig. 5g), hence providing valuable inputs for the data-driven battery management system.

) A A -1 0 Cycle number Cycling Capacity retention (%) RI' (10 -4 RIU

Discussions and conclusions

We have demonstrated that TFBG sensors can be used for simultaneous operando deciphering of temperature and electrolyte refractive index in practical 18650 Na-ion batteries under real working conditions. These sensors, that couple the core and cladding modes via a controlled tilt of the grating planes, provide a more simplified, explicit, and reproducible method to measure refractive index than the previous optical sensors relying on the inscribing of grating on cladding-etched fibers 26 . Moreover, we provide evidence that TFBG's can assess the turbidity of electrolytes while also enabling to identify the (electro-)chemical reaction pathways during the SEI formation, both of which were unattained previously. Lastly, by generalizing the methodology to a few electrolyte formulae, we unravel the strong correlations between the capacity loss and the two electrolyte observables derived from TFBG signals, providing new inputs for artificial intelligence 34 to better understand and predict cell ageing. Despite these encouraging results, we identify some weaknesses of the current TFBG methodology together with possible curing solutions, that enlists an optimization of the inscription system to minimize the response variance between sensors. This can be done at the engineering level or indirectly by machine learning algorithms on the full spectrum as presently being explored in our group. Equally, to simplify the refractive index analysis and address rapidly the possible wavelength drift, a possible approach could consist in taking a Fast Fourier Transform of the TFBG spectra 35 with a Hanning window as shown in Fig. S14. Besides, to achieve a better reliability of the data (Fig. 5e), we need to carefully control the polarization states of light by polarizer and polarization controller. Also, to tackle the concerns arising from the gold reflector, we are simultaneously optimizing the coating technique and exploring the transmission method. Finally, we have ensured the inertness of the TFBG's sensors to the targeted battery environment in terms of chemical reactivity with the presently used electrolytes by conducting SEM on the fibers (Fig. S8g,h) and examining their spectra (Fig. S15) after the tests. Nevertheless, more comprehensive studies under harsh conditions are still in need.

Overall, we present the feasibility and diversity of TFBGs to monitor the state of electrolytes in an operando way. Since each resonance responds differently to RI, T, and ε (Fig. 2c, 2d, andS3), the multiple modes of TFBG offer a viable platform to acquire at the same time multiple observables that can be decoupled. Along that line and in light of our previous work 4 , we are presently exploring to write TFBG in MOF to monitor internal pressure as a n th observable. New opportunities that combine inputs of surface plasmon resonance-based TFBG sensors with simulations and quantum calculations can also be envisioned as well for decoding delicate chemical information at the molecular scale inside the battery. The further combination with new processing innovations for simplifying the inscribing of such sensors on the fiber as well as major advance in data collection and treatment algorithms should help in realizing a "lab-on-fiber" analytical platform for field battery monitoring.

Methods

Fabrication of TFBG

Gratings were inscribed in hydrogen-loaded fiber (SMF-28, Corning) using 193 nm excimer laser (COMPexPro110), and a phase mask with pitch of 1098.19 nm. The applied energy of the excimer laser was 115 mJ with a repetition rate of 30 Hz and a scan velocity of 20 μm s -1 . During grating fabrication, we kept the phase mask and the fiber in parallel and rotated them at an angle of 16 o around the axis of the laser beam. Note that the tilted angel of 16 o were determined by our simulation package to cover the working range of electrolytes. The lengths of the grating region were ~15 mm in length, with the Bragg resonance at 1,589 nm. Finally, the sensor is specially designed with a gold mirror with a thickness of ~100 nm on the flattened fiber end by using the sputtering technique (TRI-S500, Polaron Instruments). Comparing to other metal reflectors such as silver, copper, Au layer is more stable (e.g., against oxidation) and has a high reflection coefficient near 1550 nm wavelength. Note that we carefully protected the grating region from the gold coating to elude the surface plasmon resonance 25 .

TFBG sensors in response to RI, T, ε, and P

The RI measurements of TFBGs were benchmarked by a series of sucrose (Sigma-Aldrich, BioXtra, ≥99.5%) solutions from 10 to 50 wt.%. in 2 wt.% increments in distilled water. TFBGs were immersed in the solutions without bending or strain, and the response spectra were recorded by the optical interrogator. The RIs of the sucrose solutions were measured by the commercial refractometer (AR200, Reichert Technologies; resolution: ±0.0001 RIU). To test the accuracy of TFBG together with the correction method of wavelength separation, another group of sucrose solutions (from 5 to 45 wt.% in 10 wt.% increments) was prepared, and their RIs were successively measured by the TFBGs and AR200 for comparison (Fig. S5c). Note that a reference point of the distilled water was taken prior to each measurement. While the reference correction was This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins automatically done in AR200, the calibration curves of TFBG were corrected relative to the reference point in order to remove the possible drifts arising from the environment or TFBG itself (Fig. S5). Note that we calibrated each TFBG individually.

The thermal calibrations of TFBGs were done in the oven (IPP110, Mermmet) from 10 to 60 o C with a step of 10 o C and a rest time of 4 hours in each step. The temporal spectra were recorded to investigate the thermal response of each resonance.

The ε calibration was conducted on two translation stages (XW-13-0.25, Lianyi) by fixing two ends of 10-cm fiber containing the 15-mm tilted grating region. While keeping one stage fixed, we moved the other stage by a step of 10 µm (i.e., 100 µε) until 50 µm (i.e., 500 µε), and the spectra were recorded by an interrogator (FS22SI, HBM) at each step after the strain was kept for 30 s.

The P calibration was done using a pressure chamber (length: 300 mm; inner diameter: 50 mm) filled with water. We increased the pressure from 0 to 20 bar in 2 bar increments, and we recorded the spectra by the optical spectrum analyser (AQ6370, YOKOGAWA) at each step after 30-s stabilization. A maximal pressure 20 bar was selected here, considering the pressure limit of safety device for 18650 cells.

Electrolyte preparation

NaPF6, DMC, EC, PC, VC, SN, and TMSPi were purchased from Stella, E-Lyte, Duoduo Chem, Solvionic, TCI Chemicals, Acros Organics, and TCI Chemicals, respectively. NaODFB was synthesized in our group 36 . The solvents of DMC, EC, and PC were dried in activated molecular sieves. Sodium methoxide and dimethyl oxalate were obtained from Alfa Aesar. We synthesized sodium methyl carbonate as previously reported 8 , see the Fourier-transform infrared spectroscopy (FT-IR, by Nicolet™ iS5, Thermo Scientific) and liquid-state nuclear magnetic resonance (NMR, by 7.046 T Avance III HD with a 5 mm HX(F) probe head, Bruker) results in Fig. S16.

Integration of TFBG into the 18650 cells

The NVPF/HC 18650 cells were provided by TIAMAT company, which were hermetically sealed in the dry room without electrolyte filling. An 0.8-mm hole was drilled on the center of the negative pole. The electrical resistance was checked before and after drilling to make sure that there was no short circuit. The drilled cells were subsequently dried in the glass oven (B-585, BÜCHI) under vacuum at 80 o C overnight. These cells were then transferred into the Ar-filled glove box and filled with ~5.3-mL electrolyte through the 0.8-mm hole. The TFBG was prebonded with a needle by epoxy for future reuse. The TFBG was inserted into the central void of jelly roll via the 0.8-mm hole with the grating region close to the negative pole (Fig. S17). They were then sealed by epoxy, which took 24 hours for curing. The cells with TFBGs were taken out of the glove box, installed into the homemade cabinets 4 in a temperature-controlled oven, and connected to the potentiostat and optical interrogator. The cells were kept in the open circuit for ~12 hours to reach the equilibrium state. Each batch of experiments contained two cells for reproducibility examination.

Electrochemical and optical measurements

We used the potentiostat (BCS-815, BioLogic) for the electrochemical signals. The 1C of NVPF/HC is 128 mAh g -1 based on the mass of NVPF. The voltage window was 2.00 to 4.25 V. During the 1C cycling, a constant voltage at 4.25 V was applied until the current reached C/5. We utilized the 8-channel interrogator (si255, LUNA) to record the time-resolved TFBG spectra between 1500 and 1600 nm at a rate of 30 or 60 s rather than 1 s to reduce the data amount. Note that the maximal rate of full spectrum measurement of the interrogator is 10 Hz.

Temperature coefficient of RI

The TFBG was inserted into a glass bottom containing 4-mL solutions (solvents or electrolytes) in an Ar-filled glove box. We avoided bending or strain on TFBGs to guarantee similar conditions to the calibrations. The interfaces were sealed by either rubber or epoxy for airtightness. The glass bottom with a TFBG was then taken out of the glove box and placed into a temperature control oven. We waited four hours for the system to reach thermal equilibrium and rose the temperature to 40 o C; meanwhile, the temporal TFBG's spectra were collected, which provided the real-time T and RI of the solutions. SEM For Fig. S8, the fiber after GITT was taken out from the cells by polishing the epoxy. Because the target was to examine whether there were some particulate depositions, we conducted the recovery in the air rather than a protective atmosphere. For the cleaned sample, we applied ethanol with wipes (Kimtech). Prior to being pasted on the carbon tape for SEM, those samples were coated with gold by the plasma sputtering coater (GSL-1100X-SPC-12, MTI). We used a SEM (FEI Magellan) equipped with an energy-dispersive X-ray spectroscopy (EDX) detector (Oxford Instruments).

Fig. 1

 1 Fig. 1 Concepts of FBG and TFBG. (a and b) Schematics and spectra of a FBG (a) and a TFBG (b). The grating plane of TFBG was tilted at an angle of 𝜃 with respect to the perpendicular of the fiber axis. A gold layer ("Au reflector" in b) was deposited on the end of TFBG to obtain the reflection probe (green arrows in b).The incident light with wavelength ranging from 1,500 to 1,600 nm was injected into FBG and TFBG (black arrows in a and b). As for FBG in (a), the light was largely confined inside the fiber core, and the backward coupled core mode gives rise to a peak and a dip in reflected and transmitted spectra, respectively21 . Turning to TFBG in (b), the light from the propagating core mode couples with the backward cladding modes (purple arrows), exhibiting numerous resonances (dips) in the collected spectrum, see the enlarged one in Fig.2a. The evanescent field of these cladding modes can penetrate and interact with the surrounding (i.e., "Electrolyte" in b), rendering the sensitivity to surrounding refractive index.

  0.04 pm o C -1

Fig. 2

 2 Fig. 2 Calibrations of TFBG. (a) The spectra of TFBG immersed in sucrose solutions with concentrations ranging from 10 to 50 wt.%. The top panel shows the individual spectra in 10 wt.% sucrose solution, where the leaky mode, guided cladding mode, and Bragg resonances are shaded by grey, yellow, and red, respectively. To visualize more features in the limited space, only 11 spectra are present. The grey, orange, and blue arrows indicate the three resonances in (c and d), while the black dash line corresponds to the Bragg resonance. The high-amplitude dip at 1,588 nm is called the "ghost" mode 21 . (b) The wavelength shift of a cladding resonance at ~1,550 nm in response to the sucrose concentration variation from 14 to 30 wt.%. The wavelength (λ) separations between the cladding and Bragg resonances are marked. (c and d) The wavelength separations between the Bragg and three cladding resonances at ~1,560 (blue), ~1,550 (orange), and ~1,540 (purple) nm as a function of RI (c) and T (d). Note that the RI increases with sucrose concentration. While scatters represent the raw data, the solid lines in (c and d) indicate the linear interpolation and linear regression ( with the slopes), respectively. The uncertainty of the slope in (d) is given by three standard deviations (±3σ). The region, where the wavelength separation varies with RI, is shaded as the response ranges in (c). The dashed rectangle in (c) indicates the example measurement range between 1.38 to 1.39 RIU as discussed.

Fig. 3

 3 Fig. 3 Decoding T and RI inside 18650 cells by TFBG. (a) A schematic showing the integration of TFBG into the central void of the jelly roll of an 18650 cell. (b) The temporal voltage (top), full (middle), and enlarged (bottom) TFBG spectrum contours during the first charge of an NVPF/HC 18650 cell containing NaPF6/DMC electrolyte at a current of C/10 to 4.25 V in a 25 o C oven. The green background (top) indicates the rest periods. The scatters and dash lines indicate the positions of selected spectra. (c and d) Full (c) and enlarged (d, dashed rectangle in c) TFBG spectra selected in (b) with the same colors. Similar to Fig. 2a, the grey and yellow backgrounds in (c) indicate the leaky mode and guided cladding mode resonances, respectively. The "ghost" mode in Fig. 2a is invisible here due to the TFBG fabrication. (e) The time-resolved Bragg wavelength shift (∆λB, top, left axis), T (top, right axis), the wavelength separation between the cladding at ~1,543 nm and Bragg resonances (middle), and RI (bottom) of the same cell as (b)'s. In the bottom panel, we subtracted the T-induced RI change of electrolyte (RI', purple line) from the original data (black line). (f) The temporal voltage (top), T (middle), and RI' (bottom) of two cells with NaPF6/DMC during the first two formation cycles at C/10. The average signals (lines) were calculated together with the error bars (shadings). Two cells do not provide statistically accurate error bars but roughly show the measurements' reproducibility.

  This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins galvanostatic intermittent titration technique (GITT) during the formation of cells containing NaPF6/DMC in order to assess the diffusion/reaction kinetics of electrolyte.

Fig. 4

 4 Fig. 4 Sensing electrolyte degradation and turbidity by TFBG. (a) The temporal voltage (top) and enlarged TFBG spectrum contour (bottom) during the GITT (30-min charge followed by 4-hour rest) of an NVPF/HC cell containing NaPF6/DMC electrolyte at a current of C/10 in a 25 o C oven. The voltage rises and decreases during the charge and the rest, respectively. We selected seven points (scatters, top) every 10 hours to show their detailed spectra. (b and c) Full (b) and enlarged (c, dash rectangle in b) spectra of TFBG at the selected points in (a) in the same colors. The arrow in (c) indicates the amplitude suppression of a guided cladding resonance after ~30 hours. (d and e) The definition of peak-to-peak amplitude (A) of one guided cladding resonance via the example at 0 hour. Similar to Fig. 2a, the grey and yellow backgrounds represent the leaky mode and guided cladding mode resonances, respectively. The dash lines in (d) are the envelopes of the spectrum, while the arrows indicate A. (f) The time-resolved voltage, T, RI', and A A0 -1 of two cells during the GITT test. The green background indicates the rest periods. The average signals (solid lines) were calculated together with the error bars (shadings). The periodic voltage patterns (top) are marked by a dashed rectangle. To examine the exothermic reactions, the dashed line in the T's panel indicates the oven T of 25 o C. The "1.3739 RIU" indicates the final RI of the test. (g) The proposed reduction pathways of DMC. The "1.3750 RIU" and "1.3652 RIU" corresponds to the refractive indices of artificial "degraded" electrolytes following Route I and Route II, respectively. The "RI ↑" and "RI →" indicate the RI change in comparison to the pristine NaPF6/DMC (~1.3654 RIU).

Fig. 5

 5 Fig. 5 Methodology generalization and the implication for capacity loss. (a) The temporal voltage (top), T (middle), and ∆RI' (bottom) of two cells for each electrolyte, including NaPF6/DMC (blue), NP30+VC (green), and Magic C (red), during the first formation cycle at C/10 with 6-hour rest between charge and discharge in a 25 o C oven. The average signals (lines) were calculated together with the error bars (shadings). The arrow (top) indicates the shift of voltage profiles with electrolyte additives. (b and c) The charge capacity (b, top), charge capacity retention (c, top, relative to the 5 th cycle), ∆RI' (middle), and A A0 -1 (bottom) as a function of cycle number during the formation at C/10 (b) and the cycling test at 1C (c). The charge capacities were selected to reflect the irreversibility during the first cycle. Except for NaPF6/DMC, C/10 was applied every ten cycles to access the full remaining capacity. To avoid complicating the figures with all the data, error bars are given based on the two cells' results. Dashed lines are provided as a guide to the eyes. The corresponding TFBG spectra are shown in Fig. S13. (d and e) The correlation between the capacity loss per cycle and the absolute ∆RI' (|∆RI'|) per cycle (d) or the A A0 -1 change (∆(A A0 -1 )) per cycle (e). Squares and circles represent the formation and cycling results, respectively. Note that the colors for different electrolytes are identical to (a)'s. The insets are the cycling results of NP30+VC and Magic C. The black and grey dash lines represent the linear regressions of the total and inset data, respectively. (f and g) The schematics showing the phenomena of RI change arising from the (electro-)chemical reactions (f) and the turbidity (g), corresponding to RI' and A A0 -1 , respectively.

Acknowledgements

J.-M.T., J.H., and L.A.B. acknowledge funding from the European Research Council (ERC) (FP/2014)/ERC Grant-Project 670116-ARPEMA, DIM RESPORE, and the International Balzan Prize Foundation. T. G. acknowledge funding from the Key Program of National Natural Science Foundation of China (No. 62035006) and the Guangdong Outstanding Scientific Innovation This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 11

Please do not adjust margins Please do not adjust margins Foundation (No. 2019TX05X383). We thank Tuncay KOÇ, Nicolas DUBOUIS, and Parth DESAI for their help in SEM, NMR, and dV/dQ analysis, respectively. We also gratefully thank Kaiwei LI for the valuable discussion, Zhengyong LIU and Hwa-Yaw TAM for their assistance in the pressure calibration. We appreciate the inspiring discussion on data science with Stephane MALLAT and Loic VALLANCE. We are indebted to TIAMAT for providing the NVPF/HC 18650 cells as well as Faurecia for supporting part of this work.

Author Contributions

J.H., T. G., and J.-M. T. conceived the idea and designed the experiments. X. H. and T. G. fabricated the TFBGs and conducted the strain and pressure calibrations. J. H. performed the experiments and the data analysis. F. L., T.G., and X. H. helped to interpret the optical data. J.H. and J.-M. T. wrote the paper with the inputs from all authors. C.G. and L.A.B helped to reviewed and edited the paper.

Conflicts of interest

The authors declare no competing financial interests.


Eloise Denis
email: eloise.denis@univ-nantes.fr

Jeanpierre Guédon
email: jean-pierre.guedon@univ-nantes.fr

Stéphane Beaumont
email: stephane.beaumont@qualiformed.com

Nicolas Normand
email: nicolas.normand@univ-nantes.fr

Discrete and continuous description of a three dimensional scene for quality control of radiotherapy treatment planning systems

Keywords: CT simulation, quality control, discrete and continuous description, DTO

Quality Control (QC) procedures are mandatory to achieve accuracy in radiotherapy treatments. For that purpose, classical methods generally use physical phantoms that are acquired by the system in place of the patient.

In this paper, the use of digital test objects (DTO) replace the actual acquisition. 1 A DTO is a 3D scene description composed of simple and complex shapes from which discrete descriptions can be obtained. For QC needs, both the DICOM format (for Treatment Planning System (TPS) inputs) as well as continuous descriptions are required.

The aim of this work is to define an equivalence model between a continuous description of the three dimensional (3D) scene used to define the DTO, and the DTO characteristics. The purpose is to have an XML-DTO description in order to compute discrete calculations from a continuous description.

The defined structure allows also to obtain the three dimensional matrix of the DTO and then the series of slices stored in the DICOM format. Thus, it is shown how possibly design DTO for quality control in CT simulation and dosimetry.

INTRODUCTION

Nowadays, radiotherapy and Therapy Planning Treatment have a important role for patient treatment. Thus, it is mandatory to control the quality of softwares used in this operations. Classical methods to assess the quality of Treatment Planning System (TPS), are to use physical test objects that are acquired with a CT installation by the system in place of the patient. However the quality assessment can be more accurate using digital test objects that can be analyze directly by the TPS. These DTO are transfered to the TPS in a DICOM (Digital Imaging and Communications in Medicine) format which is a discrete image format. However, it can be interesting to have a continuous description of the shapes composing the test object, in order to control dosimetric calculation for example. Thus, a structure is defined allowing an equivalence between a continuous description of the object and a discrete version of it.

Radiotherapy and quality control

Radiotherapy consists in a great ionization of cancerous cells caused by radiations. This will deteriorate the genetic information composition of the cancerous cells in order to make them unable to reproduce. It is thus necessary to deliver a maximum of proportion of ionizing x-rays to the tumor while saving the maximum of neighboring healthy tissues. In order to target the tumor and to have an accurate treatment, therapy planning treatment may be used to simulate the treatment before to treat. Is it thus conformational radiotherapy. A Treatment Planning System (TPS) computes every parameter of the treatment using a virtual patient generated by a set of transverse slices acquired with a CT scanner of the patient in treatment position. [START_REF]A Practical Guide to CT Simulation[END_REF][START_REF] Beaumont | New requirements and technology in virtual simulation[END_REF][START_REF] Beaudre | Simulation virtuelle : moyens et méthodologie[END_REF] This analyze of the virtual patient is called CT simulation. CT simulation is divided in two parts. First, there is the definition of a ballistic allowing a good target covering and the lowest irradiation for normal tissues. The second part consists of the dose distribution calculation. The first step begins with the CT scan acquisition of the patient in treatment position in order to create the virtual patient. From these dataes, various calculations are computed with or without the intervention of radiotherapist :

• The doctor contours the tumor on several slices of the CT data with manual and automatic graphic tools on the TPS graphic interface. The TPS computes the volume, the contouring on each slice from this information.

• Then, there is an automatic computation of the target volume expansion. This is done in order to consider contouring uncertainties of the radiotherapist, set-up errors that can occur during the treatment, the movements of the target (internal movements and external patient movements) and beam's penumbra,

• The TPS computes the position of the isocenter, i.e. the convergence point of all beam axis.

• The next step is the computation of each beam form and orientation for the radiation. The intersection of the beams must define the target.

• Then the TPS computes some reference points to tattoo on the patient's skin to allow a pre-positioning during the treatment, and a DRR for each beam. A Digitally Reconstructed Radiograph (DRR) is a computed-generated radiograph of the virtual patient from CT data and they are used to get the patient actual positioning for treatment. [START_REF]A Practical Guide to CT Simulation[END_REF][START_REF] Goitein | Multidimensional treatment planning: II. beam's eye view, back projection, and projection throughout CT sections[END_REF] All this procedure gives the treatment parameters. Thus, the accuracy of the treatment directly depend on the reliability of the TPS softwares. If the targeting does not fit well the tumor, some healthy tissues can be irradiated or some part of the tumor can not be removed. However, it is mandatory to control the quality of each algorithm of the TPS.

Digital Test Object

Quality assessment of TPS is classically done using phantoms i.e. Physical Test Objects (PTO). [START_REF] Mutic | Quality assurance for computed-tomography simulators and the computed-tomography-simulation process: Report of the AAPM Radiation Therapy Committee Task Group No. 66[END_REF][START_REF] Andreo | Commissioning and quality assurance of computerized planning systems for radiation treatment of cancer[END_REF][START_REF] Fraas | American Association of Physicists in Medicine Radiation Therapy Committee Task Group 53: Quality assurance for clinical radiotherapy treatment planning[END_REF] There exists a PTO for each quality criterion. [START_REF] Craig | A quality assurance phantom for three-dimensional radiation treatment planning[END_REF] For the quality assessment procedure, the PTO is put down on the scanner table and an acquisition of it is made. Like for a real patient, a 3D model is computed by the scanner and used by the TPS. The results of the various calculations and image computations from this data are analyzed and the quality of the TPS can be assess. This way to control the TPS softwares quality is skewed because the controlled system is not only the TPS but the scanner and the TPS. The phantom in input of the TPS is deteriorated by the scanner acquisition and reconstruction. Thus it is difficult to know if the default on the results are due to the TPS or to the scanner. A solution to avoid this disadvantage is to use Digital Test Objects (DTO) instead of physical phantoms. [START_REF] Denis | Digital reconstructed radiography quality control with software methods[END_REF] A phantom, or test object, is an object whose features are precisely known. It is used for input of imagery systems in order to determine the characteristics of these systems. A DTO is a 3D matrix that describes the virtual object in input of the TPS. The value of each voxel of this 3D matrix represents the Hounsfield number of the corresponding material. A DTO is composed of 3D geometrical shapes with particular density, and behaves like the CT data of a physical phantom for the TPS. The advantage is that the geometrical properties of the phantom structure are not deteriorated at the entrance of the TPS. As the objects are not physical but virtual, it is easy to create as many test objects as necessary to refine the assessment of the quality if the system. For example, a quality criterion for the DRR is the divergence of each ray. A physical phantom can present only a few divergence angles to control. [START_REF] Craig | A quality assurance phantom for three-dimensional radiation treatment planning[END_REF] A DTO can adapt to the system it controls. In the example, every needed divergence angle can be tested with a DTO. It is easy and fast to compute a new DTO with new characteristics. Thus, the quality assessment of a system can be more precise if it is done with DTOs than with PTOs because DTO can be adapted to each system. Another advantage of using DTOs for TPS quality control is that it is much faster. Indeed, using PTOs requires many CT acquisitions for each criteria (equivalent to 200 to 500 patients for a CT simulation software control) that takes much time and heats the scanner. Moreover, PTO are not easy to handle and to align with the CT and these problems do not exist with DTOs. Thus, this method makes it possible to have a precise and fast quality control of TPS, avoiding the phantom damaging by the CT scanner. This method have moreover the capacity to evolve to follow the technique and the regulations. DTO are created with a particular software and the quality assessment is managed by another specific software. DTO is transfered between these two software in a DICOM format, like a regular virtual patient, but it is important to preserve the knowledge of the geometrical structure of the object, which is lost with the DICOM format. Thus, a parallel description of the DTO geometry is mandatory.

Solid modeling

3D solid modeling became an important problem with the development of computer graphics. The aim is to obtain an accurate representation of the shape of each object in a three dimensional scene. There exists three main representations used to model solids that are used in CAD systems mostly [START_REF] Jara | About solid modeling by using feature-based models[END_REF] : Constructive Solid Geometry (CSG), Boundary representation (Brep) and spatial subdivision. CSG is a representation based on boolean operations of primitive shapes as parallelepiped, sphere, cylinder, cone and torus. Usual allowed boolean operations are union, intersection and subtraction. Rigid transformations as translation, scaling and rotation can be applied on each shape. The shapes are located on a global coordinate system but each one has its own coordinate system. Boundary representation represents the solids by their surfaces, edges and vertices. Spatial subdivision consists in decomposing the space into cells. In this representation, the space is divided according to a binary tree which defines a recursive subdivision of the 3D space. If a subdivision contains a shape, it is subdivided again until the unit cell. This way to represent the space is close to the voxel representation. CSG and Brep allow to manipulate features, contrary to spatial subdivision which does not contain any concept of feature. Hybrid representations can be defined as CSG-Boundary representation. For example, CSG can be improved with boundary representation for volume modeling in a discrete space. [START_REF] Emmerling | A system for modelling in threedimensional discrete space[END_REF] In this work by Emmerling et al., every operation and transformation are done in a discrete space representation. An extension of CSG is used : Constructive Volume Geometry (CVG) in which objects are represented by their scalar fields. [START_REF] Chen | Constructive volume geometry[END_REF] In CVG, shapes can be defined by a mathematical scalar field as well as a discrete volume dataeset. Discrete and continuous shape representations are mixed into a hierarchical structure. CSG can moreover be improved with free-form modeling tools to sculpt virtual objects. [START_REF] Boerentzen | Octree-based volume sculpting[END_REF] [START_REF] Bertrand | Border map: A topological representation for nd image analysis[END_REF] by inter-pixel surfels, lignels and pointels. Discrete surfaces can be obtained like continuous ones with a marching-cubes like algorithm. [START_REF] Daragon | Discrete frontiers[END_REF] A reversible polygonalization of these discrete surfaces is moreover defined by Sivignon. [START_REF] Sivignon | Reversible polygonalization of a 3D planar discrete curve: Application on discrete surfaces[END_REF] It is moreover possible to compute boolean operations on solids represented by their boundaries as Adams and Dutré show in their work. [START_REF] Adams | Interactive boolean operations on surfel-bounded solids[END_REF]

Boundary representation can be used for solid modeling. The most usual way to represent object boundaries is the use of polygon meshes. The shapes surfaces are composed of polygons (that are frequently triangles). These polygons are formed by connecting vertices. An other way to represent object boundaries is implicit surfaces where surfaces are defined by functions. Nurbs and Point-based modeling 15 are continuous examples of this representation. A discrete representation of surfaces is defined by Bertrand

METHODS

The aim of this work is to obtain a data structure framework to store the digital test objects in a way that there is an equivalence between a discrete and a continuous version of it. The DTO can be translated into a series of DICOM files like a series of CT slices, but the same description leads to a unique continuous description of the three dimensional scene that will be exploited with assessment purposes.

The XML format used to store the DTO with its structure characteristics is now described. Then, the file structure describing a DTO is explained. Finally the method to obtain a discrete version of a DTO from its continuous description is shown in the last part of this section.

XML format

Extensible Markup Language (XML) is a text format derived from SGML (Standard Generalized Markup Language). It is a World Wide Web Consortium standard. [START_REF]World Wide Web Consortium[END_REF] XML is not a language but a meta-language which is used to create flag languages that can be used to describe all kinds of structured data and texts. Every XML user can define his own flags and create his own structure language. That represents an obvious interest to use this format to describe DTOs since a rigid structure can be created specially for our needs in terms of medical imaging quality control.

An XML file is structured in "elements" using "tags" which mark the beginning and the end of each element. An element can contain text or other elements. The whole XML document data is contained in a single element called "root". Each element can have attributes in order to precise its contents.

The structure of an XML file can be formally described. A simple text data structure is defined into a DTD (Document Type Definition) which is associated with the type of file. A more complex structure of data of multiple nature is defined in a XML Schema Description (XSD). A XSD file is a XML file and can be manipulated like any other XML file. This structure definition file allows for specifying each data type contained in the XML file. This point is important for a geometry definition because it is mandatory to check if each parameter is really an integer or a float, or any other type of data.

Another advantage of using a XML format to describe DTO lies in the fact that its extensive uses have changed the databases format and access.

Defining a DTO with the specific XML format

A specific XML format was designed to describe DTOs. This format is divided into two parts. The first one contains general data on the three dimensional scene and the second one contains a description of each geometrical shape forming the DTO. The two parts are XML elements and are children of the root element "DTO".

General data of the DTO

The first part contains all data of the DTO that is not a geometrical shape. This information is mandatory to convert the DTO in DICOM RT format. [START_REF]Digital Imaging and Communications in Medicine (DI-COM)[END_REF] The DICOM format not only contains an image but information about the patient and the treatment. The 3D volume of the virtual patient is described by a series of DICOM 3 files. In addition, the DICOM format for radiotherapy (RT) is composed by three types of files : RT-Image, RTstructure and RT-Plan. DRRs are stored in RT-image files. General and geometrical information about patient and virtual patient are to be find in this file. RT-structure files contain informations on outlined structures and skin-marking, and RT-Plan files contain all beams parameters for the treatment. All the information required for DICOM RT is stored in this XML file part , like for instance slice thickness, space between slices and image resolution.

Geometrical data of the DTO

The second part of the XML file contains the geometrical structure of the DTO. The DTO three dimensional scene is made up of 3D shapes of different densities i.e. the Hounsfield number of the material they represent. The shapes can be combined to make more complex shapes. Thus they have to be ordered in a structure. The easiest way to do it is to arrange them into a tree whose root is the DTO itself. The tree leaves are primitives forms. The nodes of the tree are combinations of shapes. The tree nodes are combinations of shapes. A node contains an operator and the operands are the children of the node. It is thus possible to generate complex shapes from primitives and from other complex shapes. Each node or leave is a shape intervening in the construction of the test object. They consequently have an associated density. This density is an attribute of the node. For a complex shape, the densities of operand shapes are not taken into account but only that of the node representing the combination of shapes. Each shape, complex or primitive, can undergo transformations. Transformations are operations on a shape that modify it. They are attributes of shapes nodes (leaves or not) in the tree.

Only few primitives are mandatory to design a DTO for radiotherapy TPS quality control. Each shape has a reference point that allows to locate it in the 3D oriented space. Before any transformation, the reference point of a primitive is centered on the origin. The shapes are referred by their name which is noted as an attribute of the node.

Parallelepiped The first primitive shape is a parallelepiped. Initially, its edges are parallel with the axis of the coordinate system. The reference point of this primitive is the corner with the smallest coordinate in every direction. Only three parameters are thus necessary to define a parallelepiped : the three dimensions on each direction. These dimensions are constrained to be integers in order to make it easier to have a discrete description of the shape.

Ellipsoid

The second available primitive shape is en ellipsoid. It is defined from three radii. The radii are the lengths along each axis of the coordinate system. If they are equal, the shape is a sphere. The reference point of this primitive is its center.

Conical frustum with elliptic base

The last primitive shape is a conical frustum with elliptic base. A conical frustum is a truncated cone created by slicing the top of the cone with a cut made parallel to the base. The cone is only defined by two radii. Thus, its base is not necessarily circular but can be elliptic. This primitive is defined by its height (constrained to be integer in order to make it easier to have a discrete description of the shape), the two radii of the first base and one radius for the second (the second radius can be deduced proportionally from the three others). If these four radii are equal, the shape becomes a cylinder. The reference point of this shape is the center of the first base. The first base is the one with the smallest coordinate in the coordinate system. It is possible to combine primitive shapes in order to obtain complex shapes. Three shapes operations are available : intersection, union and subtraction. A complex shape can be a combination of primitives or of already computed complex shapes. It is possible to combine primitive shapes in order to obtain complex shapes. Three shapes operations are available : intersection, union and subtraction. A complex shape can be either a combination of primitives or of already computed complex shapes. A shape can undergo some rigid transformations. Available transformations are translation and rotation. No homothety is available because it is not useful in DTO design. Even complex shapes can undergo transformations. Translations are made along the coordinate system axis with integer values. Rotations are made around the axis of the coordinate system with the origin as an invariant point. They are written down in degrees in the XML file. Rotations and translations do not commute. A rotation depends on an invariant point. A shape can rotate around the origin or around its own point of reference. The chosen method for shape rotation is to center it on the origin of the coordinate system. If the rotation is computed before any translation, the shape rotates around its reference point. Thus a first rotation is allowed on shapes before any translation. This is not sufficient to design DTOs. 1. This permits to have shapes at exactly the same distance of a given point (that can be the isocenter during quality assessment). Thus the shape elements of the XML file contain two series of rotation attributes : the first one, which is applied before translations, is named "rotIntern" and the second, which is applied after translations, is named "rot".

It is interesting to have a rotation after a translation in order to obtain a circle of shapes (for contrast resolution of DRR computation control for example) as shown in figure

An example of DTO structure can be seen at figure 2. This DTO can be used to control the divergence of ray casting in DRR computation in the same way as Craig et al. phantom.

Shapes discretization

When the DTO is translated into a series of DICOM files, the continuous description of the 3D scene is converted into a three dimensional matrix. Thus each voxel of the 3D matrix must correspond to one and only one shape in order to attribute a value to the voxel. For sake of simplicity, voxels are consider as a uniform unit volume. Hence, they belong to a shape or not, but they do not belong partially to it. For that purpose, the voxels of the DTO are traversed and for each voxel a value, or shape membership must be determined.

The center of the voxel whose value is being determined has discrete coordinates in the 3D space. The method consists on traversing the tree that contains the shapes and looking for each node if the voxel belongs to the shape. A shape can be included into another one. Thus, the way to traverse and construct the tree is important. The route is made in the width of the tree. If a shape is included into another, it must be encountered in a second time during the route. In this way, the value of the voxel will be the one of the included shape. Thus, it is mandatory to have some function determining if a voxel belongs to a shape or not. For a complex shape, its subtree should be studied as follows: For a complex shape, its subtree should be studied as follows:

• if the shape is a union between two shapes, the voxel belongs to it if it belongs to almost one subtree shape,

• if it is an intersection, the voxel belongs to the shape if it belongs to the two shapes of the subtree,

• if it is a subtraction, the voxel belongs to the shape if it belong to the first subtree shape and not to the second one.

Primitives discretization

It is quite easy to determine if a voxel belongs to a parallelepiped or not. Parallelepiped were constrained to have integer dimensions and they are aligned with the discrete grid. They are forced to have an integer number of voxels in each direction for an obvious sampling (it is also easy to know if a voxel belongs to a parallelepiped if there are no rotation apply on it).

To know if a voxel belongs to an ellipsoid, it is necessary to calculate the distance between the center of the ellipsoid and the voxel. If this distance is inferior to the radius (in a direction), the voxel belongs to the shape. Two questions comes up. The first one is about the choice of the distance that must be used. A discrete distance like the Chamfrein distance is useful for distance map calculation. It is not here interesting to have such properties. The most appropriated distance is the Euclidean distance. Accordingly to the ellipsoid equations, a point belongs to an ellipsoid if:

(x -x 0 ) 2 R x 2 + (y -y 0 ) 2 R y 2 + (z -z 0 ) 2 R z 2 ≤ 1, (1)
where x, y and z are the point coordinates, x 0 , y 0 and z 0 the ellipsoid center coordinates, R x is the length along the X-axis, R y is the length along the Y-axis and R z is the length along the Z-axis. The second question is about the choice of the point coordinate to represent the voxel. Does a voxel must be considered in the ellipsoid if only a part of it verify the equation 1 or if the whole volume that it describes verify this equation? There are two opposite cases: the farthest voxel's point from the center of the ellipsoid is taken for the distance calculation in equation 1 or the nearest voxels point from the center is taken. In the first case, the volume of the discrete ellipsoid will be decreased compared to the volume of the continuous ellipsoid and in the second case, the discrete volume will be increased. An intermediate solution is to take the center of the voxel to refer it. Thus, x, y and z in equation 1 are the voxel center coordinates.

Determining if a voxel belongs to a conical frustum is done in two steps. A conical frustum primitive is constrained to have an axis parallel to the Z-axis of the coordinates system. Thus, this shape can be seen like a stack of ellipse. The height of the shape is forced to have an integer value. So, it has an exact number of voxels along the height. The discrete shape can be define like a stack of discrete ellipse. The 3D problem of discretization is thus reduced to a series of 2D discretizations. If the Z-coordinate of the voxel corresponds to a discrete ellipse of the conical frustum, the voxel belongs to the shape if the distance to the center of the ellipse is inferior or equal to the radius. As the the ellipsoid case, the Euclidean distance is chosen and the center of the voxel is taken as the voxel reference point. Thus, accordingly to the ellipse equations, a point belongs to an ellipse if:

(x -x 0 ) 2 R x 2 + (y -y 0 ) 2 R y 2 ≤ 1, (2)
where x and y are the center of the voxel coordinates in the plane (X, Y ), x 0 and y 0 the ellipse center coordinates in the plane (X, Y ), R x is the length along the X-axis, R y is the length along theY-axis.

Transformations

Translation are constrained to be along the axis of the coordinates system and with integer values. Thus, they do not influence the discretization problem. Rotations give shapes that are not necessary aligned with the discrete grid. . To know if a voxel of a DTO belongs to a shapes that underwent transformations, the method is to considerate the coordinate of the center of this voxel, and apply to it the inverse transformations in the opposite order. New coordinates are obtained and the voxel belongs to the shape if the new point belongs to the continuous shape (see 2.3.1). In homogeneous coordinates, geometrical transformations are computed by matrix multiplication. Let R 1x , R 1y and R 1z the rotation matrices for the first rotation, T the translation matrix and R 2x , R 2y and R 2z the rotation matrices for the first rotation. If they are applied to the shape in this order, the new point coordinates are :

⎛ ⎜ ⎜ ⎝ x y z 1 ⎞ ⎟ ⎟ ⎠ = R . ⎛ ⎜ ⎜ ⎝ x y z 1 ⎞ ⎟ ⎟ ⎠ (3)
where x, y and z are the center of the voxel coordinates, x , y and z are the new coordinates and R is defined in equation 4 :

R = R -1 2z R -1 2y R -1 2x T -1 R -1 1z R -1 1y R -1 1x . (4)
This method to constrain many parameters to have integer values can not permit a precise shape construction. However, the voxel size (in millimeters) is require to translate the scene in DICOM format. Thus, to have a more precise shape definition, it is just necessary to reduce the voxel size.

RESULTS

In this part, a very simple DTO is presented in order to illustrate the method of DTO description. The chosen DTO is a simple phantom that can be used to control the beam divergence in digital reconstructed radiograph computation. A DRR is a virtual radiograph of the virtual patient. For each pixel of the resulted digital image, a ray is casted from the center of the pixel to the source in the 3D matrix of the virtual patient. Along this ray, the theoretical ray attenuation by the crossed materials is calculated. The rays are casted in a cone beam geometry. Thus it is mandatory to control the divergence of this cone beam. This divergence can be controlled with a phantom that contains a shape with the same divergence as the beam one.

The DTO that illustrates the work is made accordingly. It is not a final DTO but a very simple one that show the way a DTO can be build in TPS quality control. This DTO is composed of a hollowed out conical frustum with an ellipsoid base (which is a divergent shape). This phantom can be used calculating a DRR of it positioning the beam source at the top of the cone used to build the frustum. If the the beam of the DRR computation is perfect, only a thin ellipse is seen in the resulted DRR. If not, the stroke is thicker. The conical frustum does not have a circle base but an ellipsoid one. Thus, many divergence angles can be tested.

The DTO is made of a complex shape for the divergence shape and a small sphere representing the isocenter (see 2). The complex shape is a subtraction between two conical frustums. Both have a height of 151 voxels (along Z-axis). The radii of the principal basis of the first frustum are 100 (along X-axis) and 50 (along Y-axis) (the unit is the length of a voxel edge). The radius along X-axis for the second basis is 50, and the radius along Y-axis that is calculated from the three other ones is 5. The second conical frustum is a little thinner. Its radii are 98 (along X-axis) and 49 (along Y-axis) for the principal basis, and 9 (along X-axis) and 4.5 (along Y-axis) for the second basis. By subtracting the second frustum from the first one, the complex shape for the divergence control can be obtained. The density of this shape is 1024, in Hounsfield number.

The DTO is named DivergenceDTO and its size is 256 × 256 × 256 voxels. A series of parameters allows to locate the DTO in the 3D space coordinate system. Each voxel is a unit cube whose sides are one millimeter length. Each corresponding CT slice is one voxel width and zero voxel between each. Consequently, there will be 256 slices for this DTO. The background density of this DTO is -1024, in Hounsfield number. The software to convert the DTO in DICOM files allow an image storage onto 12 or 16 bits. The XML tag "storage" specify which option to choose for the DICOM conversion. Then, a description of the DTO is stored in the XML file. This describe the procedure to control a quality criterion with this phantom and how the result should be. Follows a series of tags specific to DICOM format requirements.

The following XML file is obtained from the previous DTO specifications: DTO <ellipsoid name="isocenter" density="1024" rotInternX="0.0" rotInternY="0.0" rotInternZ="0.0" transX="0" transY="0" transZ="0" rotX="0.0" rotY="0.0" rotZ="0.0"> <dimension> <dimX>1.0</dimX> <dimY>1.0</dimY> <dimZ>1.0</dimZ> </dimension> </ellipsoid> <complex name="divergence shape" density="1024" rotInternX="0.0" rotInternY="0.0" rotInternZ="0.0" transX="0" transY="0" transZ="-75" rotX="90.0" rotY="0.0" rotZ="0.0"> <operation>Subtraction</operation> <shape1> <conicalFrustum name="conicalFrustum1" density="1024" rotInternX="0.0" rotInternY="0.0" rotInternZ="0.0" transX="0" transY="0" transZ="0" rotX="0.0" rotY="0.0" rotZ="0.0"> <dimension> <height>151.0</height> <basis1> <radiusX>100.0</radiusX> <radiusY>50.0</radiusY> </basis1> <basis2> <radiusX>10.0</radiusX> <radiusY>5.0</radiusY> </basis2> </dimension> </conicalFrustum> </shape1> <shape2> <conicalFrustum name="conicalFrustum2" density="1024" rotInternX="0.0" rotInternY="0.0" rotInternZ="0.0" transX="0" transY="0" transZ="0" rotX="0.0" rotY="0.0" rotZ="0.0"> <dimension> <height>151.0</height> <basis1> <radiusX>98.0</radiusX> <radiusY>49.0</radiusY> </basis1> <basis2> <radiusX>9.0</radiusX> <radiusY>4.5</radiusY> </basis2> </dimension> </conicalFrustum> </shape2> </complex> </DTOstructure> </DTO> A series of DICOM CT slices are computed from this DTO XML file. Three of them are presented at figure 3. These images are in conformity with the DTO description. The divergence of the shape can be checked and slices of a hollowed out ellipsoidal conical frustum can be recognized. The series of DICOM files can be transfered to the TPS in order to control the beam divergence in DRR computation.

APPLICATIONS

The target application is the quality control of radiotherapy devices. The presented framework will allows for the DTO creation, the DTO storage, the DTO experiments and the DTO results analysis without any kind of error due to the device acquisition or to the object sampling.

DTO storage for DTO creation software

The method to store 3D scene in XML format, specifically for digital test objects can be employed to store DTO during their creation in a specific software. All the information is here to translate into DICOM format to obtain all images of a virtual phantom for treatment planning systems quality assessment. A DTO can thus be modified much more easily than if it was only saved in DICOM because the geometrical structure information is recorded. For instance, if the size of a shape has to be changed in order to make the control more precise, the scene has to be created again from scratch if only the DICOM version had been stored. With the XML file, only a parameter have to be changed and the DICOM files can be easily computed.

Information for quality control tests

The software to manage the quality assessment with DTO is being developped and tested. The phantom used in input of the TPS corresponds to the DICOM version, as a series of CT slices. The role of this software is to manage the scene under test, the phantom characteristics and the computation for each test between the result of the operation made by the software under test operating onto the phantom on one side and the corresponding DTO on the other side. All these information are not stored in the DICOM slices but in the XML file.

CONCLUSION

In this paper, a description of digital test objects has been defined. This description allows for a continuous representation of the phantom and its equivalent discrete representation can be obtained. DTO's three dimensional scene were defined into a hierarchical tree structure. The leaves are primitives and the nodes correspond to complex shapes obtained by boolean operations. Rigid transformations are applied on each shapes. XML format was chosen to store this continuous description. The file is divided into two parts. The first one contains general DTO data, mostly for DICOM translation. The second part correspond to the shape definition tree. A method to obtain a discrete version of the DTO was exposed. The corresponding digital discrete phantoms can be translated into DICOM files and sent to treatment planning systems for quality control. This continuous description of digital phantoms is also adapted to translate DTOs into PENELOPE format. Indeed, a future work will be to create a platform to convert both PENELOPE continuous phantom descriptions to DICOM discrete files and, to convert discrete phantoms to PENELOPE format. The DICOM CT files do not represent a sufficient information to perform this conversion, whereas the XML DTO description is able to do it. This DTO conversion to PENELOPE format will allow to perform the dosimetric calculation quality control.

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Figure 1 .

 1 Figure 1. Example of shapes rotation. The first shape is created and duplicated seven times. Each shape is rotation with a different angle around the origin.

Figure 2 .

 2 Figure 2. Shapes tree of a DTO than can be used to control ray divergence in digital reconstructed radiograph computation.

  (a) This slice is near the beam source, thus the ellipsoid is small. (b) This slice is in the middle of the DTO. The mark for the isocenter can be seen in the center of the image.(c) This slice is far from the beam source, thus the ellipsoid is big.

Figure 3 .

 3 Figure 3. DICOM slice image of the divergence DTO.

  DTO to control divergence of ray casting in DRR computation. The beam source-isocenter distance should be 92.28 millimeters, the gantry angle should be -90 and the table angle sould be 90 for DRR computation. If the beam divergence is correct, a thin ellipsoid is drawn in the resulted DRR. If the distance between the isocenter and the projection plane is ...

		<nbVoxZ>256</nbVoxZ>
		</DTOSize>
		<DTOPosition>
		<posDTOX>-127</posDTOX>
		<posDTOY>-127</posDTOY>
		<posDTOZ>-127</posDTOZ>
		</DTOPosition>
		<slices>
		<nbSlices>256</nbSlices>
		<slicesWeight>1</slicesWeight>
		<slicesSpacing>0</slicesSpacing>
		</slices>
		<voxelSize>
		<sizeVoxX>1.0</sizeVoxX>
		<sizeVoxY>1.0</sizeVoxY>
		<sizeVoxZ>1.0</sizeVoxZ>
		</voxelSize>
		<Backgrounddensity>-1024</Backgrounddensity>
		<storage>16</storage>
		<description>(example) A </description>
		<dicom>
		<frameOfReferenceUID>1.3.6.1.4.1.5962.99.1.3395834295.18746387.1137267233207.1.0
		</frameOfReferenceUID>
		<seriesUID>1.3.6.1.4.1.5962.99.1.3395.1874.1137267233207.1.3.1.1</seriesUID>
		<studyUID>1.3.6.1.4.1.5962.99.1.3395.1874.1137267233207.1.2.1</studyUID>
		</dicom>
		</DTO_info>
		<DTOstructure>
		XML file
	%\begin{tabular}[h]{ll}
	%	\multicolumn{2}{ll}{
	%\begin{verbatim}
	<?xml version="1.0" encoding="UTF-8"?>
	<DTO>
		<DTO_info>
		<name>DivergenceDTO</name>
		<idDTO>IDDTO</idDTO>
		<creationDate>20060114</creationDate>
		<DTOSize>
		<nbVoxX>256</nbVoxX>
		<nbVoxY>256</nbVoxY>

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