# Full-spectrum fitting method applied to YAG:Dy: Impact of oxygen content and laser fluence on wall-temperature phosphor thermometry for combustion

Tobias Guivarch, Hugo Samson, Jérôme Bonnety, Jessy Elias, Sébastien

Ducruix, Clément Mirat, Christopher Betrancourt, Guilhem Dezanneau,

Ronan Vicquelin

► To cite this version:

Tobias Guivarch, Hugo Samson, Jérôme Bonnety, Jessy Elias, Sébastien Ducruix, et al. Full-spectrum fitting method applied to YAG:Dy: Impact of oxygen content and laser fluence on wall-temperature phosphor thermometry for combustion. Proceedings of the Combustion Institute, 2025, 41, pp.105845. 10.1016/j.proci.2025.105845. hal-05469686

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Full-Spectrum Fitting Method Applied to YAG:Dy :
Impact of Oxygen Content and Laser Fluence on
Wall-Temperature Phosphor Thermometry for Combustion

Tobias Guivarch<sup>a,*</sup>, Hugo Samson<sup>a,*</sup>, Jérôme Bonnety<sup>a</sup>, Jessy Elias<sup>a</sup>, Sébastien Ducruix<sup>a</sup>, Clément Mirat<sup>a</sup>, Christopher Betrancourt<sup>a</sup>, Guilhem Dezanneau<sup>b</sup>, Ronan Vicquelin<sup>a</sup>

<sup>a</sup>Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C, Gif-sur-Yvette, France

<sup>b</sup>Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire SPMS, Gif-sur-Yvette, France

**Abstract**

Achieving the European net-zero greenhouse gas emissions target requires the development of sustainable com-
bustion processes across various industrial sectors. These promising alternatives introduce new challenges, such
as modifying wall heat transfer. Accurate surface temperature measurements are essential for understanding these
effects. Laser-Induced Phosphorescence (LIP) provides a semi-invasive method that exploits the temperature-
dependent phosphorescence spectra of thermographic phosphors. YAG:Dy is a thermographic phosphor that emits
a phosphorescence signal over the range of 300 K to 2000 K. However, its poor sensitivity with the intensity ratio
method and its low sensitivity at lower temperatures with the lifetime method limit its use to high-temperature
combustion applications. Additionally, its sensitivity to ambient oxygen reduces the accuracy of those methods.
This study evaluates the performance of the Full-Spectrum Fitting (FSF) method, developed by the EM2C Labora-
tory in Lechner et al. (2022), when applied to YAG:Dy. The method leverages the phosphor's spectral temperature
dependence over a wide range (303 to 1773 K), achieving an accuracy of 0.3 K and a precision of 8.4 K under
given experimental conditions. It is observed that there is a laser fluence threshold above which temperature de-
termination using the FSF method becomes independent of laser fluence. The impact of YAG:Dy's sensitivity to
oxygen concentration on temperature measurement is quantified. In the worst case, uncertainty in oxygen concen-
tration can introduce a temperature error ranging from 7 to 19 K. Guidelines are provided to help mitigate these
sensitivities in combustion applications.

Keywords: Phosphor Thermometry; Laser Diagnostic; Oxygen effect; Laser Fluence effect; YAG:Dy; FSF method
Information for Editors and Reviewers

1) Novelty and Significance Statement

The novelty of this research is the application of the Full-Spectrum Fitting (FSF) Method — a spectral variant of Laser-Induced Phosphorescence (LIP) — to YAG:Dy thermographic phosphors, specifically examining the influence of oxygen content and laser fluence on the normalized phosphorescence spectra; additionally, X-ray diffraction (DRX) was performed on the YAG:Dy sample to determine its exact crystal structure.

The significance lies in the method's demonstrated accuracy (0.3 K) and precision (8.4 K) across a broad temperature range (303–1773 K) under controlled experimental conditions. Beyond benchmark performance, the investigation provides valuable insights into how laser fluence and oxygen content affect phosphorescence spectra and temperature determination. From these insights, practical guidelines are provided for deploying the FSF method with YAG:Dy in real-world combustion chambers, ensuring reliable thermometry while minimizing temperature determination biases.

2) Author Contributions

* TG : Performing experiments, Designing research, Analyzing data, Writing, Review and Editing.

• HS : Performing experiments, Designing research, Analyzing data, Writing, Review and Editing.

* JB : Performing experiments, Analyzing data, Designing Test bench, Writing, Review and Editing.

* JE : Designing Test bench.

* SD : Review, Editing and Acquiring Fundings.

* CM : Designing research, Analyzing data, Designing Test bench, Writing, Review and Editing.

* CB : Designing research, Analyzing data, Designing Test bench, Writing, Review, Editing and Acquiring Fundings.

* GD : Performing experiments, Designing research, Analyzing data, Review and Editing.

* RV : Designing research, Analyzing data, Writing, Review, Editing and Acquiring Fundings.
# 1. Introduction

The European Union's ambition to achieve climate neutrality by 2050 necessitates the rapid deployment of technologies capable of attaining net-zero greenhouse gas emissions. Among these, sustainable combustion processes play a crucial role in decarbonizing various industrial sectors, including transportation, energy production, and steam generation. However, promising alternatives to conventional industrial combustion methods present new challenges, such as modifying heat transfer to the walls or the load. For instance, in CH₄ or H₂ oxy-combustion, the high concentration of CO₂ and/or H₂O in the burnt gases significantly impacts heat transfer [1].

Accurate and non-intrusive surface temperature measurements are essential for assessing thermal loads in combustion chambers. Among available methods, Laser-Induced Phosphorescence (LIP) thermometry is a semi-intrusive laser diagnostic technique that leverages the temperature-dependant phosphorescence emissions of luminophore materials (thermographic phosphors). In this method, a phosphorescent coating is applied to the target surface, which, upon laser excitation, emits a phosphorescence signal that correlates with temperatures [1–3]. In the combustion community, for applications such as IC engines or gas turbines, LIP has recently attracted significant interest, beyond its semi-intrusive nature, accuracy, and ability to provide two-dimensional temperature fields [4–6].

To ensure reliable temperature measurements, LIP requires a calibration step in which the phosphorescence signal is recorded at known temperatures. Two main approaches have been developed in the literature [2, 3]: the lifetime method and spectral methods. The lifetime method is based on the temperature-dependant decay time of the phosphorescence signal [7], whereas spectral methods analyze variations in the emission spectrum. Within spectral methods, two techniques exist: the intensity ratio method [8], which evaluates intensity variations at two distinct wavelength bands, and the Full-Spectrum Fitting (FSF) method, a recently developed and applied technique at Laboratory EM2C [9, 10]. The FSF method leverages the entire emission spectrum by fitting its shape, offering improved measurements precision.

Various thermographic phosphors have been used in LIP thermometry, each with specific advantages and limitations [3]. Some phosphors exhibit sensitivity to oxygen concentration in the surrounding atmosphere [7, 11–15], particularly in lifetime-based methods. In combustion applications, and more specifically in oxy-combustion, where oxygen levels fluctuate due to the presence of burned or fresh gases, this sensitivity can introduce measurement and calibration uncertainties. Additionally, some thermographic phosphors display dependencies on laser fluence, which may affect the accuracy of LIP methods [9, 16–18]. Furthermore, different phosphors are suited for different temperature ranges, making the

selection of an appropriate thermographic phosphor crucial for reliable measurements [3].

For instance, Mg₃.₅FGeO₅:Mn, which is the only thermographic phosphor tested with the FSF method to date, is known to be insensitive to oxygen concentration [12] but presents spectral sensitivity to laser fluence [9] and becomes impractical for measurements above 1000 K due to diminished signal intensity and lifetime [1].

Conversely, Y₃Al₅O₁₂:Dy (YAG:Dy) has been widely used in high temperature environments with both intensity ratio and decay time methods at temperature exceeding 1200 K [6, 19–23]. This thermographic phosphor exhibits spectral dependence on temperature and remains detectable at high temperatures, making it a good candidate for the FSF method on a wide range of temperatures. In some studies, no effect of oxygen concentration on YAG:Dy phosphorescence has been observed [11, 21, 24], while others report an influence [7, 15]. In particular, Nilsson et al. [7] observe an increase in lifetime with higher oxygen content, whereas Ishiwada et al. [15] report the opposite. Both have shown that oxygen concentration affects both the lifetime and intensity of YAG:Dy phosphorescence. Despite this, limited information is available on the effect of oxygen concentration [15] and on the impact of laser fluence [18] on the normalized spectra of this thermographic phosphor. Understanding these effects on YAG:Dy phosphorescence spectra is crucial for ensuring the reliability and accuracy of the FSF method.

This study investigates the feasibility of using the FSF method for accurate temperature measurement based on the temperature-dependent spectral dynamics of YAG:Dy. It aims to be applied on industrial-like combustion chambers, where the steady-state temperature is generally reached over the course of several tens of minutes and where temperatures can range from ambient to 1200 K within just a few centimeters [1].

Furthermore, it examines the performance of the FSF method when applied to YAG:Dy, considering both oxygen and laser fluence dependencies.

This article is structured as follows: First, the experimental approach used in this study is presented. Next, the FSF method and its application to YAG:Dy are introduced. Finally, the effects of fluence and oxygen on temperature determination are investigated.

# 2. Experimental Approach

The thermographic phosphor (YAG:Dy) is deposited in powder form in an 70 µL AL₂O₃ crucible. This assembly is mounted in a precise thermal and atmospheric control stage and excited with a pulsed laser at 355 nm. An imaging spectrometer collects the phosphorescence spectra from $\lambda = 438$ to 612 nm at temperature varying from 303 K to 1773 K. Figure 1 displays the experimental setup as described below.
<figure><img src="image_2.png" /><figcaption>Fig. 1: Schematic diagram of the experimental set-up.</figcaption></figure>

## 2.1. Excitation source, Laser Fluence, Temperature and Atmosphere Control

A 10 Hz pulsed Nd:YAG laser (Continuum Surelite SL II-10), of 10 ns pulse duration, operating at its third harmonic 355 nm, is used as the excitation source. To achieve laser fluences ranging from 2.5 mJ/cm² to 77.5 mJ/cm², an energy attenuator (EKSMA Optics 990-0070-355) is used to adjust the output laser energy. The laser fluence is measured following the same procedure as a previous study on the FSF method [9].

The sample is mounted on a thermal and atmospheric control stage (Linkam TS1500, S-type class 1 thermocouple), which allows temperature regulation from ambient up to 1773 K. The gas environment within the stage is controlled using a flow meter (Bronkhorst F-201CV-100-AAD-33V), delivering 60 Nml/min of Air or pure N₂ (impurity level of oxygen of 5 ppm). This setup ensures precise control over both thermal and atmospheric conditions during the acquisitions.

## 2.2. Phosphorescence detection and spectra acquisition

A telescope oriented at 45° of the laser path and locked on the laser beam center is used to collect the phosphorescence signal. The telescope is composed of two two-inch achromatic lenses ($f_1=150$ mm and $f_2=100$ mm, Thorlabs AC508-150-A) [9]. The sample is positioned at the focal point of the first lens to optimize data acquisition. The collected light is then focused onto a ∅200 µm multimode optical fiber (Thorlabs TM200R5S1 A) and delivered to a spectrometer (SpectraPro-500i, 500 mm focal length, 150 grooves mm⁻¹ grating, blazed at 300 nm). With a 1.5 magnification, the phosphorescence signal is collected from an elliptic surface (275 µm minor axis, 385 µm major axis) with a homogeneous laser fluence distribution, and recorded using an ICCD camera (Princeton Instruments PI-MAX4:1024f Gen III

HRf, 1024×1024 resolution, 16-bit depth). The laser, the spectrometer and the camera are synchronized with an external delay generator (BNC Model 577, Pulse Generator). The spectra present in this work are calibrated not in intensity but in wavelength using a mercury lamp (INTCAL-WL-CALIB), using the *Broad auto-calibration mode* in LightField®. It yielded an RMS error of 0.073 nm. Spectra were sampled with a maximum spacing of 0.17 nm.

The camera settings are selected to maximize the signal-to-noise ratio (SNR) and prevent interference from other laser-induced emissions. The gain and the vertical hardware binning of the intensity are adjusted to ensure a Standard Error of the Mean (SEM) of less than 2% independently of the temperature and laser fluence.

The camera gate delay (GD) is chosen to be as close as possible to the end of the laser pulse to capture the most intense part of the phosphorescence spectra.

The duration of the phosphorescence signal of the YAG:Dy sample studied varies from 70 µs to 270 µs across explored temperature, laser fluence and oxygen content. However, YAG:Dy showed a short-lived broadband signal (Fig. 2), with its lifetime decreasing significantly as temperature increased [25]. Due to these broadband short-decay phosphorescence signals, the normalized phosphorescence spectra depend on the GD within the first 20 µs after the laser pulse. Therefore, a GD of 20 µs is selected for YAG:Dy and the choice of the camera gate width (GW) only impacts the SNR and not the levels of the normalized spectra.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Sensitivity of YAG:Dy phosphorescence spectra to gate delay at 303 K and 45 mJ/cm² with a gate width of 0.2 µs</figcaption></figure>

For the YAG:Dy database, a gate width (GW) of 15 µs is selected to achieve the best SNR preventing the camera saturation for a sample at 303 K. This choice of GW ensures a good SNR at high temperatures as well, given the relatively small variations in intensity and phosphorescence lifetime between 303 K and 1773 K [3, 7, 15].
## 2.3. YAG:Dy specifications

The thermographic phosphor studied is the Y₃Al₅O₁₂:Dy (YAG:Dy) from Phosphor Technology (QMK66/F-X 3m/o Dy).

It is known that thermographic phosphor synthesis process have an important impact on its radiative properties which makes direct comparisons with the literature challenging [12, 26]. Thus, the YAG:Dy is characterized by X-ray Diffraction (Figure 3), using an Aeris Panalytical diffractometer working with Cu Kα₁,₂ wavelength in the Bragg-Brentano geometry. Diffractograms are acquired between 10° and 90° in 2-theta with a 0.02° angular step. Analysis is performed using the Profex software [27] making use of the reference phases as found in the COD database [28].

<figure><img src="image_4.png" /><figcaption>Fig. 3: X-Ray Diffraction pattern of the YAG:Dy thermographic phosphor</figcaption></figure>

This analysis shows that the YAG:Dy sample mainly consists of an yttrium aluminium garnet phase Y₃Al₅O₁₂ (reference number cod4312142 in the COD database). The orthorhombic YAlO₃ parasitic phase (cod1533069, COD) is identified for ≈5% of mass fraction. For both phases, the refined cell parameters i.e. a = 12.009 Å for the observed Y₃Al₅O₁₂ and a = 5.182 Å, b = 5.324 Å and c = 7.375 Å for the observed YAlO₃ are very close to the cell parameters of the original reference phases, concretely a = 12.01 Å for Y₃Al₅O₁₂ and a = 5.161 Å, b = 5.301 Å and c = 7.342 Å for orthorhombic YAlO₃.

## 2.4. Database acquisition

A database is constructed from the acquisitions of single-shot phosphorescence spectra of YAG:Dy during a temperature ramp of 0.4 K/s, ranging from Tmin = 303 K to Tmax = 1773 K, at a fixed laser fluence and a controlled oxygen concentration in the surrounding atmosphere. For each database, background acquisitions are recorded using the same temperature ramp with identical camera parameters as the signal acquisitions, under the same oxygen concentration and without laser.

Each single-shot spectrum is then corrected using the corresponding background acquisition, ensuring

identical camera settings and a temperature matching within ±0.5 K as measured by the thermal stage. Every 1 K, the mean spectra are obtained by averaging 25 corrected single-shots. These mean spectra are then filtered using a third-order Savitzky-Golay smoothing filter with a 13-points moving window, and normalized to maximum intensity.

A total of 4 databases are acquired under varying laser fluences and oxygen content. Three databases are acquired in N₂ at laser fluences of Fmin = 2.5 mJ/cm², Fmid = 42.3 mJ/cm² and Fmax = 77.5 mJ/cm², and one database is acquired in Air at Fmax. The database at Fmax and N₂ will be considered as the reference database in the following.

# 3. FSF Method using YAG:Dy for thermometry

## 3.1. Method

The FSF method relies on the analysis of the dynamics of normalized spectrum from the thermographic phosphor as temperature changes. The accuracy of temperature determination critically depends on the quality of both the reference database and the acquired single-shot spectra.

With the FSF method, the computation of Tfound, corresponding to the temperature of a phosphorescence spectrum denoted as Sstudied, requires finding the closest match to a filtered, normalized reference spectrum. This is achieved by solving the following optimization problem:

$$ \min_{T \in [T_{\text{min}}, T_{\text{max}}]} \{\min_{\alpha} d(\alpha S^{\text{studied}}, S_{T}^{\text{ref}})\} \quad (1) $$

where d(·, ·) represents a distance metric between two spectra and α a coefficient of normalization.

This classification problem is solved using several distance metrics [29]. Among them, the L₂ distance and the Pearson χ² distance, which were chosen for their best performance in the case of this study, are defined as:

$$ d_{L_2}(S^{\text{studied}}, S^{\text{ref}}) = \sqrt{\sum_{\lambda} (S_{\lambda}^{\text{studied}} - S_{\lambda}^{\text{ref}})^2} \quad (2) $$

$$ d_{\text{Pearson} \chi^2}(S^{\text{studied}}, S^{\text{ref}}) = \sum_{\lambda} \frac{(S_{\lambda}^{\text{studied}} - S_{\lambda}^{\text{ref}})^2}{S_{\lambda}^{\text{ref}}} \quad (3) $$

The performance of both distance will be tested to retrieve the temperature using the FSF method on the reference database.

## 3.2. YAG:Dy use cases

The temperature-dependent evolution of YAG:Dy normalized phosphorescence spectra is displayed in Figure 4. Significant spectral variations are observed
<figure><img src="image_5.png" /><figcaption>Fig. 4: Sensitivity of YAG:Dy phosphorescence spectra to temperature at F<sub>max</sub> in N<sub>2</sub>.</figcaption></figure>

1 as a function of temperature. Although no strong vari-
ation is evident in the intensity ratio between the pri-
mary peak located around 580 nm and the secondary
peaks in the 480–500 nm region of the YAG:Dy phos-
phorescence spectra, a more pronounced difference
appears when comparing the 580 nm peak to the fea-
ture at 460 nm. The temperature sensitivity of the
YAG:Dy spectrum makes this thermographic phos-
phor a strong candidate for the FSF method.

10 A cross-validation procedure with 5-folds is per-
11 formed to estimate the statistical accuracy and stan-
12 dard deviation of the temperature deviation on the ref-
13 erence database: ΔT = T<sub>found</sub> − T<sub>recorded</sub>. In this pro-
14 cedure, all single-shots are randomly split into five
15 folds of approximately 5 per 1 K each. Four folds,
16 representing approximately 20 single-shots per 1 K,
17 are used to construct the mean-normalized spectra
18 database, while the remaining fold serves as the test
19 set. This process is rotated across all folds, resulting
20 in five iterations. The estimated temperature devia-
21 tion obtained from each test fold are aggregated in
22 Figure 5. The left panel of this figure shows the evo-
23 lution of the mean and standard deviation of the tem-
24 temperature deviations across the full temperature range.
25 Each point corresponds to the mean and standard de-
26 viation of the deviations within ±50 K, representing
27 roughly 2,500 single shots per point. The right panel
28 shows the histogram of temperature deviations over
29 the entire temperature range, with the corresponding
30 summary statistics provided in the caption.

31 The histogram of Figure 5 illustrates that the Pear-
32 son χ² distance yields better results compared to the
33 L₂ distance with a sub-kelvin accuracy (0.3 K) and a
34 standard deviation below 8.4 K for the whole range of
35 temperature studied.

36 In detail, the accuracy of the temperature devia-
37 tion ΔT as a function of the recorded temperature re-
38 mains constant around zero while the evolution of the
39 standard deviation slightly increase with the recorded
40 temperature. These results are of particular interest
41 considering that, over the broad temperature range,
42 they correspond to a remarkably low relative error.
43 The Pearson χ² distance is used in the following to

44 retrieve the temperature with the FSF method.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Effects of distance metric on temperature deviation ΔT with the reference database at F<sub>max</sub> in N<sub>2</sub>. ΔT/L<sub>2</sub> = -1.8 K, σ<sub>ΔT,L<sub>2</sub></sub> = 12.5 K, and ΔT/χ<sup>2</sup> = 0.3 K, σ<sub>ΔT,χ<sup>2</sup></sub> = 8.4 K.</figcaption></figure>

4. Laser Fluence and Oxygen Effects on
Temperature determination

In combustion applications, the composition of the
gas surrounding the thermographic phosphor can ex-
hibit significant spatial and temporal fluctuations in
oxygen concentration, as well as substantial laser
fluence extinction (soot particules, small gaseous
species, PAHs...). Ishiwada [15] and Nilsson et al. [7]
have shown that oxygen concentration affects both the
lifetime and intensity of YAG:Dy phosphorescence.
To the authors' knowledge, only few information ex-
ists regarding the effect of oxygen concentration [15]
and on the impact of laser fluence [25] on YAG:Dy
normalized spectra. Characterizing these effects on
normalized YAG:Dy phosphorescence spectra is es-
sential to ensure the reliability of the FSF method.

To this end, temperature determinations of single-
shot database acquired under various laser fluences
and atmospheric conditions are compared against the
reference database obtained at a laser fluence of Fmax
in an N₂ atmosphere.

4.1. *Effect of Laser Fluence*

To investigate the effect of laser fluence on the
temperature determination using the FSF method,
databases of single-shot spectra are acquired under
N₂ atmosphere at two laser fluences Fmid and Fmin re-
spectively corresponding to a 50% and 97% extinc-
tion of the laser fluence Fmax.

Figure 6 displays the comparison of the YAG:Dy
normalized spectra for the extrema of the databases
i.e. Fmid spectra vs. Fmax spectra at Tmin and Tmax with
both N₂ and Air atmosphere. In this figure, the dis-
played spectra are obtained from the average of 250
corrected single-shot spectra. In the first column, the
top graph shows two normalized spectrum obtained
at Fmin and Fmax at temperature Tmin. The evolution
<figure><img src="image_7.png" /><figcaption>Fig. 6: Normalized intensity of the YAG:Dy phosphorescence spectrum at different conditions. Gray regions correspond to normalized intensity below 0.02. Displayed spectra are obtained from the average of 250 corrected single-shot spectra.</figcaption></figure>

of the relative difference is ≥15% for the first spectral band 471–502 nm, and less than 5% on the second band 564–603 nm. At high temperatures, the bottom graph shows that the relative difference is about 12% at 439 nm and decreases linearly to reach 3% at 515 nm and less than 3% value throughout the rest of the spectrum. It is interesting to note that increasing temperature reduces the effect of laser fluence on the normalized spectra.

Figure 7 represents the temperature deviation $\Delta T$ between the temperature of single-shots acquired at $F_{\text{min}}$ or $F_{\text{max}}$ and the temperature determined by the FSF method identified using the reference database. The gray area represents the accuracy of the method as a function of temperature, as shown in Fig. 5.

The temperature deviation for single-shots at $F_{\text{min}}$ increases with temperature, reaching $\overline{\Delta T}_{F_{\text{min}}} = 84.4$ K at $T_{F_{\text{min}}} = 1650$ K, as well as the standard deviation of $\overline{\Delta T}_{F_{\text{min}}}$. As seen in the distribution of $\overline{\Delta T}_{F_{\text{min}}}$ over all temperatures shown on the right of Fig. 7, the average temperature error of the FSF method is $\overline{\Delta T}_{F_{\text{min}}} = 22.5$ K in this case.

Conversely, when single-shots acquired at $F_{\text{mid}}$ are compared to the $F_{\text{max}}$ reference database, the absolute mean and standard deviation of the temperature deviation are comparable to those obtained using both averaged signals and single-shots from the reference database cross-validated, respectively $\overline{\Delta T}_{F_{\text{mid}}} = -2.6$ K, $\sigma_{\Delta T, F_{\text{mid}}} = 10.5$ K and $\overline{\Delta T}_{F_{\text{max}}} = 0.3$ K, $\sigma_{\Delta T, F_{\text{max}}} = 8.4$ K.

This suggests the existence of a laser fluence threshold value in the FSF method for this YAG:Dy sample. This effect was already observed in [18]. Effectively, using a database done at a laser fluence well above this threshold allows the temperature determination without any bias due to uncertainties of the laser energy.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Effect of laser fluence on temperature deviation $\overline{\Delta T}$. $\overline{\Delta T}_{F_{\text{mid}}} = -2.6$ K, $\sigma_{\Delta T, F_{\text{mid}}} = 10.5$ K. $\overline{\Delta T}_{F_{\text{min}}} = 22.5$ K, $\sigma_{\Delta T, F_{\text{min}}} = 28.7$ K.</figcaption></figure>

## 4.2. Effect of Oxygen

Figure 6 displays the comparison of the YAG:Dy normalized spectra for the extrema of our databases, i.e. $N_2$ vs. Air atmosphere at $T_{\text{min}}$ and $T_{\text{max}}$ with both $F_{\text{min}}$ and $F_{\text{max}}$ laser fluences. At low temperatures on Figure 6, the bottom graph shows that the relative difference remains $\le 8\%$ on the first spectral band and $\le 4\%$ on the secondary spectral band. At high temperatures, the evolution of the relative difference shows a difference of around $\ge 3\%$ on the first spectral band, and $\le 15\%$ on the secondary spectral band. The third column illustrates that at low laser fluence, the influence of oxygen concentration in the surrounding gas is negligible. Overall, these observations indicate that oxygen primarily induces minor variations in the normalized spectra of the YAG:Dy sample.

As mentioned in Sec. 4.1 the effect of oxygen concentration on the FSF method can be observed independently of the laser fluence, as long as it is greater than $F_{\text{mid}}$. To investigate this further, a single-shot database is collected in Air at a laser fluence of $F_{\text{max}}$. This data is then evaluated using a reference database
comprised of averaged single-shot spectra recorded in an N₂ atmosphere under the same laser fluence conditions. Temperature deviations obtained with the FSF method are shown in Figure 8.

Results indicate that the mean temperature deviation increases from approximately -7 K at low temperatures to -19 K at higher temperatures. Similarly, the standard deviation of the temperature deviation rises from 4 K at low temperatures to 15 K at higher temperatures.

Results indicate that the mean temperature deviation increases from approximately -7 K at low temperatures to -19 K at higher temperatures. Similarly, the standard deviation of the temperature deviation rises from 4 K at low temperatures to 15 K at higher temperatures.

<figure><img src="image_9.png" /><figcaption>Fig. 8: Effect of oxygen on temperature deviation $\Delta T$. $\bar{\Delta T}_{Air} = -9.6$ K, $\sigma_{\Delta T,Air} = 11.1$ K.</figcaption></figure>

For air combustion system application, the uncertainty on oxygen concentration on the temperature determination by FSF method on YAG:Dy decrease acceptably the accuracy at 16 K around 1700 K and at $F_{max}$, which corresponds to the worst case scenario.

### 4.3. Guidelines for YAG:Dy FSF Method application on Combustion Chambers

This section proposes some guidelines to perform LIP measurements using YAG:Dy with FSF method in combustor.

It is important to note that the FSF method, like any other LIP thermometry method (lifetime and intensity ratio), requires prior calibration with a specific acquisition setup and a fixed thermographic phosphor sample, which must remain unchanged during temperature measurements [3]. In the case of the FSF method, the calibration consists of the creation of a database of normalized spectra for a temperature range of interest.

In the case of YAG:Dy, its normalized spectra show a dependence of laser fluence and O₂ concentration on temperature (Fig. 7 & Fig. 8). This apparent reliance necessitates the creation of multiple databases according to application needs (e.g. external or internal walls temperature measurements of a combustion chamber under rich or lean conditions). The

present results indicate the existence of a threshold fluence beyond which temperature determination becomes independent of the laser fluence used for the reference database. However, in practical applications, the medium may exhibit absorption and scattering properties. Therefore, it is recommended to select a sufficiently high laser fluence to prevent potential reductions in incident energy.

Furthermore, the results show that, when using a reference database in N₂ at a laser fluence higher than the threshold, the influence of oxygen leads to a noticeable but limited difference in precision and accuracy. To minimize temperature measurement uncertainty, it is beneficial to construct a database at an oxygen concentration close to the operating conditions. For instance, in lean combustion applications, the reference database should ideally reflect the equilibrium oxygen concentration. Similarly, for rich or stoichio-metric combustion conditions, it is recommended to establish a database in an N₂ environment. Moreover, it is worth mentioning that in practical application, the thermographic phosphor will be mixed with a binder, embedding it in a matrix and insulating it from the surrounding atmosphere. This could significantly reduce the influence of oxygen content.

Finally, several interference sources may arise in practice. A part from the laser extinction mentioned above, another one is spectral absorption of emitted light by media like H₂O or CO₂, though this mainly affects the infrared and has minimal impact in the visible range used here. In combustion chambers, absorption can be further reduced, for example by applying the thermographic phosphors to quartz windows to avoid and/or minimize optical path through absorbing gases. Flame emissions may also interfere from several sources. Spontaneous emissions from radicals such as OH* and CH* are commonly observed, but since they lie outside our spectral region of interest, they would not interfere. In very fuel-rich hydrocarbon flames, however, emissions from species like C₂ or C₃ may overlap with the visible range of interest. In such cases, their impact can be reduced by ignoring the corresponding spectral bands, for instance by applying masks during data processing. Furthermore, when measurements are performed under stationary conditions, background subtraction further limits the influence of these spontaneous emissions. Laser excitation can also stimulate emissions, notably from OH and CH radicals. Nevertheless, these emissions do not significantly affect the measurements, as their fluorescence lifetimes are very short (on the order of 400–600 ns [30, 31]) compared to the system’s gating, making their contribution negligible. Another source of interference comes from continuous spectral emissions. Thermal radiation in the infrared can be strong but typically falls outside the spectral window of interest. By contrast, soot can emit strongly in the visible range and may disturb the measurement. When this occurs in steady conditions, its contribution can also be effectively minimized by subtracting the background.
## 5. Conclusion

This study investigated the spectral dynamics of YAG:Dy phosphorescence signals with varying temperatures for thermometry applications using the FSF method. The method was successfully employed over a wide temperature range from 303 K to 1773 K.

Over the studied temperature range, YAG:Dy exhibits a strong spectral dependence, making it advantageous over lifetime-based methods below 1200 K.

An improved signal processing approach was proposed by selecting a more effective spectral distance metric, Pearson $\chi^2$ distance, which resulted in better temperature determination accuracy. At a given operating point, using an appropriate distance metric and minimization method, the deviation between the recorded and found temperature remained sub-kelvin on average, with a standard deviation of 8.4 K.

For combustion chamber applications, laser fluence can be affected by the presence of UV semi-transparent gases and by fluctuations in oxygen levels in gases. The sensitivity to these factors of YAG:Dy phosphorescence spectra, applied to the FSF method, was evaluated under different operating conditions.

The results indicate that YAG:Dy is sensitive to laser fluence, especially at low laser fluences, but there is a threshold above which the temperature determined by the FSF method is no longer affected by variations in laser fluence.

The presence of oxygen affects the response of the phosphor, but its influence is limited. The relative error remains below 1.5% across the entire measurement range, even under conditions of high laser fluence and high temperature, where the effects are most noticeable.

The study concludes with practical guidelines for implementing the FSF method in combustion chambers. To minimize sensitivity to both laser fluence and oxygen concentration, a balanced approach is required. Maximizing laser fluence improves the signal-to-noise ratio and mitigates the sensitivity observed at low laser fluence levels. However, laser fluence should not be excessively high to avoid additional variability cause by fluctuations in oxygen content.

Future work will extend this analysis to YAG:Dy mixed with a binder, aiming to study the sensitivity of this mixture to fluence and oxygen levels. Additionally, applications in combustion chambers will be explored.

## Declaration of competing interest

The author declares that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgement

This study was conducted as part of the HyMaX and OXY3C projects, both funded by the French National Research Agency under the projects "ANR-23-

CD50-0021-01" and France 2030 program, reference "ANR-22-PESP-0009", respectively.

This work also received financial support from the LabEx LaSIPS (ANR-10-LABX-0032-LaSIPS), managed by the French National Research Agency under the "Investissements d'Avenir" program (ANR-11-IDEX-0003-02).

For open access purposes, a CC-BY license has been applied by the authors to this document and will be applied to any subsequent version up to the author's manuscript accepted for publication resulting from this submission.

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