Dirk Borghys
email: dirk.borghys@rma.ac.be

Patrick Bas
email: patrick.bas@centralelille.fr

Helena Bruyninckx
email: helena.bruyninckx@rma.ac.be

Facing the Cover-Source Mismatch on JPHide using Training-Set Design

Keywords: Security and privacy → Intrusion/anomaly detection and malware mitigation, Malware and its mitigation, Digital image steganalysis, JPEG domain, cover-source mismatch, image processing pipeline, forensics-aware steganalysis

This short paper investigates the influence of the image processing pipeline (IPP) on the cover-source mismatch (CSM) for the popular JPHide steganographic scheme. We propose to deal with CSM by combining a forensics and a steganalysis approach. A multiclassifier is first trained to identify the IPP, and secondly a specific training set is designed to train a targeted classifier for steganalysis purposes. We show that the forensic step is immune to the steganographic embedding. The proposed IPP-informed steganalysis outperforms classical strategies based on training on a mixture of sources and we show that it can provide results close to a detector specifically trained on the appropriate source.

INTRODUCTION

For digital images, machine learning based steganalysis is currently the methodology that achieves the best performances in a controlled environment, i.e. whenever the steganographic scheme, the payload size and the image source are known. However if one of these three parameters remains unknown, the performance of the steganalysis scheme can be jeopardized. The problem of Cover-Source Mismatch (CSM) occurs when the analyzed image sources are unknown. To the best of our knowledge, it has been identified in 2008 by the pioneering works of Cancelli et al. [START_REF] Cancelli | A comparative study of ±1 steganalyzers[END_REF] and confirmed during the BOSS contest [START_REF] Bas | Break our Steganographic System -the ins and outs of organizing BOSS[END_REF]. It states that a mismatch can occur and consequently degrades the classification performances if the source of the testing set is different from the source of the training set. As an example, during the BOSS contest and when applying the detectors optimized on BossBase (processed in a specific manner), to "real-world" images, it was noted that the performance dramatically drops.

Note that the CSM effect may be particularly observable when the training set comes from BossBase images. Indeed, if this database enables to compare steganographic and steganalysis results, its development pipeline is however extremely formatted: RAW images are first transformed into spatial (ppm) images using the free software DCraw with specific parameters. The images are then rescaled such that the largest dimension was 512 pixels and converted to greyscale, and for JPEG steganalysis the ppm images are compressed using standard quantization tables. All operations are performed using the 'convert' Unix command, which is very restrictive.

If the CSM can easily be observed, accurate characterization of the source in the literature is not straightforward. The term 'source' has been coined in 2011 [START_REF] Bas | Break our Steganographic System -the ins and outs of organizing BOSS[END_REF][START_REF] Fridrich | Breaking HUGO -The Process Discovery[END_REF] and became an important topic in steganalysis research from 2012 onwards (e.g. [7-9, 11, 13, 14, 16]), definitions of a source are diverse and stay informal.

Ker and Pevny characterize a source as an actor [START_REF] Ker | A Mishmash of Methods for Mitigating the Model Mismatch Mess[END_REF], i.e. one user uploading a set of images on his social network account. The authors provide options to mitigate the CSM by normalizing independently the features of each user. Pasquet [START_REF] Pasquet | Steganalysis with Cover-Source Mismatch and a small learning database[END_REF] et al. consider a source as a cluster of features, and they combine unsupervised and supervised training to conduct steganalysis. Finally, Kodovsky et al. [START_REF] Kodovsky | Study of Cover Source Mismatch in Steganalysis and Ways to Mitigate its Impact[END_REF] proposed to deal with different sources (here cameras) by training on a mixture of images coming from different sources and Lubenko and Ker [START_REF] Lubenko | Going from small to large data in steganalysis[END_REF] proposed to adopt a similar strategy on millions of images using a simple on-line classifier.

Recently Giboulot et al. [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] conducted an investigation to characterize the set of parameters that specify a 'source'. This paper considered the case were RAW images were acquired using various cameras and developed to JPEG images using photographic development softwares. The impact of the choice of camera, the acquisition parameters and the image processing pipeline (IPP) were considered. The paper showed that the acquisition parameters (including the camera type) have only a minor impact, but that the image processing parameters as well was the quantization table have the largest impact. The investigated processing parameters were sharpening, denoising, color adjustments and the choice of the development software.

The current paper follows the same methodology as [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] while investigating some complementary development pipelines such as white-balancing and demosaicing. It focuses on the popular JPHide embedding scheme. This scheme has been selected because the embedding is fast, and its detectability has already been analyzed within the CSM paradigm by Ker and Pevny [START_REF] Ker | A Mishmash of Methods for Mitigating the Model Mismatch Mess[END_REF]. Moreover, this

Cover image

RAW domain

Developed domain

Figure 1: Pipeline of the cover image generation process which can be decomposed into four main steps (scene, device, acquisition, developing) representing parameters of the whole process.

work enables to highlight complementary conclusions with respect to [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF]. A strategy to mitigate the impact of the CSM due to the image processing pipeline is also proposed. This strategy consists first of a forensics analysis by using steganalysis features to identify a processing pipeline similar to the one applied on the test image. Similarly to [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF][START_REF] Comby | How to augment a small learning set for improving the performances of a CNN-based steganalyzer?[END_REF], we show that the best detection results are obtained when the training is performed on an image database coming from a source similar to the one generating the test images.

The Image Processing Pipeline

A source can be defined w.r.t. the image generation process depicted in Figure 1 which shows that the creation of a cover image is linked to the succession of different parameters represented by (1) the scene that is captured, (2) the device which is used, (3) the acquisition settings used during the capture and (4) the developing step.

Each parameter is linked with a set of sub-parameters. The scene fluctuates according to the subject, but also according to the illumination or the orientation of the camera. The device is composed mainly of two elements: the sensor (which can be CMOS, CCD; color or monochrome) and the lens.

The acquisition phase relies on three parameters originating from the device: the lens aperture, the ISO sensitivity and the exposure time and one parameter which is the time of capture.

Finally, the developing step which is studied in this paper, contains a lot of processing steps and we list here the most important ones:

-the white-balance is a color transform needed to adjust to human perception of color under different illuminations, -Gamma correction is a sample-wise transform which maps to a different tone, -the demosaicing or Color Filter Array (CFA) interpolation step predicts two missing color components for each pixel from neighboring photo-site values, -and the user can also apply other image processing operations such as denoising or sharpening.

METHODOLOGY

The methodology explored in this paper for reducing the CSM (cf. Figure 2) consists in first determining the image processing pipeline (IPP) that was applied to an image, and then exploiting that information for building an adequate training set that is used to train the steganalysis detectors. First, a multi-classifier is trained to identify the closest development process among a set of predefined ones. This operation is possible by extracting features from databases specifically developed from a database of RAW images. Secondly, the closest database of cover images is used as a training database for steganalysis by generating a corresponding set of stego images. Finally, a classical steganalysis methodology is applied by extracting features and training a classifier which is afterward used on the test image. Note that such a methodology is an example of forensics-aided steganalysis which was already briefly explored by Barni et al. [START_REF] Barni | Forensics aided steganalysis of heterogeneous images[END_REF] for distinguishing camera images from computer generated images before performing steganalysis.

EXPERIMENTAL SETUP

We chose to study a specific camera (the Leica M9) and in order to have a complete control of the image processing pipeline, the RAW images available in the BossBase are used in our experiments.

In the original BossBase 2758 RAW images of the Leica M9 are available. These are used for creating test images corresponding to different choices of the processing parameters. After processing, the 2758 images are cropped into non-overlapping 512x512 images, resulting in a total of over 160000 images. This procedure thus allows an artificial increase of the image database. The selected cropping method results in a very high variation in scene content between different sub-images but the local statistics caused by the processing pipeline are the same as for the full-sized images.

Facing the Cover-Source Mismatch on JPHide using Training-Set Design Conference'17, July 2017, Washington, DC, USA Three photographic development tools were used in the experiment: the open-source software DCraw v9.25 (denoted "DC" in this paper) and RawTherapee v4.1.0 (http://rawtherapee.com/) ("RT") and the commercial software Adobe Lightroom© v6.0 ("LR6").

The three softwares were used for converting the RAW images into color JPEG images with a standard quantization table with quality factor 100 (STD100) for DCraw and RawTherapee and the Adobe Level 12 quantization table (Adobe12) for Lightroom. A 4:2:2 color sub-sampling was used in the JPEG conversion.

The steganographic method used in the current investigation is JPHide.

As mentioned in Giboulot et al. [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] the IPP in general modifies the content details of a picture and, hence, the resulting number of nonzero AC coefficients (nzac). In order to perform a fair comparison between the photographic developments performed by different IPPs, the payload size should remain constant over the different developments. Contrary to [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF], note that we did not use the same message length for all images. The image contents of the different crops is so diverse that we decided to fix the message length for each of the crops but to keep it constant over the different developments applied to each cropped image. The message length is set to 10% of the nzac in the images developed by a specific processing chain (i.e. DCraw using a bilinear CFA interpolation). However, we believe that using a constant payload through all images and developments or using a constant payload only through developments should lead to similar conclusions.

For each of the investigated processing parameters, stego/cover pairs were created for the 160000 cropped images.

The used steganalytic detector is the Ensemble Classifier (EC) [START_REF] Kodovsky | Ensemble classifiers for steganalysis of digital media[END_REF] based on the CC-JRM feature set [START_REF] Kodovsky | Steganalysis of JPEG Images Using Rich Models[END_REF] and used in a clairvoyant scenario, i.e. both the steganographic method and the embedding rate are known to the steganalyst. The false alarm, missed-detection and total error probabilities, (P f a , P md and P E = (P f a + P md )/2) were considered as performance metrics. In order to estimate these performance metrics, 10000 cover/stego image pairs were randomly selected from the set of 160000 images for training the detector. Another (disjoint) set of 10000 image pairs was used for validation. This was repeated five times in order to obtain an average value and a standard deviation for the performance metrics. For compactness, the paper reports only the average values for P E .

IMPACT OF IMAGE PROCESSING PARAMETERS

Because Giboulot et al. [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] already investigated many image processing parameters, the current paper focuses on parameters not yet examined in that paper. These include white balancing, gamma correction, CFA demosaicing and the choice of the development software. For investigating the impact of white balancing and gamma correction, DCraw was used.

Impact of white balancing

The choice of the white balancing method influences the color appearance of an image. By default, DCraw uses a fixed white balance based on a color chart illuminated with a standard D65 lamp (cf. user manual of DCraw), which roughly corresponds to the average midday light in Northern/Western Europe.

Besides this default white balancing (WBdef) method, DCraw also allows to select two other types of white balance: camera (WBcam) and average (WBave). In WBcam the white balance is defined by the camera. In practice the photographer can choose between automatic white balancing (AWB) or a number of preset values depending on the lighting conditions (e.g. sunset, clear sky, clouded sky, ...). Each choice determines a color temperature applied in the white balancing [START_REF]Photography tutorials: White balance[END_REF].

In WBave the white balance is calculated by averaging over the complete image.

The white balance is thus partly defined by the camera during image acquisition, but can be overridden by the development software.

In the current experiment DCraw is used with all of its parameters set to their default value. Only the white balancing method is varied. The three available white balancing methods are applied and compared.

Figure 3 shows the results obtained for P E for a steganalysis detector trained on images created by one of the three white balancing modes of DCraw (shown on the left of the table) and applied to images created by each of the three methods (top of the table). A colormap is assigned to the values for an easier visualization of the mismatch. The values on the diagonal correspond to the matched case and represent the "intrinsic difficulty" of the considered source [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF].

The figure shows that the largest mismatch if found when training on WBdef and applying the trained detector to any of the two other methods. Training on WBdef and applying to the two other modes results in a more than tenfold increase of P E . The mismatch between the two other modes is much milder.

Impact of gamma correction

While [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] examines a range of manual tone adjustments in their investigation of the dependence on color adjustment, the current paper focuses on the more automatic process of gamma correction (GC). In DCraw four gamma correction methods are available: BT-709, Adobe, ProPhoto and sRGB. BT709 is the default GC method in both DCraw and RawTherapee. Details on the various gamma correction methods and their parameters can be found in [START_REF] Rawpedia | Gamma differential[END_REF][START_REF] Tooms | Colour Reproduction in Electronic Imaging Systems: Photography, Television, Cinematography[END_REF]. The impact of gamma correction on the CSM is illustrated in figure 4. The largest mismatch is found between the default GC (GCdef) and the three other methods. Training on GCdef and applying the trained detector to the images created using the other three GC methods leads again to a more than tenfold increase of P E w.r.t. the respective fully-matched cases. Between the three other methods the relative increase in P E is between 1. testing on GCprophoto) and 4.1 (for training on GCprophoto and testing on GCsrgb). GCprophoto exhibits a higher intrinsic difficulty (i.e. the value on the diagonal corresponding to the fully-matched case) than the three other methods.

Impact of CFA interpolation and development software

For the conversion from RAW image to JPEG in this paper three development softwares are used: DCraw (DC), RawTherapee (RT) and Adobe Lightroom 6.0 (LR6). The first step in the conversion from RAW is the CFA interpolation (demosaicing). In this section the combined effect of the CFA interpolation and the choice of development software is investigated. Eleven IPPs were defined and examined. The results of the mismatch between them is presented in figure 5. Details about the eleven IPPs are given below. DCraw and RawTherapee were used with all parameters set to their default values. Only the demosaicing method was varied. For DCraw the (bi)linear, AHD, VNG and PPG interpolations were used (resp. denoted DClin, DCahd, DCvng, DCppg on the figure's axes). For RawTherapee AHD, Amaze and IGV were applied (RTahd, RTamaze and RTigv). LR6 uses a proprietary demosaicing method for which no detailed documentation is available. For LR6 we considered four processing pipelines. In LR6Def all parameters were left to their default value. LR6 uses its own quantization tables (QTs) and in particular the QT at highest quality (level 12) differs from the standard table at quality factor QF=100. Therefore we also created LR6 images with the standard QT at QF=100 (LR6Std), consistent with the one used in the two other softwares. The LR6Std images were created using LR6 with all parameters set to their default value, but by exporting TIFF images instead of JPEG. The TIFF images are then converted to JPEG using the Python PIL library. The only difference between LR6Def en LR6Std is thus the QT.

LR6 performs several operations by default (denoising, sharpening, etc.). The default sharpening in LR6 is set to "level 25". For LR6 we also applied two other sharpening methods: a rather extreme sharpening in the development module at "level 125" (LR6DS125) and the "standard screen" (LR6SScr) method in the export module.

Figure 5 shows the results of the study of the mismatch between the various demosaicing methods and choice of the development softwares.

The figure clearly exhibits a block structure corresponding to the three softwares. The largest mismatch is thus obtained between different development softwares. Note that in [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] the development software was found to have only moderate impact. The different result we observe here is probably due to the different choice of the feature set; DCTR in [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF] versus CC-JRM in the current paper. We intend to examine this further.

The difference in QT seems to be an important factor in the mismatch found between LR6 and DCraw. LR6Std shows indeed a much smaller mismatch w.r.t. DCraw than LR6Def.

The intrinsic difficulty of a source is lowest for images processed by DCraw and much higher for images processed by RT and LR6. The LR6DS125 images have the highest intrinsic difficulty. The authors think this is caused by the highly non-linear character of the sharpening applied in LR6 which leads to a high variability within the corresponding training set.

The largest relative increase of P E due to a mismatch in demosaicing method (within the same development software) is between 2.2 (for training on RTigv and testing on RTamaze) and 4.8 (for training on DCvng and testing on DClin).

IMAGE PROCESSING PIPELINE (IPP) CLASSIFIER

The fact that steganalysis results depend on the IPP suggests that the used steganalysis feature set is sensitive to this IPP. We have therefore investigated whether it is possible to use the same feature set for detecting the IPP. Several papers have been published showing the usefulness of steganalysis features for digital image forensics and in particular for detecting image manipulations [START_REF] Boroumand | Scalable Processing History Detector for JPEG Images[END_REF][START_REF] Qiu | A universal Image Forensic Strategy based on Steganalytic Model[END_REF].

The ensemble classifier (EC) yielding excellent results for steganalysis using large feature sets, in the current paper the EC is also used for constructing a supervised classifier of the IPP.

For assigning one of the N examined IPPs to a given test image an N-class classifier is needed. For constructing this classifier from the binary ECs, an aggregation of one-to-one EC classifiers is applied: each EC is trained to distinguish between two IPPs. This is done for all pairs of IPPs, leading to N (N -1)/2 binary classifiers each voting for one of the IPPs in its pair. For assigning an IPP to an image under test, these N (N -1)/2 classifiers are applied and the final decision is the IPP that receives the majority of the votes.

For training the IPP-classifier we considered only the 11 IPPs discussed in section 4.3.

Figure 6 shows the results of the classification obtained after training and validation on 10000 cover images of each processing pipeline. The figure shows the confusion matrix of the classification. The value in row i, column j is the probability that an image created by the IPP noted on row i is classified as being created by the IPP in column j. For the sake of clarity, zero values are omitted.

The results show that the classifier is capable to identify the different IPPs with a very high accuracy. In particular, it is possible to distinguish between the different types of CFA interpolation. Note also that, except for the LR6Std there is no confusion between the LR6 generated images and those from DC or RT.

Interestingly, when applying the IPP-classifier trained on the cover images for classifying the IPP of the stego images, a very similar classification accuracy Acc1 is obtained. The obtained Acc is 96.1% and 95.9% for resp. the cover and stego images. This means that, while steganalysis performance is highly dependent on the processing chain, the detection of the processing chain suffers only a minor influence of the presence of steganography (for the experiments conducted in this paper).

D C li n D C p p g D C vn g D C ah d R T ah d R T am az e R T ig v L R 6D ef L R 6S td L R 6D S

MITIGATION OF THE CSM -THE IPP-INFORMED DETECTOR

The results of the IPP-classifier can be used for selecting the detector that was trained on the closest (and possibly same) source, i.e. an IPP-informed detector. For each tested image, the IPP-classifier discussed in section 5 is applied. In the second step the steganalysis detector that was trained on the detected IPP is applied for deciding whether the test image is cover or stego. This is done for 10000 randomly picked images for each of the considered IPPs.

In this test we also include images developed with DCraw/ AHD/ GC=Prophoto (DCCGPP) and DCraw /AHD/ WB= Camera (DCW-Bcam). Note that neither of these two processing pipelines were used for training the IPP-classifier or for training the steganalysis detectors.

In the test we also included 10000 JPEG images collected from Flickr. The selected images correspond to images acquired with the Leica M9 camera and with quantization table corresponding to Adobe level 12. The images were center-cropped to a size of 512×512 in a way that preserves the DCT structure. The corresponding stegoimages were created with an embedding rate of 0.1 bpnac.

Figure 7 compares steganalysis results obtained by four different detection strategies:

• 'Fully matched' case: training and test images come from the same source. This is the baseline for the comparison. It represents the best results that can be obtained using the chosen feature set and the EC classifier. Figure 7 shows that the 'Class Boss' method clearly suffers the most of the CSM. The 'Mixed training' considerably reduces the impact of the CSM compared to the 'Class Boss' approach, except for the case where the latter is almost fully-matched (DCppg and DCahd). The 'IPP informed' method proposed in the current paper results in the smallest increase of P E with respect to the fullymatched detector.

The proposed method also behaves better than 'Mixed training' for the two processing pipelines that were not used for training the IPP-classifier or the steganalysis detectors. Note that the increase of P E w.r.t. the fully matched case is the highest for DCWBcam. However, the increase for both DCWBcam and DCGCPP is much smaller than the mismatch found in respectively figure 3 and4 between WBdef/WBcam and GCdef/GCprophoto. The type of approach as presented in this paper thus also provides some robustness with respect to unknown IPPs. For the Flickr images the IPP-informed and the mixed training detectors obtain similar results. The large difference w.r.t. the 'Fully matched' case suggests that the LR6 developments used for training our models should be expanded, particularly w.r.t. the down-sampling operations that are present in the Flickr database. We also noted that the IPP-classifier classes 99.7% of the Flickr images as one of the three LR6 developments. The remainder is classified as RT developments.

CONCLUSIONS AND FURTHER WORKS

The paper investigates the influence of the image processing pipeline on the cover-source mismatch for JPHide. It also proposes a simple classifier of the IPP and shows how it can be exploited for reducing the CSM due to the IPP. We show that within this setup, the proposed IPP-informed steganalysis outperforms approaches based on mixed training over the examined sources. Partitioning the image data prior to steganalysis thus seems a promising approach for mitigating the CSM (see also [START_REF] Pasquet | Steganalysis with Cover-Source Mismatch and a small learning database[END_REF]).

According to [START_REF] Giboulot | Steganalysis into the Wild: How to Define a Source?[END_REF], the impact of the image processing pipeline on the CSM is more important than the choice of camera or the image acquisition parameters. The current paper additionally shows that the CSM can be significantly reduced by combining IPP classification with training set design. For the latter the RAW images

Figure 2 :

 2 Figure 2: Schematic overview of the examined methodology.

Figure 3 :

 3 Figure 3: Influence of white balancing (P E in %).

Figure 4 :

 4 Figure 4: Influence of gamma correction (P E in %).

Figure 5 :

 5 Figure 5: Influence of demosaicing and development software (P E in %).

  • 'Class Boss': training on the classical BossBase, i.e. resized (spatially interpolated) images developed with DCraw using PPG demosaicing as explained in the introduction of the paper, • 'Mixed training': the results of training the EC on a mix of the 11 sources (consisting of 1000 images from each source) as proposed in [13], • 'IPP informed': the results of the proposed IPP-informed steganalyzer. For DCGCPP and DCWBcam the values of the 'Fully matched' case in figure 7 are extracted from figures 3 and 4. For the images downloaded from Flickr the presented values for the 'Fully matched' case are the average results over five 5000/5000 random splits of the available images. For the 'Mixed training' of the Flickr images, we decided to use only images from LR6Def, LR6DS125 and LR6SScr for training (3400 of each IPP).

Figure 6 :

 6 Figure 6: Confusion matrix for the supervised classification of the image processing pipeline (IPP). D C li n D C p p g D C vn g D C ah d R T ah d R T am az e R T ig v L R 6D ef L R 6S td L R 6D S 12 5 L R 6S S cr D C G C P P D C W B ca m F li ck r

Figure 7 :

 7 Figure 7: Comparison of P E (in %) for the four detection strategies.

  3 (for training on GCsrgb images and Conference'17, July 2017, Washington, DC, USA Dirk Borghys, Patrick Bas, and Helena Bruyninckx

		G C de f	G C ad ob e	G C pr op ho to	G C sr gb
	GCdef GCadobe GCprophoto GCsrgb	0.24 2.16 2.06 1.7	4.12 0.3 0.78 0.69	4.49 0.77 0.52 0.69	3.3 0.82 0.91 0.22	0 1 2 3 4 5

Acc=ratio of correctly classified items to the total number of classified items; expressed as a percentage

The authors expect that for mitigating the impact of image acquisition a similar approach could be followed, based on a carefully designed expansion of the BossBase, i.e. spanning a larger variation of acquisition parameter settings.Future work will assess the current methodology on other steganographic schemes in the pixel or JPEG domain.

ACKNOWLEDGMENTS

The authors would like to thank Samuel Tap who, in the frame of an internship at the Royal Military Academy, coded most of the Python™ scripts used for generating the results presented in this paper. This work was partially supported by the French ANR DEFALS program (ANR-16-DEFA-0003) and by the Belgian Royal Higher Institute for Defence (projects DAP16-01 and DAP18-01).


Stéphane Amiel
email: stephane.amiel@laposte.net

Etienne Copin

Thierry Sentenac

Philippe Lours

Yannick Le Maoult

On the thermal sensitivity and resolution of a YSZ:Er 3+ /YSZ:Eu 3+ fluorescent thermal history sensor

Keywords:

This paper deals with the problem of thermal history analysis of high temperature components for applications such as furnaces, nuclear reactors and jet engines. It focuses on fluorescent thermal history sensors, which exhibit permanent changes in their luminescence properties when exposed to high temperature. These changes can then be quantitatively evaluated to determine the temperature of exposure from a previous thermal event. The main objective of this paper is to investigate the thermal sensitivity and the thermal resolution of a yttria-stabilized zirconia (YSZ) Er 3+ -doped phosphor produced by a solgel route and combined with a thermal history insensitive YSZ:Eu 3+ reference, which was selected for its high sensitivity to thermal history above 1173 K. In particular, the interest of this YSZ:Er 3+ /YSZ:Eu 3+ sensor is discussed in the view of the physical properties of sol-gel deposited YSZ coatings, the selection of an appropriate excitation wavelength and the practical measurement of coatings fluorescence properties. The sensitivity and the resolution of two thermal history measurement fluorescence methods, based on intensity ratios and lifetime analysis, were determined and compared. A comparison is also made with standard non-contact temperature measurement methods such as infrared thermography and thermochromic paints.

Introduction

For many industrial processes in energy [START_REF] Courtois | IR thermography diagnostics for the WEST project[END_REF], aeronautical [START_REF] Douglas | An Integrated Approach to the Application of High Bandwidth Optical Pyrometry to Turbine Blade Surface Temperature Mapping[END_REF], automobile engineering [START_REF] Thevenet | Measurements of brake disc surface temperature and emissivity by two-color pyrometry[END_REF] or in microelectronics [START_REF] Kuball | Time-resolved temperature measurement of AlGaN/GaN electronic devices using micro-raman spectroscopy[END_REF], temperature is a key parameter for their design, for their control and for the durability of their associated components. However, temperature measurement under high heat-flux conditions and in confined environments such as furnaces, nuclear reactors and aircraft jet engines remains challenging. In particular, the use of standard on-line measurement methods (thermocouples [START_REF] Kuball | Time-resolved temperature measurement of AlGaN/GaN electronic devices using micro-raman spectroscopy[END_REF], IR thermography methods [START_REF] Gaussorgues | La thermographie infrarouge: principes, technologies, applications[END_REF][START_REF] Kasem | An emissivity-corrected method for the accurate radiometric measurement of transient surface temperatures during braking[END_REF][START_REF] Loarer | Noncontact surface temperature measurement by means of a modulated photothermal effect[END_REF], etc.) is sometimes not appropriate in harsh environments involving limited optical access and fast-moving components such as jet turbine engines [START_REF] Sentenac | Bi-color near infrared thermoreflectometry: a method for true temperature field measurement[END_REF]. Such environments require robust, reliable and non-intrusive sensors that can be used with the relevant component surface. Some type of sensors, called thermal history sensors, have the ability to record the temperature to which they are exposed during a thermal event so that annealing temperatures can be extracted from a later off-line analysis at room temperature.

The most widely-used thermal history sensors are thermochromic paints [START_REF] Lempereur | Surface temperature measurement on engine components by means of irreversible thermal coatings[END_REF], which exhibit permanent changes of colour with temperature and duration of exposure. These paints are for instance used for off-line temperature determination on coated parts after running a test engine in a predefined cycle [START_REF] Chamberlain | Temperature Indicating Paint and Method of Preparing a Specimen With the Same[END_REF][START_REF] Hodgkinson | Temperature Indicating Paint[END_REF][START_REF] Hughes | Temperature Indicating Paint[END_REF]. However, the thermal resolution of such temperature-sensitive paints, which relies on the number of their discrete colour changes, varies between 10 K and more than 100 K [START_REF] Lempereur | Surface temperature measurement on engine components by means of irreversible thermal coatings[END_REF]. Furthermore, some substances present in the pigments are now restricted by European Union REACH regulations.

This context has led to the development of a new alternative class of thermal history sensors, based on temperature-driven changes in the emission properties of fluorescent markers embedded within a coating [START_REF] Feist | Determining Thermal History of Components[END_REF][START_REF] Rabhiou | Phosphorescent thermal history sensors[END_REF]. These markers, or phosphors, are made up of an inorganic matrix containing luminescent centres, typically trivalent lanthanide ions, which have the ability to emit photons when excited at an appropriate wavelength, as a result of radiative electronic transitions. For short-time exposure to high temperature, the temperature-induced physicochemical changes occurring within a phosphor at the atomic scale can permanently modify the electronic structure of the activator ions and the radiative electronic transition probabilities, hence causing permanent changes in the spectral (wavelength and intensity) and temporal (decay time) fluorescence emission properties. The off-line analy-sis at room temperature of its fluorescent properties can thus reveal the peak temperature undergone by the fluorescent sensor under stationary annealing conditions. Changes in the fluorescence characteristics have an advantage over colour changes, in that they are continuous and readily measurable quantitatively using standard spectroscopic equipment, making it possible to measure a continuous spectrum of temperature rather than temperature thresholds.

Currently, crystal phase transition process [START_REF] Salek | Mn2+ doped Zn3(PO4)2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF], enhancement of crystallinity [START_REF] Feist | Determining Thermal History of Components[END_REF][START_REF] Rabhiou | Phosphorescent thermal history sensors[END_REF][START_REF] Heyes | Thermal History Sensing With Thermographic Phosphors[END_REF][START_REF] Feist | Off-line temperature profiling utilizing phosphorescent thermal history paints and coatings[END_REF], oxidation of activator ions [START_REF] Rabhiou | Oxidation of divalent rare earth phosphors for thermal history sensing[END_REF][START_REF] González | Reusable thermal history sensing via oxidation of a divalent rare earth ion-based phosphor synthesized by the sol-gel process[END_REF] and diffusion of activator or sensitizer/quencher species [START_REF] Rabhiou | Phosphorescent thermal history sensors[END_REF][START_REF] Lan | Determination of thermal history by photoluminescence of core-shelled quantum dots going through heating events, part[END_REF] are the four main thermoactivated mechanisms identified in fluorescent thermal history sensors which can cause a temperature sensitivity appropriate for thermal history sensing. Phase transitions between allotropic forms of Mn 2+ doped Zn 3 (PO 4 ) 2 , synthesized by Salek et al. [START_REF] Salek | Mn2+ doped Zn3(PO4)2 phosphors: irreversible thermochromic materials useful as thermal sensors[END_REF] caused strong changes in its fluorescence emission chromaticity in the range 873 K-1273 K, making it suitable for recording thermal history. Gonzàlez et al. [START_REF] Rabhiou | Oxidation of divalent rare earth phosphors for thermal history sensing[END_REF][START_REF] González | Reusable thermal history sensing via oxidation of a divalent rare earth ion-based phosphor synthesized by the sol-gel process[END_REF][START_REF] Yá Ñez-González | A detailed characterization of BaMgAl10O17: Eu phosphor as a thermal history sensor for harsh environments[END_REF] observed that the process of oxidation from Eu 2+ to Eu 3+ in a BaMgAl 10 O 17 is temperaturesensitive up to 1673 K. The emission ratio built from the 445 nm and 611 nm emission lines of Eu 2+ and Eu 3+ ions after a 20 min-long isothermal heat treatment exhibited a threefold order of magnitude increase from 973 K to 1373 K, with repeatability of the ratio better than 10 K. On the same principle, Rabhiou et al. [START_REF] Rabhiou | Oxidation of divalent rare earth phosphors for thermal history sensing[END_REF], from the same team, observed that the phosphor SrAl 14 O 25 :Eu 2+/3+ could provide a dynamic range extending from 873 to 1573 K. The same authors also demonstrated that an amorphous-to-crystalline transition in sol-gel synthesized Y 2 SiO 5 :Tb 3+ after 20 min-long heat treatments causes a monotonic increase in fluorescence intensity and decay time over a temperature range from 773 K up to 1073 K, which also makes this phosphor suitable for thermal history sensing [START_REF] Rabhiou | Phosphorescent thermal history sensors[END_REF][START_REF] Heyes | Thermal History Sensing With Thermographic Phosphors[END_REF][START_REF] Rabhiou | Oxidation of divalent rare earth phosphors for thermal history sensing[END_REF]. The accuracy of these phosphors, when put in suspension in a commercial binder and painted on a disk submitted to the flame of a burner for 40 min was estimated to be better than 50 K [START_REF] Heyes | Thermal History Sensing With Thermographic Phosphors[END_REF]. A water-based paint containing an amorphous Eu doped matrix developed by the same team also showed monotonic variation in its decay time within the temperature range 373-1073 K, with excellent repeatability. Finally, other thermal history sensor coatings for high temperature based on the enhancement of crystallinity were also reported by Pilgrim et al. [START_REF] Pilgrim | Thermal history sensors for non-destructive temperature measurements in harsh environments[END_REF] (Eu 3+ and Dy 3+ doped YAG, 573 K-1073 K) and Stenders et al. [START_REF] Stenders | Sol-gel deposited thermographic phosphors as possible thermal history coatings[END_REF] (Eu 3+ /Tb 3+ doped Y 2 O 3 , 973 K-1273 K).

Over the last few years, the Institut Clément Ader has been developing YSZ phosphors and coatings prepared by a sol-gel route for high temperature sensing in thermal barrier coatings, such as YSZ:Eu 3+ and YSZ:Er 3+ [START_REF] Pin | Characterisation of thermal barrier sensor coatings synthesised by sol-gel route[END_REF][START_REF] Copin | Feasibility of luminescent multilayer sol-gel thermal barrier coating manufacturing for future applications in through-thickness temperature gradient sensing[END_REF][START_REF] Copin | Fonctionnalisation de barrières thermiques aéronautiques YSZ issues de la voie sol-gel : mesure de température et diagnostic de L'endommagement par fluorescence[END_REF]. In particular, the latter was found to be a suitable candidate for thermal history sensing [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF]: the continuous enhancement of crystallinity of YSZ:Er 3+ powders produced by a sol-gel route with temperature for 15 min long heat treatments between 1173 K and 1423 K induced substantial and consistent increases of their green emission intensity and fluorescence decay time in the ranges 1223 K-1423 K and 1173 K-1373 K respectively [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF]. As shown in Fig. 1, the intensity of the main emission lines at 540 nm and 560 nm were indeed observed to increase with crystallinity by a factor of almost 50 after 15 min at 1423 K. These strong temperature dependencies could allow off-line temperature sensing with an estimated theoretical resolution for those temperatures ranging between 0.3 and 1 K and between 6 and 2 K for intensity and decay time respectively, surpassing the resolution of actual thermochromic paints in that temperature range. Preliminary investigations confirmed the potential of an intensity ratio approach, using a red emitting, temperature insensitive YSZ:Eu 3+ reference (Fig. 1), as a robust method regarding small variations in experimental measurement conditions for future applications in off-line temperature mapping. Furthermore, the stability of the thermal exposure temperature sensing capability for relatively long time heat treatments below 973 K that was observed is expected Fig. 1. Evolution of the relative intensity increase of the fluorescence emission of a sol-gel synthesized YSZ:Er 3+ powder with the temperature of exposure after 15 min long heat treatments [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF]. The position of the main emission peaks of YSZ:Eu 3+ , which could be used as a reference because of its little sensitivity to temperature of exposure when fully crystallized, is also indicated.

to allow to directly co-deposit these two YSZ:Eu 3+ and YSZ:Er 3+ phosphors as a thermal history sensing coating using sol-gel deposition methods such as air-spraying followed by a low temperature consolidation heat treatment (<973 K).

This paper aims to provide a more in-depth analysis of this fluorescent YSZ:Er 3+ thermal history sensor, in regards with its practical application in the form of a coating deposited by a sol-gel process in combination with a thermal history insensitive YSZ:Eu 3+ reference. In particular, the interest of this YSZ:Er 3+ /YSZ:Eu 3+ coating is discussed in the view of the physical properties of sol-gel deposited YSZ coatings, the selection of an appropriate excitation wavelength and the practical measurement of coatings fluorescence properties. The sensitivity and the resolution of a hybrid YSZ:Er 3+ /YSZ:Eu 3+ phosphor for both an intensity ratio and lifetime analysis based approaches, determined from temperature calibration curves from earlier work [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF], are investigated and compared with standard methods for measuring temperature.

Experimentation

2.1. Preparation of YSZ: Eu and YSZ: Er phosphor and coatings YSZ:Er 3+ powder of composition (YO 1.5 ) 0.083 (ErO 1.5 ) 0.015 (ZrO 2 ) 0.902 and YSZ :Eu 3+ powder of composition (YO 1.5 ) 0.078 (EuO 1.5 ) 0.02 (ZrO 2 ) 0.902 were synthesized by a sol-gel route using the protocol described in reference [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF]. Samples of the YSZ:Er 3+ powder, in a partially crystalline state after calcination at 973 K for two hours, were further annealed for 15 min under isothermal conditions at various temperature between 1173 K and 1423 K with 50 K steps. During these heat treatments, the samples were introduced in the furnace already set at the intended temperature and were removed after 15 min and let for cooling in open air, in order to recreate conditions of thermal history sensing close to that of real applications of thermochromic paints (3-5 min) [START_REF] Chamberlain | Temperature Indicating Paint and Method of Preparing a Specimen With the Same[END_REF][START_REF] Hodgkinson | Temperature Indicating Paint[END_REF][START_REF] Hughes | Temperature Indicating Paint[END_REF].

The YSZ:Eu 3+ powder, also in a partially crystalline state after calcination at 973 K for two hours, was simply annealed for 2 h at 1373 K to ensure full crystallization [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF], as this phosphor was selected to play the role of a reference with little sensitivity of its fluorescence emission properties to thermal history when further calcined for 15 min between 1173 K and 1423 K.

Finally, 20-40 m thick YSZ:Eu 3+ coatings were deposited on Ni-base super alloy coupons using a sol-gel method involving air spraying at room temperature. The coatings were then consolidated at a temperature below 973 K, before undergoing a heat treatment at 1273 K to ensure complete crystallization. Complete details of the preparation of these coatings cannot be disclosed for the sake of confidentiality.

Characterisation of fluorescence properties

Fluorescence excitation spectra

The excitation spectra of YSZ:Eu 3+ coatings and YSZ:Er 3+ sintered disks in the spectral range between Ultra-Violet (200 nm) and near infrared wavelengths (1000 nm) were collected with a spectral scanning multimode reader (Varioskan, Thermo Fisher) [START_REF] Raitio | International Calibration System of Thermo Scientific Varioskan Flash with Improved Sensitivity, Accuracy and Dynamic Range[END_REF][START_REF][END_REF]. The excitation wavelength was selected using a xenon flash lamp as a light source, combined to two adjustable monochromators connected serially for scanning the excitation range. The bandwidth selection was determined by the monochromator slit width. The intensity of the emission signal at a fixed wavelength, corresponding to an emission line of the phosphor, is collected for each excitation wavelength by a photomultiplier tube equipped with two other monochromators connected serially. The resolution of such a device is about 1 nm.

The bandwidth of the excitation window and the gain of the experimental set-up were adjusted at 5 nm and using the autoscale function of the Varioskan (after an initial 10 ms flash used to select the correct photo-multiplier tube gain) respectively, in order to optimize the signal-to-noise ratio R S/N of excitation peaks without significant detrimental effect on quality and resolution of spectra. The bandwidth of the detection integration window was set to 10 nm to remain consistent with the 10 nm integrating window corresponding to the bandwidth of the optical filters used for the collection of emission spectre later on. Only the excitation peaks with R S/N values above 3 were considered as appropriate excitation wavelengths [START_REF] Max | Méthodes et techniques de traitement du Signal[END_REF].

Fluorescence emission spectra

Fluorescence emission spectra of phosphors were measured under the excitation of a frequency-doubled, continuous wave diode-pumped Nd:YAG laser irradiating at 532 nm with maximum power of 1.1 W and a beam diameter of 1.2 mm (CNI laser) redirected to the samples using a mirror. Emission intensity spectra in the 400-700 nm range were collected with a USB 2000 + spectrometer (Ocean Optics, spectral resolution of 0.15 nm) equipped with an optical fibre which collecting lens was located 20 cm above the sample surface. A high-pass filter with a cut-off wavelength of 535 nm was also used to protect the spectrometer from contributions of the laser beam. The signal sensitivity to the detection angle was investigated by modifying the detection angle of the optical fibre head, defined by the angle between the viewing direction of the fibre and the normal to the sample surface.

Fluorescence emission intensity maps were measured on YSZ:Eu 3+ coating specimen (26 mm × 20 mm) in order to check thickness homogeneity. The experiments were performed with the spectral scanning multimode reader Varioskan configured with an excitation wavelength of 535 nm while measuring the intensity of the emission peak of Eu 3+ ions at 611 nm. The spot size for the construction of the map was around 1 mm.

Fluorescence decay time

Finally, fluorescence decay-time measurements were carried out on the annealed YSZ: Er 3+ powder using an experimental setup dedicated to lifetime analysis, illustrated in Fig. 2. An acousto-optic modulator operating in digital mode (1250C model, Isomet), combined with a diaphragm, was used to generate short laser pulses with the 1st order of the diffracted beam of the continuous 532 nm laser used previously for collecting emission spectra. A pulse generator was used to control pulse duration (from 20 s to 1 ms) and frequency (10 Hz). For all measurements, the pulse duration was finally set at 200 s, in order to avoid phosphor saturation, and so as to obtain the maximum fluorescence signal and a stable lifetime with the pulse length. The fluorescence intensity decay after each pulse was collected with a Si photomultiplier (SensL) equipped with a narrow bandpass filter (FWHM ∼10 nm) centred on the main emission line of the phosphors investigated (560 nm for Er 3+ ions). The signal was then digitized and averaged over 64 consecutive pulses with a semi-digital oscilloscope (Fluke), and post-processed using the commercial software Matlab.

Electron relaxation from an excited energy level is the result of a combination of radiative and non-radiative processes. In most cases the number of excited electrons over time can be expressed by an exponential decay. If it is assumed that the emission intensity is proportional to the electron population, with a lifetime that depends on the temperature viewed by the sample during a past thermal event, then the phosphor intensity decay can often be described by an exponential decay sum which is expressed by the following equation:

I(t) = n i=1 A i .exp - t i (T ) n = 1, 2... ( 1
)
where A i is the amplitude of the exponential i, t is the time and i is the time constant of the exponential i for the studied phosphor. The number of the exponential which parameters have to be estimated depends on the fluorescent site in the phosphor under consideration: in the case of two closely electronic states in the forbidden band, two non-radiative relaxation pathways can be considered, which induce two different decay rates [START_REF] Berciaud | Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes[END_REF]. In another way, two close emission lines could also generate two additional decay exponential signals. Lifetime values were therefore estimated from the fit of the experimental data using a Nonlinear Least-Square approach (NLS) [START_REF] Istratov | Exponential analysis in physical phenomena[END_REF][START_REF] Fuhrmann | On the mono-exponential fitting of phosphorescence decays[END_REF][START_REF] Brübach | An algorithm for the characterisation of multi-exponential decay curves[END_REF] and Laplace-Padé approximation [START_REF] Hellen | Padé-Laplace analysis of signal averaged voltage decays obtained from a simple circuit[END_REF][START_REF] Claverie | Identification des modèles à fonction de transfert: la méthode padé-transformée en z[END_REF][START_REF] Bajzer | Padé-Laplace method for the analysis of time-resolved fluorescence decay curves[END_REF] with a theoretical mono-exponential model (Eq. ( 1)). Both methods gave nearly equivalent results for the parameter estimations, more particularly for a noisy signal. These algorithms appear to be robust in the case of a poor quality signal with a signal-to-noise ratio equal to 5. Therefore the two methods are reliable with close accuracy. However, the Laplace-Padé approximation appears to be faster than the least-square method, and is independent of the signal quality.

Other algorithms such as the Prony method [START_REF] Zhang | Prony's method for exponential lifetime estimations in fluorescence-based thermometers[END_REF], modulating functions [START_REF] Ortin | Thermogenesis: identification by means of modulating functions[END_REF], method of the moments [START_REF] Isenberg | Studies on the analysis of fluorescence decay data by the method of moments[END_REF] or the Tittlebach-Helmrich method [START_REF] Tittelbach-Helmrich | An integration method for the analysis of multiexponential transient signals[END_REF] were also studied, but they were not sufficiently robust for our signal analysis.

Results

Determination of thermal history sensing using a fluorescence intensity approach

As it can be seen in Fig. 1, using an intensity-based approach would allow to take advantage of the strong sensitivity to thermal history of the fluorescence intensity of the YSZ:Er 3+ marker. Thermal history sensing in application domains such as energy and aerospace engineering requires the capacity to perform precise temperature measurements on large or complex shaped parts, for which intensity ratio methods using CCD cameras are common, efficient and robust strategies. They rely on the monitoring of the ratio of the intensity of a peak sensitive to the temperature with, for instance, the intensity of a peak that is not or only slightly sensitive to temperature, and which is used as a reference to determine temperature [START_REF] Rabhiou | Oxidation of divalent rare earth phosphors for thermal history sensing[END_REF][START_REF] Khalid | Thermographic phosphors for high temperature measurements: principles, current state of the art and recent applications[END_REF]. In the case of YSZ:Er 3+ , a previous work [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF] has shown that YSZ:Eu 3+ fluorescence emission could play the role of a chemically compatible reference in a YSZ:Er 3+ /YSZ:Eu 3+ phosphor coating. The emission spectra of YSZ:Er 3+ presents two emission peaks at 545 nm and 562 nm that depend on the annealing temperature (Fig. 1). In contrast, YSZ:Eu 3+ has two emission peaks at 590 nm and 606 nm which are weakly dependent of temperature (for 15 min heat treatments) when already in a fully crystallized state [START_REF] Copin | Fonctionnalisation de barrières thermiques aéronautiques YSZ issues de la voie sol-gel : mesure de température et diagnostic de L'endommagement par fluorescence[END_REF]. The intensity ratio method selected is therefore based on the reference YSZ:Eu 3+ emission peak at 606 nm (better resolved), assumed to be little dependent of temperature in the range of interest (fully crystallized), and the temperature-dependent peaks of YSZ:Er 3+ at 545 nm or 562 nm. The corresponding intensity ratio R(T) is expressed as follows (Eq. ( 2)):

R (T ) = 1 I Er 3+ (T ) (562 nm or 545 nm) 2 I Eu 3+ (T ) (606 nm) (2)
with I Er 3+ (T ) and I Eu 3+ are the absolute fluorescence intensities of erbium and europium ions for the selected emission peaks, and 1 and 2 are the integration window widths (10 nm for both peaks). In the envisioned application, YSZ:Er 3+ (partially crystallized) and YSZ:Eu 3+ (fully crystallised) powders, synthesized separately, would be intimately mixed in appropriate proportions before deposition as a coating by a sol-gel process, so that the intensity ratio R(T) is derived from a direct reading of the absolute intensities I Er 3+ (T ) and I Eu 3+ . Such an intensity ratio would allow to be independent of geometric effects such as angle distribution of fluorescence signal and coating thickness inhomogeneity, which were observed to be quite significant on the YSZ:Eu 3+ coatings deposited by a sol-gel process.

YSZ:Eu 3+ coatings: effects of thickness homogeneity and fluorescence angle distribution

The air-spray sol-gel process that was used allowed to obtain fully crystallized, crack-free YSZ:Eu 3+ coatings after consolidation and calcination at 1273 K, with various thicknesses between 20 and 40 m. The thickness homogeneity of coatings, which could affect the quality of fluorescence intensity measurements, was evaluated with 2D intensity cartography (excitation wavelength of 535 nm). A typical spatial distribution of the fluorescence intensity of the 606 nm peak for a 26 mm × 20 mm YSZ:Eu 3+ coating (30 m average) is shown on Fig. 3(a). This map shows the fluorescence inhomogeneity of the coating and underlines an emission gradient over the sample length, which illustrates the coating handing. As the coating is obtained by sol-gel deposition through air-spraying, a thickness gradient appears on the coating. From the intensities map, a profile was extracted and plotted in Fig. 3(b), which confirms the inhomogeneity due to the thickness difference. This gradient of thickness, of around 20 m for this 30 m thick coating, was confirmed by confocal scanning

The signal sensitivity to the detection angle is also an important issue, in particular for parts with significant curvatures like turbine blades for instance. Fig. 4 shows the angle distribution of the europium fluorescence obtained on the same YSZ:Eu 3+ coating. The angle  is defined by the angle between the viewing direction of the spectrometer fibre and the normal to the sample surface. The experimental curve shows that up to a 45 • angle the signal is higher than 80% of the normal value. Therefore, it is estimated that for practical applications the signal quality can be maintained with a viewing angle between 0 and 30 • . For a skirting angle higher than 30 • , the fluorescent emission falls rapidly. Working with angle range where the signal is less sensitive to the viewing direction allows to identify geometry where a measurement correction is not necessary. Besides, for intensities ratio method, a low sensitive angle measurement ensures to work with a constant ratio which only depends to the annealing temperature.

The fluorescent angle distribution can be described by a Lambertian profile which is modelled by the following equation:

I  = I (0) .cos  (3)
with I() the fluorescent intensity at the viewing angle . Using this law, experimental measurements in industrial processes can be corrected to find the normal intensity value, although using an intensity ratio approach eliminate the need for such a correction. The same behaviour has been observed for coating thicknesses in the range 10-40 m and for annealing temperatures in the range 1173-1473 K. Considering the material thickness that the fluorescence emission, collected by the detector, passes through as the optical path, this behaviour can be explained by a thickness effect: for a volume illuminated by the incident flux remaining constant, the optical path increases when the viewing angle increases, therefore the viewing vertical depth penetration decreases. Indeed, the excitation spot can be considered as a point source with 1.2 mm diameter, which is small compared to the distance to the collection lens which is about 20 cm. For small viewing angles (observation direction close to that of the laser incidence direction), the observed volume is described by the illuminated volume, whereas for high angles the proportion of the emitted flux in the observation direction is smaller due to the lower viewing depth penetration and the flux absorption by the material.

In terms of practical applications of YSZ:Er 3+ /YSZ:Eu 3+ coatings, it is expected that small thickness effects on the fluorescence intensity caused by coatings inhomogeneity and the variation of the viewing angle problem would be easily overcome by the use of an intensity ratio approach from Er 3+ and Eu 3+ emissions. Optical data (transmission, reflection, absorption, scattering) available in the literature for air-plasma sprayed and EB-PVD YSZ coatings [START_REF] Eldridge | Depth-penetrating temperature measurements of thermal barrier coatings incorporating thermographic phosphors[END_REF][START_REF] Yang | Evaluation of the in-depth temperature sensing performance of Eu-and Dy-doped YSZ in air plasma sprayed thermal barrier coatings[END_REF][START_REF] Pilgrim | On the effect of temperature gradients and coating translucence on the accuracy of phosphor thermometry[END_REF][START_REF] Pilgrim | High resolution erosion detection in thermal barrier coatings using photoluminescent layers[END_REF], and from an earlier work for sol-gel deposited YSZ coatings [START_REF] Copin | Fonctionnalisation de barrières thermiques aéronautiques YSZ issues de la voie sol-gel : mesure de température et diagnostic de L'endommagement par fluorescence[END_REF] shows that the relative difference in absorption at the wavelength of Er 3+ green emissions (545 nm) and of Eu 3+ red emissions (606 nm) should be comprised between 5% and 20%. Therefore, the intensity ratio R(T) built from the green thermal history sensitive emission of Er 3+ ions and the red thermally insensitive emission of Eu 3+ ions (Eq. ( 2)) should not be significantly impacted by thickness inhomogeneities and for variations of the viewing angle involving small variations of the probed volume (15-20 m). However, this might not be the case if the thermal treatment involves the formation of any contaminant surface layers that might generate more significant differential attenuation at the Er 3+ and Eu 3+ emission wavelengths, such as combustion by-products in an engine test. The selected viewing angle for our measurements is about 0 • .

Excitation wavelength selection

Excitation spectra of YSZ:Er 3+ and YSZ:Eu 3+ sintered disks are shown on Fig. 5. The excitation spectrum of YSZ:Er 3+ exhibits three main excitation peaks at 380 nm, 488 nm and 515 nm, while YSZ:Eu 3+ main excitation peaks are at 398 nm, 467 nm and 535 nm. In the case of a coating or a powder with several dopants, multiple excitation sources can be useful, but a common excitation source for both activators can be also defined here. Indeed, the product of the two different excitation spectra, normalized by their higher respective peaks, leads to a general excitation spectrum, which helps to define an overall excitation source. Using the product of the normalized spectra of europium and erbium, the best excitation wavelength common to both dopants was identified at 535 nm (cf. Fig. 5), a little higher than the wavelength of the frequencydoubled Nd:YAG laser (532 nm) selected for fluorescence intensity measurements. This figure illustrates that the selected wavelength is close to optimal for exciting both Er 3+ and Eu 3+ .

Thermal sensitivity of the intensity ratio R(T)

The calculation of the ratio absolute sensitivity, which is the derivative of the calibration law relating R(T) (Eq. ( 2)) to temperature, requires to establish the calibration curves. These calibration curves for YSZ:Er 3+ and YSZ:Eu 3+ powders in proportions 1:1 (molar) are plotted in Fig. 6, for annealing temperatures ranging from 1223 K to 1423 K. Over this range of temperature, the ratio built with the Er 3+ 545 nm emission and the Er 3+ 562 nm emission increases by a factor of 11 and 10 respectively. These calibration curves show again that the intensity ratio method is an efficient method to determine temperature with good resolution, as discussed in reference [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF]. This method uses a relative intensity measurement rather than an absolute intensity measurement for temperature determination, thus avoiding significant sources of errors, such as geometric errors. However, the method would remain sensitive to any selective attenuation at the wavelength of Fig. 5. Normalized excitation spectra of YSZ:Eu 3+ (phosphor coating) and YSZ:Er 3+ (sintered disk) samples annealed at 1273 K, considering the emission wavelengths of 610 nm (Eu 3+ ) and 562 nm (Er 3+ ). The product of the two normalized spectra is plotted as a black solid line. Fig. 6. Intensity ratios as a function of the annealing temperature for YSZ:Er 3+ sample (phosphor powder), considering two emission lines at 562 nm and 545 nm (excitation wavelength at 532 nm). YSZ:Eu 3+ powder is used as a reference for calculating the ratios.

Eu 3+ and/or Er 3+ emissions by contaminant surface layers that could potentially form during heat treatments involving a combustion environment.

The curves which express the intensity ratio as a function of the annealing temperature can be modelled with a simple monoexponential function between 1223 and 1423 K. It should be noted that beyond 1423 K, the intensity ratio calibration curve cannot be extrapolated due to an asymptotic behaviour toward the intensity ratio obtained with YSZ:Er 3+ in its assumed final state (fully crystallized). The derivative of the function gives the absolute sensitivity of the sensor material regarding thermal history, which evolution with temperature is plotted around each experimental data point in Fig. 7. These sensitivity curves show that the phosphor YSZ:Er 3+ /YSZ:Eu 3+ offers a growing sensitivity with the increase of temperature. The ratios built with the 545 nm and 562 nm wavelengths exhibit close sensitivities in spite of an amplitude difference. The sensitivity obtained with the Er 3+ emission line at 545 nm increases from 0.001 K -1 to 0.015 K -1 whereas with the emission line at 562 nm it increases from 0.0004 K -1 to 0.009 K -1 . Since the sensitivity increases over the temperature range 1223 K-1423 K, it appears that this YSZ:Er 3+ /YSZ:Eu 3+ sensor would be especially appropriated for measuring temperatures higher than 1273 K, which are representative of the targeted industrial process operating temperatures (eg. gas turbines).

Resolution of the method (noise equivalent temperature difference)

In order to discuss the thermal resolution of this YSZ:Er 3+ /YSZ:Eu 3+ phosphor, and to compare its performance with other temperature measurement methods, the determination of the Noise Equivalent Temperature Difference is introduced. Noise Equivalent Temperature Difference (NETD) is a classic indicator of the temperature resolution of a thermal radiation detector, and is often used in infrared thermography [START_REF] Gaussorgues | La thermographie infrarouge: principes, technologies, applications[END_REF]. Commonly, the NETD is determined with a 303 K blackbody, from temperature absolute sensitivity and signal to noise ratio, to express infrared camera thermal resolution. In our case, the NETD calculation is extended to a higher temperature range, based on the fact that in Fig. 7. Absolute sensitivity of the intensity ratio method as a function of the annealing temperature for YSZ:Er 3+ samples (phosphor powder), considering two emission lines at 562 nm and 545 nm (excitation wavelength at 532 nm). YSZ:Eu 3+ powder is used as a reference for calculating the ratios (Eq. ( 2)).

the case of a thermal history sensor the actual measurements are made at room temperature, although the results are related to a high temperature experienced beforehand. NETD is therefore calculated for each experimental data point to compare the efficiency with classical thermography technics. Its expression is given by the following equation (Eq. ( 4)):

NETD = i S T i ( 4
)
where i is the standard deviation of the measured intensity corresponding to the thermal treatment temperature, relating to the uncertainty of the detector (spectrometer), and S T i is the sensor absolute sensitivity around the thermal treatment temperature T i , given by the following equation (Eq. ( 5)):

S T i = dR dT T =T i (5)
The evolution of the absolute sensitivity with temperature is determined using the exponential model previously identified between 1223 K and 1423 K (Fig. 7). For each temperature, the uncertainty of the detector was estimated by considering the standard deviation from over the 30 averaged spectra. Since the ratio is built from the measurements of two different emission lines (for YSZ:Er 3+ and YSZ:Eu 3+ respectively), the uncertainty i considered takes into account the standard deviation of the measurement for both phosphors.

Fig. 8 shows the evolution of NETD as a function of the heat treatment temperature for the two considered intensity ratios (Er 3+ peaks at 545 nm and 562 nm). The NETD are first observed to decrease from 4.9 K to a minimum value of 1.5 K between 1223 K to and 1323 K, before increasing slightly afterwards until reaching roughly 2.1 K at 1423 K. Overall, the NETD calculations between 1223 K and 1423 K give a theoretical temperature resolution between 1.6 K and 5 K. These NETD values will be further discussed and compared with the performance of other methods (infrared thermography and thermal indicating paints) in the Discussion section.

Determination of the thermal history sensing using lifetime analysis

Previous work [START_REF] Copin | Novel erbia-yttria co-doped zirconia fluorescent thermal history sensor[END_REF], dealing with the luminescence lifetime study of the YSZ:Er 3+ system (sol-gel synthesized powder), has shown that the fluorescence lifetime of the 562 nm emission line exhibits a linear increase with the annealing temperature between 1173 K and 1373 K as a result of the enhancement of the crystallinity of the material. The decay time was observed to increase from 28 to 42 s over this temperature range. Beyond this temperature range, this linear behaviour cannot be extrapolated since after 15 min at 1423 K the lifetime has already converged to the value obtained with the assumed fully crystallized final state (44 s).

Since the model which describes the evolution of the lifetime with temperature is linear, the absolute sensitivity of the fluorescence lifetime of YSZ:Er 3+ with the temperature is a constant value (0.061 s/K). As done previously with the theoretical thermal resolution calculated for the intensity ratios (i.e. NETD, Eq. ( 4)), the theoretical thermal resolution is estimated considering this linear model. The standard deviation of this calculation considers the general uncertainty with its enlargement coefficient expressed through the error bars on Fig. 9. As shown in Fig. 9, the NETD values are comprised between 1.7 K-5.8 K in the temperature range 1173 K and 1373 K. As expected, the graph does not exhibit any specific NETD tendency with the sample annealing temperature, and the lowest values are obtained for 1323 K and 1373 K.

Discussion

YSZ:Er 3+ phosphor produced by a sol-gel route exhibit a strong sensitivity of its fluorescence emission with temperature for short duration heat treatments (Fig. 1), which makes it a potential indicator of the temperature experienced during past thermal events. Results obtained with YSZ:Eu 3+ coatings shows that a sol-gel process combined with an air-spray deposition method would be a suitable solution to deposit this YSZ:Er 3+ sensor for practical measurement of thermal history in applications such as jet turbine engine design and testing.

As for direct measurement of temperature by phosphor thermometry, a typical intensity ratio approach using fully crystallized YSZ:Eu 3+ emission as a reference (Fig. 5) can be used to improve the robustness of the sensor regarding experimental conditions which Fig. 8. NETD as a function of the annealing temperature for intensity ratios (YSZ:Er 3+ samples phosphor powder), considering two emission lines at 562 nm and 545 nm (excitation wavelength at 532 nm). Fig. 9. NETD as a function of the annealing temperature for lifetime analysis (YSZ:Er 3+ samples phosphor powder), considering emission line at 562 nm (excitation wavelength at 532 nm).

directly affect absolute intensity measurements, such as thickness uniformity and angle of observation (Fig. 3 and Fig. 4). The deposition of the corresponding self-referenced coating would simply be achieved through the co-deposition of YSZ:Er 3+ and YSZ:Eu 3+ powders mixed in appropriate proportions (prepared individually instead of co-doping YSZ, to avoid energy transfer between Eu 3+ and Er 3+ ions) by air-spraying. However, results obtained with YSZ:Er 3+ and YSZ:Eu 3+ coatings were not introduced in this paper for the sake of confidentiality.

Alternatively, single YSZ:Er 3+ coatings could be applied if the linear increase of fluorescence lifetime of Er 3+ ions with heat treatment temperature is to be used as an indicator of thermal history instead. Although more complex to put in application than an intensity mapping approach, fluorescence lifetime mapping would have the advantage to make the use of the YSZ:Eu 3+ reference unnecessary and to be more robust regarding possible contamination by optically absorbing contaminant surface layers in combustion environments.

Analysis of intensity and lifetime-based calibration curves

shows that NETD appears to be a useful tool for comparison between temperature measurement methods, as a formal indicator of the temperature resolution of the sensor for a given detector across the whole investigated temperature range. Indeed, sensitivity alone does not take into account the uncertainties brought by the detector, which can significantly impact the actual resolution at a given temperature. Hence, while the absolute sensitivity of the intensity ratio built from the 545 nm Er 3+ emission line steadily increase from 0.0013 K -1 to about 0.0143 K -1 over the 1223 K-1423 K range (Fig. 7), the NETD achieve a minimum of 1.5 K at 1323 K before stabilizing at around 2 K for higher temperatures (Fig. 8). This difference in behaviour is caused by the increase of the uncertainty from the detector with increasing level of intensity collected at some point: in the considered temperature range the calculated standard deviation i increases from 0.008 to 0.0205, which attenuates a bit the potential benefits on the thermal resolution of the exponentially growing sensitivity of YSZ:Er 3+ . Table 1 show the evolution of NETD, absolute sensitivity, and relative sensitivity of intensity ratios R(T) and the lifetime (T ) across the range 1173 K-1423 K. The relative intensity ˛(T i ) around a given temperature T i is defined by Eq. ( 6):

˛Ti = 1 A(T i ) . dA dT T =T i (6)
where A(T i ) is the output at T i in %/K (either the intensity ratio R or the fluorescence lifetime ). It expresses the output increase, as a percentage of the local output A(T i ), per increment of temperature.

In the case of the intensity ratio, which follows a simple exponential model, the relative sensitivity is thus constant with temperature, while the relative sensitivity of the fluorescence lifetime, which follows a linear model, decreases with the reciprocal of lifetime.

Comparing relative sensitivity values, the fluorescence lifetime appears to be much less sensitive to thermal history than the intensity ratios (relative sensitivity between 6 and 8 times lower), yet both methods have relatively similar NETD over the whole temperature range, which means that both methods would in theory produce similar temperature-resolved measurements if carried out in the same conditions than presented in this paper (punctual measurements). The choice of one method over the other will therefore also greatly depend on the level of complexity tolerable (for coatings preparation) and the presence of optically absorbing contaminant surface. However, the NETD results presented here cannot be extended to temperature mapping, as it will depend on the performance of the chosen detectors, likely to be different between intensity mapping and lifetime mapping.

The NETD therefore appear to be a relevant complementary metric to the sensitivity to illustrate the performance of a thermal history sensor for a given detector. For thermal history sensing in critical areas on turbine components, where knowing precisely the temperature could allow to design systems with better optimized upper limit operating temperature, NETD might become a better criteria than sensitivity for selecting the measurement method. Results have shown that for punctual measurement, YSZ:Er/Eu sensor would be interesting to use in critical areas subjected to the hottest temperature range in such application (close to 1473 K), because of its small theoretical resolution when compared to other methods such as thermochromic paints [START_REF] Hodgkinson | Temperature Indicating Paint[END_REF][START_REF] Hughes | Temperature Indicating Paint[END_REF][START_REF] Watson | Temperature indicating paint[END_REF]. For areas where less precision on temperature is acceptable (eg. lower temperature range 900 • C-1000 • C), it might be less relevant though, especially for thin coatings (potentially stained by contaminants) where low fluorescence intensity levels can be expected.

Table 2 compares the thermal resolution of fluorescent methods with those of classical thermography technics, through the NETD expressions. Classic temperature measurement methods used in industrial processes are presented, such as infrared technology and thermochromic paints with their NETD [START_REF] Lempereur | Surface temperature measurement on engine components by means of irreversible thermal coatings[END_REF][START_REF] Vollmer | Infrared thermal imaging: fundamentals[END_REF][START_REF]Annual Conference of Doctoral Students, WDS'13 "Week of Doctoral Students 2013[END_REF][START_REF] Azar | Thermal Measurements in Electronics Cooling[END_REF]. In the high temperature range (above 1223 K), the fluorescent thermal sensors present efficient thermal resolution with an NETD lower than 5 K, but still higher than IR methods. In the temperature range between 253 K and 1773 K, infrared cameras (operating between 3 and 5 m), have typically a NETD value between 0.03 K and 0.3 K. With infrared camera, if the measurement range is increased to superior temperature range, the NETD could be higher due to the decreased sensitivity of the camera. It is the result of the filter insertion and unchanged noise. The IR measurements performed in band III exhibit an NETD lower than 1 K with a value around 0.6 K. This value was calculated from over 300 consecutive images acquired in front of a black body to determine the standard deviation. The band II takes a higher sensitivity then the band III, however at low temperatures the signal noise is more present. The IR technology offers advantages over an online 2D surface temperature measurement. However, this technology is difficult to implement, due to optical access, in case of inaccessible harsh environment. Besides, the emissivity value is a main issue for infrared temperature monitoring. Furthermore, infrared measurements are very sensitive to reflective fluxes more particular in case of metallic surface. Thermochromic paints give information on the maximum temperature history with an offline analysis, and therefore can readily be used in areas difficult to access with other methods. However, theoretical resolution are significantly less good, with "NETD" values exceeding 10 K and in some cases reaching values as high as 100 K, due to the discrete nature of the colour changes used to determine temperature. In addition, this method requires a skilled operator to link colour changes with the surface temperature seen by the part during a past thermal event, which adds to the already relatively poor theoretical resolution.

Therefore, these fluorescent methods applied to the YSZ:Er 3+ /YSZ:Eu 3+ phosphor (lifetime analysis and intensity ratios), appear to be relevant methods to measure temperature in areas which are difficult to access, as an alternative to thermochromic paints. The calculated NETD, presented in Table 1, are the result of the spectral characterization of the YSZ:Er 3+ /YSZ:Eu 3+ phosphor with punctual detectors, but other phosphors could also work in different temperature ranges with different NETDs. It should be also noted that NETD values might be very different if using 2D detectors such as cameras for temperature mapping. Thus, fluorescent thermometric methods are alternative candidates for temperature measurements in industrial processes in the form of coatings.

Conclusion

Overview

In this paper, the offline analysis of fluorescent thermal history sensors has been introduced through the example of Eu 3+ and Er 3+ doped YSZ. The paper describes both spectral and temporal methods suitable for complex sample geometry. The comparison between the intensity ratio method and the lifetime analysis method (Table 3) underlines that the first method is more sensitive to the thermal history for the studied sample.

In the temperature range 1223 K-1423 K, the YSZ:Er 3+ /YSZ:Eu 3+ sample, with an efficient sensitivity and a thermal resolution between 2 and 5 K, appears to be a very good candidate for thermal history sensing. The lifetime analysis is more independent of experimental conditions and staining by contaminants than the intensity ratio method, but the low sensitivity of the method is a working limit, more particularly for temperatures higher than 1273 K where the intensity ratio method is more efficient.

These two methods offer a better theoretical resolution (estimated with Noise Equivalent Temperature Difference, NETD) than thermochromic paints, and appear to be easier to use because they do not need subjective colour comparison. As shown in Table 2, thermochromic paints still provide a complementary temperature sensing range from 423 to 1423 K, although with an increasing NETD with temperature. The NETD appears to be a relevant metric complementary to sensitivity for comparison of the performance of different methods, as the integration of the uncertainties brought by the detector can provide a better insight of the theoretical resolution that can be achieved in the considered temperature range. Infrared cameras work in various harsh environments where realtime analysis with a fast acquisition frequency is major issue in surface monitoring. Consequently an optical access to the target is required. In spite of a higher NETD value, fluorescent methods still offer a large application field where they could be more suitable than IR methods, more particular in the offline analysis. In conclusion, the two fluorescent methods are complementary, and their applications depend on the studied material, the accuracy required and the measurement environment constraints.

Future work

The experimental setup introduced in this paper is a multipurpose setup which is intended to perform intensity acquisition and lifetime analysis. For a better study of the excitation angle dependence, the excitation source can be improved using a fibered laser. By using the optical fibre, the excitation direction can easily be directed to the studied sample and allow a wide and easy range of angle.

The fluorescent thermography method can be also extended to 2D measurements for building an intensity ratio map from measurement at two different wavelengths. Therefore, thermal history maps could be obtained instead of punctual measurement, allowing to study large surfaces of interest as required in industrial pro-cess involving thermal history sensing. Future work will look at the NETD that could be achieved in temperature mapping with the developed YSZ:Er 3+ /YSZ:Eu 3+ coatings. The experimental setup has already been upgraded to install LED technology, which is used in many scientific domains [START_REF] Xu | A lamp light-emitting diode-induced fluorescence detector for capillary electrophoresis[END_REF][START_REF] Ryškevič | Concept design of a UV light-emitting diode based fluorescence sensor for real-time bioparticle detection[END_REF][START_REF] Ek | Compact fiber-optic fluorosensor employing light-emitting ultraviolet diodes as excitation sources, spectrochim[END_REF]. LEDs allow a large range of wavelengths in order to study various phosphors with different excitation wavelengths. LEDs could offer source stability to obtain better measurement accuracy and the combination of several different LEDs used with samples doped with various phosphors offers a useful modularity of the bench. The main issue with LED is the power limit in the UV range. However in visible range numerous wavelengths are available. The possibility for using the current diode technology as a pulsed source will be investigated.

Fig. 2 .

 2 Fig. 2. Experimental setup used for fluorescence lifetime analysis.

Fig. 3 .

 3 Fig. 3. (a) Intensities map of the fluorescence emission of a 30 m average thick YSZ:Eu 3+ coating annealed at 1273 K, considering the emission line at 606 nm (excitation wavelength at 535 nm), and (b) intensity profile extracted from the same intensity map in (a).

Fig. 4 .

 4 Fig. 4. Angular distribution of fluorescence emission of an average 30 m thick YSZ:Eu 3+ coating annealed at 1273 K, considering the emission line at 606 nm (excitation wavelength at 535 nm).

Table 1

 1 Sensitivity and NETD of the intensity ratio and the lifetime analysis methods as a function of the temperature ranges between 1173 K and 1423 K for YSZ: Er 3+ samples (phosphor powder).

	Temperature (K)		1173 K	1223 K	1273 K	1323 K	1373 K	1423 K
	Lifetime Analysis	Sensitivity S (s K -1 )	6.10E-2	6.10E-2	6.10E-2	6.10E-2	6.10E-2	-
		Relative sensitivity ␣ (% K -1 )	0.216	0. 192	0.174	0.154	0.148	-
		NETD (K)	5.8	3.5	5.7	1.7	2.3	-
	Intensity Ratio (545 nm)	Sensitivity S (K -1 )	-	1.30E-3	2.18E-3	4.89E-3	8.71E-3	1.43E-2
		Relative sensitivity ␣ (% K -1 )	-	1.24	1.24	1.24	1.24	1.24
		NETD (K)	-	4.7	2.5	1.5	1.7	1.9
	Intensity Ratio (562 nm)	Sensitivity S (K -1 )	-	9.50E-4	1.61E-3	3.49E-3	6.05E-3	9.38E-3
		Relative sensitivity ␣ (% K -1 )	-	1.18	1.18	1.18	1.18	1.18
		NETD (K)	-	4.9	2.7	1.7	2	2.1

Table 2

 2 NETD comparative table between different temperature measurement methods for various temperature ranges.

	Method	NETD (K)	Temperature Range (K)	Reference
	Lifetime Analysis	2-5	1173-1373	-
	Intensity Ratio (540 nm)	1.5-4.8	1223-1423	-
	Intensity Ratio (560 nm)	1.7-5	1223-1423	-
	IR Camera (8-12 m)	0.6-0.7	1273-1473	-
	IR Camera (3-5 m)	0.03-0.1	253-423	[48]
	IR Camera (3-5 m)	0.3	253-1773	[49]
	Thermochromic Paint	10-20	423-583	[50]
	Thermochromic Paint	10-100	853-1253	[9]

Table 3

 3 Comparative table between the intensity ratio method and the lifetime analysis method.

	Intensity Ratio

Acknowledgements

The authors would like to thank Guillaume Pujol for his kind assistance with the materials synthesis and the deposition of the coatings. This research is included in the FRIMATT programme from Aerospace Valley with funding from OSEO, the Aquitaine & Midi-Pyrénées Regions and the department of the Ariège.