Jean-François Rontani
email: jean-francois.rontani@mio.osupytheas.fr

Use of gas chromatography-mass spectrometry techniques (GC-MS, GC-MS/MS and GC-QTOF) for the characterization of lipid photooxidation and autoxidation products in senescent autotrophic organisms

Keywords: Senescent phototrophs, Unsaturated lipids, Photooxidation, Autoxidation, Gas chroma-25 tography-mass spectrometry, Specific tracers, TMS derivatives, EI fragmentation. 26 27 chromatography-mass spectrometry

This paper reviews applications of gas chromatography-mass spectrometry techniques for the characterization of lipid photooxidation and autoxidation products in senescent phototrophic organisms. Particular attention is given to: (i) the selection of oxidation products that are sufficiently stable and specific to each lipid class and degradation route, (ii) the description of electron ionization mass fragmentation of trimethylsilyl derivatives of these compounds and (iii) the use of specific fragment ions for monitoring the oxidation of the main unsaturated lipid components of phototrophs. The techniques best geared for this task were gas chromatography-quadrupole-time of flight to monitor fragment ions with very high resolution and accuracy, and gas chromatography-tandem mass spectrometry to monitor very selective transitions in multiple reaction monitoring mode. The extent of the degradation processes can only be estimated if the oxidation products are unaffected by fast secondary oxidation reactions, as it is notably the case of  5 -sterols, monounsaturated fatty acids, chlorophyll phytyl side-chain, and di-and triterpenoids. In contrast, the primary degradation products of highly branched isoprenoid alkenes possessing more than one trisubstituted double bond, alkenones, carotenoids and polyunsaturated fatty acids, appear to be too unstable with respect to secondary oxidation or other reactions to serve for quantification in senescent phototrophs.

Introduction

Phototrophic organisms (mainly green plants, algae, cyanobacteria and some protists) [START_REF] Halliwell | Oxidative damage, lipid peroxidation and antioxidant protection in chloroplasts[END_REF] carry out photosynthesis i.e. conversion of sunlight energy, carbon dioxide and water plex lipids into their constituent fatty acids, plus glycerol, phosphate, sterol or sugar groups [START_REF] Volkman | Lipid markers for marine organic matter[END_REF], and then (iii) conversion of polar compounds to volatile derivatives (derivatization). Despite this added time-consuming pre-treatment (which is not necessary with HPLC-MS analyses), GC-MS techniques involving electron ionization (EI) and chemical ionization (CI) are widely employed for the characterization of lipid oxidation products [START_REF] Xia | Techniques for the analysis of minor lipid oxidation products derived from triacylglycerols: epoxides, alcohols, and ketones[END_REF][START_REF] Xu | Monitoring oxidative stability and changes in key volatile compounds in edible oils during ambient storage through HS-SPME/GC-MS[END_REF][START_REF] Barden | GC-MS analysis of lipid oxidation products in blood, urine, and tissue samples[END_REF]. Indeed, EI provides more structural information than the soft ionization techniques such as electron spray ionization (ESI) or atmospheric pressure chemical ionization (APCI) employed in HPLC-MS analyses, notably as it enables easy determination of the position of functional groups of lipid oxidation products [START_REF] Koek | Quantitative metabolomics based on gas chromatography mass spectrometry: status and perspectives[END_REF]. However, the relatively soft ESI and APCI ionization modes used during HPLC-MS analyses allow structural characterization of thermally-labile compounds (e.g. hydroperoxides) [START_REF] Frankel | Lipid oxidation[END_REF]. Moreover, the possibility to work in reverse-phase liquid chromatography also allows the analysis of compounds too heavy or polar to be amenable by GC (e.g. triacylglycerides) [START_REF] Frankel | Lipid oxidation[END_REF][START_REF] Schick | Analysis of mono-, di-, triacylglycerols, and fatty acids in food emulsifiers by high-performance liquid chromatography-mass spectrometry[END_REF]. Note that other powerful non-chromatographic techniques such as matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) [START_REF] Han | Direct tissue analysis by MALDI-TOF mass spectrometry in human hepatocellular carcinoma[END_REF][START_REF] Leopold | Recent developments of useful MALDI matrices for the mass spectrometric characterization of lipids[END_REF], ion-mobility mass spectrometry (IM-MS) [START_REF] Paglia | Applications of ion-mobility mass spectrometry for lipid analysis[END_REF][START_REF] Leaptrot | Ion mobility conformational lipid atlas for high confidence lipidomics[END_REF], and nuclear magnetic resonance (NMR) [START_REF] Merkx | Rapid quantitative profiling of lipid oxidation products in a food emulsion by 1 H NMR[END_REF] also appeared to be very useful for the characterization of lipid oxidation products.

In this review, particular attention is given to the use of gas chromatography-tandem mass spectrometry (GC-MS/MS) and gas chromatography-quadrupole-time of flight (GC-QTOF) techniques for the characterization of trimethylsilyl (TMS) derivatives of lipid oxidation products in senescent phototrophic organisms. GC-MS/MS can perform analyses in multiple reaction monitoring (MRM) mode based on specific collisioninduced fragmentations of precursor ions, which substantially increase signal-to-noise ratios and method sensitivity [START_REF] He | Comparison of GC-MS/MS and LC-MS/MS for the analysis of hormones and pesticides in surface waters: advantages and pitfalls[END_REF]. GC-QTOF offers high mass resolution and accuracy, and can use narrow mass intervals reducing interferences and background noise, making it particularly suitable for identifying unknown lipid oxidation products in complex natural extracts.

Trimethylsilylation is the method most commonly employed for derivatization of lipids in GC-MS analyses [START_REF] Pierce | Silylation of Organic Compounds[END_REF][START_REF] Evershed | Biomolecular archaeology and lipids[END_REF]. TMS derivatives are produced by replacing the active hydrogen atom of alcohols, acids, amines and thiols by a trimethylsilyl group. These derivatives are highly volatile, thermally stable and present outstanding gas chromatographic characteristics. EI mass spectra of TMS derivatives generally exhibit a significant [M -15] + ion formed by loss of a silicon-bonded methyl group, which is especially useful for determining molecular mass. Fragmentations of these derivatives are also hugely informative for structural elucidations [START_REF] Goad | Mass Spectrometry of Sterols[END_REF][START_REF] Harvey | Mass spectrometric fragmentation of trimethylsilyl and related alkylsilyl derivatives[END_REF].

Abiotic oxidation of lipid components of autotrophic organisms

Type II photosensitized oxidation

Due to the presence of chlorophyll, which is a very efficient photosensitizer [START_REF] Foote | Photosensitized Oxidation and Singlet Oxygen: Consequences in Biological Systems[END_REF][START_REF] Knox | Singlet oxygen and plants[END_REF], visible light-induced photosensitized processes act intensively during the senescence of autotrophic organisms. In healthy cells, the excited singlet state of chlorophyll ( 1 Chl) formed after absorption of a quantum of light energy, leads predominantly to the characteristic fast photosynthesis reactions [START_REF] Foote | Photosensitized Oxidation and Singlet Oxygen: Consequences in Biological Systems[END_REF]. However, a small proportion of 1 Chl undergoes intersystem crossing (ISC) to form the longer live triplet state ( 3 Chl) [START_REF] Knox | Singlet oxygen and plants[END_REF], which is not only itself potentially damaging in type I reactions [START_REF] Knox | Singlet oxygen and plants[END_REF] but can also generate ROS and, in particular, singlet oxygen ( 1 O2) by reacting with ground state oxygen ( 3 O2) (type

II processes).

As a defense against oxidative damage, there are many antioxidant compounds (e.g. carotenoids and vitamin E) and enzymes (e.g. superoxide dismutase and catalase) that operate in chloroplasts [START_REF] Foote | Photosensitized Oxidation and Singlet Oxygen: Consequences in Biological Systems[END_REF][START_REF] Halliwell | Oxidative damage, lipid peroxidation and antioxidant protection in chloroplasts[END_REF].

As fast photosynthesis reactions are clearly not operative in senescent phototrophic organisms, potentially damaging 3 Chl and 1 O2 [START_REF] Nelson | Rates and possible mechanism of light-dependent degradation of pigments in detritus derived from phytoplankton[END_REF] are produced at an accelerated rate exceeding the quenching capacity of the photoprotective system and thus damage the membranes (photodynamic effect [START_REF] Merzlyak | Free radical metabolism, pigment degradation and lipid peroxidation in leaves during senescence[END_REF]). 1 O2 readily oxidizes cellular components of senescent autotrophic organisms such as unsaturated lipids (including  5 -sterols, unsaturated fatty acids, chlorophyll phytyl side-chain, carotenoids and alkenes), proteins, and nucleic acids [START_REF] Glaeser | Singlet oxygen stress in microorganisms[END_REF]. The rate of reaction of 1 O2 with olefins is controlled by the degree of substitution and the configuration (cis-or trans-) of the double bond [START_REF] Hurst | The ene reaction of singlet oxygen: kinetic and product evidence in support of a perepoxide intermediate[END_REF], with highlysubstituted and cis-double bonds being the more reactive. Type II photosensitized oxidation of unsaturated lipids affords allylic hydroperoxides (for reviews see [START_REF] Rontani | Photo-and Free Radical-Mediated Oxidation of Lipid Components during the Senescence of Phototrophic Organisms[END_REF][START_REF] Rontani | Photo-and autoxidation of unsaturated algal lipids in the marine environment: an overview of processes, their potential tracers, and limitations[END_REF]).

Free radical oxidation (autoxidation)

Due to spin restriction [START_REF] Krumova | Overview of Reactive Oxygen Species[END_REF], the unpaired electrons of ground-state triplet molecular oxygen 3 O2 can only interact with unpaired electrons of organic radicals, which drive autoxidation reactions. Autoxidation involves free-radical-mediated oxidation chain reactions, which can be divided into three steps: chain initiation, propagation, and termination [START_REF] Schaich | Lipid Oxidation: Theoretical Aspects[END_REF]. Initiation of autoxidation requires initiators that are able to produce radicals by removing an electron to the substrate molecule or breaking a covalent bond.

The most common initiators are heat, light, redox-active metal ions undergoing oneelectron transfer (e.g. Fe 2+ , Co 2+ , Fe 3+ , Cu 2+ , Mn 2+ , Zn 2+ , Mg 2+ , V 2+ ), and certain enzymes (lipoxygenases). The propagation step involves a succession of reactions in which each radical produced in one reaction is consumed in the next [START_REF] Fossey | Free Radicals in Organic Chemistry[END_REF]. It generally proceeds via:

(i) hydrogen atom abstraction from tertiary, allylic or  to oxygen positions, and (ii) addition of peroxyl radicals to double bonds. Termination results from reactions of radicals affording non-radical products. In senescent phototrophic cells, initiation of autoxidation processes is generally attributed to the cleavage (induced by heat, light, metals or enzymes) of hydroperoxides resulting from type II photosensitized oxidation of cellular components to hydroxyl, peroxyl and alkoxyl radicals [START_REF] Girotti | Lipid hydroperoxide generation, turnover, and effector action in biological systems[END_REF][START_REF] Rontani | Photochemical oxidation and autoxidation of chlorophyll phytyl side chain in senescent phytoplanktonic cells: potential sources of several acyclic isoprenoid compounds in the marine environment[END_REF].

Characterization of the oxidation products of lipids

This chapter briefly describes the mechanisms of photooxidation and autoxidation of the main unsaturated lipids of phototrophic organisms. A focus is given to the selection of oxidation products sufficiently stable and specific to act as tracers of these processes under environmental conditions, as well as to the mechanisms of fragmentation of TMS derivatives of these compounds during electron ionization. Some application examples of these tracers are also shown. Note that accurate masses of the different fragment ions formed are given, which makes them amenable to use in GC-QTOF analyses, while the corresponding unit masses can still be used in GC-MS/MS or classical GC-MS analyses.

Chlorophyll phytyl side-chain

Attack of 1 O2 on the tri-substituted double bond of the chlorophyll phytyl sidechain affords two allylic hydroperoxides, which may be recovered in the form of 6,10,14trimethylpentadecan-2-ol and 3-methylidene-7,11,15-trimethylhexadecan-1,2-diol (phytyldiol) after NaBH4 reduction and alkaline hydrolysis [START_REF] Rontani | Photodegradation of chlorophyll phytyl chain in senescent leaves of higher plants[END_REF] (Scheme 1). The stable and highly specific phytyldiol was proposed as biogeochemical marker of chlorophyll photodegradation in the natural environment [START_REF] Cuny | On the widespread occurrence of 3-methylidene-7,11,15-trimethylhexadecan-1,2-diol in the marine environment: a specific isoprenoid marker of chlorophyll photodegradation[END_REF]. In contrast, free radical oxidation (autoxidation) of chlorophyll phytyl side-chain and subsequent reduction and hydrolysis gives 3,7,11,15-tetramethylhexadec-3-en(Z/E)-1,2-diols, 3,7,11,15-tetramethyl-hexadec-2en(Z/E)-1,4-diols and 3,7,11,15-tetramethyl-hexadec-1-en-3-ol (isophytol) [START_REF] Rontani | Characterization of isomeric allylic diols resulting from chlorophyll phytyl side-chain photo-and autoxidation by electron ionization gas chromatography/mass spectrometry[END_REF][START_REF] Rontani | Autoxidation of chlorophyll phytyl side chain in senescent phototrophic organisms: a potential source of isophytol in the environment[END_REF] (Scheme 1). These compounds have been proposed as specific tracers of chlorophyll phytyl sidechain autoxidation in environmental samples [START_REF] Rontani | Characterization of isomeric allylic diols resulting from chlorophyll phytyl side-chain photo-and autoxidation by electron ionization gas chromatography/mass spectrometry[END_REF][START_REF] Rontani | Autoxidation of chlorophyll phytyl side chain in senescent phototrophic organisms: a potential source of isophytol in the environment[END_REF].

R 1 CH 2 O C R 2 O R 1 OOR CH 2 O C R 2 O R 1 OOH R 1 CH 2 O C R 2 O HOO R 1 OH R 1 CH 2 OH OH R 1 CH 2 OH OH (CH 2 ) 2 Pyr R 1 = R 2 = Pyr =

 5 -sterols

Reaction of 1 O2 with the double bond of  5 -sterols mainly affords a  6 -5hydroperoxide and to a lesser extent  4 -6-hydroperoxides [START_REF] Kulig | Sterol metabolism. XXV. Cholesterol oxidation by singlet molecular oxygen[END_REF][START_REF] Korytowski | Photoperoxidation of cholesterol in homogeneous solution, isolated membranes, and cells: comparison of the 5-and 6-hydroperoxides as indicators of singlet oxygen intermediacy[END_REF] (Scheme 3). Under environmental conditions 6 -5-hydroperoxide undergoes fast allylic rearrangement to unstable and unspecific 7-hydroperoxides (Scheme 3).  4 -Stera-3,6-diols resulting from NaBH4-reduction and alkaline hydrolysis of  4 -6-hydroperoxides were thus proposed as specific tracers of type II photosensitized oxidation of the corresponding  5 -sterols [START_REF] Christodoulou | Use of lipids and their degradation products as biomarkers for carbon cycling in the northwestern Mediterranean Sea[END_REF][START_REF] Rontani | The fate of marine lipids: biotic vs. abiotic degradation of particulate sterols and alkenones in the northwestern Mediterranean Sea[END_REF].

Autoxidation of  5 -sterols mainly affords unstable and unspecific 7hydroperoxides after hydrogen atom abstraction at the allylic carbon atom 7 [START_REF] Smith | Cholesterol autoxidation 1981-1986[END_REF]) (Scheme 3). Smaller proportions of isomeric 5,6-and 5,6-epoxysterols are also produced after addition of peroxyl radical to the double bond [START_REF] Morrisey | Oxysterols: formation and biological function[END_REF] (Scheme 3). Stable and specific 3,5,6-trihydroxysterols resulting from the hydrolysis of these epoxides during alkaline hydrolysis and in environmental conditions were proposed as specific tracers of the autoxidation of  5 -sterols [START_REF] Christodoulou | Use of lipids and their degradation products as biomarkers for carbon cycling in the northwestern Mediterranean Sea[END_REF][START_REF] Rontani | The fate of marine lipids: biotic vs. abiotic degradation of particulate sterols and alkenones in the northwestern Mediterranean Sea[END_REF].

RO RO OOH RO O RO OOH RO OOH HO OH HO HO OH HO OH C R 1 O SO 3 H
Type-II photosensitized oxidation 1 gives accurate masses for the  4 -stera-3,6-diols of the more common sterols, thus emerged as very useful for the monitoring of  5 -sterol photooxidation and autoxidation in phototrophic organisms. An example of their application is given in Fig. 2.

Unsaturated fatty acids

Type II photosensitized oxidation and autoxidation rates of unsaturated fatty acids logically increase with their number of double bonds [START_REF] Frankel | Lipid Oxidation[END_REF][START_REF] Rontani | Identification of a "pool" of lipid photoproducts in senescent phytoplanktonic cells[END_REF]. Unfortunately, oxidation products of the more reactive polyunsaturated fatty acids (PUFAs) are not sufficiently stable under environmental conditions to be used as tracers of these degradation processes in situ. Note that isoprostanoids (cyclopentane-containing oxylipins) resulting from autoxidation of C18, C20 and C22 PUFAs are often used as biomarkers for in vivo oxidative stress in animals and plants [START_REF] Vigor | Nonenzymatic lipid oxidation products in biological systems: assessment of the metabolites from polyunsaturated fatty acids[END_REF]. These compounds could be detected in higher plants and algae by using GC-MS in negative-ion chemical ionization (NICI) mode [START_REF] Vigor | Nonenzymatic lipid oxidation products in biological systems: assessment of the metabolites from polyunsaturated fatty acids[END_REF][START_REF] Imbusch | Formation of isoprostane F2-like compounds (phytoprostanes F1) from α-linolenic acid in plants[END_REF]. However, in the literature there are no reports of such compounds in environmental samples.

In contrast, oxidation products of monounsaturated fatty acids (MUFAs) are sufficiently stable for use as tracers of type-II photosensitized oxidation and autoxidation processes in situ [START_REF] Marchand | Characterisation of photo-oxidation and autoxidation products of phytoplanktonic monounsaturated fatty acids in marine particulate matter and recent sediments[END_REF]. During type II photosensitized oxidation of MUFAs, attack by 1 O2 of the two ethylenic carbon atoms of the double bond leads to the formation of two trans-allylic hydroperoxides [START_REF] Rontani | Identification of a "pool" of lipid photoproducts in senescent phytoplanktonic cells[END_REF][START_REF] Frankel | Analysis of autoxidized fats by gas chromatography-mass spectrometry: V. Photosensitized oxidation[END_REF], which subsequently undergo stereoselective radical allylic rearrangement to afford two other isomers with a trans-double bond [START_REF] Porter | Mechanisms of free radical oxidation of unsaturated lipids[END_REF] (Scheme 5). Note that if type II photosensitized oxidation of MUFAs involves UV radiation, then four corresponding cis-allylic hydroperoxides also get produced [START_REF] Christodoulou | Comparative study of UV and visible light induced degradation of lipids in non-axenic senescent cells of Emiliania huxleyi[END_REF] (Scheme 5). In contrast, free radical oxidation of these compounds affords only two cis-allylic hydroperoxides (corresponding to the oxidation of the two allylic positions of MUFAs) in addition to the four trans-isomeric hydroperoxides [START_REF] Porter | Mechanisms of free radical oxidation of unsaturated lipids[END_REF] (Scheme 5). Consequently, in senescent autotrophic organisms a dominance of these two cisisomers (among the four cis-isomers) points to the involvement of autoxidation processes, while a dominance of all four cis-isomers points to UV-induced

photodegradation. R R 1 R R 1 R R 1 R 1 R R 1 R OOH R R 1 R R 1 HOO OOH OOH OOH OOH R 1 = -(CH 2 ) m -COOR 2 R = -(CH 2 ) n -CH 3

Free radical oxidation

Tracers of MUFA autoxidation and UV-induced photooxidation

R 2 = -(CH 2 ) m -COOH 1-NaBH 4 reduction 2-Alkaline hydrolysis R 1 OOH R HOO R 1 R 1 PAR-induced photooxidation UV-induced photooxidation R R 2 R R 2 R 2 R R 2 R OH R R 2 R R 2 HO OH OH OH OH R 2 OH R HO R 2 R 1
Specific tracers of MUFA UV-induced photooxidation MRM analyses of TMS derivatives of MUFA oxidation products involve intense and selective transitions from the ions resulting from -cleavage (precursor ions) to the fragment ion at m/z 129 (product ion) (Scheme 6). Note that this transition is more efficient with precursor ions containing the terminal methyl group than with precursor ions containing the TMS ester group, which can easily lose neutral TMSOH molecules (Scheme 6, Fig. 4). Fig. 5 gives an example of how MRM analyses can be applied.

Pentacyclic triterpenes

Pentacyclic triterpenes and their derivatives, which are widely found in angiosperms [START_REF] Jäger | Pentacyclic triterpene distribution in various plants-rich sources for a new group of multi-potent plant extracts[END_REF], are divided into three main classes, i.e. lupanes, oleananes and ursanes.

Lupanes

Type-II photooxidation and autoxidation of lupanes have so far only been studied

for betulin [START_REF] Galeron | Oxidation products of betulin: new tracers of abiotic degradation of higher plant material in the environment[END_REF], but the results obtained can be extended to lupeol or betulinic acid (the main triterpenoids with betulin of the lupane group). In contrast, the autoxidation of betulin mainly involves peroxyl radical addition to the C20-C29 double bond and mainly affords a diperoxide that is unaffected by NaBH4 reduction and converted to stable lupan-20-one-3,28-diol during hot GC injection [START_REF] Galeron | Oxidation products of betulin: new tracers of abiotic degradation of higher plant material in the environment[END_REF] (Scheme 7). Lupan-20-one-3,28-diol, lupan-20-one-3-ol (arising from lupeol) and lupan-20-one-3-ol-28-oic acid (arising from betulinic acid) can be used as specific tracers of the autoxidation of lupanes in angiosperms [START_REF] Galeron | Oxidation products of betulin: new tracers of abiotic degradation of higher plant material in the environment[END_REF][START_REF] Rontani | Lipid Oxidation Products: Useful Tools for Monitoring Photo-and Autoxidation in Phototrophs[END_REF].

The EI mass spectra of the TMS derivatives of lup-20(30)-ene-3,28,29-triol and lupan-20-one-3,28-diol exhibit intense fragment ions at m/z 481.3860 and m/z 395.3305, respectively, whose formation involves elimination of a neutral molecule of TMSOH and subsequent loss of the CH2OTMS group borne by the carbon 28 [START_REF] Galeron | Oxidation products of betulin: new tracers of abiotic degradation of higher plant material in the environment[END_REF] (Scheme 8). These fragment ions make good candidates for monitoring type-II photosensitized oxidation and autoxidation of betulin, respectively, in environmental samples. As the formation of these ions involves the loss of the group borne by carbon 28, they can be also used as tracers of the oxidation of lupeol and betulinic acid. Fig. 6

Ursanes et oleanes

Studies on type II photosensitized oxidation and autoxidation of ursanes and oleanes have mainly focused on -and -amyrins [START_REF] Galeron | Oxidation products of -and-amyrins: potential tracers of abiotic degradation of vascular-plant organic matter in aquatic environments[END_REF]. -and -amyrins were found to be totally unaffected during photodegradation experiments, due to steric hindrance preventing 1 O2 reaction with their double bond [START_REF] Galeron | Oxidation products of -and-amyrins: potential tracers of abiotic degradation of vascular-plant organic matter in aquatic environments[END_REF]. Autoxidation of amyrins mainly involves hydrogen abstraction and specifically produces 11-hydroperoxyamyrins [START_REF] Galeron | Oxidation products of -and-amyrins: potential tracers of abiotic degradation of vascular-plant organic matter in aquatic environments[END_REF] (Scheme 9). appeared to be useful for GC-QTOF monitoring of TMS derivatives of 11-oxo-amyrins in environmental samples (see example given in Fig. 7A). MRM analyses using the transitions m/z 273 → 135 and m/z 232 → 217 also appeared to be well suited to the detection of traces of these compounds (see Fig. 7B).

Dehydroabietic acid

Dehydroabietic acid (8,11,13-abietatrien-18-oic acid), a component of conifers, has long be used as a tracer of gymnosperms [START_REF] Brassell | The geochemistry of terpenoids and steroids[END_REF][START_REF] Otto | Conifer and angiosperm biomarkers in clay sediments and fossil plants from the Miocene Clarkia Formation, Idaho, USA[END_REF]. Autoxidation of this compound involves hydrogen atom abstraction at the benzylic carbon atom 7 to give 7hydroperoxydehydroabietic acids [START_REF] Rontani | EIMS Fragmentation pathways and MRM quantification of 7α/β-hydroxy-dehydroabietic acid TMS derivatives[END_REF], which are reduced to the corresponding hydroxyacids during NaBH4-reduction (Scheme 11). 7-hydroxydehydroabietic acids are useful tracers of dehydroabietic autoxidation in gymnosperms. → 417 [M -isopropyl group] + emerged as better suited to detecting traces of these compounds in environmental samples (Fig. 8). and Rhizosolenia genera [START_REF] Belt | The Arctic sea ice biomarker IP25: a review of current understanding, recommendations for future research and applications in palaeo sea ice reconstructions[END_REF][START_REF] Belt | Source-specific biomarkers as proxies for Arctic and Antarctic sea ice[END_REF]. During the senescence of these organisms, 1 O2 attack is focused on the lesser sterically-hindered trisubstituted double bonds of these alkenes affording 2 or 4 allylic hydroperoxides according to the E or Z configuration of the double bond [START_REF] Schulte-Elte | Photooxygenation of 3, 3-dialkylsubstituted allyl alcohols. Occurrence of syn preference in the ene addition of 1 O2 at E/Z-isomeric allyl alcohols[END_REF]. As an example, Scheme 13 shows type II photosensitized oxidation of Z and E isomers of HBI III, which are ubiquitous throughout the world's oceans [START_REF] Belt | Identification of C25 highly branched isoprenoid (HBI) alkenes in diatoms of the genus Rhizosolenia in polar and sub-polar marine phytoplankton[END_REF]. In this case, 1 O2 attack acts mainly on the C9-C10 double bond and to a lesser extent to the more sterically-hindered C7-C20 double bond affording 9-and 7-hydroperoxides, respectively, as the major oxidation products. Autoxidation processes also act very quickly on HBI III, producing numerous autoxidation products, but predominantly 9hydroperoxides resulting from hydrogen atom abstraction at the allylic carbon 11 (Scheme 13) [START_REF] Rontani | Sequential photo-and autoxidation of diatom lipids in Arctic sea ice[END_REF]. Indeed, the major oxidation pathway of this compound involves hydrogen abstraction at the bis-allylic C8 position to afford conjugated dienes, which are particularly prone to peroxyl radical additions and readily undergo copolymerization with oxygen (Scheme 13). Consequently, the 7-alcohol resulting from NaBH4-reduction of the corresponding hydroperoxide could be used as specific tracer of type II photosensitized oxidation of HBI III (Scheme 13). However, the reduction products of 9hydroperoxides will only be indicative of oxidation of this specific HBI alkene.

Unfortunalely, in the case of HBI alkenes (such as HBI III) possessing several trisubstituted double bonds, photooxidation and autoxidation products are unable to accumulate due to the involvement of fast secondary oxidation reactions [START_REF] Rontani | Sequential photo-and autoxidation of diatom lipids in Arctic sea ice[END_REF]. All these tracers can thus only serve to give qualitative indications. C37 methyl alkenones, respectively) varies positively with the growth temperature of the alga [START_REF] Prahl | Calibration of unsaturation patterns in long-chain ketone compositions for palaeotemperature assessment[END_REF][START_REF] Prahl | Further evaluation of long-chain alkenones as indicators of paleoceanographic conditions[END_REF] and is thus now routinely used for paleotemperature reconstructions (e.g. [START_REF] Brassell | Applications of biomarkers for delineating marine paleoclimatic fluctuations during the Pleistocene[END_REF][START_REF] Müller | Calibration of the alkenone paleotemperature index based on core-tops from the eastern South Atlantic and the global ocean (60° N-60° S)[END_REF]). Due to the trans-geometry of the alkenone double bonds [START_REF] Rechka | Characterisation of alkenone temperature indicators in sediments and organisms[END_REF], which is poorly reactive with 1 O2 [START_REF] Hurst | The ene reaction of singlet oxygen: kinetic and product evidence in support of a perepoxide intermediate[END_REF], alkenones are not affected by type II photosensitized oxidation processes [START_REF] Rontani | Stability of long-chain alkenones in senescing cells of Emiliania huxleyi: effect of photochemical and aerobic microbial degradation on the alkenone unsaturation ratio[END_REF][START_REF] Mouzdahir | Visible light-dependent degradation of long-chain alkenes in killed cells of Emiliania huxleyi and Nannochloropsis salina[END_REF]. However, they are highly reactive to autoxidation processes [START_REF] Rontani | Free radical oxidation (autoxidation) of alkenones and other microalgal lipids in seawater[END_REF].

Autoxidation of alkenone double bonds (separated by five or three methylene groups) affords six hydroperoxides as in the case of MUFAs (see chapter 3.3). Isomeric alkenediols resulting from NaBH4 reduction of these oxidation products could make unfortunately they fail to accumulate due to the subsequent oxidation of the other double bonds [START_REF] Rontani | Biotic and abiotic degradation of alkenones and implications for paleoproxy applications: a review[END_REF]. Note that TMS derivatives of alkene-triols, tetraols or pentaols obtained after NaBH4 reduction and derivatization of secondary oxidation products of di-, tri-or tetraunsaturated alkenones are too heavy and labile to be analyzed by GC-MS.

The characterization of alkenone autoxidation products in sediments or phytodetritus with more adapted analytical techniques constitutes a very important challenge.

Carotenoids

Carotenoids, which are important antioxidant constituents of thylakoid membranes, play special roles in the protection of tissues against damage caused by light and oxygen [START_REF] Britton | Structure and properties of carotenoids in relation to function[END_REF]. These compounds can very efficiently quench 1 O2 by energy transfer (quenching), but also by chemical reaction (scavenging) [START_REF] Boon | Factors influencing the chemical stability of carotenoids in foods[END_REF]. They are also good scavengers of ROS [START_REF] Tan | Carotenoids: how effective are they to prevent age-related diseases?[END_REF]. The attack of -carotene by 1 O2 affords -carotene-5,8endoperoxide (Scheme 15) [START_REF] Fiedor | Cyclic Endoperoxides of β-Carotene, potential pro-oxidants, as products of chemical quenching of singlet oxygen[END_REF]. If this compound is generally considered as a useful early signal of 1 O2 production in plant leaves [START_REF] Ramel | Carotenoid oxidation products are stress signals that mediate gene responses to singlet oxygen in plants[END_REF], it may be also formed during autoxidation of -carotene [START_REF] Boon | Factors influencing the chemical stability of carotenoids in foods[END_REF] and is clearly not stable enough to serve as a viable environmental tracer. Unfortunately, the reaction of 1 O2 and ROS with carotenoids produces oxidation products that are not sufficiently stable and specific (production of similar compounds by enzymatic processes) [START_REF] Boon | Factors influencing the chemical stability of carotenoids in foods[END_REF] to be used as unequivocal indicators of type-II photosensitized oxidation or autoxidation of carotenoids in senescent phototrophic organisms and environmental samples. Scheme 15. Reaction of 1 O2 with -carotene.

Conclusion

In this review, a focus was given to the selection and characterization of stable and specific tracers of photooxidation and autoxidation of lipid components (chlorophyll phytyl side-chain,  5 -sterols, MUFAs, pentacyclic triterpenes and dehydroabietic acid) of phototrophs. The author hope that it will contribute to a better consideration of photooxidative and autoxidative processes almost ignored so far in the literature when studying the degradation of autotrophic organisms in marine and terrestrial environments.

The different oxidation products selected could be used as indicators of: (i) oxidative stress of specific phototrophic organisms, (ii) paleoenvironmental changes of the conditions of sedimentation (oxic or anoxic), (iii) abiotic alteration of paleoproxies in ' 37 K U oxic environments, (iv) environmental problems related to ozone depletion, and (v) abiotic degradation of permafrost released under the effect of global warming [START_REF] Rontani | Lipid Oxidation Products: Useful Tools for Monitoring Photo-and Autoxidation in Phototrophs[END_REF].

In the future, a special attention should be given to the detection of oxidation products of alkenones and HBI alkenes (possessing several trisubstituted double bonds) sufficiently stable and specific to act as tracers of oxidative alteration of these proxies in oxic environments (water column of oceans and oxic layer of sediments). MALDI-MS and IM-MS techniques, which allow simultaneous characterization of all molecular species in biological tissues and reduce sample preparation artifacts arising from extensive purification procedures [START_REF] Kliman | Lipid analysis and lipidomics by structurally selective ion mobility-mass spectrometry[END_REF], seem to be particularly well-adapted to this task. NICI GC-MS, HPLC-MS and IM-MS techniques should be also used to give evidence of the presence of isoprostanoids resulting from PUFA oxidation in environmental samples. Due to the very high reactivity of PUFA towards photooxidation and autoxidation processes, such compounds could be very sensitive tracers of the early stages of oxidative damages.

Funding: The author thanks the Centre National de la Recherche Scientifique (CNRS) and Aix-Marseille University for providing financial support over the years. Thanks are also due to the FEDER project OCEANOMED (No. 1166-39417) for the funding of the GC-QTOF and GC-MS/MS employed.

R = Scheme 2 .

 2 Scheme 2. Main EI mass fragmentations of TMS derivatives of phytyldiol, 3,7,11,15tetramethylhexadec-3-en(Z/E)-1,2-diols and 3,7,11,15-tetramethyl-hexadec-2-en(Z/E)-1,4diols.

Figure 1 .

 1 Figure 1. Partial TOF ion chromatograms (m/z 353.3235 and 245.1388) showing the presence of TMS derivatives of phytol and its main photooxidation and autoxidation products in senescent cells of the diatom Thalassiosira sp.

Scheme 3 .Scheme 4 .

 34 photooxidation

Figure 2 .

 2 Figure 2. Partial TOF ion chromatogram (m/z 431.3710 and 486.4260) showing the presence of TMS derivatives of 24-ethylcholest-5-en-3-ol (sitosterol) ([M] +• = 486.4260) and its photo-([M -143.0887] + = 431.3710) and autoxidation ([M -H2O -143.0887] + = 431.3710) products in senescent leaves of Smilax aspera.

2 Scheme 5 .

 25 Scheme 5. Type II photosensitized oxidation (induced by PAR and UV radiations) and autoxidation of MUFAs.

Scheme 6 .

 6 Scheme 6. Examples of EI fragmentations of TMS derivatives of MUFA oxidation products.

Figure 3 .

 3 Figure 3. Partial TOF ion chromatograms showing TMS derivatives of MUFA oxidation products in senescent cells of the haptophyte Emiliania huxleyi irradiated by visible light (A), and after aging (B), and of the diatom Thalassiosira sp. irradiated by (visible + UV) light (C).

Figure 4 .

 4 Figure 4. Collision-induced dissociation (CID) (5 eV) of fragment ions at m/z 227 and 329.

Figure 5 .

 5 Figure 5. MRM chromatogram (m/z 199 → 129, m/z 213 → 129, m/z 329 → 149 and m/z 343 → 163) showing the presence of TMS derivatives of palmitoleic acid (C16:19) oxidation products in senescent cells of Thalassiosira sp. irradiated by sunlight.

Scheme 7 .

 7 Photooxidation tracers

-CH 2 OTMSScheme 8 .

 28 Scheme 8. Main EI fragmentations of the TMS derivatives of lup-20(30)-ene-3,28,29triol and lupan-20-one-3,28-diol.

Figure 6 .

 6 Figure 6. Partial TOF ion chromatograms (m/z 395.3305, 498.3908 and 500.4053) showing the presence of autoxidation products of lupeol and betulin in higher plant debris collected in the Rhône River.

22 Scheme 9 .Scheme 10 .

 22910 Scheme 9. Autoxidation of -and -amyrins.

Figure 7 .

 7 Figure 7. Partial TOF ion chromatogram (m/z 512.4063, 383.3308, 273.2213 and 232.1822) (A) and MRM chromatogram (m/z 273 → 135 and m/z 232 → 217) (B) showing the presence of oxidation products of amyrins in senescent leaves of Quercus ilex.

Scheme 11 .Scheme 12 .

 1112 Scheme 11. Autoxidation of dehydroabietic acid.

Figure 8 .

 8 Figure 8. Partial MRM chromatogram (m/z 234 → 191 and m/z 252 → 237) showing the presence of autoxidation products of dehydroabietic acid in senescent needles of Pinus halepensis.

Scheme 13 .Scheme 14 .Figure 9 .

 13149 Scheme 13. Type II photosensitized oxidation and autoxidation of HBI III.

3. 78 .

 78 AlkenonesAlkenones are a class of mono-, di-, tri-, tetra-and penta-unsaturated C35-C40 methyl and ethyl ketones, which are produced by certain haptophytes[START_REF] Volkman | Long-chain alkenes and alkenones in the marine coccolithophorid Emiliania huxleyi[END_REF][START_REF] Volkman | Alkenones in Gephyrocapsa oceanica: implications for studies of paleoclimate[END_REF][START_REF] Marlowe | Long chain (n-C37-C39) alkenones in the Prymnesiophyceae. Distribution of alkenones and other lipids and their taxonomic significance[END_REF][START_REF] Prahl | Alkenone paleothermometry: biological lessons from marine sediment records off western South America[END_REF][START_REF] Jaraula | Origin and tentative identification of tri-to penta-unsaturated ketones in sediments from Lake Fryxell, East Antarctica[END_REF]. The unsaturation ratio of C37 alkenones, which is defined by the equation: = [C37:2] / ([C37:2] + [C37:3]) (where [C37:2] and [C37:3] are the concentrations of di-and tri-unsaturated

  of autoxidative alterations of the unsaturation ratio , but

Table 1 .

 1 Accurate masses of the [M -143.0887]

	 5 -sterols

+ fragment ion of TMS derivatives of  4stera-3,6-diols arising from the more common  5 -sterols. Specific fragment ions [M -143.0887] + , for which Table

Table 2 .

 2 Accurate masses of the main fragment ions produced during EI fragmentation of silylated allylic hydroxyacids resulting from NaBH4-reduction of photo-and autoxidation products of some common MUFAs.

	MUFAs	(OH-position) m/z	(OH-position) m/z	(OH-position) m/z	(OH-position) m/z
	C16:19	(9-) 199.1518 a	(8-) 213.1675 a	(10-) 329.1968 b	(11-) 343.2125 b
	C16:111	(11-) 171.1206	(10-) 185.1363	(12-) 357.2280	(13-) 371.2437
	C18:19	(9-) 227.1830	(8-) 241.1987	(10-) 329.1968	(11-) 343.2125
	C18:111	(11-) 199.1518	(10-) 213.1675	(12-) 357.2280	(13-) 371.2437
	C20:19	(9-) 255.2139	(8-) 269.2295	(10-) 329.1968	(11-) 343.2125
	C20:111	(11-) 227.1830	(10-) 241.1987	(12-) 357.2280	(13-) 371.2437
	C22:19	(9-) 283.2451	(8-) 297.2607	(10-) 329.1968	(11-) 343.2125
	C22:111	(11-) 255.2139	(10-) 269.2295	(12-) 357.2280	(13-) 371.2437

a Fragments containing the terminal methyl group.

b Fragments containing the trimethylsilyl ester group.

Acknowledgements: Special thanks are due to Dr. C. Aubert for the many friendly and fruitful discussions we have had over the years concerning the mechanisms of lipid fragmentation upon electron impact. Thanks are also due to three anonymous reviewers for their useful and constructive comments.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable.

Conflict of Interest:

The author declare no conflict of interest.


Stephane Bazeille

Yvan Maillot

Frédéric Cordier

Cécile Riou

Christophe Cudel

Stéphane Bazeille

Light-field image acquisition

Keywords: Optics, light field, camera. *

Introduction

With the development of optical sensors and small powerful computers, 3D imaging is gaining more and more interest over the last decades. 3D imaging sensors are usually classified into two different modalities: active and passive. The principle of active sensors is to emit a light flow and measure its reflections from the scene; examples of active sensors are time-of-flight cameras or structured-light cameras. Unlike active sensors, passive sensors do not require any additional light sources; instead, the measurements are made using the ambient light. Examples of passive sensors are stereo cameras or light-field cameras. The light-field camera has been introduced by Lippmann. 1 The idea consists in capturing more information about the light emanating from a scene: the intensity and wavelength of the light and the direction of the light rays. Standard cameras are not able to capture the directional information. A light-field camera allows generating a series of different viewpoints of the same scene simultaneously called sub-aperture images. [START_REF] Lam | Computational photography with plenoptic camera and light field capture: tutorial[END_REF] enables performing a wide range of processing such as depth estimation, post-capture digital refocusing, post-capture focal length or aperture adjustment, perspectives shift, image segmentation, video stabilization and material classification. [START_REF] Lam | Computational photography with plenoptic camera and light field capture: tutorial[END_REF][START_REF] Wu | Light field image processing: An overview[END_REF] Until now, active systems (structured-light and laser technologies) have been the most widely-used technology for 3D visual inspection because of their accuracy and ease of use. However, with the emergence of light-field cameras, passive systems are gaining more interest since they offer new alternatives for accurate 3D measurements.

For these reasons, light field cameras are increasingly used in a large variety of applications such as: digital photography, microscopy, robotics or machine vision. In this paper, we present a device, namely the mini-lens ring extension (see Fig. 1), that can be added to any standard digital camera to convert it into a light-field camera. This device bridges the gap between stereo vision systems and the first light field device (see Fig. 2). It is composed of a main lens and 4 mini-lens with a focused plenoptic configuration (2.0). This device is very simple to use, cost-effective and compact. In addition, its optical properties are modifiable so that it can be adapted to a wide range of scenes with different dimensions. This makes our device particularly suitable for automatic defect detection. The remaining of the paper is organized as follows: in Section 2 is given the state of the art in the domain of light-field devices; in Section 3, a description of our device and its mathematical model are given. In Section 4, the functioning of the device is demonstrated with a simulation and with real-world data. In Section 5, refocused images are generated with our device and compared with the ones obtained using the Raytrix camera. The last section concludes the paper and gives several suggestions for future work.

Related work

Light-field technology is an area of interest since many years, leading to the publication of several survey papers. [START_REF] Wu | Light field image processing: An overview[END_REF][START_REF] Levoy | Light fields and computational imaging[END_REF][START_REF] Ihrke | Principles of light field imaging: Briefly revisiting 25 years of research[END_REF] Several types of light-field cameras have been proposed in the literature. The first type is based on a temporal multiplexing and is composed of a single camera equipped with coded aperture mask placed in front of the main lens to capture different viewpoints sequentially.

The second type makes use of spacial multiplexing to capture different points of view. This can be done using a camera array [START_REF] Wilburn | High performance imaging using large camera arrays[END_REF] or a lens array placed in front of a single image sensor. [START_REF] Levin | Image and depth from a conventional camera with a coded aperture[END_REF] In case of the plenoptic cameras, a micro-lenses array is inserted between the main lens and the image sensor of a camera. Two different configurations have been proposed for plenoptic cameras. The first one also The point P 0 is located at the height h 0 with respect to the optical axis of the main lens and at the distance Z. P 0 is imaged on P 1 through the main lens L. Then, P 1 is imaged on P 2,a through the mini-lens ml a (orange rays) and on P 2,b through the mini-lens ml b (green rays). Our method estimates b and c such that the 2 sharp images of the object fit within the surface area of the camera sensor.

called configuration 1.0 is described by Adelson et al. [START_REF] Adelson | Single lens stereo with a plenoptic camera[END_REF] The micro-lens array is placed in the focal plane of the main lens. As a consequence, the main lens concentrates the light rays on the microlenses; depending on their orientation with respect to the optical axis, the rays are then distributed over the areas of the image sensor. The second configuration is described by [START_REF] Lumsdaine | The focused plenoptic camera[END_REF] following the work of. [START_REF] Ng | Digital light field photography[END_REF] This model is called focused plenoptic camera or 2.0 because the raw image is composed of a series of focused sub-aperture images, each of these image being generated by a micro-lens. Other prototypes have also been proposed, such as the kaleidoscopic cameras, where several points of view are obtained using a tube of mirrors. [START_REF] Reshetouski | Three-dimensional kaleidoscopic imaging[END_REF] The raw data collected from light-field cameras can be used to produce different types of images: sub-aperture images that are a collection of synthetic points of view, [START_REF] Isaksen | Dynamically reparameterized light fields[END_REF] full focused images, stacks of refocused images, epipolar images and disparity images. Also, several algorithms have been proposed to perform depth estimation [START_REF] Jeon | Accurate depth map estimation from a lenslet light field camera[END_REF][START_REF] Tao | Depth from combining defocus and correspondence using light-field cameras[END_REF][START_REF] Wanner | Globally consistent depth labeling of 4d light fields[END_REF][START_REF] Lke | Depth from light fields analyzing 4d local structure[END_REF] using the data from the light-field cameras.

In this paper, we present a light-field camera that belongs to the focused plenoptic configuration.

The main drawback of these devices is the low spatial resolution that limits the use and applicability of the camera and the narrow baseline that reduces the depth estimation range and accuracy.

The main reason is that every plenoptic camera suffers from the fundamental tradeoff between spatial and angular resolutions. Commercial products [START_REF]Lytro[END_REF] or 18 based on this technology are (or were) available on the market but their main drawback is their cost. In this paper, we propose a new device: a simple 4 mini-lens ring that allows recording the light-field from a regular camera (see Fig. 1). On the market, this system can be classified between stereo systems with 2 views and the pelican imaging light field camera (see Fig. 2). Instead of having a large number of micro-lenses that project small sub-images of the scene such as, [START_REF] Montilla | Design and laboratory results of a plenoptic objective: From 2d to 3d with a standard camera[END_REF] our device is composed only of 4 mini-lenses with a large pitch. One important advantage of choosing a small number of lenses is that the device has a large baseline, which, in turn, provides a better depth resolution and the ability to record in one picture different modalities of the scene by adding polarimetric filters. [START_REF] Gendre | Interest of polarimetric refocused images calibrated in depth for control by vision[END_REF] Unlike conventional lightfield systems, this camera has also a larger spatial resolution (sub-aperture images of ≈1060x1060 pixels). This is an advantage because these raw sub-aperture images are readily usable by standard image processing (matching, tracking, etc.). On the other hand, our system has a smaller angular resolution which limits the refocusing capabilities and induces artefacts. Although the angular resolution is smaller compared to 18 or to the plenoptic ring proposed in, [START_REF] Montilla | Design and laboratory results of a plenoptic objective: From 2d to 3d with a standard camera[END_REF] we will show in this paper that performing post-capture refocusing calibration in depth with only 4 sub-aperture images is possible. This was proved in [START_REF] Riou | Calibration and disparity maps for a depth camera based on a four-lens device[END_REF] where a simple calibration algorithm based on the properties of the variable homography was used to produce refocused images at a specific depth without any feature extraction or feature matching. The main advantage of this method is that the computation cost is very small and thus the processing can be done on embedded computers (no GPU is required).

Such refocused images calibrated in depth can be used efficiently in industrial visual applications such as highlighting a working plane, detecting measure defects in images, as it is illustrated in. [START_REF] Riou | Interests of refocused images calibrated in depth with a multi-view camera for control by vision[END_REF] Another advantage is that the distance between the ring and the main lens and the distance between the ring and the image sensor are adjustable, which makes the device adaptable to different sizes and locations of objects in the scene.

3 Numerical modeling of the camera

System overview

The camera is composed of 2 components which are: the main lens (L in Fig. 3) with a focal length F L and a radius R L , the image sensor I whose dimensions are h s × w s with nb pixel and a ring of 4 mini-lens (see Fig. 1.b). These 4 mini-lenses are identical; their focal lengths and radius are noted F ml and R ml respectively. The vertical and horizontal distances between the centers of the mini-lens is 2h ml . The horizontal distance between the main lens and the mini-lens ring is b, the distance between the ring and the image sensor is c (see Fig. 3). For the sake of simplicity, only 2 of the 4 mini-lens are represented in this figure. A ray is originating from the point P 0 (highest point of the object located at a height h 0 and a distance Z from the main lens). P 0 is imaged in P 1 by the main lens (P 1 has a height h 1 and is located at a distance b 1 from the main lens). Then P 1 is imaged twice on the image sensor in P 2,a and P 2,b by the mini-lens. The portion of the rays emanating from P 0 and passing through the upper and lower mini-lenses are depicted in orange and green respectively.

Optical model assumptions

We assume that all the lenses are thin lenses i.e. the distance along the optical axis between the 2 lenses is negligible compared to the radius of curvature of these lenses. Thus, all computation is made based on the paraxial ray approximation. The paraxial ray approximation implies the following properties:

• all incoming rays parallel to the optical axis are directed through the lens focal point,

• all rays emanating from the focal point become parallel to the optical axis after passing through the lens,

• the rays that pass through the center of the lens do not change their direction,

The thin lens approximation gives the following relationship between the distances Z and b 1 , b 1 being the distance between the lens and the main lens image plane,

1 F L = 1 Z + 1 b 1 ⇐⇒ b 1 = Z.F L Z -F L (1)
Also, the relationship between the height h 0 of the point P 0 and the height h 1 of its image P 1 is:

h 0 Z = h 1 b 1 (2)
Similar equations are derived for the 2 mini-lenses ml a and ml b :

1 F ml = 1 b 2 + 1 c ⇐⇒ c = b 2 .F ml b 2 -F ml (3)
Equivalently, the equation for the relationship between the position of P 1 and its image P 2,b through the second mini-lens ml b is:

h ml -h 1 b 2 = h 2,b c (4)
where h ml is the distance between the center of the mini-lens and the optical axis of the main lens.

h 2,b is the distance between P 2,b and the optical axis of the mini-lens.

Lens position estimation in simulation

To simplify the experimental procedure as proposed in, [START_REF] Hahne | Light field geometry of a standard plenoptic camera[END_REF] we developed a method to automatically estimate the lens positions depending on the scene definition and a ray-tracing simulator in 2D (presented on Fig. 4) to validate our results. The lens positions are represented by the parameters b and c as shown on Fig. 3, and the scene is defined by the object size and the working distance Z. It has to be noted that the diameter of the lenses is not considered in the equations to compute b and c. However, these parameters are taken into account in our ray-tracing simulation so that the results can be fully simulated in 2D before experimenting with the real camera prototype.

Lens positions estimation only considering the magnification factor

Some of the camera parameters are fixed by the geometric properties of the components chosen by the user. Thus, the estimation of the camera parameters using the simulator requires the user to provide the following information (see Fig. 3):

• the focal length F L and the radius R L of the main lens.

• the focal length F ml and the radius R ml of the mini-lenses.

• the width w s and the height h s of the image sensor. • the object size 2h 0 and an estimatation of its distance Z to the main lens.

Then, the position b of the mini-lenses and the position c of the image sensor are calculated such that the images captured by the sensor are sharp and the magnification factor of the object is maximum. This magnification factor denoted by G is the ratio between the apparent size of an object on the image sensor and its real size. Its value is defined by:

G = G × G (5)
where G and G are the magnification factor of the main lens and the mini-lenses.

G = h 1 h 0 = b 1 Z and G = h 2,b h 1 = c b 2 (6)
From Eq. 1 and Eq. 3 we obtain:

G = F L Z -F L and G = F ml b 2 -F ml = F ml b -b 1 -F ml = F ml b -Z.F L Z-F L -F ml (7)
Hence, the magnification factor is:

G = F L Z -F L × F ml b -Z.F L Z-F L -F ml = F L .F ml (Z -F L )(b -F ml ) -Z.F L (8)
The position b of the mini-lenses is now expressed as a function of F L , F ml , h 0 , Z and the desired magnification factor G:

b = F L ( F ml G + Z) (Z -F L ) + F ml (9)
The position c of the image sensor is computed by using Eq. 3 and by replacing b 2 by (b -b 1 ):

c = F ml (b -Z.F L Z-F L ) F ml + b -Z.F L Z-F L (10)
The magnification factor G is maximum when the 2 images placed one above the other exactly fit within the height of the image sensor: I a = I b = h s /2 (see Fig. 3). In that case, the disparity for the points of the object is zero. The maximum magnification factor G max is given by:

G max = hs 2 2h 0 = h s 4h 0 (11)
h 0 being half of the height of the real object and h s the height of the image sensor. The position b of the mini-lenses is then obtained from Eq. 9 by replacing G by G max . With the following experimental parameters:

• an image sensor with width w s = 6.14mm and height h s = 4.60mm. The resolution is 4912 × 3684 pixels (IDS UI-3590LE) and the size of a pixel is 1.25 µm.

• 4 mini-lenses with focal length F ml = 5mm, radius R ml = 1mm and whose distance with respect to the optical axis of the main lens is h ml = 1.05mm.

• a camera lens LINOS MeVIS-C with a focal length F L = 16mm, a radius R L = 21mm, a flange focal distance F F D = 17.526mm and the c-mount screw length ST = 3.8mm.

• an object with size 2h 0 = 0.1mm. The distance between the object and the main lens is

Z = 300mm.
The values of b and c corresponding to the maximum magnification factor are b = 34.1mm and c = 6.59mm. The result given by our ray-tracing simulator using these values is shown in Fig. 4. This ray-tracing simulation is computed with 5 source points located at different heights (-0.05, -0.025, 0, 0.025, 0.05m) on the object whose size is 2h 0 = 0.1m. These 5 points are emitting light in the direction of the main lens; only the rays that pass through the main lens are drawn.

In blue, we show the rays that hit the main lens but do not reach the mini-lenses. The lines in green are the rays going through the main lens and the lower mini-lens. The rays going through the main lens and the upper mini-lens are depicted in orange. A zoom of the image sensor of Fig. 4 in shown in Fig. 5.a and one can see that the 5 source points have an image through both minilenses. One can observe that the size of the images is equal to the value predicted by Eq. 9 and 11;

we have I a and I b equal to hs 2 . The result of the experiment is presented in Fig. the sensor because the central part of the sensor does not receive any rays. The details about the image acquisition prototype will be presented in the next section.

Estimating the lens positions using the magnification factor and the image position

In the previous estimation, we did not taken into account the position of the image. In order to put the object image inside the image sensor, we have to consider the height of the highest object pixel represented by the point P 2,a in Fig. 3. Rewriting the equation presented in Sec. 3.2 for the upper mini-lens in the reference frame defined by the optical axis of the upper mini lens we obtain:

h 1 b 2 = h 2,a c (12)
Then by combining this equation with the Eq. 1 and 2 we have for the upper and lower mini-lens: In the reference frame defined by the optical axis the main lens we have:

h 2,a = c(h ml + b 1 . 2h 0 Z ) b 2 h 2,b = c(-h ml + b 1 . 2h 0 Z ) b 2 (13) (a) (b)
H 2,a = h ml + c(h ml + b 1 . 2h 0 Z ) b 2 H 2,b = -h ml + c(-h ml + b 1 . 2h 0 Z ) b 2 (14)
To compute the lens positions and to ensure that the magnification factor is maximum while keeping the image of the object inside the image sensor we need H 2,a = h s /2 in Eq. 14. From Eq. 14 by replacing b 2 by (b -b 1 ) and replacing b 1 by its value depending on Z and F L we have:

h ml + c(h ml + b 1 . 2h 0 Z ) (b -b 1 ) = h s 2 ⇐⇒ b = c(h ml + Z.F L Z-F L . 2h 0 Z ) ( hs 2 -h ml ) + Z.F L Z -F L (15)
We obtain the second result: b = 37.4mm, and c = 6.61mm which corresponds to the simulation presented in Fig. 6.a and the experiment with our prototype in Fig. 6.b.

Validation of our first use case: 10cm object at a distance of 0.3m

As shown in Fig. 6 the estimation gives correct values and the experimentation with our prototype confirmed the result obtained in simulation. Note that our system does not compute the amount of light passing through the lenses, and therefore cannot be used to estimate the vignetting effect.

Once the size and position of the images have been calculated, we then compute the other parameters of the light-field prototype, which are the disparity and the overlapping ratio. The disparity is used to estimate the accuracy of the 3D information, and the overlapping ratio gives the portion of the image on which the 3D information is available. The disparity d is defined as the difference in pixels between 2 corresponding points in a couple of images acquired with our system (see H 2,a and H 2,b on Fig. 3). d and o can be computed as follows:

d = H 2,a -( hs 2 + H 2,b ) t pix = 1 t pix ( 4h ml -h s 2 + 2h ml .c (b -Z.F L Z-F L ) ) and o = 1 - d I a (16)
where I a is the size of the image produced by the upper mini-lens on the image sensor. These equations give d = 382 pixels and o = 0.73 (i.e. 73%) for the use-case we studied. The vertical size of the image I a and I b was equal to 0.78 × h s /2. To complete these results, we estimated from Eq. 16 the range of the disparity for an interval of distances Z while keeping the distances b and c fixed. This result is shown in Fig. 7. For distance values that range from 0.3m to 1.0m, the range of the disparity is [382 -361] i.e. slightly larger than 20 pixels for 70cm which seems good to get enough accuracy in depth. The disparity is important because there is a shift between the sub-aperture images explained by the overlapping ratio of 0.7. To modify this overlapping ratio, a new mini-lens ring with a smaller h ml is necessary. In the future, we plan to investigate the effect of modifying h ml in the system. For these experiments, we decided to put the 4 mini-lens as close as possible (0.5mm between the border of 2 mini-lenses) to maximize the portion of the sensor that is receiving light rays.

Example with different objects at different distances

In the previous section, we have given the equations to compute the position b of the mini-lenses and the position c of the image sensor for a given scene (a particular object at a given distance).To illustrate the versatility of our prototype, we show in Fig. 8 another object of size 10cm and placed at different distances with respect to the main lens. For each distance, we estimated the distances b and c and the corresponding magnification factor and overlapping ratio. One can observe that the magnification factor and overlapping ratio decrease when the distance between the main lens and the object increases. The reason is that the size of the camera sensor prevents the image to go up.

In this case, to keep the entire image of the object inside the sensor area, the magnification has to be lowered. In Fig. 9 is shown the same result for a larger object (i.e. size 60cm). One can observe that the object image does not fit within the sensor area if its distance to the main lens is smaller than 0.7m. distance is called B (see Fig. 10.a) and is defined as:

B = b 2 + F F D -ST = c.F ml c -F ml + 0.017526 -0.00038 = 0.0376m = 37.6mm (17)
where FFD is the flange focal distance and ST the length of the screw thread. To demonstrate the efficiency of our simulation we have placed the object, the main lens and the mini-lens ring at the distances calculated in the previous section and the image has been recorded. In Fig. 5.b and 6.b, we show the 2 images obtained with our light-field prototype corresponding to the simulation results presented in Fig. 5.a and 6.b. The results from the experimental setup closely match the parameters estimated with our simulation program. However, the image produced by our camera prototype is reversed compared to our simulation (see Fig. 3). This is because the electronic circuit associated with the sensor generates an inverted image by default so that the image produced by a camera with a single lens is upright. In the remaining of the paper, the image is rotated.

5.2 Refocusing at a specific depth using a 4 sub-aperture images

In this section, we demonstrate post-capture refocusing using the method proposed in. [START_REF] Riou | Interests of refocused images calibrated in depth with a multi-view camera for control by vision[END_REF] In Fig. allows performing numerical refocusing. However, it can be seen that the quality of refocused images is not perfect; this is due to our camera prototype design: the 4 mini-lenses inside the ring are not perfectly aligned and the components of the optical device (main lens, mini-lens ring, image sensor) are not exactly parallel and centered to the same axis. Finally, we have used minilenses with a value N of f-number of 2.5 (the f-number of an optical system is the ratio of the system's focal length to the diameter of the entrance pupil). This value is close but above the limit of diffraction defined by d = 2.44.λN =3 µm. Even by activating the binning mode to record images, the value is still above the limit of diffraction with a pixel size of 1.25 µm.

Comparison with a Raytrix camera

This section provides a comparison between the refocusing with the 4 mini-lens ring and the refocusing using the Raytrix camera. The experiment with the 3 depth planes (coffee cup, book, As one may observe, the quality of rendering is higher for the Raytrix camera than for the 4 mini-lens ring. In the future, we plan to improve the rendering quality by increasing the resolution. On the other hand, the quality of refocusing using the 4 mini-lens ring with the method by [START_REF] Riou | Interests of refocused images calibrated in depth with a multi-view camera for control by vision[END_REF] is good. This is an advantage given the fact the 4 mini-lens ring is much cheaper and easy to use since it only requires 2 images at 2 known distances (see [START_REF] Riou | Interests of refocused images calibrated in depth with a multi-view camera for control by vision[END_REF] for more details).

Conclusion and future work

A new device to convert any digital camera into a light-field camera has been described. Usually, light-field cameras are classified in 2 groups: the camera array and the plenoptic models. The cameras array only gives 4 points of views with large aperture angle. On the other hand, plenoptic cameras which are composed of a micro-lens array placed between the main lens and the image sensor, produce a series of sub-images representing a small part of the scene due to the small aperture angle. Even if the light field is captured in both cases, these approaches leads to different methods of reconstructions. In case of the camera array, the raw data are exploited by using the "plane and parallax" approaches, while more complex algorithms must be used to process each sub-view of the plenoptic devices. In this paper, we proposed a different approach which consists of adding a plenoptic ring to transform a standard camera into a plenoptic one but keeping the advantage of the camera array (i.e. larger baseline and larger spatial resolution). Together with the proof of concept of this new device, a method is proposed to estimate the positions of each optical component depending on the working distance and the object size set by the user. Realworld results recorded with our 4 mini-lens ring prototype are presented. In the future, we plan to improve the design and increase the resolution of the 4 mini-lens ring by using a camera with a larger image sensor and larger pixel size. We will also make some experiments using mini-lenses with larger diameter. This should help to decrease the diffraction effects and improve the image quality of the 4 mini-lens ring. [START_REF] Georgiev | Plenoptic camera resolution[END_REF] We also plan to develop algorithms to compute depth images using the data from the 4 mini-lens ring.

Acknowledgments

This work has been funded by the french state, FUI project TRAC, grant number DOS0068206/00. References 1 G. Lippmann, " Épreuves réversibles donnant la sensation du relief," J. Phys. Theor. Appl.

7(1), 821-825 (1908).

Fig 1

 1 Fig 1 The camera prototype. In (a) is shown the 3 components of the system: the camera lens (also identified as the main lens) on the right, the mini-lens ring (black square attached to the horizontal base in orange colour) in the middle, the image sensor (attached to the vertical base in orange colour) on the left. The image sensor is fixed and the lenses are able to slide along their rails to adjust the projected image. In (b) are shown a zoom of the mini-lens ring and the image sensor. The integration of the 4 the mini-lenses into a camera ring extension is shown in (c); the mini-lens is mounted in a tube which is placed between the main lens and the image sensor)

Fig 2

 2 Fig 2 Different multi-views cameras. (a) stereo camera ENSENSO, (b) the mini-lens ring inserted between the image sensor and the main lens of a standard camera (c) Pelican imaging camera array, (d) Stanford multi camera array, (e) Raytrix light field camera.

Fig 3 A

 3 Fig 3 A 2D representation of our light-field camera.The point P 0 is located at the height h 0 with respect to the optical axis of the main lens and at the distance Z. P 0 is imaged on P 1 through the main lens L. Then, P 1 is imaged on P 2,a through the mini-lens ml a (orange rays) and on P 2,b through the mini-lens ml b (green rays). Our method estimates b and c such that the 2 sharp images of the object fit within the surface area of the camera sensor.

Fig 4

 4 Fig 4 Simulated view of the whole system obtained with our 2D ray-tracing simulator. The parameters in meters are the following: F L = 0.016m, R L = 0.021m, F ml = 0.005m, R ml = 0.001m, h ml = 0.00105m, h s = 0.0046m, h 0 = 0.05m, Z = 0.3m, and Ia = h s /2. All units are in meters. Orange rays going through the upper mini-lens. Green rays going through the lower mini-lens.

Fig 5

 5 Fig 5 Results of the first parameter estimation (parameters detailed in Fig. 4 for an object of 0.1m at 0.3m. (a) Zoom on the simulated view, (b) Real image acquired with our experimental prototype.

Fig 6

 6 Fig 6 Results of the optimized parameter estimation for an object of 0.1m at 0.3m. In this case I a = I b = 0.78 × h s . (a) Zoom on the simulated view, (b) Real image. On this image, we plotted the sub-aperture image size for this particular example.

Fig 7

 7 Fig 7 Range of the disparity for the fixed optical parameters b = 37.4mm and c = 6.61mm, (a) When the distance Z is varying from 0.1m to 6.0m the disparity is around 400 pixels, (b) On the second plot we plotted only the disparity variations (that can be used to extract the depth) for Z varying from 0.3m to 1m.

Fig 8 Fig 9 Fig 10

 8910 Fig 8 An object of size 0.1m placed at different distances with respect to the main lens. (a) Values of b and c (b) Magnification factor (c) Overlapping ratio.

Fig 11

 11 Fig 11 Refocusing experiments, (a) Refocusing on the Pisa Tower, (b) Refocusing on the chessboard, (c) Zoom on the Pisa tower in the refocused image, (d) Zoom on the chessboard in the refocused image.

Fig 12

 12 Fig 12 Results obtained with a Raytrix camera with a main lens focal length of 50mm. (a) Raw image, (b) Focusing on the background, (c) Focusing on the foreground.

Christophe Cudel received his Ph.D. from the University of Reims Champagne Ardenne in 1995.

He joined the Université Haute-Alsace and the laboratory MIPS in 1997, first as assistant professor and now as professor. His researches are focused on computer vision, eye-tracking, light-field and multi-view cameras. He teaches computer vision for industrial control, robotics and signal processing.