Claire Lefort
email: claire.lefort@xlim.fr

A review of biomedical multiphoton microscopy and its laser sources

Keywords: biomedical multiphoton microscopy, two photon fluorescence, three photon fluorescence, second harmonic generation, third harmonic generation, comparison of laser sources, score and pondered score

Multiphoton microscopy (MPM) has been the subject of major development efforts for about 25 years for imaging biological specimens at micron scale and presented as an elegant alternative to classical fluorescence methods such as confocal microscopy. In this topical review, the main interests and technical requirements of MPM are addressed with a focus on the crucial role of excitation source for optimization of multiphoton processes. Then, an overview of the different sources successfully demonstrated in literature for MPM is presented, and their physical parameters are inventoried. A classification of these sources in function with their ability to optimize multiphoton processes is proposed, following a protocol found in literature. Starting from these considerations, a suggestion of a possible identikit of the ideal laser source for MPM concludes this topical review.

Context of multiphoton microscopy (MPM)

In the infinite universe of biomedical discoveries, the development of high-performance microscopes is crucial. The needs of microscopic characterization of biological specimens have become more and more precise, deep, diverse and fast [START_REF] Vo-Dinh | Biomedical Photonics Handbook[END_REF]. Among all of the existing methods of microscopy, optical microscopy pertains to those compatible with living sample imaging, or in vivo studies without sample destruction. Various kinds of light-tissue interaction can occur, and constitute an immense field of scientific knowledge and research. Light probes the medium in a minimally invasive manner, where an incident photon on a biological sample can be absorbed, scattered or transmitted. Different information about pathologies or physiology of tissues can be deduced depending on the characteristics of the response. In this context, MPM has been the subject of major development efforts for about 25 years [START_REF] Denk | Two-photon laser scanning fluorescence microscopy[END_REF] as an essential tool able to generate optical biopsies where conventional light microscopes have revealed their limits. For example, confocal microscopy [START_REF] Pawel | Handbook of Biological Confocal Microscopy[END_REF][START_REF] Masters | Confocal microscopy and multi-photon excitation of human skin in vivo Opt[END_REF] is a traditional optical method adapted for imaging biological samples at micron scale, labelled or not, in vivo or ex vivo. Its principle is based on one-photon fluorescence (OPF) where incident light intensity is linearly dependent with fluorescence intensity emitted. But it presents a low level of beam penetration depth, uses a highly energetic excitation beam provoking non-negligible photodamage, and OPF is the exclusive modality of imaging available. Thus, MPM appeared as an elegant alternative with technical advantages [START_REF] Masters | Confocal microscopy and multi-photon excitation of human skin in vivo Opt[END_REF][START_REF] So | Twophoton excitation fluorescence microscopy[END_REF][START_REF] Konig | Multiphoton microscopy in life sciences[END_REF][START_REF] Zipfel | Nonlinear magic: multiphoton microscopy in the biosciences[END_REF][START_REF] Oheim | Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches[END_REF][START_REF] Diaspro | Two-photon fluorescence excitation and related techniques in biological microscopy Q[END_REF][START_REF] Ustione | A simple introduction to multiphoton microscopy[END_REF][START_REF] Masters | Antecedents of two-photon excitation laser scanning microscopy[END_REF]: higher beam penetration depth, 3D imaging thanks to optical sectioning, decreased outof-focus background, photodamage restricted to focal point, better signal-to-noise ratio, excitation of UV-absorbing dyes, multiple imaging processes, technically simpler (no confocal pinhole required), etc.

In 1999, two groups reviewed the growing interest of MPM [START_REF] Piston | Imaging living cells and tissues by twophoton excitation microscopy[END_REF][START_REF] Masters | Multiphoton excitation microscopy, confocal microscopy, and spectroscopy of living cells and tissues; functional metabolic imaging of human skin in vivo Multiphoton Excitation Microscopy[END_REF] and identified an obstacle to its development in the exorbitant cost and complexity of laser sources required. At that time, they estimated that 'appropriate turn-key lasers have now been introduced, and their cost should decrease'. Today, 18 years after this statement, no real evolution concerning that point is noticeable: expensive commercial laser sources (more than 100 k€) are often implemented on multiphoton microscopes, which represent its first expenditure. The discussion about the best excitation source technically applicable to MPM, and judiciously or reasonably expensive, is still in the spotlight. Since 1995, several articles have proposed an overview of laser sources currently demonstrated for MPM with their technical specificities [START_REF] Konig | Multiphoton microscopy in life sciences[END_REF][START_REF] Diaspro | Two-photon fluorescence excitation and related techniques in biological microscopy Q[END_REF][START_REF] Denk | Two-photon molecular excitation in laser-scanning microscopy Handbook of Biological Confocal Microscopy[END_REF][START_REF] Squier | High resolution nonlinear microscopy: A review of sources and methods for achieving optimal imaging[END_REF][START_REF] Girkin | Optical physics enables advances in multiphoton imaging[END_REF][START_REF] Girkin | Advances in laser sources for confocal and multiphoton microscopy[END_REF][START_REF] Xu | Recent advances in fibre lasers for nonlinear microscopy[END_REF][START_REF] Wise | Laser for nonlinear microscopy[END_REF][START_REF] Young | A pragmatic guide to multiphoton microscope design[END_REF]. But the evolution of laser technologies or recent uses of old laser technologies for MPM justify the need for an updated review about laser sources employed for MPM. To go further than a simple list, a commentary concerning the more or less good compatibility of each source with biomedical MPM is discussed, following a protocol suggested in literature.

To address this subject, theoretical and technical requirements of MPM are first exposited. The context of application of MPM for biological and medical discoveries is then illustrated, and the substantial role of the excitation source is highlighted. Then, a review of the excitation sources already demonstrated in MPM is presented, with a classification of the compatibility of each of them with this application. All of these points allow proposing a possible identikit for the ideal excitation source for MPM.

Theory of multiphoton processes and technical requirements for biomedical MPM

1.1.1. Multiphoton processes involved in multiphoton imaging modalities. Processes involved in MPM are based on high-order nonlinear light-matter interactions, where multiple photons are required for contrast generation. MPM is characterized by an optical emission which has a quadratic or higher-order dependence on excitation power. MPM is thus commonly called 'nonlinear microscopy'. Phenomena involved can be categorized as fluorescence, harmonic generation and vibrational scattering. Each of these is described by a Jablonski diagram. Two-photon fluorescence (TPF) is the most widespread multiphoton phenomenon involved in MPM, but other high-order processes also exist in MPM: second harmonic generation [START_REF] Mohler | Second harmonic generation imaging of endogenous structural proteins[END_REF][START_REF] Campagnola | Second-harmonic imaging microscopy for visualizing biomolecular arrays in cells, tissues and organisms[END_REF][START_REF] Filippidis | Imaging of Caenorhabditis elegans samples and sub-cellular localization of new generation photosensitizers for photodynamic therapy, using non-linear microscopy[END_REF] (SHG), coherent control [START_REF] Ogilvie | Use of coherent control for selective two-photon fluorescence microscopy in live organisms[END_REF][START_REF] Pastirk | Selective two-photon microscopy with shaped femtosecond pulses[END_REF][START_REF] Tada | Adaptively controlled supercontinuum pulse from a microstructure fiber for two-photon excited fluorescence microscopy[END_REF], three-photon fluorescence (ThPF) or four-photon fluorescence [START_REF] Hell | Three-photon excitation in fluorescence microscopy[END_REF][START_REF] Sinefeld | Adaptive optics in multiphoton microscopy: comparison of two, three and four photon fluorescence[END_REF][START_REF] Mahou | Multicolor two-photon tissue imaging by wavelength mixing[END_REF][START_REF] Horton | In vivo three-photon microscopy of subcortical structures within an intact mouse brain[END_REF][START_REF] Wang | Going deep: brain imaging with multi-photon microscopy Opt[END_REF][START_REF] Markowicz | Direct fourphoton excitation of amplified spontaneous emission in a nonlinear organic chromophore[END_REF], four-wave mixing such as coherent anti-Stokes Raman scattering or stimulated Raman scattering (CARS/SRS) [START_REF] Zumbusch | Threedimensional vibrational imaging by coherent anti-Stokes Raman scattering[END_REF][START_REF] Cheng | Laserscanning coherent anti-Stokes Raman scattering microscopy and applications to cell biology[END_REF][START_REF] Amor | A compact instrument for adjusting laser beams to be accurately coincident and coaxial and its use in biomedical imaging using wave-mixed laser sources[END_REF][START_REF] Kano | In vivo multi-nonlinear optical imaging of a living cell using a supercontinuum light source generated from a photonic crystal fiber[END_REF][START_REF] Freudiger | Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy[END_REF][START_REF] Rigneault | Background-free coherent Raman imaging: the CARS and SRS contrast mechanisms Raman[END_REF][START_REF] Sun | Labelfree multimodal nonlinear optical microscopy reveals fundamental insights of skeletal muscle development[END_REF], and third or fourth harmonic generation [START_REF] Sun | Labelfree multimodal nonlinear optical microscopy reveals fundamental insights of skeletal muscle development[END_REF][START_REF] Débarre | Imaging lipid bodies in cells and tissues using thirdharmonic generation microscopy[END_REF][START_REF] Krmpot | 3D imaging and characterization of microlenses and microlens arrays using nonlinear microscopy[END_REF][START_REF] Renaud | Characterization of microscope objective lenses from 1400 to 1650 nm to evaluate performance for long-wavelength nonlinear microscopy applications[END_REF], for example.

Shen described the theory of these processes [START_REF] Shen | The Principles of Nonlinear Optics[END_REF] in 1984, in a work which was thoroughly reviewed 20 years later by Shen [START_REF] Shen | The Principles of Nonlinear Optics[END_REF] and Boyd [START_REF] Boyd | Nonlinear Optics[END_REF]. They rest on an interaction between sample and electric field strength E from an intense laser beam. This light-matter interaction induces a macroscopic polarization P of matter detailed by equation (1):

P = P P + ε 0 χ (1) E + χ (2) E 2 + χ (3) E 3 + . . . ( 1
)
P p being the macroscopic permanent polarization, ε 0 the vacuum permittivity, χ (i) is a tensor which describes medium susceptibility. First order of susceptibility χ (1) represents the refractive index of the medium, and contributes to the fluorescence imaging process. χ (2) and χ (3) are nonlinear tensors responsible for several nonlinear effects usually involved in MPM, such as harmonic generation, multiphoton fluorescence and four-wave mixing. A few fundamental points, indispensable for MPM, recalled here, illustrated by the Jablonski diagrams presented in figure 1.

TPF results from the third-order of susceptibility of the fluorophore χ (3) . It relies on a first step of two-photon absorption (TPA). Historically, TPA was first theoretically predicted by Maria Goeppert-Mayer in the thirties [START_REF] Goppert-Mayer | Uber Elementarakte mit zwei Quantensprungen[END_REF], and exper imentally highlighted 30 years later by Kaiser et al [START_REF] Kaiser | Fluorescence and optical maser effects in CaF 2 : Sm++[END_REF] in a crystal of CaF 2 : Sm 2+ . TPF has then been demonstrated 30 years later by Webb's team on biological samples with two-photon imaging of chromosomes stained with a UV-excitable chromophore [START_REF] Denk | Two-photon laser scanning fluorescence microscopy[END_REF].

TPA happens when two identical photons are quasi-simultaneously absorbed by a fluorophore at sub-femtosecond scale [START_REF] Vo-Dinh | Biomedical Photonics Handbook[END_REF][START_REF] So | Twophoton excitation fluorescence microscopy[END_REF][START_REF] Piston | Imaging living cells and tissues by twophoton excitation microscopy[END_REF]. When their combined energy is sufficient, and matches the energy gap between ground and excited states, a molecular transition to an excited electronic state occurs after reaching a virtual intermediate state. For each fluorophore, transition to an excited electronic state is possible only for an adapted spectral range of excitation, described by TPA cross sections or TPA spectra. In literature, several measures of two-or three-photon absorption cross sections of exogenous or endogenous fluorophores are centralized in high level publications [START_REF]Developmental resource for biophysical imaging optoelectronics[END_REF][START_REF] Mütze | Excitation spectra and brightness optimization of twophoton excited probes[END_REF][START_REF] Heinze | Simultaneous two-photon excitation of distinct labels for dual-color fluorescence crosscorrelation analysis[END_REF][START_REF] Xu | Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm[END_REF][START_REF] Zipfel | Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation[END_REF].

Molecular transition can be induced by other combinations of photons, provided that the total energy is adapted to the energy gap of fluorophore: two photons not having exactly the same central wavelength [START_REF] Masters | Multiphoton excitation microscopy, confocal microscopy, and spectroscopy of living cells and tissues; functional metabolic imaging of human skin in vivo Multiphoton Excitation Microscopy[END_REF], or a single photon, or threeor more-photons. Then a relaxation process occurs, consisting of a molecular transition back to the electronic ground state, joined with isotropic emission of a photon of fluorescence. This process is described by the Jablonski diagrams in figure 1. The emission spectrum of a fluorescent substance is a function of its molecular constitution, and is independent of excitation wavelength as long as the latter lies within the excitation spectrum (Kasha's rule [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF]). Each individual fluorophore has its own spectral properties depending on its chemical structure and environment. Emission spectrum is considered as similar whatever the mode of excitation with one, two or three photons; only its microenvironment, mainly polarity of solvent, can induce some modifications.

1.1.1.2. Harmonic generation. Harmonic generation is an instantaneous phenomenon of nonlinear coherent light scattering combining at least two photons and requiring phase-matching conditions [START_REF] Zipfel | Live tissue intrinsic emission microscopy using multiphoton-excited native fluorescence and second harmonic generation[END_REF]. The best known phenomenon is SHG, first proposed by Sheppard and Kompfner [START_REF] Sheppard | Resonant scanning optical microscope[END_REF] in 1978, and demonstrated later by Freund et al [START_REF] Freund | Second-harmonic microscopy of biological tissue[END_REF]. This second-order nonlinear process happens when the medium involved presents a second order of susceptibility not equal to zero (χ (2) ≠ 0). This is produced exclusively in a medium where a breaking of symmetry exists, and is thus named 'noncentrosymmetric medium'. In contrast to multiphoton fluorescence, SHG happens without energy absorption: the energy of incident photons is scattered with a harmonic up-conversion. Consequently, a noncentrosymmetric structure under a laser light at frequency ω generates a harmonic at frequency 2ω; this phenomenon is thus wavelength dependant. The emitted SHG is anisotropic, and propagates mainly in the forward direction, with a directionality tilted compared to the incident laser light path [START_REF] Mertz | Second-harmonic generation by focused excitation in inhomogeneously distributed scatterers[END_REF][START_REF] Burke | Secondharmonic generation scattering directionality predicts tumor cell motility in collagen gels[END_REF]. A second harmonic can also be generated in backward direction, with constraints on excitation characteristics depending on structural dimensions [START_REF] Zipfel | Nonlinear magic: multiphoton microscopy in the biosciences[END_REF][START_REF] Mertz | Second-harmonic generation by focused excitation in inhomogeneously distributed scatterers[END_REF][START_REF] Burke | Secondharmonic generation scattering directionality predicts tumor cell motility in collagen gels[END_REF]; this imposes requirements to govern especially its (i) alignment compared to the sample, (ii) central wavelength and (iii) polarization. This point has a fundamental importance in MPM in the case of utilization for in vivo microscopy, where only backward SHG is possible.

Third harmonic generation (THG), more recently involved in MPM, is a third-order process requiring a condition of negative phase mismatch [START_REF] Barad | Nonlinear scanning laser microscopy by third harmonic generation[END_REF] only occurring in a nonhomogeneous medium. THG does not impose constraint on the symmetry of structure but occurs in a medium presenting rough parts in its refractive index or in its nonlinear susceptibility, for example. Conversely, no THG can happen in a homogeneous and isotropic medium; THG is known for the identification of interfaces between two media.

1.1.1.3. Raman scattering. Raman scattering is an inelastic phenomenon resulting from energy exchange between excitation photons and scattering molecules generating the vibration of chemical bonds [START_REF] Rigneault | Microscopy, fast and labelfree[END_REF]. Raman spectroscopy gives information about the density of chemical bonds of a single functional group. But weak, difficult to detect signals result from spontaneous Raman scattering. To improve it, CARS/SRS has been proposed [START_REF] Djaker | Microscopie Raman Stimulée[END_REF][START_REF] Supatto | Advances in multiphoton micrscopy for imaging embryos[END_REF]. This multiphoton method consists of constraining the excitation of a specific chemical bond. Technically, it presents a major difference compared to multiphoton fluorescence or harmonic generation: a dual-color excitation (pump and Stokes waves) spatially and temporally superimposed is indispensible. Even if a commercial SRS setup is available (e.g. that from Invenio Imaging inc.), we can estimate that CARS/SRS is as yet only marginally involved in standard commercial multiphoton microscopes, and so will not be considered in this article. and technical principles involved for generation and detection of multiphoton processes. Some of these have a direct impact on the physical parameters of the excitation source. Here is a general overview of the technical requirements of MPM illustrated by figure 2. A focus on (i) excitation parameters (spectral range and bandwidth), (ii) spatiotemporal confinement of excitation and (iii) modes of detection and scanning are proposed. In MPM, the adapted excitation spectrum depends on the probe imaged and the multiphoton process involved. By definition, the excitation beam has a longer spectral range than the emitted one (figure 1). Moreover, whatever the process involved in MPMfluorescence or harmonic generation-most of the targeted substances are emitting in the near UV or visible ranges, easily detectable. The excitation spectrum of MPM is consequently mainly in the near infrared range (NIR). Table 1 synthesizes excitation and emission spectral ranges usually found in MPM, depending on multiphoton process involved.

These spectral ranges constitute a major asset of MPM for tissue safety and penetration depth: the longest wavelengths are less energetic and damaging than the shortest; tissues are basically more transparent to infrared than visible light. This is due to the presence of absorbing constituents inside biological samples, such as water, hemoglobin or chromophore proteins. Ideal spectral windows have thus recently been identified [START_REF] Vo-Dinh | Biomedical Photonics Handbook[END_REF][START_REF] Sordillo | Deep optical imaging of tissue using the second and third near-infrared spectral windows[END_REF]. Specific attention to these windows could allow extended penetration depth with limited photodamage.

1.1.2.1.2. Excitation spectral bandwidth. TPA cross sections of usual fluorophores are often ranked between 650 and 1000 nm, and can be partially or sometimes totally superimposed. In standard multiphoton microscopes, the excitation spectral bandwidth is about a few nanometers at full width at half maximum (FWHM), and can be tuned. The simultaneous excitation of several fluorophores is thus possible if by chance parts of their TPA spectra are superimposed. But their simultaneous imaging by MPM is only possible if a part of the emission spectrum of each is independent from the others, allowing selective filtering and avoiding fluorescence crosstalk.

To circumvent this risk, two strategies exist. The first one consists of using two distinct multiphoton processes, such as TPF and SHG, with a single and short spectral bandwidth of excitation: the emitted beams are spectrally distinct by definition. But SHG is a phenomenon limited to specific structures (see section 1.1.1.2.). The second strategy, already demonstrated [START_REF] Butko | Simultaneous multipleexcitation multiphoton microscopy yields increased imaging sensitivity and specificity[END_REF], consists of using a multiline laser or a wideband laser for imaging multiple fluorescent probes. Several spectral ranges of excitation can be simultaneously selected, facilitating simultaneous imaging of several fluorescent probes without fluorescence crosstalk. Spatial confinement is ensured by a focusing element. Outside the focal point, photon density is not high enough to generate multiphoton processes. Photodamage is consequently restricted to focal point. This major asset of MPM compared to confocal microscopy removes the necessity of implementing a confocal pinhole, making MPM confocal by definition. Usually in MPM the focalization is managed by a microscope objective. Its magnification and numerical aperture (NA) influence, respectively, the field of view (FOV) dimensions and resolution of images [START_REF] Negrean | Optimal lens design and use in laser-scanning microscopy[END_REF][START_REF] Oheim | Two-photon microscopy in brain tissue: parameters influencing the imaging depth[END_REF].

The resolution is also governed by the dimensions of the interaction volume [START_REF] Squier | High resolution nonlinear microscopy: A review of sources and methods for achieving optimal imaging[END_REF]. Considering this theory, a higherorder multiphoton process corresponds to a better resolution [START_REF] Gu | Resolution in three-photon fluorescence scanning microscopy[END_REF]. Following diffraction limited focusing properties, the resolution of TPF is theoretically about 0.5 µm in a plane orthogonal to the optical axis (XY) and about 1 µm in a plane along the optical axis (XZ or YZ). Experimentally, it is more usual to find resolutions about 1 µm in XY and several µm in XZ or YZ. For very high resolutions, some very sophisticated optical solutions exist, such as stimulated emission depletion (STED), saturated and/or structured illumination microscopy (S and/or SIM), etc, which are beyond the scope of this article. A complete presentation of these super-resolution techniques was published two years ago [START_REF] Hell | The 2015 super-resolution microscopy roadmap[END_REF] in a topical review from Journal of Physics D: Applied Physics.

The temporal confinement of photons of excitation is favored either by an absolute high quantity of photons incoherent temporally or by a lowest quantity, temporally coherent and synchronized [START_REF] Dyba | Ultrafast dynamics microscopy[END_REF]. This last condition, possible thanks to pulsed lasers, is less energetic and damaging than the first one, ensured by continuous-wave (CW) lasers, which involves high average powers. The pulse duration is thus a fundamental consideration for optimizing multiphoton excitation. This point will be addressed in more detail in the second part of this article. and thin, a multiphoton signal can be detected in the forward direction without disrupting scattering or absorption. This is represented by position 3 in figure 2(a). Moreover, this position is optimum for the detection of SHG and THG, which are anisotropic and preferentially emitted in the forward direction. But this organization is well adapted neither to imaging in vivo nor to thick specimens where only backward detection is accessible. Concerning backward detection, descanned or non-descanned positions are possible, respectively illustrated by situations 1 and 2 (figure 2(a)). A non-descanned geometry enhances photon collection, and a photomultiplier tube (PMT) or an avalanche photodiode ideally cooled can detect even a single photon emitted from the sample. More usual PMTs, coupled with adapted filters whose characteristics can be adjusted in central wavelength, selectivity and spectral bandwidth, can detect the presence of multiphoton emission in the sub-microwatt range. But this emitted beam moves simultaneously with scan. By consequence, the descanned position is better adapted for spectral imaging involving a fixed spectrometer.

Optical sectioning and laser scanning: 3D-image reconstruction.

Image formation is possible if the sample is moved under the excitation beam, or if the excitation spot is raster scanned across the area of interest with a pattern defined by the scanning mechanism. The latter strategy, faster than the former, is often chosen in commercial MPM. It produces a 2D-image reconstructed point-by-point thanks to synchronization between scanning system and detection module. A 3D-image is reconstructed with a superimposition of 2D-images at different depth.

Several 2D-scanning systems exist, more or less fast, miniaturized, expensive and complex. The optimal model depends on the microscope architecture, speed and precision of scan required. The more widely implemented solution consists of two galvanometer mirrors [START_REF] Flusberg | Fiber-optic fluorescence imaging[END_REF] driven and synchronized electronically. As presented in figure 2, each mirror is mounted on a movable support rotating around an axis-respectively X and Y-with an angle defined as a function of the FOV required and the scan pattern chosen. Each mirror gives a 1D scan with an adjustable speed. One of the two galvanometer mirrors can be replaced by a resonant one, increasing scanning speed. When a high level of miniaturization is indispensable, some alternative strategies exist. A single mirror mounted on microelectromechanical systems (MEMS) has been successfully demonstrated for fiber-based multiphoton endoscopy [START_REF] Tang | Design and implementation of fiber-based multiphoton endoscopy with microelectromechanical systems scanning[END_REF][START_REF] Huang | Miniature fiber-optic multiphoton microscopy system using frequency-doubled femtosecond Er-doped fiber laser[END_REF].

For endomicroscopy, a piezoelectric tube fixed at the fiber tip is frequently presented [START_REF] Flusberg | In vivo brain imaging using a portable 3.9 g two-photon fluorescence microendoscope[END_REF]; the fiber tip is mechanically shaken with an amplitude provoking its mechanical resonance with a spiral pattern.

A scan in depth, usually named 'Z-scan' is then required to obtain a succession of 2D-images, which are then reconstructed in a volumetric 3D-image. This property is often managed by the vertical motion of the microscope objective or the sample holder having a sub-micrometric mechanical resolution. Alternatives for Z-scan have also been demonstrated. One of these takes advantage of the temporal dispersion induced by the optical elements of the microscope structure, such as lenses and microscope objective. The first one consists of generating spatial confinement with a highly dispersive lens. The central wavelength of excitation is then tuned over a range compatible with the absorption bandwidth of the fluorophore to be imaged [START_REF] Straub | Fluorescence lifetime threedimensional microscopy with picosecond precision using a multifocal multiphoton microscope[END_REF]. Thus, the focal point is moved axially for each spectral bandwidth. The second approach consists of tuning the second order of dispersion (SOD) by a device placed before the microscope objective [START_REF] Durst | Simultaneous spatial and temporal focusing in nonlinear microscopy[END_REF]. The temporal confinement is thus managed by the SOD, and adapted for different levels of depth. This method is named SSTF, for simultaneous spatial and temporal focusing, or SSFS, for soliton self-frequency shift [START_REF] Wang | Optimal spectral filtering in soliton self-frequency shift for deep-tissue multiphoton microscopy[END_REF][START_REF] Rowlands | Wide-field three-photon excitation in biological samples[END_REF].

Consequences of laser-scanning method (LSM).

In MPM, LSM constrains several image parameters, which must be correctly adjusted to avoid imaging mistakes such as 'ghost' pixels where no multiphoton signal is detected on several pixels due to technical limitations (and not to specificities of the sample imaged). Table 2 resumes the physical parameters of a multiphoton microscope concerned by this specific attention.

The combination of image size Ω iz (pixels) and pixel dwelltime δ t (s/pix) governs the frame rate ϕ ps expressed in frame per second (fps) following equation (2):

δ t = 1 Ω iz ϕ ps = N pp f . (2)
Laser repetition rate f is often a fixed value. The combination of Ω iz and δ t must be limited by a bottom value resulting in at least one pulse per pixel, avoiding 'ghost' pixels. But with one pulse per pixel, image formation can potentially be sensitive to mis-synchronizations between repetition rate and scanning system. It is safer to choose a number of pulses per pixel at least equal to N pp = 2. In that case, the number of excitation pulses is reduced at best to a minimum value, thus limiting superfluous excitation photons.

In conclusion, for each situation and depending on adjustable parameters, a compromise must be studied between frame rate ϕ ps , pixel dwell-time δ t , FOV, resolution and laser repetition rate f. Moreover, a following section of this article will show that a slower repetition rate is better suited to generating TPF.

Summary of the parameters of the excitation source

involved in MPM. Table 3 collects in a list the optimal parameters of the excitation source for MPM, based on its requirement highlighted in previous sections.

MPM in biomedical imaging

1.2.1. Label-free and multimodal imaging method with low energetic radiations. Thanks to its specific features exposed in the previous part and its technical simplicity compared to other methods such as CARS/SRS, STED or SIM, MPM has been profusely developed commercially. Comparing to classical one-photon-confocal microscopes working in the visible range, several advantages are linked to multiphoton technology which allows notably imaging living specimens at the micron scale with excitation wavelength in the NIR (lowly energetic) and without labeling.

Some substances naturally present in biological tissues at the intracellular scale and in the extracellular matrix are intrinsically fluorescent; they are named endogenous fluorophores. Despite their low quantum efficiencies, MPM is a label-free technique. Concerning the intracellular matrix, the most common endogenous fluorophores are nicotinamide adenine dinucleotide (NADH), a substance involved in intracellular redox metabolism, and flavoproteins such as flavin adenine dinucleotide (FAD), an endogenous marker of cellular metabolism. Concerning the extracellular matrix, elastin, collagen and keratin are also endogenous fluorophores. These substances are witnesses to physiological or morphological phenomena. The characterization of their absorption spectrum in one-or twophoton excitation has been reported in literature such as illustrated in [START_REF] Zipfel | Nonlinear magic: multiphoton microscopy in the biosciences[END_REF][START_REF] Mütze | Excitation spectra and brightness optimization of twophoton excited probes[END_REF][START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF][START_REF] Xu | Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy[END_REF][START_REF] Peyrot | Development of a nonlinear fiber-optic spectrometer for human lung tissue exploration[END_REF].

The interest of imaging these substances by TPF, rather than OPF for example, has been presented in previous parts: higher beam penetration depth, decreased out-of-focus background, better signal to noise ratio, photodamage restricted to focal point, 3D imaging … all of which has huge importance regarding microscopy for biomedical imaging.

Additionally to TPF, the use of a pulsed excitation in the NIR allows harmonic generation, another kind of imaging modality happening for specific kinds of tissue organisation (see section 1.1). Indeed, some biological constituents or tissues present structures compatible with SHG (noncentrosymmetric chiral crystalline organization) or THG (interfaces and inhomogeneities in the optical medium) [START_REF] Friedl | Biological second and third harmonic generation microscopy[END_REF]. The most noncentrosymmetric biological targets imaged by SHG are structures of collagen fibers, better known for their ability to generate SHG than to be fluorescent. Other structures have also been reported as good candidates for SHG: myosin fibers, tubulins and DNA. In those cases, SHG modality probes the macromolecular organization of these substances. THG is another modality of imaging, which has also been involved in biological MPM for imaging lipids or oxyhemoglobin but is also involved in the imaging of myosin or collagen [START_REF] Friedl | Biological second and third harmonic generation microscopy[END_REF]. Table 4 shows some example of endogenous substances generating multiphoton processes demonstrated in MPM.

Striking application of biomedical MPM.

MPM is involved in many areas, from plant imaging [START_REF] Talamond | Secondary metabolite localization by autofluorescence in living plant cells[END_REF] to pathology identification [START_REF] Strupler | Second harmonic imaging and scoring of collagen in fibrotic tissues Opt[END_REF], oncology [START_REF] Kirkpatrick | Endogenous optical biomarkers of ovarian cancer evaluated with multiphoton microscopy Cancer Epidermiol[END_REF] and meat quality characterization [START_REF] Odin | Collagen and myosin characterization by orientation field second harmonic microscopy[END_REF]. Among these, the imaging of brain tissues to understand their functioning and to evaluate the impact of pharmacological or chemical treatments takes a prominent place. The early detection of cancerous sites and inflammatory markers in the body is also a major concern where MPM has been identified as an essential tool.

Currently, several strategies exist for the identification of pathologies such as cancers. The most widespread and reliable involves a biopsy where the resected sample is labeled and analyzed by anatomopathologists [START_REF] Kantelhardt | Imaging of brain and brain tumor specimens by time-resolved multiphoton excitation microscopy ex vivo[END_REF][START_REF] Najari | Pilot study of the correlation of multiphoton tomography of ex vivo human testis with histology[END_REF]. To illustrate the essential role of MPM in medical discoveries, the example of multiphoton histology of cancerous tissues is chosen. Several groups have demonstrated that imaging the sample by MPM gives better image quality than routine labeling processes such as hematoxylin and eosin (H&E) staining. A recent work by Hu and colleagues has demonstrated the value of MPM in the histology of pancreatic tissues, which present a structure composed by several endogenous optical biomarkers such as NADH (TPF), FAD (TPF) or collagen fiber (SHG) [START_REF] Hu | Nonlinear optical microscopy for histology of fresh normal and cancerous pancreatic tissues[END_REF]. The MPM images restitute the same biological structure of tissue without labeling and with a better accuracy than standard hematoxylin and eosin (H&E) labeling. In other words, MPM is a label-free method able to deliver histological images of resected samples having a subcellular resolution. Another group has demonstrated that MPM images clearly distinguish between structures of normal versus tumorigenic pancreatic tissues [START_REF] Chen | Multiphoton microscopy as a diagnostic imaging modality for pancreatic neoplasms without hematoxylin and eosin stains[END_REF]. Figure 3 presents images of normal and deteriored pancreatic tissues imaged by MPM and by standard H&E staining, extracted from [START_REF] Chen | Multiphoton microscopy as a diagnostic imaging modality for pancreatic neoplasms without hematoxylin and eosin stains[END_REF] with author's and editor's reprint permissions. Thanks to the colocalization, it appears that unstained multiphoton images deliver similar information with a better resolution than H&E staining. Multiphoton histology presents four major advantages compared to standard histology. (i) It is label-free, (ii) with a subcellular resolution, (iii) 3D-images can be generated, and (iv) can potentially be performed in vivo thanks to multiphoton endomicroscopes now in development [START_REF] Tang | Design and implementation of fiber-based multiphoton endoscopy with microelectromechanical systems scanning[END_REF][START_REF] Hamzeh | Optimization and characterization of nonlinear excitation and collection through a gradient-index lens for high-resolution nonlinear endomicroscopy[END_REF]. These arguments taken together show MPM ready to be a diagnostic imaging modality and a major alternative to standard histological approaches-which must first be adopted by anatomopathologists.

Laser sources implemented in MPM

Today, laser sources implemented in standard commercial MPM are nearly all similar: a mode-locked femtosecond laser source delivering 10 nm of spectral width tunable between 700 and 1000 nm. In this part, this source is first reviewed, with its complementary modules and its physical parameters. Starting from the identification of its limitations, alternative excitation sources found in the literature and developed especially for MPM are listed. A synthesis of their physical parameters is proposed.

Laser technology usually implemented on commercial multiphoton microscopes

Commercial turn-key solutions of multiphoton microscopes are proposed by companies such as Olympus, Nikon, Leica or Zeiss. They often include commercial elements for detection systems, scanning modules, optics and excitation laser sources.

For this last point, mode-locked titanium-doped sapphire laser [START_REF] Brockman | Pulsed injection control of a titanium-doped sapphire laser[END_REF][START_REF] Theer | Two-photon imaging to a depth of 1000 mm in living brains by use of a Ti:Al 2 O 3 regenerative amplifier[END_REF][START_REF] Liu | Progress in Cherenkov femtosecond fiber lasers[END_REF] (Ti: Sa) is the technology most widely implemented in multiphoton microscopes. It is suited to a microscope workstation: reasonably (non-)voluminous, turnkey, user-friendly, stable and reliable. Its physical parameters fulfill the requirements of MPM listed in table 3: a pulse duration of 150 fs at the FWHM, with a repetition rate about 80 MHz, a reserve of average power until several watts, a central wavelength tunable in the NIR between 700 and 1000 nm, a peak-power around 100 kW with a linear polarization. Consequently, these sources, mainly commercialized by Coherent Inc. and Spectra-Physics, are today implemented deservedly on the overwhelming majority of commercial multiphoton microscopes. Pulse duration is sometimes modulated with the compensation of chromatic dispersion (Deep See ® , for example) occurring inside the microscope and based on more or less complex technologies, such as chirped mirrors [START_REF] Szipöcs | Chirped multilayer coatings for broadband dispersion control in femtosecond lasers[END_REF], prism-line [START_REF] Tang | Effect of pulse duration on two-photon excited fluorescence and second harmonic generation in nonlinear optical microscopy[END_REF] or grism-based stretcher [START_REF] Lefort | Sub-30 fs pulse compression and pulse shaping at the output of a 2 m-long optical fiber in the near-infrared range[END_REF].

To access all modalities of MPM, especially THG or ThPF, a larger excitation range in the NIR is necessary (table 1). A solution commercially available consists in coupling a complementary module with the Ti: Sa source. This technique is based on parametric down conversions occurring into a birefringent nonlinear crystal. These optical parametric oscillators or amplifiers (OPO or OPA) convert the excitation wavelengths in longer wavelengths [START_REF] Mojzisova | When multiphoton microscopy sees near infrared[END_REF]. They are pumped by a Ti: Sa source, extending the range of excitation wavelengths available between 0.5 µm up to about 2.5 µm [START_REF] Tragardh | Exploration of the two-photon excitation spectrum of fluorescent dyes at wavelengths below the range of the Ti:Sapphire laser[END_REF][START_REF] Andresen | Infrared multiphoton microscopy: subcellular-resolved deep tissue imaging[END_REF][START_REF] Wang | Extension of imaging depth in two-photon fluorescence microscopy using a long-wavelength high-pulse-energy femtosecond laser source[END_REF].

But covering the whole of this spectral range continuously requires the use of different kinds of OPOs or OPAs. These modules are particularly expensive (~100 k€), and not adapted for simultaneous excitation with at least two spectral bandwidths: multispectral excitation is complex to implement with this method. Moreover, a Ti: Sa source presents a limited spectral bandwidth of 10 nm at FWHM. For example, in the case of multiphoton fluorescence, this spectral bandwidth gives access to the simultaneous imaging of two or three fluorophores at best, provided that (i) the TPA spectra have superimposed regions, (ii) the excitation spectrum is included in this superimposed region and (iii) the emission spectra have insulated parts free from crosstalk-being in this way compatible with individual detection.

In parallel, the development of alternative laser sources specially designed to substitute Ti: Sa sources in MPM based on alternative technologies has increased since the 2000s. The next part presents a list gathering the main excitation sources developed in the literature especially for MPM, except usual commercial solutions such as Ti: Sa sources and its complementary modules.

Alternative laser sources demonstrated for biomedical MPM

Thanks to the versatility of the technology involved, a huge number of sources can be created, having their own parameters: spectral range and bandwidth, pulse duration, repetition rate and average power. Several pulsed lasers are based on a gain medium included into a more or less complex optical setup coupled with a pumping element such as an external CW laser source for example. The detail of these technologies is beyond the scope of this article; interested readers have at their disposition several high level books or publications concerning this subject [START_REF] Wise | Laser for nonlinear microscopy[END_REF]. To summarize, this technology is based on a soliton-type pulse shaping: a precise combination of linear group-velocity dispersion and nonlinear self-phase modulation occurs inside the gain medium under the effect of the monochromatic CW source. Pulses are thus created, and can propagate without change. A crystal of sapphire, doped with titanium ions constitutes the gain medium of standard Ti: Sa sources implemented on MPM. Changing the crystal and the doping ions to other combinations give access to new spectral bandwidths. For example, two doping elements in a crystal structure are well-known for their emission in a spectral range between 1000 and 1100 nm: neodymium ions in a crystal of YAG, YLF or YVO 4 [START_REF] Wokosiny | Three-photon excitation fluorescence imaging of biological specimens using an all-solid-state laser[END_REF] or ytterbium ions doping PCF [START_REF] Tang | Developing compact multiphoton systems using femtosecond fiber lasers[END_REF].

Table 5 gathers the main laser sources especially developed and demonstrated in literature for MPM. They are organized, depending on pulse duration, into four categories: femtosecond, picosecond, nanosecond and CW. In the range of femtosecond durations, literature shows that solid-state systems and fibered systems are compatible with MPM and a high interest of wideband sources appeared in 2005 thanks to a femtosecond Ti: Sa source broadened into a PCF-which is not yet a commercial system. Parameters of commercial femtosecond Ti: Sa sources from Coherent Inc. and Spectra Physics usually implemented in multiphoton microscopes are reminded in table 5 and referenced with source n° 0. Standard parameters are considered: 10 nm, 1 W, 80 MHz, 150 fs, 700-1000 nm. Concerning picosecond and nanosecond sources for MPM, the majority of these result from the use of laser diodes which have fixed central wavelengths, spectral bandwidths, pulse durations and repetition rates.

Table 5 presents the panorama of the excitation sources which have so far been demonstrated in MPM in literature. The first consideration in studying this list is that each of them is adapted for biomedical MPM. But each situation is different, technically, in terms of physical parameters of the source, technology involved or application illustrations and fields. Judging such or such laser source better for MPM with only this table comes under clairvoyance. In order to classify them, and to identify the best one for MPM, or to depict its identikit, an objective comparison must be led first. This is the aim of the next part.

Comparison of sources implemented for biomedical MPM

Theoretical elements of laser source comparison

Efficiency of multiphoton processes is influenced by (i) focalization characteristics, (ii) characteristics of the biological sample imaged and (iii) excitation source and its parameters. A theory considered as a reference for the comparison of sources for MPM is precisely described by Webb et al [START_REF] Denk | Two-photon laser scanning fluorescence microscopy[END_REF][START_REF] Denk | Two-photon molecular excitation in laser-scanning microscopy Handbook of Biological Confocal Microscopy[END_REF][START_REF] Xu | Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm[END_REF], and is regularly recalled for pulsed lasers [START_REF] Diaspro | Two-photon fluorescence excitation and related techniques in biological microscopy Q[END_REF][START_REF] Girkin | Optical physics enables advances in multiphoton imaging[END_REF][START_REF] Kawakami | In vivo two-photon imaging of mouse hippocampal neurons in dentate gyrus using a light source based on a high-peak power gains-witched laser diode[END_REF][START_REF] Niederriter | Compact diode laser source for multiphoton biological imaging[END_REF][START_REF] Lefort | Multicolor multiphoton microscopy based on a nanosecond supercontinuum laser source[END_REF][START_REF] Zhang | Cell vialbility and DNA denaturation measurements by two-photon fluorescence excitation in CX Al:GaAs diode laser optical traps[END_REF], in the case of mode-locked systems or alternative technologies. This evaluation is based either on the estimation of the number of photons emitted by TPF or on the number of photons absorbed by TPA. Here, the time average fluorescence photon flux F emitted by a fluorophore is chosen for the comparison. Table 6 reviews the experimental parameters influencing the emission of TPF and the related properties following Webb's theory.

The complete expression of F, such as described by Webb's team, respecting paraxial approximation [START_REF] Xu | Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy[END_REF], is:

F ≈ 1 2 φη 2 Cδ ξ f τ P 2 0 8n πλ = k ξ f τ P 2 0 = kS (3) k ≈ 1 2 φη 2 Cδ 8n πλ ( 4
)
with k a constant defined by equation ( 4); ξ = 0.664 for a Gaussian temporal profile and ξ = 0.588 for a hyperbolicsecant square (sech 2 ) pulse.

Each excitation sources presented in table 5 has a specific combination of pulse duration τ, average power P 0 , central wavelength λ, spectral bandwidth Δλ and repetition rate f. S defined by equations ( 3) and ( 5) is only function with the physical parameters of the laser. It represents the score of the source, corresponding to its peak-power. A pondered score P s is defined as follows, and treated in more detail in the next section.

S = ξ P 2 0 f τ = ξ P 2 0 × P S . (5)
For the comparison of laser sources gathered in table 5, we consider only the parameters linked with laser sources; fluorophore and microscope objective are fixed. Thus, theoretical bases for the optimization of TPF intensity with the excitation source are given, allowing the comparison of laser sources employed in MPM. For a higher order process such as three-or four-photon fluorescence, the multiphoton fluorescence intensity S α is following equation ( 6), α being the number of photon absorbed for each photon of fluorescence emitted:

S α = P α ( f τ ) α-1 . ( 6
)

Comparison of laser sources

3.2.1.

Comparison with S score. The evolution of TPF intensity F is described by equation [START_REF] Pawel | Handbook of Biological Confocal Microscopy[END_REF]. Considering k as a constant (fluorophore and microscope objective fixed), F is exclusively a function of the physical parameters of the laser: temporal pulse width τ and profile ξ, repetition rate f and average power P 0 . The evolution of F is thus described by S, the score of the laser calculated for each source and gathered in table 5. This comparison can also be described with a 'figure-of-merit' (FOM) [145]. For a pulsed source, F is linearly proportional to the peak power of the excitation source. But the information concerning the temporal pulse profile ξ being seldom given, a compromise between a Gaussian and a sech 2 profile is chosen for the comparison: ξ = 0.626. In the specific case of a CW excitation, Xu et al [START_REF] Xu | Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy[END_REF] have considered the ratio ξ/( fτ) equal to 1. When a laser parameter indispensible for the calculation of S is missing, an estimated value written in italic is given, based on the elements found in the text.

3.2.2.

Comparison with pondered score P s . The score S is proportional to P 2 0 . Experimentally, the average power is quite easy to modify-for example with an optical density-and consequently distorts the relevance of the score S: for identical f and τ, a higher average power is necessarily associated with a higher score. But in biomedical MPM, too high an average power might generate photodamages. This question is fundamental in MPM, and justifies a complete study by itself [146-148], which is beyond the scope of this article. To be free from this level-headedness, and for a visual classification of sources, a pondered score P S is calculated by considering only 1/(fτ). For a better visualization, P s values are nor malized by the P s value of source number 27, having a central place in the range of P s values and consequently equal to 100. Resulting values of P s are named 'P s norm ' in table 5.

For CW sources, the work of Hell et al [START_REF] Hell | Two-photon nearand far-field fluorescence microscopy with continuouswave excitation[END_REF] is followed. They explained that the value of such sources stands in the high number of excitation wavelengths available. They also reported that CW sources are approximately 200 times less good for MPM than standard Ti: Sa sources. Consequently, the P S norm value for these sources is arbitrarily given as 0.01. The comparison is visually highlighted by figure 4, which plots the score of each source with their associated pondered value.

Figure 4 shows that for MPM and with the way of compariso n chosen, femtosecond sources are well adapted and CW sources not. Between these two extrema, the use of a picosecond or a nanosecond source can present some interests or limitations. One of the laser source presented is undeniably better for MPM than the others. The source number 15, tested recently by Oshima et al [START_REF] Oshima | Intravital multiphoton fluorescence imaging and optical manipulation of spinal cord in mice, using a compact fiber laser system Laser[END_REF], has a central wavelength of 1045 nm with very low average power of 0.6 mW, repetition rate of 100 kHz and pulse duration of 700 fs. That corresponds to the highest P s norm value equal to 570. By the way, this source looks the better among all sources already existing and tested for MPM, but has a very low repetition rate not very well suited to laser scanning MPM, as presented in section 1.1.2.

Proposition of an identikit for the ideal laser source for MPM

The principles of MPM have been presented in previous parts, with its related excitation sources. These objective statements make it possible now to have an opinion about what ideal laser source is better adapted for MPM. Forgetting all technical difficulties that can be encountered in laser source manufacturing, the purpose of this last section is to propose an identikit for the ideal physical parameters of the excitation source for MPM.

With a basic analysis of equation ( 5), the ideal excitation source has the highest average power possible, with the lowest pulse duration and the lowest repetition rate. But this primitive consideration must be pondered in light of the technical requirements of MPM reviewed in previous sections, as presented in following points.

Repetition rate

Considering equation ( 5), a slow repetition rate is favorable for MPM. But by definition, the repetition rate has a bottom value due to LSM of MPM. A standard image size of Table 5. Laser sources and their physical features employed in MPM. Wavelength conversion devices (conv. dev.) are often used for shifting the spectral bandwidth (PPLN, PCF…). Score (S) and its pondered value (P s ) are defined in part 3.

Source n°L aser system

Δλ (nm)

P 0 max (mW) f (MHz) τ λ 0 (nm)

Spectral range and bandwidth

The score S of the sources does not consider the impact of the spectral bandwidth Δλ on the optimization of excitation processes. As related in the first part, the emission spectra of fluorophores are independent of the excitation wavelength: as long as the excitation wavelength is inside the TPA spectrum (Kasha's rule), the absorption and emission processes can occur. The excitation sources listed in table 5 often have a short spectral bandwidth Δλ of few tens of nanometers at best. But with such a unique and short excitation bandwidth, fluorophores with highly distant TPA spectra cannot be imaged simultaneously. The possibility of multiplying the number of spectral bandwidths with tunable central wavelength and width is of first interest. This would generate a versatile excitation spectral bandwidth highly sought for MPM: whatever the fluorophore involved, the excitation spectrum can be adapted. The ideal excitation source for MPM might have multiple and tunable spectral bandwidths, on all the two-and three-photon absorption spectra of the common exogenous or endogenous fluorophores. This specific property permits the selection of several spectral bandwidths Δλ of excitation compatible with the TPA spectrum of fluorophores imaged, each of them covering a minimum spectral width of a few nm. The spectral bandwidths of the ideal source for MPM are multiples (multicolor) with adjustable width and tunable in central wavelength between 500 nm and 1.9 µm (table 1).

Pulse duration and profile

Considering equation ( 5), short pulse durations with a Gaussian profile are ideal for MPM. More, TPA being a sub-femtosecond phenomenon, femtosecond pulse duration constitutes its bottom value. According to femtosecond pulse durations found in the literature (table 5) 5 fs FWHM generated by a mode-locked system seems the best. With such a short duration, the spectral bandwidth at 800 nm is at least 200 nm for perfectly compressed pulses (Fourier transform). Depending on TPA spectra, such a spectral bandwidth is often unnecessary in its totality. It is likely to result in photodamage or blur and noise in the resulting image. Reducing this value in order to adapt the spectral bandwidth to the TPA spectrum is necessarily associated with increased pulse duration. For example, 10 nm of spectral bandwidth corresponds to a pulse duration equal to 100 fs FWHM. The relevance of mode-locked systems in MPM is thus in question. A proportion between pulse duration and spectral bandwidth is not adapted to a totally versatile system with a tunable central wavelength and adjustable spectral width. In the case of a multiphoton imaging of several fluorophores with TPA spectra broadened on a large spectral range, alternative laser technologies might be better adapted provided that a freedom on spectral bandwidths exists and does not influence pulse duration. Such a system does exist: it is the case for example in ultra-wide band sources based on laser diodes broadened in optical fibers [128].

Average power

For the definition of the optimal average power, the question of sample safety must be considered. It is difficult to settle on a precise value, because the sample safety is different for each situation. It depends, for example, on the environment of the sample, its constitution and the excitation wavelength. In the literature, it is quite common to find average powers around a few tens of mW for resected samples. In the case of in vivo experiments, imaging in depth often requires a few hundreds of mW without significant tissue damage highlighted, thanks to the circulation of physiological flows. The precise definition of this value would need a complete study of the relation between image quality, depth of imaging, and photodamage or photodestruction as a function of the average power with fixed pulse duration and repetition rate. To build the identikit of an ideal excitation source for MPM, let us consider that the average power can be easily reduced thanks, for example, to neutral densities or beam splitters; no highest average power is defined. Following the average powers presented in table 5, we can observe that it is usual to involve from few mW until few hundreds of mW. Let us consider routine conditions where a spectral bandwidth Δλ = 10 nm is associated with an average power of 30 mW, corresponding to 3 mW nm -1 . By extrapolation, for a spectral bandwidth of 1400 nm (from 500 nm to 1.9 µm), the total average power of the corresponding source is about 4.2 W, coupled with a microscope setup having unavoidable losses. An average power of 10 W uniformly spread over the whole spectral range is comfortable. Finally, femtosecond systems are the best adapted for MPM considering figure 4, which highlights that the majority of sources demonstrated for MPM in the literature are femtosecond and based on mode-locked technologies. But they are also the most expensive and complex technically.

With the goal of a democratization of multiphoton microscopes in labs, the choice of a cheaper solution, for example based on laser diodes, should not be neglected. Figure 4 shows that some picosecond sources can be as efficient as femtosecond systems. Equivalent efficiencies for MPM of very different lasers can be evaluated thanks to a basic calcul ation from equation ( 5), illustrated in figure 5. It represents the evo lution of P s as a function of pulse duration between 100 fs and 5 ns, and for different repetition rates between 100 kHz and 1 GHz. It shows that for different pairings of repetition rate and pulse duration, the same value of pondered score can be obtained, illustrated in figure 5 by the horizontal red dashed line corresponding to P s = 3.10 3 . This value exists for the paired values of { f, τ}: {100 kHz, 2.5 ns}, {500 kHz, 500 ps}, {1 MHz, 250 ps}, {10 MHz, 25 ps}, {100 MHz, 2.5 ps}, {500 MHz, 500 fs}, {1 GHz, 250 fs}.

Before reaching the perfect excitation source for MPM, a more accessible identikit can be proposed. For example, an adapted excitation source for MPM might have these physical parameters:

Conclusion

MPM is an outstanding method employed in a large number of biomedical research works where the study of living cells, organs, organisms or samples at the micron scale is indispensable. Thanks to the concordance of two facts: (i) MPM being a solution to a problem and (ii) the technology involved being close to its maturity, several applicative areas in biomedical fields have already been improved or made possible thanks to MPM, being user-friendly with technical advantages and features delivering incomparable results. Despite this encouraging context, MPM has probably not yet reached its apogee: this microscopy technique is relatively infrequently applied in labs routinely using optical microscopy, compared to other techniques such as one-photon-confocal microscopy. The technological efforts required to achieve a totally completed tool are maybe not so numerous. To understand these points, two elements must be inventoried first: (i) the ins and outs of MPM for biological imaging and (ii) what technological evolutions have been already done in this domain. These fundamental starting elements have been developed in the present article. A limitation has thus been highlighted, linked to the excitation source usually implemented in MPM: it is well adapted but has spectral and temporal limitations and is very In this publication, a panorama of the excitation sources which have so far been demonstrated in the literature for MPM is presented. Then, and based on the original paper of W W Webb's team in 1990 about MPM, a comparison of these sources is proposed. Finally, with this method of comparison, an identikit for ideal excitation source for MPM is proposed, concluding on the ideal physical parameters of the excitation laser source for MPM:

-A repetition rate of 2 MHz -100 fs to 0.5 ps of pulse duration -Several spectral bandwidths delivered simultaneously with tunable central wavelengths between 500 nm until 1.9 µm and adjustable spectral widths -An average power about 7 mW nm -1 Commercially, this ideal source does not exist yet, and maybe will never exist. But before fully reaching all of these ideal parameters, compromises could be found: longer pulse duration could be compensated by a slower repetition rate provided that the limits of the other parameters are respectedleaving the resulting excitation source nevertheless suitable for MPM.

1. 1 . 1 . 1 .

 111 Multiphoton fluorescence. Several references in literature precisely detail the principle of multiphoton fluorescence, involving the time-dependent Schrödinger equation and Hamiltonian. Interested readers can find this lecture in the excellent and highly rigorous 'Biomedical Photonics Handbook'[START_REF] Vo-Dinh | Biomedical Photonics Handbook[END_REF].

Figure 1 .

 1 Figure 1. Jablonski diagrams of one-, two-and three-photon fluorescence and second and third harmonic generation.

1. 1 . 2 .

 12 Technical requirements for biomedical MPM. The structure of a multiphoton microscope is defined by physical

Figure 2 .

 2 Figure 2. Structure of a multiphoton microscope. (a) General architecture; three possible positions for the detection device. (b) Example of three scanning systems: galvanometric, MEMS and PZT.

1. 1 . 2 . 3 .

 123 Detection and scanning modes. 1.1.2.3.1. Multiphoton detection. The strategy of detection is a fundamental point depending on features of the sample to be imaged. Two parameters of detection must be adjusted: position and technology of detection. If the sample is resected

Figure 3 .

 3 Figure 3. Comparison between multiphoton histology (left) and standard H&E staining (right). Up: normal pancreatic tissue. Down: pancreatic colloid carcinoma. Reproduced with permission from [87].

Figure 4 .

 4 Figure 4. Graphical comparison of laser sources tested for MPM in the literature. Horizontal axis represents each source with its number attributed in table3. Score S (blue) of each source and its pondered value (yellow) are plotted in a logarithm scale; a superimposition between S and P s norm appears in green.

4. 5 .

 5 Balance sheet of the optimal physical parameters of the excitation source 4.6. An identikit more accessible technically

Figure 5 .

 5 Figure 5. Pondered score as function of pulse duration and repetition rate. Horizontal red dashed line represents a single value of P s which can be obtained thanks to several couples of { f, τ}.

Table 1 .

 1 Usual excitation ranges for multiphoton processes and resulting emissions in the UV/visible range.

	Multiphoton	Excitation	Emission
	process	range (µm)	range (µm)
	SHG	0.8 → 1.1	0.4 → 0.55
	TPF	0.6 → 1.2	0.3 → 0.8
	ThPF	0.7 → 1.9	0.3 → 0.8
	THG	1.2 → 1.8	0.4 → 0.6

Table 2 .

 2 Parameters of a multiphoton imaging constrained by LSM.

		Direct user	Indirect
	Parameter	adjustment	adjustment
	Laser repetition rate f (Hz)	No	No
	Image size Ω iz (pixels)	Yes	No
	Pixel dwell-time δ t (s/pix)	Yes	No
	Number of pulses per pixel N pp	No	Yes, with δ t
	Image rate ϕ ps (fps)	No	Yes, with Ω iz

Table 3 .

 3 Main physical features of excitation beam for optimal MPM.

		Consequence on the properties
	MPM characteristics	of the excitation beam
	Multiphoton absorption/	Excitation wavelength in the
	scattering	near infrared range
	Several modalities switchable	Tunable central wavelength on
		a wide spectral range
	Broad spectral bandwidth of	Adjustable spectral bandwidth
	absorption
	Temporal confinement	Pulsed
	Backward detection	Tunable polarization
	Phenomena lowly probable	Peak-power in the kW range
	Laser scanning method (at least	Repetition rate in the MHz
	2 fps)	range

Table 4 .

 4 Endogenous substances generating multiphoton processes.For example, for a laser repetition rate of 80 MHz, the fastest frame rate for an image size of Ω iz = 512 × 512 pixels is 150 fps, resulting in a pixel dwell-time δ t = 25 ns/pix for N pp = 2. A galvanometric scanning system delivers, more usually, δ t = 1 µs/pix, resulting in N pp = 80 pulses/pix. For such values of Ω iz and δ t , N pp = 2 is within reach of a laser repetition rate of 2 MHz, and corresponds to ϕ ps = 4 fps. Now, let us consider in vivo measurements. In this case, a movie rate of ϕ ps = 16 fps is more comfortable for live experiments. With δ t = 1 µs/pix and N pp = 2 pulses/pix, the ideal excitation laser has a repetition rate f = 2 MHz and image size Ω iz is reduced to 250 × 250 pixels. For a standard FOV of 500 µm × 500 µm, the XY resolution is consequently reduced to 2 µm due to the laser scanning method, and no longer due to the physical principal of MPM presented above.

		Multiphoton
	Fluorophore	process	λ excitation (nm)	λ emission (nm)
	NADH	TPF	650-800	430-490
	FAD	TPF	700-1000	490-650
	Elastin	TPF	750-870	400-600
	Collagen	TPF	700-800	450-600
	Keratin	TPF	760-860	400-575
	Myosin	SHG	λ excitation	λ excitation /2
	Collagen	SHG	λ excitation	λ excitation /2
			(>800 nm)	(>400 nm)
	Lipids	THG	λ excitation	λ excitation /3

Table 5 .

 5 (Continued ) 512 × 512 pixels, with 1 µs/pixel and 2 pulses per pixel (see section 1.1.2.4), corresponds to an imaging speed of ~2 frames per second. With these parameters, the

repetition rate of the ideal excitation source for MPM is about 2 MHz.

Table 6 .

 6 Parameters influencing the emission of photons by TPF.

	Element of the multiphoton
	microscope	Parameter involved	Parameter influencing multiphoton imaging
	Microscope objective	NA		Spatial confinement of excitation photons
		Magnification
		Fluorescence collection efficiency φ	Collection efficiency
		Wavelength transmission efficiency
	Fluorophore	TPA cross-section δ	TPA efficiency
		Fluorescence quantum efficiency η 2	Absolute quantity of TPA processes
		Refractive index of sample medium n
		Concentration C
	Excitation source	f	Repetition rate	Temporal confinement of photons
		τ	Temporal pulse width (FWHM)	Peak power
		P 0	Average power
		ξ	Temporal pulse shape
		λ	Central wavelength

J. Phys. D: Appl. Phys. 00 (2017) 000000