What is 3-photon excitation?
In 3-photon excitation, 3 photons are absorbed by a fluorophore molecule. The fluorophore is promoted to an excited state. The absorbed energy is typically lost through radiationless relaxation before decay to the ground state, accompanied by the emission of a longer wavelength photon.
For GFP, excitation may occur through absorption of a blue photon at ~470 nm (linear or single-photon excitation), of two infrared photons at ~910 nm (2-photon excitation), or of three infrared photons at ~1300 nm (3-photon excitation) and fluorescence emission is in the green spectrum at ~510 nm.
Transitions of the fluorophore between energy states are often illustrated schematically with a Jablonski diagram (Jablonski, 1933).
The absorption of a single photon results in a linear relationship between illumination and fluorescence intensities. 2-photon and 3-photon excitation exhibit quadratic and cubic dependence of fluorescence on illumination intensity, respectively. The intrinsic optical sectioning of 2- and 3-photon excitation results from the non-linear relationship between illumination intensity and fluorescence.
There are two windows for biological 3-photon excitation, at ~1300 nm and ~1700 nm.
Many fluorophores used in 3-photon microscopy undergo linear excitation in the visible spectrum, generally at 450-550 nm, 2-photon excitation in the near IR at 800 nm - 1.1 µm, and 3-photon excitation in the near IR at 1-2 µm. Water absorbs across the infra-red spectrum. The extinction coefficient of absorption by water increases abruptly beyond ~1.1 µm (Curcio & Petty, 1951; Hale & Querry, 1973; Bertie & Lan, 1996) and absorption by water can present challenges for biological imaging at IR wavelengths beyond 1 µm. However, there are two regions in which the extinction coefficient of water is reduced, resulting in two favourable windows for biological imaging with 3-photon excitation, at 1300 and at 1700 nm. Fortunately many green and red fluorescent proteins are excited efficiently at 1300 and 1700 nm, respectively (Horton et al., 2013; Deng et al., 2019).
For fluorophores commonly used in biological imaging, such as GFP, calculated 3-photon PSFs are usually slightly larger than calculated 2-photon PSFs.
3-photon excitation employs longer wavelengths than 2-photon excitation, resulting in a larger point spread function (PSF). This effect is partially offset by the cubic relationship between illumination intensity and excitation probability, the net result usually being a 3-photon PSF that's slightly larger than the 2-photon PSF. For 2- and 3-photon excitation of GFP at 910 nm and 1300 nm, the calculated full width half maximum (FWHM) of the central peak of the 3-photon PSF is ~15-20% greater in both transverse and axial dimensions than 2-photon excitation. Transverse FWHM for 3-photon excitation is very approximately ~0.33 lambda / NA.
Calculated PSFs for linear, 2- and 3-photon excitation at 490, 910 and 1300 nm. PSFs were calculated using vectorial diffraction theory (Richards & Wolf, 1959) for NA 0.9 and water immersion with no aberrations. (Code available on the Downloads page.) Transverse FWHM for linear, 2- and 3-photon excitation 0.31, 0.41 and 0.49 µm. Axial FWHM 1.24, 1.66 and 1.95 µm.
3-photon PSFs measured from test slides and deep in cortical tissue are consistent with PSFs calculated with vectorial diffraction theory. Yildirim et al. (2019) measured transverse and axial FWHM at 0.45 ± 0.05 μm and 1.9 ± 0.2 μm for 100 nm beads in agarose, similar to calculated values of 0.45 and 1.44 μm (1300 nm, NA 1.02). PSFs changed little when imaging into layers 5 and 6 of mouse visual cortex, indicating that ~1 mm of cortical grey matter adds only mild aberrations (lateral and axial FWHM of 0.5 and 2.5 μm; Yildirim et al., 2019).
A key advantage of 3- over 2-photon excitation is that 3-photon excitation permits deeper imaging into biological tissue.
With non-linear excitation, fluorescence is generated preferentially in the focal plane, but measurable fluorescence can also arise from outside the focal plane (Ying et al., 1999; Theer et al., 2003). When imaging deep in biological tissue, high illumination intensities are often necessary to generate sufficient intensity at the focus and these high intensities can drive 2-photon excitation of fluorophores above and below the focal plane (Theer & Denk, 2006; Takasaki et al., 2020). Out-of-focus fluorescence reduces image contrast and often limits the depth at which images can be formed with 2-photon excitation (Theer & Denk, 2006; Takasaki et al., 2020).
In tissue with a uniform spatial distribution of fluorophore molecules, the depth limit of 2-photon excitation occurs where in- and out-of-focus fluorescence are equal, at ~3 scattering length constants, 400-600 µm in cortical grey matter (Theer & Denk, 2006; Takasaki et al., 2020). When the focal plane is shallower than the depth limit, fluorescence is mostly from the focal plane. As the focus is shifted deeper into tissue, illumination energy must be increased to maintain intensity at the focus, which maintains constant excitation probability in the focus but drives greater out-of-focus fluorescence. Beyond the depth limit, most fluorescence originates from outside the focal plane. Since the depth limit is a function of out-of-focus fluorescence, the depth limit will be greater in tissues with few fluorophore molecules outside the focal plane.
3-photon excitation generates less out-of-focus fluorescence than 2-photon excitation, due to the steeper relationship between 3-photon excitation and illumination intensity (Takasaki et al., 2020). The result is an extended depth limit and deeper imaging (Horton et al., 2013; Kobat et al., 2009; Kobat et al., 2011; Ouzounov et al., 2017; Yildirim et al., 2019; Takasaki et al., 2020). The depth limit of 3-photon excitation commonly results from tissue heating, not out-of-focus fluorescence. (Takasaki et al., 2020) and 3-photon imaging in mouse brain is possible to ≥1.4 mm below the tissue surface at 1300 nm (Takasaki et al., 2020) and ≥1.6 mm at 1700 nm (Kobat et al., 2009; Kobat et al., 2011).
Attenuation: scattering and absorption
In 3-photon microscopy, as in other forms of microscopy, attenuation by biological tissue reduces the intensity of ballistic photons at the focal volume. Scattering and absorption each contribute to attenuation, with scattering playing a greater role than absorption.
The strength of scattering and of absorption by biological tissue are often expressed as scattering and absorption coefficients (proportional to the number of photons absorbed or scattered per unit distance) or as length constants, the distances over which intensity is reduced e-fold. Coefficients and length constants are reciprocals.
Attenuation is the sum of scattering and absorption. Hence,
μe = μs + μa and 1/le = 1/ls + 1/la
μe is the attenuation coefficient, μs is the scattering coefficient, and μa is the absorption coefficient.
le is the attenuation length constant, ls is the scattering length constant, and la is the absorption length constant.
At visible wavelengths and near-IR wavelengths commonly used for 2-photon excitation, scattering dominates. Scattering length constants are ~100 um at 500 nm and ~200 um at 910 nm (Theer & Denk, 2006). Length constants for absorption by water are ≥3 orders of magnitude greater, at >100 mm at 500-900 nm.
Scattering and absorption each change with wavelength. Scattering decreases (the scattering length constant increases) with increasing wavelength. The wavelength-dependence of absorption depends on the absorbing species, major absorbing species in the brain being water and haemoglobin. Broadly, absorption increases with increasing wavelength. Scattering length constants are ~2- and 4-fold greater at 1300 and 1700 nm than at 900 nm (Jacques, 2013). Length constants for water absorption at 1300 nm and 1700 nm are ~10 mm and 1 mm. Although absorption increases 2 orders of magnitude from 900 to 1700 nm, scattering still dominates.
Attenuation by biological tissues declines with increasing wavelength across the spectrum used for multi-photon excitation. Attenuation lengths have been measured in rodent neocortical grey matter (Kleinfeld & Denk, 2000; Kobat et al., 2009; Wang et al., 2018a; Yildirim et al., 2019):
le ≈ 130 μm at 775 nm
le ≈ 200 μm at 800-850 nm
le ≈ 250-300 μm at 1300 nm
le ≈ 400 um at 1700 nm
Tissue attenuation necessitates an increase in illumination intensity with imaging depth, to maintain intensity at the focus. The increase per unit depth is less for 3- than for 2-photon excitation. 3-photon excitation at ~1 mm is often possible with surface intensities of only ~25-50 mW.
Tissue heating, and the need to avoid thermal damage to the tissue, often limits imaging depth and speed during 3-photon excitation.
Damage to biological tissue can occur via non-linear and via linear absorption.
The damage threshold for non-linear absorption depends on the point spread function and pulse characteristics, including duration and shape, and may differ between microscopes. In one experiment, likely representative of many others, the damage threshold was ~2 nJ pulse energy with 40 fs pulses (Yildirim et al., 2019). For a 1 MHz repetition rate, 2 nJ pulse energy corresponds to 2 mW of illumination at the focal plane. Only a minority of incident photons converge at the focus when imaging deep into biological tissue, necessitating >2 mW illumination at the tissue surface to drive significant 3-photon excitation in the focal plane. Illumination intensities of ~30 mW are commonly used to drive 3-photon excitation at 1300 nm ~800 µm below the surface of mouse brain without causing non-linear photodamage, even during prolonged imaging.
The dominant mechanism of linear absorption in many biological tissues is absorption by water molecules, resulting in tissue heating. Linear absorption is largely independent of point spread function and pulse characteristics and is likely similar across microscopes. Heating-related photodamage occurs with >250 mW of prolonged illumination at 800-1040 nm or >120 mW at 1320 nm (Podgorski & Ranganathan, 2016; Wang et al., 2020a). This ~2-fold difference in damage threshold is conststent with the ~2-fold difference in the extinction coefficient for absorption by water at 920 and 1320 nm (Curcio & Petty, 1951; Hale & Querry, 1973; Bertie & Lan, 1996). Likely heating, rather than non-linear photodamage or other factors, determines the maximum depth of 3-photon excitation in many biological imaging experiments.
Imaging pixel and frame rates are typically lower for 3- than for 2-photon excitation.
In multiphoton excitation, one pulse drives more excitation than the equivalent power distributed across multiple pulses, in the absence of fluorophore saturation (Prevedel et al., 2016; Weisenburger et al., 2019). One pulse per pixel also maximizes the acquisition rate.
Pulses per pixel across a 256 pixel line with a 4 kHz resonant galvanometer.
The rate of 3-photon image acquisition is fundamentally limited by the repetition rate of the laser. Lasers suitable for 3-photon excitation commonly have repetition rates in the 1-4 MHz range, therefore permitting acquisition from one to four million pixels per second at one pulse per pixel. For a 512 x 512 pixel image, a 1 MHz laser therefore supports 1,000,000 / (512 x 512) = 3.81 images per second with a linear galvanometer.
Faster image rates can be acquired with resonant galvanometers. With resonant galvanometers, the speed at which the laser is swept across the sample changes across the scan field, resulting in fewer pulses per pixel in the center of the field of view than toward the edges. For a 256 x 256 image acquired with a 4 kHz resonant galvanometer, 4 MHz is the minimum pulse rate required for at least one pulse at every pixel. 4 MHz lasers are available, permitting 3-photon excitation at ~32 images per second.