Fluorescence imaging with two-photon evanescent wave excitation

Abstract

We demonstrate broad-field, non-scanning, two-photon excitation fluorescence (2PEF) close to a glass/cell interface by total internal reflection of a femtosecond-pulsed infrared laser beam. We exploit the quadratic intensity dependence of 2PEF to provide non-linear evanescent wave (EW) excitation in a well-defined sample volume and to eliminate scattered background excitation. A simple model is shown to describe the resulting 2PEF intensity and to predict the effective excitation volume in terms of easily measurable beam, objective and interface properties. We demonstrate non-linear evanescent wave excitation at 860 nm of acridine orange-labelled secretory granules in live chromaffin cells, and excitation at 900 nm of TRITC-phalloidin-actin/GPI-GFP double-labelled fibroblasts. The confined excitation volume and the possibility of simultaneous multi-colour excitation of several fluorophores make EW 2PEF particularly advantageous for quantitative microscopy, imaging biochemistry inside live cells, or biosensing and screening applications in miniature high-density multi-well plates.

Appendix

Two-photon evanescent wave excitation volume

Assuming no stimulated emission or self-quenching, the number of fluorescence photons collected per unit time following a m ^th-order excitation process is given by:

$$ {F(t) = {1 \over 2}\phi \eta _{{m\omega }} {\left( {\sigma _{{m\omega }} {\int\limits_V {I^{m} ({\bf{x}},t)C({\bf{x}},t)\,{\rm{d}}{\bf{x}}} }} \right)}} $$

(A1)

where φ, η _mω , σ _m and C are the collection efficiency, the quantum efficiency, m-photon excitation cross-section and the fluorophore concentration, respectively. The term in brackets is the number of absorbed photons. In the absence of saturation and photobleaching, $F(t) \propto I^m (t)$ and C(x,t)=C=const. Let W(x) and I(t) denote the spatial and temporal excitation profile. We further introduce a volume contrast:

$$ \gamma _{{m\omega }} = {{\int\limits_V {W^{2}_{{m\omega }} ({\mathbf{x}})\,{\text{d}}{\mathbf{x}}} }} \mathord{\left/ {\vphantom {{{\int\limits_V {W^{2}_{{m\omega }} ({\mathbf{x}})\,{\text{d}}{\mathbf{x}}} }} {{\int\limits_V {W_{{m\omega }} ({\mathbf{x}})\,{\text{d}}{\mathbf{x}}} }}}} \right. \kern-\nulldelimiterspace} {{\int\limits_V {W_{{m\omega }} ({\mathbf{x}})\,{\text{d}}{\mathbf{x}}} }} $$

(A2)

Then:

$$ {F(t) = {1 \over 2}\phi \eta _{{m\omega }} \sigma _{{m\omega }} CI^{m} (t){\left( {\gamma ^{{ - 1}}_{{m\omega }} {\int\limits_V {W_{{m\omega }} ({\bf{x}})\,{\rm{d}}} }{\bf{x}}} \right)}} $$

(A3)

where the term in brackets denotes the excitation volume, V _mω . In practice, we only measure the time-averaged photon flux $\left\langle {F(t)} \right\rangle$:

$$ \left\langle {F(t)} \right\rangle = {1 \over 2}c_{m\omega } \left\langle {I(t)} \right\rangle ^m V_{m\omega } $$

(A4)

where φη_mωσ_mωC and the m ^th-order temporal coherence $g = {{\left\langle {I^m (t)} \right\rangle } \mathord{\left/ {\vphantom {{\left\langle {I^m (t)} \right\rangle } {\left\langle {I(t)} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {I(t)} \right\rangle }}^m$ are combined to a fluorophore and instrument parameter c _mω . The average fluorescence is proportional to the average intensity raised to the m^th power and the m-photon excitation volume.

In the case of m-photon evanescent-field excitation, the beam's half width w _r and the angle of incidence ϑ at the reflecting interface ($n_{2,m\omega } > n_{1,m\omega }$) determine the spatial excitation profile, $W_{m\omega } (r) \propto \exp \left( {{{ - mr^2 \cos \vartheta } \mathord{\left/ {\vphantom {{ - mr^2 \cos \vartheta } {2w_r^2 }}} \right. \kern-\nulldelimiterspace} {2w_r^2 }}} \right)$ and $W_{m\omega } (z) \propto \exp \left( { - mz/w_z (\vartheta )} \right)$. Here r and z denote distances within and perpendicular to the interface plane, respectively, w _r is the half-width of the illumination beam in the specimen plane at normal incidence (ϑ=0), and $w_z (\vartheta ) = {\lambda \mathord{\left/ {\vphantom {\lambda {\left( {4\pi (n_2^2 \sin ^2 (\vartheta ) - n_1^2 )^{1/2} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {4\pi (n_2^2 \sin ^2 (\vartheta ) - n_1^2 )^{1/2} } \right)}}$ is the distance over which the evanescent-field intensity decays to 1/e of its value at the reflecting interface at z=0 (typically called "penetration depth"). For through-the-objective EW excitation, w _r and ϑ can be approximated as: $\emptyset _{{\rm{pupil}}} w_0 /(2f_{{\rm{FL}}} {\rm{)}}$ and arcsin ($M\rho /(n_{2,m\omega } f_{{\rm{TL}}} )$, respectively. $\emptyset _{{\rm{pupil}}},$ M and ${n_{{2,m\omega }} }$ denote the diameter of the objective's back pupil, magnification and refractive index of the immersion medium, respectively, w ₀ is the beam's half-width at the focusing lens, and f _FL and f _TL are the focal lengths of the focusing lens and tube lens, respectively (see Fig. 1); ρ denotes a radial displacement of the focused beam relative to the optical axis.

Substituting the expressions for W(r) and W(z) into Eqs. (A2) and (A3) and integrating over a volume element rdrdϕdz we obtain $\int {W_{m\omega } (x)} \,{\rm{d}}x \propto 2{{\pi w_r^2 w_z (\vartheta )} \mathord{\left/ {\vphantom {{\pi w_r^2 w_z (\vartheta )} {\left( {m^2 \cos (\vartheta )} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {m^2 \cos (\vartheta )} \right)}}$ and $\gamma = {\textstyle{1 \over 4}}$, independent of m. Thus for non-linear evanescent-field fluorescence excitation, the excitation volume is given by:

$$ V_{m\omega } \approx {{8\pi } \over {m^2 \cos (\vartheta )}}w_r^2 w_z (\vartheta ) $$

(A5)

Substituting in Eq. (A4):

$$ \left\langle {F(t)} \right\rangle = {{4\pi c_{m\omega } w_r^2 } \over {m^2 \cos (\vartheta )}}\left\langle {I(t)} \right\rangle ^m w_z (\vartheta ) $$

(A6)

from which we note that the total generated fluorescence is proportional to w _z (ϑ). We can thus determine, at a beam angle ϑ, w _z (ϑ) from a linear fit to a plot of $\left\langle {F(t)} \right\rangle$, normalized by instrument and fluorophore parameters, versus the average EW intensity raised to the m ^th power.

How does Eq. (A5) compare with the excitation volume in two-photon scanning microscopy? For the Gaussian–Lorentzian intensity profile of a tightly focused excitation beam: $V_{2\omega }^{({\rm{GL}})} = {\textstyle{{16} \over 3}}\pi ^2 w_r^2 z_0$ and $\gamma = {\textstyle{3 \over {16}}}$ (Mertz 1998). We approximate $w_r \approx {{0.26\lambda } \mathord{\left/ {\vphantom {{0.26\lambda } {\sin \vartheta _{{\rm{NA}}} }}} \right. \kern-\nulldelimiterspace} {\sin \vartheta _{{\rm{NA}}} }}$ and $z_0 = {{4\pi w_r^2 } \mathord{\left/ {\vphantom {{4\pi w_r^2 } \lambda }} \right. \kern-\nulldelimiterspace} \lambda }$ is the Rayleigh length, where NA>0.8 has been assumed. ϑ_NA is the half-angle spanned by the NA. Thus, for a 0.9-NA water immersion objective, $V_{2\omega }^{({\rm{GL}})}$≈7 fl. To observe 2PEF upon EW excitation with w _z ≈0.2 µm at comparable levels of incident power, we hence need to restrict the lateral spot size to w _r ≈3 µm, close to what was observed experimentally (Fig. 2B). As fluorescence is excited within a volume section of w _z (ϑ)/m thickness, the effective excitation depth in one and multiphoton EW microscopy are equal, for excitation of the same fluorophore.