1. Introduction

Two-photon (2P) laser scanning fluorescence microscopy [1, 2] has become an important imaging modality for biological applications due to its large penetration depth, intrinsic optical sectioning capability, and minimum background signal. Optimum realization of 2P-microscopy requires knowledge of the two-photon excitation cross-section spectra to enhance the signal-to-noise ratio while avoiding photo-damage of the biological system of interest. Methods for measuring two-photon excitation action cross section include both absolute measurement [3, 4] and relative one with respect to a reference fluorophore [5–8] at different excitation wavelengths. The conventional approach for measuring two-photon action cross section is usually by using a tunable laser. For example, Xu and Webb measured the cross sections of several commonly used fluorophores over a wavelength range from 690 nm to 1050 nm [3]. In their work, the temporal and spatial distribution of the laser beam at the focal region and the spectral response of various optics and detector were calibrated or calculated. Fluorescence signal was measured as the excitation wavelength was tuned. In order to avoid the complicated characterization of the temporal and spatial field distribution in the focal region, relative measurement method [5–8] has also been employed routinely, where the fluorescence signal of the fluorophore of interest is measured relative to that of a reference fluorophore whose cross section is known. In these previous studies, wavelength tuning is required and the measurement procedure is often quite time-consuming. To overcome this limitation, here we report on a new method that can be used to measure the two photon action cross section over a broad wavelength range in a single shot. Specifically, we first use a nonlinear photonic crystal fiber [9] to broaden the spectrum of the excitation beam and thereby allow for measurement over a broad wavelength range. Next, similar to wavelength division imaging [10–12] different wavelengths of the excitation beam are focused to different lateral positions by purposely introduced angular dispersion. Finally, fluorescence excited at different wavelengths is measured simultaneously with an arrayed detector (e.g., a CCD camera).

2. Theoretical background on relative 2P action-cross-section measurement

For thick sample, the average two-photon excited fluorescence photon flux is given by [3, 7]

where ϕ is the system collection efficiency, η is the fluorescence quantum efficiency, C is the fluorophore concentration, σ is the two-photon absorption cross section, and n is the refractive index of the sample, I(t) and S(r) describe the temporal and spatial distribution of the excitation beam, and P(t) is the instantaneous power. The second-order temporal coherence (g) is given by g=<I ²(t)>/<I(t)>². Under the same experimental conditions, the fluorescence signal of the unknown fluorophore of interest (U) is measured relative to a reference dye molecule (R) with known excitation cross-section using the following equation:

where f and d are the effective transmittance of the filters used and the quantum efficiency of the detector respectively. The refractive indices (n_U,n_R) of the solvents at room temperature can be obtained from reference tables. Since C_i, f_i, and d_i(i=U, R) can be either measured or calculated, the action cross section (σ_TPE≡ησ) of fluorophore U can be determined relative to that of R as shown in the following.

In the above derivation, we assume that the refractive indices n_U and n_R are approximately the same. If the fluorescence emission bands of the unknown and the reference are similar, the filter transmission and detector response in Eq. (3) can be canceled out, which further simplifies it to become

3. Experiments and results

The schematic diagram of our experimental system is shown in Fig. 1. The femtosecond laser pulses (KM Labs, average power ~400 mW, center wavelength: ~810 nm, bandwidth: ~30 nm full-width-half-maximum) are first coupled into a 2-meter-long photonic crystal fiber (Blazephotonics SC-5.0-1040) using an objective lens (NA: 0.65) to broaden its spectrum. The fiber output is collimated by another objective (NA: 0.65) before being dispersed by a prism and then focused by a lens (L₁) of 150-mm focal length. The angularly dispersed excitation beam is subsequently steered towards the sample using a dichroic mirror, a lens L₂ (focal length: 300 mm), and an objective lens L₃ (Achromatic 100x, NA 1.25) which form an imaging system. Finally, the emitted two-photon fluorescence is separated from the excitation beam by a dichroic mirror and further filtered by a combination of three short pass filters (Chroma). Since the excitation wavelengths spread out into a mini-rainbow-like spectrum, fluorescence excited at different wavelengths are directly imaged onto a CCD camera (Apogee AP32ME) and simultaneously detected. The horizontal axis of the CCD corresponds to different excitation wavelengths which are calibrated. This is done by placing a narrow slit at the back focal plane of L1 (see Fig. 1) to block all but a small window of wavelengths. The light passing through the slit is first sent to an optical spectrum analyzer (Ando AQ 6315E) to determine its peak wavelength. Then, its corresponding position on the CCD camera is determined. This process is repeated at three or four different positions on the CCD camera to calibrate the dependence of wavelength on pixel position.

 

Fig. 1. Schematic diagram of the experimental setup. L1: 150 mm focal length. L2: 300mm focal length. L3: objective lens, achromatic, N.A. 1.25.

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We first characterized the excitation pulses. A representative spectrum of these spectrally broadened excitation pulses is shown in Fig. 2(a) (measured by using an optical spectrum analyzer, Ando AQ 6315E), which has a bandwidth of ~100 nm (full-width-half-maximum). The main mechanism for the spectral broadening is self phase modulation [13]. The spectrum can be further expanded to cover a larger wavelength range by increasing the laser power coupled into the fiber or selecting a proper fiber (e.g., a highly nonlinear fiber with a small core diameter and a zero-group-velocity-dispersion wavelength close to the central wavelength of the input laser). The output excitation pulses are chirped due to group velocity dispersion (GVD). We estimate the pulse width at the fiber output to be about 20 ps by using Δτ~DLΔλ [13] (D~100 ps/km nm, L=2 m, Δλ~100 nm). The time-delay between adjacent wavelength channels induced by the GVD can be helpful for reducing cross talk noise.

 

Fig. 2. (a). Spectral broadening of femtosecond laser pulses using photonic crystal fiber. The broadened spectrum was generated by coupling femto-second laser pulses into a photonic crystal fiber (Blazephotonics SC-5.0-1040, 2 meters). The output was coupled into a multimode fiber and its spectrum was measured by an optical spectrum analyzer (Ando AQ 6315E). (b) A snapshot of two-photon fluorescence signal of rhodamine green excited at multiple excitation wavelengths (horizontal axis) simultaneously. The heterogeneity of the 2P-fluorescence image correlates with the excitation wavelength band shown in (a).

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The system was then used to excite two-photon fluorescence in three different dyes (rhodamine green, fluorescein, and DiI-C₁₈). These samples were prepared in deep-well slides. Stock solutions of rohdamine green (Molecular Probes; R6107, MW=507.89 g/mol, ε=78,000), fluorescein (Sigma; F-6377, MW=376.3 g/mol, ε=93,000), and DiI-C₁₈ (Molecular Probes; D282, MW=933.88 g/mol, ε=148,000) are made and used as received from the suppliers without further purification. The samples were diluted to ~10 µM or ~100 µM in water, pH 11 water, and in methanol, respectively, for the measurements reported here. For fluorescein sample, the pH of the water was adjusted using 1 M NaOH. The exact concentration of these dyes was further measured using absorption spectroscopy.

A typical fluorescence pattern of rhodamine green (concentration C=82.8 µM) is shown in Fig. 2(b). The horizontal axis corresponds to different excitation wavelengths which were calibrated. The heterogeneity of the fluorescence signal correlates with that of the excitation pulses shown in Fig. 2(a). When the sample was replaced by pure buffer, the detected background signal was negligible. Due to the heterogeneity of the excitation pulse spectrum distribution, it is critical to examine the power dependence of the detected fluorescence signal and to ensure a genuine two-photon fluorescence signal as well as a non-saturation regime of both the CCD and the fluorophore emission. To verify that the detected signal is due to genuine two-photon fluorescence, we measured the excitation-power dependence of fluorescence signal. In these measurements, a tunable neutral density filter (with nearly constant optical density over a wide wavelength range) was inserted between the collimating objective lens (at the photonic crystal fiber output) and the prism to attenuate the excitation laser power on the sample. The fluorescence signal was averaged over a square of 20×20 pixels in the CCD image. Figure 3 shows the logarithmic power-dependence curves of the detected fluorescence signal at three representative excitation wavelengths (750 nm, 818 nm, and 863 nm). The inset shows the slope (of the power-dependence curve) as a function of excitation wavelength. In the central part of the excitation bandwidth the slope is about 1.95, indicating very good quadratic relationship. At the wings it decreases to ~1.7, which is likely caused by measurement error due to the relatively weak fluorescence signal there. Notice that the excitation power at a particular wavelength is proportional to the total excitation power since the neutral-density filter has nearly constant attenuation over a broad wavelength range. Therefore, these results confirm that the detected signal is indeed due to two-photon fluorescence of the fluorophore of interest. It is worth mentioning that similar results were also obtained at a lower concentration (C ~10 µM) with this technique, which is an order of magnitude lower that those concentrations often used with conventional methods.

 

Fig. 3. Excitation-power dependence of the observed rhodamine fluorescence reveals genuine two-photon excitation. The slope of logarithmic dependence of fluorescence signal on the total excitation power for different wavelengths is ~1.95 (at the central region), and ~ 1.7 (near the spectral edge). ‘+’ shows the power dependence at excitation wavelength 818 nm. ‘o’ shows the power dependence at excitation wavelength 750 nm. ‘∗’ shows the power dependence at excitation wavelength 863 nm. The excitation power at a particular wavelength is proportional to the total excitation power. The inset shows the slope at different excitation wavelengths.

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Following the characterization of the experimental setup, we used fluorescein (C=82.8 µM) as a reference (whose cross section was published previously using conventional approach [3]) for relative measurements of the two-photon action cross-section spectra of rhodamine green (C=87.4 µM). Representative action cross section of rhodamine green is shown in Fig. 4(a) (solid line). Since the fluorescence emission bands of fluorescein (emission peak 515 nm) and rhodamine green (522 nm) are fairly similar (emission spectra can be found on Molecular Probes website at http://probes.invitrogen.com/servlets/spectra/), Eq. (4) was used for calculation based on the two-photon fluorescence image [e.g., Fig. 2(b)]. In order to minimize the effect of aberration caused by the different refractive indices of the cover glass and fluorophore solutions [3, 14], during the experiments we first focused manually the excitation beam to the interface between the cover glass and fluorophore solution and then used a computer-controlled linear stage to translate the sample cells by the same amount of distance (30 µm–60 µm). The spatial and temporal field distributions in both measurements were therefore approximately the same. In addition, to minimize scattering noise only ten rows near the center were considered when processing fluorescence patterns captured by the CCD camera [e.g., Fig. 2(b)], which effectively serves as a virtual confocal slit to further suppress contribution from out-of-focus region. Note that the detailed temporal and spatial field distribution near the focal region in our system is quite complicated. Cross-talk between different wavelength channels may exist. We inserted a narrow slit at the back focal plane of L₁ to filter the spectrum of the excitation beam (FWHM bandwidth ~4 nm). Fluorescence signal excited at different wavelengths was obtained by mechanically scanning the slit. The measured two-photon action cross section of rhodamine green by using slit-scanning is also shown in Fig. 4(a) (circle) which is close to the single-shot line measurement result and suggests that the effect of cross talk is relatively not significant. For comparison, the action cross section of rhodamine green measured by using the conventional approach with a tunable femtosecond Ti:Sapphire laser is also shown in Fig. 4(a) (star). In this measurement, the two-photon fluorescence signal of rhodamine green and fluorescence (as a reference) at known concentrations was measured at different excitation wavelengths, which were obtained by manually tuning the laser (with 10 nm steps). The results of the three measurements in general agree with each other. Since rhodamine green is a photostable dye molecule that is usually used to calibrate fluorescence correlation spectroscopy (FCS) [15], these results will be helpful for two-photon FCS measurements in single-molecule studies. Finally, we also measured two-photon action cross section of DiI-C₁₈, which is a lipid marker that is specific to the gel phase in biomembrane studies, by using the same one-shot approach to further verify the reliability of our approach. Fluorescein was also used as reference here. The experimental result is shown in Fig. 4(b) (circle), which agrees well with that [represented by ‘∗’ in Fig. 4(b)] published in Ref. [3]. The fluorescence emission peak of DiI-C₁₈ is 565 nm which is not too far from that of fluorescein (515 nm). We estimated that the filter/detector response was similar and Eq. (4) was again used for calculation. It should be noted that rigorously speaking the filter and detector response should also be calibrated.

 

Fig. 4. (a). Relative measurements of two-photon action cross section of Rhodamine Green. Solid line: data measured by using single-shot line excitation method; ‘o’: data measured by slit-scanning method; ‘∗’: data measured by conventional approach using tunable laser. (b) Relative measurements of two-photon action cross section of DiI-C₁₈. ‘o’: two-photon action cross section measured by single-shot line excitation method. ‘∗’: two-photon action cross section published in Ref. [3] by using tunable laser method.

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4. Summary

In summary, we have demonstrated a single-shot technique to measure the two-photon action cross section. The achievable measurement wavelength range depends on the amount of spectral broadening occurred in the nonlinear photonic crystal fiber. Note that supercontinuum covering a wavelength range of more than 1000 nm can be routinely generated by using a highly nonlinear photonic crystal fiber [16]. But as the spectrum of the excitation beam becomes broader and broader it often tends to develop complex spectral structures due to the interplay between nonlinearity and dispersion. The power of each wavelength channel also decreases accordingly. How these effects may influence the action cross section measurement requires further investigation. Finally, we should point out that the action cross sections measured by using relatively long (narrow-band) pulses as in our method and ultrashort (broad-band) pulses may differ from each other. The spectral phase and the detailed pulse-shape of the ultra-short pulses can play a significant role and may lead to considerably different fluorescence emission [17, 18].