Axial scanning with pulse shaping in temporal focusing two-photon microscopy for fast three-dimensional imaging

Yu Ding; Angela C. Aguilar; Chunqiang Li

doi:10.1364/OE.25.033379

1. Introduction

Two-photon excitation has the advantages of reduced photobleaching, photodamage and background signal suppression compared with one-photon excitation and has been widely used in biomedical research, particularly for in vivo imaging. Conventional two-photon microscopic techniques use tightly focused laser beam and raster scanning to achieve efficient two-photon excitation and 2D imaging. Since last decade, temporal focusing two-photon microscopy has shown its advantage of wide field imaging (x & y) with a CCD camera as the detector, and axial (z) sectioning capability [1–3]. Since there is no scanning mechanism, its imaging speed is limited by fluorescent photon flux and detector sensitivity only. Based on the success of this technique, several groups have adopted temporal focusing on imaging particles and cells, and ablating tissue [4–9]. Since it does not require scanning the laser beam, it could reach 1000 frames/second 2D imaging speed with an amplified femtosecond laser system as the light source [10].

In lots of applications, especially in live animal imaging, it is necessary to acquire information in all three dimensions (3D) [11]. In conventional laser scanning microscopes, 3D imaging is achieved by mechanically scanning the sample in z direction or changing the focus in depth by manipulating the spatial phase front of the excitation laser beam [12]. These scanning mechanisms limit the imaging speed and require sophisticated feed-back loop control and synchronization of beam steering. In temporal focusing two-photon microscope, it has been demonstrated that changing the group velocity dispersion (GVD) of femtosecond laser pulses leads to the shift of the plane of the temporal focus along the axial direction of the objective lens, yielding z-scanning as a function of GVD [13, 14]. However, the current GVD control is still achieved by moving a prism pair or a piezo-bimorph mirror [14, 15]. Femtosecond laser pulse shaping is a technique that spreads femtosecond laser pulse spectrum in space, and each individual monochromatic component is modulated with a spatial light modulator (SLM) to arbitrarily shape an ultrafast pulse [16, 17]. Hence, pulse shaping could electrically control the GVD of the femtosecond laser pulse without any mechanical motion, which could further control the z-scanning in temporal focusing two-photon microscope.

In this study, we integrate pulse shaping into temporal focusing two-photon microscopy to achieve 3D volumetric imaging without any mechanical scanning. This microscope eliminates current 2D laser beam scanning mechanisms typically used in confocal and two-photon microscopes with temporal focusing, and adds a third dimensional axial scanning by electronic input. The development of this scan-less two-photon microscope could lead to high 3D volumetric imaging speed which is suitable for tracking fast dynamic processes in vivo. Since there is no actual mechanic scanning, the image speed is currently limited by fluorophore’s brightness and detector’s sensitivity.

2. Optical Setup

The temporal focusing two-photon microscope is set up as shown in Fig. 1. The femtosecond laser pulses come from a chirped pulse amplifier (CPA) laser system (Solstice ACE, Newport, Santa Clara, California, USA) with wavelength at 800 nm, pulse width at 35 fs, repetition rate of 5 kHz, and maximum power of 6 W. A half wave plate (HWP) and a polarizing beam splitter (PBS) control the power delivered to the microscope.

Fig. 1 Experimental setup of the temporal focusing two-photon microscope with pulse shaping technique. HWP: half-wave plate, PBS: polarizing beam splitter, AOM: acousto-optic modulator, AFG: arbitrary function generator, DM: dichroic mirror, M: mirror, L: lens, BP: bandpass filter.

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Lenses made of thick glasses can cause GVD and wave front distortion for such short laser pulses. Therefore, a telescope composed of two gold-coated reflective concave mirrors (M1 and M2) is used for shrinking the beam size to fit later apertures and to limit the spatial dispersion when the laser pulse passes through an acousto-optic modulator (AOM). A pair of prisms is used to pre-compensate the GVD from all the optical elements in order to achieve the shortest pulse width at the focal plane of objective lens. The broad spectrum (~40 nm) of the short laser pulses is separated in space by a diffraction grating (900 lines/mm, Edmund Optics, Barrington, New Jersey, USA), and is collimated by a concave mirror (M3, f = 500 mm), and then is diffracted by an AOM (TED8-200-50-800, Brimrose, Sparks, Maryland, USA) with an active aperture size of 1 mm × 35 mm. This AOM is driven by an RF wave with the center frequency at 200 MHz from its driver, and this RF wave is further modulated by an arbitrary function generator (AFG 3102C, Tektronix, Beaverton, Oregon, USA). This modulation can change the amplitude, phase, and frequency of the RF wave. This AFG is synchronized to the femtosecond laser pulse at 5 kHz. The AFG outputs a voltage applied on the RF driver. When this voltage scans from 0 to 10 V, the frequencies of the RF wave from the driver is scanned from 180 to 220 MHz. In this range of scanning, the frequency has a linear dependence on the voltages applied. The 1st order diffracted beam from the AOM is reflected by another reflective concave mirror (M4, f = 1000 mm). After passing through a lens (L1) and a long-pass dichroic beam splitter (FF665-Di02, Semrock, Rochester, New York, USA), the beam shoots into the microscope objective lens (LD plan-NEOFLUAR 63 × , NA 0.75, Zeiss, Jena, Germany). Here M3 and M4 form a 4-f system, L1 and the objective (L2) form another 4-f system. The laser beam spot on the diffraction grating goes through Fourier transformation and inverse Fourier transformation twice, and is mapped onto the objective focal plane. The size of the illuminated spot size (A₁) on the sample is determined by the original beam size (A₀) on the grating and focal lengths of M3, M4, L1 and L2. Hence, A₁ = f₄/f₃ × f₂/f₁ × A₀, where f₁, f₂, f₃, f₄ are the focal lengths of the two lenses and two concave mirrors labeled in Fig. 1. Thus, the illuminated area on the sample can be easily tuned by changing the focal lengths of one or a group of lenses. Each monochromatic beam after grating diffraction is collimated from Grating to M3, is focused from M3 to AOM, is expanding from AOM to M4, is collimated from M4 to L1, is focused then expanded from L1 to objective lens (L2), and is collimated after L2. These collimated monochromatic beams overlap at the focal plane of the objective lens to form the imaging area with a diameter about 100 µm in this experiment. The CPA laser is at its optimal working conditions (pulse width, mode) with output power of 6 W. The HWP and PBS are placed in front to the CPA laser to lower the power to our microscopic system (Fig. 1). We only use around 100 mW of the laser power passing through the AOM. To avoid tight focus at the AOM, the focal length of the concave mirror (M3) is 500 mm. The efficiency of the 1st order output power of the AOM is measured at 20%. The resulting power at the imaging plane is in the range of 10-20 mW. The fluorescent signal from the sample is epi-collected by the same objective lens. An EMCCD camera (iXon Ultra 897, Andor Technology, Belfast, UK) is used to detect the signal. A bandpass filter (607nm/36nm, Edmund Optics, Barrington, New Jersey, USA) is placed in front of the camera. The sample is mounted on a motorized translational stage (NPXYZ100SG, Newport, Irvine, California, USA).

The axial scanning mechanism controlled by AOM is briefly explained in Fig. 2. The AOM driver generates an RF wave fed into AOM. The acoustic transducer creates an acoustic wave at the same frequency which travels across the AOM. When the laser beam passes through the AOM, different components of the spectrum are diffracted by this acoustic wave at different places along the AOM aperture (Fig. 2(a)). The diffraction condition is described as nλ = 2Λsinθ, where n is an integer, λ is the laser wavelength, Λ is the acoustic wavelength, 2θ is the angle between the incident beam and the diffracted beam. In our system, λ is centered at 800 nm, and Λ is given by v/f, where v is the speed of the acoustic wave traveling in the AOM material made of TeO₂, which is about 4200 m/s, and f is the RF wave frequency which is 200 MHz. After plugging all the parameters, we can calculate the angle for the 1st order diffraction beam to be about 1°. For such a small angle θ, and n = 1, we approximately have θ = λf/v. Here v has a fixed value, however λ is a function of location λ(x). The spectra of the laser pulse is spread out from λ-Δλ to λ + Δλ, where λ is the center wavelength, Δλ is the FWHM of the laser spectrum, which is 40 nm. When the RF wave has a constant frequency f and assuming Δλ is much smaller than λ, the diffraction angle θ is the same for all wavelength components. In reality Δλ induces slight θ change, and causes slight spatial dispersion in the recombined femtosecond laser beam at the focal plane of the objective lens [16]. By adjusting f as a function of time f(t) = a + bt, where a and b are constants, the travelling acoustic wave has chirped frequency (Δf) along the AOM aperture (Fig. 2(b)). This chirped RF frequency corresponds to applying GVD on the laser spectrum. In a simple ray tracing explanation, such chirped frequency causes different diffraction angle θ for different wavelength components. For instance, the longer wavelength component and shorter wavelength component both deflect towards the center, thus causing the shift of the focal plane in axial direction.

Fig. 2 Schematic explanation of shifting the temporal focal plane in a temporal focusing two-photon microscope with GVD control. (a) constant RF frequency, (b) chirped RF frequency. AOM: acousto-optic modulator.

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3. Materials and Methods

The imaged samples are fluorescent microspheres with diameter of 1 µm and emission wavelength peak at 605 nm (FluoSpheres carboxylate-modified, F8821, Thermo Fisher Scientific, Waltham, Massachusetts, USA). The original concentration of the microspheres is diluted with distilled water at the ratio of 1:2000. For the first part of the experiment, microspheres were dried on a cover glass. For the second part of the experiment, microspheres were suspended uniformly in the solution with the help of a vortex mixer and were placed and contained in a cylindrical volume between a slide and a cover glass. The entire preparing process was implemented in a completely dark environment to preserve the optical properties of the sample.

4. Results

To demonstrate the capability of shifting the temporal focal plane via pulse shaping, a series of voltage functions from the AFG that control the chirped frequencies of the RF waves were applied on the AOM driver. For each applied AFG voltage function, the z position of the sample was scanned by moving the 3D sample stage with x and y positions fixed, and a fluorescence image was acquired at each z position. This varying voltage function induced GVD on the laser spectrum and changed the temporal focal plane as shown in Fig. 3(a). When the applied voltage is a constant, the applied GVD is 0 fs². Because the femtosecond laser spectrum still has residual GVD, the temporally focused laser beam achieves its shortest width at focus (the first row of Fig. 3(a)) when the applied voltage is a saw tooth function with total amplitude of 7.2 V (marked with half of its value 3.6 V in figure), with the RF wave sweeping frequency (Δf) of 28.8 MHz. This changing RF wave frequency corresponds to applying GVD of 1.7 × 10⁵ fs² (see Appendix). This step is to compensate the residual GVD caused by the optic system. In this configuration, the temporal focal plane overlaps with geometric focal plane of the objective lens (z = 0 µm with + z direction indicating sample moving towards objective lens), and we define that the extra GVD for shifting temporal focal plane as 0 fs². When the applied voltage is a saw tooth function with amplitude of 8 V, the RF wave sweeping frequency of 32 MHz. This changing RF wave frequency corresponds to applying total GVD of 1.94 × 10⁵ fs², and the extra GVD for shifting the temporal focal plane is 2.4 × 10⁴ fs². Therefore, the temporal focal plane is shifted to the plane at z = 20 µm (the second row of Fig. 3(a)). This shifting of the temporal focal plane by applied GVD depends on several parameters, such as laser spectral FWHM, and the numerical aperture of the objective lens. The temporal focal plane was further shifted to z = 40 µm plane and z = 60 µm plane by applying the saw tooth function with amplitude changed of 9 V and 10.2 V respectively. This separation of temporal focal plane from geometric focal plane has negative effect on the image quality. When the temporal focal plane is slightly shifted away from the geometric focal plane in the range of ± 10 μm, the single fluorophore PSF image indeed becomes blurry. When this shift is larger, the single PSF image has the characteristics of concentric rings in defocused images with peak intensity in the outermost ring, and the central lobe becomes blurred as shown in the second to fourth row in Fig. 3(a). At the temporal focal plane the femtosecond laser pulse reaches its shortest temporal width that leads to the highest two-photon excitation efficiency. However, the fluorescence signal collection efficiency of the objective lens always remains highest at its geometric focal plane. As the temporal focal plane shifts away from the geometric focal plane, less collection efficiency decreases the images quality. Therefore, there are two intensity peaks when scanning the fluorophore in z direction: one at the temporal focal plane and the other at the geometric focal plane. In Fig. 3 (b) all lines have a smaller peak at z = 0 (not shown in the plot). This ring structure does not present when the sample is moving away from the objective (z < 0 μm) as observed in another wide-field fluorescence imaging experiment [18].

Fig. 3 Temporal focal plane shift by varying GVD. (a) Series of fluorescent images of microspheres at different z positions (z = −10 to 80 µm) after the temporal focal plane is shifted at z = 0, 20, 30, and 40 µm planes with varying GVD. (b) Maximum intensity plots along axial dimension for images in (a). (c) Theoretical maximum two-photon (2P) excitation plane shift vs. GVD (blue curve), and experimental data (red dots). (d) Spatial overlap at the focus of objective lens.

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The total two-photon excitation (TPE) signal at an axial plane of position z has been derived in [14] as:

T P E (z) = \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} I^{2} (x, z, t) d x d t = \frac{C}{{{[1 + {βΩ}^{2} \frac{z - f}{Z_{M}}]}^{2} + {[\frac{f - z + β Ω^{2} Z_{R}}{Z_{R}}]}^{2}}^{\frac{1}{2}}}

where C is a constant independent of z, f is the focal length of the objective lens, 2

β

is the GVD,

\sqrt{2 l n 2} Ω

is the full-width half maximum (FWHM) of the frequency spectrum of the pulse, Z_M is the Rayleigh length of the focused monochromatic beam, Z_R is the Rayleigh length of the focused spatially-chirped beam. Let

{βΩ}^{2} = u

and

\frac{z - f}{Z_{M}} = v

, the denominator of the equation can be simplified as

{{(1 + u v)}^{2} + {(u - \frac{Z_{M}}{Z_{R}} v)}^{2}}^{1 / 2}

. The temporal focal plane is the plane where

T P E (z)

reaches its maximum. And such condition is met when the denominator is at its minimum. i.e. when

z = \frac{(1 - \frac{Z_{M}}{Z_{R}}) u}{(u^{2} + {(\frac{Z_{M}}{Z_{R}})}^{2})} Z_{M} + f

For a given microscopic system, all parameters are constants except u, which is a unitless quantity and proportional to the value of GVD.

The z-sectioning capability of temporal focusing two-photon microscope depends on several factors such as laser spectrum bandwidth and the numerical aperture of objective lens. The maximum fluorescence intensity change in axial dimension is plotted in Fig. 3(b). As the voltage scan increases, the focal plane shifts towards the objective lens. For an increase of 3 V which corresponds to 90,000 fs², the focal plane shifts as much as 60 µm. Each curve is labeled with the normalized GVD applied, i.e. $u = {βΩ}^{2}$ with $Ω = 7.7 \times 10^{13} Hz$ in this case. The FWHM is less than 10 μm at z = 0 plane. It becomes wider when the axial focal plane shifts away from objective focal plane [14]. Implementing defocused imaging for temporal focusing two-photon microscope is more challenging because the ring intensity in defocused images is much lower than that in in-focus image. To increase the signal to noise ratio, an EMCCD camera working at low temperature (−80 °C) was used to collect signals. The theoretical dependence of temporal focal plane shift on applied GVD is plotted in Fig. 3(c) (blue curve); and the experimental data from Fig. 3(b) are plotted as blue dots that show close fit with the theory. The theoretical curve is close to a linear curve, when the normalized GVD is small, i.e. ${βΩ}^{2} < 100$ . And the shifted temporal focal plane reaches its peak, when ${βΩ}^{2} = 220$ . Further increasing GVD will instead move the z plane with highest two-photon excitation back closer to the origin (z = 0 plane). Such phenomenon can be explained with the spatial overlap requirement. When ${βΩ}^{2}$ is very large, theoretically different frequency components in the laser spectrum can only temporally overlap when they propagate far away from the origin. However, at such far away z plane, they can’t spatially overlap as indicated in Fig. 3(d). Therefore, there is a range (z_max) for shifting the temporal focal plane determined by the spatial overlap requirement. In this experiment, it is about 60 µm. Currently we had not reached the descending part of the curve in Fig. 3(c) because the applied voltage has reached the highest allowed voltage of AOM which is about 10 V. Other factors affect the practical limit of shifting the temporal focal plane, such as the bandwidth of AOM (which determines the maximum amount of GVD that can be applied), and the SNR of images. In current setup several changes can be made to reach the descending part of the curve, such as using a short focal length M3 at a tradeoff of a smaller illuminating area in the sample, or using a new pair of prisms with larger GVD to adjust the initial GVD of the AOM to reach shortest pulse.

Since the AOM driver and AFG were synchronized with the femtosecond laser pulse sequence, the axial scan was automatically controlled by electronics. Therefore, the speed of this electronic control can be much faster than mechanic control. In principle, the axial scan can be set at a high speed such as 5 kHz which is the repetition rate of this CPA, or even higher at MHz range to match the repetition rate of some commercial products on the market. However, the bottleneck is the signal-to-noise ratio (SNR). When the scan frequency increases, the signal noise ratio decreases. For the purposes of demonstration, we recorded a video at 10 Hz to visualize this axial scanning effect more clearly (Visualization 1). In this video, four different voltages were applied as an amplitude modulation programmed into the AFG (Fig. 4(a)). The axial scan can be easily visualized in four steps. Each step the axial focal plane shifts. The fluorescent microspheres float in the liquid with Brownian motion. When microspheres are in the objective focal plane, it shows up as an in-focus spot. When the microspheres are out of the objective focal plane, they show as an out-focus ring structure. The center position of the ring can determine the x and y location of the microspheres. The z location of the beads is determined by its ring radius [19]. Figure 4(b) shows one frame from Visualization 1. Based on these defocused images, and the characterized relations between z and ring radius, the 3D position of these particles are calculated and presented in Fig. 4(c).

Fig. 4 (a) AFG voltage function (bottom) is synchronized with laser pulse sequence (top) for automatically shifting the temporal focal plane. (b) One frame taken out from Visualization 1 (c) Particle 3D position calculated based on acquired images.

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5. Discussion

In summary, we developed a high-speed 3D volumetric microscopic imaging system by integrating two techniques, temporal focusing and pulse shaping. It has the capability of acquiring 3D volume information at high speed. The improvement and novelty in this paper, compared to previous one, is that we explored the feasibility of volume scanning (Visualization 1) with fast electronics control. Instead of taking pictures layer by layer in depth slowly, the temporal focal plane is scanned quickly by the applied voltage on the AOM driving wave for fast 3D imaging. There are practical limitations in this setup for the maximal amount of depth scan by changing the GVD, such as the bandwidth of the AOM and image SNR. This high speed 3D imaging capability will enable researchers to explore and analyze previously unobtainable fast dynamic information with the aid of an automatic 3D image analysis software. Some ongoing applications in our laboratory include studying virus infection, visualization of nanoparticle transportation, and brain imaging. Its applications will extend to many other fields, where conventional laser scanning two-photon microscopes are being used, such as tracing cellular dynamics in live animals. One phenomenon is in the obtained defocused images the rings form in an asymmetric way in positive and negative z direction from objective focal plane. The reason of that is due to the construction of the objective lens. Several objective lenses were tested under the same optical alignment. Different objective lens forms different ring patterns. Specifically, for each objective, the dependence of the ring size D(z) is a function of z. This function is determined by the structure of each objective lens, with the same condition of optical alignment.

Appendix

This first part of this appendix is to estimate the amount of GVD applied on the femtosecond laser spectrum when a certain RF frequency sweep is applied on the acoustic wave in the AOM. When the laser pulse passes through the AOM, the input-output relation of optical field in frequency domain, E_in an E_out respectively, can be written as

\begin{array}{l} E_{o u t} (ω) = E_{i n} (ω) e^{i (2 π f_{A} + ϕ) t} = E_{i n} (ω) e^{i (2 π (f_{A 0} + Δ f_{A} t + ϕ) t)} \\ = E_{i n} (ω) e^{i (2 π (f_{A 0} + ϕ) t)} e^{i 2 π Δ f_{A} t^{2}}, \end{array}

where

f_{A}

is the acoustic wave frequency driven by the RF wave. To apply GVD this RF wave frequency is modulated with a saw tooth function

f_{A} (t) = f_{A 0} + Δ f_{A} t

. The center of this RF frequency is 200 MHz, which only contributes to a constant group velocity shift. The sweep frequency

Δ f_{A}

is changing at 100 kHz and period T = 10⁻⁵ s, which contributes to GVD. When the AFG voltage output scans from 0 to 10 V at period of 10⁻⁵ s, the acoustic frequency

f_{A} (t)

changes from 180 MHz to 220 MHz, hence

Δ f_{A} = \frac{220 MHz - 180 MHz}{10^{- 5} s} = 4.0 \times 10^{12} s^{- 2}

When the acoustic wave travels in AOM, the laser pulse spectrum reaches AOM. Therefore, there is a one-to-one mapping between laser spectrum frequency (

ω

) and the location (x) on the AOM, which further maps to the acoustic traveling time in AOM (t). Both mappings are linear by considering first order terms only:

e^{i 2 π Δ f_{A} t^{2}} \overset{t to ω}{\to} e^{i 2 π Δ f_{A} {(a + b ω)}^{2}}

The AOM aperture size is 3.5 cm and the acoustic wave speed in TeO₂ AOM is 4200 m/s. Therefore, the acoustic wave travelling time in AOM is

Δ t_{t r a v e l} = \frac{0.035 m}{4200 m / s} = 8.3 \times 10^{- 6} s

Therefore, the mapping parameter b can be calculated as

b = \frac{Δ t_{t r a v e l}}{Δ ω} = \frac{8.3 \times 10^{- 6} s}{1.2 \times 10^{14} s^{- 1}} = 6.9 \times 10^{- 20} s^{2}

where Δω is the optical frequency span along the AOM aperture. Hence, Eq. (5) can be written as

e^{i 2 π Δ f_{A} {(a + b ω)}^{2}} = e^{i 2 π Δ f_{A} (a^{2} + 2 a b ω)} e^{i 2 π Δ f_{A} b^{2} ω^{2}}

Here, the term

e^{i 2 π Δ f_{A} b^{2} ω^{2}}

contributes to GVD. For an AFG output voltage of 10 V,

GVD = 2 \times 2 π Δ f_{A} b^{2} = 2.4 \times 10^{5} {fs}^{2}

The second part of this appendix is to list the parameters used to calculate the shift distance of temporal focal plane in Eqs. (1) and (2). We followed the method established in [13, 14]. The full-width half maximum (FWHM) of the laser spectrum is $\sqrt{2 l n 2} Ω$ , and

Ω = 2 π c (\frac{1}{λ_{1}} - \frac{1}{λ_{2}}) = 7.7 \times 10^{13} s^{- 1}

The focal length of the objective lens is estimated as

f = 2.2 \times 10^{- 3} m .

The center wavelength wave vector is $k_{0} = \frac{2 π}{λ} = 7.9 \times 10^{6} m^{- 1}$ with λ = 800 nm.

The spatial FWHM of each monochromatic beam is $\sqrt{2 l n 2} s$ with $s = 10^{- 4} m$ .

Z_M is the Rayleigh length of the focused monochromatic beam, and

Z_{M} = \frac{2 f^{2}}{k_{0} s^{2}} = 1.2 \times 10^{- 4} m

Z_R is the Rayleigh length of the focused spatially-chirped beam calculated as

Z_{R} = \frac{2 f^{2} / k_{0}}{s^{2} + α^{2} Ω^{2}} = 5.4 \times 10^{- 7} m

where

α

is a constant proportional to the groove density of the grating and the focal length of the collimating lens, and here

α Ω = 1.5 \times 10^{- 3} m

.

6. Funding

National Science Foundation (NSF) (1429708, 1205302). National Institute of Health (SC2GM103719).

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Axial scanning with pulse shaping in temporal focusing two-photon microscopy for fast three-dimensional imaging

Abstract

1. Introduction

2. Optical Setup

3. Materials and Methods

4. Results

5. Discussion

Appendix

6. Funding

References and links

Supplementary Material (1)

Cited By

Figures (4)

Equations (12)

Optics Express