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Spiral scanning fiber-optic two-photon endomicroscopy with a double-cladding antiresonant fiber

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Abstract

Two-photon endomicroscopy is an optical biopsy tool that satisfies clinical requirements for real-time subcellular-resolution imaging to assist pathological biopsy in diagnosis. Herein, we present a two-photon endomicroscopy system based on a piezoelectric ceramic tube scanner. A dual-channel amplitude-modulated sine wave drives the fiber to realize spiral scanning, a double-cladding antiresonant fiber is used for 920-nm femtosecond light-pulse low dispersion transmission, and fluorescence collection occurs with no fiber-tip engineering. The field of view is ∼200 µm, the resolution is 3.1 µm, and the frame rate is 0.7 fps. Pollen grain, GFP-labeled mouse brain section, and human stomach tissue imaging verify the capability of the two-photon endomicroscopy system.

© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Since the invention of two-photon laser scanning fluorescence microscopy in 1990 by Winfried Denk and co-workers [1], this technique has been extensively applied in neuroscience, disease diagnosis, and other research fields. Compared to single-photon microscopy, two-photon fluorescence microscopy has advantages such as the fact that it is label-free and offers deeper penetration depth, higher spatial resolution, and less photodamage and photobleaching [2]. The two most commonly detected two-photon signals are two-photon excited fluorescence (TPF) and second-harmonic generation (SHG).

With the development of two-photon microscopy imaging technology alongside its applications in different fields, two principal system architectures have gradually emerged, namely, benchtop two-photon microscopy and miniature two-photon microscopy. In benchtop two-photon microscopy, conventional resonant galvanometers are used for two-dimensional raster scanning, and a high-numerical aperture (NA) objective provides high-quality imaging [3,4]. However, these bulky systems do not meet the needs of researchers carrying out in-vivo imaging in freely moving animals. Miniature two-photon microscopy imaging systems can be classified into two typical forms based on the scanning method: microelectromechanical (MEMS) scanning [59] and piezoelectric ceramic actuator scanning [1015]. Recent developments in miniature multi-photon microscopy based on MEMS scanning can achieve imaging quality comparable to that of benchtop multi-photon fluorescence microscopy [16,17] and provide clear and stable images of neurons and synaptic activity changes in the brains of freely behaving mice. Unlike MEMS scanning, piezoelectric ceramic actuator scanning does not require beam folding, resulting a more compact probe. This method may be more suited to the requirements of miniature two-photon endomicroscopy for real-time imaging of cells in the internal organ of living animals. Recent developments in miniature two-photon endomicroscopy based on piezoelectric ceramic actuator scanning has also demonstrated its ability on two-photon label-free metabolic imaging of biological tissues [18] and neuroimaging of motor cortices [19].

As a typical optoelectromechanical system, two-photon endomicroscopy integrates two-photon excitation principles into endoscopic equipment to realize real-time tissue imaging. The main technical challenges involved in two-photon endomicroscopy design include micro-objective design, dispersion compensation management, beam scanning and femtosecond laser pulse delivery and fluorescence signal collection. In miniature two-photon microscopy, variable refractive-index (gradient-index, GRIN) lenses and ordinary optical lenses (group) are the two main options for the micro-objective lens. GRIN lenses are simple, but they are not, in general, achromatic [20]. Standard optical lens groups can correct aberrations, depending on their design, but they cannot satisfy the requirements of deep brain imaging because they are not sufficiently compact [21]. Using different voltage driving signals, spiral [2225], raster [26,27], and the Lissajous [28] fiber scanning trajectories can be realized by piezoelectric ceramic actuator scanning method. A double-cladding fiber is used in to realize femtosecond light transmission and fluorescence collection. Different types of double-cladding fibers, including solid core [29,30] and hollow core [31] fibers, are used to both transmit and collect light. Femtosecond pulses transmitted through solid fibers undergo severe pulse broadening, and hence sophisticated dispersion compensation is required. Recently, A. Kudlinski et al. [32] have reported the first double cladding tubular antiresonant hollow core fiber for nonlinear endomicrsocopy. One fiber-tip engineering method has been proposed for enlarging the fiber numerical aperture. By splicing a silica bead at the fiber output, the NA of the antiresonant fiber is improved from 0.023 to 0.2. The objective with 1.6× magnification is used to cooperate with the nonlinear imaging of antiresonant fiber attached with silica bead.

In this paper, we present a prototype two-photon endomicroscopy system based on a double-cladding antiresonant fiber. The imaging ability of antiresonant fiber is verified in nonlinear endomicroscopy without any fiber-tip engineering method for the first time, combining with higher magnification finite objective. First, we evaluate the structural parameters and attenuation and dispersion characteristics of the double-cladding antiresonant fiber. The results indicate that even without dispersion compensation devices, the double-cladding antiresonant fiber performs excellently with respect to low-dispersion transmission of femtosecond pulses. Second, we measure the resonant characteristics of the two axes of the PZT fiber scanner. Spiral scanning is achieved by using two-channel sinusoidal amplitude-modulated sine waves to drive the scanner. A fiber scanning trajectory correction method is proposed that involves adjusting the voltage and phase of the PZT along both axes. Finally, we demonstrate the ability of the proposed system to image biological tissues such as pollen grains, GFP-labeled mouse brain slices, and stained stomach tissue.

2. Method

2.1 Two-photon endomicroscopy system design

A scheme of the proposed two-photon endomicroscopy system is presented in Fig. 1. The femtosecond pulse excitation light path is depicted in red, whereas the fluorescence collection light path is depicted in green. A wavelength-tunable Ti:Sapphire femtosecond pulse laser (Chameleon Vision II, Coherent) is used as the light source; the repetition rate is 80 MHz. The working wavelength of the system is selected to be 920 nm, which allows effective excitation of typical biomarkers such as GFP and GCaMP6. A half-wave plate (AHWP05M-980, Thorlabs) and polarization beam splitter PBS (PBS103, Thorlabs) are employed for light intensity modulation. The femtosecond pulse light is transmitted through dichroic mirror DM (DMLP650R, Thorlabs) into coupling lens CL (354850 B, Lightpath) with effective focal length 22 mm and NA = 0.13, which couples the femtosecond pulse light into a double-cladding antiresonant fiber core (DCF) effectively. Amplitude-modulated sine and cosine signals are applied to the four quadrants of the piezoelectric (PZT) ceramic tube (PT230.94, Physik Instruments) with outer diameter of 3.2 mm and inner diameter of 2.2 mm. Due to the inverse piezoelectric effect, the fiber produces submillimeter movements with different ranges of motion at different voltages, driving the optical fiber to achieve spiral scanning. The micro-objective used in this two-photon endomicroscopy system has been described in detail in a previous study [33]. This finite-distance miniature objective is designed and manufactured for operation at 920 nm with package diameter of 4.1 mm and package length of 12.2 mm. As the endomicroscopy needs to be close to the biological tissue for imaging, the objective’s working distance is designed to be 150 µm. Compared to conventional gradient index lenses, the objective limits axial chromatic aberration and allows improved fluorescence collection efficiency. This miniature objective is designed with 3× magnification and theoretical NA = 0.2 at the fiber tip output, thus the imaging NA at the sample is up to 0.6. The fluorescence signal is collected by the cladding of the antiresonant fiber and transmitted back to the dichroic mirror (DMLP650R, Thorlabs). It then passes through a filter (FF01-530/43-25, Semrock) and collection lens (LA1951-A, Thorlabs) and is detected by a photomultiplier tube (PMT; H10770PA-40-SEL, Hamamatsu). The output voltage signal is connected to a signal acquisition module for analog-to-digital conversion and high-speed acquisition. A home-built LabVIEW (National Instruments) reconstruction algorithm is used to achieve spiral imaging.

 figure: Fig. 1.

Fig. 1. Scheme of the two-photon endomicroscopy system (M1 and M2, plane mirrors; DM, dichroic mirror; CL, coupling lens; PMT, photomultiplier tube; L2, collection lens; DCF, double-cladding antiresonant fiber; PZT, piezoelectric ceramic tube). The femtosecond pulse excitation light path is shown in red and the fluorescence collection light path is shown in green.

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2.2 Double-cladding antiresonant fiber evaluation

Hollow-core antiresonant fibers are a new type of microstructured hollow-core fiber. The femtosecond pulse is confined to the fiber core for stable transmission based on the antiresonant effect [3436]. This hollow-core antiresonant fiber inherits the advantages of photonic bandgap hollow-core fibers. Moreover, its wide bandwidth allows the system to accommodate imaging applications with different excitation wavelengths, expanding the imaging range of multiphoton endomicroscopy systems.

Figure 2(a) shows the scanning electron microscopy (SEM) image of the customed-designed double-cladding antiresonant fiber used in the two-photon endomicroscopy system. The core, silica outer cladding, and fiber diameters are 24, 134, and approximately 250 µm, respectively. The inner cladding is a plurality of six uniformly distributed antiresonant capillary structures around the same center, responsible for limiting femtosecond pulse in the fiber core. The thickness of capillary is about 240 nm. The fiber core is used to transmit femtosecond pulsed light with low dispersion and attenuation, and the silica cladding is used to collect the fluorescence signals. Unlike the germanium-doped core and fluorine-doped silica cladding of traditional solid-core fibers, both the core and cladding of this double-cladding antiresonant fiber are undoped. Hence, interfering autofluorescence signals from doped media are avoided, resulting in improved image quality. The coating layer is a fluorine-doped acrylate with a lower refractive index than quartz. This not only enhances the mechanical strength of the optical fiber but also allows realization of total internal reflection transmission of the fluorescence in the cladding. The NA of the fiber can be determined from the slope of the straight line of a plot of measured 1/e2 spot size versus distance from the fiber end-face. The NA of the fiber core is 0.034 (Photon Nanoscan, Ophir Optronics Solutions), as depicted in Fig. 2(b). A 532-nm green light source (CPS532, Thorlabs) was selected for the fiber-cladding NA measurement, and a coupling lens (355150 B, Lightpath) was used; hence, the NA of the cladding is determined to be approximately 0.5 at 532 nm.

 figure: Fig. 2.

Fig. 2. (a) SEM image of the double-cladding antiresonant fiber used in the endoscopy system. (b) Fiber-core NA measurement at 920 nm. The inset shows the single-mode Gaussian beam spot measured at the output of the fiber.

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A Fiber attenuation curve with wavelength range from 800 nm to 1000 nm is depicted in Fig. 3(a); in this case, the total length of the fiber is 203 m and the cutback length is 163 m. The transmission loss of the fiber at a working wavelength of 920 nm is approximately 0.1 dB/m. The ratio of 0.8 m fiber output power to the input power before coupling lens is about 70%−80%, and the loss mainly includes coupling loss and transmission loss. When we bend the fiber, there is no obvious change in power output. The dispersion characteristics of the double-cladding antiresonant fiber was also tested, and an autocorrelator (Pulsecheck, APE) was employed to determine the pulse-width parameters of the 920-nm femtosecond pulse at the laser and fiber outputs. The normalized autocorrelation curve is shown in Fig. 3(b). The autocorrelation full width at half maximum (FWHM) of the 50-mW 920-nm femtosecond pulse is 182 fs; assuming a hyperbolic secant pulse shape, the ratio of the autocorrelation FWHM to the pulse FWHM is 1.54, and hence the width of the laser output is calculated to be 118 fs. The autocorrelation FWHM after transmission through 0.8 m of fiber is 197 fs, and the corresponding pulse FWHM is 127 fs.

 figure: Fig. 3.

Fig. 3. (a) Fiber attenuation over 800–1000 nm. (b) Measured autocorrelation of the 50-mW 920-nm femtosecond pulse at the laser output (blue) and at the fiber output (red).

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The group delay dispersion (GDD) of L = 0.8 m double-cladding antiresonant fiber can be calculated by the following the formula 1 and 2 [37]:

$${\tau _{out}} = {(1 + {(\frac{{{T_c}}}{{{\tau _{in}}}})^4})^{\frac{1}{2}}} \times {\tau _{in}}$$
$${T_c} = 2\sqrt {\ln 2 \times |{{\varphi_2}} |} $$
where ${\mathrm{\tau }_{\textrm{in}}}$ and is ${\mathrm{\tau }_{\textrm{out}}}$ the input and output of femtosecond pulse autocorrelation FWHM. ${\textrm{T}_\textrm{c}}$ is the critical pulse width, which is a convenient variable to evaluate the influence of medium length on pulse width. The group delay dispersion ${\mathrm{\varphi }_2}$ of 0.8 m double-cladding antiresonant fiber is calculated to be about 2000 $\textrm{f}{\textrm{s}^2}$.

Then the group velocity dispersion (GVD) can be calculated by the formula 3:

$$GVD ={-} (\frac{{2\pi c}}{{{\lambda ^2}}}) \times \frac{{{\varphi _2}}}{L}$$
where c is the light speed constant, $\lambda $ is the working wavelength and L is the fiber length. The group velocity dispersion (GVD) at 920 nm is calculated to be approximately 5.5 ps/km/nm. Compared to the photonic bandgap fiber, the GVD dispersion of femtosecond pulse light at 920 nm is reduced by more than 10 times [16,25,38]. We point out that even without dispersion compensation devices, the hollow core tubular antiresonant fiber performs excellent characteristics in terms of the low-dispersion transmission of femtosecond pulses in this endomicroscopy system.

2.3 PZT fiber scanner characteristics

Piezoelectric ceramic actuator scanner are used in two-photon endomicroscopy principally because they facilitate the realization of compact integrated probes. In the two-photon endomicroscopy system, the PZT-driven fiber scanner a has a reverse fixed structure [39], which is advantageous because the optical fiber is located within the piezoelectric ceramic tube, permitting a shorter rigid length for the integrated probe. The setup for evaluating the scanning trajectory of the PZT optical fiber scanner is shown in Fig. 4. A 920-nm femtosecond pulse is coupled into the double-cladding fiber core through a coupling lens (354850 B, Lightpath), and the PZT and fiber are fixed with epoxy resin to form a piezoelectric tube fiber scanner. The cantilever length of the PZT fiber scanner is approximately 30 mm. A signal generator (AFG1022, Tektronix) is used to generate the sine wave drive signal to drive the scanner and realize spiral scanning, via a voltage amplifier (TD250, PiezoDrive). The femtosecond light exiting the optical fiber passes through an objective (NA = 0.4) with focal length 17 mm (uPlan Apo 10×, Olympus) and a planoconvex lens with focal length 35 mm (LA1027-A, Thorlabs) before converging at a CMOS camera (Panda,4.2 M PCO), which detects the trajectory. The composition magnification of the PZT fiber scanner trajectory text system is about 2×. A near-infrared absorption-type neutral density filter (GCC-301121B, GCC 301119 B, Daheng Optics) is applied for light intensity attenuation.

 figure: Fig. 4.

Fig. 4. Schematic of the PZT fiber scanner trajectory test system (CL, coupling lens; DCF, double-cladding anti-resonant fiber; PZT, piezoelectric ceramic tube; OL, objective lens; FL, focusing lens).

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 figure: Fig. 5.

Fig. 5. Evaluation of the scanning characteristics of the PZT fiber scanner: (a) X-axis (blue) and Y-axis (red) scan range versus scanning frequency and (b) X-axis (blue markers) and Y-axis (red markers) scan range versus driving voltage.

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We first evaluated the relationships between the scan ranges of the X- and Y-axes and the frequency, and those between the scan ranges and the driving voltages near the resonant point. When a peak-to-peak voltage of ±87.5 V is applied to the PZT, the X- and Y-axis scan ranges varies with frequency. As depicted in Fig. 5(a), the second-order resonance frequency of the X- and Y-axes is 716 Hz. There is a mismatch between the resonant frequency points of the two axes, which may be due to the mechanical asymmetry of the PZT and the optical fiber assembly. Subsequently, the assembly process was further optimized. During frequency sweep testing, the first-order resonance point of the PZT fiber scanner was found to be approximately 167 Hz. The higher the resonant frequency, the faster the scanning speed. To satisfy the system requirements for the scan range and imaging frame rate, further drive signal generation, testing, and correction was performed around the second-order resonance point near 716 Hz. The X- and Y-axis scan ranges Dscan vary with the driving voltage, as displayed in Fig. 5(b), and the applied voltage has a linear relationship with the scan voltage.

Additional synchronous dual-channel sine amplitude-modulated sine waves were applied to the PZT fiber scanner for spiral scanning. Theoretically, the driving voltages of the two axes should be the same for achieving spiral scanning and the phase difference should be 90°. The imaging FOV can be expressed as:

$$FOV = {D_{scan}}/M$$
where is Dscan the fiber scan range and M is the objective magnification. Therefore, for a particular optical fiber length and specific PZT structure parameters, increasing the driving voltage and reducing the magnification of the objective lens should increase the FOV.

The X- and Y-axis drive trajectories are coupled because of the curing stress of the epoxy resin, and as a result of the asymmetry of the PZT fiber geometry and assembly. Even when a single-axis drive voltage is added to the PZT fiber scanner, the trajectories continue to exhibit two-axis motion components, resulting in image distortion [4042]. When the ideal circular track driving signal is applied to the PZT optical fiber scanner, for example, the same peak-to-peak voltage of ±63.75 V is applied to both axis electrodes of the PZT with a phase difference of 90°, the scan trace is elliptical as depicted in Fig. 6(a).

 figure: Fig. 6.

Fig. 6. PZT-fiber scanner trajectory (a) before and (b) after trajectory correction.

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By changing the amplitude parameters and phase parameters of the two-channel drive signals in the FPGA program to change the voltage value and phase relationship applied to the both axis electrodes of the PZT, and then observe the change of the scan trajectory. We note that when the X-axis drive voltage is ±63.75 V, the Y-axis drive voltage is ±93.75 V, and the phase difference between the two output axes is 96°, a scan trajectory significantly corrected on the CMOS camera can be obtained as shown in Fig. 6(b). Here we calibrate the correction quality by the elliptical distortion, that is, we calculate the ratio of the difference between the long axis and the short axis of the ellipse to the long axis by the formula 5:

$$\delta = \frac{{|{y - x} |}}{y} \times 100\%$$
where x and y are the short and long axis of the elliptical trajectory, respectively. The ellipticity of the trajectory was corrected from 36.7% to 3.3%. A two-channel sinusoidal amplitude-modulated signal with 512 circles was applied to the piezoelectric fiber scanner to realize spiral scanning. The amplitude modulation signal was gradually increased, and the fiber was steadily scanned outward from the origin and vice versa.

3. Experimental results

To verify the imaging performance of the two-photon endomicroscopy system, imaging experiments were first performed using pollen grains at an excitation wavelength of 920 nm. The obtained pollen structure is clear in Fig. 7. 0.1 g pollen and 1 ml 75% alcohol are mixed in a 1.5 ml eppendorf tube, after fully ultrasonic for 5mins, a small amount of pollen solution is taken out and placed on the slide. Thirty images were averaged to improve the signal-to-background ratio (SBR) of the image.

 figure: Fig. 7.

Fig. 7. Two-photon imaging of pollen grain (each image shown is the average of 30 image acquisitions).

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Further, the FOV performance of the system was tested using a grid standard. The length of each square in the grid was 25 µm. The imaging FOV was approximately 200 µm, as shown in Fig. 8.

 figure: Fig. 8.

Fig. 8. Two-photon imaging of 25-µm standard grid for FOV measurement (the image shown is the average of 30 image acquisitions).

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The lateral resolution of the proposed two-photon endomicroscopy system was tested using 380-nm diameter fluoro Max green-fluorescent polymer microspheres (Thermo Scientific) (Fig. 9). After adding 0.5 µL of beads to 1 of mL alcohol, 10 µL of the mixed solution was used to form the bead sample. Cross-sections of two imaged beads, bead 1 and bead 2, are depicted in Fig. 9(b), and the FWHMs of the beads are 3.10 and 3.19 µm, respectively.

 figure: Fig. 9.

Fig. 9. (a) Two-photon imaging of 380-nm polymer microspheres for lateral resolution measurement (the image shown is the average of 30 image acquisitions). (b) Normalized intensity profiles of two beads.

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Thy1-GFP-labeled mouse brain slices were used to verify the brain-imaging capability of the two-photon endomicroscopy system. Two-photon images of the mouse brain slices are displayed in Fig. 10. These confirm that the soma, axon, and dendrites of neurons can be observed using the two-photon endomicroscopy system. The sample thickness is about 300 µm.

 figure: Fig. 10.

Fig. 10. Two-photon imaging of the GFP-target mouse brain slices (the images shown are averages of 30 image acquisitions).

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Stained stomach tissue slices (No.61, BRESSER Prepared Slides 100 pcs) were used to demonstrate two-photon endomicroscopy imaging of internal organ tissue. An inverted microscope (Olympus IX83) was used to observe the sections under white light, as shown in Fig. 11(a). Two-photon images of the same area of the stomach tissue slice are shown in Figs. 11(b) and 11(c). The gastric pit, gland, and gastric epithelium structures are all clearly visible, verifying the capability of the two-photon endomicroscopy system for morphological tissue imaging. The sample thickness is about 100 µm.

 figure: Fig. 11.

Fig. 11. (a) White-light microscope image of stomach tissue slices. (b, c) Two-photon imaging of the same area of the stomach tissue section (the images shown are averages of 30 image acquisitions).

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4. Conclusion

In this study, we constructed a two-photon endomicroscopy system and demonstrated its biological-tissue imaging capability. Two key technologies were developed and realized: the use of a single double-cladding antiresonant fiber for femtosecond pulse transmission with low dispersion and low attenuation as well as fluorescence signal collection, and a PZT fiber scanner for spiral scanning. A dual-channel amplitude modulated sine wave was used to drive the fiber for spiral scanning. The imaging ability of double cladding antiresonant fiber is verified in nonlinear endomicroscopy without any fiber-tip engineering method for the first time, combining with higher magnification finite objective. The imaging FOV of the two-photon endomicroscopy system was approximately 200 µm, the lateral resolution was 3.1 µm, and the frame rate was 0.7 fps.

In the future, several approaches can be taken for the optimization of the current system. First, the lateral resolution is limited by the large mode field diameter and low NA of the double-cladding antiresonant fiber. Here, two ideas to improve the system resolution are proposed from the perspective of the fiber and the objective. A double-cladding photonic crystal bandgap fiber with a higher numerical aperture could be a good choice to improve the lateral resolution of the system. Other fiber-tip engineering methods can also be combined with the antiresonant fiber for resolution improvement [4345]. In addition, the system resolution can also be enhanced by designing the objective with higher magnification. Second, by simulating and optimizing the resonant frequency of the PZT scanner, the increased imaging speeds can be achieved. Third, the broadband nature and low-attenuation transmission capacity of the antiresonant fiber could be exploited to expand the two-photon imaging wavelength range. Femtosecond pulse excitation with different wavelengths can achieve imaging of different contrasts within living tissues. Multi-channel signal detection (such as SHG, THG) will increase the amount of information in biological tissue imaging [46]. Further development of the integrated probe system will render the proposed two-photon endomicroscopy system ideally suited for real-time imaging of organs and disease diagnosis.

Funding

National Key Research and Development Program of China, (2020YFB1312802); National Natural Science Foundation of China, (61973019, 31830036, 61975002) ; Beijing Transcend Vivoscope Biotech Co., Ltd, (YF-20103).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (11)

Fig. 1.
Fig. 1. Scheme of the two-photon endomicroscopy system (M1 and M2, plane mirrors; DM, dichroic mirror; CL, coupling lens; PMT, photomultiplier tube; L2, collection lens; DCF, double-cladding antiresonant fiber; PZT, piezoelectric ceramic tube). The femtosecond pulse excitation light path is shown in red and the fluorescence collection light path is shown in green.
Fig. 2.
Fig. 2. (a) SEM image of the double-cladding antiresonant fiber used in the endoscopy system. (b) Fiber-core NA measurement at 920 nm. The inset shows the single-mode Gaussian beam spot measured at the output of the fiber.
Fig. 3.
Fig. 3. (a) Fiber attenuation over 800–1000 nm. (b) Measured autocorrelation of the 50-mW 920-nm femtosecond pulse at the laser output (blue) and at the fiber output (red).
Fig. 4.
Fig. 4. Schematic of the PZT fiber scanner trajectory test system (CL, coupling lens; DCF, double-cladding anti-resonant fiber; PZT, piezoelectric ceramic tube; OL, objective lens; FL, focusing lens).
Fig. 5.
Fig. 5. Evaluation of the scanning characteristics of the PZT fiber scanner: (a) X-axis (blue) and Y-axis (red) scan range versus scanning frequency and (b) X-axis (blue markers) and Y-axis (red markers) scan range versus driving voltage.
Fig. 6.
Fig. 6. PZT-fiber scanner trajectory (a) before and (b) after trajectory correction.
Fig. 7.
Fig. 7. Two-photon imaging of pollen grain (each image shown is the average of 30 image acquisitions).
Fig. 8.
Fig. 8. Two-photon imaging of 25-µm standard grid for FOV measurement (the image shown is the average of 30 image acquisitions).
Fig. 9.
Fig. 9. (a) Two-photon imaging of 380-nm polymer microspheres for lateral resolution measurement (the image shown is the average of 30 image acquisitions). (b) Normalized intensity profiles of two beads.
Fig. 10.
Fig. 10. Two-photon imaging of the GFP-target mouse brain slices (the images shown are averages of 30 image acquisitions).
Fig. 11.
Fig. 11. (a) White-light microscope image of stomach tissue slices. (b, c) Two-photon imaging of the same area of the stomach tissue section (the images shown are averages of 30 image acquisitions).

Equations (5)

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τ o u t = ( 1 + ( T c τ i n ) 4 ) 1 2 × τ i n
T c = 2 ln 2 × | φ 2 |
G V D = ( 2 π c λ 2 ) × φ 2 L
F O V = D s c a n / M
δ = | y x | y × 100 %
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