2.1.

Modeling and Resonant MODE Analysis of the PZT Fiber Scanner

Figure 1 shows a schematic diagram of a forward-fixed PZT fiber scanner. This scanner comprised three main parts: a PZT, a spacer, and a DCF designed for femtosecond pulses and fluorescence in a common-path configuration. The spacer was physically connected to the PZT, allowing for precise positioning of the fiber and the PZT element. Table 1 presents the detailed geometric and material parameters of the PZT, including an OD (${\mathrm{OD}}_{\text{PZT}}$) of 1 mm, an inner diameter (${\mathrm{ID}}_{\text{PZT}}$) of 0.4 mm, a length ($L_{\text{PZT}}$) of 8 mm, and PZT-5A as the selected material. Table 2 indicates the structural and material parameters of the built forward-fixed PZT fiber scanner, with a fiber cantilever length ($L_{\text{fiber}}$) of 14.3 mm.

Fig. 1

A schematic diagram of the PZT fiber scanner (PZT: piezoelectric ceramic tube; DCF: double-cladding fiber).

Table 1

Parameters of the PZT mechanical structure.

Table 2

Parameters of the PZT fiber scanner mechanical structure.

We built the forward-fixed PZT fiber scanner using commercial software based on the finite element analysis method. The PZT geometric model was established with plane A as the reference plane, and the spacer and DCF geometric models were established with plane B as the reference plane. This device functioned as a model that combined solid mechanics and electrostatic fields. Furthermore, the four quadrants of the PZT’s outer wall were defined by the driving voltage conditions, the inner wall by the ground condition, and the bottom of the PZT by fixed constraints.

The PZT fiber scanner functions by driving the resonant fiber cantilever through the inverse piezoelectric effect. The scanner achieved maximum deflection at specific frequencies, denoted as resonant modes of different orders. Figures 2(a) and 2(b), respectively, illustrate the scanner’s first- and second-order resonant modes, which had corresponding theoretical resonant frequencies of 799.1 and 2981.9 Hz.

Fig. 2

PZT fiber scanner resonant mode analysis. (a) First-order resonant mode. (b) Second-order resonant mode.

2.2.

Frequency Domain Analysis of the PZT Fiber Scanner

The effect of the driving voltage on the PZT fiber scanner’s first- and second-order resonant characteristics was investigated using frequency domain analysis. Driving signals were applied to a single pair of PZT electrodes (e.g., $+X$ and $-X$) to ensure motion along a single axis for single-axis scanning. As shown in Fig. 3(a), the first-order frequency domain characteristics were obtained at 775 to 825 Hz frequency range (with 1 Hz increments). Meanwhile, as illustrated in Fig. 3(b), the second-order frequency domain characteristics were at 2850 to 3150 Hz frequency range (with 5 Hz increments). Among the six simulated data groups obtained by varying the driving voltage U from $\pm 12.5$ to $\pm 75\mathrm{V}$ with $\pm 12.5\mathrm{V}$ increments, the first-order mode exhibited maximum scan ranges ($D_1$) of 0.126, 0.253, 0.379, 0.506, 0.633, and 0.76 mm. Correspondingly, the second-order mode exhibited maximum scan ranges ($D_2$) of 0.103, 0.206, 0.311, 0.415, 0.519, and 0.618 mm. To evaluate the PZT fiber scanner’s driving capability, the driving coefficient, denoted by ${\sigma }_i$, was introduced. The slope of the fitted line, representing the scanner’s scan range as a function of the driving voltage, was used to calculate the driving coefficient. In this case, $i$ signifies different resonant orders. The calculated driving coefficients ${\sigma }_1$ and ${\sigma }_2$ corresponding to the first- and second-order resonant modes were determined to be 5.07 and $4.15\mu \mathrm{m}/\mathrm{V}$, respectively. According to these findings, the first-order driving coefficient ${\sigma }_1$ was approximately 1.22 times greater than the second-order driving coefficient ${\sigma }_2$ for an identical driving voltage.²⁵

Fig. 3

Frequency domain characteristics of the PZT fiber scanner under different driving voltages. (a) First-order. (b) Second-order.

Following that, a systematic investigation of the PZT structural parameters, specifically the PZT length and inner diameter, was carried out to evaluate their effects on the resonant characteristics of the PZT fiber scanner. The PZT length was varied between 6 and 10 mm (in 1 mm increments). The frequency domain characteristics corresponding to the first- and second-order resonant modes are depicted in Figs. 4(a) and 4(b), respectively, under a driving voltage of $\pm 50\mathrm{V}$. The maximum scan ranges ($D_1$) of the first-order resonant mode in the context of the five datasets obtained from this parameterized analysis were 0.348, 0.424, 0.506, 0.598, and 0.696 mm. Correspondingly, the maximum scan ranges ($D_2$) of the second-order resonant mode were 0.225, 0.303, 0.415, 0.600, and 0.981 mm. The results showed that as the PZT length increased, the scanner’s resonant frequency decreased, tending toward lower frequencies. The resonant frequencies of the scanner’s first-order resonant mode were 803, 801, 800, 798, and 796 Hz. On the other hand, the resonant frequencies of the scanner’s second-order resonant mode were 3010, 2995, 2985, 2950, and 2905 Hz.

Fig. 4

Frequency domain characteristics of the PZT fiber scanner with different PZT lengths. (a) First-order. (b) Second-order.

Figures 5(a) and 5(b) depict the effect of the PZT inner diameter (${\mathrm{ID}}_{\mathrm{PZT}}$) on the first- and second-order characteristics of the PZT fiber scanner. Five datasets were generated by increasing the PZT inner diameter from 0.1 mm to 0.3 mm (in 0.05 mm increments). Regarding the first-order resonant mode, the maximum scan ranges ($D_1$) of the first-order resonant mode were 0.371, 0.430, 0.506, 0.610, and 0.756 mm as the ${\mathrm{ID}}_{\mathrm{PZT}}$ varied. Correspondingly, the maximum scan ranges ($D_2$) of the second-order resonant mode were 0.308, 0.354, 0.415, 0.495, and 0.611 mm. Notably, increasing ${\mathrm{ID}}_{\mathrm{PZT}}$ decreased the thickness of the PZT tube wall, resulting in an expanded scan range for both the first- and second-order resonant modes.

Fig. 5

Frequency domain characteristics of the scanner with different PZT inner diameters. (a) First-order. (b) Second-order.

Figures 6(a) and 6(b) depict the effect of fiber cantilever length on the PZT fiber scanner’s first- and second-order resonant characteristics was also investigated. The initial length of the fiber cantilever, denoted as $L_{\text{fiber}}$, was set to 14.3 mm (shown in Table 2). A length coefficient, denoted as $\eta$, was introduced to aid in this investigation. The length of the fiber cantilever was expressed within this framework as $\eta \times L_{\mathrm{fiber}}$. The simulated data set included five datasets obtained by increasing the length coefficient $\eta$ by 0.05 increments from 0.9 to 1.1. The first-order resonant mode’s maximum scan ranges ($D_1$) were 0.467, 0.490, 0.506, 0.520, and 0.526 mm. Meanwhile, the second-order resonant mode’s maximum scan ranges ($D_2$) were 0.479, 0.441, 0.415, 0.395, and 0.380 mm. In this case, as the length coefficient $\eta$ varied from 0.9 to 1.1, the scanner’s resonant frequency decreased, approaching lower frequencies. The resonant frequencies of the scanner’s first-order resonant mode were 996, 891, 800, 723, and 654 Hz. On the other hand, the resonant frequencies of the scanner’s second-order resonant mode were 3690, 3315, 2985, 2695, and 2450 Hz.

Fig. 6

Frequency domain characteristics of the scanner with different fiber cantilever lengths. (a) First-order. (b) Second-order.

2.3.

Fiber Eccentricity Impact Analysis of the PZT Fiber Scanner

The resonant characteristics of the scanner differed along the $X$ and $Y$ axes due to asymmetry in the fabricated PZT fiber scanner.²⁹ Thus, we also simulated the effect of fiber outer cladding eccentricity on resonant characteristics at various orders. Setting fiber cantilever eccentricity (${\mathrm{Dec}}_{\text{fiber}}$) values at 0, 20, and $40\mu \mathrm{m}$, the first-order resonant frequencies for the $X$- and $Y$-axes exhibited differences of 0.4, 5.96, and 38.14 Hz, respectively, while the second-order resonant frequencies for the $X$- and $Y$-axes exhibited corresponding differences of 1.4, 11.2, and 69.4 Hz, as depicted in Figs. 7(a) and 7(b). Apparently, non-uniformity in fiber fabrication could result in differences in the scanner’s characteristics along the $X$- and $Y$-axes, posing challenges for image reconstruction.

Fig. 7

Frequency domain characteristics of the scanner with different fiber eccentricity values. (a) First-order. (b) Second-order.

3.1.

Measurement Analysis of the PZT Fiber Scanner

Using a four-quadrant tubular PZT with an OD of 1 mm, a forward-fixed PZT fiber scanner with a cantilever length of $\sim 14.3\mathrm{mm}$ was fabricated. Figure 8 shows a schematic representation of the static measurement platform for this PZT fiber scanner. A voltage amplifier (TD250, PiezoDrive) amplified the driving voltage signals before being applied to the tubular PZT fiber scanner via a signal generator (AFG1022, Tektronix). A CMOS camera (Panda, 4.2 M PCO) was used to record the first- and second-order resonant characteristics of the PZT fiber scanner.

Fig. 8

A schematic diagram of the PZT fiber scanner measurement platform (CL: coupling lens, 354850 B, Lightpath. DCF: double-cladding fiber. Objective: uPlan Apo $10\times$, Olympus. TL: tube lens, LA1027-A, Thorlabs. CMOS camera: 4.2 M PCO, Panda).

Figure 9(a) illustrate the first-order resonant characteristics of a PZT fiber scanner driven by a $\pm 50\mathrm{V}$ voltage over a frequency range of 785 to 835 Hz. Meanwhile, Fig. 9(b) depicts the voltage-scan range curves corresponding to the resonance frequency of 810 Hz. The PZT fiber scanner’s first-order driving coefficients ${\sigma }_1$ along the $X$- and $Y$-axes were measured at $5.34\mu \mathrm{m}/\mathrm{V}$. Similarly, Fig. 9(c) depicts the scanner’s second-order frequency scanning characteristics in the 3000 to 3250 Hz frequency range. Consequently, Fig. 9(d) illustrates the voltage-scan range curve corresponding to the resonance frequency of 3130 Hz. The PZT fiber scanner’s second-order driving coefficients ${\sigma }_2$ along the $X$- and $Y$-axes were measured to be 3.86 and 3.$24\mu \mathrm{m}/\mathrm{V}$, respectively. These experiment results agreed with the theoretical simulation results, indicating that at the same driving voltage, the driving coefficients for the first-order resonant mode are greater than those for the second-order resonant mode.

Fig. 9

Resonant characteristic results of the PZT fiber scanner. (a) Scan range versus scanning frequency curve for the first-order resonant mode. (b) Scan range versus driving voltage curve for the first-order resonant mode. (c) Scan range versus scanning frequency curve for the second-order resonant mode. (d) Scan range versus driving voltage curve for the second-order resonant mode.

3.2.

Two-Photon Endomicroscopy Probe Integration

A common-path fiber-optic TPEM platform was developed, as shown in Fig. 10(a). The double-cladding antiresonant fiber (DC-ARF) was a delivery fiber for femtosecond pulse and fluorescence signals. The 920-nm femtosecond pulse was coupled into the core of the DC-ARF and guided to the probe’s distal end. A photomultiplier tube (PMT) collected and detected two-photon-excited fluorescence signals. Previous reports contained more detailed information on the TPEM hardware platform.³⁰ Figure 10(b) displays the integrated TPEM probe, with an OD of 2.7 mm, a rigid length of 24 mm, and a weight of 0.33 g. Figure 10(c) depicts the schematic of the miniature TPEM probe. The lensed fiber technique aided in realizing objective-lens-free two-photon endomicroscopic imaging,^23,31,32 and detailed information on lensed fiber fabrication could be found in one Ref. 30. The lensed fiber had a working distance of $\sim 240\mu \mathrm{m}$. The PZT fiber scanner was activated by dual-channel amplitude-modulated sinusoidal and cosine voltage waveforms, allowing for a two-dimensional spiral pattern. The scanner’s increased and decreased amplitude periods each had 512 turns. The scanner’s increased amplitude period was used for imaging, i.e., single-side scanning, at a calculated frame rate of $\sim 0.79$ frame per second (fps). The PZT fiber scanner and lensed fiber were integrated into a three-segmented probe housing in this design, with a glass window at the end for protection.

Fig. 10

Fiber-optic scanning TPEM. (a) A schematic diagram of TPEM (DM: dichroic mirror, DMLP650R, Thorlabs. CL: coupling lens, 354850 B, Lightpath. DC-ARF: double-cladding antiresonant fiber. Filter: FF01-530/43-25, Semrock. FL: focusing lens, LA1951-A, Thorlabs. PMT: photomultiplier tube, H10770PA-40-SEL, Hamamatsu). (b) Photograph of the integrated probe. (c) A schematic diagram of the integrated probe.

Figure 11(a) shows the two-photon imaging results of a 380 nm fluorescent microsphere (G400 Fluoro-max, Thermo Scientific). The lateral resolution measurement results in Fig. 11(b) were obtained by extracting the horizontal intensity distribution of the microsphere and performing Gaussian fitting. This probe’s measured lateral resolution was $\sim 2.47\mu \mathrm{m}$.

Fig. 11

(a) Two-photon imaging results of the fluorescent microsphere. (b) Lateral resolution measurement results. Blue circle: raw data. Red line: Gaussian curve fitting.

Figures 12(a) and 12(b) illustrate the results of two-photon endomicroscopic imaging of green-fluorescent-protein-expressing mouse ex-vivo heart and brain tissue, revealing the structural features of myocardial fibers and neuronal somas, respectively. In this case, the peak-to-peak driving voltages for the PZT fiber scanner along the $X$- and $Y$-axes were $\pm 63.75$ and $\pm 56.25\mathrm{V}$, respectively, yielding a field of view of $\sim 440\mu \mathrm{m}$. These findings supported the miniature PZT fiber scanner’s suitability for the TPEM platform.

Fig. 12

Ex-vivo two-photon endomicroscopic imaging results. (a) Heart tissue. (b) Brain tissue.