We develop a fiber based probe that is capable of two-dimensional scanning applicable in optical coherence tomography (OCT). Based on the resonance of the fiber cantilever with asymmetry structure which has two distinguished resonant frequencies in orthogonal directions, Lissajous pattern is produced suitable for two-dimensional scanning upon a sample. Orthogonal resonances of the fiber cantilever are simultaneously excited by single piezo bender actuator with one driving signal consisting of two components corresponding to above-mentioned two resonant frequencies. By integrating a backward-placed two-dimensional position sensitive detector (PSD) into the probe, real-time lateral position of the scanning pattern is registered simultaneously for image reconstruction. Dynamical characteristics of the fiber cantilever are experimentally studied with special consideration on factors determining the resolution of the scanning pattern, including frequency and amplitude ratios between two components of the driving signal and fetching duration used for an en face image. With the developed probe implemented in our established OCT system, en face OCT images of typical samples are obtained with satisfying resolution and contrast, demonstrating the feasibility of such fiber cantilever with asymmetry structure for realizing two dimensional scanning by single actuator, potentially applicable to endoscopic OCT imaging.
©2009 Optical Society of America
Optical coherence tomography (OCT) is a rapidly developing biomedical imaging technique, allowing noninvasive high-resolution imaging of highly scattering media such as biological tissue . However, limited penetration depth of OCT imaging is a major shortcoming in comparison with existing whole-body imaging methods such as ultrasound imaging and computed tomography. In order to alleviate this limitation for internal organ-tissue imaging, various OCT based endoscopic systems have been developed over the last decade [2–8].
Based on the light firing direction relative to the endoscopic probe, OCT probes can be categorized into side-view imaging and forward-view imaging probes. The side-view imaging probe utilizes rotation assembly [3–4] to perform scanning. The entire endoscope assembly has to be mechanically rotated. Other approaches adopt rotary optical coupler and microelectromechanical systems (MEMS) [5–7]. The rotary optical coupler has limited imaging speed and duty cycle. The MEMS scanner can be actuated to provide high speed raster scanning necessary for en face imaging and three-dimensional imaging in Fourier domain OCT systems. The MEMS-based probes are currently expensive to fabricate with adequate precision, and difficult to preserve their functionalities in rigorous clinical environments [6–7]. The other category of the probe is forward-view probe which images target area in front of the probe. A few groups [5–6] have already demonstrated the use of MEMS-based mirrors in the forward-view imaging probes. Compared with MEMS-based side-view imaging probes, the MEMS-based forward-view imaging probes are more complicated in mechanical and optical design. Other strategies include the utilization of electro active polymers , fiber bundles , counter-rotating graded-index (GRIN) lenses  and piezo actuator [7–8]. The piezo actuator is able to drive the fiber cantilever at the distal end for scanning. It has the advantage of compact structure, low cost and quick response. Boppart et al.  proposed the first fiber cantilever by piezo bender actuator to realize lateral scanning. Alternatively, Liu et al.  reported a fiber probe capable of lateral scanning by a small monolithic ceramic layer piezo tube. For piezo-actuated two-dimensional scanning, methods based on piezo tube  and cross-connected two piezo benders  have been proposed.
Because of its structure, the piezo bender actuator (e.g. bimorph actuator) is an ideal device to realize a larger sideways motion than the monolithic ceramic layer piezo tube, and has been widely used in many traversal deflection applications [9–10]. Typically, the displacement of a bimorph actuator is estimated by
where d 31 is the strain coefficient, U is the operating voltage, L is the length of the actuator, h is the thickness of the bimorph [11–12]. On the other hand, the formula estimating the lateral displacement of the piezo tube is
where ID is the inner diameter, d is wall thickness. For example, if the bimorph thickness h is 0.5mm, the inner diameter ID of the tube is 1mm, and the wall thickness d of the tube is 0.6mm, then the calculated displacement of the bimorph actuator is almost two times larger than that of the piezo tube under the same operating voltage. Furthermore, the latest piezo bender actuators consisting of several ceramic layers can realize adequate traversal displacement at drastically reduced operating voltage, which is much superior to the monolithic ceramic layer piezo tube.
In this paper, we put forward the method of two-dimensional scanning by an asymmetry fiber cantilever driven by single piezo bender actuator. In contrast to cross-connected piezo benders based probe , the single piezo bender actuated asymmetry fiber cantilever probe benefits from smaller size and more flexible selectivity of resonance frequencies. In comparison with piezo tube based probe , the distal end of the fiber cantilever forms two-dimensional scanning pattern by one-dimensional driving signal rather than two-dimensional base excitation. Such realization reduces complex electronic devices and simplifies the probe assembly. Furthermore, if piezo bender actuator with multiple ceramic layers is used in the proposed probe, operating voltage can be drastically reduced. This is an additional benefit of implementation piezo bender actuator in contrast to piezo tube where monolithic ceramic layer is usually implemented for bending.
The schematic of the proposed fiber cantilever with asymmetry structure is illustrated in Fig. 1(a). It consists of a light transmitting single mode optical fiber, a piezo bender actuator, a stiffening rod and a protruding rod. The optical fiber and the protruding rod are glued to the upper and lower surface of the piezo bender actuator, respectively. The stiffening rod is perpendicularly glued to the optical fiber at one end and the protruding rod at the other end. The optical fiber and the protruding rod are parallel to each other, with horizontal displacement; make the stiffening rod form an angle of about 45 degree to the upper surface plane of the piezo bender actuator. As shown in Fig. 1(a), rigid frame BDEC is formed by fiber cantilever (FC) terminated with free fiber end A, stiffening rod (SR), protruding rod (PR) and line CE lying on end surface of piezo bender (PB). The rigid frame like character ‘H’ introduces the asymmetry characteristic to the fiber cantilever.
A theoretical force analysis of the fiber cantilever with asymmetry structure demonstrates the mechanics of two-dimensional resonant scanning driven by single piezo bender actuator. Figure 2 shows the asymmetry fiber cantilever viewed from the different direction. Figure 2(a) represents a three-dimensional view, and Fig. 2(b)–2(d) represent the front-view, right-view and top-view of the cantilever respectively if we take rigid frame BDEC as the horizontal plane. As shown in Fig. 2(a), there is no extra force applied to the elements between point ‘C’ and the free fiber end point ‘A’. Thus, the motion of the free fiber end is driven by the force at point ‘C’. The direction of the driving force F on ‘C’ offered by the piezo bender actuator is perpendicular to the upper surface plane of piezo bender as shown in Fig. 2(b). The driving force F can be decomposed to two component forces with orthogonal directions, one component force F1 is normal to the rigid frame BDEC plane; the other one is in the rigid frame BDEC plane. As the vibration of the beam follows the linear differential equation , the vibration of the free fiber end can be ascribed to the result of the linear superposition of the two component forces. When the driving signal frequency of the piezo bender reaches around the resonant frequency ω1 corresponding to the fiber segment ‘AC’, the component force F1 will drive the free fiber end resonating in the plane perpendicular to the rigid frame plane, as shown in Fig. 2(c). When the frequency of the driving signal reaches around the resonant frequency ω2 corresponding to the fiber segment ‘AB’, the component force F2 will drive the free fiber end resonating in the rigid frame plane, as shown in Fig. 2(d).
The basic mechanical central resonant frequency of the single mode fiber is given by 
where EI, ρ, l, r are the flexural rigidity, the density, the free vibration length and the radius of the optical fiber, respectively. In the experiments, the standard single mode optical fiber is used with E=72.4GN/m2, I=1.2×10-17m4, ρ=2.203g/cm3 and r=62.5µm. The length labeled as ‘AC’ and ‘AB’ in Fig. 1(a) is ~20.5mm and ~16mm, respectively. Based on Eq. (3), the two resonant frequencies corresponding to the fiber segments ‘AC’ and ’AB’ are theoretically calculated to be 238Hz and 391Hz.
When a driving signal applied to the piezo bender actuator contains two components whose frequencies are near above-mentioned two resonant frequencies, both driving component forces F1 and F2 excite the free fiber tip ‘A’ vibrating resonantly along orthogonal directions, resulting in a two-dimensional scanning in the form of Lissajous pattern.
3. Experiment and results
Resolution of the scanning fiber cantilever based probe is affected by two factors, one is the size of the focus spot, and the other is sampling interval on the sample. The focus spot size is determined by the diameter of fiber core and magnification of the optical system in the probe. The sampling interval on the sample is determined by the filling density of the scanning pattern. The dynamical characteristics including frequency and amplitude ratios between the two components of the driving signal, and the frame rate of en face imaging can affect the filling density of the pattern. In order to study the dynamical characteristics of the fiber cantilever, the motion of the fiber was monitored through detection of light projected from the free fiber end using a 632.8nm laser source. Light projected from the actuated fiber cantilever was detected using a position sensitive detector (PSD). The PSD (S2044, HAMAMATSU) is an optoelectronic position sensor utilizing photodiode surface resistance to detect light spot position in two-dimensions. The PSD is metal packaged with outer diameter of 7.5mm and light sensitive area of 4.7mm*4.7mm. Electrical current from the position sensitive detector was converted to voltage using a standard current-to-voltage circuit and then sampled by a data acquisition card (PCI-6115, National Instruments). The data acquisition interface and reconstruction of the Lissajous pattern was facilitated by a custom-built program written in Visual C++. Four different Lissajous patterns were recorded and the results are shown in Fig. 3. Different Lissajous patterns were produced with different frequency ratios applied to the piezo bender actuator in the condition that the initial phase difference and frame rate are kept constant. Figure 3(a), 3(b), 3(c) and 3(d) correspond to the frequency ratio of 259Hz/185Hz, 142.10Hz/159.90Hz, 260.90Hz/226.10Hz and 455.95Hz/371.53Hz, respectively. As shown in Fig. 3, the filling density of the pattern dramatically varied from Fig. 3 (a) to 3(d). The time period required for both harmonic motions at two applied frequencies starting from a common position and back to the common position is the repetition period of the Lissajous pattern. Within this repetition period both harmonic motions should oscillate an integral number of times with their ratio to be a simple fraction. To determine the repetition period, the integral number should be divided by its corresponding applied frequency. For example, as shown in Fig. 3(b), the frequency ratio of 142.10Hz/159.90Hz leads to a simple fraction of 1421/1599, then the repetition period is given by 1421/142.10Hz to be 10 seconds. For another pair of applied frequencies, 259Hz/185Hz in Fig. 3(a), the simple fraction is 259/185, and the repetition period is 1 second. The frequency ratio determined repetition period can be used to estimate the filling density of the Lissajous pattern, and the filling density can be modified through finely tuning the two applied frequencies near the resonant frequency.
The filling density of the Lissajous pattern is affected by both ratios of frequency and amplitude between two components of the driving signal. By increasing the amplitude of the driving signal, the scanning area, i.e. field of view (FOV) for imaging can be enlarged. With increased amplitude of the driving signal while the other parameters including frame rate, frequency ratio, and size of focus spot keeps the same, the uncovered area increases and thus the filling density of the pattern decreases. Therefore, the filling density of the pattern can be adjusted through finely tuning of the amplitude ratio between the two components of the driving signal.
Besides resolution, another important factor of in vivo biomedical imaging system is imaging speed which can be modified by the frame rate. Figure 4 demonstrates Lissajous patterns and their zoomed-in views recorded at three different frame rates. The filling density of the pattern varies evidently with different frame rates. At 10 frames per second shown in Fig. 4(a), too much uncovered area by the scanning pattern is evident, while with reduced frame rates shown in Fig. 4(b) and 4(c), the scanning patterns are satisfying as to filling density. However, as we can see from zoomed-in views shown in Fig. 4(e) and 4(f), the filling density of Lissajous pattern acquired at 2 frames per second is not improved much but with higher redundancy of scanning in compared with 4 frames per second. Some gray spots appear in Fig. 4(f) because of light diffraction when adjacent scanning traces are closer than their spot sizes. A reduced frame rate is preferable to enhance the imaging resolution while the imaging speed decreases simultaneously. There is a trade-off between the resolution and frame rate. Therefore, an appropriate sampling period, reciprocal of the frame rate, shorter than the repetition period of scanning pattern is usually set to ensure a satisfying resolution with less redundancy of scanning. For example, under a frame rate of 4 frames per second, only 0.4% of uncovered area by the scanning pattern is realized, which could be suitable for imaging in terms of resolution and speed.
The frequency response of the asymmetry fiber cantilever is experimentally studied by recording x/y displacement versus applied frequency for a constant voltage of 1.5 V. The results are shown in Fig. 5. The measured resonant frequency is 236.5Hz in x direction and 383.6Hz in y direction, in good agreement with the expected ones. The maximum scanning range in x and y direction is 1mm and 0.8mm, respectively. It is evident that the two resonant frequencies are far separated and the frequency overlapping between two response curves is negligible. Such characteristic of frequency response is favorable to the stability of the scanning pattern under small perturbations. We did not observe noticeable variations in the Lissajous pattern when a slight tapping on the asymmetry fiber cantilever is executed. Anyway, the integrated PSD can trace the variations of the Lissajous pattern and reconstruct the pattern correctly even if the Lissajous pattern is altered.
The tetra-lateral PSD used to record the trajectory of the light spot has some nonlinear error. Although small nonlinear error introduced negligible influence on the conclusion in above dynamical characterization of the fiber cantilever, it is desirable the measured position from PSD is calibrated for correct registration of scanning position for image reconstruction. The position signal was calibrated using a precision stage (YA05A-R2, Kohzu Precision Co., Ltd.) to move the PSD relative to the stationary fiber cantilever. In every 10 microns step, the measured value from PSD (xc, yc) and the shifted position of stage (x, y) were recorded. Then the correction coefficient of this position (x/xc, y/yc) is calculated. As the calibrated positions in steps are discrete, the coefficients of positions which are not directly measured should be numerically interpolated. The interpolation for x-direction and y-direction is the same. Take x-direction as an example, the formula of interpolation is
where β is the correction coefficient in x-direction. β2, β1 are the coefficients of the neighboring positions. xc is the current position, and xc1, xc2 are the neighboring positions which have been calibrated. The measured and calibrated curves are presented in Fig.6.
Figure 7 illustrates the OCT system and the designed probe based on the proposed asymmetry fiber cantilever. The power of the low-coherence light source is 4mW, resulting in approximately 1mW for the sampling probe. The center wavelength of the light source is 1310nm and the bandwidth is 65nm, so the coherence length in air is ~11µm. An aiming source is used to provide the monitoring light at 632.8nm suitable for the PSD in the probe. As shown in the Fig. 7, the probe consists of the asymmetry fiber cantilever (FC), a GRIN lens with dichroic coating (DC), and a backward-placed PSD for position feedback. The DC on one end face of the GRIN lens is used to reflect the monitoring light to the PSD for trajectory recording and transmit the probing light to the sample without attenuations. The bender actuator currently employed is a piece of piezo bimorph (55mm*2.2mm*0.7mm). The GRIN lens has a diameter of 2.5mm and a pitch of 0.23, corresponding to a length of 4.42mm. The spacing between the end of fiber and the GRIN lens is 2.2mm, and the working distance is calculated to be 2.2mm to achieve a unit magnification of the GRIN lens. The light from the scanning fiber is focused by the GRIN lens resulting in 10µm spot size according to the diameter of the fiber core. The fiber cantilever, the GRIN lens and the PSD are encased in an aluminum tube with inner diameter of 18mm. The overall rigid length is 60mm and the outer diameter of the final packaged probe is 22mm. The photo of the prototype probe developed and its designed drawings are demonstrated in Fig. 8. As shown in the designed drawings and corresponding prototype picture, the assembled prototype probe is made by two separated units. One is the detection unit encasing the fiber cantilever and GRIN lens, and the other is the feedback unit mounting the PSD. To ensure measuring precision of the PSD, it is favorable that the aiming beam illuminates the PSD surface at normal angle. To achieve this purpose and guarantee the correct alignment of the fiber, the GRIN lens and the PSD, an additional PSD is used during alignment procedure. Firstly, the GRIN lens is properly fixed to the feedback unit. Then by placing an additional PSD perpendicularly to the axis of the GRIN lens, the position of the fiber tip of the asymmetry fiber cantilever connected to a visible laser can be monitored. With the help of this auxiliary position signal, the alignment and fixation of the fiber cantilever is done. Finally, the integrated PSD is aligned and fixed by matching its position signal to the auxiliary position signal while the fiber tip is oscillated.
It should be mentioned that the dimensions of the packaged probe illustrated in this paper are somewhat bigger than that required for endoscopic applications. However, this prototype probe demonstrates the feasibility of the asymmetry fiber cantilever driven by single piezo bender actuator for two dimensional scanning. Actually, the miniaturization of the developed probe is mainly limited by the dimension of the currently used PSD, which is a commercial one from the shelf. If a custom-built miniaturized PSD is adopted, just as the case as a miniaturized CMOS sensor in a capsulated camera, the rigid length and overall diameter of the final assembled probe can be greatly reduced, suitable for in vivo endoscopic application in OCT.
Several samples including the coin and the infrared sensor card are imaged with the developed probe. The results are shown in Fig. 9 and Fig.10, where images are acquired at 4 frames per second with area size of ~1mm*0.8mm.
Figure 9 shows en face OCT images of character ’H’ from a coin. Apparently, the imaging resolution of Fig. 9(c) and 9(d) is higher than that of Fig. 9(b) because of the smaller scanning areas. The feature of adjustable scanning area offers capability of fast preview on whole FOV and high-resolution imaging on a selectable region of interest (ROI) of the sample. En face images at two different depths as well as the reconstructed cross sectional image of an infrared sensor card (Newport, Inc.) are illustrated in Fig.10. Since the phosphor particles whose average size ranges from 0.4µm to 20µm are differentiated clearly, the experimental determined lateral resolution could be estimated to 20µm at least. In the deeper layer of the infrared sensor card which is almost made up of phosphor particles, we observe aggregation of several phosphor particles showing strong OCT signal in Fig. 10(b).
Two-dimensional scanning fiber cantilever with asymmetry structure driven by single piezo bender actuator is developed and its performance is experimentally confirmed. Dynamical characteristics of the fiber cantilever are studied by recording the motion of the fiber cantilever using a PSD. We found that through finely tuning the frequency and amplitude ratios between two components of the driving signal and adjusting the frame rate for one en face image, the filling density of the Lissajous pattern can be changed. By choosing an appropriate frame rate, the trade-off between resolution and imaging speed can be optimally compromised. The designed probe incorporated a backward-placed PSD to record the scanning simultaneously offers position registration for correct image reconstruction that is never realized before. En face images of coin and infrared sensor card are acquired with an established OCT system at 4 frames per second with estimated lateral resolution of 20µm, demonstrating the feasibility of the proposed asymmetry fiber cantilever for two dimensional scanning, potentially applicable to endoscopic OCT imaging.
This work was supported by National High Technology Research and Development Program of China (2006AA02Z4E0) and Natural Science Foundation of China (60878057).
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