# Endoscopic Optical Imaging Technologies and Devices for Medical Purposes: State of the Art
## 4 Scanning Principle
### Resonant Scanner  
The distal tip of the fiber can achieve higher displacement when it is vibrated at resonance. In other words, the amplitude of the beam scanning and the obtainable resolution can be maximized by exciting the distal free end of the optical fiber at its natural (first resonant) frequency. From the vibrational  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Forward View** & **Side View** & **References.** \\ \hline Probe diameter & \textgreater{}250 μm (proximal scanning) & \textgreater{}250 μm (proximal scanning) & [54; 56; 77] \\ Rigid length & \textgreater{}1.65 mm (distal scanning) & \textgreater{}2.4 mm (distal scanning) & \\ Rigid length & \textgreater{}9 mm & \textgreater{}11 mm & [64; 79] \\ FOV & 50–400 μm & \textgreater{}3–4 mm & [23; 53; 75] \\ Image orientation & en face & Peripheral surface & \\  & Can be used for image guidance to & Can image the finer cavities of & \\  & relocate and control the position of & the body, gives information & \\ Advantages & the medical devices, can directly & about the wall/section of tissue & \\  & image the extent of the & layer involved in the & \\  & malignancy and cancerous surface & malignancy, higher field of & \\  & Limited field of view, limitation of & view, less expensive & \\ Disadvantages & miniaturization limits the ability & Difficult to guide the probe in & \\  & to image the narrower sections & the body due to lack of & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison between forward and side view scanners.  
theory, the resonance frequencies for a clamped-free configuration (called cantilevered) of the beam are given by:  
\[f_{n}=\frac{\beta_{n}{}^{2}}{2\pi}\sqrt{\frac{EI}{\rho AL^{4}}}, \tag{6}\]  
where \(E\), \(I\), \(\rho\), \(L\), \(A\), and \(\beta_{n}\) are [PERSON]'s modulus, moment of inertia, density, length, cross-section area of the cantilevered beam, and the coefficient value depending on the resonance mode, respectively [80].  
A large number of scanning fiber endoscopes are based on the first mode of resonance to scan the light. The proximal end of the fiber is usually excited at resonant frequency using piezoelectric [2; 12; 13; 15], electromagnetic [16; 17; 18], electrothermal [19; 20; 21], shape memory alloy [25], or electroactive ionic polymer [26] actuators. The distal end follows the mode shape shown in Figure 12. Various resonant scanners in the literature are compared in [81].  
In most cases, the cantilevered fiber scanners are characterized by having a symmetrical cylindrical section. In cases when the beam structure is excited with large displacements near its resonance frequency, the cross-coupling of the motion between the planes perpendicular to the beam axis leads to a whirling phenomenon. This nonlinear tip response of the excited fiber is highly unstable. In very small frequency ranges, a stable whirling motion can be produced, which allows the fiber to trace an elliptical shape pattern. The equation of motion describing the whirling phenomenon was studied by [PERSON] and [PERSON] in [82], and further developed by [PERSON] in the case of a cantilever beam [83].  
It is possible to avoid the undesired whirling motion by changing the shape of the optical fiber beam or finding the two eigendirections on the beam where the excitation can cancel the whirling effect [84]. It is even seen that the whirling effect can be positively exploited for 2-D scanning using a single actuator. It is experimentally shown in [85] that exciting the cantilevered fiber at a second mode of resonance gives a stable circular-shaped pattern by tip displacement. Thus, it can be beneficially used for scanning the target area by sweeping the circular area by continuously increasing the driving voltage of the exciting actuator [85].