Real-time Lissajous imaging with a low-voltage 2-axis MEMS scanner based on electrothermal actuation

: Laser scanning based on Micro-Electro-Mechanical Systems (MEMS) scanners has become very attractive for biomedical endoscopic imaging, such as confocal microscopy or Optical Coherence Tomography (OCT). These scanners are required to be fast to achieve real-time image reconstruction while working at low actuation voltage to comply with medical standards. In this context, we report a 2-axis Micro-Electro-Mechanical Systems (MEMS) electrothermal micro-scannercapable of imaging large ﬁelds of view at high frame rates, e.g. from 10 to 80 frames per second. For this purpose, Lissajous scan parameters are chosen to provide the optimal image quality within the scanner capabilities and the sampling rate limit, resulting from the limited A-scan rate of typical swept-sources used for OCT. Images of 233 px × 203 px and 53 px × 53 px at 10 fps and 61 fps, respectively, are experimentally obtained and demonstrate the potential of this micro-scannerfor high deﬁnition and high frame rate endoscopic Lissajous imaging.


Introduction
Biomedical endoscopic imaging is on the rise thanks to recent breakthroughs such as the miniaturization of catheters, scanning systems, optical components and the capability to integrate components at a smaller scale. Many medical modalities take full advantage of it, making optical biopsies more and more prevalent and appreciated for their low invasiveness and non-delayed diagnosis [1].
In this framework, confocal microscopy, multi-photon, photo-acoustic, fluorescence and especially OCT imaging techniques stand at the heart of this development. They are usually based on laser beam scans, retrieving images of surfaces or even volumes. Indeed, recent trends in medical imaging have shown a shift towards volumetric screening [2]. Today, 3D imaging is sought for "enhanced" diagnostics and interventional procedures, still allowing downgrading to 2D for the selection of specific slices in the bulk [3]. In the case of, e.g., spectral-domain OCT [4,5], the axial dimension of the probed volume is obtained through spectrally-resolved measurements, whereas the other two result from a 2D scan, hence justifying the conspicuous need for 2D scanners compatible with endoscopic requirements. Among them, endoscopic apparatuses face increasing challenges in reaching more and more remote and restricted areas (colonoscopy, esophagus, veins) [6], requiring drastic means to downsize the systems. In order to meet the specifications of miniaturization, MEMS are particularly appreciated for their compact design, simplicity of fabrication, integrability and low-cost [7,8].
In addition, in vivo operation safety standards require these micro-systems to comply with low voltages [9]. Among all actuation methods, such as electrostatic [10], electromagnetic or piezoelectric [11], electrothermal actuation is the preferred candidate to tackle the issues of both low driving voltage and compactness. Besides, it provides large angular displacements and a relatively linear control compared to electromagnetic actuation, its major competitor [12,13]. Next to compactness and low-voltage actuation, real-time image delivery has become a key criterion of endoscopic scanners performances. Indeed, fast delivery of images allows reducing measure artifacts linked to random disturbances occurring inside the human body such as heartbeat, lung respiratory cycles, organs motion; but also allows pathologists to provide fast prognostics. For this purpose, mirror actuation should be as fast as possible. Electrothermal highest rotational resonant modes usually reach a ceiling around 1.4 kHz [14], despite a few counter-examples achieving frequencies of 2.2 kHz [15] when they are composed of Al/SiO 2 bimorphs and 2.74 kHz [16], or even 12.8 kHz [17] with a smaller mirror plate based on Cu/W bimorphs but exhibiting reliability issues due to Cu oxidation [18], drastically attenuated magnitudes or mirror plate dynamic distortions. Although raster scans are more uniform than Lissajous ones, the strong frequency imbalance between the two axes avoids, on both axes, to benefit from the angular gain and improved stability when working near the mechanical resonance. Among conventional scanning patterns, only spiral [19] and Lissajous [20] methods enable reaching high 2D scan rates within the frequency range allowed by electrothermal time constants, since they rely on high frequencies on both axes.
In the following, we consider the Lissajous method in a resonant mode in order to improve the stability and reduce the driving voltage [21,22], rather than the spiral pattern which is more adapted to resonant bare-fiber scanners [23][24][25][26][27]. Hence, we propose a MEMS scanner composed of electrothermal actuators deflecting a mirror plate along two orthogonal axes in order to perform Lissajous scans. It is set up in a side-viewing configuration for further use into an endoscopic probe system for eventual OCT luminal imaging. Although, our prototype does not claim to compete with the smallest endoscopic probes' miniaturization scope, it is still compatible with current commercial endoscope's instrument ports (ranging up to 4.2 mm in diameter [28]) and was developed for an endoscopic catheter for in vivo imaging. Depending on the medical application and discipline, it could be further miniaturized if necessary. In the following, the capability of the micro-device to perform real-time imaging of samples until 61 fps with very low voltage amplitude (< 1 V) is experimentally demonstrated.

Lissajous principle and specifications
Lissajous scans result from the superposition of two sinusoidal movements along two orthogonal axes: with A x , A y the amplitudes of the sinusoidal movements, f x , f y the frequencies with respect to ì x and ì y axes and ψ is the phase difference between the sine curves. In this work, only repeating Lissajous scanning is considered, since non-repeating scans are likely to generate temporal jitters [29]. In this context, the real-time criterion is the frame rate (FR) defined as the inverse of the repeating time of a pattern (as defined in Eq. (2) where GCD is the greatest common divisor), and limited to 1 fps (lower limit) in the case the axial frequencies f x and f y are coprime integers.
Although, several groups have realized Lissajous trajectory imaging by resonant scanning fibers or MEMS mirrors at several fps [30,31], frame rates closer to video rate or higher could be highly appreciated in dynamic in vivo screening for their imaging fluidity and motion artifact reduction [29]. Lissajous image quality depends on the beam trajectories and in particular on the density of lines scanned across the field of view (FOV) during one frame. This density is inherent to the number of lobes N of the scanned pattern, limited by the maximum achievable working frequency: with N x and N y the respective number of lobes along ì x and ì y (we set f x > f y in all the following). Therefore, due to the dimensions of the electrothermal mirrors as well as the materials they are made of (Al/SiO 2 ), each axis resonance is limited to about 1400 Hz, limiting the number of lobes to, e.g., 33 at 82 fps, 43 at 61 fps, 139 at 20 fps and 279 at 10 fps. Consequently, in order to maximize the number of lobes for each considered frame rate, the resonance frequency should be increased for both axes as close as possible to the upper threshold, so that the requirements of both high frame rate and image quality can be fulfilled.

Design
The scanner presented in this work stands out in terms of performances compared to former electrothermal devices dedicated to real-time imaging. For instance, one was characterized by higher voltage and much lower working frequency (205 Hz on one axis) [32] whereas a closer design [33,34] showed higher resonant frequencies on both axes (750 Hz) but still limiting its ability to reach the expectations of high definition and high fill factor (FF) Lissajous imaging.
The microscanning device, shown in Fig. 1(a), is composed of a central reflective circular plate coated with aluminum on both sides and referred to as the micro-mirror. It is connected to a frame via four double S-shaped actuators enabling three degrees of freedom along axes ì x and ì y in tip-tilt mode and a piston motion over ì u, perpendicular to the surface of the micro-mirror plate. The electrothermal actuators employed in this design were first introduced by Todd et al. [35] and widely investigated in [36]. Actuators dimensions were adapted to the amplitude and frequency needs with custom width of 18 µm, length of 325 µm (length of a single S-shape) and thicknesses of 1.0 µm of aluminum and 1.1 µm of SiO 2 . A close-up view of one actuator is presented in Fig. 1(b) after release. The frame carries the central micro-mirror and constrains its initial tilt. Note that the four actuators are designed to be identical but that axes asymmetry is expected from parameters scattering of both fabrication and thermal behavior discrepancies from the model. After release, the array of passive bimorphs releases its intrinsic stress causing the frame to bend out of the substrate. A pair of mechanical stoppers leans against the vertical walls of the handle layer, thus restraining the frame from reaching higher angles than 45°with respect to the substrate, latching the scanner in a side-viewing configuration at 45°. A zoom in the pit of one of the stoppers is shown in Fig. 1(c). The device was fabricated on a silicon on insulator (SOI) wafer whose process flow has been described in [32], and is compatible with both a wafer-level integration and a low-cost production [33]. Indeed, the wafer diameter is 100 mm on which 300 scanners are fabricated. After release, the residual stress of the four actuators shifts the micro-mirror plate of the frame plane (along +ì u) of about 170 µm. This initial clearance sets the maximum static displacement so that the actuators can only pull the micro-mirror plate down towards the frame (in the direction of -ì u) when heated up, as depicted by the arrow in Fig. 1(b). Each actuator is controllable independently by applying a signal of a custom waveform on the corresponding pad. To deflect the micro-mirror along one axis (axis ì x for instance), i.e. around axis ì y while maintaining the center of the micro-mirror stationary upon actuation, two opposite-phase signals of amplitude V x are applied onto the two opposite actuators Act + x and Act − x on top of a DC voltage offset V b applied on all the actuators as illustrated in Fig. 2. From the model established, the actuators were designed to provide an angular characteristic of 3.
a thermal cutoff frequency of 100 Hz, a Q ≈ 40, close to the former device design composed of a similar electrothermal actuator and a resonance magnitude of 15 dB. In the following, V b is set at 3 V DC to ensure working within the linear behavior of the scanner. However, performing a scan of Lissajous requires the micro-mirror plate to sweep both axes with sines of different frequencies along ì x and ì y without exciting the piston mode (along ì u). Consequently, symmetric signals apply on top of common biases onto axes ì x, ì y with respective frequencies f x , f y and amplitudes V x , V y : The output of each axis can be expressed as a distance (see Eq. (1)) or as an angular displacement of amplitude θ opt i = 1 2 θ opt i pp , the amplitude peak to peak of the beam scanned over axis i. The output frequency f i is equal to the input frequency and ψ i is the phase difference between the output and the input. To maximize the line density, the difference of phases ψ = |ψ x − ψ y | must equal π/2 if N is even and 0 otherwise. This amplitude is measured in Section 3.2 through characterization of the frequency response for each axis.

Optical setup
The optical setup, sketched in Fig. 3, uses a He-Ne laser (Thorlabs HRP050) beam, shaped by a beam expander [BE], and splits into two paths re-directed towards each side of the micro-mirror [MM]. Its backside reflects the beam to impinge on a position sensing detector (PSD) (Thorlabs PDP90A) whereas the frontside deflects the beam towards a sample. The latter is characterized by a spatially varying binary pattern allowing to measure the transmitted light (by a first photodetector -PD1) or the reflected one (by a second photodetector -PD2). Both photodetectors are PDA36A-EC from Thorlabs. The [MM] is driven through a National Instruments DAQ USB-6363 acquisition card programmed in Python, used to generate the analog signals required for the different experiments. The same card can be used for acquisition as well, but with a limited sampling frequency f s (in multi-channel mode: 1 MSa/s shared between 4 channels). It was then only employed for the acquisitions reported in Section 3.2 whereas an oscilloscope (Agilent DSO-9254A) with 20 GSa/s maximum sampling rate was used for acquisitions reported in Section 5.2. A power amplifier custom card was designed to drive the actuators of the micro-mirror and is powered by a TENMA 72-2540 power supply. As a summary, the optical setup is a 2-in-1 setup consolidating the characterization (utilized in the current section) with the optical imaging gear (exploited in Section 5.). Firstly, only the PSD is used to monitor the angular position of the micro-mirror as a function of the amplitude, frequency and phase of the driving signal in order to characterize and calibrate the scanning device itself (reported in Section 3.  in conditions close to the applicative specifications. The beam illuminating the sample from this second path is focused by a lens of focal length 50 mm [L3] producing a numerical aperture (NA) of 0.03, a full width at half maximum (FWHM) of 15 µm (experimentally measured using the knife-edge method [37]) and a depth of field (DOF) of about 800 µm. Such focal length has been chosen for ease of characterization but could be significantly shortened as long as the mirror can be placed between the lens and the sample. This would eventually lead to a much better optical resolution. Note that the scanner is mounted on a PCB used here to connect and hold the device but which would not be required in a probe tip. The sample is placed in the focal plane of [L3]. The intensity transmitted (reflected) through the sample is collected by the photodiode [PD1] ([PD2]) and combined with the real-time discrete positions of the micro-scannerrecorded on the PSD to reconstitute the gray-shaded intensity profile of the sample, and hence a so-called "transmission (reflection) image". Although, in the following, only transmission images are reported, a comparable quality of images in reflection was observed.

Micro-scanner characterization
Using the setup described above, the frequency response of the scanner, plotted in Fig. 4(a), was measured in the frequency range of 10 Hz to 1500 Hz with increment of 1 Hz, applying a common offset V b = 3 V DC and sine signals of amplitude varying between 0.1 V pp and 0.5 V pp on one axis at a time and measuring the swept amplitude of the beam (referred to as θ opt pp ) deflected by the micro-mirror on the surface of the PSD along both direct (ì x · ì x and ì y · ì y) and coupled axes (ì x · ì y and ì y · ì x).
The normalized Bode diagram of the direct systems plotted in Fig. 4(a) reveals a first-order thermal system (with a cutoff frequency at 93 Hz) followed by a mechanical second order with a characteristic phase drop of π rad at the resonance as plotted in Fig. 4(b). It shows two distinct resonances at 1186 Hz and 1179 Hz for the horizontal and vertical axes, respectively. We take advantage of this discrepancy -resulting from the fabrication parameters drift -to reduce the axis cross-coupling, illustrated in Fig. 4(c), and revealing a superposition of the modes in agreement with the phase drop of 2π rad. Although the maximum cross-axis coupling -with Q-factors of about 60 in the coupled axes -represents about 20%, avoiding the resonance is preferred to guarantee an exploitable shape of the scan, also because the required voltage remains significantly low. Resonant frequencies are stable (an insignificant drift of less than 2 Hz from 0.1 V pp up to 0.5 V pp was observed) and Fig. 4(d) reveals a linear behavior over the same voltage range. In addition, the quality factors remain quite constant and were respectively measured at 38.3 and 39.3 for the horizontal and vertical axes of the direct systems, corresponding to respective FWHM of 31 Hz and 30 Hz.
Large static angles are reached for ultra-low voltages and increase by a factor of 5 in resonant mode. The measured angles come within the scope of the displacement ranges reported in the literature [12,38] and are about 15 times higher than for electrostatic actuation [10]. Indeed, under static actuation, the micro-scannerdemonstrates deflections of 6.8 • opt /V DC and 4.0 • opt /V DC for ì x and ì y axes respectively and deflections of 3.67  Fig. 4(a)) and corresponding to a driving voltage equal to or lower than 0.5 V pp . The selection of meaningful frequency couples and ensuing scan parameters are detailed in Section 4.

Scan parameters selection
As mentioned in Section 2.1, Lissajous images are built upon two orthogonal sine movements. However, the resulting patterns can differ drastically, from a simple line or ellipse to an entire, densely covered FOV. This pattern is a function of these two signal frequencies -resulting in an odd number of lobes in our case -and their amplitudes, and should be finely adjusted to optimize the FOV and the resolution of the image, according to the features of the scanner. In order to determine the optimal parameters of the Lissajous pattern, we use in the following the method proposed by Bazaei et al. [39]. It consists of identifying the image resolution with the maximum distance between two lines in the center of the image, where the density is the lowest. This distance hereafter referred to as h in Fig. 5(a), derives from the coordinates of the vertices of the diamond-like pattern, or crossing points P 0 , P 1 and P 2 developed in Eq. (4).
The distance h is given by Eq. 5: Setting the image resolution h to the optical resolution, i.e., to the beam FWHM, then allows expressing the optimal size of a squared scan (assuming A x = A y = A): In order to retrieve an image from the laser scanning, the beam movements should be spatially quantified by building a uniform grid of points. In other terms, the digital image is built by filling sequentially its pixels along the Lissajous trajectory with the corresponding value recorded by the photodiode. This spatial quantification corresponds to the distance between two samples and thus, to the size of one pixel dP of the digital image. The pixelwise field of view can then be expressed as : This distance dP is also equal to the inverse of the spatial sampling frequency. This frequency should be of the order of the cutoff frequency of the modulation transfer function (MTF) that is related to the spatial resolution of the optical system, characterized by its point spread function (PSF). In the case of a Gaussian beam, the cutoff frequency is equal to 1/FWHM. Hence, according to the Nyquist-Shannon sampling theorem, the spatial sampling frequency should be at least twice the cutoff frequency, i.e. 2/FWHM. The same theorem can be interpreted in terms of distance such that the pixel size dP should be smaller than FWHM/2. In practice, a more restrictive criterion is often employed, setting the pixel size to FWHM/3 [40], in order to avoid, during the pixelation process, a reduction of the contrast [41]. In the following, the pixel size is consequently set at, at least, FWHM/2, and preferably at FWHM/3. Setting dP equal to a fraction of the FWHM then allows defining the pixelwise FOV as a function of the number of lobes exclusively (7). In the case in point (N x = 6 and N y = 5), the FOVs, rounded up to the next integer, are respectively equal to 11 px × 11 px for dP = FWHM/2 and 16 px × 16 px for dP = FWHM/3. Figures 5(b) and 5(c) display the corresponding Lissajous scanning patterns. It clearly appears that the beam trajectory does not meet all the pixels. The FF defined as the ratio between the scanned surface and the total surface in pixels, is directly related to the Lissajous scanning parameters and the pixel size dP. We consider that a pixel is "lit" as soon as the beam trajectory overlaps its surface, even partially. The pixels that are not met by the beam trajectory are blackened out in Figs. 5(b) and 5(c). When strictly applying the Nyquist-Shannon sampling theorem, i.e., setting dP = FWHM/2, only 4 pixels are left out, leading to a FF greater than 97%.
The FF drops to about 86% for a pixel size of FWHM/3. As stated in Section 3.2, the operating frequency range of the proposed scanner spans from 1140 Hz and 1230 Hz. This range yields 4095 frequency combinations (f x , f y ) of coprime integers. According to Eq. (2), these combinations allow us to use frame rates between 1 fps and 82 fps, and a number of lobes (Eq. (3)) ranging from 2459 to 29, respectively. Among these combinations, the frequency couples allowing a high frame rate (fixed at FR 60 fps) are selected, narrowing down the number of couples to few tens. Finally, among these couples, we single out the ones showing the maximum number of lobes, leading to the highest pixel density whereas selecting frequencies in order to maintain cross-axis coupling under 5%.
In the case of our scanner, and for a frame rate larger than 60 fps, the highest number of lobes is obtained for a frame rate FR = 61 fps. The corresponding number of lobes is then 39 (N x = 20, N y = 19) for f x = 1159 Hz and f y = 1220 Hz. Setting dP = FWHM/3 with FWHM = 15 µm leads to an image resolution of 53 px × 53 px corresponding to a FOV of 265 µm × 265 µm. Table 1 reports representative configurations for high frame rate imaging using the same range of scanner frequencies. Using the maximum frame rate of 82 fps results in a reduction of 45% of the FOV, shrinking the image to 200 µm × 200 µm (corresponding to an image resolution of 40 px × 40 px). Conversely, decreasing the frame rate increases the FOV. For instance, a FR of 10 fps -often considered as a threshold for real-time imaging -allows using a higher number of lobes (N = 239), providing an image resolution of 323 px × 323px or a FOV of 1.62 mm × 1.62 mm. At 20 fps, which is the flicker vision rate, guaranteeing exploitable real-time imaging, a number of 119 lobes enables a FOV of 805 µm × 805µm corresponding to 161 px × 161 px. For these parameter sets and a pixel size of FWHM/3, the FF is always located around 86%. This value is independent of the number of lobes and can be considered as the upper FF limit for a pixel size of FWHM/3. Moreover, these FF values are obtained while assuming continuous Lissajous trajectories, and therefore infinite acquisition sampling rates. However, this approximation remains valid only if the sampling frequency is much larger than the frequency interval F cp between two successive crossing points (e.g. P 0 and P 1 ), which is given by: Figure 6(a) shows the behavior of the FF as a function of the reduced sampling frequency defined as f s = f s /F cp . For sampling frequencies equal to F cp , i.e. f s = 1, the FF is limited to about 40%, regardless to the considered scanning configurations. Reaching a FF value exceeding 80% requires to set the sampling frequency at least to 6 times the cross-point frequency F cp , which corresponds, concerning a frame rate of 10 fps, to a sampling rate exceeding 3.43 MHz. However, swept-source OCT systems demonstrating the highest A-scan rates (sampling frequencies), are currently limited by the availability of commercial swept-sources. Indeed, typical sweep frequencies range from 20 to 200 kHz except for a single company providing sources up to 1 MHz [40]. Obtaining a FF above 80% under such restrictions on the sampling frequency can only be achieved using the highest frame rates. For FR = 61 fps and 82 fps, according to Fig. 6(a), a FF of 80% is obtained for sampling frequencies below 1 MHz, i.e., for 310 kHz and 560 kHz respectively. Nevertheless, concerning frame rates of 10 fps and 20 fps, 1 MHz sampling frequency leads to a FF of 59% and 72%, respectively ( Fig. 6(b)). One solution to relax the demand on the sampling frequency is then to impose a lower FOV for a given number of lobes. This allows densifying the trajectories by decreasing the distance h. Keeping the pixel size constant will then result in an increase in the FF. This is illustrated in Fig. 6(b) for the scanning configurations corresponding to frame rates of 10 fps and 20 fps. The reported data show the evolution of the FF as a function of the FOV for a sampling frequency fixed at 1 MHz. Fill factors higher than 80% can then be obtained for FOVs of 1150 µm × 1150 µm (at 10 fps) and 700 µm µ 700 µm (at 20 fps) (black dotted line in Fig. 6(b)).
As a summary, the chosen method aims at optimizing the FOV as a function of the optical resolution by setting the spatial frequency (pixel size) to a fraction of the spot size (FWHM). This is done by identifying the optical resolution to the maximum distance between two lines of the trajectory at the center of the image (Eq. (7)). The pixel size is then set at FWHM/3 which leads to a FF of 86% in the case of continuous trajectories, i.e. for sampling frequencies much larger than the frequency interval between two successive nodes F cp (Eq. (8)). Maintaining a FF larger than 80%, as generally required in the context of optical imaging, requires the use of a sampling frequency f s at least equal to 6 x F cp . An insufficient sampling frequency (< 6 x F cp ) can be compensated by a reduction of the FOV in order to maintain a high FF (>80%) while keeping the optical resolution. FOV, FR and F cp therefore have to be evaluated for all the possible combinations of frequencies within the operating frequency ranges of the scanner (defined by a positive angular gain). Hence, the optimal frequency couple can be chosen according to a figure of merit gathering parameters such as scanner frequency response, mechanical coupling, or FR, with a weight chosen as a function of the targeted application.

Samples
The samples used for experimental imaging are binary patterns fabricated by Cr evaporation onto a glass substrate, thus reflecting or transmitting the incident laser beam depending on its position within the focal plane. As shown in Fig. 3(a), two different patterns, the femto-st institute logo and a "gator", mascot of the University of Florida (an alligator head) have been prepared with characteristic sizes of few tens of microns. Unlike a more conventional target, such samples allow to image rather large FOVs at a uniform resolution in the order of magnitude of the laser beam FWHM. The letters of the employed femto-st pattern are written with a 30 µm-wide line, whereas the ones of & are 7.5 µm wide.

Laser scanning based imaging
The construction of the image is illustrated on the two first letters "fe" of the femto-st pattern in Fig. 7 along three main successive steps. It is realized at the frame rate of 61 fps, with parameters corresponding to the second line of Table 1.  The sampling frequency of 1 MHz has been chosen because it corresponds to the upper limit of current commercially available OCT swept-sources. This step consists in adjusting the amplitudes to generate the correct FOV according to the method presented in Section 4. Actuation voltage amplitudes were adjusted to cover a squared FOV of 265 µm × 265 µm although it exhibits a slight cross-axis coupling (reported in Fig. 4(c)) emphasizing a slanting trend on the horizontal axis without affecting the exploitability of the pattern samples. Indeed, as it can be seen in Fig. 7, cross-axis coupling is responsible for distortion of the FOV margins but not of the image. The pixel size dP is chosen at FWHM/3 and provides a pixelated image of 53 px × 53 px shown in Fig. 7(b) depicting an intensity image in shades of gray in transmission mode. The real FOV, slightly distorted due to coupling, is thus identified by applying a convex hull algorithm. Therefore, missing data are represented in blue. On Fig. 7(b), an experimental FF of 85% is achieved within the convex hull limits. Finally, Fig. 7(c) shows the image where the scattered data have been interpolated (natural neighbor interpolation method) within the convex hull figured in blue, leading to a remarkable rendering. Note that such treatment can be quickly operated, since it requires e.g. 14 ms per image acquired at FR=61 fps, 100 kS/s, when performed on a Xeon E5-1620 (3.50 GHz) without relying on multi-core and GPU (graphics computing unit) computing.
As mentioned in Section 4, a limited sampling frequency, consecutive to speed acquisition or swept-source A-scan rate, can be compensated by reducing the FOV. This solution, particularly required for lower FR, is illustrated in Fig. 8. The same pattern is imaged three times with different FOVs without visibly affecting the quality. This assessment is supported by the close Perception based Image Quality Evaluator (PIQE) scores for the three images (78.58, 73.78 and 78.37). Figure 8(a) shows the "gator" acquired at a FR of 10 fps and a sampling frequency of 1 MHz, for which the FOV is reduced to 1.165 mm × 1.015 mm in the focal plane. The scanner is then driven by voltage amplitudes V = 325 mV for both axes, corresponding to a maximum angle of 4.45 • opt and a maximum power consumption of 72 mW. With a pixel size of 5 µm, the reduced FOV corresponds to 233 px × 203 px and maintains a FF of about 82%. When downsizing the FOV of the scan further to the size of the "gator" (770 µm × 475 µm), a frame rate of 20 fps can be reached at V x = 189 mV and V y = 120 mV ensuring a FF of 80%, as depicted in Fig. 8(b). Consequently, we show that for the same sampling frequency, the quality of an image can be maintained while increasing the frame rate by a reduction of the FOV and the driving voltage and power consumption as a result. Finally, even at high frame rate, the details of the image of the "gator" are preserved at 61 fps as shown in Fig. 8(c) with a reduction of 5 times the FOV obtained at 20 fps in Fig. 8(b). Voltages applied are also significantly lower: V x = 65 mV and V y = 70 mV entailing an angular amplitude of 1.18 • opt on both axes.
The sampling frequency limitation can also be expressed in terms of resolution. Scan resolution is the largest distance between two scattered points within the FOV, and is estimated by Delaunay triangulation [22]. As plotted in Fig. 9(a) for experimental points recorded at FR = 10 fps, the trend of the evolution of the resolution with respect to the sampling frequency drops quickly up to 100 kHz and slopes gently downward from this same frequency onward, barely affecting the resolution change. Note that the reduced FOV method at an under-sampled 1 MHz frequency, allows almost reaching the beam FWHM, i.e. 15 µm of optical resolution. Hence, a 10 times lower sampling frequency of 100 kHz only degrades the resolution by a factor 2 (30 µm). Resolution oscillations versus sampling frequency visible in the Fig. 9(a) are resulting from aliasing effect. The latter are created from f s < F CP and become predominant when f s < F CP /2. This tendency is mostly illustrated by the loss of details in the & pattern, between Figs. 9(b) and 9(c), remaining relatively low despite the significant sampling frequency drop from 1 MHz to 200 kHz, whereas an equivalent loss of details occurs over a smaller drop (from 200 kHz to 100 kHz) between Figs. 9(c) and 9(d). In Fig. 9(d), it is noticeable that the pattern & is illegible because the dimension of the (7.5 µm)-wide letters is not resolved anymore at that sampling rate. On the other hand, the femto-st pattern, whose lines are (30 µm)-wide, stays well-resolved at the different considered sampling frequencies. This is confirmed by the evaluation of an image comparison parameter such as the Structural SIMilarity (SSIM) index [42] that can be employed to compare digital images having the same FOV. When 1 MHz sampling frequency is taken as a reference (SSIM index = 1), the image quality only slightly deteriorates (index reduced by 3% of the entire dynamic corresponding to indices ranging from 0.58 at 2.5 kHz and 1 at 1 MHz) while the sampling frequency drops towards 200 kHz. At 100 kHz, the reduction is about 6% whereas it reaches 75% at 10 kHz.
Finally, another way to exploit the high frame rate capability of the scanner is to perform sequential stitching of elementary images acquired at a higher frame rate. This approach allows working at a very low level of voltage (70 mV pp ) while providing extended FOV (See Visualization 1). In addition, it may help to get rid of unwanted sample motions during acquisitions. In this framework, Fig. 10 provides an example of a tens of frames acquired at 61 fps swept along the femto-st sample and stitched together to recompose the full logo as a banner. Based on the same method, automated processes can be carried out to perform mosaicing [43,44].

Conclusions
It was demonstrated that an electrothermal MEMS scanner resonating on both of its axes around 1.2 kHz at about 15 dB could be used to perform real-time imaging thanks to Lissajous patterns. In particular, a method has been described to select the scan parameters in order to achieve high image qualities and proposes trade-offs whenever no high sampling frequencies are available. Furthermore, high frame rates are experimentally reported at very low voltages, e.g. 61 fps at 70 mV pp . Real-time quality images as large as 1.165 mm × 1.015 mm at 10 fps have been obtained despite a sampling frequency limited on purpose at 1 MHz. Finally, we show that adjusting the FOV makes the scanner compatible with A-scan rates of most of commercial SS-OCT.