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A low-distortion 3×3 interrogation algorithm requires the accurate parameters calibration of the 3×3 coupler-based Michelson interferometer. The ellipse fitting method with a frequency modulation conducted on the laser is one way that contributes to the implementation of the calibration. However, the unused dangling tail fiber of the 3×3 coupler-based Michelson interferometer generates a harmful echo and leads to an unexpected triple-beam interference. Consequently, it gives rise to a drastic fluctuation on the desired elliptical Lissajous figure, which damages the accuracy and stability of the calibration greatly. In this paper, the echo influence on the calibration is studied theoretically and experimentally. A theoretical model is built based on the coupled mode theory and the interference theory, which is verified by the experiment. According to the model, the echo coefficient, the input state of polarization and the length of the unused dangling tail fiber are three factors that affect the intensity of the fluctuation. Two practical methods of angle cleaving and pulse delay are adopted to suppress the echo influence and restore the accuracy of the calibration in the paper, which are both demonstrated to be feasible and stable. In the end, the suitable applications of the two methods are discussed, which are different for them due to their characteristics. This research has laid the foundation for the practical application of the frequency-modulation-based calibration to the 3×3 coupler-based Michelson interferometric probe.

A dielectric barrier discharge (DBD) in atmospheric pressure air was excited by a high-voltage pulse power supply. Capacitors with different capacitance were connected in the discharge circuit and their effects on discharge power calculation were evaluated. The average power deposited into the discharge were calculated by three different methods: 1) Lissajous figure; 2) product of voltage and current; and 3) watt-hour meter. Further studies showed that the capacitor with 10 nF was suitable for power calculation. At applied voltage of 9 kV, discharge power calculated by three methods were similar (around 25–27 W). However, with the increase of applied voltage, the discharge power obtained by product of voltage and current was far beyond the real value. Lissajous method has proven more appreciable for discharge power calculation in a pulsed plasma at high voltage. This study provides a practical guide for power calculation in a pulsed-driven DBD system.

As the light-emitting diode (LED) size gradually decreases, it is difficult to conventionally transfer an LED onto a donor substrate. In this paper, we propose a print transfer method that selectively transfers an LED onto a UV release tape, i.e., the donor substrate, via focused laser scanning with Lissajous patterns. We implemented an optical system based on focused laser scanning to perform selective transfer; this can adjust the scanning area immediately without changing the donor substrate size according to the LED size. Because the commercialized UV release tape is utilized as a donor substrate, the adhesion between the LED and donor substrate can be constantly maintained even after repeated experiments. In this study, several LEDs were transferred to a flexible printed circuit board—arranged in a circular and square shape to demonstrate a high degree of freedom of the system—and turned on.

In scan-based 3-D systems, the achievable measurement time is strongly restrained by the moving mass. This limitation can be relaxed, by scanning the optical path instead of moving the entire sensor, such that a higher measurement speed can be achieved. This article deals with the design, the control, and the measurement results of a scanning triangulation sensor, in which the illumination and reflection paths of the sensor are scanned by a fast steering mirror (FSM). The system architecture is determined using ray-tracing simulations, such that the performance of the scanning system can be determined in advance. To scan the area of interest with the FSM, conventional raster trajectories and Lissajous trajectories are employed, which provide an early overview of the scan area. For tracking these trajectories, PID and dual-tone controllers are used, respectively. The experimental results demonstrate that for both scan trajectories, the sample can be captured correctly, with a frame rate of 1 frame/s, a maximum spatial resolution of 130 $\mu \text{m}$ , and a field of view of $11.5\,\,\times 18.5\,\,{\mathrm{ mm}}^{2}$ .

We present software-based methods for automatic phase control and for mosaicing high-speed, Lissajous-scanned images. To achieve imaging speeds fast enough for mosaicing, we first increase the image update rate tenfold from 3 to 30 Hz, then vertically interpolate each sparse image in real-time to eliminate fixed pattern noise. We validate our methods by imaging fluorescent beads and automatically maintaining phase control over the course of one hour. We then image fixed mouse brain tissues at varying update rates and compare the resulting mosaics. Using reconstructed image data as feedback for phase control eliminates the need for phase sensors and feedback controllers, enabling long-term imaging experiments without additional hardware. Mosaicing subsampled images results in video-rate imaging speeds, nearly fully recovered spatial resolution, and millimeter-scale fields of view.

This paper proposes a phase modulation method for Lissajous scanning systems, which provides adaptive scan pattern design without changing the frame rate or the field of view. Based on a rigorous analysis of Lissajous scanning, phase modulation constrains and a method for pixel calculation are derived. An accurate and simple metric for resolution calculation is proposed based on the area spanned by neighboring pixels and used for scan pattern optimization also considering the scanner dynamics. The methods are implemented using MEMS mirrors for verification of the adaptive pattern shaping, where a 5-fold resolution improvement in a defined region of interest is demonstrated.

Aluminum nitride (AlN) started to draw attentions as a material for piezoelectric actuation owing to its CMOS process compatibility and safeness for biomedical applications. Due to its relatively low piezoelectric coefficients, AlN-based piezoelectric actuators have been mostly operated in resonance modes, especially in optical scanning. This paper presents a novel design of a 2-axis-tilt microscanner with AlN piezoelectric quad-actuators and meander-shaped hinges for reasonable quasi-static operation. Through finite-element-method simulation, it is shown that the proposed device can have about 9 degree of optical scan angle in two dimensions with the voltage amplitude of 50 V. Lissajous scanning operation of the device is demonstrated as well via simulation.

Parametrically-resonant micro-mirrors have proven highly effective in generating large amplitude, high-frequency motion for laser scanning in endoscopic microscopy, using Lissajous scan patterns to create a 2D image. However, Lissajous scanning produce low scanning density at the center of an image. In this work, a strategy for exciting additional harmonic behavior in a parametrically-resonant electrostatic micro-mirror is identified. The mirror’s nonlinear dynamics produce substantial changes in natural frequency with bias voltage. This allows a biased, duty-cycled square wave to produce higher harmonic oscillations that can be naturally synchronized with primary resonance in integer ratios. This in turn allows for alternate scanning distributions in 2D imaging that increase pixel sampling near the center of an image. In simulation, use of a biased square wave signal is found to be capable of producing steady-state oscillations at first and third harmonics of natural frequency for a micro-mirror operated via parametric resonance. Multiple harmonic motion is also realized without increasing input voltage amplitude beyond nominal amplitude, with a greater than 50% reduction fill time for the center of the imaging region. Parameterized relationships between input and output oscillations are identified, sensitivity of output trajectory to model variation, and impact on scanning density for a 2D MEMS micro-mirror are briefly described.

The Schmidt decomposition is exploited to study the spatial entanglement of laser transverse modes analogous to quantum Lissajous states. Based on the inverse Fourier transform, the stationary Lissajous state can be analytically derived as a coherent superposition of degenerate Hermite–Gaussian eigenmodes. With the derived stationary state, the Schmidt modes and the participation number N can be employed to evaluate the spatial localization and the quantum entanglement. The larger the participation number, the more localized is the stationary coherent state on the Lissajous figure. Moreover, the larger the participation number, the higher is the spatial entanglement.

This paper applies image processing metrics to tracking of perturbations in mechanical phase delay in a multi-axis microelectromechanical system (MEMS) scanner. The compact mirror is designed to scan a laser beam in a Lissajous pattern during the collection of endoscopic confocal fluorescence images, but environmental perturbations to the mirror dynamics can lead to image registration errors and blurry images. A binarized, threshold-based blur metric and variance-based sharpness metric are introduced for detecting scanner phase delay. Accuracy of local optima of the metric for identification of phase delay is examined, and relative advantages for processing accuracy and computational complexity are assessed. Image reconstruction is demonstrated using both generic images and sample tissue images, with significant improvement in image quality for tissue imaging. Implications of non-ideal Lissajous scan effects on phase detection and image reconstruction are discussed.

We propose a method for the design of metalenses generating and focusing so-called vector Lissajous beams (VLBs), a generalization of cylindrical vector beams (CVBs) in the form of vector beams whose polarization vector is defined by two orders (p, q). The designed metalenses consist of subwavelength gratings performing the polarization transformation of the incident linearly polarized laser beams and a sublinearly chirped lens term for the realization of the beam focusing. The possibility of using VLBs for the realization of laser beams with a complex Poynting vector is theoretically shown. The certain choice of orders (p, q) of the generated VLBs makes it possible to control the type of various electromagnetic field components as well as the components of the complex Poynting vector. For example, in contrast to VLBs, the classical types of CVBs cannot provide an imaginary part in the longitudinal component of the Poynting vector. Such light fields are promising for exciting non-standard forces acting on the trapped nano- and microparticles.

Light-transport represents the complex interactions of light in a scene. Fast, compressed, and accurate light-transport capture for dynamic scenes is an open challenge in vision and graphics. In this paper, we integrate the classical idea of Lissajous sampling with novel control strategies for dynamic light-transport applications such as relighting water drops and seeing around corners. In particular, this paper introduces an improved Lissajous projector hardware design and discusses calibration and capture for a microelectromechanical (MEMS) mirror-based projector. Further, we show progress towards speeding up the hardware-based Lissajous subsampling for dual light transport frames, and investigate interpolation algorithms for recovering back the missing data. Our captured dynamic light transport results show complex light scattering effects for dense angular sampling, and we also show dual non-line-of-sight (NLoS) capture of dynamic scenes. This work is the first step towards adaptive Lissajous control for dynamic light-transport.

A phase-shifted demodulation technique with a 3 × 3 coupler and ellipse fitting algorithm (EFA) for the interrogation of interferometric sensors is proposed. To reduce the error of the EFA as to measure small phase signals, additional phase modulation is introduced. The additional modulation provides a walk of the operating point along the Lissajous ellipse large enough to permit calculation of the ellipse parameters at every moment. Experimental result shows that this technique demonstrates high accuracy and stability for measuring small phase signals. The setting of this technology expands the application of the EFA in fiber-optic phase demodulation technology.

We report an objective-lens-free endomicroscopic catheter for compact Lissajous scanned confocal endomicroscopic system using a scanning lensed-fiber. The fiber scanner comprises a single-mode fiber (SMF) spliced with a coreless silica fiber segment and quadrupole piezoelectric tube. An objective lens was directly formed at the distal end of an SMF using a fusion splicer. The lensed fiber eliminates the need for conventional beam focusing elements such as a gradient index rod lens and precise optical alignment, allowing low cost and facile fabrication of an exceptionally short endomicroscopic catheter. The endomicroscopic scanner was fully packaged within a stainless tube of 2.6 mm in outer diameter and 20 mm in length, which can be easily inserted through the working channel of conventional laparoscope or colonoscope. The microscopic images of a stained kidney section and ear of a mouse were successfully obtained with the Lissajous scanning confocal endomicroscope. The compact Lissajous scanning lensed fiber can provide a new route for diverse in vivo endomicroscopic applications.

Lissajous curves have been used in various engineering applications such as optics, imaging, antenna scan, machining, as well as mobile robotics. In this article, we propose and analytically justify a Lissajous curve based trajectory planning strategy for aerial multi-agent systems to achieve the following objectives simultaneously: (i) Collision free paths for repeated coverage of a region while maintaining a closed sensor ring around a specified center for all time. (ii) Guaranteed detection of any stationary or moving object enclosed within the ring in finite time without the possibility of undetected escape. This leverages known and some novel properties of Lissajous curves that we establish as a part of this work. This has several potential applications in civil and military missions such as search and surveillance, repeated patrolling, target detection and capture, and the proposed strategy meets all these objectives simultaneously. We validate the proposed strategy through simulations and experiments using differential drive ground robots. We also demonstrate the applicability of this strategy for aerial surveillance through a Software-In-Loop-Simulation for quadrotors.

In this paper, a complete system of a frequency-modulated gyroscope with digital output for future low-power, high-stability, and wide full-scale applications is presented. The system includes the microelectromechanical transducer, two analog oscillators, two mixed-signal frequency to digital converters, and a fundamental mixed-signal block for the real-time extraction and digitization of the demodulation phase reference. With an overall consumption of 406 $\mu$ A, the system has a 90 dB dynamic range on a 50 Hz bandwidth, with a $\text{5 }^{\circ }$ /hr stability after 20-min observation interval, and a scale-factor drift coefficient of 20 ppm/K only.

The theoretical expression of the Gaussian beams carried singular Lissajous lines passing through an astigmatic lens is derived, which is used to study evolution behavior of singular Lissajous lines in the presence of an astigmatic lens. The singular Lissajous lines are unstable and disappears after passing through the lens. Being different from the case of a singular Lissajous line in which appearance of no singularities or only one singularity takes place, more singularities may appear in the field. Comparisons with the interaction of two singular Lissajous line in free-space propagation and in the presence of an ideal lens are made.

The invention of the nanotechnology adds a new branch to investigate and control the physical properties of matters at atomic level. The aim of this technology is to image the characteristics of metals, biological organs, and polymers. Scanning probe microscopy (SPM) opens a new branch to analysis the atomic properties of the matters. Atomic force microscopy (AFM), a branch of SPM, is a versatile tool of nanotechnology to image both conductive and non-conductive matters with high resolution. Commercial AFM uses raster scanning technique to produce image of the matters that is responsible for low scanning speed and image quality. The performances of AFM are hampered due to low bandwidth of the scanning unit and vertical Proportional-Integral (PI) controller and may damage the surface of the samples. Different non-raster scanning techniques such as sinusoidal, rotational, spiral, cycloid, and lissajous scanning have been proposed to overcome the limitations of raster scanning method by providing high scanning speed, image quality, and resolution. This paper presents a survey of raster and non-raster scanning methods for high speed AFM and provides a compression between them in term of scanning speed, bandwidth and highest achievable scanning frequency. The control techniques applied to the AFM for improving raster, sinusoidal, spiral, cycloid, and lissajous scanning methods are studied in this paper to find most optimum scanning technique for AFM.

The accuracy of phase shift extraction has a significant influence on measurement results in surface micro-topography interferometry. Phase shifting errors are mainly caused by nonlinearity of the employed phase shifter, environmental turbulence, camera imperfection and so on. In this paper, a general algorithm based on Lissajous figures and ellipse fitting is proposed for extracting the phase distribution from a set of phase-shifting interferograms with random noise. Two sets of pixels with π ∕ 2 phase difference in all the investigated interferograms are selected and used for ellipse fitting. Both numerical simulations and optical experiments have proven the validity, rapidity, and accuracy of the proposed method. Experiments show that the proposed method is a general phase extraction method, which can work for straight fringe patterns, circle fringes patterns and other anomalous features.

In this research, we present the feasibility testing results of a simple distance measurement system using microfabricated scanning micromirrors. Two different configurations have been tested with different types of micromirrors. In the first configuration, Lissajous scan pattern has been generated with horizontal scan frequency of 715 Hz, and the intensity of the laser beam reflected from the object has been measured with avalanche photodiode to estimate the distance. The position of the beam has been tracked using a separate position sensitive detector. Signals from both sensors are synchronized by eliminating the signal delay, which enables the detection of the distance of a specific point in the 2-dimensional scan pattern. In the simplified configuration, faster scanning micromirror with horizontal scan frequency of 28.8 kHz has been used to increase the resolution and position sensitive detector has been removed from the system by synchronizing the driving current waveform with the avalanche photodiode signals. Distance measurement from 20 to 50 cm has been demonstrated with the developed system.

A polarized laser beam steering system using multiply cascaded rotating polarization gratings (PGs) is presented. The rotating PGs steer incident circularly polarized beams with high optical throughput because the theoretical limitation of the PG diffraction efficiency is 100%. The system also offers more rapid rotation when compared with wedge prism pairs because of the weight of the PGs. The beam steering performance was analyzed theoretically for schemes using two and four rotating PGs. The system’s feasibility was demonstrated experimentally by projecting Lissajous and raster patterns using PGs fabricated from photocrosslinkable polymer liquid crystal films via a photo-alignment technique. The steered beam’s diffraction efficiency and ellipticity were maintained at 83 ∼ 89 % and 96 ∼ 99 % , respectively, during PG rotation. This beam steering system will be applicable to light detection and ranging, optical imaging, and laser displays.

Small-surface optical components with complex shapes and high-precision requirements are increasingly needed in the fields of mobile communications, in vivo diagnosis, and other fields. Some scholars have studied and proposed a two-dimensional vibration actuated polishing (2D-VAP) method based on small polishing tools for the preparation of small-surface optical elements. Using the nonresonant 2D-VAP device developed by the author, the frequency and amplitude of 2D-VAP are precisely adjusted to generate a random-like Lissajous polishing trajectory, which can overcome the problem that most of the existing 2D-VAP methods generate a circular or elliptical polishing trajectory at the small polishing tool, resulting in leaving periodic polishing marks on the workpiece surface. The removal function model under the condition of random-like Lissajous polishing motion with a small polishing tool is established. In addition, the removal function verification experiments and surface polishing experiments are carried out. The experimental results show that the measured removal function is in good agreement with that obtained by numerical simulation. Compared with the circular polishing trajectory, the random-like Lissajous polishing trajectory can significantly improve the material removal rate, and there are no obvious periodic polishing marks on the workpiece surface.

Increasing the field of view (FOV) of optical coherence tomography (OCT) for the high-resolution posterior eye imaging with a continuous scan is demonstrated. The combination of a Lissajous trajectory, which is designed for high-resolution imaging, and a slow drift was applied to scan the probing beam. The FOV is increased as the slow drift progresses. The motion artifacts are suppressed by motion estimation and correction in post-processing. The high-resolution, motion-free OCT and OCT angiography imaging with a FOV of over 6.75 mm is achieved.

Constructing an image acquired by a non-uniform scanning pattern is a difficult task. The main challenges are:(1) resampling technique (2) discrepancy between demanded (dictated by control signal) and actually performed, empirical scanning path. Here, we show how to calibrate the scanning path of MEMS scanner using Galvanometric Scanner and to what extent the time of acquisition impacts the resulting image.

An adaptive driving beam (ADB) for vehicle headlights has been developed using a microelectromechanical systems optical scanner. A piezoelectric scanner is constructed using thin-film lead-zirconate-titanate oxide (PbZrTiO3, PZT) on a bonded silicon-on-insulator (SOI) wafer, respectively, processed by ion-milling and deep reactive ion etching. The PZT layer is laminated in metal films on the SOI layer to form a piezoelectric unimorph actuator, which are then arranged as a pair of twisting suspensions to drive the scanner at resonance. The same piezoelectric actuators are also arranged into another form of meandering suspensions to generate a large deflection angle. By the combination of these two mechanisms, two-dimensional optical scanner is constructed in a single chip. The scanner is used to draw a Lissajous pattern of a blue laser light on a phosphor material to create a structured light source that is projected forward for illumination. The lighting patterns and positions are electronically controlled and reconfigured depending upon the location of leading/oncoming vehicles, pedestrians, road signs, and the cruising speed of the vehicle. The paper discusses on the design of the piezoelectrically driven optical scanner along with the optomechanical performances. We also report on the road-test result of the developed on-vehicle ADB module.

In order to overcome the coherence-induced artifacts, the illumination heterogeneity as well as a limited dynamic range when using full-field technique, a solution employing a galvanometric beam-steering is proposed, demonstrating the possibility for real-time imaging in terahertz domain. Working toward industrial applications, different imaging illumination process, including Lissajous pattern for fast beam steering, are evaluated thanks to the versatility of the lighting method.

Passive motion correction methods for optical coherence tomography (OCT) use image registration to estimate eye movements. To improve motion correction, a multi-image cross-correlation that employs spatial features in different image types is introduced. Lateral motion correction using en face OCT and OCT-A projections on Lissajous-scanned OCT data is applied. Motion correction using OCT-A projection of whole depth and OCT amplitude, OCT logarithmic intensity, and OCT maximum intensity projections were evaluated in retinal imaging with 76 patients. The proposed method was compared with motion correction using OCT-A projection of whole depth. The comparison shows improvements in the image quality of motion-corrected superficial OCT-A images and image registration.

This paper proposes an algorithm to reduce motion artifacts in Lissajous-scanned images taken from a custom-built endomicroscope based on microelectromechanical system (MEMS) laser scanning. The proposed algorithm uses an extended Kalman Filter to estimate uncertain perturbation to the position of the scanner relative to tissue during the Lissajous scan. The estimated states, which describe the estimated position perturbation to the scanner, are used to update the inferred laser trajectory during image reconstruction. To aid in estimation, the Jacobian matrix of a measurement function from other nearby points in the Lissajous pattern is computed using a trend of previous pixel values. For validation, the proposed algorithm was tested on both artificially generated blur images and real tissue images taken with the prototype confocal fluorescence endomicroscope. The reconstructed images with the estimated states showed reduced motion artifacts compared to the original images. The algorithm can be used in other single-pixel imaging applications that rely on beam steering technology to estimate the scanner’s real trajectory and reduce motion artifacts.

Experimental analyses of motions of a double-leg circle were conducted for a smooth and dynamic movement. A motion capture system provided the data for two different gymnasts; one is well trained and the other has an average skill level. Lissajous analysis was done for a tip-toe circling motion and a rolling motion around a longitudinal axis of a body. The results show that synchronization between the tip-toe circling and the body-rolling around the body’s longitudinal axis is crucial. Muscle activity was also analyzed from electromyogram data when the gymnasts performed double-leg circles, and the muscle activity characteristics of synchronized rolling-type circles were uncovered.

In most industrial applications, Fault Detection (FD) is an important function. Understanding equipment's conditions help engineers and operators avoiding the inevitable catastrophe that could lead to a significate impact on system reliability and safety. For electromechanical devices such as asynchronous motors, which play an essential role in production lines, mastering vibrations for Fault Detection is interesting. Downtime, costly maintenance, and energy waste are damages resulting from faults. The paper presents an overview of different techniques used in asynchronous motors fault detection. Vibrations signals processing and techniques for extracting characteristic features from them are largely developed. Spectrum analysis of the envelope signal is employed to process vibration signals resulting from rolling bearings. The paper also proposes rotors broken bars detection using Park Transformation. It was shown that Park's transformation is an effective tool to detect broken bars even at the incipient stage, which gives to it the merit to be a complementary technique to vibration analysis.

We propose a nanometer-scale displacement or vibration measurement system, using an optical quadrature interferometer and the post-processing technique that extracts the parameters necessary for characterizing the interferometric system. Using a 3 &times, 3 fiber-optic coupler, the entire complex interference signal could be reconstructed with two interference signals measured at two return ports of the coupler. The intrinsic phase difference between the return ports was utilized to obtain the quadratic part of the interference signal, which allowed one to reconstruct the entire complex interference signal. However, the two measured signals were appreciably affected by the unequal detector gains and non-uniform intrinsic phases of the coupler. Fortunately, we could find that the Lissajous curve plotted by the two signals of the interferometric system would form an ellipse. Therefore, by fitting the measured Lissajous curve to an ellipse, we could extract the parameters characterizing the actual system, which allowed the nanometer-scale measurement. Experimental results showed that a 20 kHz sinusoidal vibration with an amplitude of 1.5 nm could be measured with a standard deviation of 0.4 nm.

In this article, a compressive sensing-based reconstruction algorithm is applied to data acquired from a nodding multibeam Lidar system following a Lissajous-like trajectory. Multibeam Lidar systems provide 3D depth information of the environment, but the vertical resolution of these devices may be insufficient in many applications. To mitigate this issue, the Lidar can be nodded to obtain higher vertical resolution at the cost of increased scan time. Using Lissajous-like nodding trajectories allows for the trade-off between scan time and horizontal and vertical resolutions through the choice of scan parameters. These patterns also naturally subsample the imaged area. In this article, a compressive sensing-based reconstruction algorithm is applied to the data collected during a relatively fast and therefore low-resolution Lissajous-like scan. Experiments and simulations show the feasibility of this method and compare the reconstructions to those made using simple nearest-neighbor interpolation.

A rapid and precise phase-retrieval method based on Lissajous ellipse fitting and ellipse standardization is demonstrated. It only requires two interferograms without pre-filtering, which reduces its complexity and shortens the processing time. The elliptic coefficients obtained by ellipse fitting are used for ellipse standardization. After compensating phase-shift errors by ellipse standardization, the phase distribution is extracted with high precision. It is suitable for fluctuation, noise, tilt-shift, simple and complex fringes. This method is effective for the number of fringes less than 1. The reliability of the method is verified by simulations and experiments, indicating high accuracy and less time consumption.

This paper presents a 2D MEMS mirror for smart headlights, combing high-Q vacuum package with AR (Anti Reflecting)-coating, piezoelectric driving and Lissajous scanning. While the vacuum package protects the MEMS device and the AR-coating suppresses parasite reflections from the glass lid, the AlN-based piezoelectric actuators are robust against shock and vibration in harsh environment, comparing to fragile capacitive finger structures. This gimbal-less MEMS mirror with a large circular aperture (diameter = 5.5 mm) utilizes Lissajous scanning possessing two perpendicular torsion modes with frequencies of fx = 2.26 kHz, fy = 2.30 kHz fulfilling high light density and large total optical scanning angles of 55°, 30° at ± 40 VAC. A 2D projection of 50° x 20° was realized, where the angle loss comparing to the 1D testing arose from pincushion distortion, whose effect was severely reduced by the redesign run. Due to the great long-term stability of AlN and protection of vacuum packages, the MEMS mirror also shows a good reliability. This paper will describe and discuss the design, fabrication and characterization results of this MEMS mirror.

Optical coherence tomography (OCT) reveals the depth-resolved structure of the posterior eye non-invasively. However, artifacts caused by involuntary eye movement is one of the largest problems. Recently, we have demonstrated a motionartifact- free, high-resolution imaging technique based on Lissajous scanning pattern and advanced motion correction algorithm. Although this method works to a certain degree, the residual artifacts are still problematic for clinical applications. In this study, we demonstrate the improvement of motion correction for en-face OCT imaging. The OCT signals are acquired with a Lissajous scanning pattern which has been modified from a standard Lissajous scan to enable OCT angiography (OCT-A) imaging. The lateral motion is estimated from several en-face images of OCT and OCT-A by using a motion estimation algorithm. Some diseased eyes exhibit abnormal patterns in OCT en-face images. Simultaneously using these images will enhance the motion estimation and will improve the motion correction at these abnormal regions. Motion-free imaging for retinal diseases is demonstrated.

We design a new absolute optical instrument by composing Luneburg lens and Lissajous lens, and analyze its imaging mechanism from the perspective of simple harmonic oscillations. The imaging positions are determined by the periods of motions in x and y directions. Besides, instruments composed with multi parts are also devised, which can form imaging or self-imaging as long as the motion periods of x and y directions are satisfied to similar conditions. Our work provides a new way to analyze the imaging of different lens by simply dissociating the equations of motions, and reveal the internal mechanism of some absolute optical instruments., 4 pages, 4 figures; This is an application of simple harmonic oscillations when I am preparing the course of University Physics; Huashuo Han, Pinchao He, Keqin Xia, and Jiaxiang Zhang are undergraduate students in Xiamen University Malaysia

Dynamic biological systems present challenges to existing three-dimensional (3D) optical microscopes because of their continuous temporal and spatial changes. Most techniques are rigid in adapting the acquisition parameters over time, as in confocal microscopy, where a laser beam is sequentially scanned at a predefined spatial sampling rate and pixel dwell time. Such lack of tunability forces a user to provide scan parameters, which may not be optimal, based on the best assumption before an acquisition starts. Here, we developed volumetric Lissajous confocal microscopy to achieve unsurpassed 3D scanning speed with a tunable sampling rate. The system combines an acoustic liquid lens for continuous axial focus translation with a resonant scanning mirror. Accordingly, the excitation beam follows a dynamic Lissajous trajectory enabling sub-millisecond acquisitions of image series containing 3D information at a sub-Nyquist sampling rate. By temporal accumulation and/or advanced interpolation algorithms, the volumetric imaging rate is selectable using a post-processing step at the desired spatiotemporal resolution for events of interest. We demonstrate multicolor and calcium imaging over volumes of tens of cubic microns with 3D acquisition speeds of 30 Hz and frame rates up to 5 kHz.

The characterization of a MOEMS endoscopic OCT probe is presented. Its capacity to perform Lissajous scanning and OCT imaging confirms that the probe is able to produce 3D OCT images in real-time.

The work presents a detailed modeling and the first-ever characterization of a frequency modulated (FM) yaw gyroscope in presence of vibrations from low frequency (30 Hz), through the main modes, and up to 40 kHz. The gyroscope two in-plane axes (around 25 kHz) are operated under a Lissajous trajectory (70 Hz period) by an integrated circuit (IC) including oscillators, frequency digitization, and digital demodulation stages. In presence of $2-g_{pk-pk}$ vibrations, no effects are visible across the spectrum apart from the region including the modes. In this range, as predicted by theory, for each axis no effect is observed for accelerations at the axis resonance (< 0.1 dps/g), but a huge effect (tens of dps/g) is visible for accelerations at an offset frequency from resonance corresponding to the mode split.

Charge transportation expressed as a Lissajous figure usually is a standard method for the analysis of discharge power and energy in surface dielectric barrier discharge (SDBD). In this paper, the charge transportation characteristics under different parameters of power supply and actuator configurations are investigated, and the mechanisms of two typical Lissajous figures are discussed theoretically. Experimental results show that when the plasma distribution is quasi-diffuse mode, the Lissajous figure is almond shape correspondingly, while the plasma distribution looks like separated-channel mode, the Lissajous figure presents a parallelogram shape. Based on an improved time-varying lumped-element circuit model, two equivalent circuits of SDBD under two plasma distributions are built, and the Lissajous figures are calculated theoretically. Calculations and analysis results indicate that the two kinds of Lissajous figures under different plasma distribution modes are due to the current pulse durations and equivalent dielectric capacitances caused by plasma distributions acting together. The protrusions of Lissajous figures are caused by the current narrow pulses in the characteristics of separated-channel mode, while Lissajous figures under quasi-diffuse mode have no protrusions.

The frequency ratios for the just diatonic scale are obtained by identifying musical intervals corresponding to Lissajous figures. The demonstration integrates the engineering physics of Lissajous patterns with the recognition of musical intervals through simple ear training. A free HTML5 app has been developed for this class activity and the program can be run online or downloaded to the desktop. A video is provided illustrating the use of the software.

Magnetic pulse compression (MPC) systems are suitable for generating dielectric barrier discharges (DBDs) owing to their capability of producing high-amplitude, short pulse voltage waves. This paper proposes a high-frequency, bipolar magnetic compression system to study DBD plasma characteristics. First, the principle of bipolar MPC is explained [a bipolar MPC system comprises a full bridge inverter circuit, pulse transformer (PT), and magnetic switch (MS)]. Additionally, the design of the PT and MS is described. Then, the waveform of the resistive load is tested and compared with PSpice simulation results. It was found that the nanosecond pulse generator produces a pulse on a resistor with an amplitude of 0–13 kV, a rise time of approximately 100 ns, and a repetition frequency of 0 to several kHz. Finally, this paper studies the plasma characteristics under the application of a high-frequency bipolar pulse, and the charge–voltage Lissajous figure of the discharge waveform is analyzed. Combining discharge photographs and theoretical calculation results yields the relationship between the discharge characteristics and the frequency, which enriches the theoretical study of high-frequency bipolar discharges.

The linear response is the key property employed by a radiation detector to determine the accurate intensity of a pulse radiation field. In this study, we investigated the high fluence rate response behavior of a LaBr3 scintillator. We used a high-intensity pulsed X-ray source called “QiangGuang-I” which could produce an X-ray pulse with a total dose of 100 Gy, full width at half maximum of 20 ± 5 ns, and an average energy of 1 MeV, to test the linear response of the LaBr3 scintillator. The Lissajous figure method was used in this experiment. The results showed that the fluence rate linear response limit was more than 1.8 × 1020 MeV/(cm2·s).

This paper presents a novel online diagnostics method capable of detecting winding deformations in two-winding single-phase transformers. The main idea is to identify changes in the short-circuit impedance. The combination of 3-D Lissajous curve methods with a Butterworth low-pass filter allows for the accurate determination of winding deformation of large power transformers in real time. The method is very robust and capable of detecting deformations at the early stage even when the measurements are noisy. Only information already available to the differential protection relay is needed. The proposed diagnostics method has been validated with circuit and finite-element simulations plus a lab experiment. The results show that the proposed online diagnostics technique has the ability to identify winding deformation problems under severe conditions, such as nonsinusoidal input, nonlinear loading, and measurement noise. Under ideal conditions (no signal noise), the inductive identification error of the proposed online diagnostics method identifies the parameters with less than 0.09% error. When accepting a measurement noise of 1%, the error on the identification of inductance is less than 0.13%.

We present a novel stereolithographic three-dimensional (3D) printing process that uses Lissajous trajectories. By using Lissajous trajectories, this 3D printing process allows two laser-scanning mirrors to operate at similar high-speed frequencies simultaneously, and the printing speed can be faster than that of raster scanning used in conventional stereolithography. In this paper, we first propose the basic theoretical background for this printing process based on Lissajous trajectories. We also characterize its printing conditions, such as printing size, laser spot size, and minimum printing resolution, with respect to the operating frequencies of the scanning mirrors and the capability of the laser modulation. Finally, we demonstrate simulation results for printing basic 2D shapes by using a noble printing process algorithm.

Signal distortion is a key issue that limits the measurement resolution and accuracy of optical encoders. In this paper, an optical encoder based on generalized grating imaging using a two-dimensional index grating is presented. The general expression of intensity distribution for generalized grating imaging including the relative displacement between the scale grating and the reading head is derived, and the formation of the signal distortion of the optical encoder is analyzed. Then, a two-dimensional index grating, which consists of multiple grating tracks with defined offsets, is proposed to suppress the dominant third and fifth order harmonic signals. The operating principle of the two-dimensional index grating is explained in detail and a reflective optical encoder is developed. In the experiment, approximately ideal Lissajous figure of the encoder signals is obtained. Fourier analysis of the encoder signals shows that both the third and fifth order harmonic distortions are below 0.6%. Experimental results show that the interpolation error of the optical encoder is within ± 0 . 18 μ m, and the accuracy is better than ± 0 . 3 μ m over 255 mm travel range with a maximum variation of 0.136 μ m.

In this paper, we present non-uniform subdivision schemes with variable parameter sequences. A locally different tension parameter is set at each edge of the initial control polygon to control locally the shape of the resulting curve such that the scheme becomes non-uniform. Due to the variable parameters, the scheme can reproduce locally different analytic curves such as conics, Lissajous, trigonometric and catenary curves. Hence blending curves including such analytic components can be successfully generated. We discuss the convergence and smoothness of the proposed non-uniform schemes and present some numerical results to demonstrate their advantages in geometric modeling. Furthermore, as an application, we propose a chamfering algorithm which can be used in designing automobile and mechanical products.

The formation of the resultant raster trajectories in machine tools are established on the basis of Lissajous figures, taking account of additional workpiece motion for finishing purposes. Kinematic and geometric formulas are obtained for the relative tool and workpiece trajectory with strict kinematic coupling. These formulas are required in practice for abrasive lapping. They permit control of the resultant abrasive-cutting trajectory in finishing the precision planes of the workpiece.