KR20200019102A - Driving Method for MEMS Mirror Scanner and Driving Device for MEMS Mirror Scanner using the method thereof - Google Patents

Abstract

The present invention relates to a MEMS mirror scanner driving method in which a mirror can rotate around an x-axis and a y-axis perpendicular to the same. The method comprises the steps of: obtaining a transfer function (T (f)) of a MEMS mirror scanner; setting a target time series output signal (d(t)) for mirror driving of the MEMS mirror scanner; converting the target time series output signal (o(t)) into an output signal (D(f)) of a Fourier target frequency domain; obtaining an input signal (V(f)) of a frequency domain from the target frequency domain output signal (D(f)) and the transfer function (T(f)) of the MEMS mirror scanner; converting the input signal (V(f)) of the frequency domain into a time series input signal (v(t)); and applying the time series input signal (v(t)) as a driving voltage to the MEMS mirror scanner. The present invention can effectively suppress unwanted residual vibration appearing in an output.

Description

Driving method for MEMS mirror scanner and MEMS mirror scanner using the above method

The present invention relates to a method for driving a MEMS mirror scanner and a device for driving a MEMS mirror scanner using the above method. MEMS mirror scanner driving apparatus using the method.

MEMS mirror scanner is a compact micro system that can drive two axes with only one mirror. In general, as shown in FIG. 1, in the MEMS mirror scanner, comb electrodes are disposed on the top, bottom, left, and right sides of a mirror disposed in the center, and a pair of comb electrodes adjacent to each other according to a signal applied to the comb electrode is disposed. The attraction due to electrostatic force is generated. Due to the above attractive force, the mirror is rotated about the hinge axis (elastic part) in the x axis or the y axis. Hereinafter, the driving in the x-axis direction will provide a driving force to rotate the mirror about the x axis, and the driving in the y-axis direction will be used to mean that the driving force is provided to rotate the mirror about the y axis.

In particular, the electrostatic driving method has advantages in terms of small size, low power consumption, and integration, and thus is widely applied in fields such as OCT, laser projection, and LiDAR. In such an imaging system, even if the optical scan angle (OSA) of scanning is the same, the usable scan range (USR) varies according to the nonuniformity of the beam steering speed.

2 (a) and 2 (b) show the nonuniformity of the scanner maximum driving angle and speed in the time domain according to the scanning output waveform, and from the USR perspective, FIG. 2 (b) Triangular scanning as shown in FIG. 2A has a wider uniform scan velocity range than sinusoidal scanning as shown in FIG. In this constant velocity scanning state, since the data point interval of the image is constant, no post processing is required, and thus the frame rate can be increased.

When a triangular input (voltage) is applied to the MEMS mirror scanner to obtain a triangular scanning output, one of the harmonics of the triangular input is close to the frequency of the torsional mode of the MEMS mirror scanner. Undesired residual oscillations can occur, which can affect the scanning output and cause severe image distortion. For reference, such a problem may be problematic for various types of inputs having harmonic components as well as triangular inputs.

FIG. 3 (a) shows an experimental result of a steady-state respose of the MEMS mirror scanner when a voltage of a triangular waveform of 20 Hz is applied to the MEMS mirror scanner. Here, although the dominant frequency of the optical scanning angle (OSA), which is an output value, is 20 Hz, it can be seen that many frequency components of undesired residual oscillation are loaded. In order to analyze the reason for the unwanted vibration, the Fourier transform of the input signal (triangle waveform) is shown in blue, and the transfer function of the MEMS mirror scanner is shown in black in FIG. 3 (b). Here, despite the fact that 260 Hz of the harmonics of the input signal have a small amplitude, it is close to the main resonance frequency (264 Hz) of the MEMS mirror scanner. Will be generated.

 Figure 3 (c) shows the OSA output value when the frequency of the input signal is 44 Hz, it can be seen that the residual vibration is less severe than when the input signal is 20 Hz, which can be seen from Figure 3 (d) As can be seen, the harmonic (220 Hz) of the input signal is relatively far from the resonant frequency (260 Hz) of the MEMS mirror scanner.

There are prior studies to solve this problem, and it is divided into open-loop control method and closed-loop control method. In input shaping with open loop control, the transfer function is measured by first measuring the frequency response of the MEMS mirror scanner and then fitting it to a 2nd order dynamic model. Obtain By applying the extracted shape input signal to the MEMS mirror scanner, unwanted residual vibration can be reduced. However, waveform error occurs when the second order transfer function does not accurately represent the spectral data for the fundamental mode. Moreover, there is a disadvantage in that undesired residual vibrations can not be avoided if there are higher order mode components that cannot be ignored.

On the other hand, the closed loop control method may move the mirror at a desired driving speed by feeding back an output of a positioning sensor. Closed loop control schemes of MEMS mirror scanners have been studied in recent years, and the angular position error of mirrors can be further reduced by additionally using a second transfer function extracted from the open loop control scheme. The closed loop control method is robust against incomplete secondary dynamic modeling, residual oscillation, and external disturbance, thereby achieving an accurate response compared to the open loop control method.

However, despite the advantages of this closed loop control, a positioning sensor must be added to the MEMS mirror scanner, where on-chip MEMS position sensors include capacitive or piezo-resistive sensors. (piezoresistive sensor) is used. However, IC integration is required for capacitive sensors, and temperature dependence exists for piezoresistive sensors. May occur.

United States Patent Application Publication US6,795,225 (2004.09.21.) US published patent US2008 / 0061026 (2008.03.13.)

The present invention reduces costs by adopting a low cost open loop control method instead of a closed loop control method which requires a high cost, and at the same time a problem of the conventional open loop control method (the transfer function is a spectrum for the main mode. Waveform errors due to inaccurate representation of the data, or unwanted residual vibration due to the neglect of higher order modes that cannot be ignored).

The present invention relates to a method of driving a MEMS mirror scanner in which a mirror can rotate about an x axis and a y axis perpendicular thereto, the method comprising: obtaining a transfer function T (f) of the MEMS mirror scanner; Setting a target time series output signal d (t) for driving the mirror of the MEMS mirror scanner; Converting the target time series output signal o (t) into an output signal D (f) in a Fourier target frequency domain; Obtaining an input signal V (f) in the frequency domain from the target frequency domain output signal D (f) and a transfer function T (f) of the MEMS mirror scanner; Converting the input signal V (f) in the frequency domain into a time series input signal v (t); And applying the time series input signal v (t) as a driving voltage to a MEMS mirror scanner.

The transfer function T (f) converts an x-axis frequency domain output signal O _xx (f) obtained by Fourier transforming an x-axis time series output signal o _xx (t) and an x-axis time series input signal i _x. and an x-axis transfer function T _x (f) obtained by dividing (t)) by the Fourier transformed x-axis frequency domain input signal I _x (f).

The process of calculating the x-axis transfer function T _x (f) using the x-axis frequency domain input signal I _x (f) and the x-axis frequency domain output signal O _xx (f) is repeated a plurality of times. The final x-axis transfer function T _x (f) may be determined by averaging the x-axis transfer function T _x (f) calculated repeatedly.

Furthermore, the transfer function can be theoretically determined by extracting the vibration characteristics through the computer simulation of the x-axis of the MEMS mirror scanner. Since the movement in the z-axis direction as well as the rotation about the x- and y-axes can be measured as the rotational movement, the residual vibration due to this higher-order mode can affect the scanning output. Therefore, we calculate the theoretical transfer function for the higher-order mode that affects the measurement, calculate the theoretical transfer function for crosstalk that the y-axis drive affects the movement of the x-axis, and then add all the theoretical transfer functions obtained earlier to obtain the final x The axis transfer function T _x (f) can be determined.

The target time series output signal d (t) is an x-axis target time series output signal d _x (t), and the x-axis target obtained by Fourier transforming the x-axis target time series output signal d _x (t). Multiplying the frequency domain output signal D _x (f) by the x-axis transfer function T _x (f) to obtain an x-axis frequency domain input signal V _x (f), and the x-axis frequency domain input signal V _A driving voltage is applied based on the x-axis time series input signal v _x (t) obtained by inverse Fourier transforming _x (f).

Furthermore, the transfer function T (f) is a frequency domain output signal obtained by Fourier transforming the x-axis time series output signal o _xx (t) generated by the x-axis time series input signal i _x (t). An xx transfer function (T _xx (f)) obtained by dividing (O _xx (f)) by the x-axis time series input signal i _x (t) by a Fourier transformed frequency domain input signal I _x (f). ; The frequency domain output signal (O _xy (f)) obtained by Fourier transforming the y-axis time series output signal (o _xy (t)) generated by the x-axis time series input signal (i _x (t)). An xy transfer function T _xy (f) obtained by dividing the input signal i _x (t) by the Fourier transformed frequency domain input signal I _x (f); The frequency domain output signal O _xy (f) obtained by Fourier transforming the x-axis time series output signal o _yx (t) generated by the y-axis time series input signal i _y (t), and the y-axis time series An yx transfer function T _xy (f) obtained by dividing the input signal i _y (t) by the Fourier transformed frequency domain input signal I _y (f); And a frequency domain output signal O _yy (f) obtained by Fourier transforming the y-axis time series output signal o _yy (t) generated by the y-axis time series input signal i _y (t), and the y-axis direction. And a yy transfer function term (T _yy (f)) obtained by dividing the time series input signal i _y (t) by the Fourier transformed frequency domain input signal I _y (f).

In another embodiment, the step of obtaining the transfer function T (f) may be performed by analyzing the vibration characteristics of the x-axis and the y-axis through computational simulation of the MEMS mirror scanner, and then theoretically Find the theoretical transfer function for the fundamental resonance, calculate the theoretical transfer function for the higher-order mode that affects the measurement, apply pulse signals independently to the x- and y-axes, and measure the displacement of different axes to cross each axis. Calculate the theoretical transfer function for torque and add all the theoretical transfer functions obtained earlier, and the xx transfer function term (T _xx (f)) where x-axis drive affects the x-axis, xy where x-axis drive affects the y-axis Transfer function (T _xy (f)), yx transfer function whose y-axis drive affects the x axis (T _yx (f)), yy transfer function term that y-axis drive affects the y axis (T _yy (f) It is characterized in that it comprises a)) extracting.

The target time series output signal d (t) includes an x-axis target time series output signal d _x (t) and a y-axis target time series output signal d _y (t), each of which is Fourier-transformed by Obtaining a target frequency domain output signal D _x (f) and a y-axis target frequency domain output signal D _y (f),

It is characterized by obtaining the x-axis frequency domain input signal V _x (f) and the y-axis frequency domain input signal V _y (f).

The x-axis time series input signal v _x (t) and the y-axis obtained by inverse Fourier transforming the x-axis frequency domain input signal V _x (f) and the y-axis frequency domain input signal V _y (f), respectively. The driving voltage may be applied based on the time series input signal v _y (t).

Furthermore, after driving the device of the MEMS mirror scanner by applying a driving voltage, feedback control may be performed to approach a desired output angle when there is a position error.

The experimentally obtaining the transfer function T (f) of the mirror scanner may be based on frequency data obtained through a frequency sweep test or an impulse response test.

The experimentally obtaining the transfer function T (f) of the mirror scanner may be based on frequency data obtained by averaging frequency data obtained through a plurality of frequency sweep tests or an impulse response test. can do.

It is possible to extract the transfer function more accurately for the main mode than the existing open loop control method, and also to effectively remove the effect even when the higher order mode exists.

1 illustrates a top view of a conventional MEMS mirror scanner.
2 shows usable scan range according to the output waveform ((a) sine wave, (b) triangle wave).
Figure 3 shows the dynamic response of the MEMS mirror scanner at 20 Hz and 44 Hz triangular wave inputs (driving voltage: 10V).
4 shows an electrode state of the MEMS mirror scanner ((a) initial state, (b) driving voltage application state).
5 shows the experimental characteristics of a MEMS mirror scanner for linearized driving with respect to the driving voltage.
6 shows an experimental setup for obtaining a transfer function of a MEMS mirror scanner.
7 is an experimental result for obtaining a transfer function of a MEMS mirror scanner, (a) shows an input impulse, (b) shows an output response, (c) shows a transfer function, and (d) shows an average value of the transfer function. Doing.
8 illustrates the output value in the time domain when ISETF according to the present invention is applied as an input value to a MEMS mirror scanner.
9 is an analysis result of ISET for various driving voltages (driving frequency 20 Hz, sampling frequency 50 kHz).
FIG. 10 analyzes input shaping with increasing driving voltage for 1.0% and 1.5% SLE.
11 shows ISET analysis results for various driving frequencies (driving voltage 25V, sampling frequency 50 kHz).
FIG. 12 analyzes input shaping with increasing driving frequency for 1.0% and 1.5% SLE.
13 to 18 are flowcharts illustrating each step of a method of driving a MEMS mirror scanner in various embodiments.

Looking at the characteristics of a single electrostatic actuator in a MEMS mirror scanner, there is inevitably a nonlinearity between the drive voltage and the torque since the driving force is proportional to the square of the voltage. However, in the case of having an electrode structure capable of applying different voltages to a pair of drivers, the torque with respect to the driving voltage may be linearly proportional. This V-linearization makes it possible to apply an Input-Shaping based on Experimental Transfer function (ISETF) to the system, described below.

The initial electrode state of the MEMS mirror scanner used in the embodiment of the present invention has a titled stationary comb (TSC) structure as shown in FIG. In order to perform V-Linearization with respect to the MEMS mirror scanner, as shown in FIG. 4 (a), the ground is applied to the first fixed electrode 101 and the bias voltage Vb is applied to the second fixed electrode 102. ) And driving voltages Vd + Vb / 2 are applied to the first and second driving electrodes 201 and 202 coupled to the mirror 200, respectively.

In this case, torques T1 and T2 applied by the first fixed electrode 101 and the second fixed electrode 102 to the first driving electrode 201 and the second driving electrode 202, respectively, are represented by Equation 1 below. It is proportional to the square of the voltage (V). However, the total torque T applied to the mirror 200 shows that the signs of the torques T1 and T2 are opposite to each other, and thus are finally proportional to the voltage V as shown in Equation (3). Under this application condition, when the driving voltage Vd is 0, the initial state is maintained as shown in FIG. 4 (a). When the driving voltage Vd is larger than 0, the driving voltage Vd rotates counterclockwise (angle in positive). Is shown in Fig. 4 (b). Although not shown in the drawing, a person skilled in the art will appreciate that the mirror 200 will rotate clockwise when the driving voltage Vd is negative.

As shown in Equation 1 (3), the electrostatic torque is proportional to the rate of change of capacitance. The result of measuring the optical scan angle (OSA) according to the DC voltage under the V-linearization condition is shown in FIG. 5, wherein the bias voltage (Vb) is 130V and the driving voltage (Vd) is in the range of − 65 V <Vd <65 V. According to the measurement result, the change in capacitance is within 1% in the range of -5 ° to 5 °, but when it is out of the above range, the capacitance changes rapidly, due to this capacitance nonlinearity (capacitive nonlinearity). It can be seen that the driving angle is saturated. This C-nonlinearity occurs because the rate of change in capacitive power proportional to the electrostatic torque is constant in the range where the driving angle is small, but decreases when the driving angle becomes larger.

The transfer function describes the relationship between input and output in the frequency domain. Such a transfer function is typically obtained through a frequency sweep test and an impulse response test. Frequency sweep tests can yield accurate transfer functions, but they are complex and time-consuming because they measure amplitude and phase by frequency. On the other hand, in the impulse response test, the transfer function is obtained by applying the pulse input signal once, but the pulse width must be short enough to sufficiently include the frequency component.

In this example, the performance of ISETF obtained from the impulse response test will be evaluated. The driving frequency is short enough (500 μs) so that at least 6 frequency components can be included even at 300 Hz, which is higher than the resonance frequency (264 Hz) of the scanner. The sampling frequency was 50 kHz, including the 10th harmonic of the maximum driving frequency (300 Hz) and sufficiently higher than the Nyquist criterion, and the sampling time was determined to be 1 second so that the frequency interval was 1 Hz.

The transfer function of the MEMS mirror scanner can be calculated from the response signal of the MEMS scanner when the impulse signal is applied. When the impulse input signal and the corresponding output signal of the applied time domain are i (t) and o (t), respectively, I (f) and O (f) of the Fourier transformed frequency domain are obtained. By dividing O (f) by I (f), the transfer function of the MEMS mirror scanner, T (f), can be obtained.

The setting of the test apparatus for obtaining the transfer function is as shown in FIG. The pulse signal generated through the function generator, preferably the two-channel function generator 301, is amplified by the amplifier 302 and then supplied as an input signal to the driving electrode of the mirror 200. After the laser beam generated by the laser generator 303, specifically, the laser diode is incident on the mirror 200 of the MEMS mirror scanner, the position information of the laser beam reflected by the mirror 200 is PSD 304; sensitive detector). At this time, in order to minimize the trigonometric error (trigonometric error), the laser incident direction and the axis of rotation of the mirror 200 is aligned so that the laser beam reflected at the initial position of the mirror 200 is perpendicular to the PSD 304 Incident in the direction. The signal processing module 305 calculates position information of the laser beam that reaches the PSD 304 as x and y axis coordinate values, respectively. The PSD signal collected for one second was digitized at 50 kHz through an oscilloscope 306 to extract a total of 50,000 data. The data extracted through the oscilloscope 306 is information about the displacement, but converted to OSA to eliminate the influence of trigonometric error.

[Impulse Response]

When the transfer function of the MEMS mirror scanner is obtained through the impulse response, the characteristics of the system reflected in the transfer function may vary depending on the width and magnitude of the pulse. Therefore, the pulse width was set short enough to 500 μs as described above, and since ISETF is applied to the linear system, the size of the pulse was set so that OSA came out within the range where C-nonlinearity did not appear.

In order to obtain an experimental transfer function (ISETF), a pulse input as shown in FIG. 7 (a) was applied to measure the time series observation value of OSA as shown in FIG. 7 (b). 7 (c) shows the obtained ETF, in which noise was carried out not only in the high frequency region but also in the low frequency region. In order to reduce the influence of measurement noise, the average of 10 repeated experiment data was averaged to obtain a final ETF as shown in FIG. Compared to FIG. 7 (c), the noise is significantly reduced in the entire frequency domain, and it can be seen that the higher peaks of the resonance frequency exist at 527 Hz and 790 Hz (before the noise removal, the higher peaks of the resonance frequency are buried in the noise. No). In general, the conventional open loop control method that second-orders the transfer function of the MEMS mirror scanner can express only the first mode. The proposed method is not only the higher peaks of the resonant frequency but also the second-order third mode or resonance. It can also include harmonic components of the frequency, there is an advantage that can eliminate the unwanted residual frequency for this. In the above embodiment, the average value was obtained from the results of ten experiments, but a person skilled in the art would readily recognize that the number of times may be adjusted as needed.

[INPUT SHAPING FOR TRIANGLE SIGNAL OUTPUT]

A desired output signal, here a triangular waveform, is set to d (t), and the input signal is shaped by using the ISETF method so that the output value is d (t).

(1) First, d (t) is Fourier transformed to obtain D (f). Since d (t) is an ideal mathematical model, it can be easily calculated using a program like matlab.

(2) Next, by dividing D (f) by T (f), which is a transfer function of the MEMS mirror scanner, as shown in Equation 3, the shaped input signal V (f) in the frequency domain can be obtained. Here, T (f) can be experimentally derived by the above-described ISETF method.

(3) The input signal v (t) in the time domain is obtained through the fast inverse FFT of the shaped input signal V (f).

(4) Store v (t) in the function generator and call v (t) as the input signal value when an output value such as d (t) is needed.

In order to examine the performance of ISETF obtained from the above process, the range of OSA is set from -1 ° to 1 °, the triangular output value having a frequency of 20 Hz is set to the ideal target value d (t), and the method presented above. After shaping the input signal to obtain v (t), the MEMS mirror scanner was driven using v (t).

In FIG. 8 (a), the red dotted line is an unshaped triangular signal, and the black solid line is an input signal shaped using ISETF. 8 (b) shows a red dotted line as an output value to be obtained, that is, d (t) and a solid black line is an output value actually obtained when v (t) is used as an input signal. The solid blue line shows the difference between the above two output values, and it is confirmed that the actual output value follows the output value (d (t)) to be obtained with a slight error while greatly reducing the unwanted residual oscillation (undesired residual oscillation). Could.

[Drive voltage]

As mentioned above, to examine the limitation of the application of ISETF to the effect of C-nonlinearity, the output value was checked by changing the input voltage (Vd). As shown in Fig. 8 (b), the red dotted line is the output value to be obtained, that is, d (t) and the black solid line is the output value actually obtained when v (t) is used as the input signal. The solid blue line shows the difference between the two outputs. 9 (a) shows Vd = 10V, FIG. 9 (b) shows Vd = 35V, FIG. 9 (c) shows Vd = 45V and FIG. 9 (d) shows Vd = 65V, when Vd = 35V. Until the residual vibration is maintained at a level that can be ignored, it was confirmed that it is difficult to ignore the residual vibration at the Vd = 65V level.

Furthermore, a criterion called scan line error (SLE) is defined to quantitatively analyze how close the ideal triangular waveform is to the scanning output value. For example, in a raster scan having 100 uniform scan lines, when a position of a scan line deviates by n intervals of scan lines, SLE = (n lines / 100 scan lines) x 100%. As a final performance index (PI), the Usable Scan Range (USR) described in FIG. 1 is used, which is a value obtained as a percentage of the entire range of a length satisfying a given SLE criterion. In order to verify the validity of the USR according to the defined SLE, the normalized root mean square error (NRMSE) was also calculated. Total Optical Scanning of a MEMS Mirror Scanner Linearized with USR (Based on SLE 1.0%, 1.2%, and 1.5%) and NRMSE According to Drive Voltage Vd (t) with Drive Voltage (DC) Shown in FIG. As shown in FIG. 10.

As shown in FIG. 10, when the SLE is 1.5%, the USR has a wide USR of 96% or more in the region where the driving voltage is 15V (TOSA 3.4 °) to 40V (TOSA 9 °), and when the driving voltage is higher or lower, It can be seen that the fall dramatically. At low voltages of 5V (TOSA 1.2 °) -10V (TOSA 2.2 °), the USR is small, even though the scanning output is close to a triangular waveform. This is because the SLE, which defines the USR, changes the reference value according to the scan angle, which indicates a relatively larger SLE for low scan angles, even if the scanning output varies with respect to the linear fitting line. Means. This is because the lower the driving voltage, the smaller the driving angle OSA, and thus the greater the influence of noise. On the other hand, USR and NRMSE deteriorate even at high voltages above 45V (TOSA 9.8 °).

The reason for this is the influence of the section (C-nonlinear) where the capacitance change rate between electrodes which directly affects torque increases as the driving angle increases, and the CTF nonlinear because the ETF contains linear system information of the C-linear section. This is because the scanner is driven in this large area (i.e., because the ETF contains linear system information of the C-linear interval, and as a result, the larger the C-nonlinearity, the larger the difference with the desired scanning output).

When the USR was calculated with SLE 1.0% and 1.5% under more stringent conditions for the scanning output, the voltage range with high USR values of 80% or more narrowed from 20V (TOSA 4.5 °) to 30V (TOSA 6.7 °). On the other hand, an increase in NRMSE when the USR is small proves that the USR is valid as a PI.

[Drive frequency]

The purpose of this study is to investigate the limitation of application of input-shaping with increasing driving frequency. On the other hand, the higher the sampling frequency, the higher frequency term (high frequency term) can be considered, so that the scanning output can be more easily approached to the desired waveform. Therefore, in the present specification, the driving frequency is changed at a fixed state of 50 kHz so as not to be affected by the sampling frequency, and the result is shown in FIG. 11. Fig. 11 (a) is 20 Hz, Fig. 11 (b) is 40 Hz, Fig. 11 (c) is 160 Hz, and Fig. 11 (d) is 300 Hz. Here, the red dotted line is the output value to be obtained, that is, d (t) and the black solid line is the output value actually obtained when v (t) is used as the input signal. The solid blue line shows the difference between the two outputs.

The voltage was Vd = 50V which was judged to be a good USR region, and the scanning outputs were analyzed for SLE and d NRMSE.

Referring to the analysis result shown in FIG. 12, it can be seen that the scanning output is very close to an ideal triangular waveform with USR of 90% or more up to 80 Hz, which is a low frequency band based on SLE 1.5%. However, from 90Hz to 220Hz, the USR value tends to change drastically, and from 240Hz, the USR value tends to decrease by less than 50%. This is because, with the sampling frequency fixed at 50 kHz, the higher the driving frequency, the less the number of harmonic frequencies that can be included in the input shaping calculation.

Triangular scanning output is preferred from the USR perspective because the measurement interval is more constant than sinusoidal scanning output. However, when the voltage of the triangular waveform is applied as it is, when one of the harmonic frequencies is in contact with the resonant frequency of the scanner, unwanted residual vibration occurs, so a control is required to compensate for this. In this study, we propose an ISETF that can efficiently remove not only the fundamental resonant frequency but also the effects of higher-order modes, and experimentally investigate its performance, application limits of driving voltage and driving frequency.

Based on SLE 1.5%, the drive voltage has a wider USR of more than 96% from 15V (TOSA 3.4 °) to 40V (TOSA 9 °), which means that the proposed ISETF works well in the linear region. In the application limit test according to the driving frequency, the USR showed a wide USR of more than 97% up to the low frequency band of 80Hz, but the fluctuation was severe or the USR value decreased significantly above 90Hz. From these experimental results, the proposed ISET can more efficiently remove residual vibration and higher crosstalk in two-axis driving.

FIG. 13 is a flowchart illustrating an implementation procedure of a MEMS mirror scanner uniaxial driving method according to an embodiment of the present invention.

The MEMS mirror scanner structure is tested using the input voltage i _x (t) (impulse or frequency sweep) for the transfer function extraction, and the input voltage i _x (t) and the output angle o _xx Digitization of (t) is performed, and I _x (f) and O _xx (f) are calculated through Fourier transform of input voltage and output angle, and the experimental transfer function T _xx (f )

Set the desired output angle d _x (t) and FT to find D _x (f). By dividing O _x (f) by T _xx (f), we can calculate the frequency domain function V _x (f) of the shaped input voltage, and convert it to the time domain function by inverse Fourier transform to the shape input. v _x (t) can be found. After the device is driven with the above input voltage, feedback control may be performed to approach the desired output angle d _x (t) when there is a position error. After the control on the X-axis is completed by the above-described process, the control on the Y-axis can be made like the above-described method.

14 shows a method of performing input shaping by extracting a theoretical transfer function from a computer simulation. First, the vibration characteristics (basic resonant frequency, spring stiffness, moment of inertia, damping coefficient, etc.) are extracted from the computer simulation of the whole MEMS mirror scanner, and then the transfer function of the corresponding vibration system is theoretically obtained. Second, we use the same method to find the theoretical transfer function for higher-order modes that affect the measurement. Third, in order to perform crosstalk analysis and modeling in which the y-axis drive affects the x-axis, the y-axis is measured using a pulse signal after the y-axis is driven by a simulation. Find the theoretical transfer function for crosstalk. By adding the theoretical transfer functions for the three vibration systems, we extract the theoretical transfer function T _xx (f) that integrates the fundamental resonance of the x-axis, the higher-order mode and the crosstalk (the effect of the y-axis drive on the x-axis). As a result, the shaped input voltage v _x (t) for the desired output angle can be obtained in the same manner as in FIG. 13 using the theoretical transfer function T _xx (f).

The embodiment of FIG. 15 shows a method of performing input shaping by extracting the theoretical transfer function from the experimental transfer function obtained in the embodiment of FIG. That is, it can be assumed that the experimental transfer function is the sum of the transfer functions for three vibration systems (basic resonant frequency, higher order mode, and crosstalk). Therefore, the three peak values correspond to the resonant frequency of each vibration system. From this condition, the spring constant, mass, and damping coefficient of each vibration system can be obtained in turn. Thus, by adding all three transfer functions obtained from the experimental transfer function, the theoretical transfer function can be finally obtained.

As described above, FIGS. 13, 14, and 15 are flowcharts illustrating an input shaping method for obtaining a desired output on one axis. In this case, crosstalk refers to a coupling phenomenon affecting each other between the x-axis and the y-axis, and FIGS. 13, 14, and 15 remove the crosstalk effect on only one axis, but do not cover the other axis.

In contrast, FIGS. 16 to 18 are flowcharts showing an implementation procedure of a driving method for both axes of a MEMS mirror scanner to which an embodiment of the present invention is applied.

Here, for the MEMS mirror scanner structure, the input voltage functions i _xx (t) and i _yy (t) (impulse or frequency sweep) for the x and y axes for extracting the transfer function of each axis are determined. a driving test using the i _xx (t), and, i _xx (t) (x-axis input signal (voltage)), o _xx (t) (i _xx (x-axis output signal (output angle) due to t)) , digitization is performed on _xy (t) (y-axis output signal (output angle) by i _xx (t)) and I _xx (f), O using Fourier transform on the input and output signals. _xx (f) and O _xy (f) are calculated, respectively, and the experimental transfer function T _xx (f) (relationship between x-axis input and x-axis output) and T _xy (f) (x-axis input) for the device And y-axis output). Similarly, after performing the same process for i _yy (t) (y-axis input signal), the experimental transfer functions T _yy (f) (y-axis input and y-axis output relation) and T _yx (f) (y-axis input and x Extract the relationship between the axis outputs (see Equation 4).

When two axes are driven, the desired output angles d _x (t) and d _y (t) are set on the x-axis and y-axis, and Fourier transform is used to find D _x (f) and D _y (f). Next, using the experimental transfer functions T _xx (f), T _xy (f), T _yy (f) and T _yx (f) and the desired output angles D _x (f) and D _y (f), You can calculate V _x (f) and V _y (f), the input voltage functions in the frequency domain for the output angle (see Equation 5), and convert them to inverse Fourier transforms into a time domain function to obtain the shape input v _x (t ) And v _y (t). After driving the device with the actual input voltage, feedback control may be performed to approach the desired output angle d _x (t) when there is a position error.

17 illustrates a method of performing input shaping by extracting a theoretical transfer function from a computer simulation. First, we analyze the vibration characteristics (basic resonant frequency, spring stiffness, damping ratio, etc.) of each axis of MEMS mirror scanner by computer simulation of the whole device and then theoretically calculate the transfer function for fundamental resonance of x and y axes. Indicate the process. Second, we use the same method as above to find the theoretical transfer function for higher order modes that affect the measurement. Since the movement in the z-axis direction as well as the rotation about the x- and y-axes can be measured as the rotational movement, the residual vibration due to this higher-order mode can affect the scanning output. By adding two theoretical transfer functions obtained from the above processes, the theoretical transfer functions T _xx (f) and T _yy (f) that integrate the fundamental resonance and higher mode for the x and y axes are extracted. Third, in order to model the crosstalk generated when the two axes are driven together, the theoretical application of the crosstalk of each axis is measured by applying the pulse signal independently to each axis by simulation and measuring the displacement of the other axis. Extract the transfer functions T _xy (f) and T _yx (f). As a result, the shaped input voltages v _x (t) and v _y (t) for the desired output angles are _calculated by the theoretical transfer functions T _xx (f), T _yy (f), T in the same manner as in FIG. Can be obtained by substituting _xy (f) and T _yx (f).

The embodiment of FIG. 18 shows a method of performing input shaping by extracting the theoretical transfer function from the experimental transfer function obtained in the embodiment of FIG. First, the vibration characteristics (resonance frequency, spring stiffness, damping ratio, etc.) of the MEMS mirror scanner are obtained from the experimental transfer functions obtained in FIG. 16. At this time, the experimental transmission functions T _xx (f) and T _yy (f) including the fundamental resonance and the higher order mode each consist of the sum of two vibration systems (basic resonance frequency and higher mode), respectively. The peak value can be assumed to be the resonance frequency of each vibration system. After each theoretical transfer function is obtained, T _xx (f) and T _yy (f) can be obtained by adding them as in 15. Secondly, in order to perform crosstalk modeling when driving two axes, the spring-mass is based on the vibration characteristics extracted from the experimental transmission function T _xy (f) assuming the relation of y-axis displacement according to the x-axis driving as one vibration system. Extract the theoretical transfer function T _xy (f) by substituting the equation for the damped vibration system. In the same process, the theoretical transfer function T _yx (f) is extracted. As a result, the shaded input voltages v _x (t) and v _y (t) for the desired output angle are calculated in the same manner as in Fig. 13 by the theoretical transfer functions T _xx (f) and T _yy (f). Can be obtained by substituting T _xy (f) and T _yx (f).

Claims (14)

A method of driving a MEMS mirror scanner in which a mirror can rotate about an x axis and a y axis perpendicular thereto,
Obtaining a transfer function T (f) of the MEMS mirror scanner;
Setting a target time series output signal d (t) for driving the mirror of the MEMS mirror scanner;
Converting the target time series output signal o (t) into an output signal D (f) in a Fourier target frequency domain;
Obtaining an input signal V (f) in the frequency domain from the target frequency domain output signal D (f) and a transfer function T (f) of the MEMS mirror scanner;
Converting the input signal V (f) in the frequency domain into a time series input signal v (t); And
And applying the time series input signal (v (t)) as a drive voltage to a MEMS mirror scanner.
The x-axis time series of claim 1, wherein the transfer function T (f) comprises an x-axis frequency domain output signal O _xx (f) obtained by Fourier transforming an x-axis time series output signal o _xx (t). MEx mirror scanner driving method characterized in that the x-axis transfer function (T _x (f)) obtained by dividing the input signal (i _x (t) by the Fourier transform x-axis frequency domain input signal (I _x (f)). .
The process of claim 2, wherein the x-axis transfer function T _x (f) is calculated using the x-axis frequency domain input signal I _x (f) and the x-axis frequency domain output signal O _xx (f). Is repeated a plurality of times, and the final x-axis transfer function T _x (f) is determined by averaging the x-axis transfer function T _x (f) calculated a plurality of times. Way.
The method of claim 2, wherein the computational simulation analysis of the MEMS mirror scanner extracts the vibration characteristics to obtain the theoretical transfer function, the theoretical transfer function for the higher-order mode affecting the measurement, and the y-axis drive Drive the MEMS mirror scanner characterized in that the final x-axis transfer function (T _x (f)) is determined by adding all of the theoretical transfer functions obtained above. Way.
The method of claim 2, wherein the target time series output signal d (t) is an x-axis target time series output signal d _x (t),
The x-axis is multiplied by the x-axis target frequency domain output signal (D _x (f)) obtained by Fourier transforming the x-axis target time series output signal (d _x (t)) and the x-axis transfer function (T _x (f)). A method of driving a MEMS mirror scanner, characterized by obtaining a frequency domain input signal (V _x (f)).
The MEMS mirror according to claim 5, wherein a driving voltage is applied based on the x-axis time series input signal v _x (t) obtained by inverse Fourier transforming the x-axis frequency domain input signal V _x (f). How to drive the scanner.
The method according to claim 1, wherein the transfer function (T (f)),
The frequency domain output signal O _xx (f) obtained by Fourier transforming the x-axis time series output signal o _xx (t) generated by the x-axis time series input signal i _x (t) is obtained. An xx transfer function (T _xx (f)) obtained by dividing the input signal i _x (t) by the Fourier transformed frequency domain input signal I _x (f);
The frequency domain output signal (O _xy (f)) obtained by Fourier transforming the y-axis time series output signal (o _xy (t)) generated by the x-axis time series input signal (i _x (t)). An xy transfer function T _xy (f) obtained by dividing the input signal i _x (t) by the Fourier transformed frequency domain input signal I _x (f);
The frequency domain output signal O _xy (f) obtained by Fourier transforming the x-axis time series output signal o _yx (t) generated by the y-axis time series input signal i _y (t), and the y-axis time series An yx transfer function T _xy (f) obtained by dividing the input signal i _y (t) by the Fourier transformed frequency domain input signal I _y (f); And
The y-axis time series output signal (O _yy (f)) obtained by Fourier transforming the y-axis time series output signal (o _yy (t)) generated by the y-axis time series input signal (i _y (t)). And a yy transfer function term (T _yy (f)) obtained by dividing the input signal i _y (t) by the Fourier transformed frequency domain input signal I _y (f). .
The method of claim 1, wherein the obtaining of the transfer function T (f) comprises:
Computational simulation of the MEMS mirror scanner analyzes the vibration characteristics of the x- and y-axes, then theoretically calculates the theoretical transfer function for the fundamental resonance of the x- and y-axes, and theoretically evaluates the higher-order modes that affect the measurement. To calculate the transfer function, apply the pulse signal to the x axis and the y axis independently, measure the displacement of different axis, calculate the theoretical transfer function for the crosstalk of each axis, and drive the x axis by adding the theoretical transfer functions. Xx transfer function term affecting this x axis (T _xx (f)), xy transfer function affecting the y axis (T _xy (f)), y axis drive affecting the x axis and yx transfer function (T _yx (f)), extracting a yy transfer function term (T _yy (f)) in which y-axis driving affects the y-axis.
The method of claim 7 or 8, wherein the target time series output signal d (t) includes an x-axis target time series output signal d _x (t) and a y-axis target time series output signal d _y (t). ,
Fourier transforms these to obtain an x-axis target frequency domain output signal D _x (f) and a y-axis target frequency domain output signal D _y (f),

And obtaining the x-axis frequency domain input signal (V _x (f)) and the y-axis frequency domain input signal (V _y (f)).
The x-axis time series input signal (v _x (t) of claim 9, wherein the x-axis frequency domain input signal (V _x (f)) and the y-axis frequency domain input signal (V _y (f)) are respectively obtained by inverse Fourier transform. And) driving voltage based on the y-axis time series input signal (v _y (t)).
The method of driving a MEMS mirror scanner according to claim 5 or 9, wherein a feedback control is performed to drive a device of the MEMS mirror scanner by applying a driving voltage and to approach a desired output angle when there is a position error.
10. The method of claim 1, wherein the experimentally obtaining the transfer function T (f) of the mirror scanner comprises: a frequency obtained through a frequency sweep test or an impulse response test A method of driving a MEMS mirror scanner, based on data.
The method of claim 10, wherein the step of experimentally obtaining the transfer function T (f) of the mirror scanner is obtained by averaging frequency data obtained through a plurality of frequency sweep tests or impulse response tests. A method of driving a MEMS mirror scanner, based on frequency data.
MEMS mirror scanner, characterized in that driven by the method of driving a MEMS mirror scanner according to any one of claims 1 to 9.

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