The present application is based on and claims priorities from Japanese Patent Application No. 2008-094587, filed on Apr. 1, 2008, and Japanese Patent Application No. 2008-326960, filed on Dec. 24, 2008, the disclosures of which are hereby incorporated by reference in their entirety.
1. Field of the Invention
The present invention relates to micro-electro-mechanical systems (MEMS), in particular, to a method of driving a MEMS mirror scanner, a method of driving a MEMS actuator scanner, and a method of controlling a rotation angle of a MEMS actuator, a MEMS micro-scanner for use, for example, in an optical deflector for obtaining and displaying an image, reducing a sensing error by diffusion of light, and sensing by scanning light, and a method of controlling such a MEMS micro-scanner.
2. Description of the Related Art
Recently, with an increase in a speed and functions of optical devices, high-speed switching of an optical path and vector drawing of a desired pattern have been required. For example, in a lightwave range finder, in order to compensate a measurement error, an inside optical path disposed inside the device and an outside optical path for measuring a distance from the device to an outside target are switched, and the optical distances are alternately measured. With an increase in a speed and functions of the device, high-speed switching of the optical paths is required.
A technique described in a light controller for a ranging device (Japanese Patent Application No. 2006-294219) requires high-speed switching of an optical path for controlling attenuation of light at a high speed. When capturing a measurement target by a lightwave range finder, a light beam has to be projected at a predefined angle at a high speed. In this case, high-speed switching of the optical path is required. In a device for displaying a line image by means of laser beam scanning, it is required to perform optical scanning corresponding to a desired pattern to be drawn.
A MEMS mirror scanner (MEMS actuator scanner) is often used for the high-speed switching of an optical path and the vector drawing of a desired pattern. Due to a small size, the MEMS mirror scanner has advantages in high speed and low power consumption.
In the MEMS mirror scanner illustrated in
However, such driving requires a time long enough to be able to ignore effects of the inertia and damping, and a part of the advantages in using a MEMS mirror scanner is lost.
On the other hand, if driving time is simply reduced, an unintended mirror angle response results from effects of the inertia and damping, which are dynamic features. For example, if one tries to change the angle of the mirror 101 from θA to θB in a reduced driving time by applying a step-like voltage, transient oscillation (ringing) is caused as illustrated in
Accordingly, driving techniques taking account of the inertia and damping, which are dynamic features of a MEMS mirror scanner have been proposed (refer to the following non-patent documents 1-6).
Non-patent document 1: V. Milanovic, K. Castelino, “Sub-100 μs Settling Time and Low Voltage Operation for Gimbal-less Two-Axis Scanners”, IEEE/LEOS Optical MEMS 2004, Takamatsu, Japan, August 2004.
Non-patent document 2: K. Castelino, V. Milanovic, D. T. McCormick, “MEMS-based high-speed low-power vector display”, 2005 IEEE/LEOS Optical MEMS and Their Applications Conf., Oulu, Finland, August 2005, pp. 127-128.
Non-patent document 3: Y. Sakai, T. Yamabana, S. Ide, K. Mori, A. Ishizuka, O. Tsuboi, T. Matsuyama, Y. Ishii, M. Kawai, “Nonlinear Torque Compensation of Comb-Driven Micromirror”, Optical MEMS 2003, TuP16.
Non-patent document 4: M. Kawai, “Research and Development of Photonic Network using Optical Burst-Switching” (NICT contract research).
Non-patent document 5: K. Ide, H. Ibe, “A Study if High Speed MEMS Mirror Drive dor Optical Wireless Communication”, Proceedings of Information and Communication Engineers Society Meeting, Vol. 2005 Electronics, No. 1 (20050307) P. 350, (2005).
Non-patent document 6: K. Ide, H. Ibe “A Resonant Compression Method of MEMS Mirror for Optical Wireless Communication”, Proceedings of Information and Communication Engineers Society Meeting, Vol. 2005, Electronics, No. 1 (20050907) P. 333 (2005).
Although the oscillation of a MEMS mirror scanner can be suppressed to some degree by the techniques disclosed in the above documents 1-6, a desired time-angle response feature required by each specific application can not be achieved.
A method of obtaining a time-mirror angle response curve 109 has been considered with a step-like function as an input signal where the function is represented by a time parameter P1 and a voltage parameter P2, as illustrated in Graph A in
In the methods illustrated in
Moreover, it takes a long time to experimentally determine the parameters. If a driving waveform is determined, a time dependency pattern of the mirror angle (mirror angle response) and the stabilization time is defined, which lowers the degree of freedom in driving. Furthermore, although in the case of the driving waveform illustrated in
It is, therefore, an object of the present invention to provide a method of driving a MEMS mirror scanner and a MEMS actuator scanner and controlling a rotation angle of a MEMS actuator, which accurately damp their oscillation to a resting state, and simplify a scheme of driving without using a large capacity memory, so as to quickly determine parameters and sufficiently ensure the degree of freedom in driving.
In order to achieve the above object, a first aspect of the present invention relates to a method of driving a MEMS mirror scanner including an electrostatic actuator. The method includes a step of driving the electrostatic actuator according to an input signal in accordance with a driving waveform obtained by the following equation.
Where B/I, κ/I, (1/I)·dCL(θ)/dθ and (1/I)·dCR(θ)/dθ are parameters to obtain the driving waveform, θ(t) is a desired mirror angle response, I is a moment of inertia of a moving part including a mirror, 2B is a damping factor (damping coefficient), κ is a spring constant, CL(θ) and CR(θ) are angle dependencies of an electric capacitance, VB is a constant bias voltage in differential driving, and C+′(θ) and C−′(θ) are ½ of the sum and the difference of the first order derivative of CL(θ) and CR(θ) with respect to θ, respectively, which are represented by the following equations.
A second aspect of the present invention relates to a method of driving a MEMS mirror scanner including an electrostatic actuator. The method includes a step of driving the electrostatic actuator according to an input signal in accordance with a driving waveform obtained by the following equation.
where B/I, κ/I, (1/I)·dCL(θ)/dθ and (1/I)·dCR(θ)/dθ are parameters for obtaining the driving waveform, θ(t) is a desired mirror angle response, I is a moment of inertia of a moving part including a mirror, 2B is a damping factor (damping coefficient), κ is a spring constant, CL(θ) and CR(θ) are angle dependencies of an electric capacitance, VB(t) is a constant bias voltage or an appropriately determined time-dependent voltage change in single side driving, and C+′(θ) and C−′(θ) are ½ of the sum and the difference of the first order derivative of CL(θ) and CR(θ) with respect to θ, respectively, which are represented by the following equations.
Preferably, at least one of the parameters is experimentally determined.
Preferably, θ(t) is two times differentiable with respect to time.
A third aspect of the present invention relates to a method of driving a MEMS actuator scanner, including steps of: defining an actuation of the MEMS actuator as a function of time; determining by an experiment or calculation terms included in the equation of motion governing motion of the MEMS actuator except a variable representing the actuation, derivatives thereof with respect to time and a variable corresponding to an input signal; and determining the input signal by substituting to the equation of motion the actuation of the MEMS actuator as the function of time and the terms in the equation of motion except the variable representing the actuation, the derivatives thereof with respect to time and the variable corresponding to the input signal.
Preferably, the variable representing the actuation is two times differentiable with respect to time.
Preferably, the MEMS actuator scanner includes an electrostatically-driven comb structure, the variable representing the actuation in the equation of motion governing motion of the MEMS actuator is a displacement or a rotation angle, the variable corresponding to the input signal is voltage, the terms in the equation of motion governing motion of the MEMS actuator except the variable representing the actuation, the derivatives thereof with respect to time and the variable corresponding to the input signal are an inertia term, a damping term, an elastic term and a first order derivative of the electric capacitance of the comb structure with respect to the displacement or the rotation angle.
Preferably, the damping term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.
Preferably, the elastic term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.
Preferably, the damping term is determined by measuring a resonance characteristic of the MEMS actuator.
Preferably, the elastic term is determined by measuring a resonance characteristic of the MEMS actuator.
Preferably, the first order derivative of the electric capacitance of the comb structure with respect to the displacement or the rotation angle is determined by measuring a relationship between quasi-statically applied voltage and the displacement or the rotation angle of the actuator.
A fourth aspect of the present invention relates to a method of controlling a rotation angle of a MEMS actuator having an angled comb structure, which is driven by voltage, comprising steps of: defining the rotation angle of the MEMS actuator as a function of time; determining by an experiment or calculation terms included in the equation of motion governing the rotation except the rotation angle, derivatives thereof with respect to time and the voltage and determining the voltage by substituting to the equation of motion the rotation angle and the terms in the equation of motion except the rotation angle, the derivatives thereof with respect to time and the voltage.
Preferably, the rotation angle of the MEMS actuator is two times differentiable with respect to time.
Preferably, the terms in the equation of motion governing the rotation of the MEMS actuator except the rotation angle, the derivatives thereof with respect to time and the voltage are an inertia term, a damping term, an elastic term and a first order derivative of an electric capacitance of the comb structure with respect to the rotation angle.
Preferably, the damping term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.
Preferably, the elastic term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.
Preferably, the damping term is determined by measuring a resonance characteristic of the MEMS actuator.
Preferably, the elastic term is determined by measuring a resonance characteristic of the MEMS actuator.
Preferably, the first order derivative of the electric capacitance of the comb structure with respect to the rotation angle is determined by measuring a relationship between quasi-statically applied voltage and the rotation angle of the MEMS actuator.
The accompanying drawings are included to provide further understanding of the invention, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the invention and, together with the specification, serve to explain the principle of the invention.
Hereinafter, a method of controlling a rotation angle of a MEMS mirror scanner, a MEMS actuator scanner and a MEMS actuator will be described with reference to the accompanying drawings.
Generally, in the case of the MEMS mirror scanner illustrated in
I{umlaut over (θ)}+2B{dot over (θ)}+κθ=TTotal(θ,w) (1)
where {umlaut over (θ)}=d2θ/dt2, {dot over (θ)}=dθ/dt
In this case, the coefficients of the rotation angle, the first order derivative of the rotation angle with respect to time and the second order derivative of the rotation angle with respect to time are denominated an elastic term, a damping term and an inertia term, respectively. When the motion of an actuator is not angular but translational, the coefficients of the displacement, the first order derivative of the displacement with respect to time and the second order derivative of the displacement with respect to time are also denominated an elastic term, a damping term and an inertia term, respectively. Ttotal(θ, w) is a sum of the driving torques of the right and left actuators.
In addition, w is a driving factor, which means voltage or current, for example.
If a desired mirror angle response is θ(t), the driving factor w(t) can be obtained according to the equation (1), and an input signal can be applied according to the driving factor w(t).
A method of determining the driving factor w(t) will be described hereinafter.
As one example of MEMS mirror scanners (MEMS actuator scanners), an angled comb MEMS electrostatic actuator 27 illustrated in
As illustrated in
The MEMS actuator scanner 27 includes a circular mirror plate 27a. This mirror plate 27a includes a pair of axis portions 27b, 27b each extending in the radial direction. The axis portions 27b, 27b are connected to fixed portions 27d, 27d via spring portions 27c, 27c, respectively. The movable combs 27e, 27e are formed in the axis portions 27b, 27b. The movable combs 27e, 27e and the fastened combs 27fA, 27fB interdigitate. They comprise a part of a pair of right and left electrostatic actuators.
The pair of the right and left actuators is used to rotate the mirror plate 27a. Voltage VL and VR is applied to a pair of the fixed combs 27fA and 27fB, respectively, and the mirror plate 27a is thereby rotated in the arrow F direction.
The angle dependencies of the electric capacitance on the right and left sides are defined as CL(θ) and CR(θ), respectively.
The driving torque in the equation (1) is given as follows.
It is now assumed that differential driving is applied by simultaneously activating both of the electrostatic actuators.
The differential operation of both of the electrostatic actuators are conducted according to the following equations (5), (6), where VB is a constant bias voltage, VV is a driving operation voltage, VL is a differential operating voltage of the left side actuator and VR is a differential operating voltage of the light side actuator.
V
L
=V
B
−V
V (5)
V
R
=V
B
+V
V (6)
It is preferable for the bias voltage VB to be set to a voltage almost half of the one corresponding to a maximum driving angle.
In the case of such differential driving, the equation of motion (1) is expressed by the following equation (7).
When assuming the angle dependencies of the electric capacitances illustrated in
If the driving operation voltage VV is solved from the equations (7), (8) and (9), an ideal driving waveform for a mirror angle response with respect to time is mathematically derived. The following equations (10) and (11) show the ideal driving waveforms of a driving operation voltage VV.
Once a desired mirror angle response θ(t) is once defined by a two times differentiable time function, the waveform VV(t) of the driving operation voltage VV can be uniquely obtained by using the equations (10) and (11). However, if a mirror angle response θ(t) behaves extremely rapid with time, the equations (10) or (11) may not hold.
When they do not hold, the voltage obtained from the equations (10) and (11) does not become a real number in a range suitable for driving.
Thus, when changing the angle of the mirror from θA to θB, the following equation (12), for example, can be used as the mirror angle response θ(t) to time.
In this case, Ts is a time proportional to a switching time and can be arbitrarily set in a range where it does not become extremely small, and erf( ) is the error function. If the time Ts is extremely small, the equations (10), (11) may not hold.
The present invention can be applied to single side driving where an appropriate signal is applied to an actuator disposed on one side, in addition to differential driving where movable combs on both sides are differentially driven at the same time.
Next, the determination of parameters B/I, κ/I, (1/I)·dCL(θ)/dθ and (1/I)·dCR(θ)/dθ in the equations of the driving waveform (10) and (11) will be described.
The parameters in the driving waveform are determined by using an experimental system illustrated in
First, the determination of the parameters B/I and κ/I will be described.
A constant voltage is applied to both or one of the right and left side actuators, so as to tilt the mirror plate 27a at a certain amount. After that, the right and left side actuators are set to 0 volt, and a transient oscillation (ringing) around a state where the driving torque is zero can be observed. If this ringing, i.e., an angle response characteristic (oscillation curve) to time of the mirror plate 27a is observed, the waveform illustrated in
By using the damping of the envelope curve of this ringing waveform, a time tD in which the envelope curve becomes 1/e is determined where, the symbol “e” represents the base of the natural logarithm. The parameter B/I can be obtained from the time tD by using the following equation.
B/I=1/tD
The period T of the ringing waveform (oscillating curve 107) is obtained by the measurement, and the parameter κ/I is obtained by the following approximate equation.
κ/I=(2π/T)2
The parameters B/I, κ/I can be more accurately obtained by the following method.
More particularly, the ringing waveform is fit to the following equation (13) representing a general damping waveform, and the parameters B/I and κ/I can be determined by using tD and TF obtained by the fitting and the equations B/I=1/tD and κ/I=(2π/TF)2−(1/tD)2.
In this case, the symbol A denotes an angular amplitude for the use in the fitting, and the symbol φ is a phase.
The parameters B/I, κ/I can be determined by another method.
A resonance characteristic curve Q illustrated in
The parameter κ/I can be determined by using the following equation.
κ/I=(2 π f0)2
The parameter B/I can be determined by using an equation, B/I=πΔf, Δf being a frequency difference between +f′0 and −f′0 corresponding to an operation amplitude about 1/√2 of the peak value θp.
Next, the determination of the parameters (1/I)·dCL(θ)/dθ, (1/I)·dCR(θ)/dθ will be described.
First, the MEMS mirror scanner 27 is driven by using either of the actuators. For example, in a state where the applied voltage VR is set to 0 volt, the applied voltage VL is changed, and the angle of the mirror plate 27a is measured relative to a standard angle (0 degree) when the angle of the mirror plate 27a is stabilized. This measurement of the angle uses an experimental system illustrated in
By this angle measurement, an applied voltage—angle curve Q″ is obtained, for example as shown in
This corresponds to a direct current characteristic of the rotation of the mirror plate 27a by using one of the actuators.
In this case where the angle of the mirror plate 27a is measured by setting the applied voltage VR to 0 and changing the applied voltage VL, the equation, κ·θ=(1/2)·{dCL(θ)/dθ}·VL2 statically holds, so that 1/I·{dCL(θ)/dθ} can be obtained by using the following equation (14).
Similarly, if the angle of the mirror plate 27a is measured by changing the applied voltage VR, where the applied voltage VL is set to 0 volt, 1/I·{dCR(θ)/dθ} can be obtained.
CL(θ) and CR(θ) can also be calculated by using numerical analyses such as a finite element method (FEM) and a boundary element method (BEM). 1/I·{dCL(θ)/dθ} and 1/I·{dCR(θ)/dθ} can be thereby obtained.
Next, single side driving which applies an appropriate signal to an actuator disposed on one side will be described.
If the voltage to be applied to the actuator, for example, the voltage VL to be applied to the left side actuator, is set to a constant voltage or an appropriately determined time-dependent voltage change VB(t), the equation of motion (1) is expressed by the following equation.
The following equation showing an ideal driving waveform for a desired mirror angle response is obtained from the above equation (15).
If a desired mirror angle response θ(t) is defined by a two times differentiable time function, a driving waveform VR(t) of the voltage which should be applied to the right side actuator is obtained by VR(t)=VV(t) given by the above equation (16).
Accordingly, when changing an angle from θA to θB, the following equation, for example, is employed for the mirror angle response θ(t).
θ(t)=θA+(θB−θA)−(1/2)·{1+erf(t/Ts)}
In this case, the time Ts proportional to the switching time can be arbitrarily set in a range where it does not become extremely small, similar to the case when driving both sides. If the Ts is extremely small, the equation may not hold, similar to the case when driving both sides.
As a special case, if the voltage VL to be applied to the left side actuator is set to 0, the motion equation becomes as follows.
An ideal driving waveform for a desired mirror angle response becomes as follows.
In this case, the driving waveform VR(t)=VV(t) is obtained by setting the voltage VL to be applied to the left side actuator to a constant voltage or an appropriately determined time-dependent voltage VB(t), for the sake of simplicity of description. Alternatively, the driving waveform VL(t)=VV(t) to be applied to the left side actuator can be obtained by setting the voltage VR to be applied to the right side actuator to a constant voltage or an appropriately determined time-dependent voltage VB(t).
A block circuit of an electric driving system for the use in these experiments is illustrated in
Referring to
Moreover, in the case of a block circuit of an electric driving system illustrated in
Furthermore, as illustrated in
A composition illustrated in
According to the present invention, an appropriate input signal QI as illustrated in Graph B in
In the meantime, it is preferable for θ(t) to be two times differentiable with respect to time.
For example, a continuous function θ(t) given by the following equation is one time differentiable but not two times differentiable with respect to time.
In this case, θ(t) is not two times differentiable only at two points, t=±2Ts, and it is possible to define a voltage driving waveform which is not continuous only at the above two points.
The discontinuous nature of the voltage driving waveform at the two points means that the voltage has to change at an infinite speed at each of the two points. However, it is impossible that the voltage actually generated from an electric driving system changes at an infinite speed. Therefore, it becomes difficult to accurately replicate the voltage driving waveform determined as described above.
On the other hand, the function defined by the equation (12), for example, is two times differentiable with respect to time. In this case, θ(t) is sufficiently smooth, the required voltage driving waveform is continuous and the rate of the voltage change is not infinite. For this reason, an electric driving system can sufficiently and accurately apply the voltage driving waveform to the MEMS actuator. Therefore, a desired θ(t) can be accurately satisfied.
As described above, according to the MEMS mirror scanner, the MEMS actuator scanner, and the method of controlling the rotation angle of the MEMS actuator, a desired angle response characteristic to time can be obtained, so that high-speed switching of an optical path and vector drawing is facilitated. By obtaining a desired mirror angle response characteristic to time, the oscillation of the MEMS mirror scanner and the MEMS actuator scanner can be accurately damped to a resting state, the driving scheme can be simplified without using a large capacity memory, the parameters can be quickly determined, and the degree of freedom in the driving can be sufficiently secured.
Although the present invention has been described in terms of exemplary embodiments, it is not limited thereto. It should be appreciated that variations may be made in the embodiments described by persons skilled in the art without departing from the scope of the present invention as defined by the following claims.
Number | Date | Country | Kind |
---|---|---|---|
2008-094587 | Apr 2008 | JP | national |
2008-326960 | Dec 2008 | JP | national |