METHOD OF DRIVING MEMS MIRROR SCANNER, METHOD OF DRIVING MEMS ACTUATOR SCANNER AND METHOD OF CONTROLLING ROTATION ANGLE OF MEMS ACTUATOR

• US 20090244668A1
• Filed: 03/31/2009
• Published: 10/01/2009
• Est. Priority Date: 04/01/2008
• Status: Abandoned Application

• Current Assignee: Kabushiki Kaisha Topcon
• Original Assignee: Kabushiki Kaisha Topcon
• Inventors: GOTO, Yoshiaki, KOBAYASHI, Akio, MARUYAMA, Hirotake, NAKANISHI, Michiko, TAMURA, Hirokazu, FUJINO, Makoto
• Application Number:
  US12/414,921
• Publication Number:
  US 20090244668A1
• Time in Patent Office: Days
• US Class Current: 359/200.600
• CPC Class Codes: G02B 26/0841 the reflecting element being moved or deformed by electrostatic means
• CPC Class Codes: G02B 26/105 with one or more pivoting mirrors or galvano-mirrors G02B26/101 takes precedence

Abstract

A method of driving a MEMS mirror scanner having an electrostatic actuator, comprising a step of driving the electrostatic actuator according to an input signal in accordance with a driving waveform obtained by the following equation,

$\mathrm{when}$ $C_{+}^{\prime }\left(\theta \right)\ne 0$ $V_V\left(t\right)=\frac{1}{\frac{C_{+}^{\prime }\left(\theta \right)}{I}}\left[\begin{array}{c}-\frac{C_{-}^{\prime }\left(\theta \right)}{I}V_B+\\ \sqrt{\begin{array}{c}-\left(\frac{1}{I}\frac{C_L\left(\theta \right)}{\theta }\right)\left(\frac{1}{I}\frac{C_R\left(\theta \right)}{\theta }\right)V_B^2+\\ \frac{C_{+}^{\prime }\left(\theta \right)}{I}\left(\ddot{\theta }+2\frac{B}{I}\stackrel{.}{\theta }+\frac{\kappa }{I}\theta \right)\end{array}}\end{array}\right]$ $\mathrm{when}$ $C_{+}^{\prime }\left(\theta \right)=0$ $V_V\left(t\right)=\frac{\ddot{\theta }+2\frac{B}{I}\stackrel{.}{\theta }+\frac{\kappa }{I}\theta }{2\frac{C_{-}^{\prime }\left(\theta \right)}{I}V_B}$

• • where, B/I, κ/I, (1/I)·dC_L(θ)/dθ and (1/I)·dC_R(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, C_L(θ) and C_R(θ) are angle dependencies of an electric capacitance, V_B 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 C_L(θ) and C_R(θ) with respect to θ, respectively, which are represented by defined equations.

Claims

1. A method of driving a MEMS mirror scanner including an electrostatic actuator, comprising a step of driving the electrostatic actuator according to an input signal in accordance with a driving waveform obtained by the following equation,

$\mathrm{when}$



C + ′



( θ

) ≠

0 $V_V(<br><br>t)=<br><br>\frac{1}{\frac{C_{+}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)}{I}}[<br><br>-\frac{C_{-}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)}{I}<br><br><br><br>V_B+<br><br>\sqrt{\begin{array}{c}-\left(\frac{1}{I}<br><br>\frac{<br><br>C_L<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right)<br><br>\left(\frac{1}{I}<br><br>\frac{<br><br>C_R<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right)<br><br>V_B^2+\\ \frac{C_{+}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)}{I}<br><br>\left(\stackrel{\mathrm{¨<br><br>}}{\mathrm{\theta <br><br>}}+2<br><br>\frac{B}{I}<br><br>\stackrel{.}{\mathrm{\theta <br><br>}}+\frac{\mathrm{\kappa <br><br>}}{I}<br><br>\mathrm{\theta <br><br>}\right)\end{array}}]$ $\mathrm{when}<br><br><br><br>C_{+}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=0<br><br><br><br>V_V<br><br>\left(t\right)=\frac{\stackrel{\mathrm{¨<br><br>}}{\mathrm{\theta <br><br>}}+2<br><br>\frac{B}{I}<br><br>\stackrel{.}{\mathrm{\theta <br><br>}}+\frac{\mathrm{\kappa <br><br>}}{I}<br><br>\mathrm{\theta <br><br>}}{2<br><br>\frac{C_{-}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)}{I}<br><br>V_B}$

where B/I, κ

/I, (1/I)·

dC_L(θ

)/dθ and

(1/I)·

dC_R(θ

)/dθ

are parameters to obtain the driving waveform, θ

(t) is a desired mirror angle response, I is a moment of inertia of an moving part including a mirror, 2B is a damping factor (damping coefficient), κ

is a spring constant, C_L(θ

), C_R(θ

) are angle dependencies of an electric capacitance, V_B 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 C_L(θ

) and C_R(θ

) with respect to θ

, respectively, which are represented by the following equations,

$\begin{array}{cc}{C}_{+}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=\frac{1}{2}<br><br>\left(\frac{<br><br>C_L<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}+\frac{<br><br>C_R<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right),& \left(8\right)\\ C_{-}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=\frac{1}{2}<br><br>\left(-\frac{<br><br>C_L<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}+\frac{<br><br>C_R<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right)& \left(9\right)\end{array}$

3. The method of driving a MEMS mirror scanner according to claim 1, wherein at least one of the parameters is experimentally determined.

4. The method of driving a MEMS mirror scanner according to claim 1, wherein θ

(t) is two times differentiable with respect to time.

2. A method of driving a MEMS mirror scanner including an electrostatic actuator, comprising a step of driving the electrostatic actuator according to an input signal in accordance with a driving waveform obtained by the following equation,

$V_V$

( t ) = θ

¨

+ 2 

B I 

θ

. + κ

I 

θ

- 1 2 

1 I 



C L 

( θ

) 

θ



V B 

( t ) 1 2 

1 I 



C R 

( θ

) 

θ

where, B/I, κ

/I, (1/I)·

dC_L(θ

)/dθ and

(1/I)·

dC_R(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, C_L(θ

) and C_R(θ

) are angle dependencies of an electric capacitance, V_B(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 C_L(θ

) and C_R(θ

) with respect to θ

, respectively, which are represented by the following equations,

$\begin{array}{cc}{C}_{+}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=\frac{1}{2}<br><br>\left(\frac{<br><br>C_L<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}+\frac{<br><br>C_R<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right),& \left(8\right)\\ C_{\_}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=\frac{1}{2}<br><br>\left(-\frac{<br><br>C_L<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}+\frac{<br><br>C_R<br><br>\left(\mathrm{\theta <br><br>}\right)}{<br><br>\mathrm{\theta <br><br>}}\right)& \left(9\right)\end{array}$

21. The method of driving a MEMS mirror scanner according to claim 2, wherein at least one of the parameters is experimentally determined.

22. The method of driving a MEMS mirror scanner according to claim 2, wherein θ

(t) is two times differentiable with respect to time.

5. A method of driving a MEMS actuator scanner, comprising 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 a 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.

6. The method of driving a MEMS actuator scanner according to claim 5, wherein the variable representing the actuation is two times differentiable with respect to time.

7. The method of driving a MEMS actuator scanner according to claim 5, wherein

the MEMS actuator 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, and

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.

8. The method of driving a MEMS actuator scanner according to claim 7, wherein the damping term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.

9. The method of driving a MEMS actuator scanner according to claim 7, wherein the elastic term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.

10. The method of driving a MEMS actuator scanner according to claim 7, wherein the damping term is determined by measuring a resonance characteristic of the MEMS actuator.

11. The method of driving a MEMS actuator scanner according to claim 7, wherein the elastic term is determined by measuring a resonance characteristic of the MEMS actuator.

12. The method of driving a MEMS actuator scanner according to claim 7, wherein 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.

13. A method of controlling a rotation angle of a MEMS actuator having a comb structure, which is driven by voltage, comprising steps of:

defining a 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.

14. The method of controlling a rotation angle of a MEMS actuator according to claim 13, wherein the rotation angle of the MEMS actuator is two times differentiable with respect to time.

15. The method of controlling a rotation angle of a MEMS actuator having a comb structure according to claim 13, wherein 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.

16. The method of controlling a rotation angle a MEMS actuator according to claim 15, wherein the damping term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.

17. The method of controlling a rotation angle of a MEMS actuator according to claim 15, wherein the elastic term is determined by measuring a transient damping oscillation around a state where applied voltage to the MEMS actuator is 0.

18. The method of controlling a rotation angle of a MEMS actuator according to claim 15, wherein the damping term is determined by measuring a resonance characteristic of the MEMS actuator.

19. The method of controlling a rotation angle of a MEMS actuator according to claim 15, wherein the elastic term is determined by measuring a resonance characteristic of the MEMS actuator.

20. The method of controlling a rotation angle of a MEMS actuator according to claim 15, wherein 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.