Patent Publication Number: US-2023152573-A1

Title: Mems actuator, mems actuator drive method, and mems actuator control program

Description:
TECHNICAL FIELD 
     The present disclosure relates to a MEMS actuator, a MEMS actuator drive method, and a MEMS actuator control program. 
     BACKGROUND ART 
     Patent Literature 1 discloses a technique for a vibration mirror and a method for controlling the swing angle of the vibration mirror. The vibration mirror described in this literature is a micro optical system to which micromachining technology is applied, and deflects a light beam by vibrating the micro mirror substrate back and forth with a torsion beam as a rotation axis. 
     Citation List 
     Patent Literature 
     Patent Literature 1: Japanese Unexamined Patent Publication No. 2004-069731 
     SUMMARY OF INVENTION 
     Technical Problem 
     Actuators by Micro Electro Mechanical Systems (MEMS) are used in the field of, for example, a vibration mirror for periodically displacing a minute movable portion. In such a technical field, when periodically displacing the movable portion, a drive voltage is periodically applied to the comb electrode of the MEMS actuator in synchronization with the displacement cycle. Then, by matching the frequency of the drive voltage with the resonance frequency of the movable portion, the movable portion can be displaced by the maximum amplitude. 
     However, the resonance frequency of the movable portion in the MEMS actuator fluctuates due to changes in temperature, humidity, and the like. If the frequency of the drive voltage deviates from the resonance frequency of the movable portion due to the fluctuation in the resonance frequency of the movable portion, the operation of the movable portion at the maximum amplitude is adversely affected. In particular, when the MEMS actuator has a configuration in which the maximum amplitude of the movable portion is large, such as a configuration in which the elastic coefficient of a portion that elastically supports the movable portion is small, the non-linearity of the amplitude with respect to the frequency increases. Therefore, even if the frequency of the drive voltage deviates slightly from the resonance frequency of the movable portion, the amplitude is greatly reduced. 
     In addition, conventionally, there has been a technique for keeping the resonance frequency of the movable portion constant by controlling the temperature of the MEMS actuator to be constant. However, in such a technique, it is necessary to add a configuration for temperature control, which is an obstacle to the miniaturization of the MEMS actuator. In addition, it is not possible to suppress a fluctuation in the resonance frequency due to a change in humidity. 
     Therefore, it is an object of the present disclosure to provide a MEMS actuator, a MEMS actuator drive method, and a MEMS actuator control program capable of bringing the frequency of a drive voltage close to the resonance frequency regardless of a fluctuation in the resonance frequency of a movable portion. 
     Solution to Problem 
     A MEMS actuator according to an embodiment includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a movable comb electrode that includes a plurality of second comb fingers and drives the movable portion by an electrostatic force generated between the fixed comb electrode and the movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a drive circuit that applies a drive voltage having a time waveform, which periodically repeats rising and falling and includes a period to be a constant voltage after the rising and before the falling, between the fixed comb electrode and the movable comb electrode; and a timing detection circuit that generates a capacitance derivative signal indicating a derivative value of a capacitance between the fixed comb electrode and the movable comb electrode by converting a current signal, which is output from the fixed comb electrode or the movable comb electrode within the period due to a change in the capacitance, into a voltage signal and detects a timing when the capacitance derivative signal reaches a threshold value. The drive circuit controls a relationship between the timing detected by the timing detection circuit and a timing of the falling to be constant. 
     A MEMS actuator according to another embodiment includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a first fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a first movable comb electrode that includes a plurality of second comb fingers and drives the movable portion by an electrostatic force generated between the first fixed comb electrode and the first movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a second fixed comb electrode including a plurality of third comb fingers and provided to the base portion; a second movable comb electrode including a plurality of fourth comb fingers, the plurality of third comb fingers and the plurality of fourth comb fingers being alternately arranged; a drive circuit that applies a drive voltage having a time waveform periodically repeating rising and falling between the first fixed comb electrode and the first movable comb electrode; and a timing detection circuit that applies a voltage including a period to be a constant voltage excluding 0 V between the second fixed comb electrode and the second movable comb electrode, generates a capacitance derivative signal indicating a derivative value of a capacitance between the second fixed comb electrode and the second movable comb electrode by converting a current signal, which is output from the second fixed comb electrode or the second movable comb electrode within the period due to a change in the capacitance, into a voltage signal, and detects a timing when the capacitance derivative signal reaches a threshold value. The drive circuit controls a relationship between the timing detected by the timing detection circuit and a timing of the falling to be constant. 
     A method for driving a MEMS actuator according to an embodiment is a MEMS actuator drive method. The MEMS actuator includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a fixed comb electrode including a plurality of first comb fingers and provided to the base portion; and a movable comb electrode including a plurality of second comb fingers and driving the movable portion by an electrostatic force generated between the fixed comb electrode and the movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged. The drive method includes a drive step for applying a drive voltage having a time waveform, which periodically repeats rising and falling and includes a period to be a constant voltage after the rising and before the falling, between the fixed comb electrode and the movable comb electrode. In the drive step, a capacitance derivative signal indicating a derivative value of a capacitance between the fixed comb electrode and the movable comb electrode is generated by converting a current signal, which is output from the fixed comb electrode or the movable comb electrode within the period due to a change in the capacitance, into a voltage signal, a timing when the capacitance derivative signal reaches a threshold value is detected, and a relationship between the timing and a timing of the falling is controlled to be constant. 
     A method for driving a MEMS actuator according to another embodiment is a MEMS actuator drive method. The MEMS actuator includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a first fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a first movable comb electrode including a plurality of second comb fingers and driving the movable portion by an electrostatic force generated between the first fixed comb electrode and the first movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a second fixed comb electrode including a plurality of third comb fingers and provided to the base portion; and a second movable comb electrode including a plurality of fourth comb fingers, the plurality of third comb fingers and the plurality of fourth comb fingers being alternately arranged. The drive method includes a drive step for applying a drive voltage having a time waveform periodically repeating rising and falling between the first fixed comb electrode and the first movable comb electrode. In the drive step, a voltage including a period to be a constant voltage excluding 0 V is applied between the second fixed comb electrode and the second movable comb electrode, a capacitance derivative signal indicating a derivative value of a capacitance between the second fixed comb electrode and the second movable comb electrode is generated by converting a current signal, which is output from the second fixed comb electrode or the second movable comb electrode within the period due to a change in the capacitance, into a voltage signal, a timing when the capacitance derivative signal reaches a threshold value is detected, and a relationship between the timing and a timing of the falling is controlled to be constant. 
     Advantageous Effects of Invention 
     According to the present disclosure, it is possible to provide a MEMS actuator, a MEMS actuator drive method, and a MEMS actuator control program capable of bringing the frequency of the drive voltage close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable portion. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a plan view showing the configuration of an optical module  1 A including a MEMS actuator. 
         FIG.  2    is a cross-sectional view taken along the line II-II of  FIG.  1   . 
         FIG.  3    is a schematic cross-sectional view of a mirror device  7  shown in  FIG.  1   . 
         FIG.  4    is an enlarged plan view of the mirror device  7  shown in  FIG.  1   . 
         FIG.  5    is a diagram schematically showing the circuit configuration of a drive unit  12 . 
         FIG.  6    is a diagram for explaining a drive voltage output from an actuator drive circuit  121 . 
         FIG.  7    is a circuit diagram showing a specific configuration example of a current-voltage conversion circuit  123 . 
         FIG.  8    is a graph showing the time change of each signal in an example. 
         FIG.  9    is a graph showing the time change of each signal in another example. 
         FIG.  10    is a graph showing the time change of each signal in still another example. 
         FIGS.  11 ( a ),  11 ( b ) and  11 ( c )  are graphs showing, as an example, measured data of time waveforms of a drive voltage Vin(t), a capacitance derivative signal Vout(t), and an output voltage Vcom(t) from a comparator  124 , respectively. 
         FIG.  12    is a graph showing a measurement result of the relationship between the frequency of the drive voltage Vin(t) and a time difference between a timing when the capacitance derivative signal Vout(t) becomes 0 V and the timing of falling PD. 
         FIG.  13    is a diagram conceptually showing ripple Ri superimposed on the drive voltage. 
         FIG.  14    is a circuit diagram showing the configuration of a current-voltage conversion circuit  123 A according to a first modification example. 
         FIG.  15    is a diagram showing the time waveforms of a drive voltage Vin(t), a current signal J 1 , an inverting input terminal voltage Va of an amplifier  123   a , a feedback current J 2 , and a capacitance derivative signal Vout(t) when a capacitance C a  does not change in a first embodiment. 
         FIG.  16    is a diagram showing the time waveforms of the drive voltage Vin(t), the current signal J 1 , the inverting input terminal voltage Va of the amplifier  123   a , currents J 3  and J 4 , the feedback current J 2 , and the capacitance derivative signal Vout(t) when the capacitance C a  does not change in a first modification example. 
         FIG.  17 ( a )  is a circuit diagram showing a clamp circuit  125  in this modification example, and  FIG.  17 ( b )  is a circuit diagram showing a general protection circuit  126  provided in an operational amplifier. 
         FIG.  18    is a circuit diagram showing the configuration of a current-voltage conversion circuit  123 B according to a second modification example. 
         FIG.  19    is a diagram illustrating the operation of the second modification example, where  FIG.  19 ( a )  shows the current-voltage conversion circuit  123 B shown in  FIG.  18    in a simplified manner and  FIG.  19 ( b )  is a graph showing a correlation between the current signal J 1  and the capacitance derivative signal Vout. 
         FIG.  20    is a diagram illustrating the operation of the second modification example, where  FIG.  20 ( a )  shows the current-voltage conversion circuit  123 B shown in  FIG.  18    in a simplified manner and  FIG.  20 ( b )  is a graph showing a correlation between the current signal J 1  and the capacitance derivative signal Vout. 
         FIG.  21    is a diagram illustrating the operation of the second modification example, where  FIG.  21 ( a )  shows the current-voltage conversion circuit  123 B shown in  FIG.  18    in a simplified manner and  FIG.  21 ( b )  is a graph showing a correlation between the current signal J 1  and the capacitance derivative signal Vout. 
         FIG.  22    is a graph relevant to the simulation results of the first modification example and the second modification example. 
         FIG.  23    is a block diagram showing the configuration of a drive unit  12 A according to a third modification example. 
         FIG.  24    is a graph showing the time change of each signal in the third modification example. 
         FIG.  25    is a diagram schematically showing the configuration of a timing detection circuit  122 A included in a mirror device of a fourth modification example. 
         FIG.  26    is a block diagram showing the configuration of a MEMS actuator  1 B as a second embodiment. 
         FIG.  27    is a diagram schematically showing a deformation state of a beam  91  when the beam  91  is located at one of vibrating ends. 
         FIG.  28 ( a )  is a diagram schematically showing a capacitance C 1  generated between a first fixed comb electrode  83  and a movable comb electrode  82  and a capacitance C 2  generated between a second fixed comb electrode  84  and the movable comb electrode  82  and  FIG.  28 ( b )  is a circuit diagram showing the current-voltage conversion circuit  123  connected to the capacitors C 1  and C 2 . 
         FIG.  29    is a graph showing the time change of each signal in an example. 
         FIG.  30 ( a )  is a graph showing the relationship between (V H ) 2  and the fluctuation width ΔC of the capacitance C a  in the first embodiment and  FIG.  30 ( b )  is a graph showing the relationship between (V H ) 2  and the fluctuation width ΔC of the capacitances C 1  and C 2  in the second embodiment. 
         FIG.  31    is a diagram schematically showing a fixed comb electrode  16  ( 18 ) and a movable comb electrode  17  ( 19 ) in the first embodiment. 
         FIG.  32    is a diagram showing a circuit for detecting the maximum and/or minimum of the displacement amount of a movable mirror  5  as a comparative example. 
         FIG.  33    is a circuit diagram showing a typical example of an envelope detector. 
         FIG.  34    is a graph showing an example of an input signal Vi to the envelope detector shown in  FIG.  33    and an output signal Vo. 
         FIG.  35    is a graph showing how the output signal Vo from the envelope detector cannot follow an actual envelope H of the input signal Vi. 
         FIG.  36    is a graph showing an example in which a signal Sb output from an arithmetic circuit  204  is measured in the circuit of the comparative example shown in  FIG.  32   . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A first MEMS actuator according to an embodiment includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a movable comb electrode that includes a plurality of second comb fingers and drives the movable portion by an electrostatic force generated between the fixed comb electrode and the movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a drive circuit that applies a drive voltage having a time waveform, which periodically repeats rising and falling and includes a period to be a constant voltage after the rising and before the falling, between the fixed comb electrode and the movable comb electrode; and a timing detection circuit that generates a capacitance derivative signal indicating a derivative value of a capacitance between the fixed comb electrode and the movable comb electrode by converting a current signal, which is output from the fixed comb electrode or the movable comb electrode within the period due to a change in the capacitance, into a voltage signal and detects a timing when the capacitance derivative signal reaches a threshold value. The drive circuit controls a relationship between the timing detected by the timing detection circuit and a timing of the falling to be constant. 
     In addition, a method for driving a first MEMS actuator according to an embodiment is a MEMS actuator drive method. The MEMS actuator includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a fixed comb electrode including a plurality of first comb fingers and provided to the base portion; and a movable comb electrode including a plurality of second comb fingers and driving the movable portion by an electrostatic force generated between the fixed comb electrode and the movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged. The drive method includes a drive step for applying a drive voltage having a time waveform, which periodically repeats rising and falling and includes a period to be a constant voltage after the rising and before the falling, between the fixed comb electrode and the movable comb electrode. In the drive step, a capacitance derivative signal indicating a derivative value of a capacitance between the fixed comb electrode and the movable comb electrode is generated by converting a current signal, which is output from the fixed comb electrode or the movable comb electrode within the period due to a change in the capacitance, into a voltage signal, a timing when the capacitance derivative signal reaches a threshold value is detected, and a relationship between the timing and a timing of the falling is controlled to be constant. 
     In the MEMS actuator and the drive method, a drive voltage having a time waveform periodically repeating rising and falling is applied between the fixed comb electrode and the movable comb electrode. Therefore, by bringing the frequency of the drive voltage close to the resonance frequency of the movable portion, the amplitude of the movable portion can be brought close to the maximum amplitude. At this time, due to the change in the capacitance between the fixed comb electrode and the movable comb electrode, a current signal is output from the fixed comb electrode or the movable comb electrode. When the time waveform of the drive voltage includes a period to be a constant voltage (excluding 0 V), the current signal within the period indicates a derivative value of the capacitance between the fixed comb electrode and the movable comb electrode. For example, when the movable portion passes through the center of the amplitude, the capacitance becomes a maximum, and the current value of this current signal momentarily becomes zero. 
     In the MEMS actuator and the drive method described above, the time waveform of the drive voltage includes a period to be a constant voltage after the rising and before the falling. Then, by converting the current signal output from the fixed comb electrode or the movable comb electrode within the period into a voltage signal, the capacitance derivative signal indicating the derivative value of the capacitance is generated. In addition, the timing when the capacitance derivative signal reaches a threshold value is detected, and the relationship between the timing and the timing of the falling is controlled to be constant. Therefore, since the position of the movable portion at the time of falling of the drive voltage can be made constant, the frequency of the drive voltage can be brought close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable portion. 
     The first MEMS actuator described above may further include a clamp circuit and/or a soft limiter circuit for shortening a fluctuation period of the capacitance derivative signal due to the rising of the drive voltage. In this case, by shortening the fluctuation period of the capacitance derivative signal at the rising of the drive voltage, it is possible to suppress a situation in which the detection of the timing when the capacitance derivative signal reaches a threshold value is interrupted by the fluctuation. 
     A second MEMS actuator according to another embodiment includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a first fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a first movable comb electrode that includes a plurality of second comb fingers and drives the movable portion by an electrostatic force generated between the first fixed comb electrode and the first movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a second fixed comb electrode including a plurality of third comb fingers and provided to the base portion; a second movable comb electrode including a plurality of fourth comb fingers, the plurality of third comb fingers and the plurality of fourth comb fingers being alternately arranged; a drive circuit that applies a drive voltage having a time waveform periodically repeating rising and falling between the first fixed comb electrode and the first movable comb electrode; and a timing detection circuit that applies a voltage including a period to be a constant voltage excluding 0 V between the second fixed comb electrode and the second movable comb electrode, generates a capacitance derivative signal indicating a derivative value of a capacitance between the second fixed comb electrode and the second movable comb electrode by converting a current signal, which is output from the second fixed comb electrode or the second movable comb electrode within the period due to a change in the capacitance, into a voltage signal, and detects a timing when the capacitance derivative signal reaches a threshold value. The drive circuit controls a relationship between the timing detected by the timing detection circuit and a timing of the falling to be constant. 
     In addition, a method for driving a second MEMS actuator according to another embodiment is a MEMS actuator drive method. The MEMS actuator includes: a base portion; a movable portion supported so as to be elastically displaceable with respect to the base portion; a first fixed comb electrode including a plurality of first comb fingers and provided to the base portion; a first movable comb electrode including a plurality of second comb fingers and driving the movable portion by an electrostatic force generated between the first fixed comb electrode and the first movable comb electrode, the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged; a second fixed comb electrode including a plurality of third comb fingers and provided on the base portion; and a second movable comb electrode including a plurality of fourth comb fingers, the plurality of third comb fingers and the plurality of fourth comb fingers being alternately arranged. The drive method includes a drive step for applying a drive voltage having a time waveform periodically repeating rising and falling between the first fixed comb electrode and the first movable comb electrode. In the drive step, a voltage including a period to be a constant voltage excluding 0 V is applied between the second fixed comb electrode and the second movable comb electrode, a capacitance derivative signal indicating a derivative value of a capacitance between the second fixed comb electrode and the second movable comb electrode is generated by converting a current signal, which is output from the second fixed comb electrode or the second movable comb electrode within the period due to a change in the capacitance, into a voltage signal, a timing when the capacitance derivative signal reaches a threshold value is detected, and a relationship between the timing and a timing of the falling is controlled to be constant. 
     In the MEMS actuator and the drive method, a drive voltage having a time waveform periodically repeating rising and falling is applied between the first fixed comb electrode and the first movable comb electrode. Therefore, by bringing the frequency of the drive voltage close to the resonance frequency of the movable portion, the amplitude of the movable portion can be brought close to the maximum amplitude. At this time, since the second movable comb electrode is also displaced together with the movable portion, a current signal is output from the second fixed comb electrode or the second movable comb electrode due to the change in the capacitance between the second fixed comb electrode and the second movable comb electrode. When a voltage including a period to be a constant voltage excluding 0 V is applied between the second fixed comb electrode and the second movable comb electrode, the current signal within the period indicates the derivative value of the capacitance between the second fixed comb electrode and the second movable comb electrode. For example, when the movable portion passes through the center of the amplitude, the capacitance becomes a maximum, and the current value of this current signal momentarily becomes zero. 
     In the MEMS actuator and the drive method described above, a voltage including a period to be a constant voltage excluding 0 V is applied between the second fixed comb electrode and the second movable comb electrode. Then, by converting the current signal output from the second fixed comb electrode or the second movable comb electrode within the period into a voltage signal, the capacitance derivative signal indicating the derivative value of the capacitance is generated. In addition, the timing when the capacitance derivative signal reaches a threshold value is detected, and the relationship between the timing and the timing of the falling is controlled to be constant. Therefore, since the position of the movable portion at the time of falling of the drive voltage can be made constant, the frequency of the drive voltage can be brought close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable portion. 
     In the second MEMS actuator described above, a distance between the second movable comb electrode and the movable portion may be shorter than a distance between the first movable comb electrode and the movable portion. In this case, since the amplitude of the second movable comb electrode can be made larger, it is possible to improve the detection accuracy of the timing when the capacitance derivative signal reaches a threshold value. 
     In the first and second MEMS actuators described above, the drive circuit may match the falling timing with the timing when the capacitance derivative signal reaches the threshold value. Similarly, in the drive step of the first and second drive methods described above, the falling timing may be made to match the timing when the capacitance derivative signal reaches the threshold value. For example, in these manners, it is possible to control the relationship between the timing when the capacitance derivative signal reaches the threshold value and the falling timing to be constant. 
     In the first and second MEMS actuators described above, the drive circuit may shift the falling timing to a predetermined time after the timing when the capacitance derivative signal reaches the threshold value. Similarly, in the drive step of the first and second drive methods described above, the falling timing may be shifted to a predetermined time after the timing when the capacitance derivative signal reaches the threshold value. For example, in these manners, it is possible to control the relationship between the timing when the capacitance derivative signal reaches the threshold value and the falling timing to be constant. Further, since it can be confirmed that the capacitance derivative signal has reached the threshold value before the drive voltage drops (that is, the capacitance derivative signal disappears), the timing when the capacitance derivative signal reaches the threshold value can be detected more reliably. 
     In the first and second MEMS actuators described above, the threshold value may be a value corresponding to a case where the current signal is zero. Similarly, in the first and second drive methods described above, the threshold value may be a value corresponding to a case where the current signal is zero. In this case, it is possible to accurately detect the timing when the movable comb electrode and the fixed comb electrode are closest to each other (in an example, the timing suitable for the falling of the drive voltage). 
     In the first and second MEMS actuators described above, the time waveform of the drive voltage may periodically include a rectangular wave with the rising and the falling, and a duty ratio of the drive voltage may be 20% or more and less than 50%. Similarly, in the first and second drive methods described above, the time waveform of the drive voltage may periodically include a rectangular wave with the rising and the falling, and a duty ratio of the drive voltage may be 20% or more and less than 50%. Assuming that the duty ratio of the drive voltage is 50%, there is a possibility that electrostatic attraction is applied at the timing when the movable comb electrode and the fixed comb electrode move away from each other due to a control error or the like. This leads to a decrease in the amplitude of the movable portion. By setting the duty ratio of the drive voltage to less than 50%, such a possibility can be reduced. In addition, by setting the duty ratio of the drive voltage to 20% or more, sufficient electrostatic attraction can be applied between the movable comb electrode and the fixed comb electrode. 
     In the first and second MEMS actuators described above, the timing detection circuit may include a comparator for comparing the capacitance derivative signal with the threshold value. Similarly, in the drive step of the first and second drive methods described above, a comparison between the capacitance derivative signal and the threshold value may be performed by using a comparator. In this case, since the timing when the capacitance derivative signal reaches the threshold value can be detected by a simple circuit, it is possible to contribute to the miniaturization and cost reduction of the MEMS actuator. 
     In the first and second MEMS actuators described above, the timing detection circuit may include a transimpedance amplifier for converting the current signal into the voltage signal. Similarly, in the drive step of the first and second drive methods described above, the current signal may be converted into the voltage signal by using a transimpedance amplifier. In this case, for example, as compared with a case where a resistor (shunt resistor) is connected in series with the fixed comb electrode or the movable comb electrode and the current signal is converted into the voltage signal by using the voltage drop in the resistor, it is possible to reduce the fluctuation in the voltage between the comb electrodes and apply a desired voltage between the comb electrodes with high accuracy. 
     The first and second MEMS actuators described above may further include an integrator circuit for time-integrating the capacitance derivative signal. By time-integrating the capacitance derivative signal, the displacement amount of the movable portion in a predetermined period can be easily detected. 
     In the first and second MEMS actuators described above, the movable portion may be a vertical vibration type. When the movable comb electrode is provided in the movable portion in the vertical vibration type, regardless of the position of the movable portion where the movable comb electrode is provided, the moment of inertia that increases is constant, and the amount of decrease in the resonance frequency is also constant. Therefore, since the number of comb fingers can be increased, a large capacitance value can be obtained. In addition, in the vertical vibration method, the speed of the movable portion is the fastest at the timing when the capacitance value is the largest (the timing when the capacitance derivative value is zero). For this reason, the time change of the capacitance derivative value increases. From the above, in the vertical vibration method, high timing detection accuracy is obtained, and accordingly, it is possible to relatively easily match the timing when the movable portion passes through a predetermined position with the falling timing of the drive signal. 
     In the first and second MEMS actuators described above, the movable portion may be a slide type. Even in this case, the effects of the first and second MEMS actuators described above can be appropriately suitably achieved. 
     A first MEMS actuator control program according to an embodiment is a program for causing a computer to execute a process for controlling the drive circuit of any of the MEMS actuators described above, and controls rising and falling timings of the drive voltage output from the drive circuit while controlling the relationship between the timing detected by the timing detection circuit and the falling timing to be constant. In addition, a second MEMS actuator control program according to an embodiment is a program for causing a computer to execute a process for realizing the drive step in the drive method according to any of the drive methods described above, and controls rising and falling timings of the drive voltage while controlling the relationship between the timing when the capacitance derivative signal reaches the threshold value and the falling timing to be constant. 
     Hereinafter, specific examples of the MEMS actuator, the MEMS actuator drive method, and the MEMS actuator control program of the present disclosure will be described with reference to the diagrams. In addition, the invention is not limited to these examples but is defined by the claims, and is intended to include all modifications within the meaning and scope equivalent to the claims. In the following description, in the description of the diagrams, the same elements are denoted by the same reference numerals, and the repeated description thereof will be omitted. 
     First Embodiment 
       FIG.  1    is a plan view showing the configuration of an optical module  1 A including a MEMS actuator.  FIG.  2    is a cross-sectional view taken along the line II-II of  FIG.  1   . The optical module  1 A can be used in an optical device such as a Fourier Transform Infrared Spectrometer (FTIR), for example. As shown in  FIGS.  1  and  2   , the optical module  1 A of the present embodiment includes a mirror unit  2  and a package  3  in which the mirror unit  2  is housed. The package  3  has a support  31 . The mirror unit  2  is arranged on one side of the support  31  in the Z-axis direction, and is attached to the support  31  by, for example, an adhesive. The support  31  is formed of, for example, copper tungsten, and has, for example, a rectangular plate shape. The mirror unit  2  includes a movable mirror  5  that moves along the Z-axis direction and a fixed mirror  6  whose position is fixed. In the optical module  1 A, an interference optical system can be formed by a beam splitter unit (not shown), the movable mirror  5 , and the fixed mirror  6 . The interference optical system is, for example, a Michelson interference optical system. 
     The mirror unit  2  includes the fixed mirror  6 , a mirror device  7 , an optical functional member  8 , and a stress reduction substrate  9 . The mirror device  7  is an example of the MEMS actuator in the present embodiment, and includes a base (base portion)  11 , the movable mirror  5  (movable portion), and a drive unit  12 . 
     The base  11  has a main surface  11   a  and a back surface  11   b  on a side opposite to the main surface  11   a . The base  11  has, for example, a rectangular plate shape, and the size of the planar shape thereof is, for example, 10 mm in the lateral direction and 15 mm in the longitudinal direction. The thickness of the base  11  is, for example, 0.35 mm. The movable mirror  5  has a mirror surface  5   a  and a mirror support portion  5   b  on which the mirror surface  5   a  is arranged. The movable mirror  5  is a movable portion using a vertical vibration method, and is elastically supported with respect to the base  11  so as to be displaceable along the Z-axis direction perpendicular to the main surface  11   a . The drive unit  12  generates a driving force for displacing the movable mirror  5  along the Z-axis direction. 
     A pair of light passing portions  7   a  and  7   b  are provided in the mirror device  7 . The pair of light passing portions  7   a  and  7   b  are arranged on both sides of the movable mirror  5  in the X-axis direction. 
     Here, the configuration of the mirror device  7  will be described in detail with reference to  FIGS.  2 ,  3  and  4   .  FIG.  3    is a schematic cross-sectional view of the mirror device  7  shown in  FIG.  1   .  FIG.  3    schematically shows the mirror device  7  in a state in which the dimension in the Z-axis direction is enlarged more than the actual size.  FIG.  4    is an enlarged plan view of the mirror device  7  shown in  FIG.  1   . 
     The base  11 , the mirror support portion  5   b  of the movable mirror  5 , and the drive unit  12  are formed by an SOI (Silicon On Insulator) substrate  20 . The mirror device  7  is formed, for example, in a rectangular plate shape. The SOI substrate  20  has a support layer  21 , a device layer  22 , and an intermediate layer  23 . The support layer  21  and the device layer  22  are silicon layers. The intermediate layer  23  is an insulating layer arranged between the support layer  21  and the device layer  22 . The SOI substrate  20  has the support layer  21 , the intermediate layer  23 , and the device layer  22  in this order from one side in the Z-axis direction. 
     The base  11  is formed by parts of the support layer  21 , the device layer  22 , and the intermediate layer  23 . The main surface  11   a  of the base  11  is a surface of the support layer  21  on a side opposite to the intermediate layer  23 . The back surface  11   b  of the base  11  is a surface of the device layer  22  on a side opposite to the intermediate layer  23 . The support layer  21  forming the base  11  is thicker than the device layer  22  forming the base  11 . The thickness of the support layer  21  forming the base  11  is, for example, about four times the thickness of the device layer  22  forming the base  11 . In the mirror unit  2 , as shown in  FIG.  2   , the back surface  11   b  of the base  11  and a surface  8   a  of the optical functional member  8  are bonded to each other. 
     The movable mirror  5  is arranged with the intersection of an axis line R 1  and an axis line R 2  as its center position (center of gravity position). The axis line R 1  is a straight line extending in the X-axis direction. The axis line R 2  is a straight line extending in the Y-axis direction. When viewed from the Z-axis direction, the mirror device 7 has a shape approximately axisymmetric with respect to each of the axis line R 1  and the axis line R 2 . The mirror support portion  5   b  of the movable mirror  5  has an arrangement portion  51 , a frame portion  52 , a pair of connection portions  53 , and a rib portion  54 . The arrangement portion  51 , the frame portion  52 , and the pair of connection portions  53  are formed by a part of the device layer  22 . The arrangement portion  51  has a circular shape when viewed from the Z-axis direction. A metal film is provided on a surface  51   a  of the arrangement portion  51  on one side in the Z-axis direction, and the surface of the metal film is the mirror surface  5   a . The mirror surface  5   a  extends vertically in the Z-axis direction and has a circular shape. The surface  51   a  of the arrangement portion  51  is a surface of the device layer  22  on the intermediate layer  23  side. 
     The frame portion  52  extends in an annular shape when viewed from the Z-axis direction, and surrounds the arrangement portion  51  at a distance from the arrangement portion  51 . Each of the pair of connection portions  53  connects the arrangement portion  51  and the frame portion  52  to each other. The pair of connection portions  53  are arranged on both sides of the arrangement portion  51  in the Y-axis direction. 
     The rib portion  54  is formed by the support layer  21  and the intermediate layer  23  arranged on the device layer  22 . The rib portion  54  has an inner rib portion  54   a , an outer rib portion  54   b , and a pair of connecting rib portions  54   c . The inner rib portion  54   a  is arranged on the surface of the arrangement portion  51  on one side in the Z-axis direction. The inner rib portion  54   a  surrounds the mirror surface  5   a  when viewed from the Z-axis direction. The outer rib portion  54   b  is arranged on the surface of the frame portion  52  on one side in the Z-axis direction. The outer rib portion  54   b  surrounds the inner rib portion  54   a  when viewed from the Z-axis direction, and surrounds the mirror surface  5   a . The pair of connecting rib portions  54   c  are arranged on the surfaces of the pair of connection portions  53  on one side in the Z-axis direction. Each connecting rib portion  54   c  connects the inner rib portion  54   a  and the outer rib portion  54   b  to each other. 
     The drive unit  12  has a first elastic support portion  13 , a second elastic support portion  14 , and an actuator portion  15 . The first elastic support portion  13 , the second elastic support portion  14 , and the actuator portion  15  are formed by a part of the device layer  22 . 
     Each of the first elastic support portion  13  and the second elastic support portion  14  is connected between the base  11  and the movable mirror  5 . The first elastic support portion  13  and the second elastic support portion  14  elastically support the movable mirror  5  so that the movable mirror  5  (mirror support portion  5   b ) can be displaced along the Z-axis direction (direction crossing the mirror surface  5   a ). 
     The first elastic support portion  13  includes a pair of levers  131 , a first link member  132 , a second link member  133 , an intermediate member  134 , a pair of first torsion bars  135 , a pair of second torsion bars  136 , a pair of non-linearity reduction springs  137 , and a plurality of electrode support portions  138 . 
     The pair of levers  131  are arranged on both sides of the light passing portion  7   a  in the Y-axis direction, and face each other in the Y-axis direction. Each lever  131  has a plate shape extending along a plane perpendicular to the Z-axis direction. The first link member  132  is hung between the end portions of the pair of levers  131  on a side opposite to the movable mirror  5 . The first link member  132  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. The second link member  133  is hung between the end portions of the pair of levers  131  on the movable mirror  5  side. The second link member  133  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. 
     The pair of levers  131 , the first link member  132 , and the second link member  133  define the light passing portion  7   a . The light passing portion  7   a  is, for example, a cavity (hole). Alternatively, a light transmissive material may be arranged in the light passing portion  7   a . 
     The intermediate member  134  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. The intermediate member  134  is arranged between the movable mirror  5  and the second link member  133  (in other words, between the movable mirror  5  and the light passing portion  7   a ). The intermediate member  134  is connected to the movable mirror  5  through the non-linearity reduction spring  137 , as will be described later. 
     The pair of first torsion bars  135  are hung between one end portion of one lever  131  and the base  11  and between one end portion of the other lever  131  and the base  11 , respectively. That is, the pair of first torsion bars  135  are connected between the pair of levers  131  and the base  11 . Each first torsion bar  135  extends along the Y-axis direction. The pair of first torsion bars  135  are arranged on the same center line parallel to the Y-axis direction. 
     The pair of second torsion bars  136  are hung between the other end portion of one lever  131  and one end of the intermediate member  134  and between the other end portion of the other lever  131  and the other end of the intermediate member  134 , respectively. That is, the pair of second torsion bars  136  are connected between the pair of levers  131  and the movable mirror  5 . Each second torsion bar  136  extends along the Y-axis direction. The pair of second torsion bars  136  are arranged on the same center line parallel to the Y-axis direction. 
     The pair of non-linearity reduction springs  137  are connected between the movable mirror  5  and the intermediate member  134 . That is, the pair of non-linearity reduction springs  137  are connected between the movable mirror  5  and the second torsion bar  136 . Each non-linearity reduction spring  137  meanders and extends when viewed from the Z-axis direction. One end of each non-linearity reduction spring  137  is connected to the intermediate member  134 , and the other end of each non-linearity reduction spring  137  is connected to the frame portion  52 . The non-linearity reduction spring  137  is configured such that, when the movable mirror  5  is displaced in the Z-axis direction, the amount of deformation of the non-linearity reduction spring  137  around the Y-axis direction is smaller than the amount of deformation of each of the first torsion bar  135  and the second torsion bar  136  around the Y-axis direction and the amount of deformation of the non-linearity reduction spring  137  in the X-axis direction is larger than the amount of deformation of each of the first torsion bar  135  and the second torsion bar  136  in the X-axis direction. Therefore, since it is possible to suppress the non-linearity in the torsional deformation of the first torsion bar  135  and the second torsion bar  136 , it is possible to suppress the degradation of the control characteristics of the movable mirror  5  due to the non-linearity. 
     The plurality of electrode support portions  138  include a pair of first electrode support portions  138   a , a pair of second electrode support portions  138   b , and a pair of third electrode support portions  138   c . Each of the electrode support portions  138   a ,  138   b , and  138   c  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. Each of the electrode support portions  138   a ,  138   b , and  138   c  extends from the lever  131  toward the side opposite to the light passing portion  7   a . The pair of first electrode support portions  138   a  are arranged on the same center line parallel to the Y-axis direction. The pair of second electrode support portions  138   b  are arranged on the same center line parallel to the Y-axis direction. The pair of third electrode support portions  138   c  are arranged on the same center line parallel to the Y-axis direction. In the X-axis direction, the first electrode support portion  138   a , the second electrode support portion  138   b , and the third electrode support portion  138   c  are arranged side by side in this order from the movable mirror  5  side. 
     The second elastic support portion  14  includes a pair of levers  141 , a first link member  142 , a second link member  143 , an intermediate member  144 , a pair of first torsion bars  145 , a pair of second torsion bars  146 , a pair of non-linearity reduction springs  147 , and a plurality of electrode support portions  148 . 
     The pair of levers  141  are arranged on both sides of the light passing portion  7   b  in the Y-axis direction, and face each other in the Y-axis direction. Each lever  141  has a plate shape extending along a plane perpendicular to the Z-axis direction. The first link member  142  is hung between the end portions of the pair of levers  141  on a side opposite to the movable mirror  5 . The first link member  142  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. The second link member  143  is hung between the end portions of the pair of levers  141  on the movable mirror  5  side. The second link member  143  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. 
     The pair of levers  141 , the first link member  142 , and the second link member  143  define the light passing portion  7   b . The light passing portion  7   b  is, for example, a cavity (hole). Alternatively, a light transmissive material may be arranged in the light passing portion  7   b . 
     The intermediate member  144  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. The intermediate member  144  is arranged between the movable mirror  5  and the second link member  143  (in other words, between the movable mirror  5  and the light passing portion  7   b ). The intermediate member  144  is connected to the movable mirror  5  through the non-linearity reduction spring  147 , as will be described later. 
     The pair of first torsion bars  145  are hung between one end portion of one lever  141  and the base  11  and between one end portion of the other lever  141  and the base  11 , respectively. That is, the pair of first torsion bars  145  are connected between the pair of levers  141  and the base  11 . Each first torsion bar  145  extends along the Y-axis direction. The pair of first torsion bars  145  are arranged on the same center line parallel to the Y-axis direction. 
     The pair of second torsion bars  146  are hung between the other end portion of one lever  141  and one end of the intermediate member  144  and between the other end portion of the other lever  141  and the other end of the intermediate member  144 , respectively. That is, the pair of second torsion bars  146  are connected between the pair of levers  141  and the movable mirror  5 . Each second torsion bar  146  extends along the Y-axis direction. The pair of second torsion bars  146  are arranged on the same center line parallel to the Y-axis direction. 
     The pair of non-linearity reduction springs  147  are connected between the movable mirror  5  and the intermediate member  144 . That is, the pair of non-linearity reduction springs  147  are connected between the movable mirror  5  and the second torsion bar  146 . Each non-linearity reduction spring  147  meanders and extends when viewed from the Z-axis direction. One end of each non-linearity reduction spring  147  is connected to the intermediate member  144 , and the other end of each non-linearity reduction spring  147  is connected to the frame portion  52 . The non-linearity reduction spring  147  is configured such that, when the movable mirror  5  is displaced in the Z-axis direction, the amount of deformation of the non-linearity reduction spring  147  around the Y-axis direction is smaller than the amount of deformation of each of the first torsion bar  145  and the second torsion bar  146  around the Y-axis direction and the amount of deformation of the non-linearity reduction spring  147  in the X-axis direction is larger than the amount of deformation of each of the first torsion bar  145  and the second torsion bar  146  in the X-axis direction. Therefore, since it is possible to suppress the non-linearity in the torsional deformation of the first torsion bar  145  and the second torsion bar  146 , it is possible to suppress the degradation of the control characteristics of the movable mirror  5  due to the non-linearity. 
     The plurality of electrode support portions  148  include a pair of first electrode support portions  148   a , a pair of second electrode support portions  148   b , and a pair of third electrode support portions  148   c . Each of the electrode support portions  148   a ,  148   b , and  148   c  has a plate shape extending along a plane perpendicular to the Z-axis direction, and extends along the Y-axis direction. Each of the electrode support portions  148   a ,  148   b , and  148   c  extends from the lever  141  toward the side opposite to the light passing portion  7   b . The pair of first electrode support portions  148   a  are arranged on the same center line parallel to the Y-axis direction. The pair of second electrode support portions  148   b  are arranged on the same center line parallel to the Y-axis direction. The pair of third electrode support portions  148   c  are arranged on the same center line parallel to the Y-axis direction. In the X-axis direction, the first electrode support portion  148   a , the second electrode support portion  148   b , and the third electrode support portion  148   c  are arranged side by side in this order from the movable mirror  5  side. 
     The actuator portion  15  generates a driving force for displacing the movable mirror  5  along the Z-axis direction. The actuator portion  15  has fixed comb electrodes  16  and  18  and movable comb electrodes  17  and  19 . The fixed comb electrodes  16  and  18  are provided on the base  11 , and the positions of the fixed comb electrodes  16  and  18  are fixed by the base  11 . The movable comb electrodes  17  and  19  are connected to the electrode support portions  138  and  148 , respectively, and are provided so as to be displaceable in the Z direction relative to the fixed comb electrodes  16  and  18 , respectively. 
     More specifically, the fixed comb electrode  16  is provided on a part of the surface of the device layer  22  of the base  11  facing the electrode support portion  138 . The fixed comb electrode  16  has a plurality of fixed comb fingers (first comb fingers)  16   a  extending along a plane perpendicular to the Y-axis direction. These fixed comb fingers  16   a  are arranged side by side at predetermined distances therebetween in the Y-axis direction. The movable comb electrode  17  is provided on the surface of each electrode support portion  138  on the movable mirror  5  side. The movable comb electrode  17  has a plurality of movable comb fingers (second comb fingers)  17   a  extending along a plane perpendicular to the Y-axis direction. These movable comb fingers  17   a  are arranged side by side at predetermined distances therebetween in the Y-axis direction. 
     In the fixed comb electrode  16  and the movable comb electrode  17 , a plurality of fixed comb fingers  16   a  and a plurality of movable comb fingers  17   a  are alternately arranged. That is, each fixed comb finger  16   a  of the fixed comb electrode  16  is located between the movable comb fingers  17   a  of the movable comb electrode  17 . The fixed comb fingers  16   a  and the movable comb fingers  17   a  adjacent to each other face each other in the Y-axis direction. The distance between the fixed comb fingers  16   a  and the movable comb fingers  17   a  adjacent to each other is, for example, about several µm. 
     The fixed comb electrode  18  is provided on a part of the surface of the device layer  22  of the base  11  facing the electrode support portion  148 . The fixed comb electrode  18  has a plurality of fixed comb fingers (first comb fingers)  18   a  extending along a plane perpendicular to the Y-axis direction. These fixed comb fingers  18   a  are arranged side by side at predetermined distances therebetween in the Y-axis direction. The movable comb electrode  19  is provided on the surface of each electrode support portion  148  on the movable mirror  5  side. The movable comb electrode  19  has a plurality of movable comb fingers (second comb fingers)  19   a  extending along a plane perpendicular to the Y-axis direction. These movable comb fingers  19   a  are arranged side by side at predetermined distances therebetween in the Y-axis direction. 
     In the fixed comb electrode  18  and the movable comb electrode  19 , a plurality of fixed comb fingers  18   a  and a plurality of movable comb fingers  19   a  are alternately arranged. That is, each fixed comb finger  18   a  of the fixed comb electrode  18  is located between the movable comb fingers  19   a  of the movable comb electrode  19 . The fixed comb fingers  18   a  and the movable comb fingers  19   a  adjacent to each other face each other in the Y-axis direction. The distance between the fixed comb fingers  18   a  and the movable comb fingers  19   a  adjacent to each other is, for example, about several µm. 
     As shown in  FIG.  1   , a plurality of electrode pads  71  are provided on the base  11 . Each electrode pad  71  is arranged on the surface of the device layer  22  in an opening formed on the main surface  11   a  of the base  11  so as to reach the device layer  22 . Some of the plurality of electrode pads  71  are electrically connected to the fixed comb electrode  16  or the fixed comb electrode  18  through the device layer  22 . The other some of the plurality of electrode pads  71  are electrically connected to the movable comb electrode  17  or the movable comb electrode  19  through the first elastic support portion  13  or the second elastic support portion  14 . In addition, a pair of electrode pads  72  used as ground electrodes are provided on the base  11 . The pair of electrode pads  72  are arranged on the main surface  11   a  so as to be located on both sides of the movable mirror  5  in the Y-axis direction. 
     In the mirror device  7  having the above configuration, a drive voltage for displacing the movable mirror  5  along the Z-axis direction is input to the drive unit  12  through a lead pin  33 . As a result, for example, an electrostatic force is generated between the fixed comb electrode  16  and the movable comb electrode  17  facing each other and between the fixed comb electrode  18  and the movable comb electrode  19  facing each other so that the movable mirror  5  is displaced to one side in the Z-axis direction. At this time, in the first elastic support portion  13  and the second elastic support portion  14 , the first torsion bars  135  and  145  and the second torsion bars  136  and  146  are twisted to generate elastic force in the first elastic support portion  13  and the second elastic support portion  14 . In the mirror device  7 , by applying a periodic drive voltage to the drive unit  12 , the movable mirror  5  is driven so as to reciprocate at its resonance frequency along the Z-axis direction. In this manner, the drive unit  12  functions as an electrostatic actuator. 
       FIG.  2    is referred to again. The optical functional member  8  has the surface  8   a  facing the back surface  11   b  of the base  11  and a back surface  8   b  on a side opposite to the surface  8   a . The optical functional member  8  is integrally formed of a light transmissive material. The optical functional member  8  is formed in a rectangular plate shape by using, for example, glass, and has a size of, for example, a width of about 15 mm, a length of about 20 mm, and a thickness of about 4 mm. In addition, the material of the optical functional member  8  is selected according to the sensitivity wavelength of the optical module  1 A so that, for example, glass is used when the sensitivity wavelength of the optical module  1 A is in the near-infrared region and silicon is used when the sensitivity wavelength of the optical module  1 A is in the mid-infrared region. The optical functional member  8  corrects the optical path difference generated between the light entering and exiting the movable mirror  5  and the light entering and exiting the fixed mirror  6 . The surface  8   a  of the optical functional member  8  is bonded to the back surface  11   b  of the base  11  by direct bonding (for example, plasma-activated bonding, surface-activated bonding, atomic diffusion bonding, anode bonding, fusion bonding, and hydrophilized bonding). 
     The fixed mirror  6  is arranged on a side opposite to the mirror device  7  with respect to the optical functional member  8 , and the position of the fixed mirror  6  with respect to the base  11  of the mirror device  7  is fixed. The fixed mirror  6  is formed on the back surface  8   b  of the optical functional member  8  by, for example, vapor deposition. The fixed mirror  6  has a mirror surface  6   a  perpendicular to the Z-axis direction. In the present embodiment, the mirror surface  5   a  of the movable mirror  5  and the mirror surface  6   a  of the fixed mirror  6  face one side in the Z-axis direction. The fixed mirror  6  reflects the light transmitted through the optical functional member  8 . 
     The stress reduction substrate  9  is attached to the back surface  8   b  of the optical functional member  8  with the fixed mirror  6  interposed therebetween. The stress reduction substrate  9  is attached to the fixed mirror  6  by using, for example, an adhesive. The coefficient of thermal expansion of the stress reduction substrate  9  is closer to the coefficient of thermal expansion of the base  11  (more specifically, the coefficient of thermal expansion of the support layer  21 ) than the coefficient of thermal expansion of the optical functional member  8 . In addition, the thickness of the stress reduction substrate  9  is closer to the thickness of the base  11  than the thickness of the optical functional member  8 . The stress reduction substrate  9  is formed in a rectangular plate shape by using, for example, silicon, and has a size of, for example, a width of about 16 mm, a length of about 21 mm, and a thickness of about 0.65 mm. 
     As shown in  FIGS.  1  and  2   , the package  3  has the support  31 , a plurality of lead pins  33 , a frame body  34 , and a light transmissive member  35 . The frame body  34  is formed so as to surround the mirror unit  2  when viewed from the Z-axis direction, and is attached to a surface  31   a  of the support  31  by using an adhesive such as silver wax. The frame body  34  is formed of, for example, ceramic, and has, for example, a rectangular frame shape. An end surface  34   a  of the frame body  34  on a side opposite to the support  31  is located on a side opposite to the support  31  with respect to the virtual plane including the main surface  11   a  of the base  11 . 
     The light transmissive member  35  is formed so as to close the opening of the frame body  34 , and is attached to the end surface  34   a  of the frame body  34  by using, for example, an adhesive. The light transmissive member  35  is formed of a light transmissive material, and has, for example, a rectangular plate shape. Here, since the end surface  34   a  of the frame body  34  is located on the side opposite to the support  31  with respect to the virtual plane including the main surface  11   a  of the base  11 , the light transmissive member  35  is spaced apart from the mirror device  7 . Therefore, in the optical module  1 A, when the movable mirror  5  reciprocates along the Z-axis direction, the movable mirror  5  and the drive unit  12  are prevented from coming into contact with the light transmissive member  35 . 
     Each lead pin  33  is provided in the frame body  34  so that one end portion  33   a  is located inside the frame body  34  and the other end portion (not shown) is located outside the frame body  34 . One end portion  33   a  of the lead pin  33  is electrically connected to the electrode pads  71  and  72  corresponding to the lead pin  33  in the mirror device  7  through a wire (not shown). In the optical module  1 A, a drive voltage for displacing the movable mirror  5  along the Z-axis direction is input to the drive unit  12  through the plurality of lead pins  33 . In the present embodiment, a stepped surface  34   b  extending in the X-axis direction is formed on both sides of the optical functional member  8  in the Y-axis direction, and one end portion  33   a  of each lead pin  33  is arranged on the stepped surface  34   b . Each lead pin  33  extends in the Z-axis direction on both sides of the support  31  in the Y-axis direction, and the other end portion of each lead pin  33  is located below the support  31  in the Z-axis direction. 
     Subsequently, the drive unit  12  will be further described.  FIG.   5    is a diagram schematically showing the circuit configuration of the drive unit  12 . As shown in the diagram, the drive unit  12  includes an actuator drive circuit  121  and a timing detection circuit  122 . In  FIG.  5   , the capacitance between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  is shown in a pseudo manner by a variable capacitance symbol. 
     The actuator drive circuit  121  is an example of a drive circuit in the present embodiment. The actuator drive circuit  121  applies a drive voltage between the fixed comb electrode  16  and the movable comb electrode  17  described above and between the fixed comb electrode  18  and the movable comb electrode  19  described above. The actuator drive circuit  121  includes, for example, a signal processing unit including an integrated circuit such as an FPGA (field-programmable gate array), a storage unit including a non-volatile memory such as an EEPROM (Electrically Erasable Programmable Read-Only Memory) electrically connected to the signal processing unit, and a high voltage generation circuit electrically connected to the signal processing unit. The signal processing unit generates a drive signal that is the basis of the drive voltage. The high voltage generation circuit generates a drive voltage based on the drive signal from the signal processing unit. The high voltage generation circuit is, for example, an HVIC (High Voltage IC). 
       FIG.  6    is a diagram for explaining a drive voltage output from the actuator drive circuit  121 .  FIG.  6    shows a graph G 1  showing the time change of the position of the movable mirror  5  and a graph G 2  showing the time waveform of the drive voltage. The horizontal axis of the graphs G 1  and G 2  indicate time. The vertical axis of the graph G 1  indicates the position of the movable mirror  5  in the Z direction, and the vertical axis of the graph G 2  indicates the magnitude of the voltage. In addition, in  FIG.  6   , FIGS. A to D showing the relative positional relationship between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) at the plurality of timings T 1  to T 4  are shown. As shown in  FIG.  6   , the actuator drive circuit  121  generates a drive voltage having a frequency that is twice the resonance frequency of the movable mirror  5 . The drive voltage is a continuous pulse signal that repeats rising and falling at fixed periods, and in the present embodiment, is a rectangular wave having a duty ratio of 20% or more and less than 50%, for example. 
     The rising timing of the drive voltage is controlled to match or slightly lag behind the timing of the maximum point and the minimum point corresponding to the turning point in the time change of the position of the movable mirror  5 . In addition, the falling timing of the drive voltage is controlled to match or be slightly delayed from the timing of the midpoint between the maximum point and the minimum point of the movable mirror  5 . In addition, in  FIG.  6   , the solid arrow indicates the direction of movement of the movable mirror  5 , and the broken arrow indicates the direction of the driving force applied to the movable mirror  5 . In addition, the fixed comb electrode  16  ( 18 ) with hatching indicates a state in which a voltage is applied, and the fixed comb electrode  16  ( 18 ) without hatching indicates a state in which no voltage is applied. 
     In addition, the relationship between the frequency of the drive voltage and the amplitude of the movable mirror  5  can be obtained by actually operating the mirror device  7 . Alternatively, the relationship between the frequency of the drive voltage and the amplitude of the movable mirror  5  may be predicted by numerical analysis, such as the Runge-Kutta method. 
       FIG.  5    is referred to again. The timing detection circuit  122  is provided in order to detect the timing when the displacement of the movable mirror  5  becomes zero (that is, the position of the movable mirror  5  is the midpoint between the maximum point and the minimum point) in the time change of the position of the movable mirror  5  (graph G 1  in  FIG.  6   ). In addition, when the displacement of the movable mirror  5  becomes zero, the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) are closest to each other. The actuator drive circuit  121  brings the frequency of the drive voltage close to the resonance frequency of the movable mirror  5  by controlling the relationship between the timing detected by the timing detection circuit  122  and the falling timing of the drive voltage to be constant (preferably match each other). 
     The timing detection circuit  122  is electrically connected to one of the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). The timing detection circuit  122  includes a current-voltage conversion circuit  123  and a comparator  124 . The current-voltage conversion circuit  123  converts the current signal output from the fixed comb electrode  16  ( 18 ) or the movable comb electrode  17  ( 19 ) into a voltage signal. The signal output end of the current-voltage conversion circuit  123  is electrically connected to the signal input end of the comparator  124 . The comparator  124  compares the voltage signal output from the current-voltage conversion circuit  123  with a predetermined threshold value (0 V in the diagram), and outputs a signal indicating the comparison result. 
     The signal output end of the comparator  124  is electrically connected to the actuator drive circuit  121 . The actuator drive circuit  121  controls the relationship between the timing when the displacement of the movable mirror  5  becomes zero and the timing when the drive voltage falls to be constant based on the output signal from the comparator  124 . 
     The actuator drive circuit  121  is controlled by using, for example, a computer provided outside the optical module  1 A. This computer includes a central processing unit (CPU), a volatile memory (RAM), and a non-volatile memory (ROM), and controls the actuator drive circuit  121  by executing a program stored in advance in the ROM. The program controls the rising and falling timings of the drive voltage output from the actuator drive circuit  121  while controlling the relationship between the timing when the displacement of the movable mirror  5  detected by the timing detection circuit  122  becomes zero and the timing when the drive voltage falls to be constant. 
       FIG.  7    is a circuit diagram showing a specific configuration example of the current-voltage conversion circuit  123 . As shown in  FIG.  7   , the current-voltage conversion circuit  123  is formed by, for example, a transimpedance amplifier (TIA) including an amplifier  123   a  and a feedback resistor  123   b . Then, one of the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) is electrically connected to the negative terminal of the amplifier  123   a . 
     When the movable mirror  5  is displaced, the capacitance between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) changes. Then, due to this change, a current signal J 1  is output from the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). When the time waveform of the drive voltage includes a period to be a constant voltage (excluding 0 V), the current signal J 1  within the period indicates a derivative value of the capacitance between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). For example, when the movable mirror  5  passes through the center of the amplitude, the magnitude (current value) of the current signal J 1  momentarily becomes zero. By using this, the timing when the movable mirror  5  passes through the midpoint between the maximum point and the minimum point can be suitably detected. 
     Hereinafter, a specific description will be given. Now, it is assumed that a drive voltage having a constant voltage period between the rising edge and the falling edge (for example, the rectangular wave shown in  FIG.  6   ) is applied to the other one of the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). That is, a drive voltage Vin(t) is expressed by the following Equation (1). V L  is a voltage value of the rectangular wave on the low voltage side, V H  is a voltage value of the rectangular wave on the high voltage side, and t is the time. 
     
       
         
           
             V 
             i 
             n 
             
               t 
             
             = 
             
               V 
               H 
             
               
             o 
             r 
               
             
               V 
               L 
             
           
         
       
     
     In addition, the current signal J 1  output from one of the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) is expressed by the following Equation (2). Q is the amount of charge stored as a capacitance between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). C a  is a capacitance value between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ). 
     
       
         
           
             J 
             1 
             = 
             
               
                 d 
                 Q 
               
               
                 d 
                 t 
               
             
             = 
             
               
                 d 
                 
                   C 
                   a 
                 
                 
                   t 
                 
                 V 
                 i 
                 n 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
             = 
             V 
             i 
             n 
             
               t 
             
             
               
                 d 
                 
                   C 
                   a 
                 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
             + 
             
               C 
               a 
             
             
               t 
             
             
               
                 d 
                 V 
                 i 
                 n 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
           
         
       
     
     In a period in which the magnitude of Vin(t) is constant, the time derivative of Vin(t) is zero. Therefore, Equation 3 is obtained. 
     
       
         
           
             J 
             1 
             = 
             V 
             i 
             n 
             
               t 
             
             
               
                 d 
                 
                   C 
                   a 
                 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
           
         
       
     
     Here, the relationship between a feedback current J 2  in the TIA and an output voltage Vout(t) is as shown in the following Equation (4). R f  is the resistance value of the feedback resistor  123   b . 
     
       
         
           
             J 
             2 
             = 
             
               
                 V 
                 o 
                 u 
                 t 
                 
                   t 
                 
               
               
                 
                   R 
                   f 
                 
               
             
           
         
       
     
     In addition, the following conditions are satisfied at the input terminal of the amplifier  123   a . 
     
       
         
           
             J 
             1 
             + 
             J 
             2 
             = 
             0 
           
         
       
     
     Therefore, the output voltage Vout(t) from the TIA is expressed by the following Equation (6). 
     
       
         
           
             V 
             o 
             u 
             t 
             
               t 
             
             = 
             − 
             
               R 
               f 
             
             V 
             i 
             n 
             
               t 
             
             
               
                 d 
                 
                   C 
                   a 
                 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
           
         
       
     
     That is, assuming that the drive voltage Vin(t) is a constant value other than zero, when the output voltage Vout(t) is zero, dC a (t)/dt is zero, and C a (t) takes an extreme value (maximum value or minimum value). That is, the timing when the movable mirror  5  passes through the midpoint between the maximum point and the minimum point can be suitably detected. For example, when V L  = 0 as shown in the graph G 2  shown in  FIG.  6   , the timing can be detected only in a period in which the drive voltage Vin(t) is V H . In a period in which the drive voltage Vin(t) is V L  (= 0), the output voltage Vout(t) is 0 V regardless of dC a (t)/dt as shown in the above Equation (6). 
     In addition, in an example, the resonance frequency of the movable mirror  5  is 500 Hz. In this case, the frequency of the drive voltage Vin(t) is 1 kHz, and the period of the drive voltage Vin(t) is 1 ms. Assuming that the time is the above-described dt, dC a  is, for example, 10 pF, and V H  is, for example, 100 V, J 1  = 1 µA is calculated. When the range of the output voltage Vout(t) is 1 V, the required resistance value R f  of the feedback resistor  123   b  is 1 MΩ. 
       FIG.  8    is a graph showing the time change of each signal in an example. In the diagram, in order from the top, the drive voltage Vin(t), the displacement amount Z(t) of the movable mirror  5 , the capacitance C a (t), the output voltage Vout(t), and the output voltage waveform Vcom(t) from the comparator  124  are shown. In addition, the vertical axis of each graph indicates voltage or capacitance, and the horizontal axis of each graph indicates time. 
     As described above, the drive voltage Vin(t) has a time waveform in which rising PU and falling PD are alternately repeated at fixed periods. In the example shown in  FIG.  8   , the duty ratio is 50%, and the length of the period from the rising PU to the falling PD (voltage value V H ) and the length of the period from the falling PD to the rising PU (voltage value V L ) are equal. Then, the timing of the rising PU of the drive voltage Vin(t) is controlled by the actuator drive circuit  121  so as to match the timing when the displacement amount Z(t) of the movable mirror  5  becomes a maximum point ZA or a minimum point ZB, which is the turning point of the reciprocating movement. In addition, the timing of the falling PD of the drive voltage Vin(t) is controlled by the actuator drive circuit  121  so as to match the timing when the movable mirror  5  passes through a midpoint ZC between the maximum point ZA and the minimum point ZB. 
     The capacitance C a (t) between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) changes according to the displacement amount Z(t) of the movable mirror  5 , and is the minimum at the timing when the displacement amount Z(t) becomes the maximum point ZA or the minimum point ZB and is the maximum at the timing when the displacement amount Z(t) passes through the midpoint ZC between the maximum point ZA and the minimum point ZB. In addition, as described above, the output voltage Vout(t) from the current-voltage conversion circuit  123  is 0 V in a period in which the drive voltage Vin(t) is V L  (= 0 V). However, in a period in which the drive voltage Vin(t) is a constant value V H  excluding 0, the output voltage Vout(t) from the current-voltage conversion circuit  123  has a value indicating the time derivative of the capacitance C a (t). In this example, the comparator  124  compares the output voltage Vout(t) with 0 V (more accurately, a predetermined threshold value corresponding to the case where the current signal J 1  is zero), and provides the actuator drive circuit  121  with the output voltage waveform Vcom(t) including a pulse PC that rises at the timing when the output voltage Vout(t) reaches 0 V (zero cross timing). 
     By using the rising timing of the pulse PC, the actuator drive circuit  121  controls the timing of the falling PD of the drive voltage Vin(t) described above. That is, the actuator drive circuit  121  matches the timing of the falling PD of the drive voltage Vin(t) with the timing when the output voltage Vout(t) reaches a predetermined threshold value. 
       FIG.  9    is a graph showing the time change of each signal in another example. In this example, the duty ratio is 50%, which is the same as in the example of  FIG.  8   , but the timing of the rising PU of the drive voltage Vin(t) is controlled by the actuator drive circuit  121  so as to be slightly delayed from the timing when the displacement amount Z(t) of the movable mirror  5  becomes the maximum point ZA or the minimum point ZB, which is the turning point of the reciprocating movement. In addition, the timing of the falling PD of the drive voltage Vin(t) is controlled by the actuator drive circuit  121  so as to be slightly delayed from the timing when the movable mirror  5  passes through the midpoint ZC between the maximum point ZA and the minimum point ZB (see the arrow in the diagram). That is, the actuator drive circuit  121  shifts the timing of the falling PD to a predetermined time after the timing when the output voltage Vout(t) reaches a predetermined threshold value. For example, the predetermined time is 0.1% or more and 15% or less of the period of the drive voltage Vin(t). 
     In this example, the drive voltage Vin(t) maintains a constant value V H  for a while even after the maximum timing of the capacitance C a (t). Therefore, the output voltage Vout(t) from the current-voltage conversion circuit  123  maintains a positive value until the drive voltage Vin(t) drops after reaching 0 V Therefore, the time width of each pulse PC included in the output voltage waveform Vcom(t) from the comparator  124  increases with the delay of the timing of the falling PD. In other words, the time from the rising edge to the falling edge of the output voltage waveform Vcom(t) indicates the delay time of the timing of the falling PD. 
       FIG.  10    is a graph showing the time change of each signal in still another example. In this example, the duty ratio is less than 50% (for example, 45%), and the timing of the rising PU of the drive voltage Vin(t) is controlled by the actuator drive circuit  121  so as to be slightly delayed from the timing when the displacement amount Z(t) of the movable mirror  5  becomes the maximum point ZA or the minimum point ZB (see the arrow in the diagram). In addition, the timing of the falling PD of the drive voltage Vin(t) is controlled so as to match the timing when the movable mirror  5  passes through the midpoint ZC, as in  FIG.  8   . 
     Here, the method of driving the mirror device  7  according to the present embodiment is summarized as follows. That is, the drive method according to the present embodiment includes a drive step of applying the drive voltage Vin(t) between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19 . The time waveform of the drive voltage Vin(t) periodically repeats the rising PU and the falling PD, and includes a period to be the constant voltage V H  after the rising PU and before the falling PD. In the drive step, a capacitance derivative signal Vout(t) proportional to the time derivative of the capacitance C a  is generated by converting the current signal J 1 , which is output from the fixed comb electrodes  16  and  18  or the movable comb electrodes  17  and  19  within the period due to the change in the capacitance C a  between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19 , into a voltage signal. Then, the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is detected, and the relationship between the timing and the timing of the falling PD is controlled to be constant. At this time, the timing of the falling PD is made to match the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value (see  FIGS.  8  and  10   ) or is shifted after a predetermined time from the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value (see  FIG.  9   ). In addition, the predetermined threshold value is set to a value (for example, 0 V) corresponding to the case where the current signal J 1  is zero. In addition, the time waveform of the drive voltage Vin(t) is made to periodically include a rectangular wave having the rising PU and the falling PD, and the duty ratio of the drive voltage Vin(t) is set to be 20% or more and less than 50%. In the drive step, the current signal J 1  is converted into the capacitance derivative signal Vout(t), which is a voltage signal, by using the TIA, and the capacitance derivative signal Vout(t) is compared with a predetermined threshold value by using the comparator  124 . 
     In addition, in the drive method described above, the drive step is realized by executing a program by a computer provided outside the optical module  1 A, for example. The program controls the timing of the rising PU and the timing of the falling PD of the drive voltage Vin(t) while controlling the relationship between the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value and the timing of the falling PD to be constant. 
     The effects obtained by the mirror device  7  and the method of driving the mirror device  7  according to the present embodiment described above will be described together with the conventional problems. Normally, the resonance frequency of the movable mirror  5  fluctuates due to changes in temperature, humidity, and the like. If the frequency of the drive voltage Vin(t) deviates from the resonance frequency of the movable mirror  5  due to the fluctuation in the resonance frequency of the movable mirror  5 , the operation of the movable mirror  5  at the maximum amplitude is adversely affected. In particular, when the maximum amplitude of the movable mirror  5  is large, such as a case where the elastic coefficient of a portion (specifically, the levers  131  and  141 , the first torsion bars  135  and  145 , and the second torsion bars  136  and  146 ) that elastically supports the movable mirror  5  is small, the non-linearity of the amplitude with respect to the frequency increases. Therefore, even if the frequency of the drive voltage Vin(t) deviates slightly from the resonance frequency of the movable mirror  5 , the amplitude is greatly reduced. 
     In response to this problem, in the present embodiment, the drive voltage Vin(t) having a time waveform periodically repeating the rising PU and the falling PD is applied between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19 . Therefore, by bringing the frequency of the drive voltage Vin(t) close to the resonance frequency of the movable mirror  5 , the amplitude of the movable mirror  5  can be brought close to the maximum amplitude. At this time, due to the change in the capacitance C a  between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19 , the current signal J 1  from the fixed comb electrodes  16  and  18  or the movable comb electrodes  17  and  19  is output. When the time waveform of the drive voltage Vin(t) includes a period to be a constant voltage (excluding 0 V), the current signal J 1  within the period indicates a derivative value of the capacitance C a  between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19 . For example, when the movable mirror  5  passes through the center of the amplitude, the capacitance C a  becomes maximum, so that the current value of the current signal J 1  momentarily becomes zero. 
     In the present embodiment, the time waveform of the drive voltage Vin(t) includes a period to be the constant voltage V H  after the rising PU and before the falling PD. Then, by converting the current signal J 1  output from the fixed comb electrodes  16  and  18  or the movable comb electrodes  17  and  19  within the period into a voltage signal, the capacitance derivative signal Vout(t) indicating the derivative value of the capacitance C a  is generated. In addition, the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is detected, and the relationship between the timing and the timing of the falling PD is controlled to be constant. Therefore, since the position of the movable mirror  5  at the time of falling PD of the drive voltage Vin(t) can be made constant, the frequency of the drive voltage Vin(t) can be brought close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable mirror  5 . 
       FIGS.  11 ( a ),  11 ( b ) and  11 ( c )  are graphs showing, as an example, measured data of the time waveform of the drive voltage Vin(t), the capacitance derivative signal Vout(t), and the output voltage Vcom(t) from the comparator  124 , respectively. In addition, in this example, the pulse height of the drive voltage Vin(t) was set to 75 Vpp, the frequency of the drive voltage Vin(t) was set to 537 Hz, the duty ratio of the drive voltage Vin(t) was set to 45%, and the resistance value of the feedback resistor  123   b  of the TIA was set to 3.3 MΩ. As is apparent from these diagrams, according to the present embodiment, it is possible to control the timing of the falling PD of the drive voltage Vin(t) in a constant relationship with respect to the timing when the capacitance derivative signal Vout(t) has a predetermined threshold value (0 V in this example). 
     In addition,  FIG.  12    is a graph showing the measurement result of the relationship between the frequency of the drive voltage Vin(t) and the time difference between the timing when the capacitance derivative signal Vout(t) becomes 0 V (that is, the timing when the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  are closest to each other) and the timing of the falling PD. In addition, the time difference is shown as a ratio of the drive voltage Vin(t) to the period (hereinafter, referred to as a peak shift rate). In this measurement, the pulse height of the drive voltage Vin(t) was set to 75 Vpp, and the duty ratio of the drive voltage Vin(t) was set to 45%. In addition, the frequency of the drive voltage Vin(t) was changed in units of 0.1 Hz, and the time difference was detected with an accuracy of about 0.1%. As is apparent from  FIG.  12   , when the output signal of Vcom(t) in  FIG.  11    is generated immediately before the falling PD, it can be seen that the peak shift rate decreases as the frequency of the drive voltage Vin(t) increases. 
     As shown in  FIGS.  8  and  10   , the actuator drive circuit  121  (in the drive step) may match the timing of the falling PD with the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value. For example, with such a configuration, the relationship between the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value and the timing of the falling PD can be controlled to be constant. 
     Alternatively, as shown in  FIG.  9   , the actuator drive circuit  121  (in the drive step) may shift the timing of the falling PD to a predetermined time after the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value. Even with such a configuration, the relationship between the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value and the timing of the falling PD can be controlled to be constant. In addition, since it can be checked that the capacitance derivative signal Vout(t) reaches a predetermined threshold value before the drive voltage drops (that is, the capacitance derivative signal Vout(t) disappears), it is possible to more reliably detect the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value. 
     As in the present embodiment, the predetermined threshold value may be a value (0 V in one example) corresponding to the case where the current signal J 1  is zero. In this case, it is possible to accurately detect the timing when the movable comb electrodes  17  and  19  and the fixed comb electrodes  16  and  18  are closest to each other (in an example, the timing suitable for the falling of the drive voltage Vin(t)). 
     As in the present embodiment, the time waveform of the drive voltage Vin(t) may periodically include a rectangular wave having the rising PU and the falling PD, and the duty ratio of the drive voltage Vin(t) may be 20% or more and less than 50%. Assuming that the duty ratio of the drive voltage Vin(t) is 50%, there is a possibility that electrostatic attraction is applied at the timing when the movable comb electrodes  17  and  19  and the fixed comb electrodes  16  and  18  move away from each other due to a control error or the like. This leads to a decrease in the amplitude of the movable mirror  5 . By setting the duty ratio of the drive voltage Vin(t) to less than 50%, such a possibility can be reduced. In addition, by setting the duty ratio of the drive voltage Vin(t) to 20% or more, sufficient electrostatic attraction can be applied between the movable comb electrodes  17  and  19  and the fixed comb electrodes 16 and  18 . 
     As in the present embodiment, the timing detection circuit  122  may include the comparator  124  that compares the capacitance derivative signal Vout(t) with a predetermined threshold value. In other words, in the drive step, the comparison between the capacitance derivative signal Vout(t) and the predetermined threshold value may be performed by using the comparator  124 . In this case, since the timing when the capacitance derivative signal Vout(t) reaches the predetermined threshold value can be detected by a simple circuit, it is possible to contribute to the miniaturization and cost reduction of the mirror device  7 . In addition, as compared with, for example, a configuration in which the capacitance derivative signal Vout(t) is compared with a predetermined threshold value by using software, the comparison can be performed only on the circuit board. In this respect as well, it is possible to contribute to the simplification of the configuration. In addition, when the above comparison is performed by using software built into a computer, it is difficult to distinguish between the timing of exceeding the threshold value from the negative side to the positive side and the timing of exceeding the threshold value from the positive side to the negative side. On the other hand, since the comparator  124  operates only in the period in which the drive voltage Vin(t) is the constant value V H , only the timing exceeding the threshold value from the negative side to the positive side is output. Therefore, the above comparison can be easily performed. In addition, this does not prevent the use of software built into the computer instead of the comparator  124  for the comparison between the capacitance derivative signal Vout(t) and the predetermined threshold value. 
     As in the present embodiment, the timing detection circuit  122  may include a TIA that converts the current signal J 1  into the voltage signal Vout(t). In other words, in the drive step, the current signal J 1  may be converted into the voltage signal Vout(t) by using the TIA. In this case, for example, as compared with a case where a resistor (shunt resistor) is connected in series with the fixed comb electrodes  16  and  18  or the movable comb electrodes  17  and  19  and the current signal J 1  is converted into the voltage signal Vout(t) by using the voltage drop in the resistor, it is possible to reduce the voltage fluctuation between the comb electrodes and apply a desired voltage between the comb electrodes with high accuracy. 
     Here, as another method of bringing the frequency of the drive voltage Vin(t) close to the resonance frequency, it is conceivable to continuously detect the displacement amount of the movable mirror  5  and control the timing of the rising PU and the falling PD of the drive voltage Vin(t) according to the maximum and/or minimum of the displacement amount of the movable mirror  5 .  FIG.  32    is a diagram showing a circuit for detecting the maximum and/or minimum of the displacement amount of the movable mirror  5  as a comparative example. In this circuit, a sinusoidal signal Sa from a sinusoidal wave generation circuit  201  is superimposed on a drive voltage from an actuator drive circuit and applied between a fixed comb electrode and a movable comb electrode. In addition, in  FIG.  32   , the fixed comb electrode and the movable comb electrode are shown as variable capacities  202 . The frequency of the sinusoidal signal Sa is sufficiently higher than the resonance frequency of the movable mirror  5 . On the other hand, a signal obtained by shifting the phase of the sinusoidal signal Sa from the sinusoidal wave generation circuit  201  by 180° is applied to a fixed capacitor  203  as a reference. Then, the currents output from the variable capacitor  202  and the fixed capacitor  203  are added, and a current obtained by the addition is input to an arithmetic circuit  204  including an operational amplifier  204   a . In this case, a signal Sb output from the arithmetic circuit  204  is expressed by the following Equation (7). In addition, Vsa(t) indicates the voltage waveform of the sinusoidal signal Sa, Vsb(t) indicates the voltage waveform of the signal Sb, C is the capacitance value of the variable capacitor  202 , C ref  is the capacitance value of the fixed capacitor  203 , and C 0  is the capacitance value of a feedback capacitor  204   b  of the arithmetic circuit  204 . 
     
       
         
           
             V 
             s 
             b 
             
               t 
             
             = 
             V 
             s 
             a 
             
               t 
             
             
               
                 
                   C 
                   
                     r 
                     e 
                     f 
                   
                 
                 − 
                 C 
               
               
                 
                   C 
                   0 
                 
               
             
           
         
       
     
     An envelope H of the signal Sb indicates the capacitance value of the variable capacitor  202 , that is, the displacement amount of the movable mirror  5 . Thereafter, the envelope H of the signal Sb is detected by an envelope detector  205 , and the detected envelope H is amplified by an amplifier  206 . Then, an amplified signal Sc is input to a low pass filter  207 , and the frequency component of the sinusoidal signal Sa is removed from the signal Sc. The signal Sc after passing through the low pass filter  207  is input to an analog-digital converter  208 , and the signal Sc is converted into a digital signal by the analog-digital converter  208 . Thereafter, the maximum timing and/or the minimum timing of the signal Sc (that is, the maximum timing and/or the minimum timing of the displacement of the movable mirror  5 ) is detected by a digital circuit (not shown). 
     However, the method shown in  FIG.  32    has a problem that the circuit scale becomes large and the circuit becomes complicated. On the other hand, according to the method of the present embodiment, by focusing only on the detection of the timing when the movable mirror  5  passes through a predetermined position (the timing when the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  are closest to each other), that is, the detection of the change in the capacitance between the comb electrodes, a similar function can be realized by a remarkably simple circuit configuration, as shown in  FIG.  5   . In addition, when the capacitance value of the variable capacitor  202  is handled as it is as in the method shown in  FIG.  32   , the time waveform is steep near the peak of the capacitance value and accordingly, noise tends to concentrate near the peak of the capacitance value. For this reason, it is difficult to accurately match the falling timing of the drive voltage with the peak of the capacitance value. On the other hand, according to the method of the present embodiment, it is easy to keep the S/N ratio of the current signal J 1  high even near the timing when the value of the capacitance C a  is a peak. Therefore, it is possible to accurately match the falling timing of the drive voltage Vin(t) with the peak of the capacitance C a . 
     In addition, the method shown in  FIG.  32    has the following problem.  FIG.  33    is a circuit diagram showing a typical example of an envelope detector. In addition,  FIG.  34    is a graph showing an example of an input signal Vi to the envelope detector shown in  FIG.  33    and an output signal Vo. As shown in  FIG.  34   , the output signal Vo from the envelope detector includes a ripple according to the frequency of the input signal Vi, unlike the actual envelope H. This causes a decrease in the detection accuracy of the displacement amount of the movable mirror  5  and a decrease in the detection accuracy of the maximum timing and/or the minimum timing of the displacement of the movable mirror  5 . In addition, if the value of the product between the capacitance value of a capacitor  211  shown in  FIG.  33    and the resistance value of a resistor  212  shown in  FIG.  33    is increased, the ripple included in the output signal Vo is reduced. In this case, however, as shown in  FIG.  35   , the output signal Vo from the envelope detector cannot follow the actual envelope H of the input signal Vi. 
     In contrast, in the present embodiment, the timing when the movable mirror  5  passes through the predetermined position is detected based on the capacitance derivative signal Vout(t) obtained by current-voltage conversion of the current signal J 1  output from the fixed comb electrodes  16  and  18  (or the movable comb electrodes  17  and  19 ) when the constant voltage V H  is applied. For this reason, since no envelope detector is required, the above-described problem relevant to ripple do not occur. Therefore, it is possible to improve the detection accuracy of the timing when the movable mirror  5  passes through a predetermined position. 
     In addition, the method shown in  FIG.  32    has the following problem. Normally, in order to generate a sufficiently large electrostatic force between the fixed comb electrode and the movable comb electrode, it is necessary to apply a high voltage such as several tens to 100 volts as the drive voltage Vin(t). Such a high voltage is generally generated by using a booster circuit, such as a DC-DC converter. In addition, in a switching type booster circuit, the occurrence of ripple due to switching is unavoidable.  FIG.  13    is a diagram conceptually showing ripple Ri superimposed on the drive voltage. As shown in the diagram, the ripple Ri is a periodic wave having the same frequency as the switching frequency, and vibrates around the drive voltage. When the ripple Ri having an amplitude ΔV is superimposed on the drive voltage, the above Equation (7) is modified as follows. 
     
       
         
           
             V 
             s 
             b 
             
               t 
             
             = 
             
               
                 V 
                 s 
                 a 
                 
                   t 
                 
                 + 
                 Δ 
                 V 
               
             
             
               
                 
                   C 
                   
                     r 
                     e 
                     f 
                   
                 
                 − 
                 C 
               
               
                 
                   C 
                   0 
                 
               
             
           
         
       
     
     In this case, assuming that Vsa(t) is 1 V and ΔV is 0.1 V, an output error of up to 10% occurs. 
     On the other hand, when the ripple Ri having the amplitude ΔV is superimposed on the constant voltage V H  in the present embodiment, the above Equation (6) is modified as follows. 
     
       
         
           
             V 
             o 
             u 
             t 
             
               t 
             
             = 
             − 
             
               R 
               f 
             
             
               
                 V 
                 i 
                 n 
                 
                   t 
                 
                 + 
                 Δ 
                 V 
               
             
             
               
                 d 
                 
                   C 
                   a 
                 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
           
         
       
     
     Since the magnitude of the constant voltage V H  is at least 10 V, the output error is 1% or less even if ΔV is 0.1 V. That is, according to the present embodiment, it is possible to obtain high detection accuracy by reducing the influence of the ripple Ri included in the drive voltage. 
     First Modification Example 
       FIG.  14    is a circuit diagram showing the configuration of a current-voltage conversion circuit  123 A according to a first modification example of the embodiment described above. As shown in the diagram, the current-voltage conversion circuit  123 A includes the amplifier  123   a , the feedback resistor  123   b , and a capacitor  123   e . The feedback resistor  123   b  is connected in series between the inverting input terminal and the output terminal of the amplifier  123   a . The capacitor  123   e  is connected in parallel to the feedback resistor  123   b  between the inverting input terminal and the output terminal of the amplifier  123   a . The noninverting input terminal of the amplifier  123   a  is connected to a reference potential line GND. In this circuit, the capacitor  123   e  is used to adjust the cutoff frequency fc of the current-voltage conversion circuit  123 A. Assuming that the resistance value of the feedback resistor  123   b  is Rf and the capacitance value of the capacitor  123   e  is Cf, the cutoff frequency fc of the current-voltage conversion circuit  123 A is given as fc = 1/(2π·Rf·Cf) By appropriately adjusting the cutoff frequency fc, it is possible to remove a high frequency component included in the capacitance derivative signal Vout(t), which is irrelevant to the actuator operation. 
     The current-voltage conversion circuit  123 A further includes a clamp circuit  125 . The clamp circuit  125  is provided in order to shorten the fluctuation period of the capacitance derivative signal Vout(t) caused by the rising PU and the falling PD of the drive voltage Vin(t). In this example, the clamp circuit  125  has switching diodes (hereinafter, simply referred to as diodes)  125   a  and  125   b . The diodes  125   a  and  125   b  are connected in parallel to each other between the reference potential line GND and a node N 2  between the fixed comb electrodes  16  and  18  (or the movable comb electrodes  17  and  19 ) and the inverting input terminal of the amplifier  123   a . The diode  125   a  is connected with the direction from the node N 2  to the reference potential line GND as its forward direction, and the diode  125   b  is connected with the direction from the reference potential line GND to the node N 2  as its forward direction. In other words, the two diodes  125   a  and  125   b  are connected in parallel in opposite directions between the node N 2  and the reference potential line GND. 
     The diode  125   a  is turned on when the potential of the node N 2  exceeds a predetermined threshold value (&gt; 0), and a current flows from the node N 2  to the reference potential line GND. In addition, the diode  125   b  is turned on when the potential of the node N 2  falls below the predetermined threshold value (&lt; 0), and a current flows from the reference potential line GND to the node N 2 . 
     Here, fluctuations in the capacitance derivative signal Vout(t) due to the rising PU and the falling PD of the drive voltage Vin(t) will be described.  FIG.  15    is a diagram showing the time waveforms of the drive voltage Vin(t), the current signal J 1 , the inverting input terminal voltage Va of the amplifier  123   a , the feedback current J 2 , and the capacitance derivative signal Vout(t) when the capacitance C a  does not change (that is, the Z-direction position of the movable mirror  5  is fixed) in the embodiment described above. Here, it is assumed that the drive voltage Vin(t) rises at time  t   0  and drops at time  t   0 ′. 
     When the drive voltage Vin(t) rises at time  t   0 , a charge corresponding to the product (C a ·V H ) between the voltage V H  and the capacitance C a  flows momentarily to the capacitor between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  to generate a positive pulse wave J 1   a  in the current signal J 1 . At this time, a negative pulse wave J 2   a  is generated in the feedback current J 2  in order to satisfy J 1  + J 2  = 0. Then, as a result of the generation of the negative pulse wave J 2   a , the voltage signal (capacitance derivative signal) Vout(t) output from the amplifier  123   a  is saturated to the negative side (waveform PA). The saturation waveform PA continues for a predetermined period according to the height of the pulse wave J 1   a  and converges at time  11 . When the voltage signal Vout(t) is saturated to the negative side, the inverting input terminal of the amplifier  123   a  cannot maintain virtual ground. Therefore, the inverting input terminal voltage Va of the amplifier  123   a  rises momentarily in order to reduce the feedback current J 2  (waveform Vaa). 
     In addition, when the drive voltage Vin(t) drops at time  t   0 ′, the charge stored in the capacitor between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  flows out momentarily to generate a negative pulse wave J 1   b  in the current signal J 1 . At this time, a positive pulse wave J 2   b  is generated in the feedback current J 2  in order to satisfy J 1  + J 2  = 0. Then, as a result of the generation of the positive pulse wave J 2   b , the voltage signal (capacitance derivative signal) Vout(t) output from the amplifier  123   a  is saturated to the positive side (waveform PB). This saturation waveform PB continues for a predetermined period according to the height of the pulse wave J 1   b  and converges at time t1′. When the voltage signal Vout(t) is saturated to the positive side, the inverting input terminal of the amplifier  123   a  cannot maintain virtual ground. Therefore, the inverting input terminal voltage Va of the amplifier  123   a  drops momentarily in order to increase the feedback current J 2 . (waveform Vab). 
     The above operation is also described in the above Equation (2). That is, Equation (2) includes the time derivative dVin(t)/dt of the drive voltage Vin(t). dVin(t)/dt can be ignored as long as the drive voltage Vin(t) is constant. However, dVin(t)/dt cannot be ignored when the drive voltage Vin(t) rises and drops, but rather has an excessive effect on the capacitance derivative signal Vout(t). For example, when the capacitance C a  is 10 pF, the dVin(t) is 100 V, and the rise (or fall) time dt is 100 ns, the second term on the right side of Equation (2) can be calculated as [Equation 10]. 
     
       
         
           
             
               C 
               a 
             
             
               t 
             
             
               
                 d 
                 V 
                 i 
                 n 
                 
                   t 
                 
               
               
                 d 
                 t 
               
             
             = 
             
               
                 10 
                 × 
                 
                   
                     10 
                   
                   
                     − 
                     12 
                   
                 
                 × 
                 100 
               
               
                 100 
                 × 
                 
                   
                     10 
                   
                   
                     − 
                     9 
                   
                 
               
             
             = 
             10 
             
               
                 m 
                 A 
               
             
           
         
       
     
     When the resistance value R f  of the feedback resistor  123   b  is, for example, 1 MΩ described above, the output voltage Vout(t) of the amplifier  123   a  is calculated to be 1000 V, and accordingly, it can be easily understood that the output voltage Vout(t) is saturated. 
     Therefore, in the period from time  t   0  to time  t   1  and the period from time  t   0 ′ to time  t   1 ′, even if the capacitance C a  between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  changes due to the movement of the movable mirror  5 , the change does not appear in the capacitance derivative signal Vout(t), and accordingly, the change cannot be detected. 
     In addition,  FIG.  36    is a graph showing an example in which the signal Sb output from the arithmetic circuit  204  is measured in the circuit of the comparative example shown in  FIG.  32   . In addition, in the diagram, a graph G 3  shows the drive voltage Vin(t), and a graph G 4  shows the signal Sb. Referring to a portion E in  FIG.  36   , it can be seen that the signal Sb is completely shaken and saturated at the rising and falling timings of the drive voltage Vin(t). Thus, the same problem as described above arises in the method of the comparative example shown in  FIG.  32   . 
     In response to the above problem, the clamp circuit  125  is provided in this modification example.  FIG.  16    is a diagram showing the time waveforms of the drive voltage Vin(t), the current signal J 1 , the inverting input terminal voltage Va of the amplifier  123   a , currents J 3  and J 4 , the feedback current J 2 , and the capacitance derivative signal Vout(t) when the capacitance C a  does not change in this modification example. Also in the diagram, it is assumed that the drive voltage Vin(t) rises at time to and drops at time  t   0 ′. In addition, for comparison, the time waveform shown in  FIG.  15    is shown by a broken line. 
     When the drive voltage Vin(t) rises at time  t   0 , the charge momentarily flows into the capacitor between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  to generate the positive pulse wave J 1   a  in the current signal J 1 . At this time, since the diode  125   a  is turned on and the current J 3  flows, the height of the pulse wave J 1   a  is suppressed. Therefore, in order to satisfy J 1  + J 2  = 0, the height of the negative pulse wave J 2   a  generated in the feedback current J 2  is also suppressed. Therefore, the saturation waveform PA to the negative side of the capacitance derivative signal Vout(t) converges in a short time. 
     In addition, when the drive voltage Vin(t) drops at time  t   0 ′, the charge stored in the capacitor between the fixed comb electrodes  16  and  18  and the movable comb electrodes  17  and  19  flows out momentarily to generate a negative pulse wave J 1   b  in the current signal J 1 . At this time, since the diode  125   b  is turned on and the current J 4  flows, the height of the pulse wave J 1   b  is suppressed. Therefore, in order to satisfy J 1  + J 2  = 0, the height of the positive pulse wave J 2   b  generated in the feedback current J 2  is also suppressed. Therefore, the saturation waveform PB to the positive side of the capacitance derivative signal Vout(t) also converges in a short time. 
     As described above, according to this modification example, by providing the clamp circuit  125 , it is possible to shorten the fluctuation period of the capacitance derivative signal Vout(t) caused by the rising PU and the falling PD of the drive voltage Vin(t). Therefore, it is possible to suppress a situation in which the detection of the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is interrupted by the fluctuation. 
     In addition,  FIG.  17 ( a )  is a circuit diagram showing the clamp circuit  125  in this modification example, and  FIG.  17 ( b )  is a circuit diagram showing a general protection circuit  126  provided in the operational amplifier. As shown in  FIG.  17 ( a ) , in the clamp circuit  125  of this modification example, diodes  125   a  and  125   b  having different orientations are connected in parallel to each other between the node N 2  and the reference potential line GND. On the other hand, as shown in the  FIG.  17 ( b ) , in the general protection circuit  126 , the anode of one diode  126   a  is connected to the node N 2 , and the cathode is connected to a positive constant potential line V+. In addition, the anode of the other diode  126   b  is connected to a negative constant potential line V-, and the cathode is connected to the node N 2 . In other words, the diodes  126   a  and  126   b  are connected in series between the constant potential line V-and the constant potential line V+ in the same direction, and the node N 2  between the diode  126   a  and the diode  126   b  is connected to the inverting input terminal of the amplifier  123   a . Therefore, the configuration of the clamp circuit  125  of this modification example is completely different from the configuration of the general protection circuit  126  provided in the operational amplifier. 
     Second Modification Example 
       FIG.  18    is a circuit diagram showing the configuration of a current-voltage conversion circuit  123 B according to a second modification example of the embodiment described above. As shown in the diagram, the current-voltage conversion circuit  123 B includes an amplifier  123   a , a feedback resistor  123   b , and a capacitor  123   e . Since the configurations thereof are the same as those in the first modification example described above, the description thereof will be omitted. 
     The current-voltage conversion circuit  123 B further includes soft limiter circuits  127  and  128 . The soft limiter circuits  127  and  128  are provided in order to shorten the fluctuation period of the capacitance derivative signal Vout(t) caused by the rising PU and the falling PD of the drive voltage Vin(t). In this example, the soft limiter circuit  127  has a switching diode (hereinafter, simply referred to as a diode)  127   a  and resistors  127   b  and  127   c . The diode  127   a  and the resistor  127   b  are connected in series to each other between the node N 2  and the output terminal of the amplifier  123   a . More specifically, the anode of the diode  127   a  is connected to the node N 2 , and the cathode of the diode  127   a  is connected to the output terminal of the amplifier  123   a  through the resistor  127   b . In addition, a node N 3  between the diode  127   a  and the resistor  127   b  is connected to the positive constant potential line V+ through the resistor  127   c . 
     In addition, the soft limiter circuit  128  has a switching diode (hereinafter, simply referred to as a diode)  128   a  and resistors  128   b  and  128   c . The diode  128   a  and the resistor  128   b  are connected in series to each other between the node N 2  and the output terminal of the amplifier  123   a . More specifically, the anode of the diode  128   a  is connected to the output terminal of the amplifier  123   a  through the resistor  128   b , and the cathode of the diode  128   a  is connected to the node N 2 . In addition, a node N 4  between the diode  128   a  and the resistor  128   b  is connected to the negative constant potential line V- through the resistor  128   c . 
       FIGS.  19 ,  20 , and  21    are diagrams for explaining the operation of this modification example.  FIGS.  19 ( a ),  20 ( a ), and  21 ( a )  show the current-voltage conversion circuit  123 B shown in  FIG.  18    in a simplified manner.  FIGS.  19 ( b ),  20 ( b ), and  21 ( b )  are graphs showing the correlation between the current signal J 1  and the capacitance derivative signal Vout. A region F 1  shown in  FIG.  19 ( b )  is a region centered on a point (that is, the origin) where both the current signal J 1  and the capacitance derivative signal Vout are zero, and there is a proportional relationship between the current signal J 1  and the capacitance derivative signal Vout. The proportional coefficient of this proportional relationship is determined by the resistance value R f  of the feedback resistor  123   b . In the region F 1 , as shown in  FIG.  19 ( a ) , the current signal J 1  and the feedback current J 2  flow toward the node N 1  and cancel each other out. In the region F 1 , the soft limiter circuits  127  and  128  do not operate. 
     On the other hand, a region F 2  shown in  FIG.  20 ( b )  is a region where the capacitance derivative signal Vout exceeds a predetermined voltage V L +, and there is a proportional relationship between the current signal J 1  and the capacitance derivative signal Vout. In the region F 2 , when the capacitance derivative signal Vout exceeds the predetermined voltage V L +, the diode  128   a  is turned on and accordingly, a feedback current J 5  flows through the diode  128   a  and the resistor  128   b . At this time, if the resistance value R g  of the resistor  128   b  is sufficiently smaller than the resistance value R f  of the feedback resistor  123   b , the feedback current J 5  becomes large enough that the feedback current J 2  can be ignored, so that the proportional coefficient between the current signal J 1  and the capacitance derivative signal Vout is determined by the resistance value R g  of the resistor  128   b . Therefore, since the proportional coefficient in the region F 2  is smaller than the proportional coefficient in the region F 1 , the inclination is reduced. 
     Similarly, a region F 3  shown in  FIG.  21 ( b )  is a region where the capacitance derivative signal Vout is below a predetermined voltage V L- , and there is a proportional relationship between the current signal J 1  and the capacitance derivative signal Vout. In the region F 3 , when the capacitance derivative signal Vout falls below the predetermined voltage V L- , the diode  127   a  is turned on and accordingly, a feedback current J 6  flows through the resistor  127   b  and the diode  127   a . At this time, if the resistance value R h  of the resistor  127   b  is sufficiently smaller than the resistance value R f  of the feedback resistor  123   b , the feedback current J 6  becomes large enough that the feedback current J 2  can be ignored, so that the proportional coefficient between the current signal J 1  and the capacitance derivative signal Vout is determined by the resistance value R h  of the resistor  127   b . Therefore, since the proportional coefficient in the region F 3  is smaller than the proportional coefficient in the region F 1 , the inclination is reduced. In addition, the resistance value R h  of the resistor  127   b  may be equal to the resistance value R g  of the resistor  128   b . In this case, the proportional coefficient in the region F 3  is equal to the proportional coefficient in the region F 2 . 
     In addition, the voltage V L+  and the voltage V L-  are determined by the following Equations (11) and (12). V F  is the forward voltage of each of the diodes  127   a  and  128   a . In addition, R i  is the resistance value of the resistor  128   c , and R j  is the resistance value of the resistor  127   c . 
     
       
         
           
             
               V 
               
                 L 
                 + 
               
             
             = 
             
               
                 
                   R 
                   g 
                 
               
               
                 
                   R 
                   i 
                 
               
             
             
               V 
               
                 R 
                 E 
                 F 
               
             
             + 
             
               
                 1 
                 + 
                 
                   
                     
                       R 
                       g 
                     
                   
                   
                     
                       R 
                       i 
                     
                   
                 
               
             
             
               V 
               F 
             
           
         
       
     
     
       
         
           
             
               V 
               
                 L 
                 − 
               
             
             = 
             − 
             
               
                 
                   
                     
                       R 
                       h 
                     
                   
                   
                     
                       R 
                       j 
                     
                   
                 
                 
                   V 
                   
                     R 
                     E 
                     F 
                   
                 
                 + 
                 
                   
                     1 
                     + 
                     
                       
                         
                           R 
                           h 
                         
                       
                       
                         
                           R 
                           j 
                         
                       
                     
                   
                 
                 
                   V 
                   F 
                 
               
             
           
         
       
     
     Also in this modification example, by the same operation as in the first modification example, the saturation waveform PA of the capacitance derivative signal Vout(t) when the drive voltage Vin(t) rises (see  FIG.  16   ) and the saturation waveform PB of the capacitance derivative signal Vout(t) when the drive voltage Vin(t) drops (see  FIG.  16   ) converge in a short time. Therefore, according to this modification example, by providing the soft limiter circuits  127  and  128 , it is possible to shorten the fluctuation period of the capacitance derivative signal Vout(t) caused by the rising PU and the falling PD of the drive voltage Vin(t). Therefore, it is possible to suppress a situation in which the detection of the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is interrupted by the fluctuation. In addition, the current-voltage conversion circuit may include the soft limiter circuits  127  and  128  of this modification example and the clamp circuit  125  of the first modification example in combination. 
       FIG.  22    is a graph relevant to the simulation results of the first modification example and the second modification example.  FIG.  22 ( a )  shows the time change of the drive voltage Vin(t). In  FIG.  22 ( a ) , the vertical axis indicates voltage (unit: V) and the horizontal axis indicates time (unit: milliseconds). In addition,  FIG.  22 ( b )  shows the time change of the capacitance derivative signal Vout(t). In  FIG.  22 ( b ) , the vertical axis indicates voltage (unit: V) and the horizontal axis indicates time (unit: milliseconds). In addition, in  FIG.  22 ( b ) , a graph G 5  shows a case where neither the clamp circuit nor the soft limiter circuit is provided, a graph G 6  shows a case where the clamp circuit  125  is provided, a graph G 7  shows a case where the soft limiter circuits  127  and  128  are provided, and a graph G 8  shows a case where the clamp circuit  125  and the soft limiter circuits  127  and  128  are provided. As is apparent from the graphs G 5  to G 8 , by providing at least one of the clamp circuit  125  and the soft limiter circuits  127  and  128 , it is possible to shorten the fluctuation period of the capacitance derivative signal Vout(t) caused by the rising PU and the falling PD of the drive voltage Vin(t). In particular, the effect when the soft limiter circuits  127  and  128  are provided is noticeable. 
     Third Modification Example 
       FIG.  23    is a block diagram showing the configuration of a drive unit  12 A according to a third modification example of the embodiment described above. The drive unit  12 A of this modification example further includes a displacement amount detection unit  129  in addition to the configuration of the drive unit  12  (see  FIG.  5   ) of the embodiment described above. The displacement amount detection unit  129  includes an integrator circuit  129   a  and an amplifier  129   b . The integrator circuit  129   a  is connected to the output end of the current-voltage conversion circuit (TIA)  123 , and receives the capacitance derivative signal Vout(t) from the current-voltage conversion circuit  123 . Then, the integrator circuit  129   a  time-integrates the capacitance derivative signal Vout(t). 
       FIG.  24    is a graph showing the time change of each signal in this modification example. In the diagram, in order from the top, the drive voltage Vin(t), the displacement amount Z(t) of the movable mirror  5 , the capacitance C a (t), the output voltage Vout(t), and the output voltage waveform V out   2 ( t ) from the integrator circuit  129   a  are shown. In addition, the vertical axis of each graph indicates voltage or capacitance, and the horizontal axis of each graph indicates time. The integrator circuit  129   a  is reset within a period in which the drive voltage Vin(t) is V L . 
     Here, the following Equation (13) is satisfied. Therefore, in order to obtain a value corresponding to ΔC a , the integration result may be divided by V H . The amplifier  129   b  is provided for that purpose and amplifies the output signal from the integrator circuit  129   a  with a gain of (1/V H ) times. 
     
       
         
           
             Δ 
             C 
             a 
               
             ∝ 
             − 
             
               1 
               
                 
                   V 
                   H 
                 
                 
                   R 
                   f 
                 
               
             
             
               
                 
                   ∫ 
                   
                     i 
                     = 
                     0 
                   
                   
                     i 
                     = 
                     1 
                   
                 
                 
                   V 
                   o 
                   u 
                   t 
                   
                     t 
                   
                   d 
                   t 
                 
               
             
           
         
       
     
     As in this modification example, the displacement amount of the movable mirror  5  in a predetermined period can be easily detected by time-integrating the capacitance derivative signal Vout(t). In addition, the displacement amount detection unit  129  of this modification example may be provided in the first modification example or the second modification example. 
     Fourth Modification Example 
     In the embodiment described above, the drive voltage Vin(t) is applied between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ), and the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is detected based on the current signal J 1  output from the fixed comb electrode  16  ( 18 ) or the movable comb electrode  17  ( 19 ). The present invention is not limited to such a form, and the drive voltage Vin(t) may be applied between a part of the fixed comb electrode  16  ( 18 ) and a part of the movable comb electrode  17  ( 19 ) while applying a voltage for timing detection between the remaining part of the fixed comb electrode  16  ( 18 ) and the remaining part of the movable comb electrode  17  ( 19 ), and the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value may be detected based on the current signal J 1  output from any of the remaining parts. 
     For example, in the configuration shown in  FIG.  4   , the first electrode support portion  138   a  ( 148   a ) is electrically separated from the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c ), and a portion  16 A ( 18 A) of the fixed comb electrode  16  ( 18 ) facing the first electrode support portion  138   a  ( 148   a ) is electrically separated from a portion  16 B ( 18 B) of the fixed comb electrode  16  ( 18 ) facing each of the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c ). Then, the drive voltage Vin(t) is applied between the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c ) and the fixed comb electrode  16 B ( 18 B) to drive the movable mirror  5 . On the other hand, the current-voltage conversion circuit  123  and the comparator  124  are connected to the first electrode support portion  138   a  ( 148   a ) or the fixed comb electrode  16 A ( 18 A), and a voltage for timing detection is applied between the first electrode support portion  138   a  ( 148   a ) and the fixed comb electrode  16 A ( 18 A). Then, based on the current signal J 1  output from the first electrode support portion  138   a  ( 148   a ) or the fixed comb electrode  16 A ( 18 A), the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is detected. 
     That is, the mirror device of this modification example has the base  11 , the movable mirror  5  (movable portion) supported so as to be elastically displaceable with respect to the base  11 , the first fixed comb electrode  16 B ( 18 B) that includes a plurality of first comb fingers (a plurality of comb fingers  16   a  ( 18   a ) facing the second electrode support portions  138   b  ( 148   b ) and the third electrode support portions  138   c  ( 148   c )) and is provided on the base  11 , and a first movable comb electrode  17 B ( 19 B) that includes a plurality of second comb fingers (a plurality of comb fingers  17   a  ( 19   a ) extending from the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c )) and drives the movable mirror  5  by the electrostatic force generated between the first fixed comb electrode  16 B ( 18 B) and the first movable comb electrode  17 B ( 19 B), the plurality of first comb fingers and the plurality of second comb fingers being alternately arranged. In addition, the mirror device of this modification example includes the second fixed comb electrode  16 A ( 18 A) including a plurality of third comb fingers (a plurality of comb fingers  16   a  ( 18   a ) facing the first electrode support portion  138   a  ( 148   a )) and provided on the base  11  and a second movable comb electrode  17 A ( 19 A) including a plurality of fourth comb fingers (a plurality of comb fingers  17   a  ( 19   a ) extending from the first electrode support portion  138   a  ( 148   a )), the plurality of third comb fingers and the plurality of fourth comb fingers being alternately arranged. Then, the actuator drive circuit  121  applies the drive voltage Vin(t) having a time waveform periodically repeating the rising PU and the falling PD between the first fixed comb electrode  16 B ( 18 B) and the first movable comb electrode  17 B ( 19 B). 
     Here,  FIG.  25    is a diagram schematically showing the configuration of a timing detection circuit  122 A included in the mirror device of this modification example. The timing detection circuit  122 A includes a voltage generation circuit  130 , a current-voltage conversion circuit  123 , and a comparator  124 . The voltage generation circuit  130  applies a voltage for timing detection including a period of constant voltage V H  excluding 0 V between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A) shown as variable capacitors. The current-voltage conversion circuit  123  generates the capacitance derivative signal Vout(t) by converting the current signal J 1 , which is output from the second fixed comb electrode  16 A ( 18 A) or the second movable comb electrode  17 A ( 19 A) within the period due to the change in the capacitance C a  between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A), into a voltage signal. The comparator  124  detects the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value. In addition, the detailed configurations of the current-voltage conversion circuit  123  and the comparator  124  are the same as those in the embodiment described above. The actuator drive circuit  121  generates the drive voltage Vin(t) so that the relationship between the timing detected by the timing detection circuit  122 A and the timing of the falling PD is constant. The drive voltage Vin(t) is applied between the first fixed comb electrode  16 B ( 18 B) and the first movable comb electrode  17 B ( 19 B) shown as variable capacitors. In addition, of the first fixed comb electrode  16 B ( 18 B) and the first movable comb electrode  17 B ( 19 B), the comb electrode on a side opposite to a side connected to the actuator drive circuit  121  is electrically connected to the constant potential wiring or has a floating potential. 
     In this modification example, the drive voltage Vin(t) having a time waveform periodically repeating the rising PU and the falling PD is applied between the first fixed comb electrode  16 B ( 18 B) and the first movable comb electrode  17 B ( 19 B). Therefore, by bringing the frequency of the drive voltage Vin(t) close to the resonance frequency of the movable mirror  5 , the amplitude of the movable mirror  5  can be brought close to the maximum amplitude. At this time, since the second movable comb electrode  17 A ( 19 A) is also displaced together with the movable mirror  5 , the current signal J 1  is output from the second fixed comb electrode  16 A ( 18 A) or the second movable comb electrode  17 A ( 19 A) due to the change in the capacitance C a  between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A). When a voltage for timing detection including a period to be constant voltage V H  excluding 0 V is applied between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A), the current signal J 1  within the period indicates the derivative value of the capacitance C a  between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A). For example, when the movable mirror  5  passes through the center of the amplitude, the current value of the current signal J 1  momentarily becomes zero. 
     In this modification example, a voltage for timing detection including a period to be constant voltage V H  excluding 0 V is applied between the second fixed comb electrode  16 A ( 18 A) and the second movable comb electrode  17 A ( 19 A). Then, by converting the current signal J 1  output from the second fixed comb electrode  16 A ( 18 A) or the second movable comb electrode  17 A ( 19 A) within the period into a voltage signal, the capacitance derivative signal Vout(t) indicating the derivative value of the capacitance C a  is generated. In addition, the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value is detected, and the relationship between the timing and the timing of the falling PD is controlled to be constant. Therefore, since the position of the movable mirror  5  at the time of falling PD of the drive voltage Vin(t) can be made constant, the frequency of the drive voltage Vin(t) can be brought close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable mirror  5 . 
     In addition, in this modification example, the drive voltage Vin(t) is applied to the plurality of comb fingers  17   a  ( 19   a ) extending from the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c ), and the voltage for timing detection is applied to the plurality of comb fingers  17   a  ( 19   a ) extending from the first electrode support portion  138   a  ( 148   a ). As shown in  FIG.  4   , the distance between the first electrode support portion  138   a  ( 148   a ) and the movable mirror  5  is shorter than the distance between the second electrode support portion  138   b  ( 148   b ) and the third electrode support portion  138   c  ( 148   c ). As described above, the distance between the movable mirror  5  and the second movable comb electrode  17 A ( 19 A) to which the voltage for timing detection is applied may be shorter than the distance between the movable mirror  5  and the first movable comb electrode  17 B ( 19 B) to which the drive voltage Vin(t) is applied. In this case, the amplitude of the second movable comb electrode  17 A ( 19 A) can be made larger, and the second movable comb electrode  17 A ( 19 A) can be made to move faster. Therefore, it is possible to improve the detection accuracy of the timing when the capacitance derivative signal Vout(t) reaches a predetermined threshold value. 
     In addition, as in the embodiment described above, when the drive voltage Vin(t) is applied to all the comb electrodes (in other words, when the comb electrode for driving and the comb electrode for timing detection are shared), the driving force can be made higher by making the electrostatic attraction larger as compared with this modification example. 
     In addition, in this modification example, as described above, the voltage for timing detection is applied to the fixed comb electrode  16 A ( 18 A) and the movable comb electrode  17 A ( 19 A) different from the fixed comb electrode  16 B ( 18 B) and the movable comb electrode  17 B ( 19 B) to which the drive voltage Vin(t) is applied. Therefore, the voltage for timing detection does not need to repeat rising and falling periodically, and for example, the constant voltage V H  may be continuously maintained. 
     Second Embodiment 
       FIG.  26    is a block diagram showing the configuration of a MEMS actuator  1 B as a second embodiment. Unlike the mirror device  7  of the embodiment described above, the MEMS actuator  1 B has a slide-type movable portion that vibrates in a direction (Y direction in the present embodiment) crossing (for example, perpendicular to) the thickness direction, that is, the Z direction. Specifically, the MEMS actuator  1 B according to the present embodiment includes a fixed comb electrode  81  and a movable comb electrode  82  arranged on a substrate  80  (base in the present embodiment). In the present embodiment, the fixed comb electrode  81  includes a first fixed comb electrode  83  and a second fixed comb electrode  84  fixed on the substrate  80 . The first fixed comb electrode  83  includes a plurality of first comb fingers  83   a . The plurality of first comb fingers  83   a  have an elongated shape with the Y direction as its longitudinal direction, and are arranged side by side in the X direction. The second fixed comb electrode  84  includes a plurality of first comb fingers  84   a . The plurality of first comb fingers  84   a  have an elongated shape with the Y direction as its longitudinal direction, and are arranged side by side in the X direction. The first fixed comb electrode  83  and the second fixed comb electrode  84  are arranged so as to face each other in the Y direction with a beam  91  (movable portion in the present embodiment) for supporting the movable comb electrode  82  interposed therebetween. The plurality of first comb fingers  83   a  and the plurality of first comb fingers  84   a  extend toward the beam  91 . 
     The movable comb electrode  82  is supported by the elastic beam  91 , and there is a gap between the movable comb electrode  82  and the substrate  80  so that the movable comb electrode  82  can be displaced in the Y direction relative to the substrate  80 . In the present embodiment, the beam  91  is integrally formed with the movable comb electrode  82 . In addition, a fixing portion  92 , which is one end portion of the beam  91 , and a fixing portion  93 , which is the other end portion of the beam  91 , are fixed to the substrate  80 . As a result, the movable comb electrode  82  has a double-sided beam structure. 
     The movable comb electrode  82  includes a plurality of second comb fingers  82   a  and a plurality of second comb fingers  82   b . The plurality of second comb fingers  82   a  have an elongated shape with the Y direction as its longitudinal direction, and are arranged side by side in the X direction. Similarly, the plurality of second comb fingers  82   b  have an elongated shape with the Y direction as its longitudinal direction, and are arranged side by side in the X direction. The plurality of second comb fingers  82   a  are arranged on the side of the first fixed comb electrode  83  with respect to the beam  91 , and extend from the beam  91  toward the first fixed comb electrode  83 . The plurality of second comb fingers  82   b  are arranged on the side of the second fixed comb electrode  84  with respect to the beam  91 , and extend from the beam  91  toward the second fixed comb electrode  84 . The movable comb electrode  82  drives the beam  91  by the electrostatic force generated between the movable comb electrode  82  and the fixed comb electrode  81 . 
     A drive voltage having a frequency that matches the resonance frequency of the beam  91  is applied between the first fixed comb electrode  83  and the movable comb electrode  82 . In addition, a drive voltage having a phase opposite to that of the drive voltage is applied between the second fixed comb electrode  84  and the movable comb electrode  82 . That is, the drive voltage applied between the first fixed comb electrode  83  and the movable comb electrode  82  and the drive voltage applied between the second fixed comb electrode  84  and the movable comb electrode  82  have a complementary relationship therebetween. When the drive voltages are applied between the fixed comb electrodes  83  and  84  and the movable comb electrodes  82 , the beam  91  vibrates in the Y direction due to the electrostatic attraction.  FIG.  27    is a diagram schematically showing a deformation state of the beam  91  when the beam  91  is located at one of the vibrating ends. 
     The MEMS actuator  1 B according to the present embodiment individually includes the actuator drive circuit  121 , the current-voltage conversion circuit  123 , and the comparator  124  shown in  FIG.  5    for each of the fixed comb electrodes  83  and  84 . Alternatively, the MEMS actuator  1 B according to the present embodiment includes, instead of the current-voltage conversion circuit  123 , the current-voltage conversion circuit  123 A according to the first modification example, the current-voltage conversion circuit  123 B according to the second modification example, or both. In addition, the MEMS actuator  1 B according to the present embodiment may further include the displacement amount detection unit  129  according to the third modification example. 
     In the first embodiment, the configuration in which the movable portion (movable mirror  5 ) vibrates in the thickness direction of the comb electrode is exemplified. However, as in the present embodiment, the movable portion (beam  91 ) may vibrate in the longitudinal direction of the comb electrode. Even in this case, as in the first embodiment, the frequency of the drive voltage Vin(t) can be brought close to the resonance frequency regardless of the fluctuation in the resonance frequency of the movable portion. 
       FIG.  28 ( a )  is a diagram schematically showing a capacitance C 1  generated between the first fixed comb electrode  83  and the movable comb electrode  82  and a capacitance C 2  generated between the second fixed comb electrode  84  and the movable comb electrode  82 . The arrow in the diagram indicates the movement direction (Y direction) of the movable comb electrode  82 . The movable comb electrode  82  vibrates in the Y direction while maintaining a constant distance ΔX in the X direction with respect to the first fixed comb electrode  83  and the second fixed comb electrode  84 . Therefore, the capacitance C 2  decreases as the capacitance C 1  increases, and the capacitance C 2  increases as the capacitance C 1  decreases. 
       FIG.  28 ( b )  is a circuit diagram showing the current-voltage conversion circuit  123  connected to the capacitors C 1  and C 2 . In the present embodiment, the movable comb electrode  82  is provided in common with respect to the first fixed comb  electrode   83  and the second fixed comb electrode  84 . Therefore, in this circuit diagram, one electrode of the capacitor C 1  and one electrode of the capacitor C 2  are short-circuited at a node N 5 . In addition, drive voltages V in   1 ( t ) and V in   2 ( t ) are applied to the other electrode of the capacitor C 1  and the other electrode of the capacitors C 2  (that is, the first fixed comb electrode  83  and the second fixed comb electrode  84 ), respectively. The drive voltage V in   1 ( t ) and the drive voltage V in   2 ( t ) are complementary to each other. That is, when the voltage value of the drive voltage V in   1 ( t ) is V H , the voltage value of the drive voltage V in   2 ( t ) is V L , and when the voltage value of the drive voltage V in   1 ( t ) is V L , the voltage value of the drive voltage V in   2 ( t ) Is V H . 
       FIG.  29    is a graph showing the time change of each signal in an example. In the diagram, the drive voltage V in   1 ( t ), the drive voltage V in   2 ( t ), the displacement amount Y(t) of the beam  91 , the capacitances C 1  and C 2 , and the output voltage Vout(t) are shown in order from the top. In addition, the vertical axis of each graph indicates voltage or capacitance, and the horizontal axis of each graph indicates time. 
     Each of the drive voltages V in   1 ( t ) and V in   2 ( t ) has a time waveform in which rising PU and falling PD are alternately repeated at fixed periods. In the example shown in  FIG.  29   , the duty ratio is 50%, the timing of the rising PU of the drive voltage V in   1 ( t ) and the timing of the falling PD of the drive voltage V in   2 ( t ) match each other, and the timing of the falling PD of the drive voltage V in   1 ( t ) and the timing of the rising PU of the drive voltage V in   2 ( t ) match each other. In addition, the timings of the rising PU of the drive voltage V in   1 ( t ) and the falling PD of the drive voltage V in   2 ( t ) are controlled by the actuator drive circuit  121  so as to match the timing when the displacement amount Y(t) of the beam  91  becomes a minimum point YB farthest from the first fixed comb electrode  83 . In addition, the timings of the falling PD of the drive voltage V in   1 ( t ) and the rising PU of the drive voltage V in   2 ( t ) are controlled by the actuator drive circuit  121  so as to match the timing when the displacement amount Y(t) of the beam  91  becomes a maximum point YA farthest from the second fixed comb electrode  84 . 
     The capacitances C 1 ( t ) and C 2 ( t ) between the fixed comb electrodes  83  and  84  and the movable comb electrode  82  change according to the displacement amount Y(t) of the beam  91 . The capacitance C 1 ( t ) becomes a maximum at the timing when the displacement amount Y(t) reaches the maximum point YA, and becomes a minimum at the timing when the displacement amount Y(t) reaches the minimum point YB. In addition, the capacitance C 2 ( t ) becomes a minimum at the timing when the displacement amount Y(t) reaches the maximum point YA, and becomes a maximum at the timing when the displacement amount Y(t) reaches the minimum point YB. Then, the output voltage Vout(t) from the current-voltage conversion circuit  123  is a value (solid line portion) indicating the time derivative of the capacitance C 1 ( t ) in a period in which the drive voltage V in   1 ( t ) is the constant value V H  excluding 0, and is a value (broken line portion) indicating the time derivative of the capacitance C 2 ( t ) in a period in which the drive voltage V in   2 ( t ) is the constant value V H  excluding 0. 
     The comparator  124  compares the output voltage Vout(t) with a predetermined threshold value (0 V in this example), and provides each actuator drive circuit  121  with an output voltage waveform including a pulse that rises when the output voltage Vout(t) reaches the threshold value. By using the rising timing of this pulse, each actuator drive circuit  121  controls the timing of the falling PD of the drive voltages V in   1 ( t ) and V in   2 ( t ). That is, the actuator drive circuit  121  matches the timing of the falling PD of the drive voltages V in   1 ( t ) and V in   2 ( t ) with the timing when the output voltage Vout(t) reaches a predetermined threshold value. In addition, as in the example shown in  FIG.  9   , the actuator drive circuit  121  may shift the timing of the falling PD after a predetermined time from the timing when the output voltage Vout(t) reaches a predetermined threshold value. Alternatively, as in the example shown in  FIG.  10   , the duty ratio may be set to be less than 50% (for example, 45%), and the timing of the rising PU of the drive voltages V in   1 ( t ) and V in   2 ( t ) may be controlled by the actuator drive circuit  121  so as to be slightly delayed from the timing when the displacement amount Y(t) of the beam  91  becomes the maximum point YA or the minimum point YB. 
       FIG.  30 ( a )  is a graph showing the relationship between (V H ) 2  and the fluctuation width ΔC of the capacitance C a  in the first embodiment.  FIG.  30 ( b )  is a graph showing the relationship between (V H ) 2  and the fluctuation width ΔC of the capacitances C 1  and C 2  in the second embodiment. In these diagrams, the vertical axis indicates the fluctuation width ΔC (unit: F), and the horizontal axis indicates (V H ) 2  (unit: V 2 ). As shown in  FIG.  30 ( b ) , in the second embodiment of the slide method, it can be said that the relationship between the fluctuation width ΔC and (V H ) 2  is almost along the straight line L 1  and the fluctuation width ΔC is almost proportional to (V H ) 2 . On the other hand, in the first embodiment of the vertical movement method, there are two proportional coefficients in the relationship between the fluctuation width ΔC and (V H ) 2 . That is, in a region where (V H ) 2  is less than a predetermined value, the relationship between the fluctuation width ΔC and (V H ) 2  is along the straight line L 2 , and in a region where (V H ) 2  is larger than the predetermined value, the relationship between the fluctuation width ΔC and (V H ) 2  is the straight line L 3 . In addition, the inclination of the straight line L 2  and the inclination of the straight line L 3  are different from each other, and the inclination of the straight line L 2  is larger than the inclination of the straight line L 3 . 
     Such characteristics in the vertical movement method are considered to be due to the following factors.  FIG.  31    is a diagram schematically showing the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) in the first embodiment. Now, as shown in  FIG.  31 ( a ) , when the movable comb electrode  17  ( 19 ) is displaced within a range in which at least a part of the movable comb electrode  17  ( 19 ) overlaps the fixed comb electrode  16  ( 18 ), the capacitance C a  between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) includes an overlap capacitance C a1  and a fringe capacitance C a2 . The overlap capacitance C a1  is a capacitance generated in a portion where the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) overlap each other. The fringe capacitance C a2  is a capacitance generated in a portion where the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) do not overlap each other. In this case, the change in the capacitance C a  is mainly due to the increase and decrease in the overlap capacitance C a1 . On the other hand, as shown in  FIG.  31 ( b ) , when the movable comb electrode  17  ( 19 ) is displaced to a range in which the movable comb electrode  17  ( 19 ) does not overlap the fixed comb electrode  16  ( 18 ), the capacitance C a  between the fixed comb electrode  16  ( 18 ) and the movable comb electrode  17  ( 19 ) includes only the fringe capacitance C a2 . In this case, the change in the capacitance C a  is mainly due to the increase and decrease in the fringe capacitance C a2 . It is considered that the characteristics shown in  FIG.  30 ( a )  occur because the degree of increase and decrease differs between the overlap capacitance C a1  and the fringe capacitance C a2 . 
     The MEMS actuator, the MEMS actuator drive method, and the MEMS actuator control program according to the present disclosure are not limited to the embodiments described above, and various other modifications can be made. For example, in each embodiment and each modification example described above, a rectangular wave is exemplified as the time waveform of the drive voltage. However, the time waveform of the drive voltage is not limited to the rectangular wave as long as the time waveform of the drive voltage is a waveform that periodically repeats rising and falling and has a period including a constant voltage excluding 0. For example, as the time waveform of the drive voltage, a trapezoidal waveform in which at least one of the rising edge and the falling edge is inclined may be applied. In addition, when the rising waveform of the drive voltage includes an inclined portion, any of the timing between the inclined portion and a constant voltage portion after the rising, the timing between the inclined portion and a portion before the rising (0 V in the embodiment described above), and the timing in the middle of the inclined portion in the rising waveform can be regarded as the rising timing in the embodiment described above. Similarly, when the falling waveform of the drive voltage includes an inclined portion, any of the timing between the inclined portion and a constant voltage portion before the falling, the timing between the inclined portion and a portion after the falling (0 V in the embodiment described above), and the timing in the middle of the inclined portion in the falling waveform can be regarded as the falling timing in the embodiment described above. 
     In addition, in each embodiment described above, the present invention is applied to two types, a vertical vibration type and a slide type. However, the operation type of the MEMS actuator is not limited to these, and the present invention can also be applied to, for example, a type in which a movable portion rotates. In addition, in the rotating mirror type, the movable portion rotates around a rotation axis formed by an elastic body. In this case, if the amplitude of the movable comb electrode is increased to improve the timing detection accuracy, the movable comb electrode is provided at a position away from the rotation axis. However, the resonance frequency of the movable portion is inversely proportional to the square root of the moment of inertia, and the moment of inertia is proportional to the square of the distance from the rotation axis. For this reason, as the movable comb electrode moves away from the rotation axis, the weight of the movable comb electrode affects the moment of inertia, and the resonance frequency of the movable portion decreases. When the resonance frequency of the movable portion decreases, the rotation speed decreases. Therefore, since the amount of time change of the capacitance, that is, the capacitance derivative signal is reduced, the degree of improvement in the timing detection accuracy is suppressed. In addition, as the number of comb fingers of the movable comb electrode becomes larger, the movable comb electrode becomes heavier. For this reason, in order to achieve the desired resonance frequency, the number of comb fingers of the movable comb electrode should be reduced. As a result, there is a problem that it is difficult to obtain a large capacitance value. On the other hand, when the movable comb electrode is provided in the movable portion in the vertical vibration method, regardless of the position of the movable portion where the movable comb electrode is provided, the moment of inertia that increases is constant, and the amount of decrease in the resonance frequency is also constant. Therefore, the amount of decrease in the resonance frequency due to the provision of the movable comb electrode is smaller than that in the rotating mirror method. From such a point, in the vertical vibration method, the number of comb fingers can be made larger than that in the rotating mirror method, so that a large capacitance value can be obtained. Therefore, since the timing detection accuracy is high, it is possible to relatively easily match the timing when the movable portion passes through a predetermined position with the falling timing of the drive signal. 
     In addition, in the slide type, the speed of the movable portion is the slowest at the timing when the capacitance value is the largest (the timing when the capacitance derivative value is zero). When the speed of the movable portion decreases, the time change of the capacitance derivative value decreases, so that the timing detection accuracy is suppressed. On the other hand, in the vertical vibration type, the speed of the movable portion is the fastest at the timing when the capacitance value is the largest (the timing when the capacitance derivative value is zero). For this reason, the time change of the capacitance derivative value increases, and high timing detection accuracy can be obtained. Therefore, in the vertical vibration type, it is possible to relatively easily match the timing when the movable portion passes through a predetermined position with the falling timing of the drive signal as compared with the slide type. 
     REFERENCE SIGNS LIST 
       1 A: optical module,  1 B: MEMS actuator,  2 : mirror unit,  3 : package,  5 : movable mirror (movable portion),  5   a : mirror surface,  5   b : mirror support portion,  6 : fixed mirror,  6   a : mirror surface,  7 : mirror device,  7   a ,  7   b : light passing portion,  8 : optical functional member,  8   a : surface,  8   b : back surface,  9 : stress reduction substrate,  11 : base (base portion),  11   a : main surface,  11   b : back surface,  12 ,  12 A: drive unit,  13 : first elastic support portion,  14 : second elastic support portion,  15 : actuator portion,  16 ,  16 A,  16 B,  18 ,  18 A,  18 B: fixed comb electrode,  16   a ,  18   a : fixed comb finger (first comb finger, third comb finger),  17 ,  17 A,  17 B,  19 ,  19 A,  19 B: movable comb electrode,  17   a ,  19   a : movable comb finger (second comb finger, fourth comb finger),  20 : SOI substrate,  21 : support layer,  22 : device layer,  23 : intermediate layer,  31 : support,  31   a : surface,  33 : lead pin,  33   a : one end portion,  34 : frame body,  34   a : end face,  34   b : stepped surface,  35 : light transmissive member,  51 : arrangement portion,  51   a : surface,  52 : frame portion,  53 : connection portion,  54 : rib portion,  54   a : inner rib portion,  54   b : outer rib portion,  54   c : connecting rib portion,  71 ,  72 : electrode pad,  80 : substrate (base),  81 : fixed comb electrode,  82 : movable comb electrode,  82   a ,  82   b : second comb finger,  83 ,  84 : fixed comb electrode,  83   a ,  84   a : first comb finger,  91 : rib (movable portion),  92 ,  93 : fixing portion,  121 : actuator drive circuit,  122 ,  122 A: timing detection circuit,  123 ,  123 A,  123 B: current-voltage conversion circuit (TIA),  123   a : amplifier,  123   b : feedback resistor,  123   e : capacitor,  124 : comparator,  125 : clamp circuit,  125   a ,  125   b : switching diode,  126 : protection circuit,  126   a ,  126   b : diode,  127 ,  128 : soft limiter circuit,  127   a ,  128   a : switching diode,  127   b ,  127   c ,  128   b ,  128   c : resistor,  129 : displacement amount detection unit,  129   a : integrator circuit,  129   b : amplifier,  130 : voltage generation circuit,  131 ,  141 : lever,  132 ,  142 : first link member,  133 ,  143 : second link member,  134 ,  144 : intermediate member,  135 ,  145 : first torsion bar,  136 ,  146 : second torsion bar,  137 ,  147 : non-linearity reduction spring,  138 ,  148 : electrode support portion,  138   a ,  148   a : first electrode support portion,  138   b ,  148   b : second electrode support portion,  138   c ,  148   c : third electrode support portion,  201 : sinusoidal wave generation circuit,  202 : variable capacitor,  203 : fixed capacitor,  204 : arithmetic circuit,  204   a : operational amplifier,  204   b : feedback capacitor,  205 : envelope detector,  206 : amplifier,  207 : low pass filter,  208 : analog-digital converter,  211 : capacitor,  212 : resistor, C a1 : overlap capacitance, C a2 : fringe capacitance, C 1 , C 2 : capacitor, F 1 , F 2 , F 3 : region, GND: reference potential line, H: envelope, J 1 : current signal, J 1   a , J 1   b : pulse wave, J 2 : feedback current, J 2   a , J 2   b : pulse wave, J 3 , J 4 : current, J 5 , J 6 : feedback current, L 1 , L 2 , L 3 : straight line, N 1  to N 5 : node, PA, PB: saturation waveform, PC: pulse, PD: falling, PU: rising, R 1 , R 2 : axis line, Ri: ripple, Sa: sinusoidal signal, Sb, Sc: signal, T 1  to T 4 : timing, V+: positive constant potential line, V-: negative constant potential line, V H : constant voltage, Va: inverted input terminal voltage, Vi: input signal, Vin, V in   1 , V in   2 : drive signal, Vo: output signal, Vout: capacitance derivative signal, YA, ZA: maximum point, YB, ZB: minimum point, ZC: midpoint.