Patent Publication Number: US-2016238835-A1

Title: Apparatus including optical deflector controlled by saw-tooth voltage and its controlling method

Description:
This application claims the priority benefit under 35 U. S. C. §119 to Japanese Patent Application No. JP2015-025221 filed on Feb. 12, 2015, which disclosure is hereby incorporated in its entirety by reference. 
     BACKGROUND 
     1. Field 
     The presently disclosed subject matter relates to an apparatus including an optical deflector controlled by a saw-tooth voltage and its controlling method, and more specifically, to a video projection apparatus and its controlling method. The video projection apparatus can be used as a pico projector, a head mount display (HMD) unit, a head up display (HUD) unit and the like. 
     2. Description of the Related Art 
     A prior art video projection apparatus is constructed by a two-dimensional optical deflector as an optical scanner manufactured by a micro electro mechanical system (MEMS) device manufactured using a semiconductor process and micro machine technology (see: JP5543468B2 &amp; US2010/0073748A1). Since the MEMS optical scanner is focus-free, the video projection apparatus can be small in size. 
     Generally, in the above-mentioned two-dimensional optical deflector, a mirror is rocked with respect to a horizontal deflection at a high frequency such as 18 kHz, while the mirror is rocked with respect to a vertical deflection at a low frequency such as 60 Hz (see: paragraph 0026 of US2010/0073748A1). Also, the mirror includes a sensor for sensing rocking vibrations thereof in the vertical deflection. As a result, the vertical deflection of the mirror is controlled by the feedback of a simple sum of the sense voltage of the sensor, thus accurately realizing the vertical deflection of the mirror (see: the summing buffer 760 of FIGS. 7 and 8 of US2010/0073748A1). On the other hand, the above-mentioned sensor can be constructed by a piezoelectric element incorporated into the optical deflector (see: U.S. Pat. No. 8,730,549B2). 
     In the above-described prior art video projection apparatus, however, since the sensor is susceptible to the fluctuation of a DC offset generated in the sense voltage thereof, it is difficult to accurately control the vertical deflection of the mirror. Also, if a circuit is added to exclude the above-mentioned fluctuation of a DC offset, the manufacturing cost would be increased. As a result, if the apparatus is a video projection apparatus, it is difficult to accurately control a projected view field. 
     Note that the fluctuation of a DC offset would be caused by the fluctuation of the piezoelectric coefficient of the piezoelectric sensor due to the fluctuation of environmental factors such as temperature and humidity and due to the fluctuation of hardness and rigidity of a substrate by the heating of the piezoelectric sensor irradiated by light. Also, the fluctuation of a DC offset would be caused by charges stored in the piezoelectric sensor when it is operated for a long time. 
     SUMMARY 
     The presently disclosed subject matter seeks to solve the above-described problem. 
     According to the presently disclosed subject matter, in an apparatus including an optical deflector and a control unit for controlling the optical deflector, wherein the optical deflector includes a mirror; a piezoelectric actuator adapted to rock the mirror around an axis of the mirror; and a piezoelectric sensor adapted to sense vibrations of the piezoelectric actuator, the control unit includes: a saw-tooth voltage generating block adapted to generate a saw-tooth voltage; an integral block adapted to calculate an integral voltage of a sum of a sense voltage of the piezoelectric sensor and a DC offset characteristic voltage; a DC offset characteristic voltage calculating block adapted to calculate the DC offset characteristic voltage in accordance with the integral voltage; a subtracter block, connected to the saw tooth voltage generating block and the integral block and adapted to generate a deviation between the saw-tooth voltage and the integral voltage; and a controller, connected to the subtracter block and adapted to generate a drive voltage in accordance with the deviation to apply the drive voltage to the piezoelectric actuator. 
     Also, in a method for controlling an optical deflector including: a mirror; a piezoelectric actuator adapted to rock the mirror around an axis of the mirror; and a piezoelectric sensor adapted to sense vibrations of the piezoelectric actuator, the method includes: generating a saw-tooth voltage; calculating an integral voltage of a sum of a sense voltage of the piezoelectric sensor and a DC offset characteristic voltage; calculating the DC offset characteristic voltage in accordance with the integral voltage; generating a deviation between the saw-tooth voltage and the integral voltage; and generating a drive voltage in accordance with the deviation to apply the drive voltage to the piezoelectric actuator. 
     According to the presently disclosed subject matter, since the integral voltage includes the sense voltage and the DC offset characteristic voltage that represents a DC offset voltage generated in the piezoelectric sensor, the DC offset voltage can be compensated for by the integral voltage, so that the deflection of the mirror can accurately be controlled. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other advantages and features of the presently disclosed subject matter will be more apparent from the following description of certain embodiments, taken in conjunction with the accompanying drawings, wherein: 
         FIG. 1  is a block circuit diagram illustrating an embodiment of the apparatus according to the presently disclosed subject matter; 
         FIG. 2  is a perspective view of the MEMS optical deflector of  FIG. 1 ; 
         FIGS. 3A and 3B  are perspective views for explaining the operation of the outer piezoelectric actuator of  FIG. 2 ; 
         FIGS. 4A, 4B and 4C  are timing diagrams for explaining the horizontal scanning operation of the HEMS optical deflector of  FIG. 1 ; 
         FIGS. 5A, 55 and 5C  are timing diagrams for explaining the vertical scanning operation of the MEMS optical deflector of  FIG. 1 ; 
         FIG. 6  is a diagram showing the relationship between a scanning locus of the MEMS optical deflector and a projected view field of the laser beam of the laser light source of  FIG. 1 ; 
         FIG. 7  is a functional block diagram of the drive voltage generating section and the drive voltage processing section for the vertical scanning operation of the MEMS optical deflector of  FIG. 1 ; 
         FIG. 8  is a flowchart of software carrying out the same operation as the operation of the adder and the PID controller of  FIG. 7 ; 
         FIG. 9  is a flowchart of software carrying out the same operation as the operation of the integral block and the DC offset characteristic voltage calculating block of  FIG. 7 ; 
         FIG. 10  is a table for storing the minimum points of the integral voltage of the same voltage of  FIG. 9 ; 
         FIGS. 11A, 11B and 11C  are timing diagrams for explaining examples of the DC offset characteristic voltage of  FIGS. 7 and 9 ; and 
         FIG. 12  is a timing diagram illustrating a relationship among the sense voltage, the integral voltage of the sense voltage, and the vertical drive voltage of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     In  FIG. 1 , which illustrates an embodiment of the apparatus according to the presently disclosed subject matter, a video projection apparatus  1  receives a video signal VS from a video source such as a personal computer or a camera system to generate a laser beam L for a screen  2 . 
     The video projection apparatus  1  is constructed by a video signal input unit  11 , a video signal processing section  12 , a frame memory  13  and a control section  14  for controlling the video signal processing section  12  and the frame memory  13 . 
     The video signal input unit  11  is an analog red/green/blue (RGB) receiver or a digital video signal receiver such as a digital video interface (DVI), or a high-definition multimedia interface (HDMI). Video signals received by the video signal input unit  11  are processed by a video signal processing section  12  and are stored in the frame memory  13  frame by frame. For example, 60 frames per second are stored in the frame memory  13 . The frame memory  13  is formed by a high-speed random access memory (RAM) such as an SDRAM, a DDR2 SDRAM or a DDR3 SDRAM. In this case, one frame of the frame memory  13  corresponds to a view field formed by a horizontal angle of 40° and a vertical angle of 25° (see:  FIG. 6 ). 
     Also, the video projection apparatus  1  is constructed by a drive voltage generating section  15 , a drive voltage processing section  16 , and a pixel data extracting section  17 . 
     The drive voltage generating section  15  generates digital drive voltages V xa  and V ya  which are transmitted via a drive unit  18  formed by digital-to-analog (D/A) converters  181  and  182 , amplifiers  183  and  184 , and inverters  185  and  186  to a MEMS optical deflector  19 . In this case, analog drive voltages V xa  and V ya  and their inverted drive voltages V xb  and V yb  are supplied from the drive unit  18  to the MEMS optical deflector  19 . Note that the analog drive voltages V ya  and V yb  are represented by the same denotations of the digital drive voltages V ya  and V yb , in order to simplify the description. On the other hand, the MEMS optical deflector  19  generates sense voltages V xsa , V xsb , V ysa  and V ysb  in response to the flexing angles of the mirror thereof which are supplied via a sense voltage input unit  20  formed by a subtracter  201 , an adder  202 , a band-pass filter  203 , a low-pass filter  204 , and analog-to-digital (A/D) converters  205  and  206  to the drive voltage processing section  16 . In this case, the band-pass filter  203  removes external noises from the sense voltage V xs  (=V xsa −V ysb )) of the subtracter  201 , while the low-pass filter  204  removes external noises from the sense voltage V ys  (=V ysa +V ysb ) of the adder  202 . The A/D converter  205  performs an A/D conversion upon the output voltage of the band-pass filter  203  to transmit a digital sense voltage V xs  to the drive voltage processing section  16 , while the A/D converter  206  performs an A/D conversion upon the output voltage of the low-pass filter  204  to transmit a digital sense voltage V ys  to the drive voltage processing section  16 . Note that the digital sense voltages V ys  and V ys  are represented by the same denotations of the analog output voltages V ys  and V ys  of the subtracter  201  and the adder  202 , in order to simplify the description. 
     The pixel data extracting section  17  generates a drive voltage which is supplied to a light source drive unit  21  formed by a D/A converter  211  and an amplifier  212  for supplying a drive current I d  to a laser light source  22 . Note that the light source drive unit  21  and the laser light source  22  can be provided for each of red (R), green, (G) and blue (B). Also, the laser light source  22  can be replaced by a light emitting diode (LED) source. 
     The drive voltage generating section  15 , the drive voltage processing section  16  and the pixel data extracting section  17  are controlled by the control section  14 . 
     In more detail, the drive voltage generating section  15  transmits extracting timing signals of pixel data to the pixel data extracting section  17 . Also, the drive voltage processing section  16  receives drive voltages similar to the drive voltages V xa  and V ya  from the drive voltage generating section  15  and the sense voltages V xs  and V ys  from the sense voltage input unit  20  to transmit a delay timing signal to the pixel data extracting section  17  due to the delay transmission of the drive voltages V xa  and V ya  to the mirror of the MEMS optical deflector  19 . Further, the pixel data extracting section  17  extracts pixel data from the frame memory  13  in accordance with the extracting timing signals of the drive voltage generating section  15  and the delay signal of the drive voltage processing section  16 . 
     In  FIG. 1 , the video signal processing section  12 , the control section  14 , the drive voltage generating section  15 , the drive voltage processing section  16  and the pixel data extracting section  17  can be formed by a single control unit  23  or a microcomputer using a field-programmable gate array (FPGA), an extensible processing platform (EPP) or a system-on-a-chip (SoC). The control section  14  has an interface function with a universal asynchronous receiver transmitter (UART) and the like. 
     In  FIG. 2 , which is a perspective view of the MEMS optical deflector  19  of  FIG. 1 , the MEMS optical deflector  19  is constructed by a circular mirror  191  for reflecting incident light L from the laser light source  22 , an inner frame (movable frame)  192  surrounding the mirror  191  for supporting the mirror  191 , a pair of torsion bars  194   a  and  194   b  coupled between the mirror  191  and the inner frame  192 , a pair of inner piezoelectric actuators  193   a  and  193   b  coupled between the inner frame  192  and the mirror  191  and serving as cantilevers for rocking the mirror  191  with respect to an X-axis of the mirror  191 , an outer frame (support frame)  195  surrounding the inner frame  192 , a pair of meander-type outer piezoelectric actuators  196   a  and  196   b  coupled between the outer frame  195  and the inner frame  192  and serving as cantilevers for rocking the mirror  191  through the inner frame  192  with respect to a Y-axis of the mirror  191  perpendicular to the X-axis, piezoelectric sensors  197   a  and  197   b  arranged symmetrically with respect to the X-axis in the proximity of the inner piezoelectric sensors  193   a  and  193   b  at an edge of the torsion bar  194   b , and piezoelectric sensors  198   a  and  198   b  arranged on the inner frame  192  in the proximity of the outer piezoelectric actuators  196   a  and  196   b.    
     The inner frame  192  is rectangularly-framed to surround the mirror  191  associated with the inner piezoelectric actuators  193   a  and  193   b.    
     The torsion bars  194   a  and  194   b  are arranged along the X-axis, and have ends coupled to the inner circumference of the inner frame  192  and other ends coupled to the outer circumference of the mirror  191 . Therefore, the torsion bars  194   a  and  194   b  are twisted by the inner piezoelectric actuators  193   a  and  193   b  to rock the mirror  191  with respect to the X-axis. 
     The inner piezoelectric actuators  193   a  and  193   b  oppose each other along the Y-axis and sandwich the torsion bars  194   a  and  194   b . The inner piezoelectric actuators  193   a  and  193   b  have ends coupled to the inner circumference of the inner frame  192  and other ends coupled to the torsion bars  194   a  and  194   b . In this case, the flexing direction of the inner piezoelectric actuator  193   a  is opposite to that of the inner piezoelectric actuator  193   b.    
     The outer frame  195  is rectangularly-framed to surround the inner frame  192  via the outer piezoelectric actuators  196   a  and  196   b.    
     The outer piezoelectric actuators  196   a  and  196   b  are coupled between the inner circumference of the outer frame  195  and the outer circumference of the inner frame  192 , in order to rock the inner frame  192  associated with the mirror  191  with respect to the outer frame  195 , i. e., to rock the mirror  191  with respect to the Y-axis. 
     The outer piezoelectric actuator  196   a  is constructed by piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  which are serially-coupled from the outer frame  195  to the inner frame  192 . Also, each of the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  are in parallel with the X-axis of the mirror  191 . Therefore, the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  are folded at every cantilever or meandering from the outer frame  195  to the inner frame  192 , so that the amplitudes of the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  can be changed along directions perpendicular to the Y-axis of the mirror  191 . 
     Similarly, the outer piezoelectric actuator  196   b  is constructed by piezoelectric cantilevers  196   b - 1 ,  196   b - 2 ,  196   b - 3  and  196   b - 4  which are serially-coupled from the outer frame  195  to the inner frame  192 . Also, each of the piezoelectric cantilevers  196   b - 1 ,  196   b   2 ,  196   b - 3  and  196   b - 4  are in parallel with the X-axis of the mirror  191 . Therefore, the piezoelectric cantilevers  196   b - 1 ,  196   b - 2 ,  196   b - 3  and  196   b - 4  are folded at every cantilever or meandering from the outer frame  195  to the inner frame  192 , so that the amplitudes of the piezoelectric cantilevers  196   b - 1 ,  196   b - 2 ,  196   b - 3  and  196   b - 4  can be changed along directions perpendicular to the Y-axis of the mirror  191 . 
     Note that the number of piezoelectric cantilevers in the outer piezoelectric actuator  196   a  and the number of piezoelectric cantilevers in the outer piezoelectric actuator  196   b  can be other values such as 2, 6, 8, . . . . 
     The piezoelectric sensors  197   a  and  197   b  serve as speed sensors that sense deflecting angle deviations of the mirror  191  mainly caused by the inner piezoelectric actuators  193   a  and  193   b . The sense voltages V xsa  and V xsb  of the piezoelectric sensors  197   a  and  197   b  are substantially the same as each other, and opposite in phase to each other. These two sense voltages V xsa  and V xsb  correspond to differentiated signals of the drive voltages V xa  and V xb . Also, the difference voltage V xb  (see:  FIG. 1 ) between the two sense voltages V xsa  and V xsb  would cancel noises included therein. Therefore, the sense voltage V xs  (=V xsa −V xsb ) of the subtracter  201  of the sense voltage input unit  20  of  FIG. 1  is a representative sense deflecting angle signal caused the inner piezoelectric actuators  193   a  and  193   b . Note that one of the piezoelectric sensors  197   a  and  197   b  can be omitted. 
     The piezoelectric sensors  198   a  and  198   b  serve as speed sensors that sense deflecting angle signals of the mirror  191  mainly caused by the outer piezoelectric actuators  196   a  and  196   b . Note that the sense voltages V ysa  and V ysb  of the piezoelectric sensors  198   a  and  198   b  are substantially the same as each other. These sense voltages V ysa  and V ysb  correspond to a differentiated voltage of the drive voltage V ya . Therefore, the sense voltage V ys  (=V ysa −V ysb ) of the adder  202  of the sense voltage input unit  20  of  FIG. 1  is a representative sense deflecting angle signal caused the outer piezoelectric actuators  196   a  and  196   b . Note that one of the piezoelectric sensors  198   a  and  198   b  can be omitted. 
     The structure of each element of the MEMS optical deflector  19  is explained below. 
     The mirror  191  is constructed by a monocrystalline silicon support layer serving as a vibration plate and a metal layer serving as a reflector. 
     The inner frame  192 , the torsion bars  194   a  and  194   b  and the outer frame  195  are constructed by the monocrystalline silicon support layer and the like. 
     Each of the piezoelectric actuators  194   a  and  194   b  and the piezoelectric cantilevers  196   a - 1  to  196   a - 4  and  196   b - 1  to  196   b - 4  and the piezoelectric sensors  197   a ,  197   b ,  198   a  and  198   b  is constructed by a Pt lower electrode layer, a lead titanate zirconate (PZT) layer and a Pt upper electrode layer. 
     The meander-type piezoelectric actuators  196   a  and  196   b  are described below. 
     In the piezoelectric actuators  196   a  and  196   b , the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3 ,  196   a - 4 ,  196   b - 1 ,  196   b - 2 ,  196   b - 3  and  196   b - 4  are divided into an odd-numbered group of the piezoelectric cantilevers  196   a - 1  and  196   a - 3 ;  196   b - 1  and  196   b - 3 , and an even-numbered group of the piezoelectric cantilevers  196   a - 2  and  196   a - 4 ;  196   b - 2  and  1966 - 4  alternating with the odd-numbered group of the piezoelectric cantilevers  196   a - 1  and  196   a - 3 ;  196   b - 1  and  196   b - 3 . 
       FIGS. 3A and 3B  are perspective views for explaining the operation of the piezoelectric cantilevers of one outer piezoelectric actuator such as  196   a  of  FIG. 2 . Note that  FIG. 3A  illustrates a non-operation state of the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  of the piezoelectric actuator  196   a , and  FIG. 3B  illustrates an operation state of the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4  of the outer piezoelectric actuator  196   a.    
     As illustrated in  FIG. 3B  which illustrates only the piezoelectric cantilevers  196   a - 1 ,  196   a - 2 ,  196   a - 3  and  196   a - 4 , when the odd-numbered group of the piezoelectric cantilevers  196   a - 1 ,  196   a - 3 ,  196   b - 1  and  196   b - 3  are flexed in one direction, for example, in a downward direction D, the even-numbered group of the piezoelectric cantilevers  196   a - 2 ,  196   a - 4 ,  196   b - 2  and  196   b - 4  are flexed in the other direction, i.e., in an upward direction U. On the other hand, when the odd-numbered group of the piezoelectric cantilevers  196   a - 1 ,  196   a - 3 ,  196   b - 1  and  196   b - 3  are flexed in the upward direction, the even-numbered group of the piezoelectric cantilevers  196   a - 2 ,  196   a - 4 ,  196   b - 2  and  196   b - 4  are flexed in the downward direction D. 
     Thus, the mirror  191  is rocked with respect to the Y-axis. 
     First, a main scanning operation or horizontal scanning operation by rocking the mirror  191  with respect to the X-axis is explained in detail with reference to  FIGS. 4A, 4B and 4C . 
     As illustrated in  FIGS. 4A and 4B , the drive voltage V xa  the drive voltage V Xb  generated from the drive unit  18  are sinusoidal at a relatively high resonant frequency f x  and symmetrical or opposite in phase to each other. As a result, the inner piezoelectric actuators  193   a  and  193   b  carry out flexing operations in opposite directions to each other, so that the torsion bars  194   a  and  194   b  are twisted to rock the mirror  191  with respect to the X-axis. 
     In the above-mentioned horizontal scanning operation, the changing rates of the drive voltages V xa  and V xb  are low at their lowest and highest levels as illustrated in  FIGS. 4A and 4B , so that the brightness thereof at the screen  2  would be particularly high. Therefore, as illustrated in  FIG. 4C , horizontal blanking periods BP X  for turning off the laser light source  22  are provided where the changing rates of the drive voltages V xa  and V xb  are low to make the brightness at the entire screen  2  uniform. Additionally, right-direction horizontal scanning periods RH alternating with left-direction horizontal scanning periods LH are provided between the horizontal blanking periods BP x , in order to increase the depicting time period, and thus the depicting efficiency can be enhanced. 
     Next, a sub scanning operation or vertical scanning operation by rocking the mirror  191  with respect to the Y-axis is explained in detail with reference to  FIGS. 5A, 5B and 5C . 
     As illustrated in  FIGS. 5A and 5B , the drive voltage V ya  and the drive voltage V yb  are saw-tooth-shaped at a relatively low non-resonant frequency f Y  and symmetrical or opposite in phase to each other. As a result, the piezoelectric cantilevers  196   a - 1 ,  196   a - 3 ,  196   b - 1  and  196   h - 3  and the piezoelectric cantilevers  196   a - 2 ,  196   a - 4 ,  196 . b - 2  and  196   b - 4  carry out flexing operations in opposite directions to each other, so that the mirror  191  is rocked with respect to the Y-axis. 
     In the above-mentioned vertical scanning operation, the changing rate of the drive voltages V ya  and V yb  are low at their lowest and highest levels as illustrated in  FIGS. 5A and 5B , so that the brightness thereof at the screen  2  would be particularly high. Therefore, as illustrated in  FIG. 5C , vertical blanking periods BP Y  for turning off the laser light source  22  are provided where the changing rates of the drive voltages V ya  and V yb  are low to make the brightness at the entire screen  2  uniform. 
     As illustrated in  FIG. 6 , which is a diagram illustrating a relationship between a scanning locus SL of the MEMS optical deflector  19  and a projected area of the laser beam L of the laser light source  22  of  FIG. 1 , a horizontal scanning line H and a vertical scanning line V by the MEMS optical deflector  19  are protruded from a projected view field F of the laser beam L defined by a horizontal angle of 40°, for example, and a vertical angle of 25°, for example. 
     In the horizontal scanning operation, the drive voltage generating section  15  includes a sinusoidal-wave voltage generating block (not shown) for generating a sinusoidal-wave voltage V ya  and a phase-locked loop block (not shown) for transmitting the sinusoidal-wave voltage V ya  the drive unit  18 . When the drive voltage processing section  16  receives the sense voltage V xs  the sense voltage input unit  20 , to calculate an integral voltage V xs ′ of the sense voltage V xs , the integral voltage V xs ′ is transmitted to the drive voltage generating section  15 , so that the phase-locked loop block generates the sinusoidal-wave voltage V xa  phase-locked to the integral voltage V xs ′. 
     The vertical scanning operation is explained in more detail with reference to  FIG. 7 , which is a functional block circuit diagram of the drive voltage generating section  15  and the drive voltage processing section  16  of  FIG. 1 . 
     In  FIG. 7 , the drive voltage generating section  15  is constructed by a saw-tooth voltage generating block  151  operated by the control section  14 , a subtracter block  152 , and a proportional/integral/derivative (PID) controller  153  formed by a proportional block  1531 , an integral block  1532 , a derivative block  1583 , and an adder block  1534 . On the other hand, the drive voltage processing section  16  is constructed by a sum (or integral) block  161  and a DC offset characteristic voltage calculating block  162  for calculating a DC offset characteristic voltage C used in the integral block  161 . 
     In the drive voltage generating section  15  of  FIG. 7 , the subtracter  152  calculates a deviation e(t) by 
         e ( t )= V   y   −V   ys ′
         where V y  is a saw-tooth voltage generated from the saw-tooth voltage generating block  151 ; and   V ys ′ is the output voltage (sum voltage or integral, voltage) of the integral block  161  of the drive voltage processing section  16 . The PID controller  153  is operated to generate the drive voltage V ya  that the deviation e(t) is brought close to zero, i.e., the integral voltage V ys ′ of the integral block  161  of the drive voltage processing section  16  is brought close to the saw-tooth voltage V y . In more detail, the proportional block  1531  calculates a proportional term u p =K p e(t), the integral block  1532  calculates an integral term u i =K i ∫e(t)dt, the derivative block  1533  calculates a derivative term u d =K d d(e(t))/dt, and the adder block  1534  calculates a vertical drive voltage V ya =u p +u i +u d . In this case, a proportion gain K p , an integral gain K i  and a derivative gain K d  are predetermined to have optimum values.       

     Note that the PID controller  153  can be another controller which includes only the proportional block  1531  and the integral block  1532 , for example. 
     In the drive voltage processing section  16 , the integral block  161  calculates an integral voltage V ys ′ of the sense voltage V ys  by 
       ( V   ys ′=∫( V   ys ( t )+ C ) dt  
         where C is a DC offset characteristic voltage representing a DC offset of the sense voltage V ys (=V ysa +V ysb ) from the piezoelectric sensors  198   a  and  198   b  deviated with respect to an optimum value.       

     The DC offset characteristic voltage C is calculated by the DC offset characteristic voltage calculating block  162  using a gradient of the integral voltage V ys ′ with respect to time. Note that the DC offset characteristic voltage C is initialized at 0. 
     The inventor has found that the gradient of the integral voltage V ys ′ represents a DC offset voltage generated in the sense voltage V ys (=V ysa +V ysb ) of the piezoelectric sensors  198   a  and  198   b.    
     The DC offset characteristic voltage calculating block  162  is constructed by a minimum point calculating block  1621  for calculating minimum points MIN 0 , MIN 1 , MIN 2 , . . . on the integral voltage V ys ′. For example, such minimum points MIN 0 , MIN 1 , MIN 2 , . . . , can be detected by differentiating the integral voltage V ys ′ with respect to time, that is, rising points as minimum points can be detected in the differentiated integral voltage V ys ′. As a result, minimum points MIN 0 , MIN 1 , MIN 2 , . . . are obtained (see:  FIGS. 11A, 11B and 11C ). Also, the DC offset characteristic voltage calculating block  162  is constructed by a straight line calculating block  163  which calculates a straight line designated by V ys ′=A·t+B approximate to the minimum points MIN 0 , MIN 1 , MIN 2 , . . . using the least square method. Note that A is a gradient of the straight line with respect to time. Further, the DC offset characteristic voltage calculating block  162  is constructed by a DC offset characteristic voltage setting block  1623  which sets the DC offset characteristic voltage C by 
     
       
      
       C=A/α 
      
     
     where α is a constant larger than 1. In this case, if the constant α is too small, i. e., α=1, the compensation rate of the DC offset voltage is too large, so that the integral voltage V ys ′ could be chattering. On the contrary, if the constant α is too large, the compensation rate of the DC offset voltage is too small. Preferably, the constant α is 2. 
     In  FIG. 7 , the minimum point calculating block  1621  can be replaced by a maximum point calculating block which calculates maximum points MAX 0 , MAX 1 , MAX 2 , . . . (see  FIGS. 11A, 11B and 11C ). The maximum points MAX 0 , MAX 1 , MAX 2 , have a gradient tendency the same as that of the minimum points MIN 0 , MIN 1 , MIN 2 , . . . . Therefore, in this case, the straight line calculating block  1622  can calculate the same straight line using the maximum points MAX 0 , MAX 1 , MAX 2 , . . . . 
     The operation of the adder  152  and the PID controller  153  of  FIG. 7  can be carried out by software illustrated by a flowchart in  FIG. 8  executed at every time period T ms such as 1 ms. 
     First, at step  801 , a deviation “e” is calculated by 
         e←V   y   −V   ys ′
         where V y  is a saw-tooth voltage generated from the saw-tooth voltage generating block  151 ; and   V ys ′ is an integral voltage of the integral block  161  of the drive voltage processing section  16 .       

     Next, at step  802 , a proportional term u p  is calculated by 
     
       
      
       u 
       p 
       ←K 
       p 
       ·e  
      
         
         
           
             where K p  is a proportional gain, 
           
         
       
    
     Next, at step  803 , an integral term u i  is calculated by 
     
       
      
       u 
       i 
       ←u 
       io 
       +K 
       i 
       ·T·e  
      
         
         
           
             where u io  is a previous integral term; and 
             K i  is an integral gain. 
           
         
       
    
     Then, the previous integral term u io  is replaced by the current integral term u i  at step  804 . 
     Next, at step  805 , a derivative term u d  is calculated by 
         u   d   ←K   d ·( e−e   0 )/ T  
         where K d  is a derivative gain; and   e 0  is a previous deviation.       

     Then, the previous deviation e 0  is replaced by the current deviation “e” at step  806 . 
     Next, at step  807 , a vertical drive voltage V ya  is calculated by 
     
       
      
       V 
       ya 
       ←u 
       p 
       +u 
       i 
       +u 
       d  
      
     
     Next, at step  808 , the vertical drive voltage V ya  is transmitted to the drive unit  18 . 
     The flowchart of  FIG. 8  is completed by step  809 . 
     The operation of the integral block  161  and the DC offset characteristic voltage calculating block  162  of  FIG. 7  can be carried out by software illustrated by a flowchart in  FIG. 9  executed at every time period T ms such as 1 ms. Note that a DC offset characteristic voltage C is initialized at 0. Also, counters “i” and “j” are initialized at 0. 
     First, at step  901 , the counter “i” is counted up by +1. 
     Next, at step  902 , it is determined whether or not i&lt;i m  is satisfied. Note that i m  is 500 corresponding to 500 ms, for example. As a result, if i≧i m , the control proceeds to steps  903  through  906  which calculate the DC offset characteristic voltage C, while if i&lt;i m , the control proceeds directly to step  907 . 
     Steps  903  through  906  are explained later. 
     At step  907 , the integral voltage V ys ′ is renewed by 
         V   ys   ′←V   ys ′+( V   ys   +C·T )
 
     Next, at step  908 , it is determined whether or not i≧3 is satisfied. As a result, if i≧3, the control proceeds to step  909 . Otherwise, i. e., if i&lt;3, the control proceeds directly to step  912 . 
     At step  909 , it is determined whether or not the following formula is satisfied: 
         V   ys2   ′&gt;V   ys1   ′&lt;V   ys ′
 
     where V ys1 ′ is a previous voltage of the integral voltage V ys ′; and 
     V ys2 ′ is a second-previous voltage of the integral voltage V ys ′. That is, it is determined whether or not the previous sampling point ((i−1)T, V ys1 ′) is a minimum point of the integral voltage V ys ′. As a result, if ((i−1)T, V ys1 ′) is a minimum point P j , the control proceeds to step  910 . Otherwise, the control proceeds directly to step  912 . At step  910 , P j =((i−1)T, V ys1 ′) is stored in a minimum point table as illustrated in  FIG. 10 . Then, the counter j is counted up by +1 at step  911 . 
     Steps  903  to  906  are explained below. 
     At step  903 , a straight line represented by V ys ′=A t+B approximate to the minimum points P j  stored in the minimum point table is obtained by a least square method. Note that A is a gradient of the straight line with respect to time. 
     Next, at step  904 , a DC offset characteristic voltage C is calculated by 
     
       
      
       C←A/α 
      
     
     where α is a constant larger than 1, preferably, 2. 
     Then, the counter “i” is initialized at 0 by step  905 , and the counter “j” is initialized at 0 by step  906 . 
     Also, at step  912 , the second-previous integral voltage V ys2 ′ is replaced by the previous integral voltage V ys1 ′, and at step  913 , the previous integral voltage V ys1 ′ is replaced by the current integral voltage V ys ′. 
     Thus, the flowchart of  FIG. 9  is completed by step  914 . 
     Note that, at step  909 , it can be determined whether or not the following formula is satisfied: 
         V   ys2   ′&lt;V   ys1   ′&gt;V   ys ′
 
     That is, it can be determined whether or not the previous sampling point ((i−1)T, V ys1 ′) is a maximum point of the integral voltage V ys ′. As a result, if ((i−1)T, V ys1 ′) is a maximum point P j , the control proceeds to step  910  which stores P j =((i−1)T, V ys1 ′) in a maximum point table similar to the minimum point table of  FIG. 10 . 
     As illustrated in  FIG. 11A , when the sense voltage V ys (=V ysa +V ysb ) has no DC offset voltage relative to a reference level REF, the mean value of the integral voltage V ys ′ is unchanged. As a result, a straight line approximate to the minimum, points MIN 0 , MIN 1 , MIN 2 , . . . (the maximum points MAX 0 , MAX 1 , MAX 2 , . . . ) is horizontal. Therefore, the DC offset characteristic voltage C is approximately 0. 
     Also, as illustrated in  FIG. 11B , when the sense voltage V ys  (V ysa +V ysb ) has a positive DC offset voltage relative to the reference level REF, the mean value of the integral voltage V ys ′ is changing downward. As a result, a straight line approximate to the minimum points MIN 0 , MIN 1 , MIN 2 , . . . (the maximum points MAX 0 , MAX 1 , MAX 2 , . . . ) is sloped downward. Therefore, the DC offset characteristic voltage C is negative. 
     Further, as illustrated in  FIG. 11C , when the sense voltage V ys =(V ysa +V ysb ) has a negative DC offset voltage relative to the reference level REF, the mean value of the integral voltage V ys ′ is changing upward. As a result, a straight line approximate to the minimum points MIN 0 , MIN 1 , MIN 2 , . . . (the maximum points MAX 0 , MAX 1 , MAX 2 , . . . ) is sloped upward. Therefore, the DC offset characteristic, voltage C is positive. 
     According to the inventor&#39;s experiment, the analog sense voltage V ys (=V ysa +V ysb ) of the adder  202 , the integral voltage V ys ′ of the integral block  161  and the vertical drive voltage V ya  in  FIG. 12  were obtained under the condition that the mirror  191  has a diameter of 1.2 mm and a thickness of 45 μm. That is, in  FIG. 12 , the integral voltage V ys ′ could completely follow the vertical drive voltage V ys . As a result, even when a DC offset voltage was generated in the piezoelectric sensors  198   a  and  198   b , the deflection of the mirror  191  could accurately be controlled. 
     In  FIG. 2 , note that the inner piezoelectric actuators  193   a  and  193   b  and the torsion bars  194   a  and  194   b  can be replaced by meander-type piezoelectric actuators. 
     It will be apparent to those skilled in the art that various modifications and variations can be made in the presently disclosed subject matter without departing from the spirit or scope of the presently disclosed subject matter. Thus, it is intended that the presently disclosed subject matter covers the modifications and variations of the presently disclosed subject matter provided they come within the scope of the appended claims and their equivalents. All related or prior art references described above and in the Background section of the present specification are hereby incorporated in their entirety by reference.