Patent Publication Number: US-7903960-B2

Title: Photographic apparatus for determining whether to perform stabilization on the basis of inclination angle

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a photographic apparatus, and in particular, to a photographic apparatus that performs a rotational movement such as an inclination correction or the like. 
     2. Description of the Related Art 
     There is known a type of image stabilization (also known as anti-shake, but hereinafter, simply “stabilization”) apparatus for a photographic apparatus. The image stabilization apparatus corrects for the effects of hand shake by moving a movable platform including an image stabilization lens or by moving an imager (an imaging sensor) in an xy plane perpendicular to an optical axis of a taking lens of the photographic apparatus, in accordance with the amount of hand shake that occurs during the imaging process. 
     Japanese unexamined patent publication (KOKAI) No. 2006-71743 discloses an image stabilization apparatus that calculates hand-shake quantity on the basis of hand shake due to yaw, pitch, and roll, and then performs a stabilization on the basis of the hand-shake quantity (the first, second, and third hand-shake angles). 
     In this stabilization operation, the following stabilization functions are performed: a translational movement including a first stabilization that corrects the hand shake caused by yaw and a second stabilization that corrects the hand shake caused by pitch, and a rotational movement including a third stabilization that corrects the hand shake caused by roll. 
     In the translational movement, the movable platform is moved in the xy plane without rotational movement. 
     In the rotational movement, the movable platform is rotated in the xy plane. 
     However, the rotational movement of the movable platform for the third stabilization limits the movable ranges of the movable platform in the x and y directions available to translational movement (the first and second stabilizations). 
     When the movable ranges of the movable platform available for the translational movement are limited, the translational movement cannot be performed accurately. 
     Conversely, the translational movement limits the movable ranges of the movable platform for rotational movement, thus preventing it from being performed accurately. 
     SUMMARY OF THE INVENTION 
     Therefore, an object of the present invention is to provide a photographic apparatus that performs both the rotational and translational movements effectively. 
     According to the present invention, a photographic apparatus comprises a movable platform and a controller. The movable platform has an imager that captures an optical image through a taking lens, and is movable and rotatable in an xy plane perpendicular to an optical axis of the taking lens. The controller performs a movement control of the movable platform for an inclination correction based on an inclination angle of the photographic apparatus formed by rotation of the photographic apparatus around the optical axis, as measured with respect to a level plane perpendicular to the direction of gravitational force, for a first stabilization for correcting hand shake caused by yaw around the y direction, and for a second stabilization for correcting hand shake caused by pitch around the x direction. The x direction is perpendicular to the optical axis. The y direction is perpendicular to the x direction and the optical axis. The controller performs at least one of a first determination of whether the first stabilization is to be performed and a second determination of whether the second stabilization is to be performed, on the basis of the inclination angle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The objects and advantages of the present invention will be better understood from the following description, with reference to the accompanying drawings in which: 
         FIG. 1  is a perspective view of the embodiment of the photographic apparatus as viewed from the rear; 
         FIG. 2  is a front view of the photographic apparatus, when the photographic apparatus is held in the first horizontal orientation; 
         FIG. 3  is a circuit construction diagram of the photographic apparatus; 
         FIG. 4  is a flowchart that shows the main operation of the photographic apparatus; 
         FIG. 5  is a flowchart that shows the details of the timer interrupt process; 
         FIG. 6  illustrates the calculations involved in the stabilization and inclination correction; 
         FIG. 7  is a construction diagram of the movable platform; 
         FIG. 8  is a flowchart showing the details of the calculation of the third digital displacement angle; 
         FIG. 9  is a front view of the photographic apparatus, when the photographic apparatus is held in the second horizontal orientation; 
         FIG. 10  is a front view of the photographic apparatus, when the photographic apparatus is held in the first vertical orientation; 
         FIG. 11  is a front view of the photographic apparatus, when the photographic apparatus is held in the second vertical orientation; 
         FIG. 12  is a front view of the photographic apparatus, and Kθ n  is the angle formed when the photographic apparatus is rotated (inclined) in a counter-clockwise direction as viewed from the front, away from the first horizontal orientation; 
         FIG. 13  is a front view of the photographic apparatus, and Kθ n  is the angle formed when the photographic apparatus is rotated (inclined) in a counter-clockwise direction as viewed from the front, away from the first vertical orientation; 
         FIG. 14  is a front view of the photographic apparatus, and Kθ n  is the angle formed when the photographic apparatus is rotated (inclined) in a counter-clockwise direction as viewed from the front, away from the second horizontal orientation; 
         FIG. 15  is a front view of the photographic apparatus, and Kθ n  is the angle formed when the photographic apparatus is rotated (inclined) in a counter-clockwise direction as viewed from the front, away from the second vertical orientation; and 
         FIG. 16  shows the position relationship between the imaging surface of the imager, the edge of the movement range, the movable ranges Hsx n  and Hsy n  before rotation, and the movable ranges Rx and Ry after rotation. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention is described below with reference to the embodiment shown in the drawings. In the embodiment, the photographic apparatus  1  is a digital camera. A camera lens (i.e. taking lens)  67  of the photographic apparatus  1  has the optical axis LX. 
     By way of orientation in the embodiment, the x direction, the y direction, and the z direction are defined (see  FIG. 1 ). The x direction is the direction perpendicular to the optical axis LX. The y direction is the direction perpendicular to the optical axis LX and the x direction. The z direction is the direction parallel to the optical axis LX and perpendicular to both the x direction and the y direction. 
     The relationships between the direction of gravitational force and the x direction, the y direction, and the z direction, change according to the orientation of the photographic apparatus  1 . 
     For example, when the photographic apparatus  1  is held in the first horizontal orientation, in other words, when the photographic apparatus  1  is held horizontally and the upper surface of the photographic apparatus  1  faces upward (see  FIG. 2 ), the x direction and the z direction are perpendicular to the direction of gravitational force and the y direction is parallel to the direction of gravitational force. 
     When the photographic apparatus  1  is held in the second horizontal orientation, in other words, when the photographic apparatus  1  is held horizontally and the lower surface of the photographic apparatus  1  faces upward (see  FIG. 9 ), the x direction and the z direction are perpendicular to the direction of gravitational force and the y direction is parallel to the direction of gravitational force. 
     When the photographic apparatus  1  is held in the first vertical orientation, in other words, when the photographic apparatus  1  is held vertically and one of the side surfaces of the photographic apparatus  1  faces upward (see  FIG. 10 ), the x direction is parallel to the direction of gravitational force and the y direction and the z direction are perpendicular to the direction of gravitational force. 
     When the photographic apparatus  1  is held in the second vertical orientation, in other words, when the photographic apparatus  1  is held vertically and the other side surface of the photographic apparatus  1  faces upward (see  FIG. 11 ), the x direction is parallel to the direction of gravitational force and the y direction and the z direction are perpendicular to the direction of gravitational force. 
     When the front surface of the photographic apparatus  1  faces in the direction of gravitational force, the x direction and the y direction are perpendicular to the direction of gravitational force and the z direction is parallel to the direction of gravitational force. The front surface of the photographic apparatus  1  is the side on which camera lens  67  is attached. 
     The imaging part of the photographic apparatus  1  comprises a PON button  11 , a PON switch  11   a , a photometric switch  12   a , a shutter release button  13 , a shutter release switch  13   a  for an exposure operation, a correction button  14 , a correction switch  14   a , a display  17  such as an LCD monitor or the like, a mirror-aperture-shutter unit  18 , a DSP  19 , a CPU  21 , an AE (automatic exposure) unit  23 , an AF (automatic focus) unit  24 , an imaging unit  39   a  in the correction unit  30 , and the camera lens  67  (see  FIGS. 1 ,  2 , and  3 ). 
     Whether the PON switch  11   a  is in the ON state or OFF state is determined by the state of the PON button  11 . The ON/OFF states of the photographic apparatus  1  correspond to the ON/OFF states of the PON switch  11   a.    
     The subject image is captured as an optical image through the camera lens  67  by the imaging unit  39   a , and the captured image is displayed on the display  17 . The subject image can be optically observed through the optical finder (not depicted). 
     When the shutter release button  13  is partially depressed by the operator, the photometric switch  12   a  changes to the ON state so that the photometric operation, the AF sensing operation, and the focusing operation are performed. 
     When the shutter release button  13  is fully depressed by the operator, the shutter release switch  13   a  changes to the ON state so that the imaging operation by the imaging unit  39   a  (the imaging apparatus) is performed, and the captured image is stored. 
     The CPU  21  performs a release-sequence operation including the imaging operation after the shutter release switch  13   a  is set to the ON state. 
     The mirror-aperture-shutter unit  18  is connected to port P 7  of the CPU  21  and performs an UP/DOWN operation of the mirror (a mirror-up operation and a mirror-down operation), an OPEN/CLOSE operation of the aperture, and an OPEN/CLOSE operation of the shutter corresponding to the ON state of the shutter release switch  13   a.    
     The camera lens  67  is an interchangeable lens of the photographic apparatus  1  and is connected to port P 8  of the CPU  21 . The camera lens  67  outputs the lens information including the lens coefficient F etc., stored in a built-in ROM in the camera lens  67 , to the CPU  21 , when the photographic apparatus  1  is set to the ON state. 
     The DSP  19  is connected to port P 9  of the CPU  21  and to the imaging unit  39   a . Based on a command from the CPU  21 , the DSP  19  performs the calculation operations, such as the image-processing operation, etc., on the image signal obtained by the imaging operation of the imaging unit  39   a.    
     The CPU  21  is a control apparatus that controls each part of the photographic apparatus  1  in its imaging operation, and in its stabilization (i.e. anti-shake) and inclination correction. 
     The stabilization and inclination correction includes both the movement control of the movable platform  30   a  and position-detection efforts. 
     In the embodiment, the stabilization includes a first stabilization that moves the movable platform  30   a  in the x direction and a second stabilization that moves the movable platform  30   a  in the y direction. 
     Furthermore, the CPU  21  stores the value of the correction parameter SR that indicates whether the photographic apparatus  1  is in the correction mode or not, the value of the release-state parameter RP, and the value of the mirror state parameter MP. 
     The value of the release-state parameter RP changes with respect to the release-sequence operation. When the release-sequence operation is performed, the value of the release-state parameter RP is set to 1 (see steps S 21  to S 28  in  FIG. 4 ), otherwise, the value of the release-state parameter RP is set (reset) to 0 (see steps S 13  and S 28  in  FIG. 4 ). 
     While the mirror-up operation is performed before the exposure operation for the imaging operation, the value of the mirror state parameter MP is set to 1 (see step S 22  in  FIG. 4 ); otherwise, the value of the mirror state parameter MP is set to 0 (see step S 24  in  FIG. 4 ). 
     Whether the mirror-up operation of the photographic apparatus  1  is finished is determined by the detection of the ON/OFF states of a mechanical switch (not depicted). Whether the mirror-down operation of the photographic apparatus  1  is finished is determined by the detection of the completion of the shutter charge. 
     Furthermore, the CPU  21  stores the values of the first digital angular velocity signal Vx n , the second digital angular velocity signal Vy n , the first digital angular velocity VVx n  the second digital angular velocity VVy n , the first digital acceleration signal Dah n , the second digital acceleration signal Dav n , the first digital acceleration Aah n , the second digital acceleration Aav n , the first digital displacement angle Kx n  (the hand-shake angle caused by yaw), the second digital displacement angle Ky n  (the hand-shake angle caused by pitch), the third digital displacement angle Kθ n  (the inclination angle of the photographic apparatus  1 ), the horizontal direction component of the position S n , Sx n , the vertical direction component of the position S n , Sy n , the rotational direction component (the inclination angle) of the position S n , Sθ n , the first vertical direction component of the first driving point, Syl n , the second vertical direction component of the second driving point, Syr n , the horizontal driving force Dx n , the first vertical driving force Dyl n , the second vertical driving force Dyr n , the horizontal direction component of the position P n  after A/D conversion, pdx n , the first vertical direction component of the position P n  after A/D conversion, pdyl n , the second vertical direction component of the position P n  after A/D conversion, pdyr n , the lens coefficient F, the hall sensor distance coefficient HSD, the first movable range Hsx n , and the second movable range Hsy n . The hall sensor distance coefficient HSD is the relative distance between the first vertical hall sensor hv 1  and the second vertical hall sensor hv 2  in the x direction of the initial state (see  FIG. 7 ). 
     In the initial state, the movable platform  30   a  is positioned at the center of its movement range in both the x and y directions, and each of the four sides of the rectangle composing the outline of the imaging surface of the imager (an imaging sensor)  39   a   1  is parallel to either the x direction or the y direction. 
     The AE unit (exposure-calculating unit)  23  performs the photometric operation and calculates photometric values based on the subject being photographed. The AE unit  23  also calculates the aperture value and the duration of the exposure operation, with respect to the photometric values, both of which are needed for the imaging operation. The AF unit  24  performs the AF sensing operation and the corresponding focusing operation, both of which are needed for the imaging operation. In the focusing operation, the camera lens  67  is re-positioned along the optical axis LX. 
     The stabilization and inclination correction part (the stabilization and inclination correction apparatus) of the photographic apparatus  1  comprises a correction button  14 , a correction switch  14   a , a display  17 , a CPU  21 , a detection unit  25 , a driver circuit  29 , a correction unit  30 , a hall-sensor signal-processing unit  45 , and the camera lens  67 . 
     The ON/OFF states of the correction switch  14   a  change according to the operation state of the correction button  14 . 
     Specifically, when the correction button  14  is depressed by the operator, the correction switch  14   a  is changed to the ON state so that the stabilization (the translational movement) and inclination correction (the rotational movement), in which the detection unit  25  and the correction unit  30  are driven independently of the other operations which include the photometric operation etc., is carried out at the predetermined time interval. When the correction switch  14   a  is in the ON state, (in other words in the correction mode), the correction parameter SR is set to 1 (SR=1). When the correction switch  14   a  is not in the ON state, (in other words in the non-correction mode), the correction parameter SR is set to 0 (SR=0). In the embodiment, the value of the predetermined time interval is set to 1 ms. 
     The various output commands corresponding to the input signals of these switches are controlled by the CPU  21 . 
     The information indicating whether the photometric switch  12   a  is in the ON state or OFF state is input to port P 12  of the CPU  21  as a 1-bit digital signal. The information indicating whether the shutter release switch  13   a  is in the ON or OFF state is input to port P 13  of the CPU  21  as a 1-bit digital signal. Likewise, the information indicating whether the correction switch  14   a  is in the ON or OFF state is input to port P 14  of the CPU  21  as a 1-bit digital signal. 
     The AE unit  23  is connected to port P 4  of the CPU  21  for inputting and outputting signals. The AF unit  24  is connected to port P 5  of the CPU  21  for inputting and outputting signals. The display  17  is connected to port P 6  of the CPU  21  for inputting and outputting signals. 
     Next, the details of the input and output relationships between the CPU  21  and the detection unit  25 , the driver circuit  29 , the correction unit  30 , and the hall-sensor signal-processing unit  45  are explained. 
     The detection unit  25  has a first angular velocity sensor  26   a , a second angular velocity sensor  26   b , an acceleration sensor  26   c , a first high-pass filter circuit  27   a , a second high-pass filter circuit  27   b , a first amplifier  28   a , a second amplifier  28   b , a third amplifier  28   c , and a fourth amplifier  28   d.    
     The first angular velocity sensor  26   a  detects the angular velocity of rotary motion of the photographic apparatus  1  around the axis of the y direction (the yaw). In other words, the first angular velocity sensor  26   a  is a gyro sensor that detects the yaw angular velocity. 
     The second angular velocity sensor  26   b  detects the angular velocity of rotary motion of the photographic apparatus  1  around the axis of the x direction (the pitch). In other words, the second angular velocity sensor  26   b  is a gyro sensor that detects the pitch angular velocity. 
     The acceleration sensor  26   c  detects a first gravitational component and a second gravitational component. The first gravitational component is the horizontal component of gravitational acceleration in the x direction. The second gravitational component is the vertical component of gravitational acceleration in the y direction. 
     The first high-pass filter circuit  27   a  reduces the low-frequency component of the signal output from the first angular velocity sensor  26   a , because the low-frequency component of the signal output from the first angular velocity sensor  26   a  includes signal elements that are based on null voltage and panning motion, neither of which are related to hand shake. 
     Similarly, the second high-pass filter circuit  27   b  reduces the low-frequency component of the signal output from the second angular velocity sensor  26   b , because the low-frequency component of the signal output from the second angular velocity sensor  26   b  includes signal elements that are based on null voltage and panning motion, neither of which are related to hand shake. 
     The first amplifier  28   a  amplifies the signal representing the yaw angular velocity, whose low-frequency component has been reduced, and outputs the analog signal to the A/D converter A/D  0  of the CPU  21  as a first angular velocity vx. 
     The second amplifier  28   b  amplifies the signal representing the pitch angular velocity, whose low-frequency component has been reduced, and outputs the analog signal to the A/D converter A/D  1  of the CPU  21  as a second angular velocity vy. 
     The third amplifier  28   c  amplifies the signal representing the first gravitational component output from the acceleration sensor  26   c , and outputs the analog signal to the A/D converter A/D  2  of the CPU  21  as a first acceleration ah. 
     The fourth amplifier  28   d  amplifies the signal representing the second gravitational component output from the acceleration sensor  26   c , and outputs the analog signal to the A/D converter A/D  3  of the CPU  21  as a second acceleration av. 
     The reduction of the low-frequency component is a two-step process. The primary part of the analog high-pass filtering is performed first by the first and second high-pass filter circuits  27   a  and  27   b , followed by the secondary part of the digital high-pass filtering that is performed by the CPU  21 . 
     The cut-off frequency of the secondary part of the digital high-pass filtering is higher than that of the primary part of the analog high-pass filtering. 
     In the digital high-pass filtering, the value of a first high-pass filter time constant hx and a second high-pass filter time constant hy can be easily changed. 
     The supply of electric power to the CPU  21  and each part of the detection unit  25  begins after the PON switch  11   a  is set to the ON state (i.e. when the main power supply is set to the ON state). The calculation of a hand-shake quantity (the digital displacement angle Kx n  and the second digital displacement angle Ky n ) and an inclination angle (the third digital displacement angle Kθ n ) begins after the PON switch  11   a  is set to the ON state. 
     The CPU  21  converts the first angular velocity vx, which is input to the A/D converter A/D  0 , to a first digital angular velocity signal Vx n  (A/D conversion operation). It also calculates a first digital angular velocity VVx n  by reducing the low-frequency component of the first digital angular velocity signal Vx n  (the digital high-pass filtering) because the low-frequency component of the first digital angular velocity signal Vx n  includes signal elements that are based on null voltage and panning motion, neither of which are related to hand shake. It also calculates a hand-shake quantity (a first hand-shake displacement angle around the y direction: a first digital displacement angle Kx n  caused by yaw) by integrating the first digital angular velocity VVx n  (the integration). 
     Similarly, the CPU  21  converts the second angular velocity vy, which is input to the A/D converter A/D  1 , to a second digital angular velocity signal Vy n  (A/D conversion operation). It also calculates a second digital angular velocity VVy n  by reducing the low-frequency component of the second digital angular velocity signal Vy n  (the digital high-pass filtering) because the low-frequency component of the second digital angular velocity signal Vy n  includes signal elements that are based on null voltage and panning motion, neither of which are related to hand shake. It also calculates a hand-shake quantity (a second hand-shake displacement angle around the x direction: a second digital displacement angle Ky n  caused by pitch) by integrating the second digital angular velocity VVy n  (the integration). 
     Furthermore, the CPU  21  converts the first acceleration ah, which is input to the A/D converter A/D  2 , to a first digital acceleration signal Dah n  (A/D conversion operation). It also calculates a first digital acceleration Aah n  by reducing the high-frequency component of the first digital acceleration signal Dah n  (the digital low-pass filtering) in order to reduce the noise component in the first digital acceleration signal Dah n . 
     Similarly, the CPU  21  converts the second acceleration av, which is input to the A/D converter A/D  3 , to a second digital acceleration signal Dav n  (A/D conversion operation). It also calculates a second digital acceleration Aav n  by reducing the high-frequency component of the second digital acceleration signal Dav n  (the digital low-pass filtering) in order to reduce the noise component in the second digital acceleration signal Dav n . 
     The CPU  21  also calculates the inclination angle (third digital displacement angle Kθ n ) of the photographic apparatus  1 , formed by rotation of the photographic apparatus  1  around its optical axis LX, as measured with respect to a level plane perpendicular to the direction of gravitational force, on the basis of the magnitude relation between the absolute value of the first digital acceleration Aah n  and the absolute value of the second digital acceleration Aav n . 
     The inclination angle (the third digital displacement angle Kθ n ) of the photographic apparatus  1  changes according to the orientation of the photographic apparatus  1  and is measured with respect to one of the first horizontal orientation, the second horizontal orientation, the first vertical orientation, and the second vertical orientation. Therefore, the inclination angle of the photographic apparatus  1  is represented by the angle at which the x direction or the y direction intersects a level plane. 
     When one of the x direction and the y direction intersects a level plane at an angle of 0 degrees, and when the other of the x direction and the y direction intersects a level plane at an angle of 90 degrees, the photographic apparatus  1  is in a non-inclined state. 
     Thus, the CPU  21  and the detection unit  25  have a function for calculating the hand-shake quantity and the inclination angle. 
     The first digital acceleration Aah n  (the first gravitational component) and the second digital acceleration Aav n  (the second gravitational component) change according to the orientation of the photographic apparatus  1 , and take values from −1 to +1. 
     For example, when the photographic apparatus  1  is held in the first horizontal orientation, in other words, when the photographic apparatus  1  is held horizontally and the upper surface of the photographic apparatus  1  faces upward (see  FIG. 2 ), the first digital acceleration Aah n  is 0 and the second digital acceleration Aav n  is +1. 
     When the photographic apparatus  1  is held in the second horizontal orientation, in other words, when the photographic apparatus  1  is held horizontally and the lower surface of the photographic apparatus  1  faces upward (see  FIG. 9 ), the first digital acceleration Aah n  is 0 and the second digital acceleration Aav n  is −1. 
     When the photographic apparatus  1  is held in the first vertical orientation, in other words, when the photographic apparatus  1  is held vertically and one of the side surfaces of the photographic apparatus  1  faces upward (see  FIG. 10 ), the first digital acceleration Aah n  is +1 and the second digital acceleration Aav n  is 0. 
     When the photographic apparatus  1  is held in the second vertical orientation, in other words, when the photographic apparatus  1  is held vertically and the other side surface of the photographic apparatus  1  faces upward (see  FIG. 11 ), the first digital acceleration Aah n  is −1 and the second digital acceleration Aav n  is 0. 
     When the front surface of the photographic apparatus  1  faces the direction of gravitational force or the opposite direction, in other words, when the front surface of the photographic apparatus  1  faces upward or downward, the first digital acceleration Aah n  and the second digital acceleration Aav n  are 0. 
     When the photographic apparatus  1  is rotated (inclined) at an angle Kθ n  in a counter-clockwise direction viewed from the front, from the first horizontal orientation (see  FIG. 12 ), the first digital acceleration Aah n  is +sin(Kθ n ) and the second digital acceleration Aav n  is +cos(Kθ n ). 
     Therefore, the inclination angle (the third digital displacement angle Kθ n ) can be calculated by performing an arcsine transformation on the first digital acceleration Aah n  or by performing an arccosine transformation on the second digital acceleration Aav n . 
     However, while the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is very small, in other words, nearly 0, the variation of the sine function is larger than that of the cosine function so that the inclination angle is best calculated by using the arcsine transformation rather than the arccosine transformation (Kθ n =+Sin −1 (Aah n ), see step S 76  in  FIG. 8 ). 
     When the photographic apparatus  1  is rotated (inclined) at an angle Kθ n  in a counter-clockwise direction viewed from the front, from the first vertical orientation (see  FIG. 13 ), the first digital acceleration Aah n  is +cos(Kθ n ) and the second digital acceleration Aav n  is −sin(Kθ n ). 
     Therefore, the inclination angle (the third digital displacement angle Kθ n ) can be calculated by performing an arccosine transformation on the first digital acceleration Aah n  or by performing an arcsine transformation on the second digital acceleration Aav n  and taking the negative. 
     However, while the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is very small, in other words, nearly 0, the variation of the sine function is larger than that of the cosine function so that the inclination angle is best calculated by using the arcsine transformation rather than the arccosine transformation (Kθ n =−Sin −1 (Aav n ), see step S 73  in  FIG. 8 ). 
     When the photographic apparatus  1  is rotated (inclined) at an angle Kθ n  in a counter-clockwise direction viewed from the front, from the second horizontal orientation (see  FIG. 14 ), the first digital acceleration Aah n  is −sin(Kθ n ) and the second digital acceleration Aav n  is −cos(Kθ n ). 
     Therefore, the inclination angle (the third digital displacement angle Kθ n ) can be calculated by performing an arcsine transformation on the first digital acceleration Aah n  and taking the negative or by performing an arccosine transformation on the second digital acceleration Aav n  and taking the negative. 
     However, while the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is very small, in other words, nearly 0, the variation of the sine function is larger than that of the cosine function so that the inclination angle is best calculated by using the arcsine transformation rather than the arccosine transformation (Kθ n =−Sin −1 (Aah n ), see step S 77  in  FIG. 8 ). 
     When the photographic apparatus  1  is rotated (inclined) at an angle Kθ n  in a counter-clockwise direction viewed from the front, from the second vertical orientation (see  FIG. 15 ), the first digital acceleration Aah n  is −cos(Kθ n ) and the second digital acceleration Aav n  is +sin(Kθ n ). 
     Therefore, the inclination angle (the third digital displacement angle Kθ n ) can be calculated by performing an arccosine transformation on the first digital acceleration Aah n  and taking the negative or by performing an arcsine transformation on the second digital acceleration Aav n . 
     However, while the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is very small, in other words, is nearly 0, the variation of the sine function is larger than that of the cosine function so that the inclination angle is best calculated by using the arcsine transformation rather than the arccosine transformation (Kθ n =+Sin −1 (Aav n ), see step S 74  in  FIG. 8 ). 
     When the front surface of the photographic apparatus  1  faces mostly upward or downward, the first digital acceleration Aah n  and the second digital acceleration Aav n  are nearly 0. In this case, this means that inclination correction, in other words, the rotational movement in accordance with the inclination angle, is not necessary, it is desirable to perform the stabilization and inclination correction with the inclination angle being minimal. 
     However, when the arccosine transformation on the first digital acceleration Aah n  or the second digital acceleration Aav n  that is nearly 0 is performed, the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is a large value. In this case, the stabilization and inclination correction is performed with the inclination angle being large, even when the rotational movement in accordance with the inclination angle is not necessary. Therefore, the inclination correction cannot be performed correctly. 
     Therefore, in order to eliminate the inclination angle, it is necessary to determine whether the front surface of the photographic apparatus  1  faces mostly upward or downward using an additional determination factor. 
     An example of the additional determination factor is the determination of whether the sum of the absolute value of the first digital acceleration Aah n  and the absolute value of the second digital acceleration Aav n  is less than a threshold value. 
     On the other hand, when the arcsine transformation on the first digital acceleration Aah n  or the second digital acceleration Aav n  that is nearly 0 is performed, the absolute value of the inclination angle (the third digital displacement angle Kθ n ) is a small value (nearly 0). In this case, the stabilization and inclination correction can be performed, with the inclination angle being small. Therefore, it is not necessary to determine whether the front surface of the photographic apparatus  1  faces mostly upward or downward by using the additional determination factor. 
     The value “n” is an integer greater than or equal to 0, and indicates the duration in milliseconds from the point when the timer interrupt process commences, (t=0, and see step S 12  in  FIG. 4 ), to when the last interrupt process of the timer is performed (t=n). 
     In the digital high-pass filtering regarding the yaw, the first digital angular velocity VVx n  is calculated by dividing the sum of the first digital angular velocity VVx 0  and VVx n-1  (calculated by the timer interrupt process before the 1 ms predetermined time interval, before the last timer interrupt process is performed) by the first high-pass filter time constant hx, and then subtracting the resulting quotient from the first digital angular velocity signal Vx n  (VVx n =Vx n −(ΣVVx n-1 )÷hx, see ( 1 ) in  FIG. 6 ). 
     In the digital high-pass filtering regarding the pitch, the second digital angular velocity VVy n  is calculated by dividing the sum of the second digital angular velocity VVy 0  and VVy n-1  (calculated by the timer interrupt process before the 1 ms predetermined time interval, before the last timer interrupt process is performed) by the second high-pass filter time constant hy, and then subtracting the resulting quotient from the second digital angular velocity signal Vy n  (VVy n =Vy n −(ΣVVy n-1 )÷hy, see ( 1 ) in  FIG. 6 ). 
     In the integration regarding the yaw, the first digital displacement angle Kx n  is calculated by summing the first digital angular velocity VVx 0  at the point when the timer interrupt process commences, t=0, (see step S 12  in  FIG. 4 ) and the first digital angular velocity VVx n  at the point when the last timer interrupt process is performed (t=n), (Kx n =ΣVVx n , see ( 7 ) in  FIG. 6 ). 
     Similarly, in the integration regarding the pitch, the second digital displacement angle Ky n  is calculated by summing the second digital angular velocity VVy 0  at the point when the timer interrupt process commences and the second digital angular velocity VVy n  at the point when the last timer interrupt process is performed (Ky n =ΣVVy n , see ( 7 ) in  FIG. 6 ). 
     The inclination angle, in other words, the third digital displacement angle Kθ n  is calculated by performing the arcsine transformation on the smaller of the absolute value of the first digital acceleration Aah n  and the absolute value of the second digital acceleration Aav n  and by adding a positive or negative sign (Kθ n =+Sin −1 (Aah n ), −Sin −1 (Aah n ), +Sin −1 (Aav n ), or −Sin −1 (Aav n ), see ( 8 ) in  FIG. 6 ). 
     Whether the positive or negative sign is added is determined on the basis of the larger of the absolute value of the first digital acceleration Aah n  and the absolute value of the second digital acceleration Aav n , and the sign of that larger value without applying the absolute value (see steps S 72  and S 75  in  FIG. 8 ). 
     In the embodiment, the angular velocity and acceleration detection operation during the timer interrupt process includes a process in the detection unit  25  and the input of the first angular velocity vx, the second angular velocity vy, the first acceleration ah, and the second acceleration av from the detection unit  25  to the CPU  21 . 
     In the calculation of the third digital displacement angle Kθ n , an integration is not performed because it is unnecessary. Therefore, the DC offset does not affect the calculation of the third digital displacement angle Kθ n , so the inclination angle can be calculated accurately. 
     When the integration including the DC offset is used, the third digital displacement angle Kθ n  represents an unspecified value even if the inclination angle is 0. Accordingly, the movable platform  30   a  including the imager  39   a   1  is rotated (inclined) compared to the initial state in order to correct the third digital displacement angle Kθ n  representing the unspecified value. 
     Because the displacement of the movable platform  30   a  in this case means the inclination of the imager  39   a   1 , the captured image displayed on the display  17  is inclined. When the operator sees the inclined image on the display  17 , the operator must visually detect the inclination of the displayed image even if the inclination is very small. 
     However, in the embodiment, because the DC offset does not exist, the inclination of the imager  39   a   1  caused by the DC offset does not exist. 
     The CPU  21  calculates the position S n  where the imaging unit  39   a  (the movable platform  30   a ) should be moved, in accordance with the hand-shake quantity (the first and second digital displacement angles Kx n  and Ky n ) and the inclination angle (the third digital displacement angle Kθ n ) calculated for the x direction, the y direction, and the rotational direction, based on the lens coefficient F and the hall sensor distance coefficient HSD (Sx n =F×tan(Kx n ), Sy n =F×tan(Ky n ), and Sθ n =HSD÷2×sin(Kθ n )). In this calculation, both the translational (linear) movement of the movable platform  30   a  in the xy plane and the rotational movement of the movable platform  30   a  in the xy plane are considered. 
     The horizontal direction component of the position S n  is defined as Sx n , the vertical direction component of the position S n  is defined as Sy n , and the rotational (inclination) direction component of the position S n  is defined as Sθ n . 
     The rotation of the movable platform  30   a  is performed by applying different forces in the y direction on a first driving point and a second driving point on the movable platform  30   a . The movement of the movable platform  30   a  in the y direction is performed by applying the same driving forces in the y direction on the first and second driving points on the movable platform  30   a . The first driving point is the point to which a first vertical electro-magnetic force based on the first vertical coil  32   a   1  is applied. The second driving point is the point to which a second vertical electromagnetic force based on the second vertical coil  32   a   2  is applied. The first driving point is set to a position close to the first vertical hall sensor hv 1 . The second driving point is set to a position close to the second vertical hall sensor hv 2 . 
     The first vertical direction component of the first driving point corresponding to the position S n  is defined as Syl n . The second vertical direction component of the second driving point corresponding to the position S n  is defined as Syr n . 
     The first vertical direction component of the first driving point, Syl n , and the second vertical direction component of the second driving point, Syr n , are calculated on the basis of the vertical direction component of the position S n , Sy n , and the rotational direction component of the position S n , Sθ n , (Syl n =Sy n +Sθ n , Syr n =Sy n −Sθ n , see ( 4 ) in  FIG. 6 ). 
     The calculations of the first digital displacement angle Kx n , the second digital displacement angle Ky n , the third digital displacement angle Kθ n , the horizontal direction component of the position S n , Sx n , the vertical direction component of the position S n , Sy n , the rotational direction component of the position S n , Sθ n , the first vertical direction component of the first driving point, Syl n , and the second vertical direction component of the second driving point, Syr n  are performed only when the correction parameter SR is set to 1 (see steps S 53  to S 64  of  FIG. 5 ). 
     When the stabilization and inclination correction is not performed (SR=0), in other words, when the photographic apparatus  1  is not in the correction mode, the position S n  (Sx n , Syl n , Syr n ) where the movable platform  30   a  should be moved is set to the initial state (see step S 54  in  FIG. 5 , Sx n =Syl n =Syr n =0). 
     The movement of the movable platform  30   a , which includes the imaging unit  39   a , is performed by using an electromagnetic force and is described later. 
     The driving force D n  is for driving the driver circuit  29  in order to move the movable platform  30   a  to the position S n . 
     The horizontal direction component of the driving force D n  for the first and second horizontal coils  31   a   1  and  31   a   2  is defined as the horizontal driving force Dx n  (after D/A conversion, the horizontal PWM duty dx). 
     The vertical direction component of the driving force D n  for the first vertical coil  32   a   1  is defined as the first vertical driving force Dyl n  (after D/A conversion, the first vertical PWM duty dyl). 
     The vertical direction component of the driving force D n  for the second vertical coil  32   a   2  is defined as the second vertical driving force Dyr n  (after D/A conversion, the second vertical PWM duty dyr). 
     The correction unit  30  is an apparatus that corrects for the effects of hand shake by moving the imaging unit  39   a  to the position S n , by canceling the lag of the subject image on the imaging surface of the imager  39   a   1  of the imaging unit  39   a , and by stabilizing the subject image displayed on the imaging surface of the imager  39   a   1 , when the stabilization and inclination correction is performed (i.e., SR=1). 
     The correction unit  30  has a fixed unit  30   b  and a movable platform  30   a  that includes the imaging unit  39   a  and can be moved in the xy plane. 
     By moving the movable platform  30   a  in the x direction, the first stabilization for correcting the hand shake caused by yaw, which is the first hand-shake displacement angle around the y direction, is performed; and by moving the movable platform  30   a  in the y direction, the second stabilization for correcting the hand shake caused by pitch, which is the second hand-shake displacement angle around the x direction, is performed (the translational movement). 
     Moreover, the correction unit  30  performs the inclination correction (the rotational movement) that corrects (reduces) the inclination of the photographic apparatus  1  formed by rotation of the photographic apparatus  1  around its optical axis LX, as measured with respect to a level plane perpendicular to the direction of gravitational force, by rotating the movable platform  30   a  including the imaging unit  39   a  around an axis parallel to the optical axis LX. 
     In other words, in the inclination correction, the movement control repositions the movable platform  30   a  so that the upper and lower sides of the rectangle composing the outline of the imaging surface of the imager  39   a   1  are perpendicular to the direction of gravitational force and the left and right sides are parallel to the direction of gravitational force. 
     Therefore, the imager  39   a   1  can be automatically leveled without using a level vial. When the photographic apparatus  1  images a subject including the horizon, the imaging operation can be performed, with the upper and lower sides of the rectangle composing the outline of the imaging surface of the imager  39   a   1  being parallel to the horizon. 
     Moreover, due to the inclination correction, the upper and lower sides of the rectangle composing the outline of the imaging surface of the imager  39   a   1  are kept perpendicular to the direction of gravitational force, and the left and right sides of the rectangle composing the outline of the imaging surface of the imager  39   a   1  are kept parallel to the direction of gravitational force. Therefore, hand shake caused by roll is also corrected by the inclination correction. In other words, rotating the movable platform  30   a  in the xy plane for the inclination correction also achieves a third stabilization for correcting the hand shake caused by roll. 
     In the embodiment, the CPU  21  performs a first determination of whether the first stabilization is to be performed and a second determination of whether the second stabilization is to be performed, on the basis of the inclination angle (the third digital displacement angle Kθ n ). 
     Specifically, the first and second determinations are performed on the basis of a relationship between the movable range of the imaging surface of the imager  39   a   1  in the movement range in the x direction, the movable range of the imaging surface of the imager  39   a   1  in the movement range in the y direction, the horizontal direction component of the position S n , Sx n , and the vertical direction component of the position S n , Sy n . 
     The movable range of the imaging surface (the movable range of the movable platform  30   a ) in the x direction changes in accordance with the rotational state of the movable platform  30   a , in other words, in accordance to the third digital displacement angle Kθ n . 
     Similarly, the movable range of the imaging surface (the movable range of the movable platform  30   a ) in the y direction changes in accordance with the rotational state of the movable platform  30   a , in other words, in accordance to the third digital displacement angle Kθ n . 
     The movable range of the imaging surface in the x direction in the initial state, which is the maximum value of the movable range, is defined as the first maximum movable range Rx (see  FIG. 16 ). 
     The movable range of the imaging surface in the y direction in the initial state, which is the maximum value of the movable range, is defined as the second maximum movable range Ry. 
     The distance between the center and the apex of the rectangular outline of the imaging surface of the imager  39   a   1  is defined as the distance Ra. 
     The angle at which a segment between the center and the apex of the rectangular outline of the imaging surface intersects the x direction in the initial state is defined as angle A. 
     The angle at which a segment between the center and the apex of the rectangular outline of the imaging surface intersects the y direction in the initial state is defined as angle B. 
     The values of the first and second maximum movable ranges Rx and Ry, the angle A, and the angle B are fixed values that are calculated in advance during the design of the movable platform  30   a.    
     Before the movable platform  30   a  including the imaging surface of the imager  39   a   1  rotates for the inclination correction, in other words in the initial state, the horizontal direction component of the position S n , Sx n , can be set within the first maximum movable range Rx, and the vertical direction component of the position S n , Sy n , can be set within the second maximum movable range Ry (|Sx n |≦Rx, and |Sy n |≦Ry). 
     When the movable platform  30   a  is rotated at an angle Kθ n  in a counter-clockwise direction viewed from the front, from the initial state, the movable range of the imaging surface in the x direction (the first movable range Hsx n ) is given as Hsx n =Rx−{Ra×sin(B+|Kθ n |)−Ra×sin(B)}, and the movable range of the imaging surface in the y direction (the second movable range Hsy n ) is given as Hsy n =Ry−{Ra×sin(A+|Kθ n |)−Ra×sin(A)}. 
     After the movable platform  30   a  including the imaging surface of the imager  39   a   1  rotates for the inclination correction, the horizontal direction component of the position S n , Sx n , can be set within the first movable range Hsx n , and the vertical direction component of the position S n , Sy n , can be set within the second movable range Hsy n  (|Sx n |≦Hsx n ≦Rx, and |Sy n |≦Hsx n ≦Ry). 
     When the absolute value of the third digital displacement angle Kθ n  becomes large, in other words, the inclination angle becomes large, the first and second movable ranges Hsx n  and Hsy n  become small. 
     When the first movable range Hsx n  is small, the movable range of the movable platform  30   a  including the imager  39   a   1  in the x direction for the first stabilization is restricted such that the first stabilization cannot be performed effectively. 
     When the second movable range Hsy n  is small, the movable range of the movable platform  30   a  including the imager  39   a   1  in the y direction for the second stabilization is restricted such that the second stabilization cannot performed effectively. 
     In the embodiment, when the inclination angle is large, in other words, when the inclination angle is greater than a variable that changes in accordance with at least one of the first and second digital displacement angles Kx n  and Ky n , at least one of the first and second stabilizations, which cannot be performed effectively, is prohibited. 
     When the absolute value of the horizontal direction component of the position S n , Sx n , is greater than the first movable range Hsx n , the movable platform  30   a  including the imager  39   a   1  has to move the position over the movement range in the x direction, therefore, the movable platform  30   a  does not reach the position Sx n , and contacts the edge of the movement range. 
     Furthermore, when the movable platform  30   a  is moved to near the edge of the movement range in the x direction, the rotatable angle of the movable platform  30   a  (the movable range of the movable platform  30   a  in the x direction for rotation) available to the rotational movement is restricted, therefore, the movable platform  30   a  cannot be rotated effectively for the inclination correction. 
     In the embodiment, in this case, the first stabilization is prohibited and the position Sx n  is set to the center of its movement range of the movable platform  30   a  in the x direction, in order to keep a sufficient rotatable angle of the movable platform  30   a  for the inclination correction (Sx n =0, see step S 61  in  FIG. 5 ). 
     Similarly, when the absolute value of the vertical direction component of the position S n , Sy n , is greater than the second movable range Hsy n , the movable platform  30   a  including the imager  39   a   1  has to move the position over the movement range in the y direction, therefore, the movable platform  30   a  does not reach the position Sy n , and contacts the edge of the movement range. 
     Further, when the movable platform  30   a  is moved to near the edge of the movement range in the y direction, the rotatable angle of the movable platform  30   a  (the movable range of the movable platform  30   a  in the y direction for rotation) available to the rotational movement is restricted, therefore, the movable platform  30   a  cannot be rotated effectively for the inclination correction. 
     In the embodiment, in this case, the second stabilization is prohibited and the position Sy n  is set to the center of its movement range of the movable platform  30   a  in the y direction, in order to keep a sufficient rotatable angle of the movable platform  30   a  for the inclination correction (Sy n =0, see step S 63  in  FIG. 5 ). 
     Thus, the inclination correction can be effectively performed by limiting the first and second stabilizations corresponding to the inclination angle. In other words, the inclination correction and the third stabilization have priority over the image stabilizing correction (the first and second stabilizations) so that the movable platform  30   a  does not bump into the edge the movement range. 
       FIG. 16  shows the movement range of the imaging surface of the imager  39   a   1 , including the movable range of the imaging surface in the x and y directions; however, it may be shown as the movement range of the movable platform  30   a , including the movable range of the movable platform  30   a  in the x and y directions. 
     Driving of the movable platform  30   a , including movement to the fixed (held) position of the initial state, is performed by the electromagnetic force of the coil unit and the magnetic unit through the driver circuit  29 , which has the horizontal PWM duty dx input from the PWM  0  of the CPU  21 , the first vertical PWM duty dyl input from the PWM  1  of the CPU  21 , and the second vertical PWM duty dyr input from the PWM  2  of the CPU  21  (see ( 6 ) in  FIG. 6 ). 
     The detected-position P n  of the movable platform  30   a , either before or after the movement effected by the driver circuit  29 , is detected by the hall sensor unit  44   a  and the hall-sensor signal-processing unit  45 . 
     Information regarding the horizontal direction component of the detected-position P n , in other words, the horizontal detected-position signal px, is input to the A/D converter A/D  4  of the CPU  21  (see ( 2 ) in  FIG. 6 ). The horizontal detected-position signal px is an analog signal that is converted to a digital signal by the A/D converter A/D  4  (A/D conversion operation). The horizontal direction component of the detected-position P n  after the A/D conversion operation, is defined as pdx n  and corresponds to the horizontal detected-position signal px. 
     Information regarding one of the vertical direction components of the detected-position P n , in other words, the first vertical detected-position signal pyl, is input to the A/D converter A/D  5  of the CPU  21 . The first vertical detected-position signal pyl is an analog signal that is converted to a digital signal by the A/D converter A/D  5  (A/D conversion operation). The first vertical direction component of the detected-position P n  after the A/D conversion operation is defined as pdyl n  and corresponds to the first vertical detected-position signal pyl. 
     Information regarding the other of the vertical direction components of the detected-position P n , in other words, the second vertical detected-position signal pyr, is input to the A/D converter A/D  6  of the CPU  21 . The second vertical detected-position signal pyr is an analog signal that is converted to a digital signal by the A/D converter A/D  6  (A/D conversion operation). The second vertical direction component of the detected-position P n  after the A/D conversion operation is defined as pdyr n  and corresponds to the second vertical detected-position signal pyr. 
     The PID (Proportional Integral Differential) control calculates the horizontal driving force Dx n  and the first and second vertical driving forces Dyl n  and Dyr n  on the basis of the coordinate data for the detected-position P n  (pdx n , pdyl n , pdyr n ) and the position S n  (Sx n , Syl n , Syr n ) following movement (see ( 5 ) in  FIG. 6 ). 
     Driving of the movable platform  30   a  to the position S n , (Sx n , Syl n , Syr n ) corresponding to the stabilization and inclination correction of the PID control, is performed when the photographic apparatus  1  is in the correction mode (SR=1) where the correction switch  14   a  is set to the ON state. 
     When the correction parameter SR is 0, PID control unrelated to the stabilization and inclination correction is performed so that the movable platform  30   a  is moved to the predetermined position (the center of the movement range) at the initial state such that each of the four sides composing the outline of the imaging surface of the imager  39   a   1  of the imaging unit  39   a  is parallel to either the x direction or the y direction, in other words, such that the movable platform  30   a  is not rotated (inclined). 
     The movable platform  30   a  has a coil unit for driving that is comprised of a first horizontal coil  31   a   1 , a second horizontal coil  31   a   2 , a first vertical coil  32   a   1 , and a second vertical coil  32   a   2 , an imaging unit  39   a  having the imager  39   a   1 , and a hall sensor unit  44   a  as a magnetic-field change-detecting element unit (see  FIG. 7 ). In the embodiment, the imager  39   a   1  is a CCD; however, the imager  39   a   1  may be of another type, such as a CMOS, etc. 
     The fixed unit  30   b  has a magnetic position detection and driving unit that is comprised of a first horizontal magnet  411   b   1 , a second horizontal magnet  411   b   2 , a first vertical magnet  412   b   1 , a second vertical magnet  412   b   2 , a first horizontal yoke  431   b   1 , a second horizontal yoke  431   b   2 , a first vertical yoke  432   b   1 , and a second vertical yoke  432   b   2 . 
     The fixed unit  30   b  movably and rotatably supports the movable platform  30   a  in the rectangular-shaped movement range in the xy plane, using balls, etc. The balls are arranged between the fixed unit  30   b  and the movable platform  30   a.    
     When the central area of the imager  39   a   1  is intersecting the optical axis LX of the camera lens  67 , the relationship between the position of the movable platform  30   a  and the position of the fixed unit  30   b  is arranged so that the movable platform  30   a  is positioned at the center of its movement range in both the x direction and the y direction, in order to utilize the full size of the imaging range of the imager  39   a   1 . 
     The rectangular form of the imaging surface of the imager  39   a   1  has two diagonal lines. In the embodiment, the center of the imager  39   a   1  is at the intersection of these two diagonal lines. 
     Furthermore, the movable platform  30   a  is positioned at the center of its movement range in both the x direction and the y direction, and each of the four sides composing the outline of the imaging surface of the imager  39   a   1  is parallel to either the x direction or the y direction, in the initial state immediately after the PON switch  11   a  is set to the ON state (see step S 11  of  FIG. 4 ). Then, the stabilization and inclination correction commences. 
     The first horizontal coil  31   a   1 , the second horizontal coil  31   a   2 , the first vertical coil  32   a   1 , the second vertical coil  32   a   2 , and the hall sensor unit  44   a  are attached to the movable platform  30   a.    
     The first horizontal coil  31   a   1  forms a seat and a spiral-shaped coil pattern. The coil pattern of the first horizontal coil  31   a   1  has lines which are parallel to the y direction, thus creating the first horizontal electro-magnetic force to move the movable platform  30   a  that includes the first horizontal coil  31   a   1 , in the x direction. 
     The first horizontal electromagnetic force is created by the current direction of the first horizontal coil  31   a   1  and the magnetic-field direction of the first horizontal magnet  411   b   1 . 
     The second horizontal coil  31   a   2  forms a seat and a spiral-shaped coil pattern. The coil pattern of the second horizontal coil  31   a   2  has lines which are parallel to the y direction, thus creating the second horizontal electromagnetic force to move the movable platform  30   a  that includes the second horizontal coil  31   a   2 , in the x direction. 
     The second horizontal electro-magnetic force is created by the current direction of the second horizontal coil  31   a   2  and the magnetic-field direction of the second horizontal magnet  411   b   2 . 
     The first vertical coil  32   a   1  forms a seat and a spiral-shaped coil pattern. The coil pattern of the first vertical coil  32   a   1  has lines which are parallel to the x direction, thus creating the first vertical electro-magnetic force to move the movable platform  30   a  that includes the first vertical coil  32   a   1 , in the y direction and to rotate the movable platform  30   a.    
     The first vertical electro-magnetic force is created by the current direction of the first vertical coil  32   a   1  and the magnetic-field direction of the first vertical magnet  412   b   1 . 
     The second vertical coil  32   a   2  forms a seat and a spiral-shaped coil pattern. The coil pattern of the second vertical coil  32   a   2  has lines which are parallel to the x direction, thus creating the second vertical electro-magnetic force to move the movable platform  30   a  that includes the second vertical coil  32   a   2 , in the y direction and to rotate the movable platform  30   a.    
     The second vertical electromagnetic force is created by the current direction of the second vertical coil  32   a   2  and the magnetic-field direction of the second vertical magnet  412   b   2 . 
     The first and second horizontal coils  31   a   1  and  31   a   2  and the first and second vertical coils  32   a   1  and  32   a   2  are connected to the driver circuit  29 , which drives the first and second horizontal coils  31   a   1  and  31   a   2  and the first and second vertical coils  32   a   1  and  32   a   2 , through the flexible circuit board (not depicted). 
     The horizontal PWM duty dx, that is a duty ratio of a PWM pulse, is input to the driver circuit  29  from the PWM  0  of the CPU  21 . The first vertical PWM duty dyl, that is a duty ratio of a PWM pulse, is input to the driver circuit  29  from the PWM  1  of the CPU  21 . The second vertical PWM duty dyr, that is a duty ratio of a PWM pulse, is input to the driver circuit  29  from the PWM  2  of the CPU  21 . 
     The driver circuit  29  supplies the same power to the first and second horizontal coils  31   a   1  and  31   a   2 , corresponding to the value of the horizontal PWM duty dx, to move the movable platform  30   a  in the x direction. 
     The driver circuit  29  supplies power to the first vertical coil  32   a   1  corresponding to the value of the first vertical PWM duty dyl and to the second vertical coil  32   a   2  corresponding to the value of the second vertical PWM duty dyr, in order to move the movable platform  30   a  in the y direction and to rotate the movable platform  30   a.    
     The positional relationship between the first and second horizontal coils  31   a   1  and  31   a   2  is determined so that the optical axis LX is located between the first and second horizontal coils  31   a   1  and  31   a   2  in the x direction, in the initial state. In other words, the first and second horizontal coils  31   a   1  and  31   a   2  are arranged in a symmetrical arrangement centered on the optical axis LX, in the x direction in the initial state. 
     The first and second vertical coils  32   a   1  and  32   a   2  are arranged in the x direction in the initial state. 
     The first and second horizontal coils  31   a   1  and  31   a   2  are arranged such that the distance between the central area of the imager  39   a   1  and the central area of the first horizontal coil  31   a   1  in the x direction is the same as the distance between the center of the imager  39   a   1  and the central area of the second horizontal coil  31   a   2  in the x direction. 
     The first and second vertical coils  32   a   1  and  32   a   2  are arranged such that in the initial state, the distance between the central area of the imager  39   a   1  and the central area of the first vertical coil  32   a   1  in the y direction is the same as the distance between the center of the imager  39   a   1  and the central area of the second vertical coil  32   a   2  in the y direction. 
     The first horizontal magnet  411   b   1  is attached to the movable platform side of the fixed unit  30   b , where the first horizontal magnet  411   b   1  faces the first horizontal coil  31   a   1  and the horizontal hall sensor hh 10  in the z direction. 
     The second horizontal magnet  411   b   2  is attached to the movable platform side of the fixed unit  30   b , where the second horizontal magnet  411   b   2  faces the second horizontal coil  31   a   2  in the z direction. 
     The first vertical magnet  412   b   1  is attached to the movable platform side of the fixed unit  30   b , where the first vertical magnet  412   b   1  faces the first vertical coil  32   a   1  and the first vertical hall sensor hv 1  in the z direction. 
     The second vertical magnet  412   b   2  is attached to the movable platform side of the fixed unit  30   b , where the second vertical magnet  412   b   2  faces the second vertical coil  32   a   2  and the second vertical hall sensor hv 2  in the z direction. 
     The first horizontal magnet  411   b   1  is attached to the first horizontal yoke  431   b   1 , such that the N pole and S pole are arranged in the x direction. The first horizontal yoke  431   b   1  is attached to the fixed unit  30   b.    
     Likewise, the second horizontal magnet  411   b   2  is attached to the second horizontal yoke  431   b   2 , such that the N pole and S pole are arranged in the x direction. The second horizontal yoke  431   b   2  is attached to the fixed unit  30   b.    
     The first vertical magnet  412   b   1  is attached to the first vertical yoke  432   b   1 , such that the N pole and S pole are arranged in the y direction. The first vertical yoke  432   b   1  is attached to the fixed unit  30   b.    
     Likewise, the second vertical magnet  412   b   2  is attached to the second vertical yoke  432   b   2 , such that the N pole and S pole are arranged in the y direction. The second vertical yoke  432   b   2  is attached to the fixed unit  30   b.    
     The first and second horizontal yokes  431   b   1  and  431   b   2  are made of a soft magnetic material. 
     The first horizontal yoke  431   b   1  prevents the magnetic field of the first horizontal magnet  411   b   1  from dissipating to the surroundings, and raises the magnetic-flux density between the first horizontal magnet  411   b   1  and the first horizontal coil  31   a   1 , and between the first horizontal magnet  411   b   1  and the horizontal hall sensor hh 10 . 
     Similarly, the second horizontal yoke  431   b   2  prevents the magnetic field of the second horizontal magnet  411   b   2  from dissipating to the surroundings, and raises the magnetic-flux density between the second horizontal magnet  411   b   2  and the second horizontal coil  31   a   2 . 
     The first and second vertical yokes  432   b   1  and  432   b   2  are made of a soft magnetic material. 
     The first vertical yoke  432   b   1  prevents the magnetic field of the first vertical magnet  412   b   1  from dissipating to the surroundings, and raises the magnetic-flux density between the first vertical magnet  412   b   1  and the first vertical coil  32   a   1 , and between the first vertical magnet  412   b   1  and the first vertical hall sensor hv 1 . 
     Likewise, the second vertical yoke  432   b   2  prevents the magnetic field of the second vertical magnet  412   b   2  from dissipating to the surroundings, and raises the magnetic-flux density between the second vertical magnet  412   b   2  and the second vertical coil  32   a   2 , and between the second vertical magnet  412   b   2  and the second vertical hall sensor hv 2 . 
     The first and second horizontal yokes  431   b   1  and  431   b   2  and the first and second vertical yokes  432   b   1  and  432   b   2  may be composed of one body or separate bodies. 
     The hall sensor unit  44   a  is a one-axis hall sensor with three component hall sensors that are electromagnetic converting elements (magnetic-field change-detecting elements) using the Hall Effect. The hall sensor unit  44   a  detects the horizontal detected-position signal px, the first vertical detected-position signal pyl, and the second vertical detected-position signal pyr. 
     One of the three hall sensors is a horizontal hall sensor hh 10  for detecting the horizontal detected-position signal px, and another of the three hall sensors is a first vertical hall sensor hv 1  for detecting the first vertical detected-position signal pyl, with the third being a second vertical hall sensor hv 2  for detecting the second vertical detected-position signal pyr. 
     The horizontal hall sensor hh 10  is attached to the movable platform  30   a , where the horizontal hall sensor hh 10  faces the first horizontal magnet  411   b   1  of the fixed unit  30   b  in the z direction. 
     The horizontal hall sensor hh 10  may be arranged outside the spiral winding of the first horizontal coil  31   a   1  in the y direction. However, it is desirable for the horizontal hall sensor hh 10  to be arranged inside the spiral winding of the first horizontal coil  31   a   1 , and midway along the outer circumference of the spiral winding of the first horizontal coil  31   a   1  in the x direction (see  FIG. 7 ). 
     The horizontal hall sensor hh 10  is layered on the first horizontal coil  31   a   1  in the z direction. Accordingly, the area in which the magnetic field is generated for the position-detecting operation and the area in which the magnetic field is generated for driving the movable platform  30   a  are shared. Therefore, the length of the first horizontal magnet  411   b   1  in the y direction and the length of the first horizontal yoke  431   b   1  in the y direction can be shortened. 
     The first vertical hall sensor hv 1  is attached to the movable platform  30   a , where the first vertical hall sensor hv 1  faces the first vertical magnet  412   b   1  of the fixed unit  30   b  in the z direction. 
     The second vertical hall sensor hv 2  is attached to the movable platform  30   a , where the second vertical hall sensor hv 2  faces the second vertical magnet  412   b   2  of the fixed unit  30   b  in the z direction. 
     The first and second vertical hall sensors hv 1  and hv 2  are arranged in the x direction in the initial state. 
     The first vertical hall sensor hv 1  may be arranged outside the spiral winding of the first vertical coil  32   a   1  in the x direction. However, it is desirable for the first vertical hall sensor hv 1  to be arranged inside the spiral winding of the first vertical coil  32   a   1 , and midway along the outer circumference of the spiral winding of the first vertical coil  32   a   1  in the y direction. 
     The first vertical hall sensor hv 1  is layered on the first vertical coil  32   a   1  in the z direction. Accordingly, the area in which the magnetic field is generated for the position-detecting operation and the area in which the magnetic field is generated for driving the movable platform  30   a  are shared. Therefore, the length of the first vertical magnet  412   b   1  in the x direction and the length of the first vertical yoke  432   b   1  in the x direction can be shortened. 
     The second vertical hall sensor hv 2  may be arranged outside the spiral winding of the second vertical coil  32   a   2  in the x direction. However, it is desirable for the second vertical hall sensor hv 2  to be arranged inside the spiral winding of the second vertical coil  32   a   2 , and midway along the outer circumference of the spiral winding of the second vertical coil  32   a   2  in the y direction. 
     The second vertical hall sensor hv 2  is layered on the second vertical coil  32   a   2  in the z direction. Accordingly, the area in which the magnetic field is generated for the position-detecting operation and the area in which the magnetic field is generated for driving the movable platform  30   a  are shared. Therefore, the length of the second vertical magnet  412   b   2  in the x direction and the length of the second vertical yoke  432   b   2  in the x direction can be shortened. 
     Furthermore, the first driving point to which the first vertical electro-magnetic force based on the first vertical coil  32   a   1  is applied can be close to a position-detecting point by the first vertical hall sensor hv 1 , and the second driving point to which the second vertical electro-magnetic force based on the second vertical coil  32   a   2  is applied can be close to a position-detecting point by the second vertical hall sensor hv 2 . Therefore, accurate driving control of the movable platform  30   a  can be performed. 
     In the initial state, it is desirable for the horizontal hall sensor hh 10  to be located at a place on the hall sensor unit  44   a  that faces an intermediate area between the N pole and S pole of the first horizontal magnet  411   b   1  in the x direction, as viewed from the z direction, to perform the position-detecting operation utilizing the full range within which an accurate position-detecting operation can be performed based on the linear output change (linearity) of the one-axis hall sensor. 
     Similarly, in the initial state, it is desirable for the first vertical hall sensor hv 1  to be located at a place on the hall sensor unit  44   a  that faces an intermediate area between the N pole and S pole of the first vertical magnet  412   b   1  in the y direction, as viewed from the z direction. 
     Likewise, in the initial state, it is desirable for the second vertical hall sensor hv 2  to be located at a place on the hall sensor unit  44   a  that faces an intermediate area between the N pole and S pole of the second vertical magnet  412   b   2  in the y direction, as viewed from the z direction. 
     The first hall-sensor signal-processing unit  45  has a signal processing circuit of the magnetic-field change-detecting element that is comprised of a first hall-sensor signal-processing circuit  450 , a second hall-sensor signal-processing circuit  460 , and a third hall-sensor signal-processing circuit  470 . 
     The first hall-sensor signal-processing circuit  450  detects a horizontal potential difference between the output terminals of the horizontal hall sensor hh 10 , based on the output signal of the horizontal hall sensor hh 10 . 
     The first hall-sensor signal-processing circuit  450  outputs the horizontal detected-position signal px to the A/D converter A/D  4  of the CPU  21 , on the basis of the horizontal potential difference. The horizontal detected-position signal px represents the location of the part of the movable platform  30   a  which has the horizontal hall sensor hh 10 , in the x direction. 
     The first hall-sensor signal-processing circuit  450  is connected to the horizontal hall sensor hh 10  through the flexible circuit board (not depicted). 
     The second hall-sensor signal-processing circuit  460  detects a first vertical potential difference between the output terminals of the first vertical hall sensor hv 1 , based on the output signal of the first vertical hall sensor hv 1 . 
     The second hall-sensor signal-processing circuit  460  outputs the first vertical detected-position signal pyl to the A/D converter A/D  5  of the CPU  21 , on the basis of the first vertical potential difference. The first vertical detected-position signal pyl represents the location of the part of the movable platform  30   a  which has the first vertical hall sensor hv 1  (the position-detecting point by the first vertical hall sensor hv 1 ), in the y direction. 
     The second hall-sensor signal-processing circuit  460  is connected to the first vertical hall sensor hv 1  through the flexible circuit board (not depicted). 
     The third hall-sensor signal-processing circuit  470  detects a second vertical potential difference between the output terminals of the second vertical hall sensor hv 2 , based on the output signal of the second vertical hall sensor hv 2 . 
     The third hall-sensor signal-processing circuit  470  outputs the second vertical detected-position signal pyr to the A/D converter A/D  6  of the CPU  21 , on the basis of the second vertical potential difference. The second vertical detected-position signal pyr represents the location of the part of the movable platform  30   a  which has the second vertical hall sensor hv 2  (the position-detecting point by the second vertical hall sensor hv 2 ), in the y direction. 
     The third hall-sensor signal-processing circuit  470  is connected to the second vertical hall sensor hv 2  through the flexible circuit board (not depicted). 
     In the embodiment, the three hall sensors (hh 10 , hv 1  and hv 2 ) are used for specifying the location of the movable platform  30   a  including the rotational (inclination) angle. 
     The locations in the y direction of the two points on the movable platform  30   a  are determined by using two of the three hall sensors (hv 1  and hv 2 ). The location in the x direction of the one point on the movable platform  30   a  is determined by using another of the three hall sensors (hh 10 ). The location of the movable platform  30   a , which includes the rotational (inclination) angle in the xy plane, can be determined on the basis of the information regarding the locations in the x direction of the one point and the location in the y direction of the two points. 
     Next, the main operation of the photographic apparatus  1  in the embodiment is explained using the flowchart of  FIG. 4 . 
     When the PON switch  11   a  is set to the ON state, the electrical power is supplied to the detection unit  25  so that the detection unit  25  is set to the ON state in step S 11 , as the initial state. In the initial state, the movable platform  30   a  is positioned at the center of its movement range in both the x direction and the y direction, and each of the four sides of the rectangle composing the outline of the imaging surface of the imager  39   a   1  is parallel to either the x direction or the y direction. Furthermore, the lens information including the lens coefficient F is communicated from the camera lens  67  to the CPU  21 . 
     In step S 12 , the timer interrupt process at the predetermined time interval (1 ms) commences. In step S 13 , the value of the release-state parameter RP is set to 0. The details of the timer interrupt process in the embodiment are explained later using the flowchart of  FIG. 5 . 
     In step S 14 , it is determined whether the photometric switch  12   a  is set to the ON state. When it is determined that the photometric switch  12   a  is not set to the ON state, the operation returns to step S 14  and the process in step S 14  is repeated. Otherwise, the operation continues on to step S 15 . 
     In step S 15 , it is determined whether the correction switch  14   a  is set to the ON state. When it is determined that the correction switch  14   a  is not set to the ON state, the value of the correction parameter SR is set to 0 in step S 16 . Otherwise, the value of the correction parameter SR is set to 1 in step S 17 . 
     When the photometric switch  12   a  is set to the ON state, the AE sensor of the AE unit  23  is driven, the photometric operation is performed, and the aperture value and the duration of the exposure operation are calculated, in step S 18 . 
     In step S 19 , the AF sensor and the lens control circuit of the AF unit  24  are driven to perform the AF sensing and focus operations, respectively. 
     In step S 20 , it is determined whether the shutter release switch  13   a  is set to the ON state. When the shutter release switch  13   a  is not set to the ON state, the operation returns to step S 14  and the process in steps S 14  to S 19  is repeated. Otherwise, the operation continues on to step S 21 . 
     In step S 21 , the value of the release-state parameter RP is set to 1, and then the release-sequence operation commences. 
     In step S 22 , the value of the mirror state parameter MP is set to 1. 
     In step S 23 , the mirror-up operation and the aperture closing operation corresponding to the aperture value that is either preset or calculated, are performed by the mirror-aperture-shutter unit  18 . 
     After the mirror-up operation is finished, the value of the mirror state parameter MP is set to 0, in step S 24 . In step S 25 , the opening operation of the shutter (the movement of the front curtain of the shutter) commences. 
     In step S 26 , the exposure operation, that is, the electric charge accumulation of the imager  39   a   1  (CCD etc.), is performed. After the exposure time has elapsed, the closing operation of the shutter (the movement of the rear curtain in the shutter), the mirror-down operation, and the opening operation of the aperture are performed by the mirror-aperture-shutter unit  18 , in step S 27 . 
     In step S 28 , the value of the release-state parameter RP is set to 0 so that the photometric switch  12   a  and the shutter release switch  13   a  are set to the OFF state and the release-sequence operation is finished. In step S 29 , the electric charge accumulated in the imager  39   a   1  during the exposure time is read. In step S 30 , the CPU  21  communicates with the DSP  19  so that the image-processing operation is performed based on the electric charge read from the imager  39   a   1 . The image on which the image-processing operation is performed is stored in the memory of the photographic apparatus  1 . In step S 31 , the image stored in the memory is displayed on the display  17 , and the operation then returns to step S 14 . In other words, the photographic apparatus  1  is returned to a state in which the next imaging operation can be performed. 
     Next, the timer interrupt process in the embodiment, which commences in step S 12  in  FIG. 4  and is performed at every predetermined time interval (1 ms) independent of the other operations, is explained using the flowchart of  FIG. 5 . 
     When the timer interrupt process commences, the first angular velocity vx, which is output from the detection unit  25 , is input to the A/D converter A/D  0  of the CPU  21  and converted to the first digital angular velocity signal Vx n , in step S 51 . The second angular velocity vy, which is also output from the detection unit  25 , is input to the A/D converter A/D  1  of the CPU  21  and converted to the second digital angular velocity signal Vy n  (the angular velocity detection operation). 
     Furthermore, the first acceleration ah, which is also output from the detection unit  25 , is input to the A/D converter A/D  2  of the CPU  21  and converted to the first digital acceleration signal Dah n . Similarly, the second acceleration av, which is also output from the detection unit  25 , is input to the A/D converter A/D  3  of the CPU  21  and converted to the second digital acceleration signal Dav n  (the acceleration detection operation). 
     The low frequencies of the first and second digital angular velocity signals Vx n  and Vy n  are reduced in the digital high-pass filtering (the first and second digital angular velocities VVx n  and VVy n , see ( 1 ) in  FIG. 6 ). 
     The high frequencies of the first and second digital acceleration signals Dah n  and Dav n  are reduced in the digital low-pass filtering (the first and second digital acceleration Aah n  and Aav n , see ( 1 ) in  FIG. 6 ). 
     In step S 52 , the hall sensor unit  44   a  detects the position of the movable platform  30   a . The horizontal detected-position signal px and the first and second vertical detected-position signals pyl and pyr are calculated by the hall-sensor signal-processing unit  45 . The horizontal detected-position signal px is then input to the A/D converter A/D  4  of the CPU  21  and converted to the digital signal pdx n , the first vertical detected-position signal pyl is then input to the A/D converter A/D  5  of the CPU  21  and converted to the digital signal pdyl n , and the second vertical detected-position signal pyr is input to the A/D converter A/D  6  of the CPU  21  and also converted to the digital signal pdyr n , both of which thus specify the present position P n  (pdx n , pdyl n , pdyr n ) of the movable platform  30   a  (see ( 2 ) in  FIG. 6 ). 
     In step S 53 , it is determined whether the value of the correction parameter SR is 0. When it is determined that the value of the correction parameter SR is 0 (SR=0), in other words, that the photographic apparatus  1  is not in the correction mode, the position S n  (Sx n , Syl n , Syr n ) where the movable platform  30   a  should be moved, is set to the initial state (Sx n =Syl n =Syr n =0) in step S 54  (see ( 4 ) in  FIG. 6 ). 
     When it is determined that the value of the correction parameter SR is not 0 (SR=1), in other words when the photographic apparatus  1  is in correction mode, the third digital displacement angle Kθ n  is calculated on the basis of the first and second digital accelerations Aah n  and Aav n , in step S 55  (see ( 8 ) in  FIG. 6 ). 
     In step S 56 , the rotational (inclination) direction component of the position S n , Sθ n , is calculated on the basis of the third digital displacement angle Kθ n  and the hall sensor distance coefficient HSD (see ( 3 ) in  FIG. 6 ). 
     The details of the calculation of the third digital displacement angle Kθ n  in the embodiment are explained later using the flowchart of  FIG. 8 . 
     In step S 57 , the first and second movable ranges Hsx n  and Hsy n  are calculated on the basis of the distance Ra, the first and second maximum movable ranges Rx and Ry, the angles A and B, and the third digital displacement angle Kθ n . 
     In step S 58 , the first and second digital displacement angles Kx n  and Ky n  are calculated on the basis of the first and second digital angular velocities VVx n  and VVy n  (see ( 7 ) in  FIG. 6 ). 
     In step S 59 , the horizontal direction component of the position S n , Sx n , and the vertical direction component of the position S n , Sy n , are calculated on the basis of the first digital displacement angle Kx n , the second digital displacement angle Ky n , and the lens coefficient F (see ( 3 ) in  FIG. 6 ). 
     In step S 60 , it is determined whether the first movable range Hsx n  is less than the absolute value of the horizontal direction component of the position S n , Sx n . When it is determined that the first movable range Hsx n  is less than the absolute value of the horizontal direction component of the position S n , Sx n , the position Sx n  is reset to the center of its movement range of the movable platform  30   a  in the x direction, in step S 61  (Sx n =0). Then, the operation continues to step S 62 . Namely, in step S 61 , the first stabilization based on yaw is prohibited. Otherwise, the operation proceeds to step S 62 . 
     In step S 62 , it is determined whether the second movable range Hsy n  is less than the absolute value of the vertical direction component of the position S n , Sy n . When it is determined that the second movable range Hsy n  is less than the absolute value of the vertical direction component of the position S n , Sy n , the position Sy n  is reset to the center of its movement range of the movable platform  30   a  in the y direction, in step S 63  (Sy n =0). Then, the operation continues to step S 64 . Namely, in step S 63 , the second stabilization based on pitch is prohibited. Otherwise, the operation proceeds to step S 64 . 
     In step S 64 , the first vertical direction component of the first driving point Syl n  and the second vertical direction component of the second driving point Syr n  are calculated on the basis of the vertical direction component of the position S n , Sy n , and the rotational (inclination) direction component of the position S n , Sθ n  (see ( 4 ) in  FIG. 6 ). 
     In step S 65 , the horizontal driving force Dx n  (the horizontal PWM duty dx), the first vertical driving force Dyl n  (the first vertical PWM duty dyl), and the second vertical driving force Dyr n  (the second vertical PWM duty dyr) of the driving force D n , which moves the movable platform  30   a  to the position S n , are calculated on the basis of the position S n  (Sx n , Sy n , Sθ n ) that was determined in step S 54 , S 59 , S 61 , or step S 64 , and the present position P n  (pdx n , pdyl n , pdyr n ) (see ( 5 ) in  FIG. 6 ). 
     In step S 66 , the first and second horizontal coils  31   a   1  and  31   a   2  are driven by applying the horizontal PWM duty dx to the driver circuit  29 ; the first vertical coil  32   a   1  is driven by applying the first vertical PWM duty dyl to the driver circuit  29 ; and the second vertical coil  32   a   2  is driven by applying the second vertical PWM duty dyr to the driver circuit  29 , so that the movable platform  30   a  is moved to position S n  (Sx n , Sy n , Sθ n ) (see ( 6 ) in  FIG. 6 ). 
     The process of steps S 65  and S 66  is an automatic control calculation that is performed by the PID automatic control for performing general (normal) proportional, integral, and differential calculations. 
     Next, the calculation of the third digital displacement angle Kθ n , which is performed in step S 55  in  FIG. 5 , is explained using the flowchart of  FIG. 8 . 
     When the calculation of the third digital displacement angle Kθ n  commences, it is determined whether the absolute value of the second digital acceleration Aav n , is larger than or equal to the absolute value of the first digital acceleration Aah n , in step S 71 . 
     When it is determined that the absolute value of the second digital acceleration Aav n  is larger than or equal to the absolute value of the first digital acceleration Aah n , the operation proceeds to step S 75 , otherwise, the operation continues to step S 72 . 
     In step S 72 , it is determined whether the first digital acceleration Aah n  is less than 0. When it is determined that the first digital acceleration Aah n  is less than 0, the operation proceeds to step S 74 , otherwise, the operation continues to step S 73 . 
     In step S 73 , the CPU  21  determines that the photographic apparatus  1  is held approximately in the first vertical orientation, and calculates the inclination angle (the third digital displacement angle Kθ n ) by performing the arcsine transformation on the second digital acceleration Aav n  and taking the negative (Kθ n =−Sin −1 (Aav n )). 
     In step S 74 , the CPU  21  determines that the photographic apparatus is held approximately in the second vertical orientation, and calculates the inclination angle (the third digital displacement angle Kθ n ) by performing the arcsine transformation on the second digital acceleration Aav n  (Kθ n =+Sin −1 (Aav n )). 
     In step S 75 , it is determined whether the second digital acceleration Aav n  is less than 0. When it is determined that the second digital acceleration Aav n  is less than 0, the operation proceeds to step S 77 , otherwise, the operation continues to step S 76 . 
     In step S 76 , the CPU  21  determines that the photographic apparatus  1  is held approximately in the first horizontal orientation, and calculates the inclination angle (the third digital displacement angle Kθ n ) by performing the arcsine transformation on the first digital acceleration Aah n  (Kθ n =+Sin −1 (Aah n )). 
     In step S 77 , the CPU  21  determines that the photographic apparatus is held approximately in the second horizontal orientation, and calculates the inclination angle (the third digital displacement angle Kθ n ) by performing the arcsine transformation on the first digital acceleration Aah n  and taking the negative (Kθ n =−Sin −1 (Aah n )). 
     Furthermore, it is explained that the hall sensor is used for position detection as the magnetic-field change-detecting element. However, another detection element, an MI (Magnetic Impedance) sensor such as a high-frequency carrier-type magnetic-field sensor, a magnetic resonance-type magnetic-field detecting element, or an MR (Magneto-Resistance effect) element may be used for position detection purposes. When one of either the MI sensor, the magnetic resonance-type magnetic-field detecting element, or the MR element is used, the information regarding the position of the movable platform can be obtained by detecting the magnetic-field change, similar to using the hall sensor. 
     Furthermore, the inclination correction is performed as a rotational movement, based on the third digital displacement angle Kθ n . However, instead of the inclination correction, a third stabilization for correcting the hand shake caused by roll (the third hand-shake displacement angle around the z direction) may be performed as the rotational movement. 
     In this case, the hand-shake angle (the hand-shake quantity) caused by roll that corresponds to the third digital displacement angle Kθ n  can be calculated by the acceleration sensor  26   c . However, it could be calculated by another sensor such as an angular velocity sensor, etc. 
     Although the embodiment of the present invention has been described herein with reference to the accompanying drawings, obviously many modifications and changes may be made by those skilled in this art without departing from the scope of the invention. 
     The present disclosure relates to subject matter contained in Japanese Patent Application No. 2008-089576 (filed on Mar. 31, 2008), which is expressly incorporated herein by reference, in its entirety.