Patent Publication Number: US-9900514-B2

Title: Lens apparatus and image capturing apparatus for performing image stabilization

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a lens apparatus which performs image stabilization. 
     Description of the Related Art 
     Conventionally, in order to reduce an aberration occurring at the time of an image blur correction (image stabilization control), a zoom lens in which a correction lens unit constituting a part of an optical system is shifted in a direction perpendicular to an optical axis and is rotated by a minute angle around one point on the optical axis as a rotation center is known. However, a plurality of lens units constituting the optical system move by zooming or focusing. Therefore, when a rotational center position (radius of curvature) of the correction lens unit is constant, there is a possibility that the optical performance is deteriorated when the correction lens unit is rotationally moved. 
     Japanese Patent Laid-open No. 2014-174270 discloses an image stabilization apparatus that variably sets the radius of curvature of a plane where an optical element (correction lens unit) for image stabilization moves to improve the optical performance when rotationally moving the correction lens unit rotationally. 
     However, Japanese Patent Laid-open No. 2014-174270 does not describe specific conditions for improving the optical performance during the image stabilization. Accordingly, it is difficult for the image stabilization apparatus disclosed in Japanese Patent Laid-open No. 2014-174270 to perform the image stabilization while maintaining a satisfactory optical performance. 
     SUMMARY OF THE INVENTION 
     The present invention provides a lens apparatus and an image capturing apparatus capable of performing image stabilization while maintaining satisfactory optical performance. 
     A lens apparatus as one aspect of the present invention includes an image capturing optical system including a correction unit configured to move in image stabilization, and a driver configured to rotationally drive the correction unit based on a rotational center position that varies depending on an object distance, and a predetermined conditional expression is satisfied. 
     An image capturing apparatus as another aspect of the present invention includes the lens apparatus and an image sensor configured to photoelectrically convert an optical image formed via the lens apparatus. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an image capturing apparatus in each embodiment. 
         FIG. 2  is a flowchart of illustrating the overall operation of image stabilizing control in each embodiment. 
         FIG. 3  is a flowchart of illustrating the overall operation of another image stabilizing control in each embodiment. 
         FIG. 4  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 1. 
         FIG. 5  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 2. 
         FIG. 6  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 3. 
         FIG. 7  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 4. 
         FIG. 8  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 5. 
         FIG. 9  is a cross-sectional view of lenses in focus states at infinity and in the close range in a zoom lens of Embodiment 6. 
         FIGS. 10A to 10C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 1. 
         FIGS. 11A to 11C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 2. 
         FIGS. 12A to 12C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 3. 
         FIGS. 13A to 13C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 4. 
         FIGS. 14A to 14C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 5. 
         FIGS. 15A to 15C  are lateral aberration diagrams of the zoom lens in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 6. 
         FIGS. 16A to 16C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 1. 
         FIGS. 17A to 17C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 2. 
         FIGS. 18A to 18C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 3. 
         FIGS. 19A to 19C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 4. 
         FIGS. 20A to 20C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 5. 
         FIGS. 21A to 21C  are lateral aberration diagrams of the zoom lens in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 6. 
         FIGS. 22A to 22C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 1. 
         FIGS. 23A to 23C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 2. 
         FIGS. 24A to 24C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 3. 
         FIGS. 25A to 25C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 4. 
         FIGS. 26A to 26C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 5. 
         FIGS. 27A to 27C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states at infinity at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 6. 
         FIGS. 28A to 28C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 1. 
         FIGS. 29A to 29C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 2. 
         FIGS. 30A to 30C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 3. 
         FIGS. 31A to 31C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 4. 
         FIGS. 32A to 32C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 5. 
         FIGS. 33A to 33C  are lateral aberration diagrams of the zoom lens during image stabilization in the focus states of the close range at the wide-angle end, the middle zoom position, and the telephoto end in Embodiment 6. 
         FIGS. 34A and 34B  are explanatory diagrams of an image stabilizer that changes a rotational center position in each embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Exemplary embodiments of the present invention will be described below with reference to the accompanied drawings. 
     First, referring to  FIG. 1 , an image capturing apparatus in this embodiment will be described.  FIG. 1  is a block diagram of an image capturing apparatus  100  in this embodiment. A lens barrel  101  (lens apparatus) holds a lens unit (image capturing optical system including a zoom unit  102 , image stabilization unit (image blur correction unit)  103 , a focus unit  104 , and an aperture stop/shutter  105 ) inside the lens barrel  101 . 
     The zoom unit  102  adjusts a focal length by moving in the optical axis direction, and it optically changes an angle of view (zoom position), i.e., it performs zooming. In this embodiment, the zoom unit  102  includes a plurality of lens units (a zoom lens unit) including a first lens unit B 1  disposed closest to an object side and a second lens unit B 2  disposed adjacent to the first lens unit B 1 ), and it changes a space between adjacent lens units during zooming. The image stabilization unit  103  is a correction unit (correction lens unit) that corrects an image blur caused by a hand shake. Specifically, the image stabilization unit  103  moves in a direction different from the optical axis direction when performing the image stabilization (rotationally moves at the radius of curvature around the rotational center position). The focus unit  104  moves in the optical axis direction during focusing. The aperture stop/shutter  105  is used for exposure control (light amount adjustment). In this embodiment, the lens barrel  101  is detachably attached to an image capturing apparatus body including an image sensor  106 . However, this embodiment is not limited thereto, and can also be applied to an image capturing apparatus where the lens barrel  101  and the image capturing apparatus body are integrally formed. 
     Light passing through the lens barrel  101  is received by the image sensor  106  using a CCD (Charge Coupled Device) sensor, a CMOS (Complementary Metal Oxide Semiconductor) sensor, or the like to be photoelectrically converted to generate an imaging signal (image signal). In other words, the image sensor  106  photoelectrically converts an optical image (object image) formed via the lens barrel  101  (image capturing optical system) to output the imaging signal. The imaging signal is input to an image processing circuit  144  where pixel interpolation processing, color conversion processing, and the like are performed on the imaging signal, and then it sent to an image memory  145  as image data. The image memory  145  is a storage unit such as a DRAM (Dynamic Random Access Memory) and an SRAM (Static Random Access Memory). 
     A display unit  146  is constituted by a TFT type LCD (thin film transistor driving type liquid crystal display) or the like, and it displays specific information such as photographing information together with the photographed image data. An electronic view finder (EVF) function for a user to adjust the angle of view can be achieved by information display such as live view. The aperture stop/shutter driver  115  calculates an exposure control value (aperture value and shutter speed) based on luminance information obtained by image processing of the image processing circuit  144 . Then, the aperture stop/shutter driver  115  performs AE (automatic exposure) control by driving the aperture stop/shutter  105  based on the calculation result (exposure control value). 
     A system controller  120  is a control unit such as a CPU (Central Processing Unit), and it controls the entire image capturing apparatus  100  by sending control commands to each unit according to the operation of the user. The system controller  120  executes various control programs stored in a nonvolatile memory  147  built in the image capturing apparatus  100  (such as control of the image sensor  106 , AE/AF control, zoom control (program for executing auto FA zoom processing or the like)). 
     A hand shake detector  136  is a vibration detection unit such as a gyro sensor and an angular velocity sensor, and it outputs vibration information (detection signal). A coefficient calculator  137  converts a vibration amount applied to the image capturing apparatus  100  into an image stabilization coefficient, i.e., image blur correction coefficient (calculates the image stabilization coefficient) based on the vibration information from the hand shake detector  136 . A position calculator  134  calculates the rotational center position of the image stabilization unit  103  based on information from a zoom position information acquirer  122  and a focus position information acquirer  124 . The rotational center position is determined depending on an object distance and a zoom position. A correction unit driver  113  (drive unit) rotationally drives the image stabilization unit  103  with reference to the rotational center position variable depending on the object distance. A position changer  135  (changing unit) changes the rotational center position of the image stabilization unit  103  based on the calculation result (information on the rotational center position) by the position calculator  134  via the correction unit driver  113 . A rotation mechanism unit  133  has a mechanism that can rotationally move during the image stabilization around one point on the optical axis or the vicinity of the optical axis so as to cancel the hand shake. An image stabilization controller  123  controls and drives the image stabilization unit  103  by using the correction unit driver  113 , the position changer  135 , and the rotation mechanism unit  133 . 
     A focus unit driver  114  drives the focus unit  104 . For example, in autofocus control by a contrast detection method, the focus unit driver  114  drives the focus unit  104  to focus on an object based on focus adjustment information (contrast evaluation value) of the image capturing optical system obtained from the image processing circuit  144 . In this embodiment, the method of the focus adjustment control is not limited, and focus control such as a phase difference detection method or a combination of the contrast detection method and another method may be used. A zoom unit driver  112  drives the zoom unit  102  according to a zoom operation instruction. 
     An operation unit  150  includes a zoom lever, a zoom button, or the like as a zoom operation member for the user to instruct the image capturing apparatus  100  to perform zooming. The system controller  120  calculates a zoom drive speed and drive direction based on an operation amount and an operation direction of the zoom operation member that is used for the zoom instruction operation. Then, the zoom unit  102  moves along the optical axis according to the calculation result of the system controller  120 . 
     The image data generated by the image capturing operation are sent to a recording unit  149  via an I/F unit  148  (interface unit) to be recorded. The image data are recorded in an external recording medium such as a memory card that is used while being attached to the image capturing apparatus  100 , the nonvolatile memory  147  built in the image capturing apparatus  100 , or both of them. 
     In addition to the zoom operation member described above, the operation unit  150  includes a release switch for instructing start of photographing, an auto FA zoom operation switch for instructing the start and end of the auto FA zoom function, and the like. An operation signal from the operation unit  150  is sent to the system controller  120 . In addition to the program data and the image data, the nonvolatile memory  147  built in the image capturing apparatus  100  stores setting information of the image capturing apparatus  100  and reference information (such as position information and size information) of the object in the auto FA zoom function. The reference information of the object is a parameter that is used for control to maintain the size of the object. 
     Each of the units in the system controller  120 , the correction unit driver  113 , and the position changer  135  may be provided in either the lens apparatus or the image capturing apparatus body. In other words, at least a part of each unit in the system controller  120 , the correction unit driver  113 , and the position changer  135  can be provided in at least one of the lens apparatus and the image capturing apparatus body. 
     Next, referring to  FIG. 2 , the overall operation of the image stabilization control in this embodiment will be described.  FIG. 2  is a flowchart of illustrating the overall operation of the image stabilization control in this embodiment, and it illustrates a method of changing the rotational center position of the image stabilization unit  103  depending on the focus position. Each step of  FIG. 2  starts when a main power supply of the image capturing apparatus  100  is turned on, and it is performed at a constant sampling cycle. Each step of  FIG. 2  is performed by each unit based on a command from the system controller  120 . 
     First, at step S 101 , the system controller  120  determines whether an image stabilization SW (image stabilization switch) of the operation unit  150  is ON. When the image stabilization SW is ON, the flow proceeds to step S 102 . On the other hand, when the image stabilization SW is OFF, the flow proceeds to step S 111 , the system controller  120  stops the drive of the image stabilization unit  103 , it ends this flow (vibration correction routine), and it waits until the next process. 
     At step S 102 , the system controller  120  (coefficient calculator  137 ) captures output signals from the hand shake detector  136  such as an accelerometer and an angular velocity meter. Subsequently, at step S 103 , the system controller  120  determines whether it is possible to perform the image stabilization (vibration correction). When it is possible to perform the image stabilization, the flow proceeds to step S 104 . On the other hand, when it is not possible to perform the image stabilization, the flow proceeds to step S 111 . At step S 103 , the system controller  120  determines whether the output signal from the hand shake detector  136  such as an accelerometer or an angular velocity meter from the start of the power supply is in a stable state. Until the output signal is stabilized, the system controller  120  determines that the image stabilization is not possible, and after the output signal is stabilized, the system controller  120  determines that the image stabilization is possible. This makes it possible to avoid degradation of the image stabilization performance in a state where the output value immediately after the start of the power supply is unstable. 
     Subsequently, at step S 104 , the system controller  120  determines whether there is focus position information. When there is the focus position information, the flow proceeds to step S 105 . On the other hand, when there is no focus position information, the flow proceeds to step S 111 . At step S 105 , the system controller  120  (focus position information acquirer  124 ) acquires focus position information. Subsequently, at step S 106 , the focus unit  104  moves along the optical axis. Subsequently, at step S 107 , the system controller  120  (position calculator  134 ) calculates the rotational center position (turning center position) of the image stabilization unit  103  based on the focus position information acquired at step S 105 . Subsequently, at step S 108 , the position changer  135  changes the rotational center position of the image stabilization unit  103  based on the information on the rotational center position calculated by the system controller  120 . 
     Subsequently, at step S 109 , the system controller  120  (coefficient calculator  137 ) calculates an image stabilization coefficient (image blur correction coefficient) such as an angular vibration correction coefficient and a parallel vibration correction coefficient according to the calculated in-focus range. Subsequently, at step S 110 , the correction unit driver  113  rotates (turns) the image stabilization unit  103  around the rotational center position determined at step S 108 , based on the image stabilization coefficient calculated at step S 109 . 
     As described above, the image capturing apparatus  100  of this embodiment changes the rotational center position of the image stabilization unit  103  depending on the focus position. Then, it can satisfactorily correct the optical performance during the image stabilization by calculating and correcting the rotational center position optimum for the image stabilization coefficient calculated according to the in-focus range of the main object at the time of capturing a moving image or still image. 
     Next, referring to  FIG. 3 , the overall operation of another image stabilization control in this embodiment will be described.  FIG. 3  is a flowchart of illustrating the overall operation of the image stabilization control, and it illustrates a method of changing the rotational center position of the image stabilization unit  103  depending on the focus position and the zoom position. Each step of  FIG. 3  starts when the main power supply of the image capturing apparatus  100  is turned on, and it is executed at a constant sampling cycle. Each step of  FIG. 3  is executed by each unit based on a command from the system controller  120 . Steps S 201  to S 203 , S 206 , S 207 , and S 210  to S 213  in  FIG. 3  are the same as steps S 101  to S 105  and S 108  to S 111  in  FIG. 2 , respectively, and accordingly descriptions thereof will be omitted. 
     At step S 204 , the system controller  120  determines whether there is zoom position information. When there is the zoom position information, the flow proceeds to step S 205 . On the other hand, when there is no zoom position information, the flow proceeds to step S 213 . At step S 205 , the system controller  120  (zoom position information acquirer  122 ) acquires the zoom position information. 
     At step S 208 , the zoom unit  102  and the focus unit  104  move along the optical axis. Subsequently, at step S 209 , the system controller  120  (position calculator  134 ) calculates the rotational center position (turning center position) of the image stabilization unit  103  based on the zoom position information and the focus position information acquired at steps S 205  and S 207 , respectively. 
     Next, the optical features of the imaging lens of this embodiment will be described. Generally, when attempting to correct the image blur by parallel eccentricity of a lens unit constituting a part of the optical system, the imaging performance is deteriorated due to the eccentric aberration. Hereinafter, the occurrence of the eccentric aberration when the image blur is corrected by moving a movable lens unit in a direction orthogonal to the optical axis in an arbitrary refractive power arrangement will be described in view of the aberration theory, based on a method described in Matsui, the 23rd, Meeting of the Japan Society of Applied Physics (1962). 
     An aberration amount ΔY1 of the entire system when a lens unit P of a part of a magnification varying optical system is decentered (eccentric) in parallel by E is given by a sum of an aberration amount ΔY before decentering (i.e., before eccentricity is given) and an eccentric aberration amount ΔY(E) as represented by expression (a) below. The aberration amount ΔY is represented by a spherical aberration (I), coma aberration (II), astigmatism (III), Petzval sum (P), and distortion (Y) as indicated by expression (b) below. The eccentric aberration ΔY(E) is represented by a first order eccentric coma aberration (IIE), first order eccentric astigmatism (IIIE), first order eccentric field curvature (PE), first order eccentric distortion (VE1), first order eccentric distortion added aberration (VE2), and first order origin movement (ΔE) as indicated by expression (c) below. The first order origin movement (ΔE), the first order eccentric coma aberration (IIE), the first order eccentric astigmatism (IIIE), the first order eccentric field curvature (PE), the first order eccentric distortion (VE1), and the first order eccentric distortion added aberration (VE2) are represented by expressions (d) to (i) below, respectively. According to expression (d), the aberrations of (ΔE) to (VE2) in expression (i) are represented by using aberration coefficients IP, IIP, IIIP, PP, and VP of the lens unit P, where αP and αaP are incidence angles of light beams entering the lens unit P in the magnification varying optical system where the lens unit P is decentered (eccentric) in parallel. Similarly, the aberration coefficients when the lens unit disposed closer to the image plane side than the lens unit P is taken as a whole of a q-th lens unit are represented by using Iq, IIq, IIIq, Pq, and Vq. 
     
       
         
           
             
               
                 
                   
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     As can be seen from the above expressions, in order to reduce the occurrence of the eccentric aberration, it is necessary to set the various aberration coefficients IP, IIP, IIIP, PP, and VP of the lens unit P to small values or to set the values of the aberration coefficients in a well-balanced manner to cancel each other as indicated in expressions (a) to (i). 
     Next, with respect to the optical action of the magnification varying optical system that has the image stabilization function in this embodiment, a mode assuming an image stabilization system that eccentrically drives a part of lens units in the image capturing optical system in a direction orthogonal to the optical axis to correct a displacement of a captured image will be described. 
     First, in order to achieve sufficiently large displacement correction with a sufficiently small eccentric drive amount, it is necessary to sufficiently increase the first order origin movement (ΔE) described above. Based on this fact, a condition for correcting the first order eccentric field curvature (PE) will be considered. The image capturing optical system is composed of three lens units of a unit o, a unit p, and a unit q in order from the object side, and the unit p is translated in the direction orthogonal to the optical axis to correct the image blur. Refractive powers of the unit o, the unit p, and the unit q are φo, φp, φq, respectively, incidence angles of the paraxial on-axis ray and the off-axial ray to each lens unit are α and αa, incident heights of the on-axis ray and the off-axis ray are denoted by h and ha, and the aberration coefficient is described by applying suffix similarly. In addition, it is assumed that each lens unit is composed of a small number of lenses, and each aberration coefficient indicates a tendency of insufficient correction. 
     When focusing on the Petzval sum of each lens unit based on the above assumption, the Petzval sums Po, Pp, Pq of each lens unit are proportional to the refractive powers φo, φp, φq of the respective lens units, and Po=Cφo, Pp=Cφp, and Pq=Cφq (C: constant) are substantially satisfied. Accordingly, the first order eccentric field curvature (PE) generated when the unit p is decentered (eccentric) in parallel can be rearranged as follows, substituting the above expressions. 
     Po: Petzval sum of the unit o 
     Pp: Petzval sum of the unit p 
     Pq: Petzval sum of the unit q 
     hp: Incidence height of the paraxial on-axis ray 
     αp: Incidence angle of the paraxial on-axis ray onto the unit p 
     φo: Refractive power of the unit o 
     φp: Refractive power of the unit p 
     φq: Refractive power of the unit q 
     αpinf: paraxial on-axis ray to the unit p when the object distance is at infinity 
     αpn: a paraxial on-axis ray to the unit p when the object distance is close-up photographing (first focus state)
 
 PE=Cφp ( hp·φq−αp )
 
     Accordingly, in order to correct the eccentric field curvature (PE), it is necessary that φp=0 or φq=αp/hp is satisfied. However, when φp=0 is satisfied, the first order origin movement (ΔE) becomes 0 and the displacement correction cannot be performed. Therefore, a solution satisfying φq=αp/hp must be obtained. That is, since hp&gt;0, it is necessary to make at least α p and φ q the same sign. In other words, since hp&gt;0 is satisfied, at least αp and φq need to have the same sign. 
     Next, a case where the incidence angle of the paraxial on-axis ray to the unit p will be described for each of the case of αp&lt;0 or αp&gt;0. 
     (1) When αp&lt;0 is Satisfied 
     The relation of φq&lt;0 is (necessarily φ0&lt;0, more necessarily φp&gt;0) is satisfied due to correction of the eccentric field curvature (PE). As described above, it is preferred that the refractive power arrangement of the optical system that can correct the first order eccentric field curvature (PE) while sufficiently increasing the first order origin movement (ΔE) satisfies Table 1 below. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 φo 
                 φp 
                 φq 
               
               
                   
               
             
            
               
                 NEGATIVE 
                 POSITIVE 
                 NEGATIVE 
               
               
                   
               
            
           
         
       
     
     First, the incidence angle of the ray on each unit varies depending on the object distance. Therefore, relational expressions (a-1) and (a-2) below are conceivable.
 
|α p inf|&gt;|α pn|   (a-1)
 
|α p inf|&lt;|α pn|   (a-2)
 
     Next, with respect to the paraxial on-axis ray, since φo is a negative unit, the incident light beam to the unit P always becomes a divergent light beam. Further, when the object distance is infinite, the absolute value increases in the case of close-up photographing (in the first focus state) with respect to substantially parallel light, and always satisfies relational expression (a-3) below.
 
|α p inf|&gt;|α p near|  (a-3)
 
     In other words, it is shown that relational expression (a-1) above does not exist. Therefore, the conditional expression related to PE is represented as Expression (g). When a parameter that does not change depending on the object distance is defined as a constant, Φp, Pq, and Pp are constants. The amount hp changes, but its change amount is very small. Therefore, a variable when the object distance changes is only αp. 
     Accordingly, the relationship between the absolute values of PEs when the object distance is at infinity and when the object distance is close-up photographing (first focus state) is as represented by relational expression (a-4) below.
 
| PE inf|&lt;| PEn|   (a-4)
 
     It is understood from the optical trace result of Numerical example 1 that relational expression (a-4) above holds.
         αpinf: −0.0803   αpn: −0.1065   hpinf: 2.8874   hpnear: 2.8509   Φp: 0.0810   Φq: 0.0342   Pp: 0.2067   Pq: 0.1245   |PEinf|: 0.0457   |PEn|: 0.0508
 
∴| pE inf|&lt;| PEn|   (a-4)
       

     (2) When αp&gt;0 is Satisfied 
     In order to correct the eccentric field curvature, φq&gt;0 (necessarily φ0&gt;0) is satisfied. Further, at this time, when φp&gt;0 is satisfied, 0&lt;αp&lt;α′p&lt;1 is satisfied. 
     In addition, the first order origin movement (ΔE) is as represented by expression (a-5) below.
 
(Δ E )=−2(α p′−αp )&gt;−2  (a-5)
 
     In other words, the eccentricity sensitivity (the ratio of a displacement of the blurring of the captured image with respect to a unit displacement of the eccentric lens unit) becomes smaller than 1. Further, as described above, the eccentricity sensitivity is 0 when φp=0 is satisfied. Accordingly, in such a case, φp&lt;0 must be satisfied. The relationships of Φo, φp, and φq are as indicated in Table 2 below. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 φo 
                 φp 
                 φq 
               
               
                   
               
             
            
               
                 POSITIVE 
                 NEGATIVE 
                 POSITIVE 
               
               
                   
               
            
           
         
       
     
     The incidence angle of the ray onto each unit varies depending on the object distance. Then, relational expressions (a-6), (a-7), and (a-8) below are conceivable.
 
|α p inf|&gt;|α pn|   (a-6)
 
α p inf&lt;α p near  (a-7)
 
|α p inf|&lt;|α pn|   (a-8)
 
     Next, with respect to the paraxial on-axis ray, since φo is a negative unit, the incident light beam to the unit P always becomes a divergent light beam. When the object distance is infinite, the absolute value increases when the object distance is close-up photographing (first focus state) with respect to substantially parallel light, and it always satisfies relational expression (a-6). 
     In other words, it means that relational expression (a-8) does not exist. Therefore, the conditional expression for PE is represented as expression (g). When a parameter that does not change with the object distance is defined as a constant, φp, Pq, and Pp are constants, and hp changes, but its change amount is very small. Therefore, a variable when the object distance changes is only αp. Accordingly, the magnitude relation of the absolute values of the PEs when the object distance is at infinity and when the object distance is close-up photographing (first focus state) is as follows.
 
 PE inf|&lt;| PE near|  (a-9)
 
     From the optical trace result of Numerical example 2, it can be seen that the magnitude relation is satisfied.
         αpinf: 0.0242   αpnear: −0.0352   hpinf: 0.9104   hpnear: 0.6451   Φp: −0.1769   φq: 0.0746   Pp: −0.4485   Pq: 0.3700   |PEinf|: 0.0487   |PEn|: 0.0580
 
∴| PE inf|&lt;| PE near|  (a-10)
       

     As described above, the refractive power arrangement of the optical system, which makes it possible to correct the first order eccentric field curvature (PE) while sufficiently increasing the first order origin movement (ΔE), is appropriately set as indicated in Table 3 below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                   
                 φo 
                 φp 
                 φq 
               
               
                   
                   
               
             
            
               
                   
                 A 
                 NEGATIVE 
                 POSITIVE 
                 NEGATIVE 
               
               
                   
                 B 
                 POSITIVE 
                 NEGATIVE 
                 POSITIVE 
               
               
                   
                   
               
            
           
         
       
     
     Next, these refractive power arrangements are applied to the imaging lens. The reason for the application to the imaging lens is to assume a situation where the vibration of an image targets a focal length region where the image quality is likely to be degraded and the image stabilization function becomes more effective. In addition, as an imaging lens, there is a four-unit zoom lens having a configuration where the refractive power arrangement of the lens unit related to zooming is positive, negative, positive, and positive in order from the object side. In the four-unit zoom lens, a configuration where a first unit, a second unit, or both the first unit and the second unit are moved on the optical axis to mainly contribute to zooming during zooming from the wide-angle end to the telephoto end, and a third lens unit is moved on the optical axis to mainly keep an image plane position constant is widely known. 
     Although the total lens length is slightly long in the imaging lens having such a configuration, it is relatively easy to satisfactorily correct various aberrations in the entire zoom range, and a fourth unit is fixed during zooming. Therefore, it is sufficient to simply arrange the zooming mechanism around the first, second, and third units, and mechanical components required for vibration compensation, such as a vibration detection sensor and a power supply, are mainly arranged around the fourth unit, and as a result it is possible to prevent the outer diameter of the lens from increasing. 
     Next, a method of performing the vibration compensation by moving a part of the lens units of the imaging lens in a direction perpendicular to the optical axis will be described. In order to prevent the deterioration of the image quality when vibration compensation is performed while preventing the increase of the imaging lens, a lens unit suitable for the vibration compensation need to be designed to have sufficiently large eccentricity sensitivity described above in the lens unit having a small outer diameter with a small amount of occurrence of the eccentric aberration. Focusing on these points, consideration is given to using each lens unit of the imaging lens or a part thereof for the vibration compensation. 
     (1-1) When Using the Second Unit or a Part Thereof 
     The first unit has a relatively strong positive refractive power, the second unit has a strong negative refractive power, and the combined power of the third and fourth units is positive. Therefore, in this case, the correction condition for the eccentric field curvature (PE) is satisfied. The second unit has a lens with a relatively small outer diameter, which is suitable for reduction in size of the apparatus. The eccentricity sensitivity is easily increased because it is a lens unit with a strong refractive power, which is an advantage. As described above, the second unit is suitable as a lens unit for vibration compensation. Thus, in this embodiment, the second unit is moved as a lens unit for the vibration compensation in a direction perpendicular to the optical axis. 
     (1-2) When Using the Third Unit or a Part Thereof 
     The refractive power of the first unit or the combined refractive power of the first unit and the second unit tends to be strong negative at the wide-angle end, and it also tends to be weak negative at the telephoto end. Since the third unit has a positive refractive power and the fourth lens unit has a relatively weak positive refractive power, the correction condition for the eccentric field curvature (PE) is not satisfied as it is. Therefore, paying attention to the fact that the fourth unit is a lens unit having a relatively weak positive refractive power, it is conceivable to solve this problem by setting the Petzval sum of this lens unit to a negative value. However, it is not possible to strengthen the refractive power of the third unit to correct variations in various aberrations caused by zooming. Therefore, as compared with the case where the second unit is used as the lens unit for the vibration compensation, the eccentricity sensitivity cannot be increased. It is also conceivable to divide the third unit into two lens units of a positive lens unit and a negative lens unit in order from the object side, and use one of the lens units for the vibration compensation to increase the eccentricity sensitivity. As described above, the third unit is suitable as a lens unit for the vibration compensation. Thus, in this embodiment, the third unit is moved as a lens unit for the vibration compensation in a direction perpendicular to the optical axis. 
     (2) When Using a Method of Performing the Vibration Compensation by Rotating a Part of the Lens Units of the Imaging Lens Around a Point on the Optical Axis 
     In the image stabilizing optical system which performs the vibration compensation by rotating a part of the lens units of the imaging lens around one point on the optical axis, the degree of freedom of the center of an inclination is increased by one. Therefore, it is possible to control various aberrations by properly giving the center of the inclination. Accordingly, by setting the center position of the inclination in a direction of canceling the various aberrations generated by moving the part of the lens unit of the imaging lens in the direction perpendicular to the optical axis to perform the vibration compensation, it is possible to satisfactorily correct the optical performance during the image stabilization. 
     (3) When Using a Method of Performing the Vibration Compensation by Rotating a Part of the Lens Units of the Imaging Lens Around a Point on the Optical Axis as a Variable Rotation Center 
     In the image stabilizing optical system which performs the vibration compensation by rotating a part of the lens unit of the imaging lens around the point on the optical axis as the rotation center in (2) described above, the center position of the inclination is set in the direction of canceling the various aberrations generated by moving in the direction perpendicular to the optical axis to perform the vibration compensation. Accordingly, it is possible to satisfactorily correct the optical performance during the image stabilization. 
     The relationship between the absolute values of the PEs when the object distance is at infinity and when the object distance is in the close-up photographing (first focus state) satisfies relational expression (a-9). This shows that amounts of various aberrations generated by performing the vibration compensation by moving a part of the lens units of the imaging lens in the direction perpendicular to the optical axis increase when the object distance is in the close-up photographing compared to the case of the infinity. Accordingly, in order to set the center position of the inclination in the direction of canceling the various aberrations caused by performing the vibration compensation by moving a part of the lens units of the imaging lens in the direction perpendicular to the optical axis, it is necessary to set the rotational center position during the close-up photographing to be short compared to the case of infinity. Thus, it is possible to satisfactorily correct the optical performance during the image stabilization. 
     Next, with respect to the lens apparatus (or image capturing apparatus  100 ) of this embodiment, conditional expressions (1) to (7) that are preferably satisfied for the image stabilization while maintaining the optical performance will be described. 
     The lens apparatus of this embodiment satisfies conditional expression (1) below.
 
| R inf|/ D−|Rn|/D &gt;0.001  (1)
 
     In conditional expression (1), symbol Rinf is a distance in the optical axis direction from an intersection of a lens surface closest to the object side of the image stabilization unit  103  and the optical axis to the rotational center position when focusing at infinity. Symbol Rn is a distance in the optical axis direction from the intersection of the lens surface closest to the object side of the image stabilization unit and the optical axis to the rotational center position when focusing in a close range (in a close-up photographing, or in a first focus state). Symbol D is a thickness on the optical axis of the image stabilization unit. Conditional expression (1) defines a difference in distance in the optical axis direction from the intersection with the lens surface closest to the object side of the lens unit from the rotational center position when focusing at the infinity and in the close range. When the lower limit of conditional expression (1) is exceeded, the rotational center position at the time of close-up photographing becomes too large, and the eccentric field curvature during the close-up photographing becomes too large, which is not preferable. 
     Preferably, the numerical range of conditional expression (1) is set as conditional expression (1a) below.
 
3.76 &lt;|R inf|/ D−|Rn|/D &lt;125.83  (1a)
 
     More preferably, the numerical range of conditional expression (1) is set as conditional expression (1b) below.
 
7.52 &lt;|R inf|/ D−|Rn|/D &lt;62.92  (1b)
 
     Preferably, the lens apparatus satisfies conditional expression (2).
 
0.01 &lt;|f 1 |/fw &lt;40.00  (2)
 
     In conditional expression (2), symbol f 1  is a focal length of the first lens unit of the zoom unit  102 , and symbol fw is a focal length of the lens apparatus (the entire lens system, i.e., image capturing optical system) at the wide-angle end. Conditional expression (2) is a conditional expression for appropriately setting the ratio of the focal length of the first lens unit to the focal length of the lens apparatus (image capturing optical system) at the wide-angle end. When the upper limit of conditional expression (2) is exceeded, the focal length of the first lens unit becomes too short, and it is difficult to suppress the field curvature in the entire zoom range. On the other hand, when the lower limit of conditional expression (2) is exceeded, the focal length of the first lens unit becomes too long, and in order to obtain a desired zoom ratio, an amount of change in a space between the first lens unit and the second lens unit increases, so that it is difficult to suppress the total lens length at the wide-angle end. 
     Preferably, the lens apparatus satisfies conditional expression (3).
 
0.01&lt;β2 t/β 2 w&lt; 100.00  (3)
 
     In conditional expression (3), symbols β 2   t  and β 2   w  are lateral magnifications at the telephoto end and at the wide-angle end of the second lens unit in the zoom unit  102 , respectively. Conditional expression (3) relates to sharing of the variable magnification of the second lens unit, and it is a conditional expression concerning the total optical length and the fluctuation of the aberration during zooming. When the lower limit of conditional expression (3) is exceeded, the sharing of the variable magnification of the second lens unit becomes small, which is disadvantageous for high magnification. In addition, it is undesirable because a moving amount of a rear unit increases for achieving a high zooming ratio and the total optical length increases. On the other hand, when the upper limit of conditional expression (3) is exceeded, it is advantageous to increase the magnification because the sharing of the variable magnification of the second lens unit increases, but it is difficult to correct fluctuations of various aberrations such as field curvature and coma aberration during zooming. 
     Preferably, the lens apparatus satisfies conditional expression (4).
 
0.01 &lt;ff/fw &lt;10.00  (4)
 
     In conditional expression (4), symbol ff is a focal length of the focus unit  104 . Conditional expression (4) is a conditional expression that appropriately sets the ratio of the focal length of the focus unit  104  to the focal length of the lens apparatus (the entire lens system, or the image capturing optical system) at the wide-angle end. When the upper limit of conditional expression (4) is exceeded and the refractive power of the focus unit is too weak, the effect of correcting the focus fluctuation during zooming is diminished, and a moving amount for focusing becomes too long. As a result, it is difficult to perform rapid focusing. On the other hand, when the lower limit of conditional expression (4) is exceeded, the refractive power of the focus unit  104  becomes too strong, the Petzval sum increases, and the field curvature increases in the entire zoom range. In addition, when it is attempted to increase the number of constituent lenses to suppress the occurrence of the filed curvature, the weight of the focus unit  104  increases and the torque for moving the focus unit  104  increases, which is not preferable. 
     Preferably, the lens apparatus satisfies conditional expression (5).
 
0.10 &lt;|fis|/fw &lt;20.00  (5)
 
     In conditional expression (5), symbol fis is a focal length of the image stabilization unit  103 . Conditional expression (5) is a conditional expression appropriately setting the ratio of the focal length of the image stabilization unit  103  to the focal length of the lens apparatus at the wide-angle end. When the upper limit of conditional expression (5) is exceeded, the focal length of the image stabilization unit  103  becomes too large and a moving amount during the image stabilization increases, and it is difficult to suppress the entire lens length. On the other hand, when the lower limit of conditional expression (5) is exceeded, the focal length of the image stabilization unit  103  becomes too small, and it is difficult to suppress eccentric aberration during the image stabilization. 
     Preferably, the lens apparatus satisfies conditional expression (6).
 
0.01&lt;| M 2 |/fw &lt;100.00  (6)
 
     In conditional expression (6), symbol M 2  is a moving amount (relative moving amount) with respect to the image plane of the second lens unit from the wide-angle end to the telephoto end. Conditional expression (6) is a conditional expression appropriately setting the ratio of the moving amount of the second lens unit at the wide-angle end to the telephoto end and the focal length of the lens apparatus (image capturing optical system) at the wide-angle end. When the upper limit of conditional expression (6) is exceeded, an amount of change in a space between the third lens unit and the second lens unit excessively decreases during zooming from the wide-angle end to the telephoto end. Therefore, in order to achieve high magnification, it is necessary to strengthen the refractive power of the second lens unit, and thus it is difficult to correct astigmatism at the wide-angle end. On the other hand, when the lower limit of conditional expression (6) is exceeded, the amount of change in the space between the third lens unit and the second lens unit excessively increases, and the space between the second lens unit and the third lens unit increases at the wide-angle end, and thus it is difficult to increase the magnification while suppressing a diameter of a front lens. 
     Preferably, the lens apparatus satisfies conditional expression (7).
 
0.01&lt;| M 1|/| M 2|&lt;200.00  (7)
 
     In conditional expression (7), symbol M 1  is a moving amount (relative moving amount) with respect to the image plane of the first lens unit from the wide-angle end to the telephoto end. Conditional expression (7) is a conditional expression appropriately setting the ratio of the moving amounts of the first lens unit and the second lens unit from the wide-angle end to the telephoto end. When the upper limit of conditional expression (7) is exceeded, the refractive power of the first lens unit becomes too small, and thus it is difficult to increase the magnification while suppressing the total length at the telephoto end. Or in this case, since the refractive power of the second lens unit becomes too large, it is difficult to suppress the chromatic aberration of magnification, the field curvature, and the coma aberration over the entire zoom range. On the other hand, when the lower limit of conditional expression (7) is exceeded, the refractive power of the first lens unit becomes too large, and thus it is difficult to correct an axial chromatic aberration, a spherical aberration, and the chromatic aberration of magnification at the telephoto end. Or in this case, since the refractive power of the second lens unit becomes too small, it is difficult to increase the zoom ratio while suppressing the diameter of the front lens. 
     More preferably, the numerical ranges of conditional expressions (2) to (7) are respectively set as conditional expressions (2a) to (7a) below.
 
1.02 &lt;|f 1 |/fw &lt;31.33  (2a)
 
0.85&lt;β2 t/β 2 w&lt; 28.32  (3a)
 
0.14 &lt;ff/fw &lt;2.00  (4a)
 
0.58 &lt;|fis|/fw &lt;7.85  (5a)
 
0.34&lt;| M 2 |/fw &lt;9.16  (6a)
 
0.09&lt;| M 1|/| M 2|&lt;7.98  (7a)
 
     Still more preferably, the numerical ranges of conditional expressions (2) to (7) are respectively set as conditional expressions (2b) to (7b) below.
 
2.04 &lt;|f 1 |/fw &lt;15.67  (2b)
 
1.70&lt;β2 t/β 2 w&lt; 14.16  (3b)
 
0.28 &lt;ff/fw&lt; 1.01  (4b)
 
1.16 &lt;|fis|/fw &lt;3.93  (5b)
 
0.68&lt;| M 2 |/fw &lt;4.58  (6b)
 
0.18&lt;| M 1 |/M 2|&lt;3.97  (7b)
 
     In this embodiment, the distortion and the chromatic aberration of magnification in various aberrations may be corrected by electrical image processing. Further, the rotational center position may be obtained based on a diameter of the aperture stop or distance map information. 
     Next, referring to  FIGS. 4 to 9 , a lens apparatus (zoom lens) in Embodiments 1 to 6 of the present invention will be described. Specific numerical values relating to the zoom lenses of Embodiments 1 to 6 are respectively indicated in Numerical examples 1 to 6 described below.  FIGS. 4 to 9  are cross-sectional views of the zoom lenses of Embodiments 1 to 6, respectively, in a focus state at infinity and in the close range. 
     In  FIG. 4  (Embodiment 1) and  FIG. 8  (Embodiment 5), symbol B 1  is a first lens unit having a negative refractive power, symbol B 2  is a second lens unit having a positive refractive power, and symbol B 3  is a positive refractive power. Symbol SP is an aperture stop, symbol GB is a glass block, and symbol IP is an image plane. In  FIG. 5  (Embodiment 2) and FIG. (Embodiment 4), symbol B 1  is a first lens unit having a positive refractive power, symbol B 2  is a second lens unit having a negative refractive power, and symbol B 3  is a positive refractive power. Symbol B 4  is a fourth lens unit having a negative refractive power, and symbol B 5  is a fifth lens unit having a positive refractive power. In  FIG. 6  (Embodiment 3) and  FIG. 9  (Embodiment 6), symbol B 1  is a first lens unit having a positive refractive power, symbol B 2  is a second lens unit having a negative refractive power, and symbol B 3  is a positive refractive power. Symbol B 4  is a fourth lens unit having a positive refractive power, and symbol B 5  is a fifth lens unit having a negative refractive power. 
     In zooming from the wide-angle end to the telephoto end in Embodiments 1 and 5, as indicated by arrows in  FIGS. 4 and 8 , the first lens unit B 1  moves toward the object side and the second lens unit B 2  moves to perform the zooming. Further, the third lens unit B 3  moves toward the object side to correct the fluctuation of the image plane due to the magnification variation. In Embodiment 2, in zooming from the wide-angle end to the telephoto end, as indicated by arrows in  FIG. 5 , the first lens unit B 1  to the fourth lens unit B 4  move to perform the zooming. Further, the fourth lens unit B 4  moves toward the image side to correct the fluctuation of the image plane due to the magnification variation. In Embodiment 4, in zooming from the wide-angle end to the telephoto end, as indicated by arrows in  FIG. 7 , the first lens unit B 1  to the fifth lens unit B 5  move to perform the zooming. Further, the fifth lens unit B 5  moves toward the object side to correct the fluctuation of the image plane due to the magnification variation. In Embodiment 6, in zooming from the wide-angle end to the telephoto end, as indicated by arrows in  FIG. 9 , the first lens unit B 1  to the fifth lens unit B 5  move to perform the zooming. Further, the fifth lens unit B 5  moves toward the image side to correct the fluctuation of the image plane due to the magnification variation. The image plane IP corresponds to an imaging plane of a solid-state image sensor (photoelectric conversion element) such as a CCD sensor and a CMOS sensor when used as an image capturing optical system of a video camera, a digital camera, or the like, and it corresponds to a film surface when used as an image capturing optical system of a silver salt film camera. 
       FIGS. 10A to 10C  relate to the zoom lens of Embodiment 1, and  FIG. 10A  is a lateral aberration diagram of a focus state at infinity at the wide-angle end.  FIG. 10B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 10C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 11A to 11C  relate to the zoom lens of Embodiment 2, and  FIG. 11A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end.  FIG. 11B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 11C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 12A to 12C  relate to the zoom lens of Embodiment 3, and  FIG. 12A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end.  FIG. 12B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 12C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 13A to 13C  relate to the zoom lens of Embodiment 4, and  FIG. 13A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end.  FIG. 13B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 13C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 14A to 14C  relate to the zoom lens of Embodiment 5, and  FIG. 14A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end.  FIG. 14B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 14C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 15A to 15C  relate to the zoom lens of Embodiment 6, and  FIG. 15A  is a lateral aberration diagram of a focus state at infinity at the wide-angle end.  FIG. 15B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position.  FIG. 15C  is a lateral aberration diagram of the focus state at infinity at the telephoto end. 
       FIGS. 16A to 16C  relate to the zoom lens of Embodiment 1, and  FIG. 16A  is a lateral aberration diagram of a focus state in the close range at the wide-angle end.  FIG. 16B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 16C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 17A to 17C  relate to the zoom lens of Embodiment 2, and  FIG. 17A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end.  FIG. 17B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 17C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 18A to 18C  relate to the zoom lens of Embodiment 3, and  FIG. 18A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end.  FIG. 18B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 18C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 19A to 19C  relate to the zoom lens of Embodiment 4, and  FIG. 19A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end.  FIG. 19B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 19C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 20A to 20C  relate to the zoom lens of Embodiment 5, and  FIG. 20A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end.  FIG. 20B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 20C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 21A to 21C  relate to the zoom lens of Embodiment 6, and  FIG. 21A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end.  FIG. 21B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position.  FIG. 21C  is a lateral aberration diagram of the focus state in the close range at the telephoto end. 
       FIGS. 22A to 22C  relate to the zoom lens of Embodiment 1, and  FIG. 22A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 22B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 22C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 23A to 23C  relate to the zoom lens of Embodiment 2, and  FIG. 23A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 23B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 23C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 24A to 24C  relate to the zoom lens of Embodiment 3, and  FIG. 24A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 24B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 24C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 25A to 25C  relate to the zoom lens of Embodiment 4, and  FIG. 25A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 25B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 25C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 26A to 26C  relate to the zoom lens of Embodiment 5, and  FIG. 26A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 26B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 26C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 27A to 27C  relate to the zoom lens of Embodiment 6, and  FIG. 27A  is a lateral aberration diagram of the focus state at infinity at the wide-angle end during the image stabilization.  FIG. 27B  is a lateral aberration diagram of the focus state at infinity at the middle zoom position during the image stabilization.  FIG. 27C  is a lateral aberration diagram of the focus state at infinity at the telephoto end during the image stabilization. 
       FIGS. 28A to 28C  relate to the zoom lens of Embodiment 1, and  FIG. 28A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization.  FIG. 28B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 28C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
       FIGS. 29A to 29C  relate to the zoom lens of Embodiment 2, and  FIG. 29A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization. FIG.  29 B is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 29C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
       FIGS. 30A to 30C  relate to the zoom lens of Embodiment 3, and  FIG. 30A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization.  FIG. 30B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 30C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
       FIGS. 31A to 31C  relate to the zoom lens of Embodiment 4, and  FIG. 31A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization.  FIG. 31B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 31C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
       FIGS. 32A to 32C  relate to the zoom lens of Embodiment 5, and  FIG. 32A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization.  FIG. 32B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 32C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
       FIGS. 33A to 33C  relate to the zoom lens of Embodiment 6, and  FIG. 33A  is a lateral aberration diagram of the focus state in the close range at the wide-angle end during the image stabilization.  FIG. 33B  is a lateral aberration diagram of the focus state in the close range at the middle zoom position during the image stabilization.  FIG. 33C  is a lateral aberration diagram of the focus state in the close range at the telephoto end during the image stabilization. 
     Each lateral aberration diagram illustrates an aberration at an image height in a Y axis direction (direction orthogonal to the optical axis (X axis)), and it is aberration diagrams at the image height of +70%, on-axis, and −70% in order from the top. Further, each lateral aberration diagram illustrates a meridional image plane, and dashed lines represent g lines and solid lines represent d lines. 
     Next, referring to  FIGS. 34A and 34B , an image stabilizer (image stabilization unit  103  and rotation mechanism unit  133 ) for changing the rotational center position based on the focus position and the zoom position in this embodiment will be described.  FIGS. 34A and 34B  are explanatory diagrams of the image stabilizer that changes the rotational center position based on the focus position and the zoom position. Each of  FIGS. 34A and 34B  illustrates the state of the focus position at infinity and in the close-up photographing (in the close range), respectively. 
     In this mechanism, several spherical bodies (balls) SB are sandwiched between a lens holder LH (holding member) and a fixed member LB adjacent to the lens holder LH. The lens holder LH can be moved by rolling of the spherical body SB with respect to the fixed member LB. In this time, by making a receiving surface of the fixed member LB with respect to the spherical body SB spherical, it is possible to rotate (turn) an image stabilization unit IS (corresponding to the image stabilization unit  103 ). Rotational center positions Lapi and Lapn (turning center) are spherical centers of the receiving surfaces at infinity and in close-up photographing, respectively. In zooming, the lens holder LH, the spherical body SB, and the fixed member LB may be integrally moved in a direction of an optical axis La. In this case, however, a distance from the lens holder LH to the rotational center position Lap is fixed independently of the magnification variation. 
     As illustrated in  FIG. 34B , in order to appropriately set the rotation center of the image stabilization unit IS when changing the focus position in the close-up photographing, with respect to an inclination amount of the image stabilization unit IS, it is necessary to set the rotational center position at which the eccentric aberration can be canceled for each focus position. Therefore, it is possible to suppress occurrence of the eccentric aberration at the zoom position and the focus position during the image stabilization, and thus satisfactory optical performance can be obtained during the image stabilization. 
     The manner of movement of the correction unit in each embodiment is not necessarily limited to the rotation along the spherical shape. Instead, it may be an aspherical shape slightly deviated from the spherical shape, for example, a paraboloid shape or an ellipsoid shape so that the rotational center position can be changed based on the focus position information and the zoom position information. In general, the occurrence of the eccentric aberration when a part of the lens units of the optical system is rotated around a predetermined rotation center is also indicated, in view of the aberration theory, similarly to the case of the parallel eccentricity described above. In this embodiment, paying attention to the fact that the eccentric aberration is generated by rotation, the remaining eccentric aberration is corrected satisfactorily by slightly rotating the eccentric lens unit having the parallel eccentricity. 
     This embodiment is configured to determine the rotation amount of minute rotation of the lens unit having the parallel eccentricity based on the magnification varying state of the magnification varying optical system and the movement amount of the parallel eccentricity, and the occurrence of the eccentric aberration is corrected to be sufficiently small depending on the respective states. In Numerical examples 1 to 6, application examples to imaging lenses are indicated, because it is realized assuming a case where the vibration compensation effect is most prominent as described above. Therefore, the technical idea of this embodiment can be suitably applied also to a magnification varying optical system having another configuration, that is, for example, a standard zoom lens or a zoom lens having a multi-unit configuration with high zoom ratio. 
     Preferably, the rotation amount of the slight rotation in this embodiment is configured to be determined depending on the magnification varying state of the magnification varying optical system and the drive amount of the parallel eccentricity. Accordingly, for the purpose of simplifying a control apparatus, for example, the control apparatus can be configured to rotate it by a predetermined amount for example only in the case of the middle focal length region, and adopts a method of only performing the parallel eccentric drive at the telephoto end and the wide-angle end and in the vicinity thereof and also performing an optimum design in this case. 
     Next, Numerical examples 1 to 6 corresponding to Embodiments 1 to 6, respectively, are indicated. In the numerical examples, symbol Ri is the radius of curvature of the i-th lens surface in order from the object side, symbol Di is the i-th lens thickness and air space from the object side, symbols Ni and vi are the refractive index and the Abbe number of the glass of the i-th lens from the object side. The optical axis is parallel to the X axis, and a traveling direction of light from the object side to the image plane side is defined as a positive direction. 
     Table 1 indicates numerical values of conditional expression (1) in each of Embodiment 1 and Embodiment 2. Table 2 indicates numerical values of conditional expression (1) in each of Embodiment 3 and Embodiment 4. Table 3 indicates numerical values of conditional expression (1) in each of Embodiment 5 and Embodiment 6. Table 4 indicates numerical values of conditional expressions (2) to (7) with respect to each of Embodiments 1 to 6. 
     Numerical Example 1 
     
       
         
           
               
             
               
                   
               
             
            
               
                 Unit mm 
               
               
                 Surface data 
               
            
           
           
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
               
               
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                 1* 
                 −61.013 
                 0.80 
                 1.82899 
                 39.4 
               
               
                 2* 
                   7.281 
                 2.70 
                   
                   
               
               
                 3 
                  13.057 
                 1.60 
                 1.95906 
                 17.5 
               
               
                 4 
                  26.234 
                 (variable) 
                   
                   
               
               
                 5 
                 ∞ 
                 0.00 
                   
                   
               
               
                 6(stop) 
                 ∞ 
                 (variable) 
                   
                   
               
               
                 7* 
                   6.743 
                 2.73 
                 1.76145 
                 48.1 
               
               
                 8* 
                  26.810 
                 0.20 
                   
                   
               
               
                 9 
                   7.604 
                 1.51 
                 1.48786 
                 70.2 
               
               
                 10 
                  15.201 
                 0.50 
                 1.85378 
                 24.3 
               
               
                 11 
                   4.242 
                 1.00 
                   
                   
               
               
                 12* 
                   7.645 
                 1.85 
                 1.69922 
                 50.3 
               
               
                 13 
                  59.503 
                 1.48 
                   
                   
               
               
                 14 
                 ∞ 
                 (variable) 
                   
                   
               
               
                 15 
                  22.031 
                 1.95 
                 1.49727 
                 69.1 
               
               
                 16 
                 −42.644 
                 (variable) 
                   
                   
               
               
                 17 
                 ∞ 
                 1.02 
                 1.51633 
                 64.1 
               
               
                 18 
                 ∞ 
                 1.19 
                   
                   
               
               
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 First surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −1.09191e−004 
                 A6 = 4.80266e−006 
               
               
                 A8 = −7.85071e−008 
                 A10 = 4.83401−010 
                   
               
            
           
           
               
            
               
                 Second surface 
               
            
           
           
               
               
               
            
               
                 K = −1.16909e+000 
                 A4 = 3.24927e−005 
                 A6 = 3.28902e−006 
               
               
                 A8 = 8.85143e−008 
                 A10 = −4.57017e−009 
                 A12 = 1.12740e−010 
               
               
                 A14 = −2.81746e−012 
                 A16 = 3.59134e−014 
                   
               
            
           
           
               
            
               
                 Seventh surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −2.44019e−004 
                 A6 = −4.74977e−006 
               
               
                 A8 = −5.07807e−008 
                 A10 = 2.68867e−009 
                   
               
            
           
           
               
            
               
                 Eighth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 =−1.97280e−004 
                 A6 = 1.13927e−006 
               
               
                 A8 = 2.59464e−007 
                 A10 =−1.78554e−009 
                   
               
            
           
           
               
            
               
                 Twelfth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −6.87784e−005 
                 A6 = 5.01732e−006 
               
               
                 A8 = 2.33868e−006 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Zoom ratio 
                 4.70 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 5.36 
                 15.09 
                 25.19 
               
               
                   
                 F number 
                 1.86 
                 3.65 
                 5.62 
               
               
                   
                 Angle of view 
                 35.75 
                 17.12 
                 10.46 
               
               
                   
                 Image height 
                 3.86 
                 4.65 
                 4.65 
               
               
                   
                 Total lens length 
                 45.49 
                 41.88 
                 51.30 
               
               
                   
                 BF 
                 4.85 
                 6.24 
                 5.26 
               
               
                   
                 d 4 
                 19.22 
                 1.73 
                 1.63 
               
               
                   
                 d 6 
                 1.05 
                 2.77 
                 −0.10 
               
               
                   
                 d14 
                 3.71 
                 14.48 
                 27.85 
               
               
                   
                 d16 
                 2.98 
                 4.38 
                 3.40 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 −12.64 
               
               
                 2 
                 7 
                 12.46 
               
               
                 3 
                 15 
                 29.51 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                 Correction lens system 
               
               
                 Number of start surface 7 Number of final surface 13 
               
               
                 Focal length of correction lens system fis +12.46 mm 
               
               
                 Thickness of correction lens system d 7.785 mm 
               
               
                 Wide-angle end 
               
               
                 Rotational center position of correction lens system 
               
               
                 (in focus position at infinity) 
               
               
                 R 173.28 mm 
               
               
                 Rotational center position of correction lens system 
               
               
                 (object distance in close-up photographing (first focus 
               
               
                 state)) 
               
               
                 R 17.53 mm 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.050 degree 
                 −0.497 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                 2.0 degrees 
                 2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                 Rotational center position of correction lens system 
               
               
                 (focus position at infinity) 
               
               
                 R 25.76 mm 
               
               
                 Rotational center position of correction lens ystem 
               
               
                 (object distance in close-up photographing (first focus 
               
               
                 state)) 
               
               
                 R 16.84 mm 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.150 degree 
                 −0.250 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                 0.5 degrees 
                 0.5 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                 Rotational center position of correction lens system 
               
               
                 (in focus position at infinity) 
               
               
                 R 18.09 mm 
               
               
                 Rotational center position of correction lens system 
               
               
                 (in object distance in close-up photographing (first 
               
               
                 focus state)) 
               
               
                 R 14.44 mm 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.200 degree 
                 −0.250 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                 0.4 degrees 
                 0.4 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     Numerical Example 2 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                   
                   
               
               
                   
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                   
                  1 
                 32.551 
                 0.70 
                 2.00069 
                 25.5 
               
               
                   
                  2 
                 23.359 
                 2.93 
                 1.49700 
                 81.6 
               
               
                   
                  3 
                 −180.163 
                 0.05 
                   
                   
               
               
                   
                  4 
                 25.014 
                 1.88 
                 1.59282 
                 68.6 
               
               
                   
                  5 
                 81.906 
                 (variable) 
                   
                   
               
               
                   
                  6* 
                 72.602 
                 0.50 
                 1.85135 
                 40.1 
               
               
                   
                  7* 
                 5.449 
                 2.45 
                   
                   
               
               
                   
                  8 
                 −11.520 
                 0.35 
                 1.71300 
                 53.9 
               
               
                   
                  9 
                 15.356 
                 0.19 
                   
                   
               
               
                   
                 10 
                 10.841 
                 1.30 
                 1.95906 
                 17.5 
               
               
                   
                 11 
                 66.873 
                 (variable) 
                   
                   
               
               
                   
                 12(stop) 
                 ∞ 
                 (variable) 
                   
                   
               
               
                   
                 13 
                 ∞ 
                 −0.70 
                   
                   
               
               
                   
                 14* 
                 5.026 
                 2.40 
                 1.49710 
                 81.6 
               
               
                   
                 15* 
                 −15.968 
                 0.91 
                   
                   
               
               
                   
                 16 
                 12.630 
                 0.40 
                 1.90366 
                 31.3 
               
               
                   
                 17 
                 4.459 
                 0.34 
                   
                   
               
               
                   
                 18 
                 5.837 
                 1.70 
                 1.61772 
                 49.8 
               
               
                   
                 19 
                 36.226 
                 (variable) 
                   
                   
               
               
                   
                 20* 
                 −45.487 
                 0.60 
                 1.53160 
                 55.8 
               
               
                   
                 21* 
                 12.014 
                 (variable) 
                   
                   
               
               
                   
                 22* 
                 9.110 
                 3.00 
                 1.53160 
                 55.8 
               
               
                   
                 23* 
                 −65.131 
                 (variable) 
                   
                   
               
               
                   
                 24 
                 ∞ 
                 0.80 
                 1.51633 
                 64.1 
               
               
                   
                 25 
                 ∞ 
                 1.34 
                   
                   
               
               
                   
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 Sixth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −4.58534e−004 
                 A6 = 1.61865e−005 
               
               
                 A8 = −2.35650e−007 
                   
                   
               
            
           
           
               
            
               
                 Seventh surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −4.40804e−004 
                 A6 = 8.63208e−006 
               
               
                 A8 = 6.81229e−007 
                   
                   
               
            
           
           
               
            
               
                 Fourteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −5.90924e−004 
                 A6 = −1.00349e−005 
               
            
           
           
               
            
               
                 Fifteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 6.12696e−004 
                 A6 = 8.10606e−006 
               
            
           
           
               
            
               
                 Twentieth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 4.29270e−003 
                 A6 = −5.74540e−004 
               
               
                 A8 = 2.56538e−005 
                   
                   
               
            
           
           
               
            
               
                 Twenty-first surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 4.75539e−003 
                 A6 = −5.71627e−004 
               
               
                 A8 = 2.37947e−005 
                   
                   
               
            
           
           
               
            
               
                 Twenty-second surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −2.02588e−004 
                 A6 = −1.59243e−006 
               
            
           
           
               
            
               
                 Twenty-third surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −9.71464e−004 
                 A6 = 1.68731e−005 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 23.40 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 4.60 
                 9.64 
                 107.76 
               
               
                   
                 F number 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 Angle of view 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 Image height 
                 3.22 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 51.40 
                 51.77 
                 67.31 
               
               
                   
                 BF 
                 3.07 
                 3.07 
                 3.07 
               
               
                   
                 d5 
                 0.37 
                 4.39 
                 23.83 
               
               
                   
                 d11 
                 14.74 
                 9.92 
                 0.49 
               
               
                   
                 d12 
                 5.30 
                 2.06 
                 1.10 
               
               
                   
                 d19 
                 3.61 
                 7.72 
                 7.87 
               
               
                   
                 d21 
                 5.04 
                 5.34 
                 11.67 
               
               
                   
                 d23 
                 1.20 
                 1.20 
                 1.20 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 35.26 
               
               
                 2 
                 6 
                 −5.37 
               
               
                 3 
                 13 
                 10.07 
               
               
                 4 
                 20 
                 −17.81 
               
               
                 5 
                 22 
                 15.25 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                   
               
               
                 Correction lens system 
               
               
                   
               
            
           
           
               
               
            
               
                 Number of start surface 
                  6 
               
               
                 Number of final surface 
                 11 
               
               
                 Focal length of correction lens system 
                 fis −5.37 mm 
               
               
                 Thickness of correction lens system 
                 d 4.792 mm 
               
               
                 Wide-angle end 
                   
               
               
                 Rotational center position of correction lens system 
                 R 314.25 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 9.14 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.038 degree 
                 −1.307 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.0 degrees 
                   2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 51.27 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 12.82 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.200 degree 
                 −0.800 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.5 degrees 
                   1.5 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 91.64 mm 
               
               
                 (in focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 30.56 mm 
               
               
                 (in object distance in close-up photographing (first 
                   
               
               
                 focus state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.050 degree 
                 −0.150 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   0.2 degrees 
                   0.2 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     Numerical Example 3 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                   
                   
               
               
                   
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                   
                  1 
                 32.903 
                 0.85 
                 1.94595 
                 18.0 
               
               
                   
                  2 
                 23.697 
                 3.39 
                 1.80420 
                 46.5 
               
               
                   
                  3 
                 239.525 
                 (variable) 
                   
                   
               
               
                   
                  4 
                 104.318 
                 0.67 
                 1.77250 
                 49.6 
               
               
                   
                  5 
                 9.356 
                 4.75 
                   
                   
               
               
                   
                  6* 
                 −18.059 
                 0.40 
                 1.76802 
                 49.2 
               
               
                   
                  7 
                 116.691 
                 0.10 
                   
                   
               
               
                   
                  8 
                 30.603 
                 1.20 
                 1.95906 
                 17.5 
               
               
                   
                  9 
                 717.339 
                 (variable) 
                   
                   
               
               
                   
                 10(stop) 
                 ∞ 
                 (variable) 
                   
                   
               
               
                   
                 11* 
                 15.470 
                 2.65 
                 1.76802 
                 49.2 
               
               
                   
                 12* 
                 −45.132 
                 0.10 
                   
                   
               
               
                   
                 13 
                 11.775 
                 2.52 
                 1.83481 
                 42.7 
               
               
                   
                 14 
                 230.169 
                 0.45 
                 1.85478 
                 24.8 
               
               
                   
                 15 
                 8.338 
                 (variable) 
                   
                   
               
               
                   
                 16 
                 30.731 
                 2.88 
                 1.49700 
                 81.5 
               
               
                   
                 17 
                 −17.952 
                 (variable) 
                   
                   
               
               
                   
                 18 
                 −22.355 
                 0.40 
                 1.85135 
                 40.1 
               
               
                   
                 19* 
                 444.580 
                 0.10 
                   
                   
               
               
                   
                 20 
                 21.426 
                 1.94 
                 1.63854 
                 55.4 
               
               
                   
                 21 
                 −542.945 
                 (variable) 
                   
                   
               
               
                   
                 22 
                 ∞ 
                 0.50 
                 1.51633 
                 64.1 
               
               
                   
                 23 
                 ∞ 
                 0.50 
                   
                   
               
               
                   
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 Sixth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −2.29119e−005 
                 A6 = 8.28299e−008 
               
               
                 A8 = −1.20260e−008 
                 A10 = 1.04155e−010 
                   
               
            
           
           
               
            
               
                 Eleventh surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −4.42389e−005 
                 A6 = 1.20948e−007 
               
            
           
           
               
            
               
                 Twelfth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 1.80026e−005 
                 A6 = 3.00368e−007 
               
               
                 A8 = −3.24113e−009 
                 A10 = 2.62387e−011 
                   
               
            
           
           
               
            
               
                 Nineteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 5.63992e−005 
                 A6 = −4.35159e−008 
               
               
                 A8 = −9.87071e−010 
                 A10 = 8.77351e−012 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 3.94 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 9.06 
                 16.39 
                 35.69 
               
               
                   
                 F number 
                 1.85 
                 2.54 
                 2.88 
               
               
                   
                 Angle of view 
                 35.52 
                 25.03 
                 12.46 
               
               
                   
                 Image height 
                 6.47 
                 7.65 
                 7.89 
               
               
                   
                 Total lens length 
                 59.14 
                 59.11 
                 67.94 
               
               
                   
                 BF 
                 8.90 
                 13.30 
                 12.40 
               
               
                   
                 d3 
                 0.31 
                 4.81 
                 15.34 
               
               
                   
                 d9 
                 12.26 
                 3.51 
                 0.70 
               
               
                   
                 d10 
                 5.34 
                 4.39 
                 0.31 
               
               
                   
                 d15 
                 8.38 
                 7.60 
                 6.58 
               
               
                   
                 d17 
                 1.40 
                 2.95 
                 10.04 
               
               
                   
                 d21 
                 8.07 
                 12.47 
                 11.57 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 50.83 
               
               
                 2 
                 4 
                 −10.03 
               
               
                 3 
                 11 
                 17.24 
               
               
                 4 
                 16 
                 23.26 
               
               
                 5 
                 18 
                 −115.71 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                   
               
               
                 Correction lens system 
               
               
                   
               
            
           
           
               
               
            
               
                 Number of start surface 
                 11 
               
               
                 Number of final surface 
                 15 
               
               
                 Focal length of correction lens system 
                 fis +17.24 mm 
               
               
                 Thickness of correction lens system 
                 d 5.711 mm 
               
               
                 Wide-angle end 
                   
               
               
                 Rotational center position of correction lens system 
                 R 114.77 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 71.48 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.131 degree 
                 −0.210 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.0 degrees 
                   2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 60.40 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 34.54 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.200 degree 
                 −0.350 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   1.0 degrees 
                   1.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 70.64 mm 
               
               
                 (in focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 28.19 mm 
               
               
                 (in object distance in close-up photographing (first 
                   
               
               
                 focus state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.100 degree 
                 −0.250 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   0.3 degrees 
                   0.3 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     Numerical Example 4 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                   
                   
               
               
                   
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                   
                  1 
                 91.764 
                 1.80 
                 1.91082 
                 35.3 
               
               
                   
                  2 
                 49.636 
                 4.38 
                 1.49700 
                 81.5 
               
               
                   
                  3 
                 −171.988 
                 0.18 
                   
                   
               
               
                   
                  4 
                 40.807 
                 3.01 
                 1.49700 
                 81.5 
               
               
                   
                  5 
                 126.402 
                 (variable) 
                   
                   
               
               
                   
                  6 
                 157.210 
                 0.95 
                 1.88300 
                 40.8 
               
               
                   
                  7 
                 8.768 
                 4.76 
                   
                   
               
               
                   
                  8 
                 −35.634 
                 0.70 
                 1.77250 
                 49.6 
               
               
                   
                  9 
                 30.470 
                 0.20 
                   
                   
               
               
                   
                 10 
                 17.427 
                 1.78 
                 1.95906 
                 17.5 
               
               
                   
                 11 
                 65.831 
                 (variable) 
                   
                   
               
               
                   
                 12(stop) 
                 ∞ 
                 (variable) 
                   
                   
               
               
                   
                 13* 
                 10.728 
                 2.99 
                 1.55332 
                 71.7 
               
               
                   
                 14* 
                 −2789.552 
                 1.65 
                   
                   
               
               
                   
                 15 
                 24.031 
                 0.60 
                 1.77250 
                 49.6 
               
               
                   
                 16 
                 11.205 
                 0.36 
                   
                   
               
               
                   
                 17 
                 15.956 
                 0.60 
                 2.00100 
                 29.1 
               
               
                   
                 18 
                 11.273 
                 2.37 
                 1.49700 
                 81.5 
               
               
                   
                 19 
                 −28.103 
                 (variable) 
                   
                   
               
               
                   
                 20 
                 31.461 
                 0.70 
                 1.70154 
                 41.2 
               
               
                   
                 21 
                 16.418 
                 (variable) 
                   
                   
               
               
                   
                 22 
                 23.373 
                 2.76 
                 1.80100 
                 35.0 
               
               
                   
                 23 
                 −20.628 
                 0.60 
                 1.84666 
                 23.8 
               
               
                   
                 24 
                 402.226 
                 (variable) 
                   
                   
               
               
                   
                 25 
                 ∞ 
                 0.50 
                 1.51633 
                 64.1 
               
               
                   
                 26 
                 ∞ 
                 0.49 
                   
                   
               
               
                   
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 Thirteenth surface 
               
            
           
           
               
               
               
            
               
                 K = −8.61394e−001 
                 A4 = 6.43510e−006 
                 A6 = 4.28494e−007 
               
               
                 A8 = −7.79572e−009 
                 A10 = 2.62605e−010 
                   
               
            
           
           
               
            
               
                 Fourteenth surface 
               
            
           
           
               
               
               
            
               
                 K = −3.11524e+006 
                 A4 = 4.30164e−006 
                 A6 = 5.58889e−007 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 41.65 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 5.00 
                 12.64 
                 208.24 
               
               
                   
                 F number 
                 3.50 
                 4.71 
                 7.07 
               
               
                   
                 Angle of view 
                 33.38 
                 17.04 
                 1.07 
               
               
                   
                 Image height 
                 3.29 
                 3.88 
                 3.88 
               
               
                   
                 Total lens length 
                 97.46 
                 94.86 
                 138.92 
               
               
                   
                 BF 
                 11.71 
                 19.65 
                 11.66 
               
               
                   
                 d5 
                 0.78 
                 13.96 
                 59.59 
               
               
                   
                 d11 
                 33.93 
                 16.43 
                 1.40 
               
               
                   
                 d12 
                 11.32 
                 4.43 
                 0.00 
               
               
                   
                 d19 
                 3.60 
                 4.14 
                 8.33 
               
               
                   
                 d21 
                 5.56 
                 5.69 
                 27.38 
               
               
                   
                 d24 
                 10.89 
                 18.82 
                 10.90 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 78.31 
               
               
                 2 
                 6 
                 −9.68 
               
               
                 3 
                 13 
                 19.63 
               
               
                 4 
                 20 
                 −49.90 
               
               
                 5 
                 22 
                 33.11 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                   
               
               
                 Correction lens system 
               
               
                   
               
            
           
           
               
               
            
               
                 Number of start surface 
                 13 
               
               
                 Number of final surface 
                 19 
               
               
                 Focal length of correction lens system 
                 fis +19.63 mm 
               
               
                 Thickness of correction lens system 
                 d 8.570 mm 
               
               
                 Wide-angle end 
                   
               
               
                 Rotational center position of correction lens system 
                 R 536.12 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 110.38 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.014 degree 
                 −0.068 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.0 degrees 
                   2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 153.35 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 51.18 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.050 degree 
                 −0.150 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   1.0 degrees 
                   1.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 347.00 mm 
               
               
                 (in focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 17.36 mm 
               
               
                 (in object distance in close-up photographing (first 
                   
               
               
                 focus state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.050 degree 
                 −1.000 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   0.2 degrees 
                   0.2 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     Numerical Example 5 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                   
                   
               
               
                   
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                   
                  1* 
                 −101.530 
                 1.00 
                 1.85135 
                 40.1 
               
               
                   
                  2* 
                 11.563 
                 2.59 
                   
                   
               
               
                   
                  3 
                 17.158 
                 1.68 
                 2.00272 
                 19.3 
               
               
                   
                  4 
                 34.327 
                 (variable) 
                   
                   
               
               
                   
                  5 
                 ∞ 
                 0.00 
                   
                   
               
               
                   
                  6(stop) 
                 ∞ 
                 (variable) 
                   
                   
               
               
                   
                  7* 
                 11.513 
                 2.45 
                 1.88202 
                 37.2 
               
               
                   
                  8* 
                 −158.863 
                 0.20 
                   
                   
               
               
                   
                  9 
                 12.241 
                 2.10 
                 1.88300 
                 40.8 
               
               
                   
                 10 
                 −46.577 
                 0.50 
                 1.85478 
                 24.8 
               
               
                   
                 11 
                 6.040 
                 2.24 
                   
                   
               
               
                   
                 12 
                 −17.396 
                 0.50 
                 1.80610 
                 33.3 
               
               
                   
                 13 
                 15.807 
                 2.21 
                 1.85135 
                 40.1 
               
               
                   
                 14* 
                 −13.421 
                 0.37 
                   
                   
               
               
                   
                 15 
                 ∞ 
                 (variable) 
                   
                   
               
               
                   
                 16 
                 44.289 
                 3.17 
                 1.59201 
                 67.0 
               
               
                   
                 17* 
                 −33.829 
                 (variable) 
                   
                   
               
               
                   
                 18 
                 ∞ 
                 1.09 
                 1.51633 
                 64.1 
               
               
                   
                 19 
                 ∞ 
                 1.61 
                   
                   
               
               
                   
                 Image plane 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 First surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −4.65961e−005 
                 A6 = 8.04510e−007 
               
               
                 A8 = −5.60379e−009 
                 A10 = −1.81010e−011 
                 A12 = 2.63709e−013 
               
            
           
           
               
            
               
                 Second surface 
               
            
           
           
               
               
               
            
               
                 K = 1.32245e−001 
                 A4 = −9.53359e−005 
                 A6 = −4.31947e−007 
               
               
                 A8 = 2.83384e−008 
                 A10 = −6.45846e−010 
                 A12 = 3.74432e−012 
               
            
           
           
               
            
               
                 Seventh surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −1.14474e−004 
                 A6 = −6.39836e−007 
               
               
                 A8 = −4.86347e−009 
                 A10 = −3.57225e−011 
                   
               
            
           
           
               
            
               
                 Eighth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −5.86274e−006 
                 A6 = 2.50952e−007 
               
               
                 A8 = −3.51576e−009 
                   
                   
               
            
           
           
               
            
               
                 Fourteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −7.75182e−005 
                 A6 = 1.40589e−007 
               
               
                 A8 = −1.78341e−007 
                   
                   
               
            
           
           
               
            
               
                 Seventeenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = 2.07327e−005 
                 A6 = −1.89462e−007 
               
               
                 A8 = 8.61167e−010 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 2.88 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 10.40 
                 15.85 
                 30.00 
               
               
                   
                 F number 
                 2.06 
                 3.75 
                 4.90 
               
               
                   
                 Angle of view 
                 32.34 
                 26.49 
                 14.75 
               
               
                   
                 Image height 
                 6.59 
                 7.90 
                 7.90 
               
               
                   
                 Total lens length 
                 52.05 
                 49.88 
                 55.62 
               
               
                   
                 BF 
                 7.45 
                 6.18 
                 5.03 
               
               
                   
                 d4 
                 17.46 
                 6.72 
                 1.44 
               
               
                   
                 d6 
                 0.00 
                 2.63 
                 −0.18 
               
               
                   
                 d15 
                 7.77 
                 14.97 
                 29.95 
               
               
                   
                 d17 
                 5.12 
                 3.85 
                 2.70 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 −21.26 
               
               
                 2 
                 7 
                 17.13 
               
               
                 3 
                 16 
                 32.89 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                   
               
               
                 Correction lens system 
               
               
                   
               
            
           
           
               
               
            
               
                 Number of start surface 
                  7 
               
               
                 Number of final surface 
                 15 
               
               
                 Focal length of correction lens system 
                 fis +17.13 mm 
               
               
                 Thickness of correction lens system 
                 d 10.198 mm 
               
               
                 Wide-angle end 
                   
               
               
                 Rotational center position of correction lens system 
                 R 138.07 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 18.33 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −122 degree 
                 −0.919 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.0 degrees 
                  2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 207.08 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 51.77 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.050 degree 
                 −0.200 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   1.0 degrees 
                   1.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 40.33 mm 
               
               
                 (in focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 13.44 mm 
               
               
                 (in object distance in close-up photographing (first 
                   
               
               
                 focus state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.100 degree 
                 −0.300 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   0.3 degrees 
                   0.3 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     Numerical Example 6 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                   
                   
               
               
                   
                 number 
                 r 
                 d 
                 nd 
                 vd 
               
               
                   
               
               
                   
                  1 
                 83.209 
                 1.30 
                 1.80610 
                 33.3 
               
               
                   
                  2 
                 50.503 
                 4.32 
                 1.49700 
                 81.5 
               
               
                   
                  3 
                 1785.592 
                 0.05 
                   
                   
               
               
                   
                  4 
                 59.632 
                 3.26 
                 1.49700 
                 81.5 
               
               
                   
                  5 
                 492.630 
                 (variable) 
                   
                   
               
               
                   
                  6 
                 200.113 
                 0.80 
                 1.88300 
                 40.8 
               
               
                   
                  7 
                 12.634 
                 5.72 
                   
                   
               
               
                   
                  8 
                 −31.799 
                 0.60 
                 1.59522 
                 67.7 
               
               
                   
                  9 
                 45.152 
                 0.07 
                   
                   
               
               
                   
                 10 
                 24.087 
                 2.20 
                 1.95906 
                 17.5 
               
               
                   
                 11 
                 76.803 
                 (variable) 
                   
                   
               
               
                   
                 12(stop) 
                 ∞ 
                 0.48 
                   
                   
               
               
                   
                 13* 
                 17.570 
                 2.24 
                 1.49710 
                 81.6 
               
               
                   
                 14 
                 120.735 
                 0.15 
                   
                   
               
               
                   
                 15 
                 16.100 
                 3.10 
                 1.60342 
                 38.0 
               
               
                   
                 16 
                 −31.145 
                 0.50 
                 1.95375 
                 32.3 
               
               
                   
                 17 
                 26.963 
                 (variable) 
                   
                   
               
               
                   
                 18* 
                 21.746 
                 2.63 
                 1.58313 
                 59.4 
               
               
                   
                 19 
                 −23.996 
                 0.06 
                   
                   
               
               
                   
                 20 
                 37.350 
                 0.50 
                 2.00100 
                 29.1 
               
               
                   
                 21 
                 12.934 
                 2.57 
                 1.51742 
                 52.4 
               
               
                   
                 22 
                 −35.766 
                 (variable) 
                   
                   
               
               
                   
                 23 
                 96.168 
                 0.50 
                 1.85135 
                 40.1 
               
               
                   
                 24* 
                 11.374 
                 0.98 
                   
                   
               
               
                   
                 25 
                 15.083 
                 1.88 
                 1.92286 
                 18.9 
               
               
                   
                 26 
                 22.778 
                 (variable) 
                   
                   
               
               
                   
                 27 
                 ∞ 
                 1.09 
                 1.51633 
                 64.1 
               
               
                   
                 Image plane 
                 ∞ 
                 1.66 
               
               
                   
               
            
           
           
               
            
               
                 Aspherical data 
               
               
                   
               
               
                 Thirteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −2.46391e−005 
                 A6 = −9.96151e−008 
               
            
           
           
               
            
               
                 Eighteenth surface 
               
            
           
           
               
               
               
            
               
                 K = 6.36520e+000 
                 A4 = −1.77282e−004 
                 A6 = −6.36937e−007 
               
               
                 A8 = 6.25782e−010 
                 A10 = −2.73714e−010 
                   
               
            
           
           
               
            
               
                 Twenty-fourth surface 
               
            
           
           
               
               
               
            
               
                 K = 0.00000e+000 
                 A4 = −2.31935e−005 
                 A6 = −1.67249e−007 
               
               
                 A8 = −3.90720e−009 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 23.66 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide-angle 
                 Middle 
                 Telephoto 
               
               
                   
               
               
                   
                 Focal length 
                 9.06 
                 27.49 
                 214.47 
               
               
                   
                 F number 
                 2.88 
                 4.66 
                 5.88 
               
               
                   
                 Angle of view 
                 37.68 
                 16.09 
                 2.12 
               
               
                   
                 Image height 
                 7.00 
                 7.93 
                 7.93 
               
               
                   
                 Total lens length 
                 93.54 
                 106.33 
                 146.99 
               
               
                   
                 BF 
                 7.55 
                 23.63 
                 38.82 
               
               
                   
                 d5 
                 1.31 
                 21.35 
                 68.24 
               
               
                   
                 d11 
                 32.99 
                 16.73 
                 1.47 
               
               
                   
                 d17 
                 9.01 
                 4.44 
                 2.52 
               
               
                   
                 d22 
                 8.40 
                 5.91 
                 1.67 
               
               
                   
                 d26 
                 5.17 
                 21.25 
                 36.44 
               
               
                   
               
            
           
           
               
            
               
                 Zoom unit data 
               
            
           
           
               
               
               
            
               
                 Unit 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 94.71 
               
               
                 2 
                 6 
                 −13.95 
               
               
                 3 
                 12 
                 46.49 
               
               
                 4 
                 18 
                 18.81 
               
               
                 5 
                 23 
                 −22.78 
               
               
                   
               
            
           
           
               
            
               
                 Data of correction lens in image stabilization 
               
               
                   
               
               
                 Correction lens system 
               
               
                   
               
            
           
           
               
               
            
               
                 Number of start surface 
                  6 
               
               
                 Number of final surface 
                 11 
               
               
                 Focal length of correction lens system 
                 fis −13.95 mm 
               
               
                 Thickness of correction lens system 
                 d 9.385 mm 
               
               
                 Wide-angle end 
                   
               
               
                 Rotational center position of correction lens system 
                 R 453.16 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 30.61 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.066 degree 
                 −0.977 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   2.0 degrees 
                   2.0 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Middle zoom position 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 135.18 mm 
               
               
                 (focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 13.52 mm 
               
               
                 (object distance in close-up photographing (first focus 
                   
               
               
                 state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.100 degree 
                 −1.000 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                   0.7 degrees 
                   0.7 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
           
               
            
               
                 Telephoto end 
               
               
                   
               
            
           
           
               
               
            
               
                 Rotational center position of correction lens system 
                 R 766.85 mm 
               
               
                 (in focus position at infinity) 
                   
               
               
                 Rotational center position of correction lens system 
                 R 307.11 mm 
               
               
                 (in object distance in close-up photographing (first 
                   
               
               
                 focus state)) 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                 (infinity) 
                 (first focus state) 
               
               
                   
               
               
                   
                 Tilt angle of Correction 
                 −0.020 degree 
                 −0.050 degree 
               
               
                   
                 lens system 
                   
                   
               
               
                   
                 Vibration correction 
                  0.25 degrees 
                  0.25 degrees 
               
               
                   
                 angle 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                   
                 Embodimen 1 
                 Embodiment 2 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Wide- 
                   
                 Tele- 
                 Wide- 
                   
                 Tele- 
               
               
                   
                 Angle 
                   
                 photo 
                 Angle  
                   
                 photo 
               
               
                   
                 End 
                 Middle 
                 End 
                 End 
                 Middle 
                 End 
               
               
                   
               
               
                 Conditional 
                 20.005 
                 1.146 
                 0.469 
                 62.915 
                 8.024 
                 12.746 
               
               
                 Expression (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                   
                 Embodiment 3 
                 Embodiment 4 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Wide- 
                   
                 Tele- 
                 Wide- 
                   
                 Tele- 
               
               
                   
                 Angle 
                   
                 photo 
                 Angle 
                   
                 photo 
               
               
                   
                 End 
                 Middle 
                 End 
                 End 
                 Middle 
                 End 
               
               
                   
               
               
                 Conditional 
                 7.524 
                 4.528 
                 7.433 
                 51.338 
                 11.922 
                 38.464 
               
               
                 Expression (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                   
                 Embodiment 5 
                 Embodiment 6 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Wide- 
                   
                 Tele- 
                 Wide- 
                   
                 Tele- 
               
               
                   
                 Angle 
                   
                 photo 
                 Angle 
                   
                 photo 
               
               
                   
                 End 
                 Middle 
                 End 
                 End 
                 Middle 
                 End 
               
               
                   
               
               
                 Conditional 
                 11.542 
                 15.230 
                 2.637 
                 46.563 
                 12.943 
                 48.986 
               
               
                 Expression (1) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                   
                 Embodiment 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Conditional 
                 2.358 
                 7.658 
                 5.608 
                 15.665 
                 2.044 
                 10.449 
               
               
                 Expression (2) 
                   
                   
                   
                   
                   
                   
               
               
                 Conditional 
                 4.783 
                 9.105 
                 1.702 
                 14.159 
                 2.625 
                 9.820 
               
               
                 Expression (3) 
                   
                   
                   
                   
                   
                   
               
               
                 Conditional 
                 0.560 
                 0.869 
                 0.441 
                 1.000 
                 0.288 
                 0.552 
               
               
                 Expression (4) 
                   
                   
                   
                   
                   
                   
               
               
                 Conditional 
                 2.324 
                 1.166 
                 1.902 
                 3.926 
                 1.647 
                 1.539 
               
               
                 Expression (5) 
                   
                   
                   
                   
                   
                   
               
               
                 Conditional 
                 4.580 
                 1.639 
                 0.689 
                 3.471 
                 1.900 
                 1.486 
               
               
                 Expression (6) 
                   
                   
                   
                   
                   
                   
               
               
                 Conditional 
                 0.237 
                 2.108 
                 1.408 
                 2.389 
                 0.181 
                 3.968 
               
               
                 Expression (7) 
               
               
                   
               
            
           
         
       
     
     According to each embodiment, a lens apparatus and an image capturing apparatus capable of performing image stabilization while maintaining satisfactory optical performance can be provided. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     The lens apparatus (image capturing optical system) of each embodiment is not limited to a zoom lens, and can be applied also to a fixed focal length lens or the like. Further, the lens apparatus of each embodiment can be applied to various image capturing apparatuses such as a digital still camera, a video camera, a surveillance camera, a broadcasting camera, an interchangeable lens, and a silver salt photography camera. 
     This application claims the benefit of Japanese Patent Application No. 2016-130289, filed on Jun. 30, 2016, which is hereby incorporated by reference herein in its entirety.