Patent Publication Number: US-6906867-B2

Title: Zoom optical system and imaging apparatus using the same

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
   This is a continuation-in-part of application Ser. No. 10/411,154, filed Apr. 11, 2003, which is abandoned. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a zoom optical system and an imaging apparatus using the zoom optical system. 
   2. Description of the Related Art 
   Requirement for compact and thin design of electronic imaging apparatuses has been more and more urgent in recent years. To meet the requirement, it is very important to shorten the total length of optical systems used in imaging apparatuses, such as a photographing optical system, a finder optical system, etc. 
   Regarding such an optical system, there is a limit to shorten the total length by reducing the number of constituent elements. Therefore, compact and thin design of the optical system in its entirety is aimed at by folding the optical system using mirrors. Furthermore, in folding the optical system, a space for a portion of folding is required. In addition, having a variator group that has a magnification varying function, a compensator group that compensates for a shift of an image surface caused by the magnification change and for aberrations, a focusing group that performs focusing on an object, etc, a zoom optical system is configured to perform magnification change and focusing by shifting, of these len&#39;s groups, predetermined lens groups along the optical axis, and thus a space for the movement of the lens groups is needed. 
   As an optical system thus configured, for example, each of Japanese Patent Application Preliminary Publication (KOKAI) No. Hei 8-248318 and Japanese Patent Application Preliminary Publication (KOKAI) No. Hei 11-220646 discloses an imaging apparatus using a zoom optical system that is given a compact size with the path of rays being folded back. 
   In such a zoom optical system, in magnification change or focusing, a motor is driven to move lenses. 
   SUMMARY OF THE INVENTION 
   A zoom optical system according to the present invention includes at least two optical-element groups and a variable optical-property optical element. The two optical-element groups are movable in a magnification change and have a magnification varying function or a compensating function for compensating for a shift of an image surface caused by the magnification change. The variable optical-property optical element has a focusing function and is disposed on the image side of the optical-element groups having the magnification varying function. 
   Also, in the zoom optical system according to the present invention, the optical-element groups includes an optical-element group that is disposed on the most object side, and the variable optical-property optical element is arranged in the optical-element group that is disposed on the most object side. 
   Also, according to the present invention, the variable optical-property optical element is provided with a rotationally asymmetric curved surface having a function for compensating for decentered aberrations. 
   Also, an imaging apparatus according to the present invention is provided with the zoom optical system set forth above. 
   These and other features and advantages of the present invention will become apparent from the following detailed description when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1A  is a sectional view that shows a lens configuration of a zoom optical system according to the first embodiment of the present invention at the wide-angle end. 
       FIG. 1B  is a sectional view that shows a lens configuration of the zoom optical system according to the first embodiment of the present invention at the intermediate position. 
       FIG. 1C  is a sectional view that shows a lens configuration of the zoom optical system according to the first embodiment of the present invention at the telephoto end. 
       FIG. 2A  is a sectional view that shows a lens configuration of a zoom optical system according to the second embodiment of the present invention at the wide-angle end. 
       FIG. 2B  is a sectional view that shows a lens configuration of the zoom optical system according to the second embodiment of the present invention at the intermediate position. 
       FIG. 2C  is a sectional view that shows a lens configuration of the zoom optical system according to the second embodiment of the present invention at the telephoto end. 
       FIG. 3A  is a sectional view that shows a lens configuration of a zoom optical system according to the third embodiment of the present invention at the wide-angle end. 
       FIG. 3B  is a sectional view that shows a lens configuration of the zoom optical system according to the third embodiment of the present invention at the intermediate position. 
       FIG. 3C  is a sectional view that shows a lens configuration of the zoom optical system according to the third embodiment of the present invention at the telephoto end. 
       FIG. 4A  is a sectional view that shows a lens configuration of a zoom optical system according to the fourth embodiment of the present invention at the wide-angle end. 
       FIG. 4B  is a sectional view that shows a lens configuration of the zoom optical system according to the fourth embodiment of the present invention at the intermediate position. 
       FIG. 4C  is a sectional view that shows a lens configuration of the zoom optical system according to the fourth embodiment of the present invention at the telephoto end. 
       FIG. 5  is sectional view that shows the state where the optical system of the zoom optical system according to the third embodiment of the present invention is compactly folded in storage. 
       FIG. 6A  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is extreme in negative direction, or −22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6B  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is extreme in negative direction, or −22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6C  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6D  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6E  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6F  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6G  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6H  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6I  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is extreme in positive direction, or 22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6J  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is extreme in positive direction, or 22.4° under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6K  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is zero under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 6L  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 28.8° and Y-direction field angle is zero under the condition where the object distance is infinite at the wide-angle end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7A  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is extreme in negative direction, or −13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7B  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is extreme in negative direction, or −13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7C  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7D  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7E  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7F  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7G  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7H  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7I  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is extreme in positive direction, or 13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7J  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is extreme in positive direction, or 13.3° under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7K  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is zero under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 7L  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 17.5° and Y-direction field angle is zero under the condition where the object distance is infinite at the intermediate position in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8A  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is extreme in negative direction, or −9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8B  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is extreme in negative direction, or −9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8C  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8D  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8E  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8F  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is zero under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8G  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8H  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8I  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is extreme in positive direction, or 9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8J  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is extreme in positive direction, or 9.37° under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8K  is an aberration diagram that shows Y-direct-ion lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is zero under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 8L  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 12.4° and Y-direction field angle is zero under the condition where the object distance is infinite at the telephoto end in the zoom optical system according to the first embodiment of the present invention. 
       FIG. 9  is a schematic configuration diagram of a digital camera&#39;s Keplerian finder using a variable optical-property mirror as the variable mirror applicable to the zoom optical system according to the present invention. 
       FIG. 10  is a schematic configuration diagram that shows another example of the deformable mirror  409  applicable as the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 11  is an explanatory diagram that shows one aspect of electrodes used in the deformable mirror shown in FIG.  10 . 
       FIG. 12  is an explanatory diagram that shows another aspect of electrodes used in the deformable mirror shown in FIG.  10 . 
       FIG. 13  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 14  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 15  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as the deformable mirror used in to the zoom optical system according to the present invention. 
       FIG. 16  is an explanatory diagram that shows the winding density of a thin-film coil  427  in the example of FIG.  15 . 
       FIG. 17  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 18  is an explanatory diagram that shows one arrangement example of the coils  427  in the example of FIG.  17 . 
       FIG. 19  is an explanatory diagram that shows another arrangement example of the coils  427  in the example of FIG.  17 . 
       FIG. 20  is an explanatory diagram that shows an arrangement of permanent magnets  426  that is suitable to the case where the coils  427  are arranged as shown in  FIG. 19  in the example of FIG.  15 . 
       FIG. 21  is a schematic configuration diagram of an imaging system using the deformable mirror  409 , as the deformable mirror applicable to the imaging apparatus using the zoom optical system according to the present invention. 
       FIG. 22  is a schematic configuration diagram that shows still another example of the deformable mirror  188  applicable as the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 23  is a schematic configuration diagram that shows one example of the micropump applicable to the deformable mirror used in the zoom optical system according to the present invention. 
       FIG. 24  is a diagram that shows a variable focus mirror, to which the variable focus lens is applied, applicable to the zoom optical system according to the present invention. 
       FIG. 25  is a schematic configuration diagram that shows still another example of the deformable mirror applicable to the deformable mirror used in the zoom optical system according to the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Preceding the description of the embodiments, the contents of the invention set forth in this specification is summarized below. 
   (1) A zoom optical system according to the present invention has at least two lens groups that have a magnification varying function or a compensating function for compensating for a shift of an image surface caused by the magnification change and that are movable in the magnification change, and a deformable mirror having a focusing function, wherein the deformable mirror is disposed on the image side of the lens groups having the magnification varying function. 
   If the focusing function is given to the deformable mirror, it is not necessary to provide a lens moving system including a motor, a driving circuit and so on required for focusing, and thus compact and low-cost design of the zoom optical system can be achieved. In addition, since its reflecting surface is instantly deformable, it is possible to realize an imaging apparatus that performs focusing at a very high speed with a low operation noise and a small power consumption. 
   Also, if the deformable mirror is disposed on the image side of the at least two lens groups that have a magnification changing function or a compensating function for compensating for a shift of the image surface and that are movable during the magnification change, since height of rays incident on the deformable mirror from the wide-angle end position through the telephoto end position is limited low, the deformable mirror is allowed to be constructed very small. Therefore, cost reduction can be achieved. 
   (2) Also, in the zoom optical system according to the present invention, the deformable mirror is arranged in the most image-side lens group. 
   In general, a zoom lens in an imaging system is required to substantially be telecentric on the image side. However, if a configuration is made so that the deformable mirror is arranged in the most image-side lens group, it is possible to minimize, in a magnification change, fluctuation of incident angle of a ray incident on the deformable mirror. 
   For example, if the deformable mirror is inserted on the object side of a lens group having a magnification varying function, angle of a ray incident on the deformable mirror greatly fluctuates in a magnification change. As a result, it is difficult to suppress fluctuation, caused by the magnification change, of decentered coma generated at the deformable mirror. On the other hand, if the configuration is made so that the deformable mirror is arranged in the most image-side lens group as in the present invention, it is possible to suppress fluctuation of the incident angle to be small and accordingly fluctuation of decentered coma to be very small. Consequently, it is possible to perform focusing while keeping good imaging performance in every condition during the magnification change. 
   (3) Also, in the zoom optical system according to the present invention, the deformable mirror is provided with a rotationally asymmetric curved surface that has a function for compensating for decentered aberrations. 
   If such a surface is provided, it is possible to suppress decentered coma generated at the deformable mirror to be very small. 
   (4) Also, in the zoom optical system according to the present invention, it is preferable that a distance from the exit pupil position as viewed from the optical system that is on the object side of the deformable mirror to the deformable mirror satisfies the following conditions (1-1) and (2-1):
 
0.5 &lt;EX   W   /f   W &lt;50.0  (1-1)
 
0.5 &lt;EX   T   /f   T &lt;50.0  (2-1)
 
where EX W  is a physical distance from the exit pupil position of the optical system as viewed from the deformable mirror to the deformable mirror at the wide-angle end, EX T  is a physical distance from the exit pupil position of the optical system as viewed from the deformable mirror to the deformable mirror at the telephoto end, f W  is a focal length of the entire system at the wide-angle end, and f T  is a focal length of the entire system at the telephoto end.
 
   Conditions (1-1) and (1-2) are conditions that limit angles of rays incident on the deformable mirror, for maintaining incident angles of rays, from axial ones to off-axial ones, as constant as possible. 
   If the lower limit of Condition (1-1) or (2-1) is not reached, the exit pupil position as viewed from the deformable mirror is so close that telecentricity fails, and accordingly, incident angles on the deformable mirror greatly vary from an axial position to an off-axial position. As a result, a large amount of decentered coma is generated, which is not preferable. On the other hand, if the upper limit value of Condition (1-1) or (2-1) is exceeded, while generation of decentered coma can be made small, it is necessary to configure the variable magnification lens system to achieve complete telecentricity, therefor with a large number of lens elements. Such a configuration prevents compact design and thus is not preferable. 
   (5) Also, in the zoom optical system according to the present invention, it is much preferable that the distance from the exit pupil position as viewed from the optical system that is on the object side of the deformable mirror to the deformable mirror satisfies the following conditions (1-2) and (2-2):
 
1.0 &lt;EX   W   /f   W &lt;40.0  (1-2)
 
1.0 &lt;EX   T   /f   T &lt;40.0  (2-2)
 
   If Conditions (1-2) and (2-2) are satisfied in place of Conditions (1-1) and (2-1), it is possible to better achieve number reduction of lens elements and size reduction, while suppressing generation of decentered coma to be small. 
   (6) Also, in the zoom optical system according to the present invention, it is still much preferable that the distance from the exit pupil position as viewed from the optical system that is on the object side of the deformable mirror to the deformable mirror satisfies the following conditions (1-3) and (2-3):
 
2.0 &lt;EX   W   /f   W &lt;30.0  (1-3)
 
2.0 &lt;EX   T   /f   T &lt;30.0  (2-3)
 
   If Conditions (1-3) and (2-3) are satisfied in place of Conditions (1-2) and (2-2), it is possible most effectively to achieve number reduction of lens elements and size reduction, while suppressing generation of decentered coma to be small. 
   (7) Also, in the zoom optical system according to the present invention, it is preferable that magnification ξ W  of a group of lenses arranged between the deformable mirror and the image surface satisfies the following condition (3-1): 
    0.3&lt;ξ W &lt;0.9  (3-1) 
   Condition (3-1) is a condition for suppressing the amount of deformation of the deformable mirror to be small. If the lower limit of Condition (3-1) is not reached, while the focal length of the group of lenses arranged between the deformable mirror and the image surface is short, to allow the amount of deformation of the deformable mirror to be small, aberrations generated in the group of lenses arranged between the deformable mirror and the image surface would become large, to necessitate, for the purpose of moderating the aberrations, a configuration including a plurality of lens elements, which is not preferable. In addition, compact design of the entire imaging system cannot be attained. On the other hand, if the upper limit of Condition (3-1) is exceeded, the amount of deformation of the deformable mirror cannot be set small, specifically, a large amount of deformation is necessary at the telephoto end, and thus such a configuration is not preferable. 
   In the range specified by Condition (3-1), it is possible to set the amount of deformation small while keeping good imaging performance. 
   (8) Also, in the zoom optical system according to the present invention, it is much preferable that the magnification ξ W  of the group of lenses arranged between the deformable mirror and the image surface satisfies the following condition (3-2):
 
0.4&lt;ξ W &lt;0.8  (3-2)
 
   If Condition (3-2) is satisfied in place of Condition (3-1), it is possible more effectively to set the amount of deformation small while keeping good imaging performance. 
   (9) Also, in the zoom optical system according to the present invention, it is still much preferable that the magnification ξ W  of the group of lenses arranged between the deformable mirror and the image surface satisfies the following condition (3-3):
 
0.5&lt;ξ W &lt;0.7  (3-3)
 
   If Condition (3-3) is satisfied in place of Condition (3-2), it is possible still more effectively to set the amount of deformation small while keeping good imaging performance. 
   (10) Also, it is preferable that the zoom optical system according to the present invention satisfies the following condition (4-1):
 
−5.0&lt;( f   a   /f   b )× f   W &lt;−0.5  (4-1)
 
where f a  is a focal length, at the wide-angle end, of a group of lenses arranged on the object side of the aperture stop, f b  is a focal length, at the wide-angle end, of a group of lenses arranged on the image side of the aperture stop, and f W  is a focal length, at the wide-angle end, of the entire optical system.
 
   Condition (4-1) limits the power ratio of the front group to the rear group, with the aperture stop being interposed between, of the zoom optical system, as normalized by the focal length of the entire system, and is a condition for securing a space for inserting the deformable mirror. 
   If the lower limit of Condition (4-1) is not reached, it forms a weak retrofocus system, which has no space for the deformable mirror to be inserted therein and thus is not preferable. On the other hand, if the upper limit of Condition (4-1) is exceeded, while the configuration enhances the degree of retrofocus characteristic of the system and thus is advantageous in view of securing the space, it degrades aberration performance such as coma, chromatic aberration of magnification, and distortion because of the asymmetric power distribution with respect to the aperture stop, and thus is not preferable. In the range specified by Condition (4-1), it is possible to secure a space for the deformable mirror without degrading the aberrations. 
   (11) Also, it is much preferable that the zoom optical system according to the present invention satisfies the following condition (4-2):
 
−4.0&lt;( f   a   /f   b )× f   W &lt;−0.8  (4-2)
 
   If Condition (4-2) is satisfied in place of Condition (4-1), it is possible more effectively to secure a space for the deformable mirror without degrading the aberrations. 
   (12) Also, it is still much preferable that the zoom optical system according to the present invention satisfies the following condition (4-3):
 
−3.0&lt;( f   a   /f   b )× f   W &lt;−1.0  (4-3)
 
   If Condition (4-3) is satisfied in place of Condition (4-2), it is possible still more effectively to secure a space for the deformable mirror without degrading the aberrations. 
   (13) Also, it is preferable that the zoom optical system according to the present invention satisfies the following condition (5-1):
 
 D&lt; 20.0 mm  (5-1)
 
where D is an effective diameter of the deformable mirror.
 
   A deformable mirror having an effective diameter for rays greater than the upper limit of Condition (5-1) involves a large amount of deformation of the surface shape, to cause difficulty in controlling the surface shape, as well as to prevent low-cost production. In addition, even if surface shape control is possible, energy required for deformation is large and thus is not appropriate in view of power saving. 
   (14) Also, it is much preferable that the zoom optical system according to the present invention satisfies the following condition (5-2):
 
 D&lt; 15.0 mm  (5-2)
 
   Satisfaction of Condition (5-2) in place of Condition (5-1) is more effective in surface shape control, low-cost production, and power saving. 
   (15) Also, it is still much preferable that the zoom optical system according to the present invention satisfies the following condition (5-3):
 
 D&lt; 12.0 mm  (5-3)
 
   Satisfaction of Condition (5-3) in place of (5-2) is still more effective in surface shape control, low-cost production, and power saving. 
   (16) Also, an imaging apparatus according to the present invention is configured to use a zoom optical system that includes, in order from the object side, a first group with a negative power, a second group with a positive power, a third group with a positive power, and a fourth group with a positive power, at least one of the second group and the third group having a magnification varying function, wherein the zoom optical system is provided with at least one of the itemized features set forth above. 
   (17) Also, an imaging apparatus according to the present invention is configured to use a zoom optical system that includes, in order from the object side, a first group with a negative power, a second group with a positive power, and a third group with a positive power, at least the second group having a magnification varying function, wherein the zoom optical system is provided with at least one of the itemized features set forth above. 
   The zoom optical systems used in the imaging apparatuses thus configured are based on a type of zoom lens system having a first group with a negative refracting power and a compound system including a second and subsequent groups with a positive refracting power, which type is typical as a photographing optical system of a digital camera. 
   (18) Also, an imaging apparatus according to the present invention is configured to use a zoom optical system that includes, in order from the object side, a first group with a positive power, a second group with a negative power, a third group with a positive power, and a fourth group with a positive power, at least the second group having a magnification varying function, wherein the zoom optical system is provided with at least one of the itemized features above. 
   (19) Also, in the zoom optical system according to the present invention, it is preferable that an angle Φ of turning of an optical axis caused by the deformable mirror satisfies the following condition:
 
70°≦Φ≦110°
 
   (20) Also, an imaging apparatus according to the present invention is configured to use any one of the zoom optical systems set forth above. 
   (21) Also, in a zoom optical system and an imaging apparatus provided with a zoom optical system according to the present invention, it is preferable to use a deformable mirror that is driven by an electrostatic force, an electromagnetic force, a piezoelectric effect or fluid. 
   (22) Also, in a zoom optical system and an imaging apparatus provided with a zoom optical system according to the present invention, an ordinary mirror maybe used in place of the deformable mirror. 
   Also, if the deformable mirror used in the zoom optical system according to the present invention is configured to be deformed into such a shape as to compensate for degradation of optical performance caused by fabrication error of other lenses, the number of defective products can be drastically reduced, to suppress fabrication cost. 
   Also, arranging the image pickup element so that its short side is parallel with the direction of decentration of the deformable mirror can reduce the effective diameter for rays of the deformable mirror, as well as is advantageous in view of compensation for aberrations, and thus is desirable. On the other hand, in view of design convenience of digital camera etc, arrangement may be made so that the long side of the image pickup element is parallel with the direction of decentration of the deformable mirror. 
   In addition, in the zoom optical system according to the present invention, a configuration in which the deformable mirror has a compensator function with pan-focus operation being performed via other lenses facilitates compact and low-cost design and thus is favorable. 
   A free-formed surface used in the present invention is defined by the following equation (a) where Z axis appearing therein is the axis of the free-formed surface: 
             Z   =         cr   2     /     [     1   +     √     {     1   -       (     1   +   k     )     ⁢     c   2     ⁢     r   2         }         ]       +       ∑     j   =   2     66     ⁢           ⁢       c   j     ⁢     x   m     ⁢     Y   n                   (   a   )             
 
The first term of Equation (a) expresses the spherical surface component. The second term of Equation (a) expresses the free-formed surface component. In the term of the spherical surface component, c is a curvature at the vertex, k is a conic constant, r=√(X 2 +Y 2 ), and N is an integer equal to or greater than 2.
 
   The term of the free-formed surface component is expanded as shown in the following equation: 
                 ∑     j   =   2     66     ⁢           ⁢       C   j     ⁢     X   m     ⁢     Y   n         =       ⁢         C   2     ⁢   X     +       C   3     ⁢   Y     +                     ⁢         C   4     ⁢     X   2       +       C   5     ⁢   XY     +       C   6     ⁢     Y   2       +                     ⁢         C   7     ⁢     X   3       +       C   8     ⁢     X   2     ⁢   Y     +       C   9     ⁢     XY   2       +       C   10     ⁢     Y   3       +                     ⁢         C   11     ⁢     X   4       +       C   12     ⁢     X   3     ⁢   Y     +       C   13     ⁢     X   2     ⁢     Y   2       +       C   14     ⁢     XY   3       +       C   15     ⁢     Y   4       +                     ⁢         C   16     ⁢     X   5       +       C   17     ⁢     X   4     ⁢   Y     +       C   18     ⁢     X   3     ⁢     Y   2       +       C   19     ⁢     X   2     ⁢     Y   3       +       C   20     ⁢     XY   4       +       C   21     ⁢     Y   5       +                     ⁢         C   22     ⁢     X   6       +       C   23     ⁢     X   5     ⁢   Y     +       C   24     ⁢     X   4     ⁢     Y   2       +       C   25     ⁢     X   3     ⁢     Y   3       +       C   26     ⁢     X   2     ⁢     Y   4       +       C   27     ⁢     XY   5       +       C   28     ⁢     Y   6       +                     ⁢         C   29     ⁢     X   7       +       C   30     ⁢     X   6     ⁢   Y     +       C   31     ⁢     X   5     ⁢     Y   2       +       C   32     ⁢     X   4     ⁢     Y   3       +       C   33     ⁢     X   3     ⁢     Y   4       +       C   34     ⁢     X   2     ⁢     Y   5       +       C   35     ⁢     XY   6       +       C   36     ⁢     Y   7                   
 
where C j  (j is integer equal to or greater than 2) is a coefficient.
 
   In general, a free-formed surface as expressed above does not have a plane of symmetry along X-Z plane or along Y-Z plane. However, upon all terms with odd-numbered powers of X being nullified, the free-formed surface can define only one plane of symmetry that is parallel to Y-Z plane. 
   The free-formed surface, which has a rotationally asymmetric curvature, can be defined in another manner by Zernike polynomial, also. The configuration of the surface is defined by the following equations (b). Z axis appearing in Equations (b) represents the axis of Zernike polynomial. The rotationally asymmetric surface is defined by height in Z axis, in terms of polar coordinate, in reference to X-Y plane, where R is a distance from Z axis in X-Y plane, and A is an azimuth about Z axis expressed by a revolution angle from Z axis:
 
 X=R ×cos( A )
 
 Y=R ×sin( A )
 
 Z=D   2 
 
+D 3   R  cos( A )+ D   4   R  sin( A )+
 
 D   5   R   2  cos(2 A )+ D   6 ( R   2 −1)+ D   7   R   2  sin(2 A )+
 
 D   8   R   3  cos(3 A )+ D   9 (3 R   3 −2 R )cos( A )+ D   10 (3 R   3 −
 
 2   R )sin( A )+ D   11   R   3  sin(3 A )+
 
 D   12   R   4  cos(4 A )+ D   13 (4 R   4 −3 R   2 )cos(2 A )+ D   14 (6
 
R 4 −6 R   2 +1)+
 
 D   15 (4 R   4 −3 R   2 )sin(2 A )+ D   16   R   4  sin(4 A )+
 
 D   17   R   5  cos(5 A )+ D   18 (5 R   5 −4 R   3 )cos(3 A )+ D   19 (10
 
R 5 −12 R   3 +3 R )cos( A )+
 
 D   20 (10 R   5 −12 R   3 +3 R )sin( A )+ D   21 (5 R   5 −4 R   3 )sin(3
 
A)+ D   22   R   5  sin(5 A )+
 
 D   23   R   6  cos(6 A )+ D   24 (6 R   6 −5 R   4 )cos(4 A )+ D   25 (15 R 
 
 6 −20 R   4 +6 R   2 )cos(2 A )+
 
 D   26 (20 R   6 −30 R   4 +12 R   2 −1)+ D   27 (15 R   6 −20 R   4 +6
 
R 2 )sin(2 A )+
 
 D   28 (6 R   6 −5 R   4 )sin(4 A )+ D   29   R   6  sin(6 A )  (b)
 
It is noted that D m  (m is integer equal to or greater than 2) is a coefficient. In order to design the surface as an optical system that is symmetric in X-axis direction, D 4 , D 5 , D 6 , D 10 , D 11 , D 12 , D 13 , D 14 , D 20 , D 21 , D 22  . . . should be used.
 
   The above equations for definition are set forth as an example for expressing a rotationally asymmetric curved surface. The same effect can be obtained by application of any other definition, as a matter of course; the configuration of a curvature can be expressed by another definition as long as it is mathematically equivalent. 
   According to the present invention, upon all terms with odd-numbered powers of X in Equations (a) being nullified, the free-formed surface can define only one plane of symmetry that is parallel to Y-Z plane. 
   A surface decentration is given by an amount of decentration (expressed by X, Y, and Z for components in X-axis direction, Y-axis direction, and Z-axis direction, respectively) of the vertex position of the surface from the center of the reference surface of the optical system and a tilt angle (expressed by α, β, and γ in degrees) of the center axis of the surface (in the case of a free-formed surface, Z axis in Equation (a)). In this case, a positive value of α, β or γ means counterclockwise rotation in reference to the positive direction of the corresponding axis. 
   Regarding the order of decentration operation, after decentration in X, Y and Z directions is operated, the coordinate system is tilted in the order of α, β, and γ, to define the definition coordinate system. 
   Also, in a case where only the tilt of a reflecting surface is to be expressed, the tilt angles of the center axis of the surface are given as the amount of decentration. 
   Also, an aspherical surface is defined by the following equation:
 
 z =( y   2   /r )/[1+{1-(1 +k )·( y/r ) 2 } 1/2   ]+ay   4   +by   6   +cy   8   +dy   10   (c)
 
where z is taken along the optical axis, y is taken along a direction perpendicular to the optical axis, k is a conical coefficient, and a, b, c, and d are aspherical coefficients.
 
   The explanation above regarding the numerical data is commonly applicable to the later presented numerical data of each embodiment according to the present invention. 
   Here, in reference to the drawings, description is made of the embodiments of the zoom optical system according to the present invention. 
   A zoom optical system and an optical apparatus according to the present invention use a variable optical-property optical element (for example, deformable mirror, liquid crystal lens, etc). In each of the zoom optical systems according to the first through fourth embodiments, a deformable mirror is used as a variable optical-property optical element. There, the deformable mirror is given a focusing function. This configuration allows power consumption to be saved in comparison with a configuration in which focusing is performed via a mechanical structure. In addition, since the mechanical structure for focusing is dispensable, the lens frame structure can be simplified. 
   Furthermore, the deformable mirror is arranged in the most image-side group. Accordingly, the mirror can be made small, to realize a low cost design. In general, a zoom lens in an imaging system is required to substantially telecentric on the image side. Under this condition, each of the zoom optical systems according to the first to fourth embodiments is configured to arrange the deformable mirror in the most image-side group. Consequently, variation of incident angle of rays incident on the deformable mirror can be made small in a magnification change. As a result, decentered aberrations generated at the deformable mirror can be made small. In this way, it is possible to perform focusing while maintaining good image performance. 
   Lens sectional views of the zoom optical systems according to the first through fourth embodiments are shown in FIGS.  1  through  FIGS. 4 , respectively.  FIG. 1A  is a sectional view that shows a lens configuration at the wide-angle end,  FIG. 1B  is a sectional view that shows a lens configuration at the intermediate position, and  FIG. 1C  is a sectional view that shows a lens configuration at the telephoto end. FIGS.  2  through  FIGS. 4  also show lens configurations at the wide-angle end, at the intermediate position, and at the telephoto end, in the manner similar to FIGS.  1 . 
   Also, FIGS.  6  through  FIGS. 8  show aberration diagrams of the zoom optical system according to the first embodiment, under the respective conditions where the object distance is infinite at the wide-angle end, where the object distance is infinite at the intermediate position, and where the object distance is infinite at the telephoto end.  FIG. 6A  shows a Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is extreme in negative direction, or −19.3°;  FIG. 6B  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is extreme in negative direction, or −19.3°;  FIG. 6C  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −19.3°;  FIG. 6D  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in negative direction, or −19.3°;  FIG. 6E  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is zero;  FIG. 6F  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is zero;  FIG. 6G  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 19.3°;  FIG. 6H  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is zero and Y-direction field angle is extreme in positive direction, or 19.3°;  FIG. 6I  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is extreme in positive direction, or 19.30;  FIG. 6J  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is extreme in positive direction, or 19.3°;  FIG. 6K  is an aberration diagram that shows Y-direction lateral aberration of a chief ray that traverses a point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is zero; and  FIG. 6L  is an aberration diagram that shows X-direction lateral aberration of the chief ray that traverses the point where X-direction field angle is extreme in positive direction, or 24.9° and Y-direction field angle is zero. FIGS.  7  and  FIGS. 8  also show lateral aberrations in the manner similar to FIGS.  6 . 
   In the lens data of the first through fourth embodiments, “ASP” signifies aspherical surface, “FFS” signifies free-formed surface, “DM” signifies deformable mirror, and “OB” signifies object distance. Regarding refractive index and Abbe&#39;s number, values for d-line rays are listed. Regarding a variable space D i  (i=1, 2, . . . ), values at the wide-angle end, at the intermediate position, and at the telephoto end are listed in this order. In the zoom optical system according to each embodiment, two plane parallel plates are inserted on the most image side. These are a cover glass of an image pickup element, an infrared cutoff filter, and a lowpass filter. In addition, η W , η S , and η T  are magnifications of the group of lenses arranged between the deformable mirror and the image surface, at the wide-angle end, at the intermediate position, and the telephoto end, respectively. 
   First Embodiment 
   
       
       Focal length: 4.0 mm˜7.0 mm˜10.0 mm, Open F-number: 2.8˜4.2 
       Dimensions of image pickup surface: 4.0 mm×3.0 mm 
       X-direction and Y-direction (Y is direction of decentration) focal lengths of deformable mirror at the proximity (OB=300): 
     
  
                                       X   Y                  W   813.0   925.9       S   305.8   359.7       T   134.4   152.0                    
Values in Conditions:
     EX W /f W =19.5, EX S /f S =10.4, EX T /f T =15.1   f a  (front group)=−7.54, f b  (rear group)=11.96   (f a /f b )×f W =−2.52, D=8.8   
                                                  Surface   Radius of   Surface       Refractive   Abbe&#39;s       Number   Curvature   Separation   Decentration   Index   Number               object   ∞   ∞       surface       1   16.47   1.20       1.7725   49.6       2   4.81   2.06       3   162.21   0.80       1.6180   63.3       4   8.65   0.24       5   6.72   1.75       1.8467   23.8       6   ASP[1]   D1 = 10.11˜3.53˜2.08       7   stop surface   1.00       8   32.80   2.49       1.6869   41.0       9   −4.10   1.37       1.8010   35.0       10   −16.86   D2 = 6.24˜5.43˜1.23        11   16.08   2.22       1.4970   81.5       12   −8.88   1.07       13   −7.49   1.14       1.8467   23.8       14   ASP[2]   D3 = 1.00˜8.38˜14.03       15   −10.82   1.00       1.8467   23.8       16   −20.92   2.00       1.7292   54.7       17   ASP[3]   4.00       18   FFS[1] (DM)   0.00   decentration[1]       19   ∞   4.43       20   ∞   1.00       1.5477   62.8       21   ∞   0.50       22   ∞   0.50       1.5163   64.1       23   ∞   0.50       image   ∞       surface                         ASP[1]                             Radius of curvature 10.91   k 0.0000                                     a −4.5842 × 10 −4     b −2.1403 × 10 −6     c 6.6036 × 10 −7     d −2.8931 × 10 −8                   ASP[2]                             Radius of curvature −10.45   k 0.0000                                     a 5.6674 × 10 −5     b −2.2981 × 10 −6     c 1.2154 × 10 −7     d −6.0421 × 10 −9                   ASP[3]                             Radius of curvature −7.05   k −2.1588 × 10 −1                                       a 4.1176 × 10 −4     b 1.2627 × 10 −6     c 9.1551 × 10 −9     d 1.3215 × 10 −9                               FFS[1]                                             W OB = ∞   S OB = ∞   T OB = ∞   W OB = 300   S OB = 300   T OB = 300               C 4     0.000   0.000   0.000   −0.4312 × 10 −3     −0.1108 × 10 −2     −0.2613 × 10 −2         C 6     0.000   0.000   0.000   −0.2273 × 10 −3     −0.5955 × 10 −3     −0.1381 × 10 −2         C 8     0.000   0.000   0.000    0.4060 × 10 −4      0.1304 × 10 −3      0.2183 × 10 −3         C 10     0.000   0.000   0.000    0.1992 × 10 −4      0.6697 × 10 −4      0.1230 × 10 −3         C 11     0.000   0.000   0.000   −0.1372 × 10 −5     −0.2383 × 10 −4     −0.9181 × 10 −5         C 13     0.000   0.000   0.000   −0.4923 × 10 −5     −0.2967 × 10 −4     −0.2217 × 10 −4         C 15     0.000   0.000   0.000   −0.1499 × 10 −5     −0.9592 × 10 −5     −0.1017 × 10 −4                      
Decentration [1]
 
                                                              X   0.00   Y   0.00   Z   0.00           α   45.00   β   0.00   γ   0.00                        
Second Embodiment
     Focal length: 4.0 mm˜7.0 mm˜10.0 mm, Open F-number: 2.8˜4.2   Dimensions of image pickup surface: 4.0 mm×3.0 mm   X-direction and Y-direction (Y is direction of decentration) focal lengths of deformable mirror at the proximity (OB=300):   
                                       X   Y                                            W   1298.7   1388.9       S   454.5   476.2       T   208.3   216.5                    
Values in Conditions:
     EX W /f W =6.2, EX S /f S =4.6, EX T /f T =3.0   ξ W =0.62, ξ S =0.62, ξ T =0.62   f a  (front group)=−8.27, f b  (rear group)=29.51   (f a /f b )×f W =−1.12, D=9.0   
                                                  Surface   Radius of   Surface       Refractive   Abbe&#39;s       Number   Curvature   Separation   Decentration   Index   Number               object   ∞   ∞       surface       1   23.31   1.20       1.7725   49.6       2   4.74   1.97       3   −52.35   1.29       1.7433   49.3       4   ASP[1]   0.52       5   11.52   5.16       1.8467   23.8       6   −66.74   D1 = 11.10˜3.25˜1.04        7   stop surface   1.00       8   56.17   5.40       1.7034   52.8       9   −5.63   1.50       1.7644   38.2       10   −23.83   D2 = 6.39˜5.77˜1.00        11   ASP[2]   4.00       1.6883   53.4       12   −22.28   0.15       13   23.11   2.00       1.7615   50.6       14   −19.32   1.00       1.7269   32.5       15   9.72   D3 = 4.50˜12.96˜19.95       16   FFS[1] (DM)   4.50   decentration[1]       17   ASP[3]   3.20       1.6935   53.2       18   −61.27   1.48       19   ∞   1.00       1.5477   62.8       20   ∞   0.50       21   ∞   0.50       1.5163   64.1       22   ∞   0.50       image   ∞       surface                         ASP[1]                             Radius of curvature 9.11   k 8.6365 × 10 −1                                       a −8.8266 × 10 −4     b −1.9953 × 10 −6     c −3.6159 × 10 −7     d −1.2075 × 10 −8                   ASP [2]                             Radius of curvature 18.26   k 2.6780                                     a −1.4977 × 10 −4     b 1.4241 × 10 −6     c −1.7758 × 10 −7     d 5.8316 × 10 −9                   ASP[3]                             Radius of curvature 10.67   k 0.0000                                     a −1.8514 × 10 −4     b −3.7065 × 10 −6     c 1.3231 × 10 −7     d −5.1639 × 10 −9                               FFS[1]                                             W OB = ∞   S OB = ∞   T OB = ∞   W OB = 300   S OB = 300   T OB = 300               C 4     0.000   0.000   0.000   −0.2717 × 10 −3     −0.7620 × 10 −3     −0.1704 − 10 −2         C 6     0.000   0.000   0.000   −0.1354 × 10 −3     −0.3933 × 10 −3     −0.8725 × 10 −3         C 8     0.000   0.000   0.000    0.1001 × 10 −4      0.2991 × 10 −4      0.5158 × 10 −4         C 10     0.000   0.000   0.000    0.4227 × 10 −5      0.1350 × 10 −4      0.2646 × 10 −4         C 11     0.000   0.000   0.000   −0.8646 × 10 −6     −0.7241 × 10 −5     0.2807 × 10 −5         C 13     0.000   0.000   0.000   −0.1088 × 10 −5     −0.5882 × 10 −5     0.5567 × 10 −5         C 15     0.000   0.000   0.000   −0.3590 × 10 −6     −0.1756 × 10 −5     0.2367 × 10 −6                      
Decentration [1]
 
   
     
       
         
             
             
             
             
             
             
             
           
             
                 
                 
             
           
          
             
                 
               X 
               0.00 
               Y 
               0.00 
               Z 
               0.00 
             
             
                 
               α 
               45.00 
               β 
               0.00 
               γ 
               0.00 
             
             
                 
                 
             
          
         
       
     
   
   Each of the zoom optical systems according to the first and second embodiments includes, in order from the object side, a first group G 1  having a negative power and fixed in a zooming operation, a second group G 2  having a positive power, a third group G 3  having a positive power, and a fourth group G 4  having a positive power. In a magnification change from the wide-angle end to the telephoto end, the second group G 2  and the third group G 3  are moved toward the object side separately from each other. By doing so, magnification change and compensation for a fluctuation of the in-focus position caused by the magnification change are performed. Also, the configuration is made so that focusing can be performed by a deformable mirror DM arranged in the fourth group G 4 . 
   In the zoom optical system according to the first embodiment, the deformable mirror is disposed on the most image side in the fourth group G 4 . In the zoom optical system according to the second embodiment, the fourth group G 4  is configured to arrange, in order from the object side, the deformable mirror and a positive lens. 
   Third Embodiment 
   
       
       Focal length: 4.0 mm˜7.0 mm˜10.0 mm, Open F-number: 2.8˜4.4 
       Dimensions of image pickup surface: 4.0 mm×3.0 mm 
       X-direction and Y-direction (Y is direction of decentration) focal lengths of deformable mirror at the proximity (OB=300): 
     
  
                                       X   Y                                            W   1098.9   1149.4       S   383.1   398.4       T   191.6   199.2                    
Values in Conditions:
     EX W /f W =3.2, EX S /f S =2.8, EX T /f T =2.6   ξ W =0.65, ξ S =0.66, ξ T =0.66   f a  (front group)=−7.68, f b  (rear group)=13.75   (f a /f b )×f W =−2.23, D=8.7   
                                                  Surface   Radius of   Surface       Refractive   Abbe&#39;s       Number   Curvature   Separation   Decentration   Index   Number               object   ∞   ∞       surface       1   19.62   1.20       1.7725   49.6       2   3.95   1.92       3   259.50   0.87       1.7433   49.3       4   ASP[1]   0.78       5   14.23   2.09       1.8467   23.8       6   −50.48   D1 = 9.59˜3.49˜1.05        7   stop surface   1.00       8   14.29   2.61       1.6843   36.5       9   −4.00   1.42       1.7813   35.0       10   34.35   1.22       11   ASP[2]   2.03       1.7386   51.4       12   −8.89   0.15       13   27.38   2.00       1.7767   50.1       14   −8.76   1.00       1.7065   29.5       15   8.70   D2 = 4.50˜11.30˜18.06       16   FFS[1] (DM)   4.59   decentration[1]       17   9.45   2.69       1.6935   53.2       18   ASP[3]   1.00       19   ∞   1.00       1.5477   62.8       20   ∞   0.50       21   ∞   0.50       1.5163   64.1       22   ∞   0.50       image   ∞       surface                         ASP[1]                             Radius of curvature 9.68   k −2.4920                                     a −7.8720 × 10 −4     b −3.4128 × 10 −5     c 1.4344 × 10 −6     d −2.0198 × 10 −7                   ASP[2]                             Radius of curvature 20.64   k −5.6838                                     a −3.9523 × 10 −4     b 7.6145 × 10 −6     c −4.4208 × 10 −7     d 1.7720 × 10 −8                   ASP[3]                             Radius of curvature −154.68   k −3.2742 × 10 23                                       a 3.0474 × 10 −4     b −1.8266 × 10 −5     c 1.9831 × 10 −6     d −7.4439 × 10 −8                               FFS[1]                                             W OB = ∞   S OB = ∞   T OB = ∞   W OB = 300   S OB = 300   T OB = 300               C 4     0.000   0.000   0.000   −0.3230 × 10 −3     −0.9158 × 10 −3     −0.1831 × 10 −2         C 6     0.000   0.000   0.000   −0.1663 × 10 −3     −0.4744 × 10 −3     −0.9507 × 10 −3         C 8     0.000   0.000   0.000    0.9096 × 10 −5      0.2975 × 10 −4      0.6359 × 10 −4         C 10     0.000   0.000   0.000    0.5969 × 10 −5      0.1655 × 10 −4      0.3414 × 10 −4         C 11     0.000   0.000   0.000   0.7262 × 10 −6     −0.4247 × 10 −5     −0.6693 × 10 −5         C 13     0.000   0.000   0.000   0.4576 × 10 −5     0.1657 × 10 −6     −0.2643 × 10 −5         C 15     0.000   0.000   0.000   0.1261 × 10 −6     −0.1100 × 10 −5     −0.1896 × 10 −5                      
Decentration [1]
 
   
     
       
         
             
             
             
             
             
             
             
           
             
                 
                 
             
           
          
             
                 
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   The zoom optical system according to the third embodiment includes, in order from the object side, a first group G 1  having a negative power, a second group G 2  having a positive power, and a third group G 3  having a positive power. A magnification change is made by moving the first group G 1  and the second group G 2  in the direction of the optical axis. In a magnification change from the wide-angle end to the telephoto end, the second group G 2  is moved toward the object side. Fluctuation of the in-focus position caused by the magnification change is compensated for by moving the first group G 1  long a locus that is convex toward the image side. Also, the configuration is made so that focusing can be performed by a deformable mirror DM arranged in the third group G 3 . 
     FIG. 5  shows the state where the optical system of the zoom optical system according to the third embodiment is compactly folded and housed. In the third embodiment, the deformable mirror is moved so that its mirror surface is perpendicular to the optical axis of the first group and the second group. This configuration contrives a storage space for the first group G 1  and the second group G 2 . In this way, according to the zoom optical system of the third embodiment, it is possible to realize an optical system that is compact in storage. 
   Fourth Embodiment 
   
       
       Focal length: 4.5 mm˜9.0 mm˜13.5 mm, Open F-number: 2.8˜4.8 
       Dimensions of image pickup surface: 4.48 mm×3.36 mm 
       X-direction and Y-direction (Y is direction of decentration) focal lengths of deformable mirror at the proximity (OB=300): 
     
  
                                       X   Y                                            W   840.3   943.4       S   219.8   245.7       T   99.3   109.3                    
Values in Conditions:
     EX W /f W =3.8, EX S /f S =2.9, EX T /f T =2.8   f a  (front group)=−9.25, f b  (rear group)=14.67   (f a /f b )×f W =−2.84, D=11.1   
                                                  Surface   Radius of   Surface       Refractive   Abbe&#39;s       Number   Curvature   Separation   Decentration   Index   Number               object   ∞   ∞       surface       1   43.06   4.00       1.7725   49.6       2   ∞   D1 = 1.00˜8.25˜8.93        3   19.74   1.00       1.7725   49.6       4   7.15   2.96       5   432.39   1.00       1.4875   70.2       6   19.19   4.50       7   −9.25   1.00       1.4875   70.2       8   21.83   3.50       1.8052   25.4       9   −103.66   D2 = 8.93˜1.68˜1.00        10   stop surface   D3 = 10.98˜5.98˜0.80       11   ASP[1]   3.00       1.5891   61.3       12   −13.72   0.20       13   −26.29   3.00       1.7725   49.6       14   −163.98   1.00       1.8010   35.0       15   61.02   D4 = 2.15˜2.45˜2.00        16   −39.10   1.20       1.8075   26.4       17   16.03   0.20       18   ASP[2]   4.63       1.5891   61.1       19   −10.62   0.15       20   −28.14   3.50       1.7322   27.6       21   −6.28   1.00       1.8173   29.2       22   −19.35   D5 = 5.00˜9.71˜15.33       23   FF5[1] (DM)   5.00   decentration[1]       24   ∞   0.40       1.5163   64.1       25   ∞   0.90       1.5477   62.8       26   ∞   0.40       27   ∞   0.38       1.5163   64.1       28   ∞   0.50       image   ∞       surface                         ASP[1]                             Radius of curvature 12.23   k 2.6846 × 10 −1                                       a −1.4355 × 10 −4     b −3.6950 × 10 −6     c 6.4302 × 10 −8     d −1.0561 × 10 −9                   ASP[2]                             Radius of curvature 9.59   k −4.9694                                     a 1.9685 × 10 −4     b −5.9577 × 10 −6     c 1.3864 × 10 −7     d −1.0045 × 10 −9                               FFS[1]                                             W OB = ∞   S OB = ∞   T OB = ∞   W OB = 300   S OB = 300   T OB = 300               C 4     0.000   0.000   0.000   −0.4174 × 10 −3     −0.1591 × 10 −2     −0.3530 × 10 −2         C 6     0.000   0.000   0.000   −0.2283 × 10 −3     −0.8523 × 10 −3     −0.1858 × 10 −2         C 8     0.000   0.000   0.000    0.3750 × 10 −4      0.1378 × 10 −3      0.2460 × 10 −3         C 10     0.000   0.000   0.000    0.2178 × 10 −4      0.7433 × 10 −4      0.1351 × 10 −3         C 11     0.000   0.000   0.000   −0.1816 × 10 −5     −0.9126 × 10 −5     −0.1579 × 10 −4         C 13     0.000   0.000   0.000   −0.3857 × 10 −5     −0.1775 × 10 −4     −0.2547 × 10 −4         C 15     0.000   0.000   0.000   −0.1527 × 10 −5     −0.5854 × 10 −5     −0.1071 × 10 −4                      
Decentration [1]
 
   
     
       
         
             
             
             
             
             
             
             
           
             
                 
                 
             
           
          
             
                 
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   The zoom optical system according to the fourth embodiment includes, in order from the object side, a first group G 1  having a positive power, a second group G 2  having a negative power, a third group G 3  having a positive power, and a fourth group G 4  having a positive power. A magnification change is made by moving the second group G 2 , the third group G 3  and the fourth group G 4 . That is, the second group G 2 , the third group G 3  and the fourth group G 4  are given a magnification varying function. Also, the first group and the aperture stop are fixed in a magnification change. In addition, configuration is made so that focusing is performed by a deformable mirror DM disposed on the image side of the fourth group G 4 . 
   The zoom optical system according to the fourth embodiment also is a zoom-type lens system typically used as the lens system for a video camera. Also, this is one of the types applicable to digital cameras. That is, this zoom optical system is based on a type of lens system composed of a positive first group, a negative second group and a positive third group. 
   While the angle Φ of turning of the optical axis caused by the deformable mirror is 90° in most of the embodiments set forth above, it is not limited to this value. Although a smaller value of angle Φ causes smaller aberrations and thus is favorable, too small a value causes competition with electronic devices, optical devices etc for a space. On the other hand, a larger value of angle Φ makes it easy to secure a space for device arrangement, but increases aberrations. Therefore, the angle Φ of turning of the optical axis caused by the deformable mirror preferably satisfies the following condition:
 
70°≦Φ≦110°
 
   In addition, it is much preferable that the following condition is satisfied:
 
80°≦Φ≦100°
 
   As stated above, the zoom optical system according to the present invention uses a variable optical-property optical element. Consequently, zooming action is smoother than a magnification change by a motor. In addition, operation noise is small and power consumption is small. Furthermore, it is not necessary to provide a motor or a driving circuit to activate the motor. Also, since the mechanical structure for moving lenses is simple, a space for providing the mechanical structure is allowed to be small. As a result, even if a zoom optical system is used, bulkiness of the apparatus is avoidable. 
   All of the descriptions above relate to the optical system using a deformable mirror. However, in a case where an ordinary (non-deformable) mirror is used in place of the deformable mirror, also, the conditional expressions and limitations set forth above may be applied unless they specifically cause inconvenience. 
   This is because the merit of compactness contributed by the folded design of the optical system using a mirror remains as it is in this case also. 
   The zoom optical system according to the present invention as described above is applicable to a film camera, a digital camera, a TV camera, a camera for a personal data assistant, a monitor camera, robot eyes, an electronic endoscope, etc. 
   Regarding the zoom optical system set forth above, the description has been made of the type configured to have a reflecting surface in a lens group. However, regarding a zoom optical system having no reflecting surface also, use of an optical element having a deformable surface, for example, a variable focus lens can achieve effects such as size reduction, cost reduction, power saving, and operation noise reduction. Moreover, a variable focus mirror that has no deformable surface is applicable to the embodiments set forth above. 
   Regarding the variable focus mirror, one example is explained in reference  FIG. 24 , later. 
   Hereafter, explanation is made of configuration examples of the deformable mirror applicable to the zoom optical system according to the present invention. 
     FIG. 9  is a schematic configuration diagram that shows a digital camera&#39;s Keplerian finder using a variable optical-property mirror, as a variable mirror that is applicable to the zoom optical system according to the present invention. This configuration example is applicable to a silver halide film camera, as a matter of course. Reference is first made to a variable optical-property deformable mirror  409 . 
   The variable optical-property deformable mirror  409  is a variable optical-property deformable mirror (hereafter simply called a deformable mirror) in which the periphery of a deformable three-layer structure composed of an electrode  409   k , a deformable substrate  409   j , and a thin film (reflecting surface)  409   a , which is an aluminum coating formed on the substrate  409   j  and functions as a reflecting surface, is fixed on a support  423 , and a plurality of electrodes  409   b  provided in a spaced relation with the electrode  409   k  are fixed on the lower side of the support  423 . The reference numeral  411   a  denotes a plurality of variable resistors connected with the electrodes  409   b , respectively. The reference numeral  412  denotes a power supply connected, as interposed between, with the electrode  409   k  and the electrodes  409   b  through variable resistors  411   b  and a power switch  413 . The reference numeral  414  denotes an arithmetical unit for controlling resistance values of the plurality of variable resistors  411   a . The reference numerals  415 ,  416 , and  417  denote a temperature sensor, a humidity sensor, and a range sensor, respectively, connected with the arithmetical unit  414 . These members and elements are arranged as shown in the figure, to constitute an optical apparatus. 
   Each of surfaces of an objective lens  902 , an eyepiece  901 , a prism  404 , a rectangular isosceles prism  405 , a mirror  406  and the deformable mirror  409  may have, not necessarily limited to planer surfaces, any shape such as a spherical or rotationally symmetric aspherical surface, a spherical, planar or rotationally symmetric aspherical surface that has a decentration in reference to the optical axis, an aspherical surface that defines planes of symmetry, only one plane of symmetry or no plane of symmetry, a free-formed surface, and a surface having a nondifferentiable point or line. In addition, irrespective of whether it is a reflecting surface or a refracting surface, any surface is applicable as long as it can exert some effect on light. Hereafter, such a surface is generally referred to as an expanded curved surface. It is noted that decentration implies either one or both of displacement (shift) and tilt. 
   Also, it is designed so that, when a voltage is applied between the plurality of electrodes  409   b  and the electrode  409   k , the thin film  409   a  is deformed by electrostatic force to change its surface shape, as in the case of the membrane mirror referred to, for example, in “Handbook of Microlithography, Micromachining and Microfabriation”, edited by P. Rai-Choudhury, Vol. 2: Micromachining and Microfabriation, p. 495,  FIG. 8.  58, SPIE PRESS or “Optics Communication”, Vol. 140, pp. 187-190, 1997. Whereby, not only can focus adjustment be made in conformance with diopter of an observer, but also it is possible to suppress degradation of image forming performance, which results from deformation or change of refractive indices of the lenses  901  and  902  and/or the prism  404 , the rectangular isosceles prism  405  and the mirror  406  caused by temperature change or humidity change, from expansion/contraction and deformation of lens frames, or from assembling errors of parts such as optical elements and frames. In this way, focus adjustment and compensation for aberrations caused by the focus adjustment can always be performed appropriately. 
   Also, the profile of the electrodes  409   b  has a concentric or rectangular division pattern as shown in  FIGS. 11 and 12 , and may be selected in accordance with deformation pattern of the thin film  409   a    
   In the case where the deformable mirror  409  is used, light from the object is refracted at each of entrance surfaces and exit surfaces of the objective lens  902  and the prism  404 , is reflected at the deformable mirror  409 , is transmitted through the prism  404 , is further reflected at the rectangular isosceles prism  405  (in  FIG. 9 , the mark “+” on the path of rays indicates that rays travel toward the rear side of the figure), is reflected at the mirror  406 , and enters the observer&#39;s eye via the eyepiece  901 . In this way, the lenses  901  and  902 , the prisms  404  and  405 , and the deformable mirror  409  constitute an observation optical system of the optical apparatus. Optimizing the surface shape and thickness of each of these optical elements can minimize aberrations on the object surface. 
   In other words, the shape of the thin film  409   a , which functions as a reflecting surface, is controlled in such a manner that resistance values of the variable resistors  411   a  are changed by signals from the arithmetical unit  414 , to optimize image forming performance. Signals that have intensities according to ambient temperature, humidity and distance to the object are input into the arithmetical unit  414  from the temperature sensor  415 , the humidity sensor  416 , and the range sensor  417 . In order to compensate for degradation of image forming performance caused by the ambient temperature and humidity and the distance to the object, the arithmetical unit  414  outputs signals for determining resistance values of the variable resistors  411   a  upon taking into account these input signals, so that voltages which determine the shape of the thin film  409   a  are applied to the electrodes  409   b . In this way, since the thin film  409   a  is deformed by voltages applied to the electrodes  409   b , or electrostatic force, it can assume various shapes including aspherical surfaces in accordance with conditions. 
   It is noted that the range sensor  417  is dispensable. In this case, it is only necessary to move the imaging lens  403 , which is provided as the imaging optical system of the digital camera, to the position where high-frequency components of an image signal from a solid-state image sensor  408  are substantially maximized, to calculate the object distance on the basis of this position, and to deform the deformable mirror  409  so that an observer&#39;s eye is focused on the object image. 
   Also, if the deformable substrate  409   j  is made of synthetic resin such as polyimide, it is favorable in that the thin film could be considerably deformed even at a low voltage. Also, to integrally form the prism  404  and the deformable mirror  409  into a unit is convenient for assembly. 
   In the example of  FIG. 9 , since the reflecting surface  409   a and the deformable electrode  409   k  are integrally formed as spaced via the deformable substrate  409   j  sandwiched between, there is a merit of choice from several manufacturing methods. Also, the reflecting surface  409   a  may be designed to be used as the electrode  409   k  also. In this case, since these two are configured into one, the structure is simplified, which is a merit. 
   Although not shown in the figure, the solid-state image sensor  408  may be integrally formed on the substrate of the deformable mirror  409  by a lithography process. 
   Also, if the lenses  901  and  902 , the prisms  404  and  405 , and the mirror  406  are formed with plastic molds, curved surfaces with any desirable shapes can be easily formed and the fabrication also is simple. In the above description, the lenses  901  and  902  are arranged separately from the prism  404 . However, if the prisms  404  and  405 , the mirror  406 , and the deformable mirror  409  can be designed to eliminate aberrations without the lenses  902  and  901 , the prisms  404  and  405  and the deformable mirror  409  will form one optical block, to facilitate assembling. A part or all of the lenses  901  and  902 , the prisms  404  and  405 , and the mirror  406  may be made of glass. Such a configuration would assure an imaging system having a better accuracy. The reflecting surface of the deformable mirror preferably is shaped as a free-formed surface, because thereby compensation for aberration is facilitated and thus is advantageous. 
   In the example of  FIG. 9 , although the arithmetical unit  404 , the temperature sensor  415 , the humidity sensor  416 , and the range sensor  417  are provided so that temperature change, humidity change, and change of the object distance are compensated for by the deformable mirror  409 , the system configuration is not necessarily limited to this specific one. That is, the arithmetical unit  414 , the temperature sensor  415 , the humidity sensor  416  and the range sensor  417  may be removed from the configuration so that the deformable mirror  409  compensates for change of the observer&#39;s diopter alone. 
     FIG. 10  is a schematic configuration diagram that shows another example of the deformable mirror  409  applicable as a variable mirror used in the zoom optical system according to the present invention. 
   In the deformable mirror  409  of this example, a piezoelectric element  409   c  is interposed between the thin film  409   a  and the electrodes  409   b , and these elements are mounted on a support  423 . By changing voltages applied to the piezoelectric element  409   c for individual electrodes  409   b  to cause different expansion or contraction in the piezoelectric element  409   c  portion by portion, the configuration allows the shape of the thin film  409   a  to be changed. Arrangement of the electrodes  409   b  may be chosen from a concentric division pattern as illustrated in  FIG. 11 , a rectangular division pattern as illustrated in  FIG. 12 , and any other appropriate pattern. 
   In  FIG. 10 , the reference numeral  424  denotes a shake sensor connected with the arithmetical unit  414 . The shake sensor  424  detects, for example, shake of a digital camera in photographing and changes voltages applied to the electrodes  409   b  via the arithmetical unit  414  and the variable resistors  411  so as to deform the thin film (reflecting surface)  409   a  for compensation for disturbance of the image by the shake. In this situation, focusing and compensation for temperature and humidity are performed upon signals from the temperature sensor  415 , the humidity sensor  416 , and the range sensor  417  also being taken into account simultaneously. In this case, since a stress that derives from the deformation of the piezoelectric element  409   c  is applied to the thin film  409   a , it is good practice to give the thin film  409   a  a considerable thickness to have an appropriate strength. It is noted that the piezoelectric element  409   c  may have, as described later, a two-layer structure denoted by  409   c - 1  and  409   c - 2 , depending on materials used. 
     FIG. 13  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as a variable mirror used in the zoom optical system according to the present invention. 
   The deformable mirror of this example differs from the deformable mirror shown in  FIG. 10  in that the piezoelectric element interposed between the thin film  409   a  and the plurality of electrodes  409   b  is composed of two piezoelectric elements  409   c  and  409   c ′ made of substances having piezoelectric characteristics of opposite directionalities. Specifically, if the piezoelectric elements  409   c  and  409   c ′ are made of ferroelectric crystals, they are arranged so that the crystal axes thereof are directed opposite to each other. In this case, when voltages are applied, since the piezoelectric elements  409   c  and  409   c ′ expand or contract in opposite directions, the force to deform the thin film (reflecting surface)  409   a  becomes stronger than in the example of  FIG. 10 , to result in an advantage that the mirror surface can be considerably deformed. Other reference numerals in  FIG. 13  are the same as those in FIG.  10 . 
   Substances usable to construct the piezoelectric elements  409   c  and  409   c ′ are, for example, piezoelectric substances or polycrystals or crystals thereof such as barium titanate, Rochelle salt, quartz crystal, tourmaline, KDP, ADP and lithium niobite; piezoelectric ceramics such as solid solution of PbZrO 3  and PbTiO 3 ; organic piezoelectric substances such as PVDF; and other ferroelectrics. In particular, the organic piezoelectric substance is preferable because it has a small value of Young&#39;s modulus and brings about a considerable deformation at a low voltage. In application of these piezoelectric elements, if they are made to have uneven thickness, it also is possible to properly deform the thin film  409   a  in each of the examples set forth above. 
   Also, as materials of the piezoelectric elements  409   c  and  409   c ′, macromolecular piezoelectric such as polyurethane, silicon rubber, acrylic elastomer, PZT, PLZT, and PVDF; vinylidene cyanide copolymer, copolymer of vinylidene fluoride and trifluoroethylene; etc. are usable. 
   Use of the organic substance having a piezoelectric property, the synthetic resin having a piezoelectric property, or the elastomer having a piezoelectric property is favorable because a considerable deformation of the surface of the deformable mirror can be achieved. 
   In the case where an electrostrictive substance such as acrylic elastomer or silicon rubber is used for the piezoelectric element  409   c  shown in  FIGS. 10 and 14 , the piezoelectric element  409   c  may have the structure in which another substrate  409   c - 1  and the electrostrictive substance  409   c - 2  are cemented together. 
     FIG. 14  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as a variable mirror used in the zoom optical system according to the present invention. 
   The deformable mirror of this example is designed so that the piezoelectric element  409   c  is sandwiched between the thin film  409   a  and a plurality of electrodes  409   d , and these are placed on the support  423 . A voltage is applied to the piezoelectric element, which is placed between the thin film  409   a  and the electrodes  409   d , via a driving circuit  425   a  controlled by the arithmetical unit  414 . Furthermore, apart from this, voltages are applied to the plurality of electrodes  409   b  also, which are formed on a bottom surface inside the support  423 , via driving circuits  425   b  controlled by the arithmetical unit  414 . Resultantly, the thin film  409   a  can be doubly deformed by electrostatic forces derived from the voltage applied between the thin film  409   a  and the electrodes  409   d  and from the voltages applied to the electrodes  409   b . Therefore, this example has a merit that a larger number of deformation patterns are possible and a faster response is achieved than in the case of any examples previously set forth. Other reference numerals in  FIG. 14  are the same as those in FIG.  10 . 
   Also, the thin film  409   a  of the deformable mirror can be deformed into either a convex surface or a concave surface upon the sign of the voltages applied between the thin film  409   a  and the electrodes  409   d  being changed. In this case, it may be designed so that piezoelectric effect causes a considerable amount of deformation while electrostatic force causes a fine shape change. Alternatively, it may be designed so that piezoelectric effect is mainly used for deformation of a convex surface while electrostatic force is mainly used for deformation of a concave surface. It is noted that the electrodes  409   d  may be constructed of a single electrode or a plurality of electrodes like the electrodes  409   b . The configuration of the electrodes  409   d  composed of a plurality of electrodes is illustrated in FIG.  14 . In this description, piezoelectric effect, electrostrictive effect, and electrostriction are generally referred to as “piezoelectric effect”. Thus, electrostrictive substance also is classified into piezoelectric substance. 
     FIG. 15  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as a deformable mirror used in the zoom optical system according to the present invention. 
   The deformable mirror of this example is designed to change the shape of the reflecting surface utilizing electromagnetic force. A permanent magnet  426  is fixed on the bottom surface inside of the support  423 , and the periphery of the substrate  409   e  made of silicon nitride, polyimide or the like is mounted and fixed on the top face of the support  423 . The surface of the substrate  409   e  is provided with the thin film  409   a  made of metal coating such as aluminum, to form the deformable mirror  409 . 
   A plurality of coils  427  are fixedly mounted on the back surface of the substrate  409   e , and are connected with the arithmetical unit  414  via the driving circuits  428 , respectively. Other reference numerals in  FIG. 15  are the same as those in FIG.  10 . When appropriate currents are supplied to the individual coils  427  from the individual driving circuits  428  based on output signals from the arithmetical unit  414 , which depend on a required change of the optical system determined by the arithmetical unit  414  on the basis of signals from the respective sensors  415 ,  416 ,  417 , and  424 , the coils  427  are repelled or attracted by the electromagnetic force acting with the permanent magnet  426 , to deform the substrate  409   e  and the thin film  409   a.    
   In this case, it can be designed so that different amounts of electric current flow through the respective coils  427 . Also, the coils  427  may be provided as a single coil. Alternatively, it may be designed so that the permanent magnet  426  is mounted on the back surface of the substrate  409   e  and the coils  427  are arranged on the bottom surface inside the support  423 . Also, fabricating the coils  427  as thin film coils by lithography process is preferable. In addition, a ferromagnetic iron core may be encased in each coil  427 . 
   In the case where thin film coils are used, it can be designed so that coil density of the thin-film coils  427  varies position by position on the back surface of the substrate  409   e , as illustrated in  FIG. 16  as a coil  428 ′, thereby to give the substrate  409   e  and the thin film  409   a  a desirable deformation. Also, the coils  427  may be provided as a single coil, or may encase ferromagnetic iron cores inserted therein. 
     FIG. 17  is a schematic configuration diagram that shows still another example of the deformable mirror  409  applicable as a variable mirror used in the zoom optical system according to the present invention. 
   According to this example, the substrate  409   e  is made of a ferromagnetic such as iron and the thin film  409   a  as a reflecting film is made of aluminum or the like. The periphery of the substrate  409   e  is mounted and fixed on the top face of the support  423 . The coils  427  are fixed on the bottom surface inside the support  423 . In this case, since thin-film coils need not be provided on the back surface of the substrate  409   e , the structure can be made simple, to reduce manufacture cost. Also, if the power switch  413  is replaced by an alternation and power on-off switch, directions of currents flowing through the coils  427  are changeable, and accordingly the substrate  409   e  and the thin film  409   a  are freely deformable. 
     FIG. 18  shows an arrangement example of the coils  427  arranged in reference to the thin film  409   a  and the substrate  409   e .  FIG. 19  shows another arrangement example of the coils  427 . These arrangements are applicable to the examples shown in  FIG. 15 , also. It is noted that  FIG. 20  shows an arrangement of permanent magnets  426  that is suitable to the case where the coils  427  are arranged in a radial pattern as shown in FIG.  19 . Specifically, the radial arrangement of the bar-shaped permanent magnets  426  as shown in  FIG. 20  can give the substrate  409   e  and the thin film  409   a  finer deformation than the example shown in FIG.  15 . In addition, deforming the substrate  409   e  and the thin film  409   a  by electromagnetic force (the examples of FIG.  15  and  FIG. 17 ) has a merit that the substrate and the thin film can be driven at a lower voltage than in the case where electrostatic force is used. 
   While several examples of the deformable mirror are described above, two or more kinds of forces may be used for deformation of a mirror formed of a thin film as set forth in the example of FIG.  14 . Specifically, two or more kinds of forces out of electrostatic force, electromagnetic force, piezoelectric effect, magnetrostriction, pressure of fluid, electric field, magnetic field, temperature change, electromagnetic wave, etc. may be simultaneously used, to deform the deformable mirror. Accordingly, if two or more different driving methods are used to make the variable optical-property optical element, substantial deformation and fine deformation can be simultaneously achieved, to realize a mirror surface with high accuracy. 
     FIG. 21  is a schematic configuration diagram of an imaging system, which uses the deformable mirror  409  as a deformable mirror applicable to the imaging apparatus using the zoom optical system according to the present invention, such an imaging system being applied to a digital camera of a cellular phone, a capsule endoscope, an electronic endoscope, a digital camera for a personal computer, and a digital camera for a PDA. 
   In the imaging optical system of this example, the deformable mirror  409 , the lens  902 , the solid-state image sensor  408 , and a control system  103  form an imaging unit  104 , namely one imaging device. In the imaging unit  104  of this example, the configuration is made so that light from an object passing through the lens  902  is reflected at the thin film (reflecting surface)  409   a  of the deformable mirror  409  to be converged and imaged on the solid-state image sensor  408 . The deformable mirror  409  is a kind of variable optical-property optical element, and is referred to as a variable focus mirror also. 
   According to this example, even when the object distance is changed, the object can be brought into focus by deformation of the reflecting surface  409   a  of the deformable mirror  409 . Therefore, the configuration does not require any motor or the like to move the lenses and thus excels in achieving compact and lightweight design and low power consumption. Also, the imaging unit  104  is applicable, as an imaging optical system according to the present invention, to each of the examples. Also, if a plurality of deformable mirrors  409  are used, an optical system such as a zoom imaging optical system or a variable magnification imaging system can be constructed. 
   It is noted that  FIG. 21  shows a configuration example of the control system  103 , which includes a boosting circuit of a transformer using coils. Specifically, use of a laminated piezoelectric transformer would facilitate compact design and thus is favorable. A boosting circuit may be used in any of the deformable mirrors and variable focus lenses of the present invention that use electricity, and, in particular, is useful for a deformable mirror or a variable focus lens that utilizes electrostatic force or piezoelectric effect. In order to use the deformable mirror  409  for focusing, it is only necessary to form an object image on the solid-state image sensor  408 , for example, and to detect a state where high-frequency components of the object image are maximized while changing the focal length of the deformable mirror  409 . In order to detect high-frequency components, it is only necessary to connect a processor including a microcomputer and so on with the solid-state image sensor  408  and to detect the high-frequency components therein. 
     FIG. 22  is a schematic configuration diagram that relates to still another example of the deformable mirror applicable to the zoom optical system according to the present invention. The deformable mirror  188  of  FIG. 22  is constructed so that fluid  161  in a pipe  106   a  is taken in and out by a micropump  180  to deform a mirror surface, which is the outside surface of a reflecting film  189  spread across the upper face of a support  189   a . This example has a merit that the mirror surface can be considerably deformed. Also, a liquid tank  168  is provided between the support  189   a  and the micropump  180 , which are connected by the pipe, so that the fluid  161  can be supplied by a preset amount inside the support  189   a.    
   The micropump  180  is, for example, a small-sized pump fabricated by micromachining technique and is configured to work using an electric power. As examples of pumps fabricated by the micromachining technique, there are those which use thermal deformation, piezoelectric substance, electrostatic force, etc. 
     FIG. 23  is a schematic configuration diagram that shows one example of the micropump. In the micropump  180 , a vibrating plate  181  is vibrated by an electric force such as electrostatic force, piezoelectric effect or the like.  FIG. 23  shows an example where vibration is caused by the electrostatic force. In  FIG. 23 , the reference numerals  182  and  183  denote electrodes. Also, the dash lines indicate the vibrating plate  181  as deformed. As the vibrating plate  181  vibrates, tips  184   a  and  185   a  of two valve  184  and  185  are opened and closed, to feed the fluid  161  from the right to the left. 
   In the deformable mirror  188  shown in  FIG. 22 , the surface of the reflecting film  189  functions as a deformable mirror upon the reflecting film  189  being deformed into a concave or convex shape in accordance with an amount of the fluid  161 . That is, the deformable mirror  188  is driven by the fluid  161 . Organic or inorganic substance, such as silicon oil, air, water, and jelly, can be used as the fluid. 
   Also, a deformable mirror, a variable focus lens or the like using electrostatic force or piezoelectric effect sometimes requires a high voltage for driving it. In this case, as shown in  FIG. 21 , for example, a boosting transformer or a piezoelectric transformer is preferably used to configure the control system. 
   Also, if the thin film  409   a  or the reflecting film  189  for reflection is provided with a non-deformable portion to be fixed to the support  423  or the support  189   a , this portion can be conveniently used as a reference surface for measuring the shape of the deformable mirror with an interferometer or the like. 
     FIG. 24  shows an example where a variable focus lens is used as the variable focus mirror in the zoom optical system according to the present invention. The variable focus mirror  565  includes a first transparent substrate  566  having first and second surfaces  566   a  and  566   b , and a second transparent substrate  567  having third and fourth surfaces  567   a  and  567   b . The first transparent substrate  566  is configured to have a flat plate shape or a lens shape and to be provided with a transparent electrode  513   a  on the inner surface (the second surface)  566   b  thereof. The second transparent substrate  567  is configured so that the inner surface (the third surface)  567   a  thereof is shaped as a concave surface, which is coated with a reflecting film  568 , on which a transparent electrode  513   b  is further provided. A macromolecular dispersed liquid crystal layer  514  is sandwiched between the transparent electrodes  513   a  and  513   b  so that an alternating-current voltage is applied thereto as the transparent electrodes  513   a  and  513   b  are connected with an alternating-current power supply  516  via a switch  515  and a variable resistor  519 . In  FIG. 24 , illustration of liquid crystal molecules is omitted. 
   In this configuration, since a ray of light incident on the mirror from the side of the transparent substrate  566  forms a path reciprocated in the macromolecular dispersed liquid crystal layer  514  by the reflecting film (reflecting surface)  568 , the macromolecular dispersed liquid crystal layer  514  exerts its function twice. Also, by changing the voltage applied to the macromolecular dispersed liquid crystal layer  514 , it is possible to shift the focal position for reflected light. In this case, since a ray of light incident on the variable focus mirror  565  is transmitted through the macromolecular dispersed liquid crystal layer  514  twice, when twice the thickness of the macromolecular dispersed liquid crystal layer  514  is represented by t, the numerical conditions set forth above are applicable in the similar manner. Also, the inner surface of the transparent substrate  566  or  567  can be configured as a diffraction grating, to reduce the thickness of the macromolecular dispersed liquid crystal layer  514 . This solution is favorable in reducing scattered light. 
   In the description set forth above, the alternating-current power supply  516  is used as a power source to apply an alternating-current voltage to the liquid crystal layer for the purpose of preventing deterioration of the liquid crystal. However, a direct-current power supply may be used to apply a direct-current voltage to the liquid crystal. Change of orientation of the liquid crystal molecules may be achieved by, not limited to the technique of changing the voltage, a technique of changing frequency of an electric field applied to the liquid crystal layer, intensity and frequency of a magnetic field applied to the liquid crystal layer, or temperature or the like of the liquid crystal layer. Some kind of macromolecular dispersed liquid crystal is nearly a solid rather than a liquid. In such a case, therefore, one of the transparent substrates  566  and  567  shown in  FIG. 24  is dispensable. 
   The optical element of the type as set forth in reference to  FIG. 24 , the focal length of which is changed by altering the refracting index of a medium that forms a macromolecular dispersed liquid crystal layer, has merits such that it facilitates mechanical design, has a simple mechanical structure and so on because of its unchanged shape. 
   In the present invention, a variable focus mirror that is non-deformable as shown in  FIG. 24  also is classified into the deformable mirror. 
     FIG. 25  is a schematic configuration diagram that shows still another example of the deformable mirror applicable as a deformable mirror used in the zoom optical system according to the present invention. In this example, explanation is made on the basis of the supposition that the deformable mirror is applied to a digital camera. In  FIG. 25 , the reference numeral  411  denotes a variable resistor, the reference numeral  414  denotes an arithmetical unit, the reference numeral  415  denotes a temperature sensor, the reference numeral  416  denotes a humidity sensor, the reference numeral  417  denotes a range sensor, and the reference numeral  424  denotes a shake sensor. 
   The deformable mirror  45  of this example is configured to provide a plurality of segmented electrodes  409   b  disposed spaced away from an electrostrictive substance  453  made of an organic substance such as acrylic elastomer, to provide an electrode  452  and a deformable substrate  451  arranged in this order on the electrostrictive substance  453 , and to provide a reflecting film  450  made of metal such as aluminum further on the substrate  451 . In this way, the deformable layer of the deformable mirror  45  has a four-layer structure. 
   This configuration has a merit that the surface of the reflecting film (reflecting surface)  450  is made smoother than in the case where the segmented electrodes  409   b  and the electrostrictive substance  453  are integrally constructed and thus aberrations are hard to generate optically. It is noted that the arrangement order of the deformable substrate  451  and the electrodes  452  may be reversed. 
   In  FIG. 25 , the reference numeral  449  denotes a button for performing magnification change or zooming of the optical system. The deformable mirror  45  is controlled via the arithmetical unit  414  so that a user can change the shape of the reflecting film  450  for magnification change or zooming by pushing the button  449 . 
   It is noted that a piezoelectric substance such as barium titanate set forth above may be used instead of the electrostrictive substance made of an organic substance such as acrylic elastomer. 
   As is commonly applicable to the various deformable mirrors described above, it is desirable that the contour of the deformable portion of the reflecting surface as viewed from a direction perpendicular to the reflecting surface is oblong in the direction of the plane of incidence of an axial ray, for example, elliptical, oval, or polygonal. The reason is as follows. The deformable mirror, as in the example of  FIG. 9 , is often used in a state where a ray of light is incident at a grazing angle. In order to suppress aberrations generated in this case, it is desirable that the reflecting surface has a shape similar to ellipsoid of revolution, paraboloid of revolution, or hyperboloid of revolution. If the contour of the deformable portion of the reflecting surface as viewed from the direction perpendicular to the reflecting surface is shaped oblong in the direction of the plane of incidence of an axial ray, the reflecting surface of the deformable mirror can be easily deformed into a shape similar to ellipsoid of revolution, paraboloid of revolution, or hyperboloid of revolution, which is advantageous for compensation for aberrations. 
   Finally, definitions of terms used in the present invention will be described. 
   The optical apparatus signifies an apparatus including an optical system or optical elements. It is not necessary that the optical apparatus can function by itself, that is, the optical apparatus may be a part of an apparatus. An imaging apparatus, an observation apparatus, a display apparatus, an illumination apparatus, a signal processing apparatus, etc. are classified into the optical apparatus. 
   As examples of the imaging apparatus, there are a film camera, a digital camera, robot eyes, a lens-exchange-type digital single-lens reflex camera, a TV camera, a motion-picture recording apparatus, an electronic motion-picture recording apparatus, a camcorder, a VTR camera, an electronic endoscope, etc. The digital camera, a card-type digital camera, the TV camera, the VTR camera, the motion-picture recording camera, etc. are examples of the electronic imaging apparatus. 
   As examples of the observation apparatus, there are a microscope, a telescope, spectacles, binoculars, a magnifying glass, a fiberscope, a finder, a viewfinder, etc. 
   As examples of the display apparatus, there are a liquid crystal display, a viewfinder, a game machine (PlayStation by SONY), a video projector, a liquid crystal projector, a head mounted display (HMD), a personal data assistant (PDA), a cellular phone, etc. 
   As examples of the illumination apparatus, there are a strobe for a camera, a headlight of an automobile, a light source for an endoscope, a light source for a microscope, etc. 
   As examples of the signal processing apparatus, there are a cellular phone, a personal computer, a game machine, a read/write apparatus for optical-discs, an arithmetical unit in an optical computer, etc. 
   The zoom optical system according to the present invention is small and lightweight, and thus is effectively used as an imaging system in an electronic imaging apparatus or in a signal processing apparatus, in particular, in a digital camera or a cellular phone. 
   The image pickup element signifies, for example, a CCD, a pickup tube, a solid-state image sensor, a photographic film, etc. A plane parallel plate is classified into the prism. Change of the observer includes the case where the diopter is changed. Change of the object includes the cases where the object distance is changed, where the object is displaced, where the object is moved, vibrated, or shaken, etc. 
   The expanded curved surface is defined as follows. 
   Not limited to a spherical, planar or rotationally symmetric aspherical surface, a surface may be configured as a spherical, planar or rotationally symmetric aspherical surface that is decentered from the optical axis; an aspherical surface defining planes of symmetry, only one plane of symmetry or no plane of symmetry; a free-formed surface; a surface having an indifferentiable point or line, or the like. In addition, irrespective of whether it is a reflecting surface or a refracting surface, any surface is applicable as long as it can exert some effect on light. According to the present invention, these surfaces are generally referred to as expanded curved surfaces. 
   A variable focus lens, a deformable mirror, a polarizing prism having a variable surface shape, a variable apex-angle prism, a variable diffraction optical element having a variable light-deflecting function, that is, a variable HOE or a variable DOE, etc. are classified into the variable optical-property optical element. A variable lens that changes not the focal length but the amount of aberrations is classified into the variable focus lens, also. Regarding the deformable mirror also, similar classification is applied. To conclude, an optical element that is changeable in light deflecting function such as reflection, refraction and diffraction is referred to as a variable optical-property optical element. 
   The data transmitter signifies an apparatus that allows data to be input therein and transmits the data, including a cellular phone; a fixed phone; a game machine; a remote controller of a TV set, a radio cassette recorder or a stereo set; a personal computer; and a keyboard, a mouse, a touchpanel, etc. of a computer. A TV monitor provided with an imaging device, and a monitor and a display of a personal computer also are classified into the data transmitter. Also, the data transmitter is classified into the signal processing apparatus.