Patent Publication Number: US-8976271-B2

Title: Optical system and image pickup apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an optical system used for image pickup apparatuses such as digital still cameras and video cameras, and particularly to an optical system suitable for a case where an image restoration process is performed on an image produced by image capturing. 
     2. Description of the Related Art 
     Images obtained by capturing an object through optical apparatuses such as digital cameras and interchangeable lenses include a blur component as an image degradation component caused by various aberrations of an image capturing optical system (hereinafter simply referred to as “an optical system”), such as spherical aberration, coma aberration, field curvature and astigmatism. Such a blur component is generated because a light flux emitted from one point of an object forms an image with some divergence on an image pickup surface, the light flux being normally converged at one point if there is no aberration or diffraction. 
     The blur component herein is optically expressed as a point spread function (PSF), which is different from blur caused by defocusing. Moreover, color blur in a color image caused due to longitudinal chromatic aberration, chromatic spherical aberration or chromatic coma aberration of the optical system can be said to be a difference between blurring degrees of respective light wavelengths. In addition, horizontal color shift caused by chromatic aberration of magnification of the optical system can be said to be position shift or phase shift of color light components caused by differences of image capturing magnifications for the respective color light components. 
     An optical transfer function (OTF) obtained by performing Fourier transform on the point spread function (PSF) is frequency component information of aberration, which is expressed by complex number. An absolute value of the optical transfer function (OTF), that is, an amplitude component is called a modulation transfer function (MTF), and a phase component is called a phase transfer function (PTF). The MTF and PTF are respectively a frequency characteristic of the amplitude component and a frequency characteristic of the phase component of image degradation caused by the aberration. The phase component is herein shown as a phase angle by the following expression where Re(OTF) and Im(OTF) respectively represent a real part and an imaginary part of the OTF.
 
 PTF =tan −1 ( Im ( OTF )/ Re ( OTF ))
 
     Thus, the optical transfer function (OTF) of the optical system degrades the amplitude component and the phase component of the image. Respective points of the object in the degraded image are asymmetrically blurred like coma aberration. 
     Moreover, the chromatic aberration of magnification is generated in an image pickup apparatus that captures, according to its spectral characteristics, color components such as R, G and B whose imaging positions are mutually shifted due to differences of imaging magnifications of its optical system for respective light wavelengths. Therefore, not only the shift of the imaging positions among the color components is generated, but also shift of imaging positions among wavelengths in each color component, that is, image spread due to the phase shift is generated. Thus, although, strictly speaking, the chromatic aberration of magnification is not merely a color shift that is parallel shift of colors, this specification treats the color shift as the chromatic aberration of magnification. 
     As a method for correcting such degradation of the amplitude component (MTF) and degradation of the phase component (PTF) in the degraded image (input image), there is known a method using information on the optical transfer function (OTF) of the optical system. This method is referred to as “image restoration” or “image recovery”, and a process for correcting the degraded image by using the information on the optical transfer function (OTF) of the optical system is hereinafter referred to as “an image restoration process” or simply “image restoration”. As one of the image restoration processes, a convolution method that performs convolution of an image restoration filter having an inverse characteristic to the optical transfer function on an input image in a real space (see Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2005-509333). Moreover, Japanese Patent Laid-Open No. 2010-56992 discloses a method of performing the image restoration process on an input image with filter coefficients held for correcting degradation of the input image. 
     On the other hand, it is generally difficult to decrease variation of aberration of an optical system due to variation of object distance. Therefore, emphasis on optical performance in a state where the optical system is focused on an infinite object distance is likely to deteriorate the aberration in a state where the optical system is focused on a closest object distance. Japanese Patent Laid-Open No. 2011-028166 discloses a method of providing a desired resolution (MTF width) by generating spherical aberration in order to perform good image restoration on an image obtained by image capturing of objects whose distances are mutually different. 
     When premising that the image restoration is performed, some aberration of an optical system is allowed, which enables downsizing of the optical system, higher magnification thereof and higher image quality over an entire object distance range. In other words, correcting, by using the image restoration image, degradation generated due to increase of refractive powers of respective lens units constituting the optical system in order to decrease its size, increase its magnification and improve image quality over the entire object distance range enables higher quality image while achieving downsizing of the optical system and higher magnification thereof. 
     However, an excessive strength of the image restoration emphasizes a noise component included in the degraded image. Moreover, an excessive allowable aberration amount for the optical system makes it impossible to sufficiently correct the image degradation by the image restoration. For example, an excessive field curvature causes tilt of an image plane on an image sensor even though there is a little manufacturing error of lenses constituting the optical system or a little tilt of the image sensor, which significantly causes an “uneven blur” which is asymmetry of resolving power. In this case, it is impossible to correct the image degradation well by the image restoration. 
     Therefore, in order to achieve the decreases in size of the optical system, the increase in magnification thereof and the improvement in image quality over the entire object distance range on the premise that the image restoration is performed, it is necessary to consider generation of appropriate aberration for the image restoration. Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2005-509333 and Japanese Patent Laid-Open Nos. 2010-56992 and 2011-028166 do not disclose such appropriate aberration for the image restoration at all. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides an optical system appropriate for downsizing, higher magnification and higher image quality over the entire object distance range on the premise that the image restoration is performed, and provides an image pickup apparatus performing the image restoration on an image produced by image capturing through the optical system. 
     The present invention provides as one aspect thereof an optical system capable of performing variation of magnification. The optical system includes, in order from an object side to an image side, a first lens unit and a second lens unit. At least one of the first and second lens units is moved during the variation of magnification. The optical system forms an optical image on an image sensor provided in an image pickup apparatus. The optical system satisfies the following conditions:
 
|(Δ TMyu+ΔTMyl )/(Δ WMyu+ΔWMyl )|&lt;0.67
 
0.75&lt;|(Δ WMyu+ΔwMyl )|/2 P&lt; 16.0
 
where, when a middle focal length closer to a wide-angle end of the optical system than to a telephoto end thereof is referred to as a wide-angle side middle focal length, another middle focal length closer to the telephoto end than to the wide-angle end is referred to as a telephoto side middle focal length, an image height corresponding to 80 percent of a maximum image height of the optical system is referred to as an 80 percent image height, and, among meridional rays passing through the optical system, an upper ray and a lower lay each passing through a position corresponding to 70 percent of an effective light flux diameter are respectively referred to as a 70 percent upper ray and a 70 percent lower ray,
 
     ΔWMyu represents a lateral aberration amount for a d-line of the 70 percent upper ray reaching the 80 percent image height at the wide-angle side middle focal length, 
     ΔWMyl represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height at the wide-angle side middle focal length, 
     ΔTMyu represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height at the telephoto side middle focal length, 
     ΔTMyl represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height at the telephoto side middle focal length, 
     P represents a pixel pitch of the image sensor, and 
     when fw represents a focal length of the optical system at the wide-angle end, ft represents a focal length of the optical system at the telephoto end, and fm=√(fw×ft), 
     the wide-angle side middle focal length fwm is expressed as fwm=√(fw×fm), and 
     the telephoto side middle focal length ftm is expressed as ftm=√(fm×ft). 
     The present invention provides as another aspect thereof an optical system capable of performing variation of magnification. The optical system includes, in order from an object side to an image side, a first lens unit and a second lens unit. At least one of the first and second lens units is moved during the variation of magnification. The optical system forms an optical image on an image sensor provided in an image pickup apparatus. The optical system satisfies the following conditions:
 
 Stm/Swm&lt; 0.67
 
0.75 &lt;Swm/ 2 P&lt; 16.0
 
where, when a middle focal length closer to a wide-angle end of the optical system than to a telephoto end thereof is referred to as a wide-angle side middle focal length, another middle focal length closer to the telephoto end than to the wide-angle end is referred to as a telephoto side middle focal length, an image height corresponding to 80 percent of a maximum image height of the optical system is referred to as an 80 percent image height, and a diameter of a spot formed by a light flux included in an area up to 70 percent of an effective light flux diameter in a point image intensity distribution of a d-line at a position where an MTF in a meridional direction for the d-line passing through the optical system and then reaching the 80 percent image height becomes peak is referred to as a 70 percent spot diameter,
 
     Swm represents the 70 percent spot diameter at the wide-angle side middle focal length, 
     Stm represents the 70 percent spot diameter at the telephoto side middle focal length, 
     P represents a pixel pitch of the image sensor, and 
     when fw represents a focal length of the optical system at the wide-angle end, ft represents a focal length of the optical system at the telephoto end, and fm=√(fw×ft), 
     the wide-angle side middle focal length fwm is expressed as fwm=√(fw×fm), and 
     the telephoto side middle focal length ftm is expressed as ftm=√(fm×ft). 
     The present invention provides as still another aspect thereof an optical system capable of an optical system capable of focusing on various object distances. The optical system includes a focus lens unit movable for focusing and another lens unit. The optical system forms an optical image on an image sensor provided in an image pickup apparatus. The optical system satisfies the following conditions in a case where an input image is produced by using output from the image sensor and an image restoration process is performed on the input image by using an image restoration filter having filter values corresponding to aberration of the optical system:
 
1&lt;|Δ yum+Δylm|/|Δyui+Δyli|&lt; 12
 
2&lt;|(Δ yum+Δylm )|/2 p&lt; 6
 
where, when an image height corresponding to 80 percent of a maximum image height of the optical system is referred to as an 80 percent image height, and, among meridional rays passing thorough the optical system, an upper ray and a lower lay each passing through a position corresponding to 70 percent of an effective light flux diameter are respectively referred to as a 70 percent upper ray and a 70 percent lower ray,
 
     Δyum represents a lateral aberration amount for a d-line of the 70 percent upper ray reaching the 80 percent image height in a state where the optical system is focused on the middle object distance, 
     Δylm represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height in the state where the optical system is focused on the middle object distance, 
     Δyui represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height in a state where the optical system is focused on an infinite object distance, 
     Δyli represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height in the state where the optical system is focused on the infinite object distance, and 
     p represents a pixel pitch of the image sensor, and 
     when f represents a focal length of the entire optical system, and dl represents a diagonal length of the image sensor, 
     the middle object distance is defined as (f/dl)×520. 
     The present invention provides as yet another aspect thereof an image pickup apparatus including an image sensor photoelectrically converting an object image formed by an optical system, and an image processor configured to perform an image restoration process on an input image input from the image sensor by using an image restoration filter having filter values corresponding to aberration of the optical system. The optical system is any one of the above optical systems. 
     Other aspects of the present invention will become apparent from the following description and the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a sectional view of a zoom lens that is Embodiment 1 (Numerical Example 1) of the present invention at a wide-angle end. 
         FIGS. 1B and 1C  are longitudinal and lateral aberration charts of this zoom lens at the wide-angle end. 
         FIGS. 2A and 2B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at a wide-angle side middle focal length. 
         FIGS. 2C and 2D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at a telephoto side middle focal length. 
         FIGS. 3A and 3B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at a telephoto end. 
         FIG. 4A  is a sectional view of a zoom lens that is Embodiment 2 (Numerical Example 2) of the present invention at a wide-angle end. 
         FIGS. 4B and 4C  are longitudinal and lateral aberration charts of this zoom lens at the wide-angle end. 
         FIGS. 5A and 5B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at a wide-angle side middle focal length. 
         FIGS. 5C and 5D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at a telephoto side middle focal length. 
         FIGS. 6A and 6B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at a telephoto end. 
         FIG. 7A  is a sectional view of a zoom lens that is Embodiment 3 (Numerical Example 3) of the present invention at a wide-angle end. 
         FIGS. 7B and 7C  are longitudinal and lateral aberration charts of this zoom lens at the wide-angle end. 
         FIGS. 8A and 8B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at a wide-angle side middle focal length. 
         FIGS. 8C and 8D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at a telephoto side middle focal length. 
         FIGS. 9A and 9B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at a telephoto end. 
         FIG. 10A  is a sectional view of a zoom lens that is Embodiment 4 (Numerical Example 4) of the present invention at a wide-angle end. 
         FIGS. 10B and 10C  are longitudinal and lateral aberration charts of this zoom lens at the wide-angle end. 
         FIGS. 11A and 11B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at a wide-angle side middle focal length. 
         FIGS. 11C and 11D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at a telephoto side middle focal length. 
         FIGS. 12A and 12B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at a telephoto end. 
         FIG. 13A  is a sectional view of a zoom lens that is Embodiment 5 (Numerical Example 5) of the present invention at a wide-angle end. 
         FIGS. 13B and 13C  are longitudinal and lateral aberration charts of this zoom lens at the wide-angle end. 
         FIGS. 14A and 14B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at a wide-angle side middle focal length. 
         FIGS. 14C and 14D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at a telephoto side middle focal length. 
         FIGS. 15A and 15B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at a telephoto end. 
         FIGS. 16A and 16B  show an image restoration filter used in an image restoration process performed on an image captured through the zoom lens of each embodiment. 
         FIGS. 17A and 17B  show correction of a point image by the image restoration process. 
         FIGS. 18A and 18B  respectively show correction of amplitude and correction of phase by the image restoration process. 
         FIGS. 19A and 19B  are lateral aberration charts showing aberration generated on a premise that the image restoration process is performed in Embodiments 1 to 5. 
         FIG. 20  is a block diagram showing a configuration of an image pickup apparatus including the zoom lens of any one of Embodiments 1 to 5 or an optical system of any one of Embodiments 6 to 8 of the present invention. 
         FIG. 21  is a sectional view of an optical system that is Embodiment 6 (Numerical Example 6) of the present invention at a wide-angle end. 
         FIGS. 22A and 22B  are longitudinal aberration charts of the optical system of Embodiment 6 at the wide-angle end and at a middle focal length in an infinite object distance in-focus state. 
         FIGS. 23A and 23B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at a telephoto end in the infinite object distance in-focus state. 
         FIGS. 24A and 24B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at the telephoto end in a closest object distance in-focus state. 
         FIGS. 25A and 25B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at the telephoto end in a middle object distance in-focus state. 
         FIG. 26  is a sectional view of an optical system that is Embodiment 7 (Numerical Example 7) of the present invention at a wide-angle end. 
         FIGS. 27A and 27B  are longitudinal aberration charts of the optical system of Embodiment 7 at the wide-angle end and at a telephoto end in an infinite object distance in-focus state. 
         FIGS. 28A and 28B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at a middle focal length in the infinite object distance in-focus state. 
         FIGS. 29A and 29B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at the middle focal length in a closest object distance in-focus state. 
         FIGS. 30A and 30B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at the middle focal length in a middle object distance in-focus state. 
         FIG. 31  is a sectional view of an optical system that is Embodiment 8 (Numerical Example 8) of the present invention at a wide-angle end. 
         FIGS. 32A and 32B  are longitudinal aberration charts of the optical system of Embodiment 8 at the wide-angle end and at a middle focal length in an infinite object distance in-focus state. 
         FIGS. 33A and 33B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at a telephoto end in the infinite object distance in-focus state. 
         FIGS. 34A and 34B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at the telephoto end in a closest object distance in-focus state. 
         FIGS. 35A and 35B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at the telephoto end in a middle object distance in-focus state. 
         FIGS. 36A and 36B  are lateral aberration charts showing aberration generated on a premise that the image restoration process is performed in Embodiments 6 to 8. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Exemplary embodiments of the present invention will be described below with reference to the accompanied drawings. 
     First of all, prior to description of specific embodiments, description will be made of definition of terms to be used in the embodiments and an image restoration process performed in the embodiments. 
     “Input Image” 
     The input image is a digital image produced by image capturing performed by an image pickup apparatus, that is, by using output from an image sensor photoelectrically converting an object image formed by an image capturing optical system. The image sensor is constituted by a photoelectric conversion element such as a CCD sensor or a CMOS sensor. The digital image is degraded in response to an optical transfer function (OTF) of the image capturing optical system constituted by lenses and various optical filters. The optical transfer function includes information on aberration of the image capturing optical system. The image capturing optical system may be constituted by reflective surfaces such as mirrors each having curvature. Moreover, the image capturing optical system may be detachably attachable (interchangeable) to the image pickup apparatus. In the image pickup apparatus, the image sensor and a signal processor that produces the digital image (input image) by using the output from the image sensor constitute an image capturing system. 
     The input image has information on color components such as R, G and B components. The color components can be also expressed by, other than the RGB, an optionally selected one of general color spaces such as LCH (lightness, chroma and hue), YCbCr (luminance, blue color difference and red color difference), XYZ, Lab, Yuv and JCh, or can be expressed by color temperature. 
     The input image and a restored image (output image) can be provided with information on an image capturing condition in the image pickup apparatus at a time of producing the input image, the image capturing condition including a focal length and an aperture value of the image capturing optical system, an image capturing distance (object distance) and the like. The information on the image capturing condition is hereinafter referred to as “image capturing condition information”. In addition, the input image can be provided with various correction information to be used for correction of the input image. When outputting the input image from the image pickup apparatus to an image processing apparatus separated therefrom and performing the image restoration process in the image processing apparatus, it is desirable to add the image capturing condition information and the correction information to the input image. The image processing apparatus can receive the image capturing condition information and the correction information from the image pickup apparatus not only by addition to the input image, but also through direct or indirect communication and through a storage medium detachably attachable to these apparatuses. 
     “Image Restoration Process” 
     The outline of the image restoration process is as follows. When g(x,y) represents an input image (degraded image) produced through image capturing performed by the image pickup apparatus, f(x,y) represents a non-degraded original image, h(x,y) represents a point spread function (PSF) that forms a Fourier pair with the optical transfer function (OTF), * represents convolution, and (x,y) represents coordinates in the input image, the following expression is established:
 
 g ( x,y )= h ( x,y )* f ( x,y ).
 
     Converting the above expression into a form of a two-dimensional frequency surface through Fourier transform provides the following expression of a form of a product for each frequency:
 
 G ( u,v )= H ( u,v )· F ( u,v )
 
where H represents a result of the Fourier transform of the point spread function (PSF), in other words, the optical transfer function (OTF), G and F respectively represent results of the Fourier transform of g and h, and (u,v) represents coordinates on the two-dimensional frequency surface, in other words, a frequency.
 
     Dividing both sides of the above expression by H as below provides the original image from the degraded image produced through the image capturing:
 
 G ( u,v )/ H ( u,v )= F ( u,v )
 
     Returning F(u,v), that is, G(u,v)/H(u,v) to a real surface by inverse Fourier transform provides a restored image equivalent to the original image f(x,y). 
     When R represents a result of the inverse Fourier transform of H −1 , performing a convolution process for an image in the real surface as represented by the following expression also enables provision of the original image:
 
 g ( x,y )* R ( x,y )= f ( x,y ).
 
     This R(x,y) in the above expression is an image restoration filter. When the input image is a two-dimensional image, the image restoration filter is generally also a two-dimensional filter having taps (cells) each corresponding to each of pixels of the two-dimensional image. Moreover, increase of the number of the taps (cells) in the image restoration filter generally improves image restoration accuracy, so that a realizable number of the taps is set depending on requested image quality, image processing capability, aberration characteristics of the image capturing optical system and the like. 
     Since the image restoration filter needs to reflect at least the aberration characteristics, the image restoration filter is different from a conventional edge enhancement filter (high-pass filter) or the like having about three taps in each of horizontal and vertical directions. The image restoration filter is produced based on the optical transfer function (OTF), which can highly accurately correct degradation of amplitude and phase components of the degraded image (input image). 
     Moreover, since an actual input image (degraded image) includes a noise component, use of an image restoration filter produced from the complete inverse number of the optical transfer function (OTF) as described above not only restores the degraded image, but also significantly amplifies the noise component. This is because such an image restoration filter raises a modulation transfer function (MTF), that is, an amplitude component of the image capturing optical system to 1 over an entire frequency range in a state where amplitude of the noise component is added to the amplitude component of the input image. Although the MTF corresponding to amplitude degradation by the image capturing optical system is returned to 1, power spectrum of the noise component is simultaneously raised, which results in amplification of the noise component according to a degree of raising of the MTF, that is, a restoration gain. 
     Therefore, the noise component included in the input image makes it impossible to provide a good restored image as an image for appreciation. Such raising of the noise component is shown by the following expressions where N represents the noise component:
 
 G ( u,v )= H ( u,v )· F ( u,v )+ N ( u,v )
 
 G ( u,v )/ H ( u,v )= F ( u,v )+ N ( u,v )/ H ( u,v )
 
     As a method for solving such a problem, there is known, for example, a Wiener filter expressed by the following expression (1), which controls image restoration degree according to an intensity ratio (SNR) of an image signal and a noise signal. 
     
       
         
           
             
               
                 
                   
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     In the above expression (1), M(u,v) represents a frequency characteristic of the Wiener filter, and |H(u,v)| represents an absolute value (MTF) of the optical transfer function (OTF). This method decreases, at each frequency, the restoration gain as the MTF is lower, in other words, increases the restoration gain as the MTF is higher. The MTF of general image capturing optical systems is high on a low frequency side and low on a high frequency side, so that the method resultantly suppresses the restoration gain on the high frequency side of the image signal. 
     An example of the image restoration filter is shown in  FIGS. 16A and 16B . For the image restoration filter, the number of the taps (cells) is decided corresponding to aberration characteristics of the image capturing optical system and required image restoration accuracy. 
     The image restoration filter shown in  FIG. 16A  is a two-dimensional filter having 11×11 taps. Although  FIG. 16A  omits values in the respective taps,  FIG. 16B  shows one cross section of this image restoration filter where values of the taps (in other words, filter values or filter coefficients, and hereinafter also referred to as “tap values”) is shown by a polygonal line. A distribution of the tap values in the image restoration filter plays a role to return signal values (PSF) spatially spread due to the aberration to, ideally, one point. 
     The image restoration process performs convolution of each tap value of the image restoration filter on each pixel (corresponding to each tap) of the input image. In the convolution, in order to improve the signal value of a certain pixel in the input image, that pixel is matched to a center tap of the image restoration filter. Then, a product of the pixel signal value of the input image and the tap value of the image restoration filter is calculated for each corresponding pair of the pixel in the input image and the tap of the image restoration filter, and the signal value of the pixel corresponding to the center tap of the filter is replaced by a total sum of the products. 
     Characteristics of the image restoration in a real space and a frequency space will be described with reference to  FIGS. 17A ,  17 B,  18 A and  18 B.  FIG. 17A  shows a PSF (point spread function) before the image restoration, and  FIG. 17B  shows a PSF after the image restoration.  FIG. 18A  shows (a) an MTF before the image restoration and (b) an MTF after the image restoration.  FIG. 18B  shows (a) a PTF (phase transfer function) before the image restoration and (b) a PTF after the image restoration. The PSF before the image restoration asymmetrically spreads, and the PTF changes non-linearly with frequency due to the asymmetry. The image restoration process amplifies the MTF and corrects the PTF to zero, so that the PSF after the image restoration becomes symmetric and sharp. 
     This image restoration filter can be obtained by inverse Fourier transform of a function designed on the basis of an inverse function of the optical transfer function (OTF) of the image capturing optical system. The image restoration filter used in the embodiments can be arbitrarily changed, and for example, the Wiener filter may be used as the image restoration filter. In the case of using the Wiener filter, the image restoration filter for the convolution on the input image in the real space can be produced by the inverse Fourier transform of the expression (1). 
     Moreover, since the optical transfer function (OTF) changes depending on image heights (positions in the input image) even though the image capturing condition is same, the image restoration filter to be used is changed depending on the image heights. 
     Description is hereinafter made of specific examples of zoom lenses as image capturing optical systems which are first to fifth embodiments (Embodiments 1 to 5) of the present invention. The zoom lens of each embodiment is capable of performing variation of magnification and achieves downsizing and higher magnification by generating appropriate aberration for correction of image degradation by the image restoration process. 
       FIGS. 1A ,  4 A,  7 A,  11 A and  13 A are respectively sectional views of the zoom lenses of Embodiments 1 to 5 at a wide-angle end. Arrows drawn below respective lens units (L 1  to L 5 ) and an aperture stop (SP) show movements thereof in an optical axis direction during variation of magnification (hereinafter simply referred to as “zooming”) from the wide-angle end to a telephoto end. 
       FIGS. 1B and 1C  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at the wide-angle end. The longitudinal aberration charts show spherical aberration, astigmatism, distortion and chromatic aberration of magnification. The lateral aberration charts show lateral aberrations at an image center and at an 80 percent image height (described later). Moreover,  FIGS. 2A and 2B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at a wide-angle side middle focal length.  FIGS. 2C and 2D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at a telephoto side middle focal length. The wide-angle side and telephoto side middle focal lengths will be described later. Furthermore,  FIGS. 3A and 3B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 1 at the telephoto end. 
     Similarly,  FIGS. 4B and 4C  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at the wide-angle end.  FIGS. 5A and 5B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at a wide-angle side middle focal length.  FIGS. 5C and 5D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at a telephoto side middle focal length. Furthermore,  FIGS. 6A and 6B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 2 at the telephoto end. 
       FIGS. 7B and 7C  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at the wide-angle end.  FIGS. 8A and 8B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at a wide-angle side middle focal length.  FIGS. 8C and 8D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at a telephoto side middle focal length. Furthermore,  FIGS. 9A and 9B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 3 at the telephoto end. 
       FIGS. 10B and 10C  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at the wide-angle end.  FIGS. 11A and 11B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at a wide-angle side middle focal length.  FIGS. 11C and 11D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at a telephoto side middle focal length. Furthermore,  FIGS. 12A and 12B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 4 at the telephoto end. 
       FIGS. 13B and 13C  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at the wide-angle end.  FIGS. 14A and 14B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at a wide-angle side middle focal length.  FIGS. 14C and 14D  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at a telephoto side middle focal length. Furthermore,  FIGS. 15A and 15B  are longitudinal and lateral aberration charts of the zoom lens of Embodiment 5 at the telephoto end. 
     In each embodiment, when fw represents a focal length of the zoom lens at the wide-angle end and fm represents a focal length thereof at the telephoto end, a middle focal length fm is defined as follows:
 
 fm =√( fw×ft )
 
     On the basis of this definition, the wide-angle side middle focal length fwm that is a middle focal length fm closer to the wide-angle end than to the telephoto end is defined as follows:
 
 fwm =√( fw×fm ), and
 
the telephoto side middle focal length ftm that is a middle focal length fm closer to the telephoto end than to the wide-angle end is defined as follows:
 
 ftm =√( fm×ft )
 
     In the sectional views of each embodiment, reference characters L 1  to L 5  denote first to fifth lens units, reference characters GB and G denote a glass block such as an optical filter or a color separation prism, reference character SP denotes an aperture stop. Moreover, reference character IP denotes an image plane. 
     In each longitudinal aberration chart, reference characters d and g respectively denote aberration for a d-line and aberration for a g-line. Moreover, reference characters AM and AS respectively denote aberration in a meridional image plane and aberration in a sagittal image plane. In addition, in each lateral aberration chart, reference character S denotes aberration of sagittal rays, and reference character M denotes aberration of meridional rays. The aberration chart of the chromatic aberration of magnification shows chromatic aberration of magnification for the g-line. 
     The zoom lens of each embodiment is designed on a premise that the image restoration process is performed, by using an image restoration filter having filter values corresponding to the aberration of the zoom lens, on an input image produced by image capturing of an object image formed by the zoom lens through the image sensor. On such a premise, the zoom lens of each embodiment satisfies the following both conditions (1) and (2). In the conditions (1) and (2), an image height corresponding to 80 percent of a maximum image height of the zoom lens, that is, an image height from a center of the image sensor (image center) to a peripheral side part thereof corresponding to 80 percent of a size of the image sensor (sensor size) is referred to as “the 80 percent image height”. Moreover, among meridional rays passing thorough the zoom lens, an upper ray and a lower lay each passing through a position corresponding to 70 percent of an effective light flux diameter are respectively referred to as “a 70 percent upper ray” and “a 70 percent lower ray”.
 
|(Δ TMyu+ΔTMyl )/(Δ WMyu+ΔWMyl )|&lt;0.67  (1)
 
0.75&lt;|(Δ WMyu+ΔWMyl )|/2 P&lt; 16.0  (2)
 
     In the conditions (1) and (2), ΔWMyu represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height at the wide-angle side middle focal length, ΔWMyl represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height at the wide-angle side middle focal length, ΔTMyu represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height at the telephoto side middle focal length, ΔTMyl represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height at the telephoto side middle focal length, and P represents a pixel pitch of the image sensor. 
     Satisfying both the conditions (1) and (2) makes it possible to achieve a zoom lens appropriate for downsizing and higher magnification on the premise that the image restoration is performed. As mentioned above, downsizing of the zoom lens and higher magnification thereof require increase of refractive powers of the respective lens units constituting the zoom lens. However, the increase of refractive powers of the lens units increases aberration variation, particularly variation of field curvature, during the zooming. Specifically, the field curvature becomes large toward an under side in a zoom range from the wide-angle end to the middle focal length, and the field curvature becomes large toward an over side in a zoom range from the middle focal length to the telephoto end. 
     In such variation of the field curvature during the zooming, correction of one of the under field curvature and the over field curvature increases the other. Therefore, conventional zoom lenses designed without the premise that the image restoration is performed are designed, in order to provide good optical performance over the entire zoom range, so as to approximately equalize (balance) variation amounts of the under field curvature and over field curvature while allowing residual field curvature over the entire zoom range. 
     In such zoom lenses having the residual field curvature, intentionally generating coma aberration makes it possible to correct the field curvature during the zooming. Description of this correction method is made with reference to  FIGS. 19A and 19B .  FIG. 19A  is typical lateral aberration charts in the zoom range from the middle focal length to the telephoto end. 
     As understood from  FIG. 19A , the meridional image plane is tilted to the over side at the 80 percent image height. This is because, especially, lower rays of the meridional rays are generated in a minus direction. Therefore, as shown in  FIG. 19B , generating upper rays of the meridional rays in the minus direction makes it possible to improve a tendency of such over side tilting of the entire meridional image plane. 
     Although the improvement of the variation of the field curvature is achieved by increasing the coma aberration and thereby resolution is deteriorated, correcting the resolution deterioration (that is, image degradation) by the image restoration enables achievement of good image quality with improvement of the variation of the field curvature. 
     Similarly, in the zoom range from the wide-angle range to the middle focal length, the meridional image plane is tilted to the under side because the lower rays of the meridional rays are generated on a plus side. Thus, generating upper rays of the meridional rays in the plus direction makes it possible to improve a tendency of under side tilting of the entire meridional image plane. 
     As described above, correcting the image degradation due to the generation of the coma aberration by the image restoration enables achievement of a zoom lens whose field curvature generated during the zooming is corrected. However, in general zoom lenses, an F-number thereof is increased from the wide-angle end toward the telephoto end, so that the coma aberration generated in the zoom range from the middle focal length to the telephoto end in order to correct the field curvature causes, in combination with an influence of diffraction, significant image degradation. In this case, the image restoration cannot provide a good restored image or extremely strong image restoration results in an image whose noise is emphasized. 
     Thus, it is desirable to optically correct the field curvature generated in the zoom range from the middle focal length to the telephoto end and, on the other hand, to decrease the field curvature generated in the zoom range from the wide-angle end to the middle focal length by generating the coma aberration and then correct the image degradation due to the coma aberration by the image restoration. Since the F-number is smaller (brighter) and the influence (image degradation) of the diffraction is also smaller in the zoom range from the wide-angle end to the middle focal length than those in the zoom range from the middle focal length to the telephoto end, it is possible to provide an image whose degradation due to the coma aberration can be sufficiently corrected by the image restoration. 
     The condition (1) limits a ratio of a coma aberration amount generated in the zoom range from the wide-angle end to the middle focal length and that in the zoom range from the middle focal length to the telephoto end. A higher value of the condition (1) than its upper limit excessively increases the coma aberration amount in the zoom range from the middle focal length to the telephoto end, which causes significant image degradation. 
     It is desirable to change the numerical range of the condition (1) as follows:
 
|(Δ TMyu+ΔTMyl )/(Δ WMyu+ΔWMyl )|&lt;0.55  (1)′
 
     The condition (2) relates to downsizing of the zoom lens, higher magnification thereof and higher image quality. A lower value of the condition (2) than its lower limit indicates that the coma aberration amount for correcting the variation of the field curvature during the zooming is insufficient. This means that sufficient refractive powers are not provided to the respective lens units constituting the zoom lens, which makes impossible to decrease the size of the zoom lens. 
     On the other hand, a higher value of the condition (2) than its upper limit excessively increases the coma aberration amount and thereby causes significant image degradation before the image restoration, which makes it impossible to perform good image restoration or which makes it necessary to perform extremely strong image restoration, resulting in increase in noise. 
     It is desirable to change the numerical range of the condition (2) as follows:
 
1.20&lt;|(Δ WMyu+ΔWMyl )|/2 P&lt; 14.0  (2)′
 
     It is more desirable to change the numerical range of the condition (2)′ as follows:
 
1.20&lt;|(Δ WMyu+ΔWMyl )|/2 P&lt; 8.0  (2)″
 
     Moreover, the zoom lens of each embodiment also satisfies both the following conditions (3) and (4). In the conditions (3) and (4), a diameter of a spot formed by a light flux included in an area up to percent of an effective light flux diameter in a point image intensity distribution of the d-line at a position where an MTF in a meridional direction for the d-line passing through the optical system and then reaching the 80 percent image height becomes peak is referred to as “a 70 percent spot diameter”.
 
 Stm/Swm&lt; 0.67  (3)
 
0.75 &lt;Swm/ 2 P&lt; 16.0  (4)
 
     In the conditions (3) and (4), Swm represent the 70 percent spot diameter at the wide-angle side middle focal length, and Stm represents the 70 percent spot diameter at the telephoto side middle focal length. 
     The conditions (3) and (4) are required to be satisfied for achieving, as well as the conditions (1) and (2), a zoom lens appropriate for downsizing and higher magnification on the premise that the image restoration is performed. The condition (3) limits, as well as the condition (1), the ratio of the coma aberration amount generated in the zoom range from the wide-angle end to the middle focal length and that in the zoom range from the middle focal length to the telephoto end. A higher value of the condition (3) than its upper limit excessively increases the coma aberration amount in the zoom range from the middle focal length to the telephoto end, which causes significant image degradation and thereby makes it impossible to perform good image restoration. 
     It is desirable to change the numerical range of the condition (3) as follows:
 
 Swm/Stm&lt; 0.55  (3)′
 
     The condition (4) relates, as well as the condition (2), to downsizing of the zoom lens, higher magnification thereof and higher image quality. A lower value of the condition (4) than its lower limit indicates that variation of the field curvature during the zooming is insufficient. This means that refractive powers of the respective lens units constituting the zoom lens are weak, which makes impossible to downsize the zoom lens. On the other hand, a higher value of the condition (4) than its upper limit excessively increases the coma aberration amount, which makes it impossible to perform good image restoration. 
     It is desirable to change the numerical range of the condition (4) as follows:
 
1.20 &lt;Swm/ 2 P&lt; 14.0  (4)′
 
     It is more desirable to change the numerical range of the condition (4)′ as follows:
 
1.20 &lt;Swm/ 2 P&lt; 8.0  (4)″
 
     Although the zoom lens of each embodiment satisfies all the conditions (1) to (4), it is not necessarily necessary to satisfy all the conditions (1) to (4). In other words, a zoom lens satisfying at least one of a pair of the conditions (1) and (2) and a pair of the conditions (3) and (4) is included in embodiments of the present invention. 
     The conventional zoom lenses are not designed in consideration of generation of appropriate come aberration for the image restoration like the zoom lens of each embodiment. In other words, the conventional zoom lenses are, even if they satisfy any one or more of the conditions (1) to (4) in part of a middle focal length range, merely zoom lenses whose optical performance is not corrected. 
     Furthermore, the zoom lens of each of Embodiments 1, 2, 4 and 5 includes, in order from an object side to an image side, a first lens unit L 1  having a positive refractive power and a second lens unit L 2  having a negative refractive power, and satisfies the following conditions:
 
0.30 &lt;f 1 /ft&lt; 1.20  (5)
 
−0.20 &lt;f 2 /ft&lt;− 0.03  (6)
 
where, as mentioned above, f 1  represents the focal length of the first lens unit L 1 , and f 2  represents the focal length of the second lens unit L 2 .
 
     These conditions (5) and (6) relate to downsizing of the zoom lens. A higher refractive power of the first lens unit L 1  making a value of the condition (5) lower than its lower limit can downsize the zoom lens but excessively increases the variation of the field curvature during the zooming, which makes it necessary to generate large coma aberration for correcting the field curvature, resulting in significant image degradation. Such significant image degradation makes it impossible to provide a good restored image even though the image restoration is performed or requires extremely strong image restoration, resulting in an image whose noise is emphasized. On the other hand, a lower refractive power of the first lens unit L 1  making the value of the condition (5) higher than its upper limit makes it impossible to downsize the zoom lens. 
     It is desirable to change the numerical range of the condition (5) as follows:
 
0.35 &lt;f 1 /ft&lt; 1.00  (5)′
 
     A higher refractive power of the second lens unit L 2  making a value of the condition (6) higher than its upper limit can downsize the zoom lens but excessively increases the variation of the field curvature during the zooming, as well as the condition (5). On the other hand, a lower refractive power of the second lens unit L 2  making the value of the condition (6) lower than its lower limit makes it impossible to downsize the zoom lens. 
     It is desirable to change the numerical range of the condition (6) as follows:
 
−0.18 &lt;f 2 /ft&lt;− 0.035  (6)
 
     The zoom lens of Embodiment 3, in order from the object side to the image side, a first lens unit L 1  having a negative refractive power and a second lens unit L 2  having a positive refractive power, and satisfies the following conditions:
 
−1.20 &lt;f 1 /ft&lt;− 0.30  (7)
 
0.20 &lt;f 2 /ft&lt; 1.10  (8)
 
where, as well as in the conditions (5) and (6), f1 represents the focal length of the first lens unit L 1 , and f 2  represents the focal length of the second lens unit L 2 .
 
     These conditions (7) and (8) also relate to downsizing of the zoom lens. A higher refractive power of the first lens unit L 1  making a value of the condition (7) higher than its upper limit can downsize the zoom lens but excessively increases the variation of the field curvature during the zooming, as with the case where the value of the condition (5) is lower than its lower limit. On the other hand, a lower refractive power of the first lens unit L 1  making the value of the condition (7) lower than its lower limit makes it impossible to downsize the zoom lens. 
     It is desirable to change the numerical range of the condition (7) as follows:
 
−1.00 &lt;f 1 /ft&lt;− 0.50  (7)′
 
     A higher refractive power of the second lens unit L 2  making a value of the condition (8) lower than its lower limit can downsize the zoom lens but excessively increases the variation of the field curvature during the zooming, as well as the condition (7). On the other hand, a lower refractive power of the second lens unit L 2  making the value of the condition (6) higher than its upper limit makes it impossible to downsize the zoom lens. 
     It is desirable to change the numerical range of the condition (8) as follows:
 
0.04 &lt;f 2 /ft&lt; 0.09  (8)′
 
       FIG. 20  shows an image pickup apparatus  10  that performs image capturing using the zoom lens of any one of Embodiments 1 to 5 as an image capturing optical system. Reference numeral  12  denotes an image sensor placed at a position of the image plane IP shown in the sectional view of each embodiment. Reference numeral  13  denotes an image processor that performs various image processes on output from the image sensor  12  to produce an image (input image) and performs the image restoration process on the image. Reference numeral  14  denotes a display/recorder that displays a resulting image (restored image) of the image restoration process on a monitor or records it to a recording medium such as a semiconductor memory. 
     Specific numerical examples (Numerical Examples 1 to 5) corresponding to Embodiments 1 to 5 are hereinafter described. 
     [Embodiment 1] 
     The zoom lens of Embodiment 1 (Numerical Example 1) shown in  FIG. 1A  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, the aperture stop SP, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative refractive power, a fifth lens unit L 5  having a positive refractive power and the glass block GB. The zoom lens of this embodiment has a maximum image height of 3.875 mm. At a position of the image plane IP, a 1/2.3″-type image sensor having a size of 4.65 mm×6.2 mm is placed. The image sensor has a pixel pitch of 1.4 μm. 
     Various numerical values of the zoom lens of Numerical Example 1 are shown below. In the numerical values, ri (i=1, 2, 3, . . . ) denotes a curvature radius of an i-th lens surface counted from the object side, and di denotes a lens thickness or an aerial distance between the i-th lens surface and an (i+1)-th lens surface. Moreover, ndi and νdi respectively denote a refractive index and an Abbe number of a material of an i-th lens for the d-line. Furthermore, an aspheric shape of an aspheric lens surface is expressed by the following expression where X represents a position (coordinates) in the optical axis direction, Y represents a position (coordinates) in a direction orthogonal to the optical axis direction and Ai (i=1, 2, 3, . . . ) denote aspheric coefficients:
 
 X =( Y   2   /R )/[1+{1−( K+ 1)( Y/R ) 2 } 1/2   ]+A 4 Y   4   +A 6 Y   6   +A 8 Y   8   +A 10 Y   10 + . . .
 
     In addition, e±M means ×10 ±M . Table 1 shows relations of Numerical Example 1 and the above-described conditions (1) to (6). 
     NUMERICAL EXAMPLE 1 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   108.138   1.80   1.72047   34.7   41.97        2   46.882   5.40   1.49700   81.5   38.17        3   −948.171   0.18           38.03        4   51.472   3.98   1.59282   68.6   37.28        5   280.538   (Variable)           36.84        6   142.905   0.95   1.88300   40.8   19.54        7   9.034   3.87           14.13        8   416.426   0.80   1.80400   46.6   13.84        9   19.874   1.93           13.27       10   −96.523   0.70   1.80400   46.6   13.28       11   62.894   0.20           13.36       12   19.599   1.99   1.94595   18.0   13.69       13   111.949   (Variable)           13.48       14 (SP)   ∞   (Variable)           8.74       15*   12.947   3.32   1.55332   71.7   12.70       16*   −54226.283   0.20           12.59       17   13.679   2.52   1.43875   94.9   12.49       18   −123.194   0.33           12.20       19   17.754   0.60   1.83400   37.2   11.42       20   9.366   (Variable)           10.62       21   21.048   0.70   1.90366   31.3   10.60       22   9.010   2.66   1.58144   40.8   10.18       23   60.714   (Variable)           10.12       24   21.195   2.14   1.49700   81.5   11.73       25   −53.651   0.60   2.00069   25.5   11.65       26   −104.874   (Variable)           11.64       27   ∞   0.30   1.51633   64.1   30.00       28   ∞   0.47           30.00       29   ∞   0.50   1.51633   64.1   30.00       30   ∞   (Variable)           30.00       IP   ∞                         Aspheric data               15th surface                         K = −2.43594e+000   A4 = 7.98678e−005   A6 = −2.91092e−007       A8 = 5.25522e−009   A10 = −3.88944e−011                     16th surface                         K = −1.89560e+010   A4 = 2.31285e−005   A6 = 2.28540e−007                         Various data       Zoom ratio 55.70                                     Tele   Wide-middle   Tele-middle   Tele               Focal length   3.86   10.55   78.70   215.00       F-number   2.87   4.00   6.00   7.07       Field angle   40.81   20.17   2.82   0.95       Image height   3.33   3.88   3.88   3.56       Entire lens length   105.00   99.99   142.21   150.99       Back focus   0.52   0.52   0.52   0.52       d5   0.78   12.45   57.11   66.09       d13   31.87   8.46   4.52   1.50       d14   19.63   14.65   2.19   1.50       d20   2.16   1.70   4.11   4.45       d23   5.84   12.92   10.83   32.80       d26   8.05   13.16   26.79   7.99       d30   0.52   0.52   0.52   0.52       Entrance pupil position   18.64   35.11   327.50   697.27       Exit pupil Position   75.99   421.93   −76.34   1211.72       Front principal point   22.70   45.93   325.62   950.44       Rear principal point   −3.34   −10.03   −78.18   −214.48                         Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               1   1   84.83   11.36   3.23   −4.14       2   6   −8.98   10.45   0.80   −7.77       SP   14   ∞   0.00   0.00   −0.00       3   15   21.73   6.96   −2.41   −6.21       4   21   −637.69   3.36   21.04   18.36       5   24   42.45   2.74   0.13   −1.60       GB   27   ∞   1.27   0.50   −0.50                         Single lens data                         Lens   Start surface   Focal length               1   1   −116.31       2   2   90.05       3   4   105.65       4   6   −10.96       5   8   −25.98       6   10   −47.27       7   12   24.85       8   15   23.39       9   17   28.22       10   19   −24.57       11   21   −17.93       12   22   17.86       13   24   30.86       14   25   −110.42       15   27   0.00       16   29   0.00                    
[Embodiment 2]
 
     The zoom lens of Embodiment 2 (Numerical Example 2) shown in  FIG. 4A  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, a third lens unit L 3  having a positive refractive power and a fourth lens unit L 4  having a positive refractive power. The third lens unit L 3  includes the aperture stop SP at its most-object side position. The zoom lens of this embodiment has a maximum image height of 13.66 mm. At a position of the image plane IP, an APS-C image sensor having a size of 16.7 mm×23.4 mm is placed. The image sensor has a pixel pitch of 4.3 μm. 
     Various numerical values of the zoom lens of Numerical Example 2 are shown below. Table 1 shows relations of Numerical Example 2 and the above-described conditions (1) to (6). 
     NUMERICAL EXAMPLE 2 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   113.657   1.90   1.84666   23.8   53.98        2   53.183   6.88   1.61800   63.4   48.92        3   523.832   0.15           47.42        4   46.041   4.39   1.80400   46.6   42.45        5   119.645   (Variable)           41.67        6*   120.426   0.05   1.51640   52.2   24.20        7   65.257   1.20   1.88300   40.8   24.12        8   11.378   5.80           17.37        9   −26.336   0.90   1.88300   40.8   16.94       10   35.376   0.15           16.40       11   26.235   5.14   1.80610   33.3   16.45       12   −26.406   0.81           15.84       13   −17.560   0.90   1.77250   49.6   15.62       14   113.521   2.48   1.80518   25.4   15.44       15   −32.837   (Variable)           15.36       16 (SP)   ∞   0.63           12.38       17   28.653   2.48   1.62588   35.7   12.72       18   −43.758   0.15           12.69       19   57.180   2.82   1.49700   81.5   12.48       20   −21.362   0.90   1.84666   23.8   12.23       21   −185.810   1.69           12.21       22*   −39.542   1.10   1.85135   40.1   12.13       23   23.050   1.97   1.84666   23.8   12.84       24   149.326   (Variable)           13.19       25   24.802   6.39   1.48749   70.2   20.47       26   −27.011   0.15           20.77       27   54.663   6.77   1.48749   70.2   20.14       28   −16.385   1.60   1.85006   40.2   19.46       29*   151.303   1.33           19.96       30   −74.814   3.32   1.48749   70.2   20.01       31   −26.114   (Variable)           20.74       IP   ∞                                         Aspheric data               6th surface                         K = 0.00000e+000   A4 = 3.31871e−005   A6 = −7.17135e−008       A8 = −3.88476e−011   A10 = 8.49129e−013                     22nd surface                         K = 0.00000e+000   A4 = 1.07044e−006   A6 = 1.54939e−007       A8 = −4.61739e−009   A10 = 4.32218e−011                     29th surface                         K = 0.00000e+000   A4 = 2.30287e−005   A6 = 8.82248e−009       A8 = −7.08911e−011   A10 = −9.36706e−014                         Various data       Zoom ratio 5.29                                     Tele   Wide-middle   Tele-middle   Tele               Focal length   15.50   23.51   54.07   82.00       F-number   3.63   4.12   5.36   5.85       Field angle   41.39   30.16   14.18   9.46       Image height   13.66   13.66   13.66   13.66       Entire lens length   130.51   137.58   159.48   170.51       Back focus   35.54   42.93   60.27   67.07       d5   2.46   11.06   27.14   35.19       d15   21.12   14.34   5.61   2.40       d24   9.34   7.19   4.40   3.81       d31   35.54   42.93   60.27   67.07       Entrance pupil position   25.33   40.80   87.54   128.46       Exit pupil Position   −55.24   −44.91   −35.13   −33.41       Front principal point   38.18   58.02   110.97   143.55       Rear principal point   20.04   19.43   6.21   −14.93                         Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               1   1   77.81   13.32   2.56   −5.29       2   6   −12.59   17.43   0.66   −13.13       3   16   86.07   11.74   −13.91   −18.89       4   25   31.42   19.56   1.86   −12.41                         Single lens data                         Lens   Start surface   Focal length               1   1   −119.78       2   2   95.25       3   4   90.68       4   6   −275.93       5   7   −15.77       6   9   −16.98       7   11   17.07       8   13   −19.63       9   14   31.87       10   17   28.03       11   19   31.67       12   20   −28.58       13   22   −16.97       14   23   31.97       15   25   27.64       16   27   26.69       17   28   −17.32       18   30   80.49                    
[Embodiment 3]
 
     The zoom lens of Embodiment 3 (Numerical Example 3) shown in  FIG. 7A  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a negative refractive power, the second lens unit L 2  having a positive refractive power, a third lens unit L 3  having a positive refractive power and a fourth lens unit L 4  having a negative refractive power. The second lens unit L 2  includes the aperture stop SP at its most-object side position. The zoom lens of this embodiment has a maximum image height of 3.875 mm. At a position of the image plane IP, a 1/2.3″-type image sensor having a size of 4.65 mm×6.2 mm is placed. The image sensor has a pixel pitch of 1.4 μm. 
     Various numerical values of the zoom lens of Numerical Example 3 are shown below. Table 1 shows relations of Numerical Example 3 and the above-described conditions (1) to (4), (7) and (8). 
     NUMERICAL EXAMPLE 3 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   295.700   2.75   1.80610   33.3   55.72        2   54.695   12.36    1.43875   94.9   53.95        3   −164.648   0.28           54.02        4   64.541   7.90   1.43387   95.1   53.09        5   −1787.494   0.20           52.40        6   41.571   6.53   1.72916   54.7   48.22        7   121.740   (Variable)           47.23        8   29.045   1.05   1.88300   40.8   18.73        9   7.595   5.10           13.38       10   −31.677   0.95   1.83481   42.7   13.22       11   23.837   0.20           13.20       12   15.622   2.56   1.92286   18.9   13.61       13   162.193   0.85   1.59282   68.6   13.36       14   56.850   (Variable)           13.08       15 (SP)   ∞   0.72           11.44       16   ∞   6.44           11.59       17   613.295   0.80   1.83481   42.7   12.91       18   17.223   2.69   1.80518   25.4   13.11       19   −104.938   0.20           13.25       20*   −251.445   4.03   1.58313   59.4   13.29       21   −10.187   0.85   1.76200   40.1   13.43       22   33.709   0.20           14.45       23   29.883   3.30   1.62299   58.2   14.75       24   −21.973   (Variable)           15.04       25   96.299   1.86   1.69680   55.5   15.07       26   −50.732   0.20           15.01       27   33.997   0.85   1.84666   23.9   14.51       28   13.453   4.33   1.69680   55.5   13.82       29   −109.010   (Variable)           13.51       30   ∞   0.80   1.52420   60.0   30.00       31   ∞   2.43   1.54400   70.0   30.00       32   ∞   1.50           30.00       33   ∞   20.00   1.58913   61.1   30.00       34   ∞   0.50   1.50000   60.0   30.00       35   ∞   (Variable)           30.00       IP   ∞                         Aspheric data               20th surface                         K = −1.27123e+000   A4 = −1.25967e−006   A6 = 3.75341e−009       A8 = −3.08875e−009   A10 = 5.88552e−011   A12 = 4.97575e−014                         Various data       Zoom ratio 19.54                                     Tele   Wide-middle   Tele-middle   Tele               Focal length   4.62   9.71   42.94   90.27       F-number   1.66   1.88   2.69   3.50       Field angle   33.00   17.16   4.00   1.90       Image height   3.00   3.00   3.00   3.00       Entire lens length   145.32   145.32   145.32   145.32       Back focus   0.80   0.80   0.80   0.80       d7   0.75   15.65   33.04   38.03       d14   37.82   22.92   5.53   0.54       d24   9.89   7.94   6.42   12.03       d29   3.63   5.57   7.09   1.49       d35   0.80   0.80   0.80   0.80       Entrance pupil position   35.22   76.90   248.71   403.07       Exit pupil Position   99.39   141.08   215.36   76.74       Front principal point   40.06   87.29   300.23   600.63       Rear principal point   −3.82   −8.91   −42.14   −89.47                         Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               1   1   55.54   30.03   14.33   −5.06       2   8   −9.59   10.71   1.49   −6.39       3   15   65.75   19.23   16.27   1.77       4   25   24.81   7.24   1.36   −3.01       G   30   ∞   25.23   8.26   −8.26                         Single lens data                         Lens   Start surface   Focal length               1   1   −83.68       2   2   95.21       3   4   143.76       4   6   83.70       5   8   −11.92       6   10   −16.17       7   12   18.58       8   13   −148.09       9   17   −21.24       10   18   18.56       11   20   18.10       12   21   −10.18       13   23   20.83       14   25   47.93       15   27   −26.80       16   28   17.44       17   30   0.00       18   31   0.00       19   33   0.00       20   34   0.00                    
[Embodiment 4]
 
     The zoom lens of Embodiment 4 (Numerical Example 4) shown in  FIG. 10A  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, the aperture stop SP, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a positive refractive power and the glass block G. The zoom lens of this embodiment has a maximum image height of 3.0 mm. At a position of the image plane IP, a ⅓″-type image sensor having a size of 3.6 mm×4.8 mm is placed. The image sensor has a pixel pitch of 2.7 μm. 
     Various numerical values of the zoom lens of Numerical Example 4 are shown below. Table 1 shows relations of Numerical Example 4 and the above-described conditions (1) to (6). 
     NUMERICAL EXAMPLE 4 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   295.700   2.75   1.80610   33.3   55.72        2   54.695   12.36    1.43875   94.9   53.95        3   −164.648   0.28           54.02        4   64.541   7.90   1.43387   95.1   53.09        5   −1787.494   0.20           52.40        6   41.571   6.53   1.72916   54.7   48.22        7   121.740   (Variable)           47.23        8   29.045   1.05   1.88300   40.8   18.73        9   7.595   5.10           13.38       10   −31.677   0.95   1.83481   42.7   13.22       11   23.837   0.20           13.20       12   15.622   2.56   1.92286   18.9   13.61       13   162.193   0.85   1.59282   68.6   13.36       14   56.850   (Variable)           13.08       15 (SP)   ∞   0.72           11.44       16   ∞   6.44           11.59       17   613.295   0.80   1.83481   42.7   12.91       18   17.223   2.69   1.80518   25.4   13.11       19   −104.938   (Variable)           13.25       20*   −251.445   4.03   1.58313   59.4   13.29       21   −10.187   0.85   1.76200   40.1   13.43       22   33.709   0.20           14.45       23   29.883   3.30   1.62299   58.2   14.75       24   −21.973   (Variable)           15.04       25   96.299   1.86   1.69680   55.5   15.07       26   −50.732   0.20           15.01       27   33.997   0.85   1.84666   23.9   14.51       28   13.453   4.33   1.69680   55.5   13.82       29   −109.010   (Variable)           13.51       30   ∞   0.80   1.52420   60.0   30.00       31   ∞   2.43   1.54400   70.0   30.00       32   ∞   1.50           30.00       33   ∞   20.00    1.58913   61.1   30.00       34   ∞   0.50   1.50000   60.0   30.00       35   ∞   (Variable)           30.00       IP   ∞                         Aspheric data       20th surface                                 K = −1.27123e+000   A4 = −1.25967e−006   A6 = 3.75341e−009       A8 = −3.08875e−009   A10 = 5.88552e−011   A12 = 4.97575e−014                         Various data       Zoom ratio 19.54                                     Tele   Wide-middle   Tele-middle   Tele               Focal length   4.62   9.71   42.94   90.27       F-number   1.66   1.88   2.69   3.50       Field angle   33.00   17.16   4.00   1.90       Image height   3.00   3.00   3.00   3.00       Entire lens length   145.32   145.32   145.32   145.32       Back focus   0.80   0.80   0.80   0.80       d7   0.75   15.65   33.04   38.03       d14   37.82   22.92   5.53   0.54       d19   0.20   0.20   0.20   0.20       d24   9.89   7.94   6.42   12.03       d29   3.63   5.57   7.09   1.49       d35   0.80   0.80   0.80   0.80       Entrance pupil position   35.22   76.90   248.71   403.07       Exit pupil Position   99.39   141.08   215.36   76.74       Front principal point   40.06   87.29   300.23   600.63       Rear principal point   −3.82   −8.91   −42.14   −89.47                         Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               1   1   55.54   30.03   14.33   −5.06       2   8   −9.59   10.71   1.49   −6.39       3   15   136.72   10.65   9.08   −0.01       4   20   115.02   8.38   12.38   7.82       5   25   24.81   7.24   1.36   −3.01       G   30   ∞   25.23   8.26   −8.26                         Single lens data                         Lens   Start surface   Focal length               1   1   −83.68       2   2   95.21       3   4   143.76       4   6   83.70       5   8   −11.92       6   10   −16.17       7   12   18.58       8   13   −148.09       9   17   −21.24       10   18   18.56       11   20   18.10       12   21   −10.18       13   23   20.83       14   25   47.93       15   27   −26.80       16   28   17.44       17   30   0.00       18   31   0.00       19   33   0.00       20   34   0.00                    
[Embodiment 5]
 
     The zoom lens of Embodiment 5 (Numerical Example 5) shown in  FIG. 13A  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, the aperture stop SP, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative e refractive power, a fifth lens unit L 5  having a positive refractive power and the glass block GB. The zoom lens of this embodiment has a maximum image height of 3.875 mm. At a position of the image plane IP, a 1/2.3″-type image sensor having a size of 4.65 mm×6.2 mm is placed. The image sensor has a pixel pitch of 0.3 μm. 
     Various numerical values of the zoom lens of Numerical Example 5 are shown below. Table 1 shows relations of Numerical Example 5 and the above-described conditions (1) to (6). 
     NUMERICAL EXAMPLE 5 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 diameter 
               
               
                   
               
               
                  1 
                 108.139 
                 1.80 
                 1.72047 
                 34.7 
                 41.98 
               
               
                  2 
                 46.878 
                 5.40 
                 1.49700 
                 81.5 
                 38.18 
               
               
                  3 
                 −948.122 
                 0.18 
                   
                   
                 38.05 
               
               
                  4 
                 51.472 
                 3.98 
                 1.59282 
                 68.6 
                 37.30 
               
               
                  5 
                 280.522 
                 (Variable) 
                   
                   
                 36.86 
               
               
                  6 
                 142.830 
                 0.95 
                 1.88300 
                 40.8 
                 19.54 
               
               
                  7 
                 9.035 
                 3.88 
                   
                   
                 14.13 
               
               
                  8 
                 417.772 
                 0.80 
                 1.80400 
                 46.6 
                 13.84 
               
               
                  9 
                 19.875 
                 1.94 
                   
                   
                 13.27 
               
               
                 10 
                 −96.447 
                 0.70 
                 1.80400 
                 46.6 
                 13.28 
               
               
                 11 
                 62.883 
                 0.20 
                   
                   
                 13.36 
               
               
                 12 
                 19.599 
                 2.00 
                 1.94595 
                 18.0 
                 13.68 
               
               
                 13 
                 111.879 
                 Variable) 
                   
                   
                 13.48 
               
               
                 14 (SP) 
                 ∞ 
                 (Variable) 
                   
                   
                 8.74 
               
               
                 15* 
                 12.943 
                 3.29 
                 1.55332 
                 71.7 
                 12.69 
               
               
                 16* 
                 −54545.449 
                 0.20 
                   
                   
                 12.58 
               
               
                 17 
                 13.671 
                 2.52 
                 1.43875 
                 94.9 
                 12.49 
               
               
                 18 
                 −123.226 
                 0.32 
                   
                   
                 12.19 
               
               
                 19 
                 17.759 
                 0.60 
                 1.83400 
                 37.2 
                 11.41 
               
               
                 20 
                 9.367 
                 (Variable) 
                   
                   
                 10.62 
               
               
                 21 
                 21.415 
                 0.70 
                 1.90366 
                 31.3 
                 10.60 
               
               
                 22 
                 8.940 
                 2.68 
                 1.59276 
                 40.1 
                 10.18 
               
               
                 23 
                 60.355 
                 (Variable) 
                   
                   
                 10.12 
               
               
                 24 
                 21.419 
                 2.14 
                 1.49796 
                 81.5 
                 11.72 
               
               
                 25 
                 −51.928 
                 0.60 
                 2.00069 
                 25.5 
                 11.64 
               
               
                 26 
                 −99.982 
                 (Variable) 
                   
                   
                 11.64 
               
               
                 27 
                 ∞ 
                 0.30 
                 1.51633 
                 64.1 
                 30.00 
               
               
                 28 
                 ∞ 
                 0.47 
                   
                   
                 30.00 
               
               
                 29 
                 ∞ 
                 0.50 
                 1.51633 
                 64.1 
                 30.00 
               
               
                 30 
                 ∞ 
                 (Variable) 
                   
                   
                 30.00 
               
               
                 IP 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspheric data 
               
               
                   
               
               
                 15th surface 
               
            
           
           
               
               
               
            
               
                 K = −2.41580e+000 
                 A4 = 7.89141e−005 
                 A6 = −3.47105e−007 
               
               
                 A8 = 6.16247e−009 
                 A10 = −4.91024e−011 
               
            
           
           
               
            
               
                 16th surface 
               
            
           
           
               
               
               
            
               
                 K = −1.89560e+010 
                 A4 = 2.26087e−005 
                 A6 = 1.86093e−007 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 55.70 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Tele 
                 Wide-middle 
                 Tele-middle 
                 Tele 
               
               
                   
               
               
                 Focal length 
                 3.86 
                 10.55 
                 78.70 
                 215.00 
               
               
                 F-number 
                 2.87 
                 5.00 
                 6.00 
                 7.07 
               
               
                 Field angle 
                 40.81 
                 20.17 
                 2.82 
                 0.95 
               
               
                 Image height 
                 3.33 
                 3.88 
                 3.88 
                 3.56 
               
               
                 Entire lens length 
                 105.00 
                 100.00 
                 142.21 
                 151.00 
               
               
                 Back focus 
                 0.52 
                 0.52 
                 0.52 
                 0.52 
               
               
                 d5 
                 0.78 
                 12.45 
                 57.12 
                 66.10 
               
               
                 d13 
                 31.86 
                 8.45 
                 4.52 
                 1.50 
               
               
                 d14 
                 19.63 
                 14.64 
                 2.19 
                 1.50 
               
               
                 d20 
                 2.01 
                 1.51 
                 3.85 
                 4.17 
               
               
                 d23 
                 5.98 
                 13.07 
                 11.05 
                 33.06 
               
               
                 d26 
                 8.08 
                 13.19 
                 26.82 
                 8.00 
               
               
                 d30 
                 0.52 
                 0.52 
                 0.52 
                 0.52 
               
               
                 Entrance pupil position 
                 18.65 
                 35.12 
                 327.64 
                 697.90 
               
               
                 Exit pupil Position 
                 76.26 
                 431.24 
                 −76.20 
                 1259.01 
               
               
                 Front principal point 
                 22.70 
                 45.93 
                 325.62 
                 949.63 
               
               
                 Rear principal point 
                 −3.34 
                 −10.03 
                 −78.18 
                 −214.48 
               
               
                   
               
            
           
           
               
            
               
                 Lens unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                 Start 
                 Focal 
                 unit 
                 principal 
                 principal 
               
               
                 Unit 
                 surface 
                 length 
                 length 
                 point 
                 point 
               
               
                   
               
               
                 1 
                 1 
                 84.84 
                 11.37 
                 3.23 
                 −4.15 
               
               
                 2 
                 6 
                 −8.98 
                 10.46 
                 0.80 
                 −7.78 
               
               
                 SP 
                 14 
                 ∞ 
                 0.00 
                 0.00 
                 −0.00 
               
               
                 3 
                 15 
                 21.73 
                 6.93 
                 −2.40 
                 −6.18 
               
               
                 4 
                 21 
                 −634.10 
                 3.38 
                 21.01 
                 18.33 
               
               
                 5 
                 24 
                 42.51 
                 2.74 
                 0.15 
                 −1.59 
               
               
                 GB 
                 27 
                 ∞ 
                 1.27 
                 0.50 
                 −0.50 
               
               
                   
               
            
           
           
               
            
               
                 Single lens data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 −116.29 
               
               
                 2 
                 2 
                 90.04 
               
               
                 3 
                 4 
                 105.65 
               
               
                 4 
                 6 
                 −10.96 
               
               
                 5 
                 8 
                 −25.98 
               
               
                 6 
                 10 
                 −47.25 
               
               
                 7 
                 12 
                 24.86 
               
               
                 8 
                 15 
                 23.39 
               
               
                 9 
                 17 
                 28.21 
               
               
                 10 
                 19 
                 −24.57 
               
               
                 11 
                 21 
                 −17.45 
               
               
                 12 
                 22 
                 17.37 
               
               
                 13 
                 24 
                 30.75 
               
               
                 14 
                 25 
                 −108.65 
               
               
                 15 
                 27 
                 0.00 
               
               
                 16 
                 29 
                 0.00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Numerical Example 1 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Numerical 
                 Numerical 
                 Numerical 
                 Numerical 
                 Numerical 
               
               
                   
                 Example 1 
                 Example 2 
                 Example 3 
                 Example 4 
                 Example 5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 |(ΔTMyu + 
                 0.497 
                 0.171 
                 0.298 
                 0.25 
                 0.636 
               
               
                 ΔTMyl)/ 
               
               
                 (ΔWMyu + 
               
               
                 ΔWMyl)| 
               
               
                 |(ΔWMyu + 
                 2.504 
                 1.577 
                 4.453 
                 3.751 
                 13.46 
               
               
                 ΔWMyl)|/2P 
               
               
                 Swm/Stm 
                 0.497 
                 0.171 
                 0.298 
                 0.25 
                 0.636 
               
               
                 Swm/2P 
                 2.504 
                 1.577 
                 4.453 
                 3.751 
                 13.46 
               
               
                 f1/ft 
                 0.395 
                 0.949 
                 −0.73 
                 0.615 
                 0.395 
               
               
                 f2/ft 
                 −0.042 
                 −0.154 
                 0.667 
                 −0.106 
                 −0.042 
               
               
                   
               
            
           
         
       
     
     Each of Embodiments 1 to 5 can achieve a compact zoom lens having a high magnification with generating appropriate aberration for the image restoration. Performing image capturing using this zoom lens and then performing the image restoration process can achieve a compact image pickup apparatus capable of providing high quality images. 
     Next, description will be made of specific examples of an optical system (image capturing optical system) which is capable of focusing on objects at various object distances and which can provide high quality images over an entire range of the object distance with a compact size by generating aberration that generates image degradation appropriate for correction by the image restoration as sixth to eighth embodiments (Embodiments 6 to 8). 
       FIGS. 21 ,  26  and  31  are respectively sectional views of the zoom lenses of Embodiments 6 to 8 at a wide-angle end. Arrows drawn below respective lens units (L 1  to L 6 ) and an aperture stop (SP) show movements thereof in an optical axis direction during variation of magnification (hereinafter simply referred to as “zooming”) from the wide-angle end to a telephoto end. Although the optical system of each of Embodiments 6 to 8 is a zoom lens capable of zooming, a fixed focal length lens which is not capable of zooming but is capable of focusing by moving a focus lens unit such that an focused image is formed on an image pickup surface (image sensor surface) is included in embodiments of the present invention. 
       FIGS. 22A and 22B  are longitudinal aberration charts of the optical system of Embodiment 6 at the wide-angle end and at a middle focal length in a state where the optical system is focused on an infinite object distance (infinity end). The state where the optical system is focused on the infinite object distance is hereinafter referred to as “an infinite object distance in-focus state”.  FIGS. 23A and 23B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at a telephoto end in the infinite object distance in-focus state. The longitudinal aberration charts show spherical aberration, astigmatism, distortion and chromatic aberration of magnification. The lateral aberration charts show lateral aberrations at an image center and at an 80 percent image height (described later). 
     Moreover,  FIGS. 24A and 24B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at the telephoto end in a state where the optical system is focused on a closest object distance (closest end). The state where the optical system is focused on the closest object distance is hereinafter referred to as “a closest object distance in-focus state”.  FIGS. 25A and 25B  are longitudinal and lateral aberration charts of the optical system of Embodiment 6 at the telephoto end in a state where the optical system is focused on a middle object distance. The state where the optical system is focused on the middle object distance is hereinafter referred to as “a middle object distance in-focus state”. 
       FIGS. 27A and 27B  are longitudinal aberration charts of the optical system of Embodiment 7 at the wide-angle end and at a telephoto end in an infinite object distance in-focus state.  FIGS. 28A and 28B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at a middle focal length in the infinite object distance in-focus state.  FIGS. 29A and 29B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at the middle focal length in a closest object distance in-focus state.  FIGS. 30A and 30B  are longitudinal and lateral aberration charts of the optical system of Embodiment 7 at the middle focal length in a middle object distance in-focus state. 
       FIGS. 32A and 32B  are longitudinal aberration charts of the optical system of Embodiment 8 at the wide-angle end and at a middle focal length in an infinite object distance in-focus state.  FIGS. 33A and 33B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at a telephoto end in the infinite object distance in-focus state.  FIGS. 34A and 34B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at the telephoto end in a closest object distance in-focus state.  FIGS. 35A and 35B  are longitudinal and lateral aberration charts of the optical system of Embodiment 8 at the telephoto end in a middle object distance in-focus state. 
     In the sectional views of each embodiment, reference characters L 1  to L 6  denote first to sixth lens units, reference characters GB denotes a glass block such as an optical filter or a color separation prism, and reference character SP denotes an aperture stop. Moreover, reference character IP denotes an image plane. 
     In each longitudinal aberration chart, reference characters d and g respectively denote aberration for a d-line and aberration for a g-line. Moreover, reference characters AM and AS respectively denote aberration in a meridional image plane and aberration in a sagittal image plane. In addition, in each lateral aberration chart, reference character S denotes aberration of sagittal rays, and reference character M denotes aberration of meridional rays. The aberration chart of the chromatic aberration of magnification shows chromatic aberration of magnification for the g-line. 
     The optical system of each embodiment (lens as an image capturing optical system) is designed on a premise that the image restoration process is performed, by using an image restoration filter having filter values corresponding to the aberration of the zoom lens, on an input image produced by image capturing of an object image formed by the optical system through the image sensor. On such a premise, the optical system of each of Embodiments 6 to 8 satisfies the following both conditions (9) and (10). In the conditions (9) and (10), an image height corresponding to 80 percent of a maximum image height of the optical system, that is, an image height from a center of the image sensor (image center) to a peripheral side part thereof corresponding to 80 percent of a size of the image sensor (sensor size) is referred to as “the 80 percent image height”. Moreover, among meridional rays passing thorough the zoom lens, an upper ray and a lower lay each passing through a position corresponding to 70 percent of an effective light flux diameter are respectively referred to as “a 70 percent upper ray” and “a 70 percent lower ray”. In addition, a middle object distance is defined as (f/dl)×520 where f represents a focal length of the entire optical system, and dl represents a diagonal length of the image sensor. The diagonal length of the image sensor is, more strictly speaking, a diagonal length of an effective image pickup area of the image sensor.
 
1 &lt;|Δyum+Δylm|/|Δyui+Δyli|&lt; 12  (9)
 
2&lt;|(Δ yum+Δylm )|/2 p&lt; 6  (10)
 
     In the conditions (9) and (10), Δyum represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height in the middle object distance in-focus state, Δylm represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height in the middle object distance in-focus state, Δyui represents a lateral aberration amount for the d-line of the 70 percent upper ray reaching the 80 percent image height in the infinite object distance in-focus state, and Δyli represents a lateral aberration amount for the d-line of the 70 percent lower ray reaching the 80 percent image height in the infinite object distance in-focus state, and p represents a pixel pitch of the image sensor. 
     The conditions (9) and (10) are conditions for providing high quality images over the entire object distance range from the infinite object distance to the closest object distance and downsizing the optical system on a premise that the image restoration is performed. 
     Variation of the object distance shifts the focal plane (imaging position) from a position of the image sensor (hereinafter referred to as “a sensor position”), and thereby generally a focus lens unit is moved such that the focal plane coincides with the sensor position. However, movement of the focus lens changes relative positional relations thereof with other lens units, which increases variation of aberration, particularly field curvature, with respect to the variation of the object distance. 
     Moreover, movement of the focus lens from an in-focus position for the infinite object distance to another in-focus position for the closest object distance varies spherical aberration and field curvature, which causes displacement of an axial focal plane and an off-axis focal plane, resulting in image quality deterioration at the sensor position. 
     Such variation of the field curvature with the variation of the object distance generates a relation that optical correction of the field curvature at a certain object distance increases the field curvature at other object distances. Therefore, conventional optical systems designed without the premise that the image restoration is performed are designed, in order to provide good optical performance over the entire object distance range, so as to equalize (balance) a variation amount of the field curvature while allowing residual variation of the field curvature with the variation of the object distance over the entire object distance range. 
     In such optical systems having the residual variation of the field curvature, intentionally generating coma aberration makes it possible to correct the variation of the field curvature with the variation of the object distance. Description of this correction method is made with reference to  FIGS. 36A and 36B .  FIG. 36A  is typical lateral aberration charts showing lateral aberration from the infinite object distance in-focus state to the closest object distance in-focus position. In the lateral aberration at the image center shown in  FIG. 36A , spherical aberration is smaller than that of general optical systems, so that an image plane where an MTF becomes peak (hereinafter referred to as “an MTF peak image plane”) approximately coincides with the focal plane. 
     In contrast, at the 80 percent image height, the meridional plane is tilted to the over side, and thus an off-axis MTF peak image plane shifts from an axial MTF peak image plane. This is because, especially, lower rays of the meridional rays are generated in a minus direction. Therefore, as shown in  FIG. 36B , generating upper rays of the meridional rays in the minus direction makes it possible to improve a tendency of such over side tilting of the entire meridional image plane. 
     Although the improvement of the variation of the field curvature is achieved by increase of the coma aberration and thereby resolution is deteriorated, correcting the resolution deterioration (that is, image degradation) by the image restoration enables achievement of good image quality with the improvement of the variation of the field curvature. 
     As described above, correcting the image degradation due to the generation of the coma aberration by the image restoration can provide an optical system capable of correcting the variation of the field curvature with the variation of the object distance. 
     The condition (9) limits a ratio of a coma aberration amount in the middle object distance in-focus state and that in the infinite object distance in-focus state. A higher value of the condition (9) than its upper limit excessively increases the coma aberration amount in the middle object distance in-focus state, which causes significant image degradation. On the other hand, a lower value of the condition (9) than its lower limit excessively decreases the coma aberration amount in the middle object distance in-focus state, which undesirably makes it difficult to correct the variation of the field curvature with the variation of the object distance. 
     It is desirable to change the numerical range of the condition (9) as follows:
 
1 &lt;|Δyum+Δylm|/|Δyui+Δyli|&lt; 10  (9)′
 
     The condition (10) relates to improvement in image quality. A lower value of the condition (10) than its lower limit excessively decreases the coma aberration amount, which undesirably makes it difficult to correct the variation of the field curvature with the variation of the object distance. On the other hand, a higher value of the condition (10) than its upper limit excessively increases the coma aberration amount and thereby causes significant image degradation before the image restoration, which makes it impossible to provide a good restored image by the image restoration or which makes it necessary to perform extremely strong image restoration, resulting in increase in noise. 
     It is desirable to change the numerical range of the condition (10) as follows:
 
2&lt;|(Δ yum+Δylm )|/2 p&lt; 5  (10)′
 
     As mentioned above, in each of Embodiments 6 to 8, the middle object distance is defined as:
 
( f/dl )×520
 
where f represents the focal length of the entire optical system, and dl represents the diagonal length of the image sensor. A longer object distance than this middle object distance makes the focal length of the entire optical system excessively large with respect to the diagonal length of the image sensor used in, for example, Embodiment 8. In this case, the middle object distance becomes too long and thereby becomes close to the infinite object distance, which makes it difficult to decrease the variation of the field curvature with the variation of the object distance. On the other hand, a shorter object distance than the above middle object distance makes the focal length of the entire optical system excessively small with respect to the diagonal length of the image sensor used in each of Embodiments 6 and 7. In this case, the middle object distance becomes too short and thereby becomes close to the closest object distance, which also makes it difficult to decrease the variation of the field curvature with the variation of the object distance.
 
     Conventional optical systems are not designed in consideration of generation of appropriate coma aberration for the image restoration like the optical systems of each of Embodiments 6 to 8. In other words, the conventional optical systems are, even if they satisfy any one of or both the conditions (9) and (10) in part of a middle object distance range, merely optical systems whose optical performance is not corrected. 
     Furthermore, the optical system of each of Embodiments 6 to 8 includes, in order from an object side to an image side, a first lens unit L 1  having a positive refractive power and a second lens unit L 2  having a positive refractive power. 
     The optical system of each of Embodiments 6 to 8 can be used for the image pickup apparatus  10  shown in  FIG. 20 . 
     Specific numerical examples (Numerical Examples 6 to 8) corresponding to Embodiments 6 to 8 are hereinafter described. 
     [Embodiment 6] 
     The optical system of Embodiment 6 (Numerical Example 6) shown in  FIG. 21  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative refractive power, a fifth lens unit L 5  having a positive refractive power, a sixth lens unit L 6  having a negative refractive power and the glass block GB. The third lens unit L 3  includes the aperture stop SP at its most-image side position. The optical system of this embodiment has a maximum image height of 21.635 mm. At a position of the image plane IP, a full-size image sensor having a size of 24 mm×36 mm is placed. The image sensor has a pixel pitch of 6.4 μm. 
     As understood from the longitudinal aberration charts at the wide-angle and telephoto ends in the infinite object distance in-focus state respectively shown in  FIGS. 22A and 22B , the aberrations are sufficiently corrected. Moreover, as understood from the lateral aberration charts at the telephoto end in the middle object distance in-focus state, the closest object distance in-focus state and the infinite object distance in-focus state respectively shown in  FIGS. 23B ,  24 B and  25 B, the generation of the coma aberration decreases the variation of the field curvature at the telephoto end over the entire object distance range. 
     Various numerical values of the optical system of Numerical Example 6 are shown below. In the numerical values, ri, di, ndi and vdi denote same values as those in Numerical Examples 1 to 5. Moreover, the aspheric shape is expressed by the above-described expression using R, X, Y and Ai. Table 2 shows relations of Numerical Example 6 and the above-described conditions (9) and (10). 
     NUMERICAL EXAMPLE 6 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   95.784   6.02   1.48749   70.2   56.00        2   737.461   0.18           55.50        3   102.717   2.10   1.61340   44.3   53.80        4   45.455   9.10   1.49700   81.5   50.97        5   2528.799   (Variable)           50.29        6   −165.094   1.20   1.83481   42.7   25.20        7   55.232   3.29           24.32        8   −45.986   1.20   1.63854   55.4   24.28        9   53.394   2.97   1.84666   23.8   24.72       10   −414.048   (Variable)           25.00       11   344.048   4.25   1.49700   81.5   25.60       12   −42.005   0.15           25.76       13   66.804   4.35   1.58913   61.1   25.41       14   −42.512   1.20   1.85026   32.3   25.09       15   −264.354   1.00           24.86       16 (SP)   ∞   (Variable)           24.61       17   −48.251   1.20   1.70154   41.2   23.00       18   40.610   3.94   1.80518   25.4   23.66       19   −169.835   (Variable)           23.80       20   −249.784   2.80   1.69680   55.5   25.20       21   −83.232   0.15           25.57       22   181.284   5.19   1.60311   60.6   25.75       23   −30.728   1.25   1.84666   23.8   25.66       24   −127.921   0.15           25.87       25   99.327   2.35   1.77250   49.6   25.86       26   −130.324   (Variable)           25.60       27   74.930   1.20   1.88300   40.8   25.03       28   29.783   3.57           24.31       29   −112.308   2.85   1.80518   25.4   24.44       30   −31.068   4.56           24.80       31   −26.035   1.25   1.88300   40.8   24.41       32   ∞   2.75           25.82       33   56.384   3.69   1.69895   30.1   29.16       34   967.801   (Variable)           29.56       35   ∞   1.13   1.51633   64.2   50.00       36   ∞   0.20           50.00       37   ∞   0.40   1.51633   64.2   50.00       38   ∞   (Variable)           50.00       IP   ∞                         Various data       Zoom ratio 4.02                                         Wide   Middle   Tele                       Focal length   72.19   135.01   290.31           F-number   4.28   4.75   5.94           Field angle   16.68   9.10   4.26           Image height   21.64   21.64   21.64           Entire lens length   185.42   214.97   239.40           Back focus   0.41   0.41   0.41           d5   3.28   32.82   57.26           d10   25.74   13.79   1.08           d16   5.86   23.88   44.40           d19   18.36   12.28   4.46           d26   13.57   11.99   0.99           d34   42.58   44.16   55.16           d38   0.41   0.41   0.41           Entrance pupil position   46.11   111.44   201.54           Exit pupil Position   −91.42   −101.46   −118.76           Front principal point   61.54   67.51   −215.38           Rear principal point   −71.79   −134.60   −289.90                             Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               L1   1   130.99   17.40   0.81   −10.78       L2   6   −35.13   8.66   1.17   −5.10       L3   11   52.01   10.95   2.38   −5.00       L4   17   −141.89   5.14   −2.20   −5.16       L5   20   47.86   11.89   5.02   −2.27       L6   27   −51.14   19.87   3.63   −12.05       GB   35   ∞   1.73   0.60   −0.60                         Single lens data                         Lens   Start surface   Focal length               1   1   225.12       2   3   −134.81       3   4   93.02       4   6   −49.45       5   8   −38.51       6   9   56.02       7   11   75.60       8   13   44.76       9   14   −59.73       10   17   −31.26       11   18   41.05       12   20   177.91       13   22   43.97       14   23   −48.05       15   25   73.29       16   27   −56.69       17   29   52.52       18   31   −29.49       19   33   85.52       20   35   0.00       21   37   0.00                    
[Embodiment 7]
 
     The optical system of Embodiment 7 (Numerical Example 7) shown in  FIG. 26  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, a third lens unit L 3  having a positive refractive power, the aperture stop SP, a fourth lens unit L 4  having a positive refractive power and the glass block GB. The optical system of this embodiment has a maximum image height of 13.66 mm. At a position of the image plane IP, an APS-C image sensor having a size of 15.2 mm×22.7 mm is placed. The image sensor has a pixel pitch of 4.3 μm. 
     As understood from the lateral aberration charts at the middle focal length in the infinite object distance in-focus state, the closest object distance in-focus state and the middle object distance in-focus state respectively shown in  FIGS. 28B ,  29 B and  30 B, the generation of the coma aberration decreases the variation of the field curvature at the middle focal length over the entire object distance range. 
     Various numerical values of the optical system of Numerical Example 7 are shown below. Table 2 shows relations of Numerical Example 7 and the above-described conditions (9) and (10). 
     NUMERICAL EXAMPLE 7 
                             Unit mm                  Surface data                                     Surface                   Effective       No.   r   d   nd   νd   diameter                1   219.691   1.98   1.84666   23.9   41.35        2   77.011   0.80           38.49        3   110.857   2.79   1.77250   49.6   38.45        4   −1566.128   0.29           37.69        5   57.811   3.26   1.77250   49.6   33.00        6   516.857   (Variable)           31.76        7*   1449.562   1.45   1.85400   40.4   29.52        8*   17.597   6.32           23.53        9   −62.504   1.16   1.69100   54.8   23.28       10   79.992   0.17           23.14       11   27.282   2.67   1.94595   18.0   23.38       12   61.859   (Variable)           22.95       13*   15.625   3.02   1.85135   40.1   13.31       14*   127.225   0.37           12.51       15   13.245   3.60   1.77250   49.6   11.81       16   2319.692   0.70   1.80518   25.4   10.32       17   8.119   1.97           8.97       18   −1265.485   1.74   1.48749   70.2   8.86       19   −42.123   0.98           8.75       20 (SP)   ∞   (Variable)           8.53       21   ∞   (Variable)           8.72       22*   600.625   5.12   1.58313   59.4   27.51       23*   −35.796   (Variable)           28.21       24   ∞   1.21   1.51633   64.1   58.13       25   ∞   1.51           58.13       26   ∞   0.60   1.51633   64.1   58.13       27   ∞   (Variable)           58.13       IP   ∞                         Aspheric data               7th surface                         K = 7.95128e+003   A4 = −8.46681e−006   A6 = 1.45376e−008                 8th surface                         K = 3.72976e−001   A4 = −1.13801e−005   A6 = −4.49670e−009       A8 = −4.98598e−010   A10 = 1.72434e−012                 13th surface                         K = −2.06246e−001   A4 = −1.23394e−005   A6 = 1.79103e−007       A8 = −4.52541e−009   A10 = 2.60955e−011                 14th surface                         K = −5.86105e+001   A4 = 8.28096e−006   A6 = 1.05159e−007       A8 = −2.30730e−009                 22nd surface                         K = 1.81624e+003   A4 = −1.28722e−005   A6 = 2.00678e−007       A8 = −8.68491e−010                 23rd surface                         K = 1.08981e+000   A4 = −2.12065e−005   A6 = 2.34886e−007       A8 = −9.22692e−010   A10 = 3.32500e−013                         Various data       Zoom ratio 3.81                                         Wide   Middle   Tele                       Focal length   18.03   47.42   68.66           F-number   2.88   4.57   5.94           Field angle   33.69   15.83   11.25           Image height   12.02   13.45   13.66           Entire lens length   87.58   100.81   110.99           Back focus   2.34   2.34   2.34           d6   1.10   14.03   20.22           d12   23.85   6.03   0.99           d20   0.77   2.42   16.50           d21   11.46   29.23   23.11           d23   6.32   5.03   6.09           d27   2.34   2.34   2.34           Entrance pupil position   28.04   50.51   65.42           Exit pupil Position   −29.96   −94.15   −169.72           Front principal point   36.01   74.62   106.68           Rear principal point   −15.69   −45.08   −66.32                             Lens unit Data                                                 Lens   Front   Rear           Start   Focal   unit   principal   principal       Unit   surface   length   length   point   point               L1   1   81.28   9.10   3.63   −1.92       L2   7   −20.76   11.78   0.97   −8.20       L3   13   23.78   12.40   −5.10   −12.01       FC   21   ∞   0.00   0.00   −0.00       L4   22   58.11   5.12   3.06   −0.18       GB   24   ∞   3.32   1.35   −1.35                         Single lens data                         Lens   Start surface   Focal length               1   1   −140.95       2   3   134.11       3   5   84.00       4   7   −20.87       5   9   −50.61       6   11   49.73       7   13   20.67       8   15   17.23       9   16   −10.12       10   18   89.34       11   22   58.11       12   24   0.00       13   26   0.00                    
[Embodiment 8]
 
     The optical system of Embodiment 8 (Numerical Example 8) shown in  FIG. 31  is constituted by, in order from the object side to the image side, the first lens unit L 1  having a positive refractive power, the second lens unit L 2  having a negative refractive power, the aperture stop SP, a third lens unit L 3  having a positive refractive power, a fourth lens unit L 4  having a negative refractive power, a fifth lens unit L 5  having a positive refractive power and the glass block GB. The optical system of this embodiment has a maximum image height of 3.875 mm. At a position of the image plane IP, a 1/2.3″-type image sensor having a size of 4.65 mm×6.2 mm is placed. The image sensor has a pixel pitch of 1.4 μm. 
     As understood from the longitudinal aberration charts at the wide-angle end and the middle focal length in the infinite object distance in-focus state respectively shown in  FIGS. 32A and 32B , the aberrations are sufficiently corrected. Moreover, as understood from the lateral aberration charts at the telephoto end in the infinite object distance in-focus state, the closest object distance in-focus state and the middle object distance in-focus state respectively shown in  FIGS. 33B ,  34 B and  35 B, the generation of the coma aberration decreases the variation of the field curvature at the telephoto end over the entire object distance range. 
     Various numerical values of the optical system of Numerical Example 8 are shown below. Table 2 shows relations of Numerical Example 8 and the above-described conditions (9) and (10). 
     NUMERICAL EXAMPLE 8 
     
       
         
           
               
             
               
                   
               
               
                 Unit mm 
               
               
                   
               
             
            
               
                 Surface data 
               
            
           
           
               
               
               
               
               
               
            
               
                 Surface 
                   
                   
                   
                   
                 Effective 
               
               
                 No. 
                 r 
                 d 
                 nd 
                 νd 
                 diameter 
               
               
                   
               
               
                  1 
                 112.067 
                 1.80 
                 1.80610 
                 33.3 
                 39.40 
               
               
                  2 
                 52.885 
                 5.03 
                 1.49700 
                 81.5 
                 35.90 
               
               
                  3 
                 −218.600 
                 0.18 
                   
                   
                 35.80 
               
               
                  4 
                 45.553 
                 3.22 
                 1.59282 
                 68.6 
                 34.70 
               
               
                  5 
                 131.490 
                 (Variable) 
                   
                   
                 34.20 
               
               
                  6 
                 120.679 
                 0.95 
                 1.88300 
                 40.8 
                 19.70 
               
               
                  7 
                 8.615 
                 4.92 
                   
                   
                 14.10 
               
               
                  8 
                 −34.305 
                 0.70 
                 1.77250 
                 49.6 
                 13.90 
               
               
                  9 
                 28.642 
                 0.20 
                   
                   
                 13.80 
               
               
                 10 
                 16.947 
                 2.30 
                 1.92286 
                 18.9 
                 14.10 
               
               
                 11 
                 89.165 
                 (Variable) 
                   
                   
                 13.80 
               
               
                 12 (SP) 
                 ∞ 
                 (Variable) 
                   
                   
                 6.68 
               
               
                 13* 
                 9.778 
                 4.30 
                 1.55332 
                 71.7 
                 9.50 
               
               
                 14* 
                 −74.715 
                 1.67 
                   
                   
                 9.50 
               
               
                 15 
                 38.527 
                 0.50 
                 1.64769 
                 33.8 
                 9.00 
               
               
                 16 
                 10.092 
                 0.37 
                   
                   
                 9.00 
               
               
                 17 
                 13.822 
                 0.50 
                 1.80400 
                 46.6 
                 9.00 
               
               
                 18 
                 8.013 
                 2.11 
                 1.48749 
                 70.2 
                 9.00 
               
               
                 19 
                 −31.006 
                 (Variable) 
                   
                   
                 8.31 
               
               
                 20 
                 −564.447 
                 0.70 
                 1.48749 
                 70.2 
                 8.60 
               
               
                 21 
                 26.449 
                 (Variable) 
                   
                   
                 8.70 
               
               
                 22 
                 20.740 
                 2.25 
                 1.78590 
                 44.2 
                 11.80 
               
               
                 23 
                 −55.591 
                 1.26 
                 1.94595 
                 18.0 
                 11.70 
               
               
                 24 
                 −1698.441 
                 (Variable) 
                   
                   
                 11.60 
               
               
                 25 
                 ∞ 
                 0.30 
                 1.51633 
                 64.1 
                 20.00 
               
               
                 26 
                 ∞ 
                 0.47 
                   
                   
                 20.00 
               
               
                 27 
                 ∞ 
                 0.50 
                 1.51633 
                 64.1 
                 20.00 
               
               
                 28 
                 ∞ 
                 (Variable) 
                   
                   
                 20.00 
               
               
                 IP 
                 ∞ 
               
               
                   
               
            
           
           
               
            
               
                 Aspheric data 
               
               
                   
               
               
                 13th surface 
               
            
           
           
               
               
               
            
               
                 K = −5.29634e−001 
                 A4 = −2.26010e−005 
                 A6 = 1.07748e−007 
               
               
                 A8 = −2.96223e−008 
                 A10 = 7.23156e−010 
               
            
           
           
               
            
               
                 14th surface 
               
            
           
           
               
               
               
            
               
                 K = −2.41360e+002 
                 A4 = −2.87477e−005 
                 A6 = 3.05881e−007 
               
               
                   
               
            
           
           
               
            
               
                 Various data 
               
               
                 Zoom ratio 33.54 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Wide 
                 Middle 
                 Tele 
               
               
                   
                   
               
               
                   
                 Focal length 
                 4.42 
                 12.77 
                 148.25 
               
               
                   
                 F-number 
                 2.70 
                 4.26 
                 5.03 
               
               
                   
                 Field angle 
                 37.01 
                 16.88 
                 1.50 
               
               
                   
                 Image height 
                 3.33 
                 3.88 
                 3.88 
               
               
                   
                 Entire lens length 
                 94.78 
                 94.62 
                 138.53 
               
               
                   
                 Back focus 
                 0.53 
                 0.53 
                 0.53 
               
               
                   
                 d5 
                 0.92 
                 17.42 
                 62.79 
               
               
                   
                 d11 
                 31.72 
                 17.57 
                 1.27 
               
               
                   
                 d12 
                 12.69 
                 0.50 
                 3.21 
               
               
                   
                 d19 
                 2.68 
                 3.23 
                 2.48 
               
               
                   
                 d21 
                 3.22 
                 5.67 
                 24.20 
               
               
                   
                 d24 
                 8.78 
                 15.48 
                 9.83 
               
               
                   
                 d28 
                 0.53 
                 0.53 
                 0.53 
               
               
                   
                 Entrance pupil position 
                 18.62 
                 47.44 
                 564.42 
               
               
                   
                 Exit pupil Position 
                 −5771.10 
                 −49.53 
                 129.32 
               
               
                   
                 Front principal point 
                 23.04 
                 56.95 
                 883.31 
               
               
                   
                 Rear principal point 
                 −3.89 
                 −12.24 
                 −147.72 
               
               
                   
                   
               
            
           
           
               
            
               
                 Lens unit Data 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Lens 
                 Front 
                 Rear 
               
               
                   
                 Start 
                 Focal 
                 unit 
                 principal 
                 principal 
               
               
                 Unit 
                 surface 
                 length 
                 length 
                 point 
                 point 
               
               
                   
               
               
                 L1 
                 1 
                 82.06 
                 10.23 
                 2.82 
                 −3.76 
               
               
                 L2 
                 6 
                 −9.87 
                 9.07 
                 0.74 
                 −6.39 
               
               
                 SP 
                 12 
                 ∞ 
                 0.00 
                 0.00 
                 −0.00 
               
               
                 L3 
                 13 
                 18.85 
                 9.45 
                 −0.20 
                 −7.09 
               
               
                 L4 
                 20 
                 −51.81 
                 0.70 
                 0.45 
                 −0.02 
               
               
                 L5 
                 22 
                 28.04 
                 3.51 
                 −0.07 
                 −1.98 
               
               
                 GB 
                 25 
                 ∞ 
                 1.27 
                 0.50 
                 −0.50 
               
               
                   
               
            
           
           
               
            
               
                 Single lens data 
               
            
           
           
               
               
               
            
               
                 Lens 
                 Start surface 
                 Focal length 
               
               
                   
               
               
                 1 
                 1 
                 −125.94 
               
               
                 2 
                 2 
                 86.21 
               
               
                 3 
                 4 
                 115.95 
               
               
                 4 
                 6 
                 −10.55 
               
               
                 5 
                 8 
                 −20.11 
               
               
                 6 
                 10 
                 22.33 
               
               
                 7 
                 13 
                 15.92 
               
               
                 8 
                 15 
                 −21.26 
               
               
                 9 
                 17 
                 −24.66 
               
               
                 10 
                 18 
                 13.30 
               
               
                 11 
                 20 
                 −51.81 
               
               
                 12 
                 22 
                 19.47 
               
               
                 13 
                 23 
                 −60.78 
               
               
                 14 
                 25 
                 0.00 
               
               
                 15 
                 27 
                 0.00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Numerical 
                 Numerical 
                 Numerical 
               
               
                   
                 Example 6 
                 Example 7 
                 Example 8 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Condition (9) 
                 9.9 
                 1.9 
                 1.3 
               
               
                   
                 Condition (10) 
                 2.9 
                 4.1 
                 2.6 
               
               
                   
                   
               
            
           
         
       
     
     Each of Embodiments 6 to 8 can achieve a compact optical system capable of improving image quality with generating appropriate aberration for the image restoration. Performing image capturing using this optical system and then performing the image restoration process can achieve a compact image pickup apparatus capable of providing high quality images. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all modifications, equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application Nos. 2012-160421 and 2012-160422, filed on Jul. 19, 2013, which are hereby incorporated by reference herein in their entirety.