Abstract:
Provided is a retrofocus type optical system including a lens or a layer made of a material satisfying the following conditions of the Abbe constant νd and partial dispersion ratios θgd and θgF,
 
νd&lt;30,
 
θ gd &lt;−3.333×10 −3   ·νd +1.40,
 
θ gF &lt;−2.615−10 −3   ·νd +0.67.
 
In the case that this layer is disposed on the front side of the aperture stop, the layer is designed to have a positive refractive power, and in the case that the layer is disposed on the rear side of the aperture stop, the layer is designed to have a negative refractive index.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an optical system in which an optical material with extraordinary partial dispersion is used, or an optical system that is suitable for an image taking optical system of a silver halide film camera, a digital still camera or a video camera, or a projection optical system of a liquid crystal projector. 
   2. Description of the Related Art 
   Conventionally, a retrofocus type lens has been known as a type of lens having a short focal length and a long back focus. In the retrofocus type lens, a long back focus can be realized by arranging a lens unit having negative refractive power as a whole in the front side (i.e. the magnification side: the object side in the case of a image taking optical system of camera and or the like, or the screen side in the case of a projection optical system of a projector or the like) of the optical system and arranging a lens unit having a positive refractive power as a whole in the rear side (i.e. the reduction side: the image side in the case of a image taking optical system of a camera or the like, or the original side in the case of a projection optical system of a projector or the like) of the optical system. In order to obtain a long back focus, it is necessary to enhance both the positive refractive power and the negative refractive power, which results in an optical system having an asymmetrical refractive power arrangement. Problems the retrofocus type lens suffers in correcting aberrations are that barrel type distortion is liable to occur, that significant chromatic aberration of magnification (lateral chromatic aberration) is liable to occur, and that secondary spectrum of chromatic aberration of magnification tends to become large. 
   As a conventional method for improving the chromatic aberration of magnification, a method of using a low dispersion lens made of extraordinary partial dispersion material such as fluorite and a method of using a diffraction optical surface have been proposed. 
   On the other hand, diffraction optical elements have an Abbe number equivalent value of as small as 3.45 (in the absolute value), and accordingly it is possible to change chromatic aberration greatly while scarcely affecting spherical aberration, coma and astigmatism etc. only by slightly changing the optical power (which is the reciprocal of the focal length) achieved by diffraction. In addition, since diffracted light is used, the optical power changes linearly depending on the wavelength of incident light, and the wavelength characteristics of the chromatic aberration coefficient is completely linear. Therefore, in order to shorten the total length of the system, aberration corrections should be mainly directed to spherical aberration, coma and astigmatism. As to chromatic aberration, since correction thereof is effected using a diffraction optical element, what is required in designing the system is only to optimize the material and optical power of the constituent lenses so as to realize linearity in the wavelength characteristics of the chromatic aberration without taking into consideration the absolute amount of the chromatic aberration that has been deteriorated by the length reduction. Thus, an optical system having excellent performance can be obtained as a consequence. 
   It has been proposed to use a resin material mixed with inorganic oxide fine particles such as ITO fine particles in a diffraction grating to improve the diffraction efficiency (see Japanese Patent Application Laid-Open No. 2001-074901 (a counterpart: EP A2 1065531). 
   Furthermore, a liquid material having relatively high dispersion and showing relatively extraordinary partial dispersion characteristics has been known as a material having a chromatic aberration correction effect similar to diffraction gratings, and an achromatic optical system using the same has been proposed (see U.S. Pat. No. 4,913,535). 
   Since the refractive index of a low dispersion lens with extraordinary partial dispersion such as a fluorite lens is low, its position in an optical system is limited when used, or it is sometimes necessary to increase the number of the lenses in the system. In addition, such lenses are very expensive and they cannot be used frequently in view of the cost. 
   Although diffraction optical elements have sufficient chromatic aberration correction effects, they suffer from the problem that diffracted light of useless diffraction orders different from the designed diffraction order becomes colored flare light that deteriorates imaging performance. Although in some cases, a so-called laminated diffraction optical element composed of a plurality of blazed diffraction gratings stacked along the optical axis direction is used so as to concentrate energy on the designed diffraction order and to reduce useless diffracted light greatly, there still remains the problem that diffracted flare is generated when an object having high luminance is photographed. 
   In manufacturing a diffraction optical element, a method of molding an ultraviolet curing resin or the like using a metal mold has been known. However, diffraction efficiency of a diffraction optical element is extremely sensitive to the manufacturing accuracy, and a very high degree of precision in the metal mold and in the molding process is required. This leads to high manufacturing costs. 
   The material disclosed in U.S. Pat. No. 4,913,535 is liquid, and a structure for sealing it is necessary and manufacturing thereof is not easy. In addition, it suffers from the problem of changes in characteristics, such as refractive index and dispersion characteristics, depending on the temperature, namely, it does not have sufficient environmental tolerance. In addition, that material suffers from the defect that it cannot achieve a sufficient chromatic aberration correction effect due to its relatively large Abbe constant, relatively small extraordinary partial dispersion and absence of interface with the air. 
   SUMMARY OF THE INVENTION 
   The present invention has been made in view of the above-described difficulties in the conventional arrangements. An object of the present invention is to provide a retrofocus type optical system that achieves favorable corrections of various aberrations represented by chromatic aberration, is easy to manufacture and has excellent environmental tolerance. 
   In an exemplary optical system according to the present invention, the height at which a paraxial marginal ray passes through the frontmost lens surface is smaller than the maximum value of the height at which the paraxial marginal ray passes through a lens surface on the rear side of the intersection P of the optical axis and a paraxial chief ray, and the optical system includes a refractive optical element made of a solid material that satisfies the following conditions concerning the Abbe constant νd and partial dispersion ratios θgd and θgF.
 
νd&lt;30
 
θ gd &lt;−3.333×10 −3   ·νd+ 1.40
 
θ gF &lt;−2.615×10 −3   ·νd+ 0.67
 
In this connection, in the case that this refractive optical element is disposed on the front side of (i.e. anterior to) the intersection P, the refractive optical element is designed to have a positive refractive power, and in the case that the refractive optical is disposed on the rear side of (i.e. posterior to) the intersection P, the refractive optical element is designed to have a negative refractive power.
 
   In the present invention, the definitions of the Abbe constant νd and partial dispersion ratios θgd and θgF are the same as those commonly known, that is, they are represented as follows using the refractive indices Ng, NF, Nd and NC for the g-line, F-line, d-line and C-line respectively,
 
ν d =( Nd −1)/( NF−NC ),
 
θ gd =( Ng−Nd )/( NF−NC ),
 
θ gF =( Ng−NF )/( NF−NC ).
 
   In the present invention, the term “solid material” refers to a material that is solid in the state used in the optical system, but it does not refers to the state in a stage (such as a manufacturing stage) prior to its use in the optical system. For example, even if a material is liquid in its manufacturing stage, a solid material obtained by solidifying it will constitutes what is called a solid material in this invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a cross sectional view of an optical system according to numerical embodiment 1. 
       FIG. 2  shows aberration diagrams for the optical system according to numerical embodiment 1 
       FIG. 3  is a cross sectional view of an optical system according to numerical embodiment 2. 
       FIGS. 4A and 4B  show aberration diagrams for the optical system according to numerical embodiment 2. 
       FIG. 5  is a cross sectional view of an optical system according to numerical embodiment 3. 
       FIGS. 6A and 6B  show aberration diagrams for the optical system according to numerical embodiment 3. 
       FIG. 7  is a cross sectional view of an optical system according to numerical embodiment 4. 
       FIGS. 8A and 8B  show aberration diagrams for the optical system according to numerical embodiment 4. 
       FIG. 9  is a cross sectional view of an optical system according to numerical embodiment 5. 
       FIGS. 10A and 10B  show aberration diagrams for the optical system according to numerical embodiment 5. 
       FIG. 11  is a cross sectional view of an optical system according to numerical embodiment 6. 
       FIGS. 12A and 12B  show aberration diagrams for the optical system according to numerical embodiment 5. 
       FIGS. 13A ,  13 B and  13 C are graphs schematically illustrating dispersion characteristics of ITO. 
       FIG. 14  is a diagram showing a paraxial configuration of a retrofocus type optical system. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Prior to descriptions of embodiments of the optical system according to the present invention, effects of high dispersion optical materials in correcting aberrations in an optical system will be firstly described. 
   Let Δφ represent the optical power variation of a refractive lens surface, let ν represent the Abbe constant, let h represent the height, from the optical axis, of the point at which an paraxial marginal ray passes the lens surface, and let H represent the height, from the optical axis, of the point at which a paraxial chief ray passes a lens surface, then the change ΔL in the coefficient of the on-axis chromatic aberration (longitudinal chromatic aberration) and the change ΔT in the coefficient of the chromatic aberration of magnification (lateral chromatic aberration) of this lens surface can be expressed as follows.
 
Δ L=h   2 ·Δφ/ν  (a)
 
Δ T=h·H·Δφ/ν   (b)
 
   In connection with this, the paraxial marginal ray is such a paraxial ray that is incident in parallel to the optical axis of the optical system with a height of 1, where the focal length of the whole optical system is normalized to 1. The paraxial chief ray is such a paraxial ray that is incident at an angle of 45° to the optical axis and passes through the intersection of the optical axis and the entrance pupil of the optical system. The incident angle is indicated by a positive value when measured in the clockwise direction from the optical axis, and by a negative value when measured in the anticlockwise direction. Here, it is assumed that the object is present in the left side of the optical system, and rays that enter the optical system from the object side travel from left to right. 
   As will be apparent from equations (a) and (b), the smaller the absolute value of the Abbe constant is (in other words, the larger the dispersion is), the larger changes in each aberration coefficient relative to changes in the power of the lens surface are. Therefore, when a high dispersion material with a small Abbe constant in absolute value is used, the change in the optical power for achieving required chromatic aberration can be made small. This means, from the standpoint of aberration theory, that chromatic aberration can be controlled without greatly affecting spherical aberration, coma, astigmatism etc. and independency of chromatic aberration correction is enhanced. In contrast, when a low dispersion material is used, the change in the power for obtaining required chromatic aberration becomes large, which involves significant changes in various aberrations such as spherical aberration. Thus, independency of chromatic aberration correction is degraded. In view of the above, it is important, from the standpoint of aberration correction, that at least one lens surface in the lenses constituting the optical system be a refractive lens surface formed by a high dispersion material. 
   Next, on the basis that the refractive lens is made of high dispersion material, effects of the optical material with a low partial dispersion ratio in correcting aberrations in an optical system will be described. 
   Concerning wavelength dependency characteristics (i.e. dispersion characteristics) of the refractive index of optical materials, it is well known that the Abbe constant represents the gradient of the dispersion characteristics curve as a whole and the partial dispersion ratio represents the curvature of the dispersion characteristics curve. 
   In optical materials in general, the refractive index is greater in the short wavelength range than in the long wavelength range (the Abbe constant is a positive value), the dispersion characteristics curve is convex downward (the partial dispersion ratio is a positive value), and changes in the refractive index relative to changes in the wavelength become larger as the wavelength decreases. In addition, the smaller the Abbe constant of an optical material is, the larger its partial dispersion ratio is, and the acuter the downwardly convex curve of the dispersion characteristics tends to be. 
   The wavelength dependency characteristic curve of the chromatic aberration coefficient of a surface of a lens made of an optical material with a large partial dispersion ratio shows a stronger curve in the short wavelength range than in the case in which an optical material with a small partial dispersion ratio is used. When the optical power of the lens is changed in order to control chromatic aberration, the overall inclination of the wavelength dependency characteristic curve of the chromatic aberration coefficient changes with a rotation center at the position of the design standard wavelength. In connection with this, changes in the short wavelength range, in particular, are large in the case of materials with large partial dispersion ratios than in the case of materials with small partial dispersion ratios, and the overall inclination will vary while involving significant changes in the curvature. For this reason, it is difficult to configure the optical system to achieve cancellation in both the overall inclination and the curvature in the wavelength dependency characteristic curve of the chromatic aberration coefficient, even if glass materials in other diffractive system portions are changed. Therefore, chromatic aberration cannot be corrected all over the wavelength range. 
   This fact will be specifically described taking chromatic aberration correction (achromatism) in an optical system composed of a refractive optical system portion GIT using a high dispersion material and the other refractive optical system portion G as an example. 
   In achromatism using high dispersion optical materials, relatively large chromatic aberration coefficients of the portion GIT and the portion G are adapted to cancel each other to produce chromatic aberration of the whole system. To this end, starting from the state in which the chromatic aberration of the portion G as a partial system is corrected to some extent, material for the a positive lens is set to a material having relatively high dispersion, and material for a negative lens is set to a material having relatively low dispersion. Then, the overall inclination of the wavelength dependency characteristic curve of chromatic aberration coefficient of the portion G changes with its linearity being improved as compared to the prior state. 
   In this state, an appropriate optical power is assigned to the portion GIT to cancel the overall inclination of the wavelength dependency characteristic curve of the chromatic aberration coefficient of the portion G. However, if the portion GIT is made of an optical material with a large partial dispersion ratio, the wavelength dependency characteristic curve of the aberration coefficient of the portion GIT has a curvature opposite to and larger than that of the portion G. Accordingly, it is not possible to cancel the curvature component even if the overall inclination component can be cancelled. 
   In contrast, if the portion GIT is made of an optical material with a small partial dispersion ratio, since the wavelength dependency characteristic curve of the chromatic aberration coefficient of the portion GIT is relatively linear, it is possible to change its inclination about the rotation center at the position of the design wavelength while maintaining its relative linearity. Therefore, it is possible, relatively easily, to cancel both the inclination component and the curvature component of the wavelength dependency characteristic of the chromatic aberration. 
   To sum up, it is important that the portion GIT be made of a material having a small partial dispersion ratio in addition to high dispersion. The following conditions (1), (2) and (3) specified by the present invention define the relationship between the Abbe constant and partial dispersion ratios with which chromatic aberration can be excellently corrected based on the principle described in the foregoing.
 
νd&lt;30  (1)
 
θ gd &lt;−3.333×10 −3   ·νd +1.40  (2)
 
θ gF &lt;−2.615×10 −3   ·νd +0.67  (3)
 
Here, νd is the Abbe constant of the refractive optical system portion (i.e. lens or layer) GIT, which is represented by the following equation using the refractive indices Nd, NF and NC for the d-line, F-line and C-line respectively.
 
ν d =( Nd− 1)/( NF−NC )
 
   In addition, θgd and θgF are the partial dispersion ratios of the refractive optical system portion (lens or layer) GIT, which are represented by the following equations respectively, using the refractive indices Ng, NF, Nd and NC the g-line, F-line, d-line and C-line respectively.
 
θ gd =( Ng−Nd )/( NF−NC )
 
θ gF =( Ng−NF )/( NF−NC )
 
   Values that do not satisfy any of the above conditions (1) to (3) are not desirable, since it is difficult to achieve good chromatic aberration with such values. 
   The following modification to the numerical range of condition (1) will further enhance effects of independent chromatic aberration correction to realize improved optical performance.
 
νd&lt;20  (1a)
 
   The following condition is more preferable.
 
νd&lt;18  (1b)
 
   The following condition is still more preferable.
 
νd&lt;16  (1c)
 
   The following condition is still more preferable.
 
νd&lt;14  (1d)
 
   The following modifications to the numerical range of conditions (2) and (3), under the assumption that condition (1), (1a), (1b), (1c) or (1d) is satisfied, can realize more excellent optical performance.
 
θ gd &lt;−3.333×10 −3   ·νd +1.30  (2a)
 
θ gF &lt;−2.615×10 −3   ·νd +0.59  (3a)
 
   The following modifications are more preferable.
 
θ gd &lt;−3.333×10 −3   ·νd +1.25  (2b)
 
θ gF &lt;−2.615×10 −3   ·νd +0.56  (3b)
 
   The following modifications are still more preferable.
 
θ gd &lt;−3.333×10 −3   ·νd +1.2375  (2c)
 
θ gF &lt;−2.615×10 −3   ·νd +0.55  (3c)
 
   The following modifications are still more preferable.
 
θgd&lt;1.1137  (2d)
 
θgF&lt;0.47  (3d)
 
   An example of the optical material that satisfies the above mentioned conditions (1) to (3) is a mixture formed by dispersing inorganic oxide (selected from those listed below) fine particles in a synthetic resin. The inorganic oxide may be TiO 2  (nd=2.2652, νd=11.8), Nb 2 O 5  (nd=2.367, νd=14.0), ITO (nd=1.8581, νd=5.53), Cr 2 O 3  (nd=2.2178, νd=13.4), or BaTiO 3  (nd=,2.4362 νd=11.3) etc. 
   ITO (indium-tin oxide) is especially preferable for its small Abbe constant as compared to the other materials. In ITO, free carriers of conductivity have an influence on the refractive index, unlike with the other materials. The dispersion characteristics of ITO (shown in  FIG. 13C ) are determined by a combination of changes in the refractive index in the short wavelength range due to ordinary electron transition (shown in  FIG. 13A ) and refractive index dispersion in the infrared range caused by free carriers. Thus, it shows wavelength dependency of dispersion characteristics having an extraordinary large gradient with an Abbe constant of 5.53. 
   The refractive index dispersion due to electron transition ( FIG. 13A ) steeply changes in the short wavelength side of the visible light range. In contrast, the refractive index dispersion due to free carriers ( FIG. 13B ) steeply changes in the long wavelength side of the visible light range. The combination of these effects makes the partial dispersion ratio small as compared to ordinary cases. 
   In connection with this, transparent materials expected to be influenced by free carriers include SnO 2 , ATO (SnO 2  doped with antimony) and ZnO. 
   ITO is known as a material used for making a transparent electrode, ant is commonly used in a liquid crystal display device or an EL (electroluminescent) device etc. Furthermore, ITO is also used in an infrared shielding element and an ultraviolet shielding element. The thickness of ITO in conventionally known applications is limited within the range of 50 to 500 nm, and it has by no means been used as fine particle mixture for correcting chromatic aberration of optical systems. 
   It is preferred that the mean diameter of the ITO fine particles be approximately 2 nm to 50 nm, in view of influences of dispersion. Dispersing agent or the like may be added to prevent aggregation. 
   The medium for dispersing ITO may preferably be a monomer, which can be formed with high mass productivity by means of photo-induced polymerization or thermal polymerization using a mold. 
   From the view point of optical constant characteristics of the monomer, a monomer with a relatively small Abbe constant, a monomer with a relatively small partial dispersion ratio or a monomer with both a small Abbe constant and a small partial dispersion ratio is preferable. N-polyvinylcarbazole, styrene, and polymethyl methacrylate (acrylic) are examples of such a monomer. In the embodiments to be described later, acrylic is used as the medium for dispersing the ITO fine particles, but the medium to be used is not limited to this. 
   The dispersion characteristic N(X) of the mixture in which nano file particles are dispersed can be easily calculated using the following equation that has been derived from the well known Drude equation. 
                   N   ⁡     (   λ   )       =       [     1   +     V   ⁢     {         N   ITO   2     ⁡     (   λ   )       -   1     }       +       (     1   -   V     )     ⁢     {         N   p   2     ⁡     (   λ   )       -   1     }         ]       1   /   2               (   c   )               
In the above equation, λ is the wavelength, N ITO  is the refractive index of the particulate material such as ITO, N p  is the refractive index of the polymer, V is the percentage of the sum of the volume of the fine particles relative to the volume of the polymer.
 
   In this embodiment, it is proposed that a material that satisfies conditions (1) to (3) be used for a lens or a layer formed on a lens surface in an optical system. In addition, by designing the refractive surface formed by this material as an aspherical surface, it is possible to correct chromatic aberration flare such as chromatic spherical aberration. Furthermore, it is preferred that an interface is formed between this material and the ambient atmosphere such as air or a material with a relatively low refractive index, since in that case chromatic aberration can be changed relatively greatly with a slight variation in the curvature of the interface. 
   In the foregoing, the description has been made of conditions that the optical material constituting the refractive optical system portion GIT is required to satisfy. 
   Next, conditions for the refractive optical system portion GIT that are required for correcting chromatic aberration of a retrofocus type optical system will be described in the following. 
     FIG. 14  is a schematic diagram showing a paraxial refractive power arrangement for illustrating effects of chromatic aberration correction in a retrofocus type optical system. In  FIG. 14 , reference signs Gn and Gp designate a front unit having a negative refractive power and a rear unit having a positive refractive power that constitute the retrofocus type optical system respectively. Reference signs GIT 1  and GIT 2  designate refractive optical system portions GIT (which will be simply referred to as components, hereinafter) included in the front unit Gn and the rear unit Gp respectively. For the sake of simplicity, we assume that all of the lenses constituting the front unit Gn and the rear unit Gp are thin single lenses and arranged on the optical axis with no gaps therebetween respectively in the front unit Gn and the rear unit Gp. We also assume that the component GIT 1  and the component GIT 2  are thin single lenses and respectively arranged on the optical axis with no intervals from the front unit Gn and the rear unit Gp respectively. What is designated by reference character Q is a paraxial marginal ray, and what is designated by reference character R is a paraxial chief ray. P is the intersection of the paraxial chief ray and the optical axis, which point coincides with the center of the aperture stop in ordinary cases. 
   Firstly, we consider an optical system in which the component GIT has not been introduced. The equations expressing the aberration coefficient of on-axis chromatic aberration (L) and the aberration coefficient of chromatic aberration of magnification (T) for the front unit Gn and the rear unit Gp are as follows: 
                   L   ⁡     (   λ   )       =           h   Gn   2     ⁡     (     λ   0     )       ⁢       ∑     i   =   1     L     ⁢         ϕ   Gni     ⁡     (     λ   0     )       /       ν   Gni     ⁡     (   λ   )             +             (   d   )                       ⁢           h   Gp   2     ⁡     (     λ   0     )       ⁢       ∑     j   =   1     M     ⁢         ϕ   Gpj     ⁡     (     λ   0     )       /       ν   Gpj     ⁡     (   λ   )             ,                               T   ⁡     (   λ   )       =           h   Gn     ⁡     (     λ   0     )       ⁢       H   Gn     ⁡     (     λ   0     )       ⁢       ∑     i   =   1     L     ⁢         ϕ   Gni     ⁡     (     λ   0     )       /       ν   Gni     ⁡     (   λ   )             +             (   e   )                       ⁢           h   Gp     ⁡     (     λ   0     )       ⁢       H   Gp     ⁡     (     λ   0     )       ⁢       ∑     j   =   1     M     ⁢         ϕ   Gpj     ⁡     (     λ   0     )       /       ν   Gpj     ⁡     (   λ   )             ,                             
where,
 ν Gni (λ)={ N   Gni (λ 0 )−1 }/{N   Gni (λ)− N   Gni (λ 0 )}ν Gpj (λ)={ N   Gpj (λ 0 )−1}/{ N   GPj (λ)− N   GPj (λ 0 )},     φφ Gni : refractive power (optical power) of each thin single lens constituting the front lens unit Gn,   φ Gpj : refractive power (optical power) of each thin single lens constituting the rear lens unit Gp,   ν Gni : Abbe constant of each thin single lens constituting the front lens unit Gn,   ν Gpj : Abbe constant of each thin single lens constituting the rear lens unit Gp,   h Gn : height of paraxial marginal ray incident on the front lens unit Gn,   h Gp : height of paraxial marginal ray incident on the rear lens unit Gp,   H Gn : height of paraxial chief ray incident on the front unit Gn,   H Gp : height of paraxial chief ray incident on the rear unit Gp,   N Gpi : refractive index of each thin single lens constituting the rear unit Gp   N Gnj : refractive index of each thin single lens constituting the front unit Gn,   λ: wavelength,   λ 0 : design wavelength.   
   In order to correct chromatic aberration of magnification more effectively using a material that satisfies conditions (1) to (3), it is preferred that the following condition be satisfied:
 
2 &lt;OTL/f&lt; 15  (4),
 
where OTL is the optical total length of the optical system and f is the focal length thereof. In the case that the optical system is a zoom lens, OTL and f shall refer to the values at the wide-angle end.
 
   Condition (4) means that the optical system is a retrofocus type lens. 
   Furthermore, it is preferred that the component GIT disposed on the front side of the intersection P satisfy the following condition:
 
0.01 &lt;φGIT /φ&lt;0.12  (5)
 
where,
     φGIT: refractive power (optical power) of the component GIT for the d-line under the assumption that the two refractive surface of the component GIT are exposed to air,   φ: refractive power (optical power) of the whole optical system for the d-line (in the case that the optical system is a zoom lens, refractive power (optical power) at the wide-angle end).   

   Furthermore, it is preferred that the component GIT disposed on the rear side of the intersection P satisfy the following condition:
 
−0.2&lt;φ GIT /φ&lt;−0.02  (6)
 
   Condition (5) is a condition for limiting the refractive power of the component GIT relative to the refractive power of the whole system in the case that the component GIT is disposed on the front side of the intersection P. When the positive refractive power of the component GIT is so weak as to be lower than the lower limit value of condition (5), chromatic aberration correction effects will be insufficient. On the other hand, when the positive refractive power of the component GIT is so strong as to be higher than the upper limit value of condition (5), the balance of the chromatic aberration generated by ordinary glass materials and the chromatic aberration generated by the component GIT will be deteriorated to make chromatic aberration worse. 
   Condition (6) is a condition for limiting the refractive power of the component GIT relative to the refractive power of the whole system in the case that the component GIT is disposed on the rear side of the intersection P. When the negative refractive power of the component GIT is so strong as to be lower than the lower limit value of condition (6), the balance of the chromatic aberration generated by ordinary glass materials and the chromatic aberration generated by the component GIT will be deteriorated to make chromatic aberration worse. On the other hand, the negative refractive power of the component GIT is so weak as to be higher than the upper limit value of condition (6), chromatic aberration correction effects become insufficient. 
   Next, embodiments in which materials satisfying conditions (1) to (3) are employed in actual optical systems will be described in the following. Here, materials in which ITO fine particles are dispersed as mentioned above are used as materials that satisfy conditions (1) to (3). 
     FIG. 1  is a cross sectional view of an optical system according to numerical embodiment 1, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a retrofocus type optical system with a focal length of 9 mm. In this example, a resin material for replicas in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 1 , reference sign GIT 1  designates the lens (layer) including ITO, and reference sign S designates an aperture stop.  FIG. 2  shows aberration diagrams of the optical system according to numerical embodiment 1 in the state in which the optical system is focused at infinity. In  FIG. 1 , the left side is the object side (front side), while the right side is the image side (rear side). This orientation also applies to numerical embodiments 2 to 4. 
   In the optical system of numerical embodiment 1, the lens (layer) made of the mixture containing ITO fine particles is employed in the object side portion, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 1  made of the mixture containing ITO fine particles is designed to have a positive refractive power to mainly correct chromatic aberration of magnification, so that a retrofocus type optical system in which chromatic aberration of magnification is excellently corrected is realized. 
     FIG. 3  is a cross sectional view showing an optical system according to numerical embodiment 2, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a wide angle zoom lens with the focal length range of 17 mm to 40 mm. In this example, acrylic in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 3 , reference sign GIT 2  designates the lens (layer) made of the mixture containing ITO fine particles, reference sign S designates an aperture stop, reference sign L 1  designates the first lens unit having a negative refractive power, reference sign L 2  designates the second lens unit having a positive refractive power, reference sign L 3  designates the third lens unit having a negative refractive power, and reference sign L 4  designates the fourth lens unit having a positive refractive power. Upon zooming from the wide-angle end to the telephoto end, the lens units are adapted to move following the loci represented by the arrows in  FIG. 3 .  FIG. 4A  shows aberration diagrams of the optical system according to numerical embodiment 2 at the wide-angle end in the state in which the optical system is focused at infinity.  FIG. 4B  shows aberration diagrams at the telephoto end in the state in which the optical system is focused at infinity. 
   In the optical system of numerical embodiment 2, the lens (layer) made of the mixture containing ITO fine particles is employed on the image side of the aperture stop S, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 2  made of the mixture containing ITO fine particles is designed to have a negative refractive power to intensively correct chromatic aberration of magnification, so that a retrofocus type optical system in which chromatic aberration of magnification is excellently corrected is realized. 
     FIG. 5  is a cross sectional view showing an optical system according to numerical embodiment 3, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a wide angle zoom lens with the focal length range of 20 mm to 35 mm. In this example, a resin material for replicas in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 5 , reference sign GIT 2  designates the lens (layer) made of the mixture containing ITO fine particles, reference sign S designates an aperture stop, reference sign L 1  designates the first lens unit having a negative refractive power, reference sign L 2  designates the second lens unit having a negative refractive power, and reference sign L 3  designates the third lens unit having a positive refractive power. Upon zooming from the wide angle end to the telephoto end, the lens units are adapted to move following the loci represented by the arrows in  FIG. 5 .  FIG. 6A  shows aberration diagrams of the optical system according to numerical embodiment 3 at the wide-angle end in the state in which the optical system is focused at infinity.  FIG. 6B  shows aberration diagrams at the telephoto end in the state in which the optical system is focused at infinity. 
   In the optical system of numerical embodiment 3, the lens (layer) made of the mixture containing ITO fine particles is employed on the image side of the aperture stop S, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 2  made of the mixture containing ITO fine particles is designed to have a negative refractive power to intensively correct chromatic aberration of magnification, so that a retrofocus type optical system in which chromatic aberration of magnification is excellently corrected is realized. 
     FIG. 7  is a cross sectional view showing an optical system according to numerical embodiment 4, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a wide angle zoom lens with the focal length range of 22 mm to 55 mm. In this example, a resin material for replicas in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 7 , reference sign GIT 1  designates the lens (layer) made of the mixture containing ITO fine particles, reference sign S designates an aperture stop, reference sign L 1  designates the first lens unit having a negative refractive power, reference sign L 2  designates the second lens unit having a positive refractive power, and reference sign L 3  designates the third lens unit having a negative refractive power. Upon zooming from the wide angle end to the telephoto end, the lens units are adapted to move following the loci represented by the arrows in  FIG. 7 .  FIG. 8A  shows aberration diagrams of the optical system according to numerical embodiment 4 at the wide-angle end in the state in which the optical system is focused at infinity.  FIG. 8B  shows aberration diagrams at the telephoto end in the state in which the optical system is focused at infinity. 
   In the optical system of numerical embodiment 4, the lens (layer) made of the mixture containing ITO fine particles is employed on the object side of the aperture stop S, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 1  made of the mixture containing ITO fine particles is designed to have a positive refractive power to intensively correct chromatic aberration of magnification, so that a retrofocus type wide-angle optical system in which chromatic aberration of magnification is excellently corrected is realized. 
     FIG. 9  is a cross sectional view showing an optical system according to numerical embodiment 5 in its wide-angle end state, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a projection optical system with the focal length range of 28 mm to 35 mm. The optical system of this example is a projection optical system for use in a projector for projecting an original image displayed on a liquid crystal panel onto a screen. In this example, acrylic in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 9 , reference sign GIT 2  designates the lens (layer) made of the mixture containing ITO fine particles, reference sign S designates an aperture stop, reference sign L 1  designates the first lens unit having a negative refractive power, reference sign L 2  designates the second lens unit having a positive refractive power, reference sign L 3  designates the third lens unit having a positive refractive power, reference sign L 4  designates the fourth lens unit having a negative refractive power, reference sign L 5  designates the fifth lens unit having a positive refractive power, and reference sign L 6  designates the sixth lens unit having a positive refractive power. Upon zooming from the wide-angle end to the telephoto end, the lens units are adapted to move following the loci represented by the arrows in  FIG. 9 . In  FIG. 9 , the left side is the screen side (front side), while the right side is the original image side (rear side). This orientation also applies to numerical embodiment 6. 
     FIG. 10A  shows aberration diagrams of the optical system according to numerical embodiment 5 at the wide-angle end (i.e. in the shortest focal length state).  FIG. 10B  shows aberration diagrams at the telephoto end (i.e. in the longest focal length state). 
   In the optical system of numerical embodiment 5, the lens (layer) made of the mixture containing ITO fine particles is employed in the original image side of the aperture stop S, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 2  made of the mixture containing ITO fine particles is designed to have a negative refractive power to intensively correct chromatic aberration of magnification, so that a retrofocus type projection optical system in which chromatic aberration of magnification is excellently corrected is realized. 
     FIG. 11  is a cross sectional view showing an optical system according to numerical embodiment 6 in its wide-angle end state, in which a lens (or layer) made of a mixture containing ITO fine particles is employed in a projection optical system with the focal length range of 28 mm to 35 mm. In this embodiment, acrylic in which ITO fine particles are mixed at a proportion of 20% is used. In  FIG. 11  reference sign GIT 1  designates the lens (layer) made of the mixture containing ITO fine particles, reference sign S designates an aperture stop, reference sign L 1  designates the first lens unit having a negative refractive power, reference sign L 2  designates the second lens unit having a positive refractive power, reference sign L 3  designates the third lens unit having a positive refractive power, reference sign L 4  designates the fourth lens unit having a negative refractive power, reference sign L 5  designates the fifth lens unit having a positive refractive power, and reference sign L 6  designates the sixth lens unit having a positive refractive power. Upon zooming from the wide-angle end to the telephoto end, the lens units are adapted to move following the loci represented by the arrows in  FIG. 11 .  FIG. 12A  shows aberration diagrams of the optical system according to numerical embodiment 6 at the wide-angle end.  FIG. 12B  shows aberration diagrams at the telephoto end. 
   In the optical system of numerical embodiment 6, the lens (layer) made of the mixture containing ITO fine particles is employed in the screen side of the aperture stop S, in which the height, from the optical axis, of the path of the paraxial chief ray is relatively high. In addition, the lens (layer) GIT 1  made of the mixture containing ITO fine particles is designed to have a positive refractive power to intensively correct chromatic aberration of magnification, so that a retrofocus type projection optical system in which chromatic aberration of magnification is excellently corrected is realized. 
   Specific numerical data of numerical embodiments 1 to 6 are presented in the following. In the data of each numerical embodiment, the suffix i generally refers to the element number (or surface number) counted from the object side, namely, ri represents the radius of curvature of the i-th optical surface (the i-th surface), di represents the on-axis distance between the i-th surface and the (i+1)-th surface, and ni and νi respectively represent the refractive index for the d-line and the Abbe constant of the i-th optical member. In addition, f represents the focal length, Fno represents the F-number and ω represents the half angle of view. 
   Furthermore, let x be the shift amount along the optical axis from the vertex, let h be the height measured along the direction perpendicular to the optical axis from the optical axis, let r be the paraxial radius of curvature, let k be the conic constant, and let B, C, D, E . . . be the aspherical coefficients of the respective orders, then the aspherical shape is expressed by the following formula. 
   
     
       
         
           
             x 
             ⁡ 
             
               ( 
               h 
               ) 
             
           
           = 
           
             
               
                 
                   ( 
                   
                     1 
                     / 
                     r 
                   
                   ) 
                 
                 ⁢ 
                 
                   h 
                   2 
                 
               
               
                 1 
                 + 
                 
                   
                     { 
                     
                       1 
                       - 
                       
                         
                           ( 
                           
                             1 
                             + 
                             k 
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               h 
                               / 
                               r 
                             
                             ) 
                           
                           2 
                         
                       
                     
                     } 
                   
                 
               
             
             + 
             
               Bh 
               4 
             
             + 
             
               Ch 
               6 
             
             + 
             
               Dh 
               8 
             
             + 
             
               
                 Eh 
                 10 
               
               ⁢ 
               
                   
               
               ⁢ 
               … 
             
           
         
       
     
   
   Incidentally, in the data of the aspherical coefficients, the expression “e±X” means “×10 ±X ”. 
   In all of the numerical embodiments, ITO is used in the state dispersed in acrylic (PMMA) at a volume fraction of 20%. The refractive index of the mixture of ITO and acrylic is calculated based on the value obtained by calculation using equation (c) mentioned before. 
   Sign Gi represents the i-th element, and the refractive indices for the d-line, the g-line, the C-line and the F-line, the Abbe constant and the partial dispersion ratios are also presented. 
   In the spherical aberration diagrams shown in  FIGS. 2 ,  4 A,  4 B,  6 A,  6 B,  8 A and  8 B, the solid lines are for the d-line, the two-dot chain lines are for the g-line, the chain lines are for the C-line and the broken lines are fore the F-line. In the astigmatism diagrams, the solid lines are for the d-line sagittal image plane, the broken lines are for the d-line meridional image plane, the chain lines are for the g-line sagittal image plane, and the two-dot chain lines are for the g-line meridional image plane. The distortion diagrams are presented for the d-line. In the chromatic aberration of magnification diagrams, the two-dot chain lines are for the g-line, the chain lines are for the C-line and the broken lines are for the F-line. 
   In the spherical aberration diagrams shown in  FIGS. 10A ,  10 B,  12 A and  12 B, the solid lines are for the wavelength of 550 nm, the two-dot chain lines are for the wavelength of 440 nm, the chain lines are for the wavelength of 620 nm and the broken lines are for the wavelength of 470 nm. In the astigmatism diagrams in  FIGS. 10A ,  10 B,  12 A and  12 B, the solid lines are for the sagittal image plane at the wavelength of 550 nm, the broken lines are for the meridional image plane at the wavelength of 550 nm, the chain lines are for the sagittal image plane at the wavelength of 440 nm, and the two-dot chain lines are for the meridional image plane at the wavelength of 440 nm. In the distortion diagrams are presented for the wavelength of 550 nm. In the chromatic aberration of magnification diagrams, the two-dot chain lines are for the wavelength of 440 nm, the chain lines are for the wavelength of 470 nm, and the broken lines are for the wavelength of 620 nm. 
   The values related to conditions (4) to (6) are presented in Table 1 for each of the numerical embodiments. 
   
     
       
             
           
             
             
             
             
           
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 1) 
             
             
               f = 8.9 FNo = 1:2.9 2ω = 113.5° 
             
             
                 
             
           
        
         
             
                r1 = 28.900 
               d1 = 2.00 
               n1 = 1.69680 
               ν1 = 55.5 
             
             
                r2 = 16.733 
               d2 = 7.05 
             
             
               *r3 = 41.159 
               d3 = 3.50 
               n2 = 1.60311 
               ν2 = 60.7 
             
             
                r4 = 24.855 
               d4 = 0.50 
               n3 = 1.59629 
               ν3 = 13.9 
             
             
                r5 = 27.428 
               d5 = 0.10 
             
             
                r6 = 22.550 
               d6 = 1.00 
               n4 = 1.69680 
               ν4 = 55.5 
             
             
                r7 = 11.640 
               d7 = 4.00 
             
             
                r8 = 24.419 
               d8 = 0.90 
               n5 = 1.77250 
               ν5 = 49.6 
             
             
                r9 = 12.204 
               d9 = 5.20 
             
             
                r10 = 92.038 
               d10 = 0.95 
               n6 = 1.69680 
               ν6 = 55.5 
             
             
                r11 = 13.058 
               d11 = 6.40 
               n7 = 1.59551 
               ν7 = 39.2 
             
             
                r12 = −41.643 
               d12 = 2.10 
             
             
                r13 = 37.448 
               d13 = 5.10 
               n8 = 1.57501 
               ν8 = 41.5 
             
             
                r14 = −6.427 
               d14 = 1.00 
               n9 = 1.77250 
               ν9 = 49.6 
             
             
                r15 = −9.282 
               d15 = 0.55 
             
             
                r16 = −10.232 
               d16 = 0.90 
               n10 = 1.77250 
               ν10 = 49.6 
             
             
                r17 = −29.514 
               d17 = 0.30 
             
             
                r18 = (stop) 
               d18 = 0.85 
             
             
                r19 = 37.309 
               d19 = 5.50 
               n11 = 1.62299 
               ν11 = 58.2 
             
             
                r20 = −10.365 
               d20 = 2.50 
               n12 = 1.74320 
               ν12 = 49.3 
             
             
                r21 = 33.296 
               d21 = 0.43 
             
             
                r22 = −141.615 
               d22 = 0.50 
               n13 = 1.92286 
               ν13 = 18.9 
             
             
                r23 = 25.888 
               d23 = 3.70 
               n14 = 1.51728 
               ν14 = 69.6 
             
             
                r24 = −11.329 
               d24 = 0.12 
             
             
                r25 = 176.338 
               d25 = 2.10 
               n15 = 1.81600 
               ν15 = 46.6 
             
             
                r26 = −26.764 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               8.94 
             
             
                 
                 
             
           
        
         
             
               Aspherical Coefficient 
             
             
               3rd surface 
             
             
                 
             
           
        
         
             
                 
               b: 4.101813e−05 
               c: 2.006611e−08 
               d: −2.784478e−10 
             
             
                 
               e: 1.312873e−12 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.69680 
               1.71234 
               1.69297 
               1.70552 
               55.5 
               1.238 
               0.543 
             
             
               G2 
               1.60311 
               1.61539 
               1.60008 
               1.61002 
               60.7 
               1.235 
               0.540 
             
             
               G3(GIT) 
               1.59629 
               1.63830 
               1.58040 
               1.62342 
               13.9 
               0.976 
               0.346 
             
             
               G4 
               1.69680 
               1.71234 
               1.69297 
               1.70552 
               55.5 
               1.238 
               0.543 
             
             
               G5 
               1.77250 
               1.79196 
               1.76780 
               1.78337 
               49.6 
               1.250 
               0.552 
             
             
               G6 
               1.69680 
               1.71234 
               1.69297 
               1.70552 
               55.5 
               1.238 
               0.543 
             
             
               G7 
               1.59551 
               1.61498 
               1.59103 
               1.60621 
               39.2 
               1.283 
               0.578 
             
             
               G8 
               1.57501 
               1.59275 
               1.57090 
               1.58476 
               41.5 
               1.280 
               0.576 
             
             
               G9 
               1.77250 
               1.79196 
               1.76780 
               1.78337 
               49.6 
               1.250 
               0.552 
             
             
               G10 
               1.77250 
               1.79197 
               1.76780 
               1.78337 
               49.6 
               1.250 
               0.552 
             
             
               G11 
               1.62299 
               1.63630 
               1.61974 
               1.63045 
               58.2 
               1.243 
               0.546 
             
             
               G12 
               1.74320 
               1.76205 
               1.73865 
               1.75372 
               49.3 
               1.251 
               0.553 
             
             
               G13 
               1.92286 
               1.98972 
               1.90916 
               1.95800 
               18.9 
               1.369 
               0.649 
             
             
               G14 
               1.51728 
               1.52638 
               1.51499 
               1.52242 
               69.6 
               1.225 
               0.533 
             
             
               G15 
               1.81600 
               1.83800 
               1.81075 
               1.82825 
               46.6 
               1.257 
               0.557 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 2) 
             
             
               f = 7.5–38.5 Fno = 1:4.1 2ω = 102.0°–58.7° 
             
             
                 
             
           
        
         
             
               *r1 = 1381.812 
               d1 = 3.50 
               n1 = 1.58313 
               ν1 = 59.4 
             
             
                r2 = 20.079 
               d2 = variable 
             
             
                r3 = −119.765 
               d3 = 1.30 
               n2 = 1.77250 
               ν2 = 49.6 
             
             
               *r4 = 26.434 
               d4 = 1.32 
             
             
                r5 = 23.868 
               d5 = 4.35 
               n3 = 1.84666 
               ν3 = 23.9 
             
             
                r6 = 50.526 
               d6 = variable 
             
             
                r7 = 0.000 
               d7 = 0.50 
             
             
                r8 = 36.740 
               d8 = 1.20 
               n4 = 1.84666 
               ν4 = 23.9 
             
             
                r9 = 20.162 
               d9 = 4.99 
               n5 = 1.51633 
               ν5 = 64.1 
             
             
                r10 = −54.769 
               d10 = 0.15 
             
             
                r11 = 33.954 
               d11 = 3.19 
               n6 = 1.67790 
               ν6 = 55.3 
             
             
                r12 = −122.644 
               d12 = variable 
             
             
                r13 = (stop) 
               d13 = 1.50 
             
             
                r14 = −50.807 
               d14 = 1.00 
               n7 = 1.86300 
               ν7 = 41.5 
             
             
                r15 = 51.180 
               d15 = 0.67 
             
             
                r16 = 161.213 
               d16 = 1.00 
               n8 = 1.72342 
               ν8 = 38.0 
             
             
                r17 = 17.174 
               d17 = 3.49 
               n9 = 1.80518 
               ν9 = 25.4 
             
             
                r18 = −4559.135 
               d18 = variable 
             
             
                r19 = 55.808 
               d19 = 5.68 
               n10 = 1.48749 
               ν10 = 70.2 
             
             
                r20 = −25.763 
               d20 = 0.50 
               n11 = 1.57159 
               ν11 = 13.5 
             
             
               *r21 = −30.372 
               d21 = 0.15 
             
             
                r22 = 134.832 
               d22 = 1.20 
               n12 = 1.83400 
               ν12 = 37.2 
             
             
                r23 = 18.611 
               d23 = 6.95 
               n13 = 1.48749 
               ν13 = 70.2 
             
             
                r24 = −56.393 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               17.51 
               28.00 
               38.50 
             
             
                 
                 
             
           
        
         
             
               Variable Interval 
             
             
                 
             
           
        
         
             
                 
               d2 
               13.74 
               13.74 
               13.74 
             
             
                 
               d6 
               24.65 
               11.15 
               5.55 
             
             
                 
               d12 
               1.01 
               6.28 
               10.73 
             
             
                 
               d18 
               10.95 
               5.68 
               1.22 
             
             
                 
                 
             
           
        
         
             
               Aspherical Coefficient 
             
             
                 
             
             
               1st surface 
             
           
        
         
             
                 
               b: 1.541946e−05 
               c: −1.703973e−08 
               d: 1.550544e−11 
             
             
                 
               e: −3.917946e−15 
             
           
        
         
             
               4th surface 
             
           
        
         
             
                 
               b: 1.588787e−05 
               c: −1.398091e−08 
               d: 7.979067e−11 
             
           
        
         
             
               21st surface 
             
           
        
         
             
                 
               b: 8.893654e−06 
               c: 4.019287e−08 
               d: −2.818461e−10 
             
             
                 
               e: 7.971370e−13 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.58313 
               1.59528 
               1.58013 
               1.58995 
               59.4 
               1.237 
               0.543 
             
             
               G2 
               1.77250 
               1.79197 
               1.76780 
               1.78337 
               49.6 
               1.250 
               0.552 
             
             
               G3 
               1.84666 
               1.89386 
               1.83655 
               1.87193 
               23.9 
               1.334 
               0.620 
             
             
               G4 
               1.84666 
               1.89386 
               1.83655 
               1.87193 
               23.9 
               1.334 
               0.620 
             
             
               G5 
               1.51633 
               1.52621 
               1.51386 
               1.52191 
               64.1 
               1.227 
               0.534 
             
             
               G6 
               1.67790 
               1.69314 
               1.67419 
               1.68644 
               55.3 
               1.244 
               0.547 
             
             
               G7 
               1.86300 
               1.88938 
               1.85682 
               1.87760 
               41.5 
               1.269 
               0.567 
             
             
               G8 
               1.72342 
               1.74800 
               1.71782 
               1.73688 
               38.0 
               1.290 
               0.583 
             
             
               G9 
               1.80518 
               1.84729 
               1.79611 
               1.82777 
               25.4 
               1.330 
               0.617 
             
             
               G10 
               1.48749 
               1.49596 
               1.48534 
               1.49228 
               70.2 
               1.220 
               0.530 
             
             
               G11(GIT) 
               1.57159 
               1.61267 
               1.55583 
               1.59815 
               13.5 
               0.970 
               0.343 
             
             
               G12 
               1.83400 
               1.86278 
               1.82738 
               1.84982 
               37.2 
               1.283 
               0.578 
             
             
               G13 
               1.48749 
               1.49596 
               1.48534 
               1.49228 
               70.2 
               1.220 
               0.530 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 3) 
             
             
               f = 20.6–34.1 Fno = 1:3.6–4.6 2ω = 92.8°–64.8° 
             
             
                 
             
           
        
         
             
               r1 = 77.005 
               d1 = 4.10 
               n1 = 1.62299 
               ν1 = 58.1 
             
             
               r2 = 236.410 
               d2 = 0.10 
             
             
               r3 = 57.918 
               d3 = 1.70 
               n2 = 1.78590 
               ν2 = 44.2 
             
             
               r4 = 22.654 
               d4 = variable 
             
             
               r5 = 39.007 
               d5 = 1.40 
               n3 = 1.80610 
               ν3 = 41.0 
             
             
               r6 = 16.676 
               d6 = 4.68 
             
             
               r7 = 116.102 
               d7 = 1.30 
               n4 = 1.77250 
               ν4 = 49.6 
             
             
               r8 = 32.443 
               d8 = 2.80 
             
             
               r9 = 25.533 
               d9 = 3.00 
               n5 = 1.84666 
               ν5 = 23.8 
             
             
               r10 = 62.480 
               d10 = variable 
             
             
               r11 = 62.563 
               d11 = 2.20 
               n6 = 1.58313 
               ν6 = 59.4 
             
             
               r12 = −61.416 
               d12 = 1.78 
             
             
               r13 = (stop) 
               d13 = 0.92 
             
             
               r14 = 42.340 
               d14 = 6.90 
               n7 = 1.62606 
               ν7 = 39.2 
             
             
               r15 = −67.037 
               d15 = 3.50 
             
             
               r16 = −16.291 
               d16 = 2.50 
               n8 = 1.84666 
               ν8 = 23.8 
             
             
               r17 = −75.129 
               d17 = 3.80 
               n9 = 1.78590 
               ν9 = 44.2 
             
             
               r18 = −19.960 
               d18 = 0.20 
             
             
               r19 = 50.544 
               d19 = 1.20 
               n10 = 1.83481 
               ν10 = 42.7 
             
             
               r20 = 24.163 
               d20 = 1.73 
             
             
               r21 = −148.267 
               d21 = 2.50 
               n11 = 1.48749 
               ν11 = 70.2 
             
             
               r22 = −25.814 
               d22 = 0.20 
             
             
               r23 = 117.509 
               d23 = 2.15 
               n12 = 1.48749 
               ν12 = 70.2 
             
             
               r24 = −61.461 
               d24 = 0.50 
               n13 = 1.59629 
               ν13 = 13.9 
             
             
               r25 = −109.320 
               d25 = variable 
             
             
               r26 = ∞ 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               20.62 
               24.00 
               34.07 
             
             
                 
                 
             
           
        
         
             
               Variable Interval 
             
             
                 
             
           
        
         
             
                 
               d4 
               7.85 
               9.85 
               7.85 
             
             
                 
               d10 
               16.78 
               10.47 
               1.47 
             
             
                 
               d25 
               0.00 
               4.31 
               15.31 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.62299 
               1.63630 
               1.61974 
               1.63045 
               58.2 
               1.243 
               0.546 
             
             
               G2 
               1.78590 
               1.80839 
               1.78059 
               1.79837 
               44.2 
               1.265 
               0.564 
             
             
               G3 
               1.80610 
               1.83115 
               1.80025 
               1.81994 
               40.2 
               1.272 
               0.569 
             
             
               G4 
               1.77250 
               1.79196 
               1.76780 
               1.78337 
               49.6 
               1.250 
               0.552 
             
             
               G5 
               1.84666 
               1.89421 
               1.83649 
               1.87210 
               23.8 
               1.335 
               0.621 
             
             
               G6 
               1.58313 
               1.59530 
               1.58014 
               1.58996 
               59.4 
               1.239 
               0.544 
             
             
               G7 
               1.62606 
               1.64655 
               1.62135 
               1.63732 
               39.2 
               1.283 
               0.578 
             
             
               G8 
               1.84666 
               1.89421 
               1.83649 
               1.87210 
               23.8 
               1.335 
               0.621 
             
             
               G9 
               1.78590 
               1.80839 
               1.78059 
               1.79837 
               44.2 
               1.265 
               0.564 
             
             
               G10 
               1.83481 
               1.85953 
               1.82897 
               1.84851 
               42.7 
               1.265 
               0.564 
             
             
               G11 
               1.48749 
               1.49596 
               1.48534 
               1.49228 
               70.2 
               1.220 
               0.530 
             
             
               G12 
               1.48749 
               1.49596 
               1.48534 
               1.49228 
               70.2 
               1.220 
               0.530 
             
             
               G13(GIT) 
               1.59629 
               1.63830 
               1.58040 
               1.62342 
               13.9 
               0.976 
               0.346 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 4) 
             
             
               f = 22.9–52.9 Fno = 1:3.9–5.9 2ω = 86.8°–44.5° 
             
             
                 
             
           
        
         
             
                r1 = 36.615 
               d1 = 1.44 
               n1 = 1.80610 
               ν1 = 40.9 
             
             
                r2 = 15.544 
               d2 = 0.54 
               n2 = 1.59629 
               ν2 = 13.9 
             
             
                r3 = 16.027 
               d3 = 7.39 
             
             
                r4 = 165.372 
               d4 = 1.20 
               n3 = 1.71999 
               ν3 = 50.2 
             
             
                r5 = 21.580 
               d5 = 0.09 
               n4 = 1.51282 
               ν4 = 50.9 
             
             
               *r6 = 18.642 
               d6 = 2.62 
             
             
                r7 = 24.450 
               d7 = 4.30 
               n5 = 1.74077 
               ν5 = 27.8 
             
             
                r8 = 152.272 
               d8 = variable 
             
             
                r9 = 25.619 
               d9 = 2.60 
               n6 = 1.51742 
               ν6 = 52.4 
             
             
                r10 = −62.378 
               d10 = 0.60 
             
             
                r11 = (stop) 
               d11 = 0.60 
             
             
                r12 = 20.136 
               d12 = 3.50 
               n7 = 1.51742 
               ν7 = 52.4 
             
             
                r13 = −177.115 
               d13 = 0.43 
             
             
                r14 = −37.539 
               d14 = 7.50 
               n8 = 1.72825 
               ν8 = 28.5 
             
             
                r15 = 17.433 
               d15 = 1.93 
             
             
                r16 = 58.669 
               d16 = 2.50 
               n9 = 1.57099 
               ν9 = 50.8 
             
             
                r17 = −21.352 
               d17 = variable 
             
             
                r18 = 0.000 
               d18 = variable 
             
             
                r19 = −36.137 
               d19 = 1.00 
               n10 = 1.71999 
               ν10 = 50.2 
             
             
                r20 = 70.937 
               d20 = 0.63 
             
             
                r21 = 236.020 
               d21 = 3.40 
               n11 = 1.71300 
               ν11 = 53.9 
             
             
                r22 = −29.793 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               22.90 
               35.05 
               52.88 
             
             
                 
                 
             
           
        
         
             
               Variable Interval 
             
             
                 
             
           
        
         
             
                 
               d8 
               26.27 
               10.86 
               1.07 
             
             
                 
               d17 
               0.00 
               4.13 
               10.20 
             
             
                 
               d18 
               1.80 
               7.88 
               16.80 
             
             
                 
                 
             
           
        
         
             
               Aspherical Coefficient 
             
             
               6th surface 
             
             
                 
             
           
        
         
             
                 
               b: −2.238197e−05 
               c: −1.062584e−07 
               d: 3.098938e−10 
             
             
                 
               e: −1.455066e−12 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.80610 
               1.83117 
               1.80025 
               1.81994 
               40.9 
               1.273 
               0.570 
             
             
               G2(GIT) 
               1.59629 
               1.63830 
               1.58040 
               1.62342 
               13.9 
               0.976 
               0.346 
             
             
               G3 
               1.71999 
               1.73795 
               1.71568 
               1.73001 
               50.2 
               1.253 
               0.554 
             
             
               G4 
               1.51282 
               1.52552 
               1.50980 
               1.51988 
               50.9 
               1.260 
               0.560 
             
             
               G5 
               1.74077 
               1.77599 
               1.73309 
               1.75975 
               27.8 
               1.321 
               0.609 
             
             
               G6 
               1.51742 
               1.52980 
               1.51444 
               1.52431 
               52.4 
               1.254 
               0.556 
             
             
               G7 
               1.51742 
               1.52980 
               1.51444 
               1.52431 
               52.4 
               1.254 
               0.556 
             
             
               G8 
               1.72825 
               1.76200 
               1.72086 
               1.74645 
               28.5 
               1.319 
               0.608 
             
             
               G9 
               1.57099 
               1.58514 
               1.56762 
               1.57886 
               50.8 
               1.259 
               0.559 
             
             
               G10 
               1.71999 
               1.73795 
               1.71568 
               1.73001 
               50.2 
               1.253 
               0.554 
             
             
               G11 
               1.71300 
               1.72943 
               1.70897 
               1.72221 
               53.9 
               1.241 
               0.545 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 5) 
             
             
               f = 28.8–34.4 Fno = 1:1.8–2.1 2ω = 46.9°–39.9° 
             
             
                 
             
           
        
         
             
                r1 = 479.991 
               d1 = 2.39 
               n1 = 1.77534 
               ν1 = 50.2 
             
             
                r2 = −174.256 
               d2 = 0.15 
             
             
                r3 = 113.827 
               d3 = 1.50 
               n2 = 1.78000 
               ν2 = 50.0 
             
             
                r4 = 28.536 
               d4 = 4.08 
             
             
                r5 = −142.555 
               d5 = 1.50 
               n3 = 1.83417 
               ν3 = 37.0 
             
             
                r6 = 54.349 
               d6 = variable 
             
             
                r7 = 250.553 
               d7 = 3.40 
               n4 = 1.77562 
               ν4 = 50.2 
             
             
                r8 = −52.927 
               d8 = 0.29 
             
             
                r9 = 36.084 
               d9 = 1.50 
               n5 = 1.48700 
               ν5 = 70.4 
             
             
                r10 = 17.823 
               d10 = 4.71 
               n6 = 1.73822 
               ν6 = 39.4 
             
             
                r11 = 71.782 
               d11 = variable 
             
             
                r12 = (stop) 
               d12 = 0.00 
             
             
                r13 = 47.077 
               d13 = 2.43 
               n7 = 1.49198 
               ν7 = 69.8 
             
             
                r14 = −259.854 
               d14 = variable 
             
             
                r15 = −83.027 
               d15 = 1.50 
               n8 = 1.54337 
               ν8 = 65.1 
             
             
                r16 = 36.053 
               d16 = variable 
             
             
                r17 = −13.389 
               d17 = 1.50 
               n9 = 1.85000 
               ν9 = 23.0 
             
             
                r18 = −47.648 
               d18 = 4.77 
               n10 = 1.76938 
               ν10 = 50.5 
             
             
                r19 = −18.838 
               d19 = 0.15 
             
             
                r20 = −345.897 
               d20 = 4.40 
               n11 = 1.78000 
               ν11 = 50.0 
             
             
                r21 = −37.216 
               d21 = variable 
             
             
               *r22 = 84.335 
               d22 = 0.01 
               n12 = 1.57160 
               ν12 = 13.5 
             
             
                r23 = 66.832 
               d23 = 4.81 
               n13 = 1.78000 
               ν13 = 50.0 
             
             
                r24 = −96.327 
               d24 = 1.82 
             
             
                r25 = ∞ 
               d25 = 41.50 
               n14 = 1.62299 
               ν14 = 58.2 
             
             
                r26 = ∞ 
               d26 = 2.60 
               n15 = 1.51633 
               ν15 = 64.1 
             
             
                r27 = ∞ 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               28.82 
               31.32 
               34.44 
             
             
                 
                 
             
           
        
         
             
               Variable Interval 
             
             
                 
             
           
        
         
             
                 
               d6 
               4.27 
               3.07 
               1.75 
             
             
                 
               d11 
               11.15 
               10.85 
               8.44 
             
             
                 
               d14 
               1.85 
               4.76 
               8.77 
             
             
                 
               d16 
               11.74 
               8.55 
               6.00 
             
             
                 
               d21 
               0.50 
               2.29 
               4.55 
             
             
                 
                 
             
           
        
         
             
               Aspherical Coefficient 
             
             
               22nd surface 
             
             
                 
             
           
        
         
             
                 
               k: −7.027492e+00 
                 
                 
             
             
                 
               b: −1.183492e−06 
               c: 2.606798e−10 
               d: −5.197561e−12 
             
             
                 
               e: 6.728677e−15 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.77534 
               1.79482 
               1.77071 
               1.78617 
               50.2 
               1.261 
               0.560 
             
             
               G2 
               1.78000 
               1.79968 
               1.77533 
               1.79094 
               50.0 
               1.261 
               0.560 
             
             
               G3 
               1.83417 
               1.86331 
               1.82755 
               1.85013 
               36.9 
               1.291 
               0.584 
             
             
               G4 
               1.77562 
               1.79511 
               1.77099 
               1.78646 
               50.2 
               1.261 
               0.560 
             
             
               G5 
               1.48700 
               1.49541 
               1.48486 
               1.49178 
               70.4 
               1.215 
               0.524 
             
             
               G6 
               1.73823 
               1.76233 
               1.73271 
               1.75146 
               39.4 
               1.285 
               0.579 
             
             
               G7 
               1.49198 
               1.50055 
               1.48980 
               1.49685 
               69.8 
               1.216 
               0.525 
             
             
               G8 
               1.54337 
               1.55361 
               1.54081 
               1.54916 
               65.1 
               1.227 
               0.533 
             
             
               G9 
               1.85000 
               1.89888 
               1.83941 
               1.87638 
               23.0 
               1.322 
               0.608 
             
             
               G10 
               1.76938 
               1.78861 
               1.76482 
               1.78007 
               50.4 
               1.260 
               0.560 
             
             
               G11 
               1.78000 
               1.79968 
               1.77533 
               1.79094 
               50.0 
               1.261 
               0.560 
             
             
               G12(GIT) 
               1.57315 
               1.61272 
               1.55531 
               1.59810 
               13.4 
               0.925 
               0.342 
             
             
               G13 
               1.78000 
               1.79968 
               1.77533 
               1.79094 
               50.0 
               1.261 
               0.560 
             
             
               G14 
               1.62299 
               1.63630 
               1.61974 
               1.63045 
               58.2 
               1.242 
               0.546 
             
             
               G15 
               1.51633 
               1.52621 
               1.51386 
               1.52191 
               64.1 
               1.228 
               0.535 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
           
             
           
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
           
         
             
                 
             
           
           
             
               (Numerical Embodiment 6) 
             
             
               f = 28.8–34.4 Fno = 1:1.8–2.0 2ω = 46.9°–39.9° 
             
             
                 
             
           
        
         
             
                r1 = −1000.000 
               d1 = 3.12 
               n1 = 1.77583 
               ν1 = 44.6 
             
             
                r2 = −75.204 
               d2 = 0.30 
               n2 = 1.57160 
               ν2 = 13.5 
             
             
               *r3 = −52.577 
               d3 = 0.15 
             
             
               (aspherical 
             
             
               surface) 
             
             
                r4 = 95.547 
               d4 = 1.50 
               n3 = 1.72355 
               ν3 = 52.7 
             
             
                r5 = 22.798 
               d5 = 5.43 
             
             
                r6 = −47.470 
               d6 = 1.50 
               n4 = 1.83007 
               ν4 = 37.9 
             
             
                r7 = 143.093 
               d7 = variable 
             
             
                r8 = −466.401 
               d8 = 2.77 
               n5 = 1.82288 
               ν5 = 39.2 
             
             
                r9 = −49.985 
               d9 = 0.15 
             
             
                r10 = 32.665 
               d10 = 1.50 
               n6 = 1.48700 
               ν6 = 70.4 
             
             
                r11 = 22.659 
               d11 = 3.20 
               n7 = 1.83364 
               ν7 = 34.0 
             
             
                r12 = 53.494 
               d12 = variable 
             
             
                r13 = 25.138 
               d13 = 3.72 
               n8 = 1.48700 
               ν8 = 70.4 
             
             
                r14 = −177.500 
               d14 = variable 
             
             
                r15 = (stop) 
               d15 = 2.04 
             
             
                r16 = 104.736 
               d16 = 1.50 
               n9 = 1.66301 
               ν9 = 30.9 
             
             
                r17 = 19.977 
               d17 = variable 
             
             
                r18 = −13.506 
               d18 = 1.50 
               n10 = 1.79814 
               ν10 = 28.5 
             
             
                r19 = 82.460 
               d19 = 6.03 
               n11 = 1.59085 
               ν11 = 61.9 
             
             
                r20 = −19.280 
               d20 = 0.52 
             
             
                r21 = −2066.276 
               d21 = 5.05 
               n12 = 1.78000 
               ν12 = 50.0 
             
             
                r22 = −32.904 
               d22 = variable 
             
             
                r23 = 66.123 
               d23 = 4.50 
               n13 = 1.80841 
               ν13 = 42.1 
             
             
                r24 = −132.913 
               d24 = 1.82 
             
             
                r25 = ∞ 
               d25 = 41.50 
               n14 = 1.62299 
               ν14 = 58.2 
             
             
                r26 = ∞ 
               d26 = 2.60 
               n15 = 1.51633 
               ν15 = 64.1 
             
             
                r27 = ∞ 
             
             
                 
             
           
        
         
             
                 
               Focal Length 
               28.82 
               31.27 
               34.43 
             
             
                 
                 
             
           
        
         
             
               Variable Interval 
             
             
                 
             
           
        
         
             
                 
               d7 
               4.86 
               3.37 
               1.87 
             
             
                 
               d12 
               8.34 
               5.82 
               2.50 
             
             
                 
               d14 
               1.85 
               3.68 
               5.80 
             
             
                 
               d17 
               8.57 
               8.38 
               7.95 
             
             
                 
               d22 
               0.50 
               2.87 
               6.00 
             
             
                 
                 
             
           
        
         
             
               Aspherical Coefficient 
             
             
               3rd surface 
             
             
                 
             
           
        
         
             
                 
               k: −8.785724e+00 
                 
                 
             
             
                 
               b: 1.117266e−06 
               c: 2.767939e−09 
               d: −1.361241e−11 
             
             
                 
               e: 2.009707e−14 
             
             
                 
                 
             
           
        
         
             
               Refractive Index at Each Wavelength 
             
           
        
         
             
                 
               d 
               g 
               c 
               f 
               νd 
               θgd 
               θgF 
             
             
                 
             
             
               G1 
               1.77583 
               1.79800 
               1.77067 
               1.78807 
               44.6 
               1.273 
               0.570 
             
             
               G2 
               1.57315 
               1.61272 
               1.55531 
               1.59810 
               13.4 
               0.925 
               0.342 
             
             
               G3 
               1.72355 
               1.74078 
               1.71942 
               1.73315 
               52.7 
               1.255 
               0.556 
             
             
               G4 
               1.83008 
               1.85834 
               1.82364 
               1.84557 
               37.8 
               1.289 
               0.582 
             
             
               G5 
               1.82288 
               1.84991 
               1.81670 
               1.83773 
               39.1 
               1.286 
               0.580 
             
             
               G6 
               1.48700 
               1.49541 
               1.48486 
               1.49178 
               70.4 
               1.215 
               0.524 
             
             
               G7 
               1.83364 
               1.86549 
               1.82648 
               1.85103 
               34.0 
               1.297 
               0.589 
             
             
               G8 
               1.48700 
               1.49541 
               1.48486 
               1.49178 
               70.4 
               1.215 
               0.524 
             
             
               G9 
               1.66301 
               1.69104 
               1.65677 
               1.67826 
               30.9 
               1.304 
               0.595 
             
             
               G10 
               1.79814 
               1.83478 
               1.79006 
               1.81803 
               28.5 
               1.310 
               0.599 
             
             
               G11 
               1.59085 
               1.60264 
               1.58794 
               1.59749 
               61.9 
               1.234 
               0.539 
             
             
               G12 
               1.78000 
               1.79968 
               1.77533 
               1.79094 
               50.0 
               1.261 
               0.560 
             
             
               G13 
               1.80841 
               1.83296 
               1.80274 
               1.82194 
               42.1 
               1.279 
               0.574 
             
             
               G14 
               1.62299 
               1.63630 
               1.61974 
               1.63045 
               58.2 
               1.242 
               0.546 
             
             
               G15 
               1.51633 
               1.52621 
               1.51386 
               1.52191 
               64.1 
               1.228 
               0.535 
             
             
                 
             
           
        
       
     
   
   
     
       
             
             
           
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Conditional 
               Embodiment 
             
           
        
         
             
               Expression 
               1 
               2 
               3 
               4 
               5 
               6 
             
             
                 
             
           
        
         
             
               (4) 
               9.14 
               7.58 
               5.41 
               4.72 
               4.18 
               4.18 
             
             
               (5) 
               0.022 
               — 
               — 
               0.038 
               — 
               0.096 
             
             
               (6) 
               — 
               −0.057 
               −0.087 
               — 
               −0.052 
               — 
             
             
                 
             
           
        
       
     
   
   This application claims priority from Japanese Patent Application No. 2004-132609 filed on Apr. 28, 2004, which is hereby incorporated by reference herein