# Patent

## Title
Image forming optical system and electronic image pickup apparatus equipped with same

## Abstract

A zoom optical system having a lens group I including two single lenses or one lens component, an aperture stop, and a lens group A disposed between the lens group I and the aperture stop, including a lens component made up of a positive lens LA and a negative lens LB that are cemented together, and having a negative refracting power as a whole. The distance between the lens group I and the lens group A on the optical axis changes for zooming, and the lens component has an aspheric cemented surface. When the shape of the aspheric surface is expressed by a certain equation, the shape of the air-contact surface of the positive lens LA and its aspheric components etc. satisfy conditional expressions (3a) and (3b).

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of PCT International Application No. PCT/JP 2009/055756 filed on Mar. 24, 2009, which designates the United States. A claim of priority and the benefit of the filing date under 35 U.S.C. §120 is hereby made to PCT International Application No. PCT/JP2009/055756 filed on Mar. 24, 2009, which in turn claims priority under 35 U.S.C. §119 to Japanese Application No. 2008-187617 filed on Jul. 18, 2008, the entire contents of each of which are expressly incorporated herein in its entirety by reference thereto.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an image forming optical system (zoom optical system) that has a high zoom ratio and good image forming performance while being slim and is particularly suitable for use as an electronic image pickup optical system, and to an electronic image pickup apparatus equipped with such an image forming optical system.
2. Description of the Related Art
Digital cameras have reached practical levels in terms of large number of pixels (high image quality), compactness, and slimness and replaced 35 mm film cameras from the view points of functions and market. As one aspect of further evolution, a further increase in the number of pixels is strongly desired to be achieved along with an increase in the zoom ratio and an increase in the angle of view while keeping the smallness and slimness as they are.
Zoom optical systems that have been used for their advantage in achieving high zoom ratios include, for example, an optical system disclosed in Patent Document 1. Patent Document 1 discloses what is called a positive-front zoom optical system including, in order from its object side, a first lens group having a positive refracting power, a second lens group having a negative refracting power, a third lens group having a positive refracting power, a fourth lens group having a negative refracting power, and a fifth lens group having a positive refracting power.
This optical system has high image forming performance while having a zoom ratio of 5 to 10 and an F-number at the wide angle end of 2.4. However, the thickness of each lens group along the optical axis direction is large. In consequence, it is difficult to make the camera body thin even if a collapsible lens barrel is used. The collapsible lens barrel refers to a lens barrel of a type in which the lens barrel unit is housed in the camera body along the thickness (or depth) direction.
Patent Document 2 discloses an optical system that is designed to be thin with thinned lens elements and a reduced number of lens components while achieving excellent correction of chromatic aberration. To achieve such an optical system, Patent Document 2 teaches to use a transparent medium having effective dispersion characteristics or partial dispersion characteristics that conventional glasses do not have. However, the shape and arrangement of the lens made of the aforementioned transparent medium is not necessarily appropriate, and it cannot be said that a sufficient reduction of the thickness of the optical system can be achieved.

    Patent Document 1: Japanese Patent Application Laid-Open No. 2003-255228
    Patent Document 2: Japanese Patent Application Laid-Open No. 2006-145823


DISCLOSURE OF THE INVENTION
Problems to be Solved by the Invention
The present invention has been made in view of the above-described problems of prior arts, and its object is to provide an image forming optical system that can achieve good correction of chromatic aberration, which is seriously needed particularly when the zoom ratio is high, while achieving slimness and a high zoom ratio and to provide an electronic image pickup apparatus equipped with such an image forming optical system.
Means for Solving the Problems
An image forming optical system according to the present invention that is intended to solve the above problems comprises a lens group I located closest to its object side, an aperture stop, a lens group A disposed between the lens group I and the aperture stop and having a negative refracting power as a whole, wherein the lens group A includes a cemented lens component made up of a positive lens LA and a negative lens LB that are cemented together, the distance between the lens group I and the lens group A on the optical axis changes for zooming, the cemented lens component has an aspheric cemented surface, and when the shape of the aspheric surface is expressed by the following equation (1) with a coordinate axis z taken along the optical axis and a coordinate axis h taken along a direction perpendicular to the optical axis:

z=h2/R[1+{1−(1+k)h2/R2}1/2]+A4h4+A6h6+A8h8+A10h10  (1),

where R is the radius of curvature of a spherical component on the optical axis, k is a conic constant, A4, A6, A8, A10, . . . are aspheric coefficients, and a deviation is expressed by the following equation (2):

Δz=z−h2/R[1+{1−h2/R2}1/2]  (2),

the following conditional expression (3a) or (3b) is satisfied:

when Rc≧0,

ΔzC(h)≦(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3a),

when Rc≦0,

ΔzC(h)≧(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3b),

where zA expresses the shape of the air-contact surface of the positive lens LA according to equation (1), zB expresses the shape of the air-contact surface of the negative lens LB according to equation (1), zC expresses the shape of the cemented surface according to equation (1), ΔzA is the deviation of the air-contact surface of the positive lens LA according to equation (2), ΔzB is the deviation of the air-contact surface of the negative lens LB according to equation (2), ΔzC is the deviation of the cemented surface according to equation (2), Rc is the paraxial radius of curvature of the cemented surface, and a is a value expressed by the following equation (4):

a=(y10)2·log10γ/fw  (4),

where y10 is the largest image height, fw is the focal length of the entire image forming optical system at the wide angle end, and γ is the zoom ratio (i.e. {the focal length of the entire system at the telephoto end}/{the focal length of the entire system at the wide angle end}) of the image forming optical system, where z(0)=0 holds for all the surfaces because the point of origin is set at the vertex of each surface.

An electronic image pickup apparatus according to the present invention comprises the above-described image forming optical system, an electronic image pickup element, and an image processing unit that processes image data obtained by picking up an image formed through the image forming optical system by the electronic image pickup element and outputs image data representing an image having a changed shape, wherein the image forming optical system is a zoom lens, and the zoom lens satisfies the following conditional expression (17) when the zoom lens is focused on an object point at infinity:

0.70<y07/(fW·tan ω07w)<0.97  (17)

where y07 is expressed by equation y07=0.7y10, y10 being a distance from the center of an effective image pickup area (i.e. an area in which images can be picked up) of the electronic image pickup element to a point farthest from the center within the effective image pickup area (or a largest image height), ω07w is the angle of the direction toward an object point corresponding to an image point formed at a position at distance y07 from the center of the image pickup surface at the wide angle end with respect to the optical axis, and fw is the focal length of the entire image forming optical system at the wide angle end.

Advantageous Effect of the Invention
The present invention can provide an image forming optical system that can achieve good correction of chromatic aberration, which is seriously needed particularly when the zoom ratio is high, while achieving slimness and a high zoom ratio and an electronic image pickup apparatus equipped with such an image forming optical system.



BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A, 1B, and 1C are cross sectional views taken along the optical axis showing the optical configuration of a zoom lens according to embodiment 1 of the present invention in the state in which the zoom lens is focused on an object point at infinity, respectively at the wide angle end, at an intermediate focal length, and at the telephoto end;
FIGS. 2A, 2B, and 2C are diagrams showing spherical aberration, astigmatism, distortion, and chromatic aberration of magnification of the zoom lens according to embodiment 1 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 2A is for the wide angle end, FIG. 2B is for the intermediate focal length, and FIG. 2C is for the telephoto end;
FIGS. 3A, 3B, and 3C are cross sectional views taken along the optical axis showing the optical configuration of a zoom lens according to embodiment 2 of the present invention in the state in which the zoom lens is focused on an object point at infinity, respectively at the wide angle end, at an intermediate focal length, and at the telephoto end;
FIGS. 4A, 4B, and 4C are diagrams showing spherical aberration, astigmatism, distortion, and chromatic aberration of magnification of the zoom lens according to embodiment 2 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 4A is for the wide angle end, FIG. 4B is for the intermediate focal length, and FIG. 4C is for the telephoto end;
FIGS. 5A, 5B, and 5C are cross sectional views taken along the optical axis showing the optical configuration of a zoom lens according to embodiment 3 of the present invention in the state in which the zoom lens is focused on an object point at infinity, respectively at the wide angle end, at an intermediate focal length, and at the telephoto end;
FIGS. 6A, 6B, and 6C are diagrams showing spherical aberration, astigmatism, distortion, and chromatic aberration of magnification of the zoom lens according to embodiment 3 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 6A is for the wide angle end, FIG. 6B is for the intermediate focal length, and FIG. 6C is for the telephoto end;
FIGS. 7A, 7B, and 7C are cross sectional views taken along the optical axis showing the optical configuration of a zoom lens according to embodiment 4 of the present invention in the state in which the zoom lens is focused on an object point at infinity, respectively at the wide angle end, at an intermediate focal length, and at the telephoto end;
FIGS. 8A, 8B, and 8C are diagrams showing spherical aberration, astigmatism, distortion, and chromatic aberration of magnification of the zoom lens according to embodiment 4 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 8A is for the wide angle end, FIG. 8B is for the intermediate focal length, and FIG. 8C is for the telephoto end;
FIG. 9 is a front perspective view showing an outer appearance of a digital camera 40 equipped with a zoom optical system according to the present invention;
FIG. 10 is a rear perspective view of the digital camera 40;
FIG. 11 is a cross sectional view showing the optical construction of the digital camera 40;
FIG. 12 is a front perspective view showing a personal computer 300 as an example of an information processing apparatus in which a zoom optical system according to the present invention is provided as an objective optical system, in a state in which the cover is open;
FIG. 13 is a cross sectional view of a taking optical system 303 of the personal computer 300;
FIG. 14 is a side view of the personal computer 300; and
FIGS. 15A, 15B, and 15C show a cellular phone 400 as an example of an information processing apparatus in which a zoom optical system according to the present invention is provided as a taking optical system, where FIG. 15A is a front view of the cellular phone 400, FIG. 15B is a side view of the cellular phone 400, and FIG. 15C is a cross sectional view of the taking optical system 405.













G1:
first lens group


G2:
second lens group


G3:
third lens group


G4:
fourth lens group


G5: 
fifth lens group


L1-L10:
lens


LPF:
low pass filter


CG:
cover glass


I:
image pickup surface


E:
viewer's eye


 40:
digital camera


 41:
taking optical system


 42:
taking optical path


 43: 
finder optical system


 44:
optical path for finder


 45:
shutter


 46: 
flash


 47:
liquid crystal display monitor


 48:
zoom lens


 49:
CCD


 50:
image pickup surface


 51:
processing unit


 53:
objective optical system for finder


 55:
Porro prism


 57: 
field frame


 59:
eyepiece optical system


 66:
focusing lens


 67:
image plane


100:
objective optical system


102:
cover glass


162:
electronic image pickup element chip


166:
terminal


300:
personal computer


301:
keyboard


302:
monitor


303:
taking optical system


304:
taking optical path


305:
image


400:
cellular phone


401:
microphone portion


402:
speaker portion


403:
input dial


404:
monitor


405:
taking optical system


406:
antenna


407:
taking optical path












DETAILED DESCRIPTION OF THE INVENTION
Prior to the description of embodiments, operations and effects of an image forming optical system according to one mode will be described.
In order to make an optical system thin, a reduction of the total optical length is required. If a reduction in the total optical length and a high zoom ratio are both to be achieved, high order components of chromatic spherical aberration and chromatic aberration of magnification with respect to the image height tend to be large. In conventional optical systems, correction of these aberrations has been difficult. Even if spherical aberration is well corrected at a reference wavelength, the presence of chromatic spherical aberration will lead to undercorrection or overcorrection at other wavelengths.
In view of this, the image forming optical system according to this mode comprises a lens group I disposed closest to the object side, an aperture stop, and a lens group A disposed between the lens group I and the aperture stop and having a negative refracting power as a whole, wherein the lens group A includes a cemented lens component in which a positive lens LA and a negative lens LB are cemented together, the distance between the lens group I and the lens group A on the optical axis changes for zooming, and the cemented lens component has an aspheric cemented surface. Here, a positive lens refers to a lens having a positive paraxial focal length, and a negative lens refers to a lens having a negative paraxial focal length.
In the image forming optical system according to this mode, the use of an aspheric surface as the cemented surface of the cemented lens component enables excellent correction of chromatic spherical aberration and chromatic aberration of magnification. The ray height of rays passing through the optical system becomes largest in the lens group A, in particular at the wide angle end. Therefore, the use of the cemented lens component in the lens group A can make it easy to correct high order components of chromatic aberration of magnification with respect to the image height at the wide angle end.
However, it is difficult to achieve satisfactory correction of chromatic spherical aberration and chromatic aberration of magnification only by designing a cemented surface simply as an aspheric surface. In other words, what is important in order to achieve satisfactory correction of chromatic spherical aberration and chromatic aberration of magnification is the shape of the aspheric surface. Referring to high order components of chromatic aberration with respect to the image height at the wide angle end, if there are such high order components, the high order components at a short wavelength (e.g. the g-line) have values on the negative side of those at a reference wavelength (e.g. the d-line) at a positive intermediate image height and have values on the positive side of those at the reference wavelength at the positive largest image height. Therefore, in order to correct such high order components, a cemented surface providing an achromatic effect should be designed to have a surface curvature in such a direction that decreases the achromatic effect at positions corresponding to principal rays of higher image heights.
Specifically, the shape of the aspheric surface is expressed by the following equation (1) with a coordinate axis z taken along the optical axis and a coordinate axis h taken along a direction perpendicular to the optical axis:

z=h2/R[1+{1−(1+k)h2/R2}1/2]+A4h4+A6h6+A8h8+A10h10  (1),

where R is the radius of curvature of a spherical component on the optical axis, k is a conic constant, A4, A6, A8, A10, . . . are aspheric coefficients, and the deviation is expressed by the following equation (2):

Δz=z−h2/R[1+{1−h2/R2}1/2]  (2),

then it is preferred that the following conditional expression (3a) or (3b) be satisfied:
when Rc≧0,

ΔzC(h)≦(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3a),

when Rc≦0,

ΔzC(h)≧(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3b),

where zA expresses the shape of the air-contact surface of the positive lens LA according to equation (1), zB expresses the shape of the air-contact surface of the negative lens LB according to equation (1), zC expresses the shape of the cemented surface according to equation (1), ΔzA is the deviation of the air-contact surface of the positive lens LA according to equation (2), ΔzB is the deviation of the air-contact surface of the negative lens LB according to equation (2), ΔzC is the deviation of the cemented surface according to equation (2), Rc is the paraxial radius of curvature of the cemented surface, and a is a value expressed by the following equation (4):

a=(y10)2·log10γ/fw  (4),

where y10 is the largest image height, fw is the focal length of the entire image forming optical system at the wide angle end, and y is the zoom ratio (i.e. {the focal length of the entire system at the telephoto end}/{the focal length of the entire system at the wide angle end}) of the image forming optical system. Since the point of origin is set at the vertex of each surface, z(0)=0 holds for all the surfaces.

If these conditions are not satisfied, the aspheric surface in the cemented surface cannot provide an advantageous effect. Conversely, if the above-described features and conditions are satisfied, it is possible to achieve correction of chromatic aberration, which can be generated greatly with size reduction and slimming, and image forming performance can be maintained or improved. If the following conditions concerning dispersion characteristics of the material are satisfied, chromatic aberration can be corrected more effectively.
In the image forming optical system according to this mode, the value of θgF and the value of νd of the positive lens LA fall within the following two ranges: the range in an orthogonal coordinate system having a horizontal axis representing ∝d and a vertical axis representing θgF that is bounded by the straight line given by the equation θgF=α×νd+β (where α=−0.00163) into which the lowest value in the range defined by the following conditional expression (5) is substituted and the straight line given by the equation θgF=α×νd+β(where αhg1=−0.00163) into which the highest value in the range defined by the following conditional expression (5) is substituted; and the range defined by the following conditional expression (6):

0.6700<β<0.9000  (5),

3<νd<27  (6),

where θgF is the relative partial dispersion (ng−nF)/(nF−nC) of the positive lens LA, and νd is the Abbe constant (nd−1)/(nF−nC) of the positive lens LA, where nd, nC, nF, and ng are refractive indices of the positive lens LA for the d-line, C-line, F-line, and g-line respectively.

If the lower limit of conditional expression (5) is exceeded, correction of axial chromatic aberration by secondary spectrum, specifically, correction of axial chromatic aberration with respect to the g-line while achromatism is achieved with respect to the F-line and the C-line will be insufficient. Therefore, it will be difficult to achieve sharpness in picked-up images. If the upper limit of conditional expression (5) is exceeded, overcorrection of axial chromatic aberration by secondary spectrum will result. In consequence, it will be difficult to achieve sharpness in picked-up images, as in the case where the lower limit is exceeded.
If either the lower limit or the upper limit of conditional expression (6) is exceeded, even achromatism with respect to F-line and the C-line will be difficult, and variations in chromatic aberration during zooming will be large. Therefore, it is difficult to achieve sharpness in picked up images.
It is more preferred that the following conditional expression (5′) be satisfied instead of the above conditional expression (5):

0.6850<β<0.8700  (5′).

It is still more preferred that the following conditional expression (5′′) be satisfied instead of the above conditional expression (5):

0.7000<β<0.8500  (5′′).

In the image forming optical system according to this mode, the value of θhg and the value of νd of the positive lens LA fall within the following two ranges: the range in an orthogonal coordinate system, which is different from the aforementioned orthogonal coordinate system, having a horizontal axis representing νd and a vertical axis representing θhg that is bounded by the straight line given by the equation θhg=αhg×νd+βhg (where αhg=−0.00225) into which the lowest value in the range defined by the following conditional expression (7) is substituted and the straight line given by the equation θhg=αhg×νd+βhg (where αhg=−0.00225) into which the highest value in the range defined by the following conditional expression (7) is substituted; and the range defined by the following conditional expression (6):

0.6350<βhg<0.9500  (7),

3<νd<27  (6),

where θhg is the relative partial dispersion (nh−ng)/(nF−nC) of the positive lens LA, and nh is the refractive index of the positive lens LA for the h-line.

If the lower limit of conditional expression (7) is exceeded, correction of axial chromatic aberration by secondary spectrum, specifically, correction of axial chromatic aberration with respect to the h-line while achromatism is achieved with respect to the F-line and the C-line will be insufficient. Therefore, purple color flare and color blur will tend to occur in picked-up images. If the upper limit of conditional expression (7) is exceeded, axial chromatic aberration by secondary spectrum is over corrected. Therefore, similar to the case in which the lower limit of conditional expression (7) is exceeded, purple color flare and color blur will tend to occur in picked-up images.
It is more preferred that the following conditional expression (7′) be satisfied instead of the above conditional expression (7):

0.6700<βhg<0.9200  (7′).

It is still more preferred that the following conditional expression (7′′) be satisfied instead of the above conditional expression (7):

0.7000<βhg<0.9000  (7′′).

It is preferred that the image forming optical system according to this mode satisfy the following conditional expression (8):

0.07≦θgF(LA)−θgF(LB)≦0.50  (8),

where θgF(LA) is the relative partial dispersion (ng−nF)/(nF−nC) of the positive lens LA, and θgF(LB) is the relative partial dispersion (ng−nF)/(nF−nC) of the negative lens LB.

If this is the case, since a positive lens (or lens LA) and a negative lens (or lens LB) are used in combination, good correction of chromatic aberration can be achieved. In particular, if the above-described conditions are satisfied with this combination, the effect of correcting axial chromatic aberration caused by secondary spectrum will be excellently achieved, resulting in an improvement in sharpness of images.
It is more preferred that the following conditional expression (8′) be satisfied instead of the above conditional expression (8):

0.10≦θgF(LA)−θgF(LB)≦0.40  (8′).

It is most preferred that the following conditional expression (8′′) be satisfied instead of the above conditional expression (8):

0.12≦θgF(LA)−θgF(LB)≦0.30  (8′′).

It is also preferred that the image forming optical system according to this mode satisfy the following conditional expression (9):

0.10≦θhg(LA)−θhg(LB)≦0.60  (9),

where θhg(LA) is the relative partial dispersion (nh−ng)/(nF−nC) of the positive lens LA, and θhg (LB) is the relative partial dispersion (nh−ng)/(nF−nC) of the negative lens LB.

If this is the case, since a positive lens (or lens LA) and a negative lens (or lens LB) are used in combination, good correction of chromatic aberration can be achieved. In particular, if the above-described conditions are satisfied with this combination, color flare and color blur can be reduced.
It is more preferred that the following conditional expression (9′) be satisfied instead of the above conditional expression (9):

0.14≦θhg(LA)−θhg(LB)≦0.55  (9′).

It is most preferred that the following conditional expression (9′′) be satisfied instead of the above conditional expression (9):

0.19≦θhg(LA)−θhg(LB)≦0.50  (9′′).

It is also preferred that the image forming optical system according to this mode satisfy the following conditional expression (10):

νd(LA)−νd(LB)≦−10  (10),

where νd(LA) is the Abbe constant (nd−1)/(nF−nC) of the positive lens LA, and νd(LB) is the Abbe constant (nd−1)/(nF−nC) of the negative lens LB.

If this is the case, since a positive lens (or lens LA) and a negative lens (or lens LB) are used in combination, good correction of chromatic aberration can be achieved. In particular, if the above-described conditions are satisfied with this combination, cancellation of axial chromatic aberration and chromatic aberration of magnification with respect to the C-line and the F-line is facilitated.
It is more preferred that the following conditional expression (10′) be satisfied instead of the above conditional expression (10):

νd(LA)−νd(LB)≦−14  (10′).

It is most preferred that the following conditional expression (10′′) be satisfied instead of the above conditional expression (10):

νd(LA)−νd(LB)≦−18  (10′′)

If the image forming optical system is a zoom lens, in order to achieve a high zoom ratio and slimness of the zoom lens at the same time, it is necessary that the lens group A have a high negative refracting power. Therefore, it is preferred that the optical material used for the positive lens LA have a somewhat low refractive index for the d-line. Specifically, it is preferred that the image forming optical system according to this mode satisfy the following conditional expression (11):

1.55≦nd(LA)≦1.90  (11),

where nd(LA) is the refractive index of the positive lens LA for the d-line.

Exceeding the upper limit of conditional expression (11) will tend to be disadvantageous in achieving slimming. Exceeding the lower limit of conditional expression (11) will make it difficult to achieve good correction of astigmatism.
It is more preferred that the following conditional expression (11′) be satisfied instead of the above conditional expression (11):

1.58≦nd(LA)≦1.80  (11′).

It is most preferred that the following conditional expression (11′′) be satisfied instead of the above conditional expression (11):

1.60≦nd(LA)≦1.75  (11′′)

It is also preferred that the image forming optical system according to this mode satisfy the following conditional expression (12):

1.52≦nd(LB)≦2.40  (12),

where nd(LB) is the refractive index of the negative lens LB for the d-line.

Exceeding the lower limit of conditional expression (12) will tend to be disadvantageous in achieving slimming. Exceeding the upper limit of conditional expression (12) will make it difficult to achieve good correction of astigmatism.
It is more preferred that the following conditional expression (12′) be satisfied instead of the above conditional expression (12):

1.58≦nd(LB)≦2.30  (12′).

It is most preferred that the following conditional expression (12′′) be satisfied instead of the above conditional expression (12):

1.67≦nd(LB)≦2.20  (12′′)

In cases where conditional expressions (11) and (12), conditional expressions (11′) and (12′), or conditional expressions (11′′) and (12′′) are satisfied, if the difference between the refractive index of the positive lens LA for the d-line and the refractive index of the negative lens LB for the d-line, or the difference in the refractive indices across the cemented surface is designed to be equal to or lower than 0.3, high order chromatic aberration components can be corrected without deterioration of aberrations with respect to a reference wavelength such as the d-line.
It is difficult to realize an optical material satisfying conditional expressions (5) and (6) using an optical glass. On the other hand, it can be realize easily by using an organic material such as a resin or an organic material in which inorganic fine particles are diffused to change optical characteristics. Therefore, it is preferred that an optical material satisfying conditional expressions (5) and (6) be a material containing an organic material such as a resin.
If the aforementioned organic material is used as the optical material for the positive lens LA, it is preferred that the positive lens LA be made as thin as possible. To this end, it is preferred that the material of the positive lens LA be an energy curable resin. In addition, it is preferred that the cemented lens component be produced by molding the positive lens LA directly on the negative lens LB.
Specifically, an energy curable resin is firstly discharged onto an optical surface of the negative lens LB. Then, the energy curable resin that is in contact with the optical surface of the negative lens LB is extended thereon. Thereafter, the energy curable resin is cured. The cemented lens component is produced by forming the lens LA in this way. In connection with this, surface processing (e.g. coating) may be applied on the lens LB beforehand. A material different from the material of which the lens LB is made is used for this surface processing. Examples of the energy curable resin include an ultraviolet curable resin and a composite material in which inorganic fine particles such as TiO2 fine particles are diffused in an ultraviolet curable resin.
With the above-described method of producing the cemented lens component, the cemented surface can easily be made aspheric. In the above-described case, an aspheric cemented surface is produced with materials (mediums) having different Abbe constants and relative partial dispersions. This aspheric surface is advantageous in correcting high order components of chromatic aberration of magnification with respect to the image height and high order chromatic aberration components such as chromatic coma and chromatic spherical aberration, unlike with the case of aspheric surfaces in normal air-contact surfaces that are exposed to the air.
In particular, in the configuration in which the lens group A having a negative refracting power is disposed closer to the object side than the aperture stop, it is preferred that the cemented surface in the lens group A be an aspheric surface. If this is the case, satisfying the above-described conditional expression (3a) or (3b) can provide a significant effect in correcting high order components of chromatic aberration of magnification with respect to the image height at wide angle focal lengths and chromatic coma. In the configuration in which there is another lens group disposed closer to the object side than the lens group A, it is particularly preferred that this another lens group have a positive refracting power. If this is the case, the above-described correction effect will be prominent. It is preferred that one or more of the conditions stated by conditional expressions (5) to (12) be satisfied.
It is preferred that the image forming optical system according to this mode satisfy the following conditional expression (13):

0.05≦|zA(h)−zC(h)|/tA≦0.95 (when h=2.5a),

where to is the thickness of the positive lens LA on the optical axis, and z(0)=0 holds in any case.

If the lower limit of conditional expression (13) is exceeded, correction of chromatic aberration will tend to be insufficient. If the upper limit of conditional expression (13) is exceeded, it is difficult to keep an adequate thickness in the peripheral region of the lens in making the positive lens thin.
It is more preferred that the following conditional expression (13′) be satisfied instead of the above conditional expression (13):

0.10≦|zA(h)−zC(h)|/tA≦0.90  (13′).

It is most preferred that the following conditional expression (13′′) be satisfied instead of the above conditional expression (13):

0.15≦|zA(h)−zC(h)|/tA≦0.85  (13′′)

It is also preferred that the image forming optical system according to this mode satisfy the following condition:

0.3≦tA/tB≦1.2  (14),

where tB is the thickness of the negative lens LB on the optical axis.

In the image forming optical system according to this mode, it is preferred that the cemented lens component made up of the positive lens LA and the negative lens LB that are cemented together be arranged in any one of the following manners (A1) to (A3). If this is the case, correction of chromatic aberration, a high zoom ratio, and correction of astigmatism can all be achieved at high levels.
(A1) Arranging the cemented lens component as the component located closest to the object side in the lens group A to provide a negative refracting power and arranging at least one positive lens on the image side of the cemented lens component.
(A2) Arranging a negative single lens as the component located closest to the object side in the lens group A and arranging the cemented lens component immediately on the image side of the negative single lens.
(A3) Arranging the cemented lens component as the component located closest to the image side in the lens group A.
It is preferred that the lens groups subsequent to the lens group A consist of one of the following sets (i) to (vii) of lens groups, in each of which the lens groups are arranged in order succeeding the lens group A.
(i) The image forming optical system consists of four lens groups in total including a lens group G3 having a positive refracting power and a lens group G4 having a positive refracting power.
(ii) The image forming optical system consists of four lens groups in total including a lens group G3 having a negative refracting power and a lens group G4 having a positive refracting power.
(iii) The image forming optical system consists of four lens groups in total including a lens group G3 having a positive refracting power and a lens group G4 having a negative refracting power.
(iv) The image forming optical system consists of five lens groups in total including a lens group G3 having a positive refracting power, a lens group G4 having a positive refracting power, and a lens group G5 having a negative refracting power.
(v) The image forming optical system consists of five lens groups in total including a lens group G3 having a positive refracting power, a lens group G4 having a negative refracting power, and a lens group G5 having a positive refracting power.
In any configuration, it is preferred that the lens group I be disposed closest to the object side and the lens group I have a reflecting optical element. The reflecting optical element is used to bend rays that contribute to imaging. This facilitates a reduction in the depth of the optical system.
In the following, correction of distortion by image processing will be described in detail. Suppose that an image of an object at infinity is formed by an optical system free from distortion. In this case, since the image has no distortion, the following equation holds:

f=y/tan ω  (15).

Here, y is the height of the image point from the optical axis, f is the focal length of the imaging optical system, ω is the angle of direction toward an object point corresponding to an image point formed at a position at distance y from the center of the image pickup surface with respect to the optical axis.
On the other hand, if an optical system is allowed to have barrel distortion only at focal length positions near the wide angle end, the following inequality holds:

f>y/tan ω  (16).

Namely, if barrel distortion is allowed to some extent as shown by the inequality (16), it means that angle of field w at the wide angle end if f and y are constant values, could be larger than a value defined by the contitional expression (15). The reason why the lens group constituting the aforementioned lens group A is normally composed of two or more lens components is to achieve both distortion and astigmatism. Since this is not necessary, this lens group may be composed only of one lens component, which can be made thin.
In view of the above, the electronic image pickup apparatus according to the present invention is adapted to process image data obtained through the electronic image pickup element by image processing. In this processing, the image data (or the shape of the image) is transformed in such a way as to correct barrel distortion. Thus, image data finally obtained will be image data having a shape substantially similar to the object. Therefore, an image of the object may be output to a CRT or a printer based on this image data.
The electronic image pickup apparatus according to this mode has an electronic image pickup element and an image processing unit that processes image data obtained by picking up an image formed through an image forming optical system, which is a zoom lens, by the electronic image pickup element and outputs image data representing an image having a transformed shape, and it is preferred that the zoom lens satisfy the following conditional expression (17) when it is focused on an object point substantially at infinity:

0.70<y07/(fW·tan ω07w)<0.97  (17)

where y07 is expressed by equation y07=0.7y10, y10 being the largest image height, and ω07w is the angle of the direction toward an object point corresponding to an image point formed at a position at distance y07 from the center of the image pickup surface at the wide angle end with respect to the optical axis. In the case of the electronic image pickup apparatus according to this mode, the largest image height is equal to the distance from the center of the effective image pickup area (i.e. the area in which images can be picked up) of the electronic image pickup element to the point farthest from the center within the effective image pickup area. Therefore, y10 also is the distance from the center of the effective image pickup area (i.e. an area in which images can be picked up) of the electronic image pickup element to the point farthest from the center within the effective image pickup area.

The above conditional expression (17) specifies the degree of barrel distortion at the wide angle end zoom position. If conditional expression (17) is satisfied, correction of astigmatism can be achieved without difficulty. An image having barrel distortion is photo-electrically converted by the image pickup element into image data having barrel distortion.
However, in the image processing unit, which is a signal processing system of the electronic image pickup apparatus, the image data having barrel distortion is subject to the electrical processing of changing the shape of the image. Thus, when the image data finally output from the image processing unit is reproduced on a display apparatus, distortion has been corrected, and an image substantially similar to the shape of the object is obtained.
If the term in conditional expression (17) has a value larger than the upper limit of conditional expression (17), in particular if it has a value close to 1, an image that is excellently corrected optically in terms of distortion can be obtained. Therefore, correction made by the image processing unit may be small. However, this is not advantageous for correction of astigmatism.
On the other hand, if the lower limit of conditional expression (17) is exceeded, the extension ratio in radial directions in the processing of correcting image distortion caused by distortion of the optical system by the image processing unit will become unduly high in the peripheral region of the angle of view. In consequence, deterioration of sharpness in the peripheral region of picked-up images will become conspicuous.
As described above, satisfying conditional expression (17) facilitates excellent correction of astigmatism, enabling slimming of the optical system and a large aperture ratio (i.e. an F-number smaller than 2.8 at the wide angle end).
It is more preferred that the following conditional expression (17′) be satisfied instead of the above conditional expression (17):

0.73<y07/(fW·tan ω07w)<0.96  (17′).

It is still more preferred that the following conditional expression (17′′) be satisfied instead of the above conditional expression (17):

0.76<y07/(fW·tan ω07w)<0.95  (17′′)

Now, a zoom lens according to embodiment 1 of the present invention will be described. FIGS. 1A, 1B, and 1C are cross sectional views taken along the optical axis showing the optical configuration of the zoom lens according to embodiment 1 of the present invention in the state in which the zoom lens is focused on an object point at infinity, where FIG. 1A is a cross sectional view of the zoom lens at the wide angle end, FIG. 1B is a cross sectional view of the zoom lens at an intermediate focal length position, and FIG. 1C is a cross sectional view of the zoom lens at the telephoto end.
FIGS. 2A, 2B, and 2C are diagrams showing spherical aberration (SA), astigmatism (AS), distortion (DT), and chromatic aberration of magnification (CC) of the zoom lens according to embodiment 1 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 2A is for the wide angle end, FIG. 2B is for the intermediate focal length position, and FIG. 2C is for the telephoto end. Sign “FIY” represents the image height. The signs in the aberration diagrams are commonly used also in the embodiments described in the following.
As shown in FIGS. 1A, 1B, and 1C, the zoom lens according to embodiment 1 includes, in order from its object side, a first lens group G1 having a positive refracting power, a second lens group G2 having a negative refracting power, an aperture stop S, a third lens group G3 having a positive refracting power, and a fourth lens group G4 having a positive refracting power. In the cross sectional views of the lenses according to this and all the embodiments described in the following, LPF denotes a low pass filter, CG denotes a cover glass, and I denotes the image pickup surface of an electronic image pickup element.
The first lens group G1 is composed of a cemented lens made up of a positive meniscus lens L1 having a convex surface directed toward the object side and a biconvex positive lens L2. The first lens group G1 has a positive refracting power as a whole.
The second lens group G2 is composed of a negative meniscus lens L3 having a convex surface directed toward the object side, and a cemented lens made up of a positive meniscus lens L4 having a convex surface directed toward the image side and a negative meniscus lens L5 having a convex surface directed toward the image side. The second lens group G2 has a negative refracting power as a whole. In this configuration, the positive meniscus lens L4 having a convex surface directed toward the image side constitutes the lens LA, and the negative meniscus lens L5 having a convex surface directed toward the image side constitutes the negative lens LB.
The third lens group G3 is composed of a biconvex positive lens L6, and a cemented lens made up of a positive meniscus lens L7 having a convex surface directed toward the object side and a negative meniscus lens L8 having a convex surface directed toward the object side. The third lens group G3 has a positive refracting power as a whole.
The fourth lens group G4 is composed of a biconvex positive lens L9. The fourth lens group G4 has a positive refracting power as a whole.
During zooming from the wide angle end to the telephoto end, the first lens group G1 is substantially fixed (slightly moves toward the image side) during zooming from the wide angle end to an intermediate focal length position and moves toward the object side during zooming from the intermediate focal length position to the telephoto end, the second lens group G2 moves toward the image side during zooming from the wide angle end to an intermediate focal length position and moves toward the object side during zooming from the intermediate focal length position to the telephoto end, the aperture stop S moves toward the object side, the third lens group G3 moves toward the object side, and the fourth lens group G4 moves toward the object side during zooming from the wide angle end to an intermediate focal length position and moves toward the image side during zooming from the intermediate focal length position to the telephoto end.
There are seven aspheric surfaces in total, which include the image side surface of the biconvex positive lens L2 in the first lens group G1, both surfaces of the positive meniscus lens L4 having a convex surface directed toward the image side in the second lens group G2, the image side surface of the negative meniscus lens L5 having a convex surface directed toward the image side in the second lens group G2, both surfaces of the biconvex positive lens L6 in the third lens group G3, and the object side surface of the biconvex positive lens L9 in the fourth lens group G4.
Next, a zoom lens according to embodiment 2 of the present invention will be described. FIGS. 3A, 3B, and 3C are cross sectional views taken along the optical axis showing the optical configuration of the zoom lens according to embodiment 2 of the present invention in the state in which the zoom lens is focused on an object point at infinity, where FIG. 3A is a cross sectional view of the zoom lens at the wide angle end, FIG. 3B is a cross sectional view of the zoom lens at an intermediate focal length position, and FIG. 3C is a cross sectional view of the zoom lens at the telephoto end.
FIGS. 4A, 4B, and 4C are diagrams showing spherical aberration (SA), astigmatism (AS), distortion (DT), and chromatic aberration of magnification (CC) of the zoom lens according to embodiment 2 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 4A is for the wide angle end, FIG. 4B is for the intermediate focal length position, and FIG. 4C is for the telephoto end.
As shown in FIGS. 3A, 3B, and 3C, the zoom lens according to embodiment 2 includes, in order from its object side, a first lens group G1 having a positive refracting power, a second lens group G2 having a negative refracting power, an aperture stop S, a third lens group G3 having a positive refracting power, and a fourth lens group G4 having a positive refracting power.
The first lens group G1 is composed of a cemented lens made up of a negative meniscus lens L1 having a convex surface directed toward the object side and a positive meniscus lens L2 having a convex surface directed toward the object side. The first lens group G1 has a positive refracting power as a whole.
The second lens group G2 is composed of a negative meniscus lens L3 having a convex surface directed toward the object side, a cemented lens made up of a positive meniscus lens L4 having a convex surface directed toward the image side and a biconcave negative lens L5, and a biconvex positive lens L6. The second lens group G2 has a negative refracting power as a whole. In this configuration, the positive meniscus lens L4 having a convex surface directed toward the image side constitutes the lens LA, and the biconcave negative lens L5 constitutes the negative lens LB.
The third lens group G3 is composed of a biconvex positive lens L7, and a cemented lens made up of a positive meniscus lens L8 having a convex surface directed toward the object side and a negative meniscus lens L9 having a convex surface directed toward the object side. The third lens group G3 has a positive refracting power as a whole.
The fourth lens group G4 is composed of a positive meniscus lens L10 having a convex surface directed toward the object side. The fourth lens group G4 has a positive refracting power as a whole.
During zooming from the wide angle end to the telephoto end, the first lens group G1 is moves toward the image side during zooming from the wide angle end to an intermediate focal length position and moves toward the object side during zooming from the intermediate focal length position to the telephoto end, the second lens group G2 moves toward the image side during zooming from the wide angle end to an intermediate focal length position and moves toward the object side during zooming from the intermediate focal length position to the telephoto end, the aperture stop S moves toward the object side, the third lens group G3 moves toward the object side, and the fourth lens group G4 moves toward the object side during zooming from the wide angle end to an intermediate focal length position and moves toward the image side during zooming from the intermediate focal length position to the telephoto end.
There are six aspheric surfaces in total, which include both surfaces of the negative meniscus lens L4 having a convex surface directed toward the image side in the second lens group G2, the image side surface of the biconcave negative lens L5 in the second lens group G2, both surfaces of the biconvex positive lens L7 in the third lens group G3, and the object side surface of the positive meniscus lens having a convex surface directed toward the object side in the fourth lens group G4.
Next, a zoom lens according to embodiment 3 of the present invention will be described. FIGS. 5A, 5B, and 5C are cross sectional views taken along the optical axis showing the optical configuration of the zoom lens according to embodiment 3 of the present invention in the state in which the zoom lens is focused on an object point at infinity, where FIG. 5A is a cross sectional view of the zoom lens at the wide angle end, FIG. 5B is a cross sectional view of the zoom lens at an intermediate focal length position, and FIG. 5C is a cross sectional view of the zoom lens at the telephoto end.
FIGS. 6A, 6B, and 6C are diagrams showing spherical aberration (SA), astigmatism (AS), distortion (DT), and chromatic aberration of magnification (CC) of the zoom lens according to embodiment 3 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 6A is for the wide angle end, FIG. 6B is for the intermediate focal length position, and FIG. 6C is for the telephoto end.
As shown in FIGS. 5A, 5B, and 5C, the zoom lens according to embodiment 3 includes, in order from its object side, a first lens group G1 having a positive refracting power, a second lens group G2 having a negative refracting power, an aperture stop S, a third lens group G3 having a positive refracting power, and a fourth lens group G4 having a positive refracting power.
The first lens group G1 is composed of a biconvex positive lens L1. The first lens group G1 has a positive refracting power as a whole.
The second lens group G2 is composed of a biconcave negative lens L2, and a cemented lens made up of a positive meniscus lens L3 having a convex surface directed toward the image side and a biconcave negative lens L4. The second lens group G2 has a negative refracting power as a whole. In this configuration, the positive meniscus lens L3 having a convex surface directed toward the image side constitutes the lens LA, and the biconcave negative lens L4 constitutes the negative lens LB.
The third lens group G3 is composed of a biconvex positive lens L and a negative meniscus lens L6 having a convex surface directed toward the object side. The third lens group G3 has a positive refracting power as a whole.
The fourth lens group G4 is composed of a biconvex positive lens L7. The fourth lens group G4 has a positive refracting power as a whole.
During zooming from the wide angle end to the telephoto end, the first lens group G1 moves toward the object side, the second lens group G2 is substantially fixed (slightly moves toward the image side), the aperture stop S moves toward the object side, the third lens group G3 moves toward the object side, and the fourth lens group moves toward the image side during zooming from the wide angle end to an intermediate focal length position and moves toward the object side during zooming from the intermediate focal length position to the telephoto end.
There are ten aspheric surfaces in total, which include both surfaces of the biconvex positive lens L1 in the first lens group, both surfaces of the biconcave negative lens L2 in the second lens group G2, both surfaces of the positive meniscus lens L3 having a convex surface directed toward the image side in the second lens group G2, the image side surface of the biconcave negative lens L4 in the second lens group G2, both surfaces of the biconvex positive lens L5 in the third lens group G3, and the object side surface of the biconvex positive lens L7 in the fourth lens group G4.
Next, a zoom lens according to embodiment 4 of the present invention will be described. FIGS. 7A, 7B, and 7C are cross sectional views taken along the optical axis showing the optical configuration of the zoom lens according to embodiment 4 of the present invention in the state in which the zoom lens is focused on an object point at infinity, where FIG. 7A is a cross sectional view of the zoom lens at the wide angle end, FIG. 7B is a cross sectional view of the zoom lens at an intermediate focal length position, and FIG. 7C is a cross sectional view of the zoom lens at the telephoto end.
FIGS. 8A, 8B, and 8C are diagrams showing spherical aberration (SA), astigmatism (AS), distortion (DT), and chromatic aberration of magnification (CC) of the zoom lens according to embodiment 4 in the state in which the zoom lens is focused on an object point at infinity, where FIG. 8A is for the wide angle end, FIG. 8B is for the intermediate focal length position, and FIG. 8C is for the telephoto end.
As shown in FIGS. 7A, 7B, and 7C, the zoom lens according to embodiment 4 includes, in order from its object side, a first lens group G1 having a positive refracting power, a second lens group G2 having a negative refracting power, an aperture stop S, a third lens group G3 having a positive refracting power, and a fourth lens group G4 having a positive refracting power.
The first lens group G1 is composed of a biconvex positive lens L1. The first lens group G1 has a positive refracting power as a whole.
The second lens group G2 is composed of a biconcave negative lens L2, and a cemented lens made up of a biconcave negative lens L3 and a positive meniscus lens L4 having a convex surface directed toward the object side. The second lens group G2 has a negative refracting power as a whole. In this configuration, the positive meniscus lens L4 having a convex surface directed toward the object side constitutes the lens LA, and the biconcave negative lens L3 constitutes the negative lens LB.
The third lens group G3 is composed of a biconvex positive lens L5 and a negative meniscus lens L6 having a convex surface directed toward the object side. The third lens group G3 has a positive refracting power as a whole.
The fourth lens group G4 is composed of a positive meniscus lens L7 having a convex surface directed toward the image side. The fourth lens group G4 has a positive refracting power as a whole.
During zooming from the wide angle end to the telephoto end, the first lens group G1 moves toward the object side, the second lens group G2 moves toward the object side, the aperture stop S moves toward the object side, the third lens group G3 moves toward the object side, and the fourth lens group G4 moves toward the image side during zooming from the wide angle end to an intermediate focal length position and is nearly fixed during zooming from the intermediate focal length position to the telephoto end.
There are ten aspheric surfaces in total, which include both surfaces of the biconvex positive lens L1 in the first lens group, both surfaces of the biconcave negative lens L2 in the second lens group G2, both surfaces of the biconcave negative lens L3 in the second lens group G2, the image side surface of the positive meniscus lens L4 having a convex surface directed toward the object side in the second lens group G2, both surfaces of the biconvex positive lens L5 in the third lens group G3, and the object side surface of the negative meniscus lens L7 having a convex surface directed toward the image side in the fourth lens group G4.
Numerical data of each embodiment described above is shown below. In numerical data in each embodiment, each of r1, r2, . . . denotes radius of curvature of each lens surface, each of d1, d2, . . . denotes a distance between two lenses, each of nd1, nd2, denotes a refractive index of each lens for a d-line, and each of νd1, νd2, denotes an Abbe constant for each lens, FNO denotes an F number, f denotes a focal length of the entire zoom lens system, D0 denotes a distance from an object up to the first surafe. Further, * denotes an aspheric data, Stop denotes a stop.
When z is let to be an optical axis with a direction of traveling of light as a positive (direction), and y is let to be in a direction orthogonal to the optical axis, a shape of the aspheric surface is described by the following expression.

z=(y2/r)/[1+{1−(K+1)(y/r)2}1/2]+A4y4+A6y6+A8y8+A10h10+A12y12 

where, r denotes a paraxial radius of curvature, K denotes a conical coefficient, A4, A6, A8, A10, and A12 denote aspherical surface coefficients of a fourth order, a sixth order, an eight order, a tenth order, and a twelfth order respectively. Moreover, in the aspherical surface coefficients, ‘E−n’ (where, n is an integral number) indicates ‘10−n’.
Example 1










Unit mm







Surface data













Surface no.
r
d
nd
νd






Object plane
∞
∞





 1
26.4450
0.8000
1.84666
23.78



 2
13.8156
2.7000
1.73077
40.51



 3*
−192.7244
Variable





 4
43.7694
0.7000
1.69680
55.53



 5
10.8906
2.2000





 6*
−15.3637
1.0000
1.63494
23.22



 7*
−6.7944
0.9000
1.74320
49.34



 8*
−208.0010
Variable





 9(Stop)
∞
Variable





10*
24.1688
1.8000
1.74250
49.20



11*
−19.2188
0.1500





12
5.4497
2.7000
1.69680
55.53



13
13.4248
0.6000
1.84666
23.78



14
4.2048
Variable





15*
10.9456
2.0000
1.58313
59.46



16
−35.4704
Variable





17
∞
0.7580
1.54771
62.84



18
∞
0.4787





19
∞
0.3989
1.51633
64.14



20
∞
1.3603





Image plane
∞










Aspherical surface data












3rd surface



K = −0.1059,



A2 = 0.0000E+00, A4 = 3.4600E−07, A6 = 4.6678E−09, A8 = 0.0000E+00,



A10 = 0.0000E+00



6th surface



K = −0.6957,



A2 = 0.0000E+00, A4 = −1.2458E−04, A6 = 3.0542E−06, A8 = 0.0000E+00,



A10 = 0.0000E+00



7th surface



K = −0.7528,



A2 = 0.0000E+00, A4 = −4.3041E−04, A6 = 2.1935E−05, A8 = 0.0000E+00,



A10 = 0.0000E+00



8th surface



K = −0.9690,



A2 = 0.0000E+00, A4 = −1.3472E−04, A6 = 7.2254E−06, A8 = 0.0000E+00,



A10 = 0.0000E+00



10th surface



K = 3.7659,



A2 = 0.0000E+00, A4 = −3.8282E−04, A6 = 1.5704E−05, A8 = 0.0000E+00,



A10 = 0.0000E+00



11th surface



K = −0.9658,



A2 = 0.0000E+00, A4 = −2.2045E−04, A6 = 1.4126E−05, A8 =



0.0000E+00, A10 = 0.0000E+00



15th surface



K = −0.9236,



A2 = 0.0000E+00, A4 = 3.1124E−05, A6 = 2.9451E−07, A8 = 0.0000E+00,



A10 = 0.0000E+00










Numerical data


Zoom ratio













Wide angle
Inter mediate
Telephoto






Focal length
7.00943
15.64607
35.00249



Fno.
2.8400
2.9504
3.8784



Angle of field
30.3°
12.9°
5.8°



Image height
3.6
3.6
3.6



Lens total length
46.9634
45.9916
55.4100



BF
1.36028
1.35268
1.35989



d3
0.65000
8.83784
14.65673



d8
17.19034
6.04002
1.50167



d9
0.80000
0.79787
0.79787



d14
7.65597
6.42400
15.77566



d16
2.12115
5.35351
4.13256










Zoom lens group data









Group
Initial
Focal length





1
1
36.57282


2
4
−9.33696


3
10
12.64978


4
15
14.57546











Table of index
List of index per wavelength of medium


of glass material
used in the present embodiment















GLA
587.56
656.27
486.13
435.84
404.66


L6
1.742499
1.737967
1.753057
1.761415
1.768384


L10
1.547710
1.545046
1.553762
1.558427
1.562262


L4
1.634940
1.627290
1.654640
1.674080
1.693923


L2
1.730770
1.725416
1.743456
1.753787
1.762674


L9
1.583130
1.580140
1.589950
1.595245
1.599635


L11
1.516330
1.513855
1.521905
1.526213
1.529768


L3, L7
1.696797
1.692974
1.705522
1.712339
1.718005


L5
1.743198
1.738653
1.753716
1.762046
1.769040


L1, L8
1.846660
1.836488
1.872096
1.894186
1.914294










Aspherical amount of each surface





6th surface












Y
ASP
SPH
ΔzA(h)






3.228
−0.35033
−0.34294
−0.00739










8th surface












Y
ASP
SPH
ΔzB(h)






3.228
−0.03150
−0.02505
−0.00645










7th surface












Y
ASP
SPH
ΔzC(h)






3.228
−0.79972
−0.81577
 0.01605









Example 2










Unit mm







Surface data













Surface no.
r
d
nd
νd






Object plane
∞
∞





 1
26.8390
0.6000
1.84666
23.78



 2
16.3344
3.8000
1.72000
43.69



 3
251.2140
Variable





 4
79.0802
0.8000
1.88300
38.50



 5
10.4013
3.9000





 6*
−15.6402
0.5000
1.63494
23.22



 7*
−11.2194
0.8000
1.83481
42.71



 8*
2.084E+04
0.2000





 9
29.3362
2.0000
1.80810
22.76



10
−42.8587
Variable





11(Stop)
∞
0.4000





12*
12.5777
1.8000
1.69350
51.80



13*
−87.4358
0.2000





14
5.3985
2.4000
1.49700
81.54



15
9.5055
0.8000
1.84666
23.78



16
4.5362
Variable





17*
14.1406
1.6000
1.69350
53.18



18
39.9405
Variable





19
∞
0.9010
1.54771
62.84



20
∞
0.5300





21
∞
0.5300
1.51633
64.14



22
∞
1.3601





Image plane
∞










Aspherical surface data












6th surface



K = −0.0535,



A2 = 0.0000E+00, A4 = 3.4485E−05, A6 = −3.6491E−08, A8 = 0.0000E+00,



A10 = 0.0000E+00



7th surface



K = −0.1837,



A2 = 0.0000E+00, A4 = −6.5454E−06, A6 = 4.1099E−06, A8 = 0.0000E+00,



A10 = 0.0000E+00



8th surface



K = 8.5769,



A2 = 0.0000E+00, A4 = 6.0909E−05, A6 = 5.5779E−07, A8 = 0.0000E+00,



A10 = 0.0000E+00



12th surface



K = −0.6890,



A2 = 0.0000E+00, A4 = 1.0899E−04, A6 = 1.6473E−05, A8 = 3.5467E−07,



A10 = 0.0000E+00



13th surface



K = 0,



A2 = 0.0000E+00, A4 = 1.9328E−04, A6 = 1.9010E−05, A8 = 4.8815E−07,



A10 = 0.0000E+00



17th surface



K = 0,



A2 = 0.0000E+00, A4 = −1.2785E−05, A6 = 6.0991E−07, A8 = −2.5404E−09,



A10 = 0.0000E+00










Numerical data


Zoom ratio













Wide angle
Inter mediate
Telephoto






Focal length
6.99897
19.80013
56.00002



Fno.
3.1000
3.7979
5.0423



Angle of field
31.7°
10.9°
3.8°



Image height
3.8
3.8
3.8



Lens total length
67.2592
58.2183
71.9432



BF
1.36011
1.36035
1.36027



d3
0.59976
10.08933
22.11095



d10
31.33058
8.25005
1.59000



d16
7.69341
5.84941
21.84350



d18
4.51433
10.90817
3.27745










Zoom lens group data









Group
Initial
Focal length





1
1
47.20195


2
4
−12.34780


3
12
17.08297


4
17
30.78406











Table of index
List of index per wavelength of medium


of glass material
used in the present embodiment















GLA
587.56
656.27
486.13
435.84
404.66


L7
1.693499
1.689469
1.702855
1.710240
1.716386


L3
1.882998
1.876228
1.899160
1.912305
1.923515


L11
1.547710
1.545046
1.553762
1.558427
1.562261


L4
1.634940
1.627290
1.654640
1.673656
1.692736


L10
1.693500
1.689551
1.702591
1.709739
1.715701


L12
1.516330
1.513855
1.521905
1.526213
1.529768


L8
1.496999
1.495136
1.501231
1.504506
1.507205


L5
1.834807
1.828975
1.848520
1.859547
1.868911


L2
1.720000
1.715105
1.731585
1.740976
1.749012


L6
1.808095
1.798009
1.833513
1.855902
1.876580


L1, L9
1.846660
1.836488
1.872096
1.894186
1.914294










Aspherical amount of each surface





6th surface












Y
ASP
SPH
ΔzA(h)






4.658
−0.69297
−0.70973
0.01676










8th surface












Y
ASP
SPH
ΔzB(h)






4.658
 0.03489
 0.00052
0.03437










7th surface












Y
ASP
SPH
ΔzC(h)






4.658
−0.96468
−1.01264
0.04796









Example 3










Unit mm







Surface data













Surface no.
r
d
nd
νd






Object plane
∞
∞





 1*
16.4189
2.2423
1.49700
81.54



 2*
−49.9548
Variable





 3*
−40.0473
0.7000
1.52542
50.50



 4*
7.1803
1.3239





 5*
−129.9255
0.5752
1.63494
23.22



 6*
−19.3026
0.8000
1.58313
59.38



 7*
16.3014
Variable





 8(Stop)
∞
−0.1000 





 9*
4.4912
1.9000
1.74320
49.34



10*
−40.0312
0.1000





11
6.2476
1.1000
1.92286
20.10



12
2.9815
Variable





13*
37.0133
2.4341
1.52542
55.78



14
−9.2906
Variable





15
∞
1.0000
1.51633
64.14



16
∞
1.2014





Image plane
∞










Aspherical surface data












1st surface



K = −0.9358,



A2 = 0.0000E+00, A4 = 1.7221E−05, A6 = −8.4549E−07, A8 = 2.0978E−08,



A10 = −3.8409E−11



2nd surface



K = −1.4315,



A2 = 0.0000E+00, A4 = 1.7746E−06, A6 = 4.2666E−08, A8 = 1.7609E−08,



A10 = −1.8044E−10



3rd surface



K = 8.5291,



A2 = 0.0000E+00, A4 = −9.1235E−04, A6 = 3.3157E−05, A8 = −5.2667E−07,



A10 = 4.2126E−09



4th surface



K = −1.6973,



A2 = 0.0000E+00, A4 = 6.6240E−04, A6 = −4.9690E−06, A8 = −1.8842E−06,



A10 = 3.4072E−08



5th surface



K = 122.9470,



A2 = 0.0000E+00, A4 = 1.2621E−03, A6 = −6.1794E−05, A8 = 0.0000E+00,



A10 = 0.0000E+00



6th surface



K = 0,



A2 = 0.0000E+00, A4 = 6.0000E−04, A6 = −3.0000E−05, A8 = 0.0000E+00,



A10 = 0.0000E+00



7th surface



K = 0,



A2 = 0.0000E+00, A4 = 0.0000E+00, A6 = −2.0000E−05, A8 = 0.0000E+00,



A10 = 0.0000E+00



9th surface



K = −0.8591,



A2 = 0.0000E+00, A4 = 1.0435E−04, A6 = −1.1049E−07, A8 = −1.9982E−06,



A10 = −2.4152E−07



10th surface



K = 29.2890,



A2 = 0.0000E+00, A4 = 4.4251E−04, A6 = −4.6420E−05, A8 = −4.3674E−07,



A10 = 0.0000E+00



13th surface



K = −4.9538,



A2 = 0.0000E+00, A4 = −2.0035E−05, A6 = 4.9528E−06, A8 = −2.3417E−07,



A10 = 3.0514E−09










Numerical data


Zoom ratio













Wide angle
Inter mediate
Telephoto






Focal length
6.77084
12.45173
25.40909



Fno.
3.6000
4.5950
5.4487



Angle of field
32.8°
17.6°
8.9°



Image height
3.84
3.84
3.84



Lens total length
31.5188
34.7815
38.2644



BF
1.20139
1.20499
1.19426



d2
0.46811
3.55999
6.84730



d7
10.58492
6.65979
0.80013



d12
3.53462
8.16389
11.69102



d14
3.65428
3.11734
5.65619










Zoom lens group data









Group
Initial
Focal length





1
1
25.14596


2
3
−7.57674


3
9
9.61953


4
13
14.39503











Table of index
List of index per wavelength of medium


of glass material
used in the present embodiment















GLA
587.56
656.27
486.13
435.84
404.66


L2
1.525419
1.522301
1.532704
1.538508
1.543381


L6
1.922856
1.909932
1.955840
1.984877
2.011316


L3
1.634940
1.627290
1.654640
1.675524
1.697965


L4
1.583126
1.580139
1.589960
1.595296
1.599721


L8
1.516330
1.513855
1.521905
1.526213
1.529768


L1
1.496999
1.495136
1.501231
1.504506
1.507205


L5
1.743198
1.738653
1.753716
1.762046
1.769040


L7
1.525420
1.522680
1.532100
1.537050
1.540699










Aspherical amount of each surface





5th surface












Y
ASP
SPH
ΔzA(h)






3.128
0.02458
−0.03766
0.06224










7th surface












Y
ASP
SPH
ΔzB(h)






3.128
0.28419
 0.30292
−0.01873 










6th surface












Y
ASP
SPH
ΔzC(h)






3.128
−0.22579 
−0.25513
0.02934









Example 4










Unit mm







Surface data













Surface no.
r
d
nd
νd






Object plane
∞
∞





 1*
16.7505
2.3212
1.49700
81.54



 2*
−34.9627
Variable





 3*
−22.8401
0.7000
1.52542
55.78



 4*
6.4242
1.8740





 5*
−21.1421
0.8000
1.58313
59.38



 6*
17.8005
0.6046
1.63494
19.00



 7*
131.5083
Variable





 8(Stop)
∞
−0.1000 





 9*
4.3682
1.8843
1.74320
49.34



10*
−63.9755
0.1000





11
5.7772
1.1000
1.92286
18.90



12
2.9400
Variable





13*
−166.6984
2.3259
1.52542
45.00



14
−8.1475
Variable





15
∞
1.0000
1.51633
64.14



16
∞
1.0793





Image plane
∞










Aspherical surface data












1st surface



K = 0.2390,



A2 = 0.0000E+00, A4 = −7.2413E−06, A6 = −4.0959E−06, A8 = 6.1260E−11,



A10 = −2.3019E−09



2nd surface



K = 4.6801,



A2 = 0.0000E+00, A4 = 8.0872E−05, A6 = −3.3793E−06, A8 = −1.8316E−07,



A10 = 2.9694E−09



3rd surface



K = 1.9022,



A2 = 0.0000E+00, A4 = −6.0586E−04, A6 = 6.1661E−05, A8 = −2.1406E−06,



A10 = 2.6928E−08



4th surface



K = −0.0906,



A2 = 0.0000E+00, A4 = −6.5916E−04, A6 = 5.0762E−05, A8 = 2.5205E−06,



A10 = −1.1728E−07



5th surface



K = 0,



A2 = 0.0000E+00, A4 = 3.2402E−04, A6 = 8.4797E−06, A8 = 0.0000E+00,



A10 = 0.0000E+00



6th surface



K = 0,



A2 = 0.0000E+00, A4 = −6.0000E−04, A6 = 0.0000E+00, A8 = 0.0000E+00,



A10 = 0.0000E+00



7th surface



K = 7.1865,



A2 = 0.0000E+00, A4 = −1.6000E−04, A6 = 0.0000E+00, A8 = 0.0000E+00,



A10 = 0.0000E+00



9th surface



K = −3.0231,



A2 = 0.0000E+00, A4 = 3.6716E−03, A6 = −1.3025E−04, A8 = 1.2545E−05,



A10 = −3.0304E−07



10th surface



K = −1.4301,



A2 = 0.0000E+00, A4 = 8.5325E−04, A6 = 2.7829E−05, A8 = 4.3372E−06,



A10 = 0.0000E+00



13th surface



K = 9.6449,



A2 = 0.0000E+00, A4 = −3.3648E−04, A6 = 2.1031E−05, A8 = −8.7568E−07,



A10 = 1.2082E−08










Numerical data


Zoom ratio













Wide angle
Inter mediate
Telephoto






Focal length
6.45208
12.51638
25.49743



Fno.
2.9708
4.1804
5.6000



Angle of field
34.1°
17.5°
8.8°



Image height
3.84
3.84
3.84



Lens total length
30.2791
33.2572
38.7555



BF
1.07930
1.13084
1.06664



d2
0.31924
2.25737
5.02792



d7
9.45827
5.36130
1.34833



d12
2.77791
9.11561
15.30831



d14
4.03440
2.78209
3.39431










Zoom lens group data









Group
Initial
Focal length





1
1
23.13109


2
3
−7.05803


3
9
8.95029


4
13
16.22159











Table of index
List of index per wavelength of medium


of glass material
used in the present embodiment















GLA
587.56
656.27
486.13
435.84
404.66


L7
1.525419
1.521949
1.533624
1.540248
1.545870


L4
1.634937
1.625875
1.659289
1.682219
1.704243


L3
1.583126
1.580139
1.589960
1.595296
1.599721


L8
1.516330
1.513855
1.521905
1.526213
1.529768


L1
1.496999
1.495136
1.501231
1.504506
1.507205


L5
1.743198
1.738653
1.753716
1.762046
1.769040


L6
1.922860
1.909158
1.957996
1.989713
2.019763


L2
1.525420
1.522680
1.532100
1.537050
1.540699










Aspherical amount of each surface





7th surface












Y
ASP
SPH
ΔzA(h)






3.410
0.02264
0.04422
−0.02158










5th surface












Y
ASP
SPH
ΔzB(h)






3.410
−0.21967 
−0.27681 
 0.05714










6th surface












Y
ASP
SPH
ΔzC(h)






3.410
0.24855
0.32968
−0.08113









Numerical data of the present example is shown below:















Example 1
Example 2
Example 3
Example 4



















fw
7.009
6.999
6.771
6.452


f2
−9.337
−12.348
−7.577
−7.058


γ
4.994
8.001
3.753
3.952


y10
3.6
3.8
3.84
3.84


a
1.291
1.863
1.251
1.364


h (=2.5a)
3.228
4.658
3.128
3.410


ΔzA(h)
−0.00739
0.01676
0.06224
−0.02158


ΔzB(h)
−0.00645
0.03437
−0.01873
0.05714


ΔzC(h)
0.01605
0.04796
0.02934
−0.08113


{ΔzA(h) + ΔzB(h)}/2
−0.00692
0.02557
0.02176
0.01778


Rc
−6.794
−11.219
−19.303
17.801


θgF(LA)
0.7108
0.6953
0.7636
0.6679


β(LA)
0.7486
0.7331
0.8014
0.7057


θhg(LA)
0.7255
0.6976
0.8205
0.6485


βhg(LA)
0.7777
0.7498
0.8727
0.7007


νd(LA)
23.22
23.22
23.22
23.22


nd(LA)
1.63494
1.63494
1.63494
1.63494


θgF(LB)
0.5528
0.5645
0.5438
0.5438


θhg(LB)
0.4638
0.4790
0.4501
0.4501


νd(LB)
49.34
42.71
59.38
59.38


nd(LB)
1.74320
1.83481
1.58313
1.58313


νd(LA) − νd(LB)
−26.12
−19.49
−36.16
−36.16


θgF(LA) − θgF(LB)
0.1580
0.1308
0.2198
0.1241


θhg(LA) − θhg(LB)
0.2617
0.2186
0.3704
0.1984


zA(h)
−0.3503
−0.6930
0.0344
−0.0129


zC(h)
−0.7997
−0.9647
−0.2551
0.3297


|zA(h) − zC(h)|/tA
0.4494
0.2717
0.2895
0.3426


tA
1.0
0.5
0.5752
0.6046


tA/tB
1.111
0.625
0.719
0.756


y07
2.52
2.66
2.69
2.69


tanω07w
0.3819
0.4059
0.4219
0.4412


y07/(fw × tanω07w)
0.9414
0.9363
0.9417
0.9450









Thus, it is possible to use such image forming optical system of the present invention in a photographic apparatus in which an image of an object is photographed by an electronic image pickup element such as a CCD and a CMOS, particularly a digital camera and a video camera, a personal computer, a telephone, and a portable terminal which are examples of an information processing unit, particularly a portable telephone which is easy to carry. Embodiments thereof will be exemplified below.
In FIG. 9 to FIG. 11 show conceptual diagrams of structures in which the image forming optical system according to the present invention is incorporated in a photographic optical system 41 of a digital camera. FIG. 9 is a frontward perspective view showing an appearance of a digital camera 40, FIG. 10 is a rearward perspective view of the same, and FIG. 11 is a cross-sectional view showing an optical arrangement of the digital camera 40.
The digital camera 40, in a case of this example, includes the photographic optical system 41 (an objective optical system for photography 48) having an optical path for photography 42, a finder optical system 43 having an optical path for finder 44, a shutter 45, a flash 46, and a liquid-crystal display monitor 47. Moreover, when the shutter 45 disposed at an upper portion of the camera 40 is pressed, in conjugation with this, a photograph is taken through the photographic optical system 41 (objective optical system for photography 48) such as the zoom lens in the first embodiment.
An object image formed by the photographic optical system 41 (photographic objective optical system 48) is formed on an image pickup surface 50 of a CCD 49. The object image photoreceived at the CCD 49 is displayed on the liquid-crystal display monitor 47 which is provided on a camera rear surface as an electronic image, via an image processing means 51. Moreover, a memory etc. is disposed in the image processing means 51, and it is possible to record the electronic image photographed. This memory may be provided separately from the image processing means 51, or may be formed by carrying out by writing by recording (recorded writing) electronically by a floppy (registered trademark) disc, memory card, or an MO etc.
Furthermore, an objective optical system for finder 53 is disposed in the optical path for finder 44. This objective optical system for finder 53 includes a cover lens 54, a first prism 10, an aperture stop 2, a second prism 20, and a lens for focusing 66. An object image is formed on an image forming surface 67 by this objective optical system for finder 53. This object image is formed in a field frame of a Porro prism which is an image erecting member equipped with a first reflecting surface 56 and a second reflecting surface 58. On a rear side of this Porro prism, an eyepiece optical system 59 which guides an image formed as an erected normal image is disposed.
In the digital camera 40 having the above-described configuration, an electronic image pickup apparatus equipped with a small and slim zoom lens having a decreased number of lenses in the image pickup optical system 41 is embodied. The present invention can be applied not only to digital cameras having a collapsible lens as described above but also digital cameras having a folded optical system.
Next, a personal computer which is an example of an information processing apparatus with a built-in image forming system as an objective optical system is shown in FIG. 12 to FIG. 14. FIG. 12 is a frontward perspective view of a personal computer 300 with its cover opened, FIG. 13 is a cross-sectional view of a photographic optical system 303 of the personal computer 300, and FIG. 14 is a side view of FIG. 12. As it is shown in FIG. 12 to FIG. 14, the personal computer 300 has a keyboard 301, an information processing means and a recording means, a monitor 302, and a photographic optical system 303.
Here, the keyboard 301 is for an operator to input information from an outside. The information processing means and the recording means are omitted in the diagram. The monitor 302 is for displaying the information to the operator. The photographic optical system 303 is for photographing an image of the operator or a surrounding. The monitor 302 may be a display such as a liquid-crystal display or a CRT display. As the liquid-crystal display, a transmission liquid-crystal display device which illuminates from a rear surface by a backlight not shown in the diagram, and a reflection liquid-crystal display device which displays by reflecting light from a front surface are available. Moreover, in the diagram, the photographic optical system 303 is built-in at a right side of the monitor 302, but without restricting to this location, the photographic optical system 303 may be anywhere around the monitor 302 and the keyboard 301.
This photographic optical system 303 has an objective optical system 100 which includes the zoom lens in the first embodiment for example, and an electronic image pickup element chip 162 which receives an image. These are built into the personal computer 300.
At a front end of a mirror frame, a cover glass 102 for protecting the objective optical system 100 is disposed.
An object image received at the electronic image pickup element chip 162 is input to a processing means of the personal computer 300 via a terminal 166. Further, the object image is displayed as an electronic image on the monitor 302. In FIG. 12, an image 305 photographed by the user is displayed as an example of the electronic image. Moreover, it is also possible to display the image 305 on a personal computer of a communication counterpart from a remote location via a processing means. For transmitting the image to the remote location, the Internet and telephone are used.
Next, a telephone which is an example of an information processing apparatus in which the image forming optical system of the present invention is built-in as a photographic optical system, particularly a portable telephone which is easy to carry is shown in FIG. 15A, FIG. 15B, and FIG. 15C. FIG. 15A is a front view of a portable telephone 400, FIG. 15B is a side view of the portable telephone 400, and FIG. 15C is a cross-sectional view of a photographic optical system 405. As shown in FIG. 15A to FIG. 15C, the portable telephone 400 includes a microphone section 401, a speaker section 402, an input dial 403, a monitor 404, the photographic optical system 405, an antenna 406, and a processing means.
Here, the microphone section 401 is for inputting a voice of the operator as information. The speaker section 402 is for outputting a voice of the communication counterpart. The input dial 403 is for the operator to input information. The monitor 404 is for displaying a photographic image of the operator himself and the communication counterpart, and information such as a telephone number. The antenna 406 is for carrying out a transmission and a reception of communication electric waves. The processing means (not shown in the diagram) is for carrying out processing of image information, communication information, and input signal etc.
Here, the monitor 404 is a liquid-crystal display device. Moreover, in the diagram, a position of disposing each structural element is not restricted in particular to a position in the diagram. This photographic optical system 405 has an objective optical system 100 which is disposed in a photographic optical path 407 and an image pickup element chip 162 which receives an object image. As the objective optical system 100, the zoom lens in the first embodiment for example, is used. These are built into the portable telephone 400.
At a front end of a mirror frame, a cover glass 102 for protecting the objective optical system 100 is disposed.
An object image received at the electronic image pickup element chip 162 is input to an image processing means which is not shown in the diagram, via a terminal 166. Further, the object image finally displayed as an electronic image on the monitor 404 or a monitor of the communication counterpart, or both. Moreover, a signal processing function is included in the processing means. In a case of transmitting an image to the communication counterpart, according to this function, information of the object image received at the electronic image pickup element chip 162 is converted to a signal which can be transmitted.
Various modifications can be made to the present invention without departing from its essence.

## Claims

1. An image forming optical system comprising:
a lens group I located closest to its object side;
an aperture stop;
a lens group A disposed between the lens group I and the aperture stop and having a negative refracting power as a whole, wherein
the lens group A includes a cemented lens component made up of a positive lens LA and a negative lens LB that are cemented together,
the distance between the lens group I and the lens group A on the optical axis changes for zooming,
the cemented lens component has an aspheric cemented surface, and
when the shape of the aspheric surface is expressed by the following equation (1) with a coordinate axis z taken along the optical axis and a coordinate axis h taken along a direction perpendicular to the optical axis:


z=h2/R[1+{1−(1+k)h2/R2}1/2]+A4h4+A6h6+A8h8+A10h10+  (1),



where R is the radius of curvature of a spherical component on the optical axis, k is a conic constant, A4, A6, A8, A10, . . . are aspheric coefficients, and a deviation is expressed by the following equation (2):


Δz=z−h2/R[1+{1−h2/R2}1/2]  (2),


the following conditional expression (3a) or (3b) is satisfied:
when Rc≧0,


ΔzC(h)≦(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3a),


when Rc≦0,


ΔzC(h)≧(ΔzA(h)+ΔzB(h))/2 (where h=2.5a)  (3b),


where zA expresses the shape of the air-contact surface of the positive lens LA according to equation (1), zB expresses the shape of the air-contact surface of the negative lens LB according to equation (1), zC expresses the shape of the cemented surface according to equation (1), ΔzA is the deviation of the air-contact surface of the positive lens LA according to equation (2), ΔzB is the deviation of the air-contact surface of the negative lens LB according to equation (2), ΔzC is the deviation of the cemented surface according to equation (2), Rc is the paraxial radius of curvature of the cemented surface, and a is a value expressed by the following equation (4):


a=(y10)2·log10γ/fw  (4),


where y10 is the largest image height, fw is the focal length of the entire image forming optical system at the wide angle end, and γ is the zoom ratio (i.e. {the focal length of the entire system at the telephoto end}/{the focal length of the entire system at the wide angle end}) of the image forming optical system, where z(0)=0 holds for all the surfaces because the point of origin is set at the vertex of each surface.

2. The image forming optical system according to claim 1, wherein the value of θgF and the value of νd of the positive lens LA fall within the following two ranges: the range in an orthogonal coordinate system having a horizontal axis representing νd and a vertical axis representing θgF that is bounded by the straight line given by the equation θgF=α×νd+β (where α=−0.00163) into which the lowest value in the range defined by the following conditional expression (5) is substituted and the straight line given by the equation θgF=α×νd+β (where αhg1=−0.00163) into which the highest value in the range defined by the following conditional expression (5) is substituted; and the range defined by the following conditional expression (6):


0.6700<β<0.9000  (5),



3<νd<27  (6),


where θgF is the relative partial dispersion (ng−nF)/(nF−nC) of the positive lens LA, and νd is the Abbe constant (nd−1)/(nF−nC) of the positive lens LA, where nd, nC, nF, and ng are refractive indices of the positive lens LA for the d-line, C-line, F-line, and g-line respectively.

3. The image forming optical system according to claim 1, wherein the value of θhg and the value of νd of the positive lens LA fall within the following two ranges: the range in an orthogonal coordinate system, which is different from the aforementioned orthogonal coordinate system, having a horizontal axis representing νd and a vertical axis representing θhg that is bounded by the straight line given by the equation θhg=αhg×∥d+βhg (where αhg=−0.00225) into which the lowest value in the range defined by the following conditional expression (7) is substituted and the straight line given by the equation θhg=αhg×νd+βhg (where αhg=−0.00225) into which the highest value in the range defined by the following conditional expression (7) is substituted; and the range defined by the following conditional expression (6):


0.6350<βhg<0.9500  (7),



3<νd<27  (6),


where θhg is the relative partial dispersion (nh−ng)/(nF−nC) of the positive lens LA, and nh is the refractive index of the positive lens LA for the h-line.

4. The image forming optical system according to claim 1, wherein the image forming optical system satisfies the following conditional expression (8):


0.07≦θgF(LA)−θgF(LB)≦0.50  (8),


where θgF(LA) is the relative partial dispersion (ng−nF)/(nF−nC) of the positive lens LA, and θgF(LB) is the relative partial dispersion (ng−nF)/(nF−nC) of the negative lens LB.

5. The image forming optical system according to claim 1, wherein the image forming optical system satisfies the following conditional expression (9):


0.10≦θhg(LA)−θhg(LB)≦0.60  (9),


where θhg(LA) is the relative partial dispersion (nh−ng)/(nF−nC) of the positive lens LA, and θhg(LB) is the relative partial dispersion (nh−ng)/(nF−nC) of the negative lens LB.

6. The image forming optical system according to claim 4, wherein the image forming optical system satisfies the following conditional expression (10):


νd(LA)−νd(LB)≦−10  (10),


where νd (LA) is the Abbe constant (nd−1)/(nF−nC) of the positive lens LA, and νd (LB) is the Abbe constant (nd−1)/(nF−nC) of the negative lens LB.

7. The image forming optical system according to claim 1, wherein the image forming optical system satisfies the following conditional expression (11):


1.55≦nd(LA)≦1.90  (11)


where nd(LA) is the refractive index of the positive lens LA for the d-line.

8. The image forming optical system according to claim 1, wherein the material of the positive lens LA is an energy curable resin, and the cemented lens component is produced by attaching the resin onto an optical surface of the negative lens LB and thereafter curing it to form the lens LA.

9. The image forming optical system according to claim 1, wherein the lens component that is located closest to the object side in the lens group A is a negative single lens, and the cemented lens component is disposed on its image side.

10. The image forming optical system according to claim 1, wherein the lens component that is located closest to the image side in the lens group A is the cemented lens component having a negative refracting power.

11. The image forming optical system according to claim 1, wherein the image forming optical system consists of four lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, and a lens group G4 having a positive refracting power.

12. The image forming optical system according to claim 1, wherein the image forming optical system consists of four lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a negative refracting power, and a lens group G4 having a positive refracting power.

13. The image forming optical system according to claim 1 wherein the image forming optical system consists of four lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, and a lens group G4 having a negative refracting power.

14. The image forming optical system according to claim 1, wherein the image forming optical system consists of five lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, a lens group G4 having a positive refracting power, and a lens group G5 having a negative refracting power.

15. The image forming optical system according to claim 1, wherein the image forming optical system consists of five lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, a lens group G4 having a negative refracting power, and a lens group G5 having a positive refracting power.

16. The image forming optical system according to claim 1, wherein the image forming optical system consists of five lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, a lens group G4 having a negative refracting power, and a lens group G5 having a positive refracting power.

17. The image forming optical system according to claim 1, wherein the image forming optical system consists of five lens groups including, in order from its object side, the lens group I, the lens group A, a lens group G3 having a positive refracting power, a lens group G4 having a positive refracting power, and a lens group G5 having a positive refracting power.

18. The image forming optical system according to claim 1, wherein the lens group I has a reflecting optical element.

19. An electronic image pickup apparatus comprising:
an image forming optical system as recited in claim 1;
an electronic image pickup element; and
an image processing unit that processes image data obtained by picking up an image formed through the image forming optical system by the electronic image pickup element and outputs image data representing an image having a changed shape, wherein
the image forming optical system is a zoom lens, and
the zoom lens satisfies the following conditional expression (17) when the zoom lens is focused on an object point at infinity:


0.70<y07/(fW·tan ω07w)<0.97  (17),



where y07 is expressed by equation y07=0.7y10, y10 being a distance from the center of an effective image pickup area (i.e. an area in which images can be picked up) of the electronic image pickup element to a point farthest from the center within the effective image pickup area (or a largest image height), ω07w is the angle of the direction toward an object point corresponding to an image point formed at a position at distance y07 from the center of the image pickup surface at the wide angle end with respect to the optical axis, and fw is the focal length of the entire image forming optical system at the wide angle end.