
[0001]
This disclosure is based on applications No. H10363664 filed in Japan on Dec. 22, 1998 and No. H1 1005056 filed in Japan on Jan. 12, 1999, the entire contents of which are hereby incorporated by reference.
BACKGROUND OF THE INVENTION

[0002]
1. Field of the Invention

[0003]
The present invention relates to a zoom lens system, and more particularly to a compact and inexpensive zoom lens system particularly suited for use in digital still cameras.

[0004]
2. Description of the Prior Art

[0005]
In recent years, as personal computers become more prevalent, digital still cameras that allow easy storage of image data on a recording medium such as a floppy disk have been coming into wider use. This trend has created an increasing demand for more inexpensive digital still cameras. This in turn has created an increasing demand for further cost reduction in imaging optical systems. On the other hand, photoelectric conversion devices have come to have an increasingly large number of pixels year by year, which accordingly demands imaging optical systems that offer higher and higher performance. To comply with such requirements, it is necessary to produce a highperformance imaging optical system at comparatively low cost.

[0006]
To achieve this objective, for example, Japanese Laidopen Patent Applications Nos. H1183615 and H9311273 propose optical systems having a first lens unit of a negativenegativepositive configuration and a second lens unit of a positivenegativepositive configuration. Moreover, the optical systems proposed in Japanese Laidopen Patent Applications Nos. H7113956, H6300969, and H763991 have a second lens unit including a doublet lens element formed by cementing together negative lens elements; and the optical system proposed in Japanese Laidopen Patent Application No. H593858 has a second lens unit including a doublet lens element formed by cementing together, from the object side, a positive lens element and a negative lens element. If a doublet lens element is considered to be a single lens element, it is assumed that those optical systems are each composed of a first lens unit of a negativenegativepositive configuration and a second lens unit of a positivenegativepositive configuration.

[0007]
Furthermore, Japanese Laidopen Patent Applications Nos. H6201993 and H1191820 propose optical systems that are composed of a first lens unit having a negative optical power, a second lens unit having a positive optical power, and a third lens unit having a positive optical power and employ a plastic lens element.

[0008]
In the optical systems proposed in the abovementioned patent applications, however, there is still plenty of room for improvement from the viewpoint of miniaturization, high performance, and cost reduction.
SUMMARY OF THE INVENTION

[0009]
An object of the present invention is to provide a compact, highresolution, and lowcost zoom lens system suitable, in particular, for use in a digital still camera by arranging plastic lens elements effectively in a twounit zoom lens system of a negativepositive configuration.

[0010]
To achieve the above object, according to one aspect of the present invention, a zoom lens system includes, from the object side, a first lens unit and a second lens unit. The first lens unit is composed of a negative, a negative, and a positive lens element and has a negative optical power as a whole. The second lens unit is composed of a positive, a negative, and a positive lens element and has a positive optical power as a whole. In the zoom lens system, zooming is achieved by varying the distance between the first and second lens units, and at least one of those lens elements is a plastic lens element.

[0011]
According to another aspect of the present invention, a zoom lens system includes, from the object side, a first lens unit having a negative optical power and a second lens unit having a positive optical power. In the zoom lens system, zooming is achieved by varying the distance between the first and second lens units, and at least a negative lens element and a positive lens element of the lens elements included in the lens units are plastic lens elements that fulfill the following condition:

−1.2<φPi/φW×hi<1.2

[0012]
where

[0013]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0014]
φPi represents the optical power of the ith plastic lens element; and

[0015]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination a 1 and the height h1, for paraxial tracing, are 0 and 1, respectively.

[0016]
According to another aspect of the present invention, an image taking apparatus is composed of a zoom lens system, a photoelectric conversion device, and an optical lowpass filter. The photoelectric conversion device has a light sensing surface on which an image is formed by the zoom lens system. The optical lowpass filter is disposed on the object side of the photoelectric conversion device. The zoom lens system is composed of, from the object side, a first lens unit and a second lens unit. The first lens unit is composed of a negative, a negative, and a positive lens element, and has a negative optical power as a whole. The second lens unit is composed of a positive, a negative, and a positive lens element, and has a positive optical power as a whole. In the zoom lens system, zooming is achieved by varying the distance between the first and second lens units, and at least one of those lens elements is a plastic lens element.

[0017]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second lens unit is composed of at least a positive and a negative lens element, and has a positive optical power. The third lens unit has a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the lens units is a plastic lens element that fulfills the following conditions:

−0.8<Cp×(N′−N)/φW<0.8

−0.45<M3/M2<0.90(where φT/φW>1.6)

[0018]
where

[0019]
Cp represents the curvature of the plastic lens element;

[0020]
HW represents the optical power of the entire zoom lens system at the wideangle end;

[0021]
N′ represents the refractive index of the objectside medium of the aspherical surface for the d line;

[0022]
N represents the refractive index of the imageside medium of the aspherical surface for the d line;

[0023]
M3 represents the amount of movement of the third lens unit (the direction pointing to the object side is negative with respect to the wideangle end);

[0024]
M2 represents the amount of movement of the second lens unit (the direction pointing to the object side is negative with respect to the wideangle end); and

[0025]
φT represents the optical power of the entire zoom lens system at the telephoto end.

[0026]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit is composed of at least a positive and a negative lens element, and has a negative optical power. The second and third lens units have a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the first lens unit is a plastic lens element that fulfills the following conditions:

φP/φ1<1.20

0.20<φ1/φW<0.70

−0.45<M3/M2<0.90(where φT/φW>1.6)

[0027]
where

[0028]
φP represents the optical power of the plastic lens element;

[0029]
φ1 represents the optical power of the first lens unit;

[0030]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0031]
M3 represents the amount of movement of the third lens unit (the direction pointing to the object side is negative with respect to the wideangle end);

[0032]
M2 represents the amount of movement of the second lens unit (the direction pointing to the object side is negative with respect to the wideangle end); and

[0033]
φT represents the optical power of the entire zoom lens system at the telephoto end.

[0034]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second lens unit is composed of at least a positive and a negative lens element, and has a positive optical power. The third lens unit has a positive optical power. In the zoom lens system, zooming is achieved by varying the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the second lens unit is a plastic lens element that fulfills the following conditions:

φP/φ2<2.5

0.25<φ2/φW<0.75

[0035]
where

[0036]
φP represents the optical power of the plastic lens element;

[0037]
φ2 represents the optical power of the second lens unit; and

[0038]
φW represents the optical power of the entire zoom lens system at the wideangle end.

[0039]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second and third lens units have a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the third lens unit is a plastic lens element that fulfills the following conditions:

−0.30<M3/M2<0.90

φP/φ3<1.70

0.1<φ3/φW<0.60

[0040]
where

[0041]
M3 represents the amount of movement of the third lens unit (the direction pointing to the object side is negative with respect to the wideangle end);

[0042]
M2 represents the amount of movement of the second lens unit (the direction pointing to the object side is negative with respect to the wideangle end);

[0043]
φP represents the optical power of the plastic lens element;

[0044]
φ3 represents the optical power of the third lens unit; and

[0045]
φW represents the optical power of the entire zoom lens system at the wideangle end.

[0046]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second and third lens units have a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the first lens unit and at least one of the lens elements included in the second lens unit are plastic lens elements that fulfill the following conditions:

−1.4<φPi/W×hi<1.4

0.5<log(β2T/β2W)/log Z<2.2

[0047]
where

[0048]
φPi represents the optical power of the ith plastic lens element;

[0049]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0050]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination α1 and the height h1, for paraxial tracing, are 0 and 1, respectively;

[0051]
β2W represents the lateral magnification of the second lens unit at the wideangle end;

[0052]
β2T represents the lateral magnification of the second lens unit at the telephoto end;

[0053]
Z represents the zoom ratio; and

[0054]
log represents a natural logarithm (since the condition defines a proportion, the base does not matter).

[0055]
According to another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second lens unit is composed of at least a positive and a negative lens element, and has a positive optical power. The third lens unit has a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the first lens unit and at least one of the lens elements included in the third lens unit are plastic lens elements that fulfill the following conditions:

−1.4<φPi/φW×hi<1.4

−1.2<log(β3T/β3W)/log Z<0.5

[0056]
where

[0057]
φPi represents the optical power of the ith plastic lens element;

[0058]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0059]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination a 1 and the height h1, for paraxial tracing, are 0 and 1, respectively;

[0060]
β3W represents the lateral magnification of the third lens unit at the wideangle end;

[0061]
β3T represents the lateral magnification of the third lens unit at the telephoto end;

[0062]
Z represents the zoom ratio; and

[0063]
log represents a natural logarithm (since the condition defines a proportion, the base does not matter).

[0064]
According to still another aspect of the present invention, a zoom lens system is composed of, from the object side, a first lens unit, a second lens unit, and a third lens unit. The first lens unit has a negative optical power. The second lens unit is composed of at least a positive and a negative lens element, and has a positive optical power. The third lens unit has a positive optical power. In the zoom lens system, zooming is achieved by moving at least two lens units so as to vary the distance between the first and second lens units and the distance between the second and third lens units, and at least one of the lens elements included in the second lens unit and at least one of the lens elements included in the third lens unit are plastic lens elements that fulfill the following conditions:

−1.4<φPi/φW×hi<1.4

−0.75<log(β3T/β3W)/log(β2T/β2W)<0.65

[0065]
where

[0066]
φPi represents the optical power of the ith plastic lens element;

[0067]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0068]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination α1 and the height h1, for paraxial tracing, are 0 and 1, respectively;

[0069]
β2W represents the lateral magnification of the second lens unit at the wideangle end;

[0070]
β2T represents the lateral magnification of the second lens unit at the telephoto end;

[0071]
β3W represents the lateral magnification of the third lens unit at the wideangle end;

[0072]
β3T represents the lateral magnification of the third lens unit at the telephoto end; and

[0073]
log represents a natural logarithm (since the condition defines a proportion, the base does not matter).
BRIEF DESCRIPTION OF THE DRAWINGS

[0074]
The objects and features of this invention will become clear from the following description, taken in conjunction with the preferred embodiments with reference to the accompanied drawings in which:

[0075]
[0075]FIG. 1 is a lens arrangement diagram of the zoom lens system of a first embodiment (Example 1) of the present invention;

[0076]
[0076]FIG. 2 is a lens arrangement diagram of the zoom lens system of a second embodiment (Example 2) of the present invention;

[0077]
[0077]FIG. 3 is a lens arrangement diagram of the zoom lens system of a third embodiment (Example 3) of the present invention;

[0078]
[0078]FIG. 4 is a lens arrangement diagram of the zoom lens system of a fourth embodiment (Example 4) of the present invention;

[0079]
[0079]FIG. 5 is a lens arrangement diagram of the zoom lens system of a fifth embodiment (Example 5) of the present invention;

[0080]
[0080]FIGS. 6A to 6I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 1;

[0081]
[0081]FIGS. 7A to 7I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 2;

[0082]
[0082]FIGS. 8A to 8I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 3;

[0083]
[0083]FIGS. 9A to 9I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 4;

[0084]
[0084]FIGS. 10A to 10I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 5;

[0085]
[0085]FIG. 11 is a lens arrangement diagram of the zoom lens system of a sixth embodiment (Example 6) of the present invention;

[0086]
[0086]FIG. 12 is a lens arrangement diagram of the zoom lens system of a seventh embodiment (Example 7) of the present invention;

[0087]
[0087]FIG. 13 is a lens arrangement diagram of the zoom lens system of an eighth embodiment (Example 8) of the present invention;

[0088]
[0088]FIG. 14 is a lens arrangement diagram of the zoom lens system of a ninth embodiment (Example 9) of the present invention;

[0089]
[0089]FIG. 15 is a lens arrangement diagram of the zoom lens system of a tenth embodiment (Example 10) of the present invention;

[0090]
[0090]FIG. 16 is a lens arrangement diagram of the zoom lens system of an eleventh embodiment (Example 11) of the present invention;

[0091]
[0091]FIG. 17 is a lens arrangement diagram of the zoom lens system of a twelfth embodiment (Example 12) of the present invention;

[0092]
[0092]FIG. 18 is a lens arrangement diagram of the zoom lens system of a thirteenth embodiment (Example 13) of the present invention;

[0093]
[0093]FIG. 19 is a lens arrangement diagram of the zoom lens system of a fourteenth embodiment (Example 14) of the present invention;

[0094]
[0094]FIGS. 20A to 20I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 6;

[0095]
[0095]FIGS. 21A to 21I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 7;

[0096]
[0096]FIGS. 22A to 22I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 8;

[0097]
[0097]FIGS. 23A to 23I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 9;

[0098]
[0098]FIGS. 24A to 24I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 10;

[0099]
[0099]FIGS. 25A to 25I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 11;

[0100]
[0100]FIGS. 26A to 26I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 12;

[0101]
[0101]FIGS. 27A to 27I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of the Example 13;

[0102]
[0102]FIGS. 28A to 28I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of the Example 14;

[0103]
[0103]FIG. 29 is a lens arrangement diagram of the zoom lens system of a fifteenth embodiment (Example 15) of the present invention;

[0104]
[0104]FIGS. 30A to 30I are graphic representations of the aberrations observed in an infinitedistance shooting condition in the zoom lens system of Example 15; and

[0105]
[0105]FIG. 31 is a schematic illustration of the optical components of a digital camera.
DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0106]
Embodiments 1 to 5

[0107]
Hereinafter, zoom lens systems embodying the present invention will be described with reference to the drawings. FIGS. 1 to 5 are lens arrangement diagrams of the zoom lens systems of a first, a second, a third, a fourth, and a fifth embodiment, respectively. In each diagram, the lefthand side corresponds to the object side, and the righthand side corresponds to the image side. Note that, in each diagram, arrows schematically indicate the movement of the lens units during zooming from the wideangle end to the telephoto end. Moreover, each diagram shows the lens arrangement of the zoom lens system during zooming, as observed at the wideangle end. As shown in these diagrams, the zoom lens systems of the embodiments are each built as a twounit zoom lens system of a negativepositive configuration that is composed of, from the object side, a first lens unit Gr1 and a second lens unit Gr2. Both the first and second lens units (Gr1 and Gr2) are movably disposed in the zoom lens system.

[0108]
The first lens unit Gr1 is composed of, from the object side, a negative lens element, a negative lens element, and a positive lens element and has a negative optical power as a whole. The second lens unit Gr2 is composed of an aperture stop S, a positive lens element, a negative lens element, and a positive lens element and has a positive optical power as a whole. In the zoom lens system, the first to sixth lens elements counted from the object side are represented as G1 to G6, respectively. Note that a flat plate disposed at the imageside end of the zoom lens system is a lowpass filter LPF. As illustrated in FIG. 31, within a digital camera the lowpass filter LPP is disposed between the zoom lens system ZLS and a photoelectric image sensor is having a lightsensing surface on which an image is formed by the zoom lens system.

[0109]
As shown in FIG. 1, in the first embodiment, the second and sixth lens elements (G2 and G6) counted from the object side (hatched in the figure) are plastic lens elements. As shown in FIG. 2, in the second embodiment, the second, third, fifth, and sixth lens elements (G2, G3, G5, and G6) counted from the object side (hatched in the figure) are plastic lens elements.

[0110]
Moreover, as shown in FIG. 3, in the third embodiment, the second, fifth, and sixth lens elements (G2, G5, and G6) counted from the object side (hatched in the figure) are plastic lens elements. As shown in FIG. 4, in the fourth embodiment, the third and fifth lens elements (G3 and G5) counted from the object side (hatched in the figure) are plastic lens elements. Lastly, as shown in FIG. 5, in the fifth embodiment, the second and sixth lens elements (G2 and G6) counted from the object side (hatched in the figure) are plastic lens elements.

[0111]
The conditions to be preferably fulfilled by an optical system will be described below. It is preferable that the zoom lens systems of the embodiments fulfill Condition (1) below.

0.25<φ1/φW51 <0.80 (1)

[0112]
where

[0113]
φ1 represents the optical power of the first lens unit; and

[0114]
φW represents the optical power of the entire zoom lens system at the wideangle end.

[0115]
Condition (1) defines, in the form of the optical power of the first lens unit, the condition to be fulfilled to achieve proper correction of aberrations and keep the size of the zoom lens system appropriate. If the value of Condition (1) is equal to or less than its lower limit, the optical power of the first lens unit is so weak that aberrations can be corrected properly, but simultaneously the total length, as well as the diameter of the frontend lens unit, of the zoom lens system becomes unduly large. In contrast, if the value of Condition (1) is equal to or greater than its upper limit, the optical power of the first lens unit is so strong that the total length of the zoom lens system is successfully minimized, but simultaneously the inclination of the image plane toward the over side becomes unduly large. In addition, barrelshaped distortion becomes unduly large at the wideangle end.

[0116]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (2) below.

0.35<φ2/φW<0.75 (2)

[0117]
where

[0118]
φ2 represents the optical power of the second lens unit.

[0119]
Condition (2) defines, in the form of the optical power of the second lens unit, the condition to be fulfilled to achieve, as in Condition (1), proper correction of aberrations and keep the size of the zoom lens system appropriate. If the value of Condition (2) is equal to or less than its lower limit, the optical power of the second lens unit is so weak that aberrations can be corrected properly, but simultaneously the total length, as well as the diameter of the frontend lens unit, of the zoom lens system becomes unduly large. In contrast, if the value of Condition (2) is equal to or greater than its upper limit, the optical power of the second lens unit is so strong that the total length of the zoom lens system is successfully minimized, but simultaneously spherical aberration appears notably on the under side.

[0120]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (3) below.

−1.2<φPi/φW×hi<1.2 (3)

[0121]
where

[0122]
φPi represents the optical power of the ith plastic lens element; and

[0123]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination α1 and the height h1, for paraxial tracing, are 0 and 1, respectively.

[0124]
Condition (3) defines, in the form of the sum of the degrees in which the individual plastic lens elements, by their temperature variation, affect the back focal distance, the condition to be fulfilled to suppress variation in the back focal distance resulting from temperature variation. When a plurality of plastic lens elements are used, it is preferable that positivelypowered and negativelypowered lens elements be combined in such a way that the degree in which they affect the back focal distance are canceled out by one another. If the value of Condition (3) is equal to or less than its lower limit, the variation in the back focal distance caused by temperature variation in the negativelypowered plastic lens element becomes unduly great. In contrast, if the value of Condition (3) is equal to or greater than its upper limit, the variation in the back focal distance caused by temperature variation in the positivelypowered plastic lens element becomes unduly great. Thus, in either case, the zoom lens system needs to be provided with a mechanism that corrects the back focal distance in accordance with temperature variation.

[0125]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (4) below.

φP/φ1<1.35 (4)

[0126]
where

[0127]
φP represents the optical power of the plastic lens element.

[0128]
Condition (4) defines, in the form of the optical power of the plastic lens element included in the first lens unit, the condition to be fulfilled to keep the variation of aberrations resulting from temperature variation within an appropriate range. If the value of Condition (4) is equal to or greater than its upper limit curvature of field, in particular, the curvature of field on the wideangle side varies too greatly with temperature.

[0129]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (5) below.

φP/φ2<2.15 (5)

[0130]
Condition (5) defines, in the form of the optical power of the plastic lens element included in the second lens unit, the condition to be fulfilled to keep, as in Condition (4), the variation of aberrations resulting from temperature variation within an appropriate range. If the value of Condition (5) is equal to or greater than its upper limit, spherical aberration, in particular, the spherical aberration on the telephoto side, varies too greatly with temperature.

[0131]
No lower limit is given for Conditions (4) and (5). This is because, as the value of either of the conditions decreases, the optical power of the plastic lens element becomes weaker, and this is desirable in terms of suppression of the variation of aberrations resulting from temperature variation. This, however, has no effect on correction of aberrations under normal temperature, and accordingly makes the use of plastic lenses meaningless. To avoid this, where the plastic lens element fulfills Condition (6) below, it is essential to use an aspherical surface.

0≦φP/φA<0.45 (6)

[0132]
where

[0133]
φA represents the optical power of the lens unit including the plastic lens element.

[0134]
Note however that this is not to discourage providing an aspherical surface on the lens surface of a plastic lens element having an optical power that makes the value of Condition (6) equal to or greater than its upper limit.

[0135]
As described above, if an aspherical surface is used, it is preferable that the following conditions be fulfilled. First, where an aspherical surface is used in the first lens unit, it is preferable that Condition (7) below be fulfilled.

−0.85<(X−X _{0})/{C _{0}(N′−N)f1}<−0.05 (7)

[0136]
where

[0137]
C_{0 }represents the curvature of the reference spherical surface of the aspherical surface;

[0138]
N represents the refractive index of the imageside medium of the aspherical surface for the d line;

[0139]
N′ represents the refractive index of the objectside medium of the aspherical surface for the d line;

[0140]
X represents the deviation of the aspherical surface along the optical axis at the height in a direction perpendicular to the optical axis (the direction pointing to the object side is negative);

[0141]
X_{0 }represents the deviation of the reference spherical surface of the aspherical surface along the optical axis at the height in a direction perpendicular to the optical axis (the direction pointing to the object side is negative); and

[0142]
f1 represents the focal length of the first lens unit.

[0143]
Condition (7) defines the surface shape of the aspherical surface and assumes that the aspherical surface is so shaped as to weaken the optical power of the first lens unit. Fulfillment of Condition (7) makes it possible to achieve proper correction of the distortion and the image plane on the wideangle side, in particular. If the value of Condition (7) is equal to or less than its lower limit, positive distortion becomes unduly large on the wideangle side, in particular, in a closeshooting condition, and simultaneously the inclination of the image plane toward the over side becomes unduly large. In contrast, if the value of Condition (7) is equal to or greater than its upper limit, negative distortion becomes unduly large on the wideangle side, in particular, in a closeshooting condition, and simultaneously the inclination of the image plane toward the under side becomes unduly large. Note that, in a case where the first lens unit includes a plurality of aspherical surfaces, at least one of those aspherical surfaces needs to fulfill Condition (7) above; that is, the other aspherical surfaces do not necessarily have to fulfill Condition (7) above, if that is advantageous for the correction of other aberrations.

[0144]
In a case where an aspherical surface is used in the second lens unit, it is preferable that Condition (8) below be fulfilled.

−0.95<(X−X _{0})/{C _{0}(N′−N)f2}<−0.05 (8)

[0145]
where

[0146]
f2 represents the focal length of the second lens unit.

[0147]
Condition (8) defines the surface shape of the aspherical surface and assumes that the aspherical surface is so shaped as to weaken the optical power of the second lens unit. Fulfillment of Condition (8) makes it possible to achieve proper correction of spherical aberration, in particular. If the value of Condition (8) is equal to or less than its lower limit, in particular, spherical aberration appears notably on the over side at the telephoto end. In contrast, if the value of Condition (8) is equal to or greater than its upper limit, spherical aberration appears notably on the under side at the telephoto end. Note that, in a case where the second lens unit includes a plurality of aspherical surfaces, at least one of those aspherical surfaces needs to fulfill Condition (8) above; that is, the other aspherical surfaces do not necessarily have to fulfill Condition (8) above, if that is advantageous for the correction of other aberrations.

[0148]
Embodiments 6 to 15

[0149]
FIGS. 11 to 19 and 29 are lens arrangement diagrams of the zoom lens systems of a sixth, a seventh, an eighth, a ninth, a tenth, an eleventh, a twelfth, a thirteenth, a fourteenth and a fifteenth embodiment, respectively. In each diagram, the lefthand side corresponds to the object side, and the righthand side corresponds to the image side. In addition, in each diagram, arrows schematically indicate the movement of the lens units during zooming from the wideangle end to the telephoto end. Note that arrows with a broken line indicate that the lens unit is kept in a fixed position during zooming. Moreover, each diagram shows the lens arrangement of the zoom lens system during zooming, as observed at the wideangle end. As shown in these diagrams, the zoom lens systems of the embodiments are each built as a threeunit zoom lens system of a negativepositivepositive configuration that is composed of, from the object side, a first lens unit Gr1, a second lens unit Gr2, and a third lens unit Gr3. In this zoom lens system, at least two lens units are moved during zooming.

[0150]
The first lens unit Gr1 has a negative optical power as a whole. The second and third lens units (Gr2 and Gr3) have a positive optical power as a whole. In the zoom lens system, the first to eighth lens elements counted from the object side are represented as G1 to G8, respectively. The lens units provided in the zoom lens system of each embodiment are each realized by the use of a plurality of lens elements out of those lens elements G1 to G8. The second lens unit Gr2 includes an aperture stop S. Note that a flat plate disposed at the imageside end of the zoom lens system is a lowpass filter LPF.

[0151]
As shown in FIG. 11, in the sixth embodiment, the second and sixth lens elements (G2 and G6) counted from the object side (hatched in the figure) are plastic lens elements. Moreover, as shown in FIG. 12, in the seventh embodiment, the second and seventh lens elements (G2 and G7) counted from the object side (hatched in the figure) are plastic lens elements.

[0152]
As shown in FIG. 13, in the eighth embodiment, the first and seventh lens elements (G1 and G7) counted from the object side (hatched in the figure) are plastic lens elements. Moreover, as shown in FIG. 14, in the ninth embodiment, the second and fifth lens elements (G2 and G5) counted from the object side (hatched in the figure) are plastic lens elements. Furthermore, as shown in FIG. 15, in the tenth embodiment, the first and seventh lens elements (G1 and G7) counted from the object side (hatched in the figure) are plastic lens elements.

[0153]
As shown in FIG. 16, in the eleventh embodiment, the second and fifth lens elements (G2 and G5) counted from the object side (hatched in the figure) are plastic lens elements. Moreover, as shown in FIG. 17, in the twelfth embodiment, the second, fifth, sixth, and seventh lens elements (G2, G5, G6, and G7) counted from the object side (hatched in the figure) are plastic lens elements.

[0154]
As shown in FIG. 18, in the thirteenth embodiment, the second, fifth, sixth, seventh, and eighth lens elements (G2, G5, G6, G7, and G8) counted from the object side (hatched in the figure) are plastic lens elements. As shown in FIG. 19, in the fourteenth embodiment, the second, sixth, and seventh lens elements (G2, G6, and G7) counted from the object side (hatched in the figure) are plastic lens elements. Referring to FIG. 29, in the fifteenth embodiment, the first and fifth lens elements (G1 and G5) are plastic lens elements.

[0155]
The conditions to be preferably fulfilled by an optical system will be described below. It is preferable that the zoom lens systems of the sixth to fifteenth embodiments fulfill Condition (9) below.

−0.8<Cp×(N′−N)/φW<0.8 (9)

[0156]
where

[0157]
Cp represents the curvature of the plastic lens element;

[0158]
φW represents the optical power of the entire zoom lens system at the wideangle end;

[0159]
N′ represents the refractive index of the objectside medium of the aspherical surface for the d line; and

[0160]
N represents the refractive index of the imageside medium of the aspherical surface for the d line.

[0161]
Condition (9) defines the optical power of the lens surface of the plastic lens element. If the optical power of the lens surface is too strong, the surface shape varies with temperature, with the result that various aberrations become unduly large. If the value of Condition (9) is equal to or less than its lower limit, the negative optical power is too strong. In contrast, if the value of Condition (9) is equal to or greater than its upper limit, the positive optical power is too strong. As a result, in the plastic lens element provided in the first lens unit, curvature of field varies too greatly with temperature, in particular; in the plastic lens element provided in the second lens unit, spherical aberration varies too greatly with temperature, in particular; and, in the plastic lens element provided in the third lens unit, spherical aberration and the coma aberration in marginal rays vary greatly with temperature, in particular.

[0162]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (10) below.

−0.45<M3/M2<0.90 (10)

[0163]
where

[0164]
M3 represents the amount of movement of the third lens unit (the direction pointing to the object side is negative with respect to the wideangle end); and

[0165]
M2 represents the amount of movement of the second lens unit (the direction pointing to the object side is negative with respect to the wideangle end).

[0166]
Condition (10) defines, in the form of the ratio of the amount of movement of the second lens unit to that of the third lens unit, the condition to be fulfilled to keep the amount of movement of the second and third lens units in appropriate ranges in order to achieve zooming efficiently. Thus, in an optical system in which a sufficient zoom ratio needs to be secured, fulfillment of Condition (10) is effective. Moreover, it is more preferable that the following condition be additionally fulfilled.

φT/φW>1.6

[0167]
where

[0168]
φT represents the optical power of the entire zoom lens system at the telephoto end.

[0169]
If the value of Condition (10) is equal to or less than its lower limit, the responsibility of the third lens unit for zooming is so heavy that spherical aberration and the coma aberration in marginal rays vary too greatly with zooming. In contrast, if the value of Condition (10) is equal to or greater than its upper limit, the amount of the movement of the second lens unit is so large that the diameter of the frontend lens unit needs to be unduly large in order to secure sufficient amount of peripheral light on the wideangle side, and simultaneously, the responsibility of the second lens unit for zooming is so heavy that spherical aberration varies too greatly with zooming.

[0170]
Moreover, where a plastic lens element is used in the third lens unit, the ability of the third lens unit to correct aberrations tends to be insufficient. To avoid this, it is preferable to make the range of Condition (10) narrower so as to obtain the following condition:

−0.30<M3/M2<0.90 (10)

[0171]
In a case where a plastic lens element is used in the first lens unit, it is preferable that Condition (11) below be fulfilled.

φP/φ1)φ1<1.20 (11)

[0172]
where

[0173]
φP represents the optical power of the plastic lens element; and

[0174]
φ1 represents the optical power of the first lens unit.

[0175]
Condition (11) defines, in the form of the ratio of the optical power of the first lens unit to that of the plastic lens element included in the first lens unit, the condition to be fulfilled to keep the variation of aberrations resulting from temperature variation within an appropriate range. If the value of Condition (11) is equal to or greater than its upper limit, curvature of field, in particular, the curvature of field on the wideangle side, varies too greatly with temperature. Moreover, to correct the aberrations that occur in the first lens unit, it is preferable to use at least a positive and a negative lens element.

[0176]
In a case where a plastic lens element is used in the second lens unit, it is preferable that Condition (12) below be fulfilled.

φP/φ2<2.5 (12)

[0177]
where

[0178]
φ2 represents the optical power of the second lens unit.

[0179]
Condition (12) defines, in the form of the ratio of the optical power of the second lens unit to that of the plastic lens element included in the second lens unit, the condition to be fulfilled to keep the variation of aberrations resulting from temperature variation within an appropriate range. If the value of Condition (12) is equal to or greater than its upper limit, spherical aberration, in particular, the spherical aberration on the telephoto side, varies too greatly with temperature. Moreover, to correct the aberrations that occur in the second lens unit, it is preferable to use at least a positive and a negative lens element.

[0180]
In a case where a plastic lens element is used in the third lens unit, it is preferable that Condition (13) below be fulfilled.

φP/φ3<1.70 (13)

[0181]
where

[0182]
φ3 represents the optical power of the third lens unit.

[0183]
Condition (13) defines, in the form of the ratio of the optical power of the third lens unit to that of the plastic lens element included in the third lens unit, the condition to be fulfilled to keep the variation of aberrations resulting from temperature variation within an appropriate range. If the value of Condition (13) is equal to or greater than its upper limit, spherical aberration and the coma aberration in marginal rays vary too greatly with temperature. Moreover, to correct the aberrations that occur in the third lens unit, it is preferable to use at least a positive and a negative lens element.

[0184]
No lower limit is given for Conditions (11) to (13). This is because, as the value of either of the conditions decreases, the optical power of the plastic lens element becomes weaker, and this is desirable in terms of suppression of the variation of aberrations resulting from temperature variation. This, however, has no effect on correction of aberrations under normal temperature, and accordingly makes the use of plastic lenses meaningless. To avoid this, where the plastic lens element fulfills Condition (14) below, it is essential to use an aspherical surface.

0≦φP/φA<0.45 (14)

[0185]
where

[0186]
φA represents the optical power of the lens unit including the plastic lens element.

[0187]
Note however that this is not to discourage providing an aspherical surface on the lens surface of a plastic lens element having an optical power that makes the value of Condition (14) equal to or greater than its upper limit.

[0188]
As described above, if an aspherical surface is used, it is preferable that the following conditions be fulfilled. First, where an aspherical surface is provided on the lens surface of the plastic lens element of the first lens unit, it is preferable that Condition (15) below be fulfilled.

−1.10<(X−X _{0})/{C _{0}(N′−N)φ1}<−0.10 (15)

[0189]
where

[0190]
C_{0 }represents the curvature of the reference spherical surface of the aspherical surface;

[0191]
N represents the refractive index of the imageside medium of the aspherical surface for the d line;

[0192]
N′ represents the refractive index of the objectside medium of the aspherical surface for the d line;

[0193]
X represents the deviation of the aspherical surface along the optical axis at the height in a direction perpendicular to the optical axis (the direction pointing to the object side is negative);

[0194]
X_{0 }represents the deviation of the reference spherical surface of the aspherical surface along the optical axis at the height in a direction perpendicular to the optical axis (the direction pointing to the object side is negative); and

[0195]
f1 represents the focal length of the first lens unit.

[0196]
If the value of Condition (15) is equal to or less than its lower limit, positive distortion becomes unduly large on the wideangle side, in particular, in a closeshooting condition, and simultaneously the inclination of the image plane toward the over side becomes unduly large. In contrast, if the value of Condition (15) is equal to or greater than its upper limit, it is impossible to make efficient use of the aspherical surface, which makes the use of an aspherical surface meaningless. As a result, the negative distortion on the wideangle side, in particular, in a closeshooting condition, and the inclination of the image plane toward the under side are undercorrected. Note that, in a case where the first lens unit includes a plurality of aspherical surfaces, at least one of those aspherical surfaces needs to fulfill Condition (15) above; that is, the other aspherical surfaces do not necessarily have to fulfill Condition (15) above, if that is advantageous for the correction of other aberrations.

[0197]
In a case where an aspherical surface is provided on the lens surface of the plastic lens element of the second lens unit, it is preferable that Condition (16) below be fulfilled.

−0.35<(X−X _{0})/{C _{0}(N′−N)f2}<−0.03 (16)

[0198]
where

[0199]
f2 represents the focal length of the second lens unit.

[0200]
Condition (16) assumes that the aspherical surface is so shaped as to weaken the positive optical power of the second lens unit. Fulfillment of Condition (16) makes it possible to achieve proper correction of spherical aberration, in particular. If the value of Condition (16) is equal to or less than its lower limit, in particular, spherical aberration appears notably on the over side at the telephoto end. In contrast, if the value of Condition (16) is equal to or greater than its upper limit, it is impossible to make efficient use of the aspherical surface, which makes the use of an aspherical surface meaningless. As a result, spherical aberration is undercorrected on the telephoto side, in particular. Note that, in a case where the second lens unit includes a plurality of aspherical surfaces, at least one of those aspherical surfaces needs to fulfill Condition (16) above; that is, the other aspherical surfaces do not necessarily have to fulfill Condition (16) above, if that is advantageous for the correction of other aberrations.

[0201]
In a case where an aspherical surface is provided on the lens surface of the plastic lens element of the third lens unit, it is preferable that Condition (17) below be fulfilled.

−0.70<(X−X _{0})/{C _{0}(N′−N)f3}<−0.01 (17)

[0202]
where

[0203]
f3 represents the focal length of the third lens unit.

[0204]
Condition (17) assumes that the aspherical surface is so shaped as to weaken the positive optical power of the third lens unit. Fulfillment of Condition (17) makes it possible to achieve proper correction of spherical aberration and the coma aberration in marginal rays. If the value of Condition (17) is equal to or less than its lower limit, spherical aberration appears notably on the over side, and simultaneously the coma aberration in marginal rays becomes unduly large. In contrast, if the value of Condition (17) is equal to or greater than its upper limit, it is impossible to make efficient use of the aspherical surface, which makes the use of an aspherical surface meaningless. As a result, spherical aberration and the coma aberration in marginal rays are undercorrected. Note that, in a case where the third lens unit includes a plurality of aspherical surfaces, at least one of those aspherical surfaces needs to fulfill Condition (17) above; that is, the other aspherical surfaces do not necessarily have to fulfill Condition (17) above, if that is advantageous for the correction of other aberrations.

[0205]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (18) below.

0.20<φ1/φW<0.70 (18)

[0206]
Condition (18) defines, in the form of the optical power of the first lens unit, the condition to be fulfilled to achieve proper correction of aberrations and keep the size of the zoom lens system appropriate. If the value of Condition (18) is equal to or less than its lower limit, the optical power of the first lens unit is so weak that aberrations can be corrected properly, but simultaneously the total length, as well as the diameter of the frontend lens unit, of the zoom lens system becomes unduly large. In contrast, if the value of Condition (18) is equal to or greater than its upper limit, the optical power of the first lens unit is so strong that aberrations become unduly large, in particular, the inclination of the image plane toward the over side becomes unduly large, and simultaneously barrelshaped distortion becomes unduly large on the wideangle side. In this case, the use of a plastic lens element, which offers a relatively low refractive index and a strictly restricted range of dispersion, makes it difficult to correct aberrations properly and thus requires more lens elements in the zoom lens system.

[0207]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (19) below.

0.25<φ2/φW<0.75 (19)

[0208]
Condition (19) defines, in the form of the optical power of the second lens unit, the condition to be fulfilled to achieve proper correction of aberrations and keep the size of the zoom lens system appropriate. If the value of Condition (19) is equal to or less than its lower limit, the optical power of the second lens unit is so weak that aberrations can be corrected properly, but simultaneously the total length, as well as the diameter of the frontend lens unit, of the zoom lens system becomes unduly large. In contrast, if the value of Condition (19) is equal to or greater than its upper limit, the optical power of the second lens unit is so strong that aberrations become unduly large, in particular, spherical aberration appears notably on the under side. In this case, the use of a plastic lens element, which offers a relatively low refractive index and a strictly restricted range of dispersion, makes it difficult to correct aberrations properly and thus requires more lens elements in the zoom lens system.

[0209]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (20) below.

0.1<φ3/φW<0.60 (20)

[0210]
Condition (20) defines, in the form of the optical power of the third lens unit, the condition to be fulfilled to achieve proper correction of aberrations and keep the size of the zoom lens system appropriate. If the value of Condition (20) is equal to or less than its lower limit, the optical power of the third lens unit is so weak that aberrations can be corrected properly, but simultaneously the total length, as well as the diameter of the frontend lens unit, of the zoom lens system becomes unduly large. In contrast, if the value of Condition (20) is equal to or greater than its upper limit, the optical power of the third lens unit is so strong that aberrations become unduly large, in particular, spherical aberration appears notably on the under side. In this case, the use of a plastic lens element, which offers a relatively low refractive index and a strictly restricted range of dispersion, makes it difficult to correct aberrations properly and thus requires more lens elements in the zoom lens system.

[0211]
Moreover, if the values of Conditions (18) to (20) are equal to or greater than their upper limits, the optical power of the plastic lens element tends to be unduly strong. Thus, it is preferable that Conditions (11) and (18); (12) and (19); and (13) and (20) be fulfilled at the same time, respectively.

[0212]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (21) below.

−1.4<φPi/φW×hi<1.4 (21)

[0213]
where

[0214]
φPi represents the optical power of the ith plastic lens element; and

[0215]
hi represents the height of incidence at which a paraxial ray enters the objectside surface of the ith plastic lens element at the telephoto end, assuming that the initial values of the converted inclination al and the height h1, for paraxial tracing, are 0 and 1, respectively.

[0216]
Condition (21) defines, in the form of the sum of the degrees in which the individual plastic lens elements, by their temperature variation, affect the back focal distance, the condition to be fulfilled to suppress variation in the back focal distance resulting from temperature variation. When a plurality of plastic lens elements are used, it is preferable that positivelypowered and negativelypowered lens elements be combined in such a way that the degree in which they affect the back focal distance are canceled out by one another. If the value of Condition (21) is equal to or less than its lower limit, the variation in the back focal distance caused by temperature variation in the negativelypowered plastic lens element becomes unduly great. In contrast, if the value of Condition (21) is equal to or greater than its upper limit, the variation in the back focal distance caused by temperature variation in the positivelypowered plastic lens element becomes unduly great. Thus, in either case, the zoom lens system needs to be provided with a mechanism that corrects the back focal distance in accordance with temperature variation.

[0217]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (22) below.

0.5<log(β2T/β2W)/log Z<2.2 (22)

[0218]
where

[0219]
β2W represents the lateral magnification of the second lens unit at the wideangle end;

[0220]
β2T represents the lateral magnification of the second lens unit at the telephoto end;

[0221]
Z represents the zoom ratio; and

[0222]
log represents a natural logarithm (since the condition defines a proportion, the base does not matter).

[0223]
In a zoom lens system of the types like those of the present invention, the responsibility of the second lens unit for zooming is heavier than that of any other lens unit. The heavier the responsibility for zooming, the larger the aberrations that accompany zooming. Thus, in order to achieve proper correction of aberrations, it is preferable to distribute the responsibility for zooming among a plurality of lens units. Condition (22) defines the responsibility for zooming of the second lens unit, to which the heaviest responsibility for zooming is distributed in a zoom lens system of the types like those of the present invention.

[0224]
If the value of Condition (22) is equal to or less than its lower limit, the responsibility of the second lens unit for zooming is so light that the aberrations occurring in the second lens unit can be corrected properly. This, however, affects the responsibility of the other lens units for correcting aberrations, and thus requires more lens elements in those other lens units, with the result that the entire optical system needs to have an unduly large size. In contrast, if the value of Condition (22) is equal to or greater than its upper limit, the responsibility of the second lens unit for zooming is so heavy that spherical aberration varies too greatly with zooming, in particular.

[0225]
It is preferable that the zoom lens systems of the embodiments fulfill Condition (23) below.

−1.2<log(β3T/β3W)/log Z<0.5 (23)

[0226]
where

[0227]
β3W represents the lateral magnification of the third lens unit at the wideangle end; and

[0228]
β3T represents the lateral magnification of the third lens unit at the telephoto end.

[0229]
Condition (23) defines the responsibility of the third lens unit for zooming. If the value of Condition (23) is negative, the third lens unit reduces its magnification during zooming. This is disadvantageous from the viewpoint of zooming. In this case, however, by moving the third lens unit during zooming, it is possible to correct the aberrations occurring in the other lens units during zooming. If the value of Condition (23) is equal to or less than its lower limit, the third lens unit reduces its magnification at an unduly high rate during zooming, and thus the resulting loss in magnification needs to be compensated by the other lens units. This requires an unduly large number of lens elements in those other lens units and thus makes the entire optical system unduly long. In contrast, if the value of Condition (23) is equal to or greater than its upper limit, the responsibility of the third lens unit for zooming is so heavy that spherical aberration and coma aberration vary too greatly with zooming.

[0230]
Moreover, it is preferable that the zoom lens systems of the embodiments fulfill Condition (24) below.

−0.75<log(β3T/B3W)/log(β2T/β2W)<0.65 (24)

[0231]
Condition (24) defines the preferable ratio of the responsibility of the second lens unit for zooming to the responsibility of the third lens unit for zooming. If the value of Condition (24) is equal to or less than its lower limit, the third lens unit reduces its magnification, and thus the responsibility of the second lens unit for zooming is excessively heavy. As a result, spherical aberration varies too greatly with zooming. In contrast, if the value of Condition (24) is equal to or greater than its upper limit, the responsibility of the third lens unit for zooming is so heavy that spherical aberration and coma aberration vary too greatly with zooming.

[0232]
Hereinafter, examples of zoom lens systems embodying the present invention will be presented with reference to their construction data, graphic representations of aberrations, and other data. Tables 1 to 5 list the construction data of Examples 1 to 5, which respectively correspond to the first to fifth embodiments described above and have lens arrangements as shown in FIGS. 1 to 5. Tables 6 to 15 list the construction data of Examples 6 to 15, which respectively correspond to the sixth to fifteenth embodiments described above and have lens arrangements as shown in FIGS. 11 to 19 and 29.

[0233]
In the construction data of each example, ri (i =1, 2, 3, . . . ) represents the ith surface counted from the object side and its radius of curvature, di (i=1, 2, 3, . . . ) represents the ith axial distance counted from the object side, and Ni (i=1, 2, 3, . . . ) and ni (i=1, 2, 3, . . . ) respectively represent the refractive index for the d line and the Abbe number of the ith lens element counted from the object side. The values listed for the focal length f and the F number FNO of the, entire zoom lens system in Examples 1 to 5; the distance between the first and second lens units; and the distance between the second lens unit and the lowpass filter LPF are the values at, from left, the wideangle end (W), the middlefocallength position (M), and the telephoto end (T).

[0234]
Moreover, the values listed for the focal length f and the F number FNO of the entire zoom lens system in Examples 6 to 15; the distance between the first and second lens units; the distance between the second and third lens units; and the distance between the third lens unit and the lowpass filter LPF are the values at, from left, the wideangle end (W), the middlefocallength position (M), and the telephoto end (T). Note that, in all of Examples, a surface whose radius of curvature ri is marked with an asterisk (*) is an aspherical surface, whose surface shape is defined by the following formulae.

X=X _{0} +ΣSA _{i} Y ^{i} (a)

X _{0} =CY ^{2}/{1+(1−εC ^{2} Y ^{2})^{½}} (b)

[0235]
where

[0236]
X represents the displacement from the reference surface in the optical axis direction;

[0237]
Y represents the height in a direction perpendicular to the optical axis;

[0238]
C represents the paraxial curvature;

[0239]
ε represents the quadric surface parameter; and

[0240]
A_{i }represents the aspherical coefficient of the ith order.

[0241]
[0241]FIGS. 6A to 6I, 7A to 7I, 8A to 8I, 9A to 9I, and 10A to 10I show the aberrations observed in the infinitedistance shooting condition in Examples 1 to 5, respectively. Of these diagrams, FIGS. 6A to 6C, 7A to 7C, 8A to 8C, 9A to 9C, and 10A to 10C show the aberrations observed at the wideangle end [W]; FIGS. 6D to 6F, 7D to 7F, 8D to 8F, 9D to 9F, and 10D to 10F show the aberrations observed at the middle focal length [M]; and FIGS. 6G to 6I, 7G to 7I, 8G to 8I, 9G to 9I, and 10G to 10I show the aberrations observed at the telephoto end [T]. In the spherical aberration diagrams, the solid line (d) represents the d line and the broken line (SC) represents the sine condition. In the astigmatism diagrams, the solid line (DS) and the broken line (DM) represent the astigmatism on the sagittal plane and on the meridional plane, respectively. In Examples 1 to 5, Conditions (1) to (5) mentioned above are fulfilled.

[0242]
[0242]FIGS. 20A to 20I, 21A to 21I, 22A to 22I, 23A to 23I, 24A to 24I, 25A to 25I, 26A to 26I, 27A to 27I, 28A to 28I, and 30A to 30I show the aberrations observed in the infinitedistance shooting condition in Examples 6 to 15, respectively. Of these diagrams, FIGS. 20A to 20C, 21A to 21C, 22A to 22C, 23A to 23C, 24A to 24C, 25A to 25C, 26A to 26C, 27A to 27C, 28A to 28C, and 30A to 30C show the aberrations observed at the wideangle end [W]; FIGS. 20D to 20F, 21D to 21F, 22D to 22F, 23D to 23F, 24D to 24F, 25D to 25F, 26D to 26F, 27D to 27F, 28D to 28F, and 30D and 30F show the aberrations observed at the middle focal length [M]; and FIGS. 20G to 20I, 21G to 21I, 22G to 22I, 23G to 23I, 24G to 24I, 25G to 25I, 26G to 26I, 27G to 27I, 28G to 28I, and 30G to 30I show the aberrations observed at the telephoto end [T]. In the spherical aberration diagrams, the solid line (d) represents the d line and the broken line (SC) represents the sine condition. In the astigmatism diagrams, the solid line (DS) and the broken line (DM) represent the astigmatism on the sagittal plane and on the meridional plane, respectively. In Examples 6 to 15, the conditions mentioned above are fulfilled.

[0243]
The variables used in Conditions (1) to (5) in Examples 1 to 5 are listed in Table 16.

[0244]
The values corresponding to Conditions (1) to (5) in Examples 1 to 5 are listed in Table 17.

[0245]
The values corresponding to Conditions (9) to (13) and (18) to (24) in Examples 6 to 15 are listed in Table 18.

[0246]
The values corresponding to Conditions (7) and (8) to be fulfilled by the aspherical surface in Examples 1 to 5 are listed in Table 19. Note that Y represents the maximum height of the optical path on the aspherical surface.

[0247]
The values corresponding to Conditions (15) to (17) to be fulfilled by the aspherical surface in Examples 6 to 15 are listed in Table 20. Note that Y represents the maximum height of the optical path on the aspherical surface.
TABLE 1 


Construction Data of Example 1 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.96 mm 3.24 mm 3.6 mm (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 11.333  d1 = 0.779  N1 = 1.85000  ν1 = 40.04 
r2 = 6.007  d2 = 1.940 
r3* = 17.418  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 6.396  d4 = 1.895 
r5 = 7.432  d5 = 1.763  N3 = 1.84666  ν3 = 23.82 
r6 = 10.246  d6 = 13.009 6.374 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.989  d8 = 1.829  N4 = 1.75450  ν4 = 51.57 
r9 = −125.715  d9 = 1.268 
r10 = −12.153  d10 = 0.635  N5 = 1.75000  ν5 = 25.14 
r11 = 9.023  d11 = 0.447 
r12* = 13.010  d12 = 2.293  N6 = 1.52510  ν6 = 56.38 
r13 = −6.778  d13 = 1.000 2.559 4.786 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.21447 × 10^{−3} 
A6 = 0.50169 × 10^{−5} 
A8 = 0.14584 × 10^{−6} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.20572 × 10^{−2} 
A6 = −0.42994 × 10^{−5} 
A8 = −0.32617 × 10^{−5} 


[0248]
[0248]
TABLE 2 


Construction Data of Example 2 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.96 mm 3.24 mm 3.6 mm (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 14.260  d1 = 0.650  N1 = 1.53359  ν1 = 64.66 
r2 = 6.334  d2 = 2.341 
r3* = 24.115  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 5.871  d4 = 1.561 
r5 = 6.894  d5 = 2.091  N3 = 1.58340  ν3 = 30.23 
r6 = 13.124  d6 = 14.102 6.837 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.164  d8 = 2.262  N4 = 1.61555  ν4 = 57.97 
r9 = −9.593  d9 = 0.479 
r10* = −5.666  d10 = 1.472  N5 = 1.58340  ν5 = 30.23 
r11 = 9.833  d11 = 0.604 
r12* = 22.822  d12 = 1.943  N6 = 1.52510  ν6 = 56.38 
r13 = −8.802  d13 = 1.000 2.422 4.454 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.16907 × 10^{−3} 
A6 = 0.35415 × 10^{−5} 
A8 = 0.80238 × 10^{−7} 
[Aspherical Coefficients of 10th Surface (r10)] 
ε = 0.10000 × 10 
A4 = 0.79103 × 10^{−3} 
A6 = 0.24186 × 10^{−4} 
A8 = 0.30525 × 10^{−5} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.25573 × 10^{−2} 
A6 = −0.15034 × 10^{−5} 
A8 = −0.18614 × 10^{−4} 


[0249]
[0249]
TABLE 3 


Construction Data of Example 3 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.96 mm 3.24 mm 3.6 mm (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 11.551  d1 = 1.213  N1 = 1.75450  ν1 = 51.57 
r2 = 6.152  d2 = 2.230 
r3* = 21.819  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 6.113  d4 = 1.835 
r5 = 7.256  d5 = 2.216  N3 = 1.69961  ν3 = 26.60 
r6 = 11.287  d6 = 13.126 6.424 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.207  d8 = 2.259  N4 = 1.61213  ν4 = 58.19 
r9 = −9.240  d9 = 0.467 
r10* = −5.774  d10 = 1.430  N5 = 1.58340  ν5 = 30.23 
r11 = 9.548  d11 = 0.601 
r12* = 22.409  d12 = 1.984  N6 = 1.52510  ν6 = 56.38 
r13 = −8.485  d13 = 1.000 2.495 4.630 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.19262 × 10^{−3} 
A6 = 0.34894 × 10^{−5} 
A8 = 0.12515 × 10^{−6} 
[Aspherical Coefficients of 10th Surface (r10)] 
ε = 0.10000 × 10 
A4 = 0.43913 × 10^{−3} 
A6 = 0.33312 × 10^{−4} 
A8 = 0.24577 × 10^{−5} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.22305 × 10^{−2} 
A6 = −0.11486 × 10^{−4} 
A8 = −0.15332 × 10^{−4} 


[0250]
[0250]
TABLE 4 


Construction Data of Example 4 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.9 mm 3.25 mm 3.6 mm (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 13.912  d1 = 1.500  N1 = 1.75450  ν1 = 51.57 
r2 = 6.626  d2 = 2.111 
r3 = 25.350  d3 = 1.000  N2 = 1.75450  ν2 = 51.57 
r4 = 7.001  d4 = 0.893 
r5* = 14.283  d5 = 4.843  N3 = 1.58340  ν3 = 30.23 
r6* = −45.283  d6 = 15.765 7.542 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.964  d8 = 4.216  N4 = 1.65656  ν4 = 55.63 
r9 = −7.373  d9 = 0.208 
r10 = −6.131  d10 = 1.300  N5 = 1.58340  ν5 = 30.23 
r11* = 9.768  d11 = 2.852 
r12 = −77.516  d12 = 1.708  N6 = 1.52200  ν6 = 65.93 
r13 = −8.818  d13 = 1.000 2.668 5.052 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 5th Surface (r5)] 
ε = 0.10000 × 10 
A4 = 0.90348 × 10^{−4} 
A6 = 0.13458 × 10^{−5} 
A8 = 0.14476 × 10^{−6} 
[Aspherical Coefficients of 6th Surface (r6)] 
ε = 0.10000 × 10 
A4 = −0.32219 × 10^{−3} 
A6 = −0.25483 × 10^{−5} 
A8 = −0.86784 × 10^{−7} 
[Aspherical Coefficients of 11th Surface (r11)] 
ε = 0.10000 × 10 
A4 = 0.20489 × 10^{−2} 
A6 = 0.27321 × 10^{−4} 
A8 = 0.40971 × 10^{−5} 
A10 = −0.20451 × 10^{−6} 


[0251]
[0251]
TABLE 5 


Construction Data of Example 5 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 3.18 mm 3.55 mm 4.08 mm (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 10.456  d1= 2.128  N1 = 1.85000  ν1 = 40.04 
r2 = 3.870  d2 = 2.166 
r3* = 16.226  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 6.827  d4 = 1.322 
r5 = 8.144  d5 = 1.514  N3 = 1.83350  ν3 = 21.00 
r6 = 13.791  d6 = 8.994 4.674 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.950  d8 = 1.897  N4 = 1.74989  ν4 = 51.73 
r9 = −43.969  d9 = 1.242 
r10 = −11.144  d10 = 0.753  N5 = 1.84714  ν5 = 25.28 
r11 = 10.245  d11 = 0.400 
r12* = 12.590  d12 = 2.297  N6 = 1.52510  ν6 = 56.38 
r13 = −6.634  d13 = 1.000 3.314 6.620 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.13045 × 10^{−2} 
A6 = 0.11643 × 10^{−4} 
A8 = 0.51406 × 10^{−5} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.22747 × 10^{−2} 
A6 = −0.36716 × 10^{−5} 
A8 = −0.32887 × 10^{−6} 


[0252]
[0252]
TABLE 6 


Construction Data of Example 6 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.74 3.11 3.60 (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 13.380  d1 = 0.650  N1 = 1.75450  ν1 = 51.57 
r2 = 5.890  d2 = 1.499 
r3* = 12.328  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 5.632  d4 = 1.632 
r5 = 7.068  d5 = 1.753  N3 = 1.84777  ν3 = 27.54 
r6 = 10.246  d6 = 10.406 5.264 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 5.643  d8 = 1.901  N4 = 1.79073  ν4 = 46.15 
r9 = −74.805  d9 = 0.921 
r10 = −12.842  d10 = 0.600  N5 = 1.72145  ν5 = 25.50 
r11 = 5.928  d11 = 0.400 
r12* = 11.144  d12 = 2.170  N6 = 1.52510  ν6 = 56.38 
r13 = −9.099  d13 = 1.000 3.519 7.154 
r14 = 11.107  d14 = 3.164  N7 = 1.51680  ν7 = 64.20 
r15 = 56.703  d15 = 0.796 
r16 = ∞  d16 = 3.400  N8 = 1.54426  ν8 = 69.60 
r17 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.38905 × 10^{−3} 
A6 = 0.24379 × 10^{−5} 
A8 = 0.38282 × 10^{−6} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.13386 × 10^{−2} 
A6 = −0.11975 × 10^{−4} 
A8 = −0.53773 × 10^{−5} 


[0253]
[0253]
TABLE 7 


Construction Data of Example 7 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.73 3.10 3.60 (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 14.718  d1 = 0.650  N1 = 1.75450  ν1 = 51.57 
r2 = 6.639  d2 = 1.307 
r3* = 11.594  d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 5.294  d4 = 1.465 
r5 = 6.937  d5 = 1.858  N3 = 1.84759  ν3 = 26.85 
r6 = 10.034  d6 = 10.621 5.340 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 6.969  d8 = 2.905  N4 = 1.85000  ν4 = 40.04 
r9 = −11.743  d9 = 0.210 
r10 = −8.399  d10 = 1.855  N5 = 1.72131  ν5 = 25.51 
r11 = 5.522  d11 = 0.400 
r12 = 11.032  d12 = 2.012  N6 = 1.75450  ν6 = 51.57 
r13 = −21.657  d13 = 1.000 3.398 6.919 
r14* = 8.536  d14 = 3.241  N7 = 1.52510  ν7 = 56.38 
r15 = 29.006  d15 = 0.676 
r16 = ∞  d16 = 3.400  N8 = 1.54426  ν8 = 69.60 
r17 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.35342 × 10^{−3} 
A6 = 0.71258 × 10^{−6} 
A8 = 0.33647 × 10^{−6} 
[Aspherical Coefficients of 14th Surface (r14)] 
ε = 0.10000 × 10 
A4 = −0.23473 × 10^{−3} 
A6 = 0.43912 × 10^{−5} 
A8 = 0.10409 × 10^{−6} 


[0254]
[0254]
TABLE 8 


Construction Data of Example 8 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.75 3.10 3.60 (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1* = 14.652  d1 = 1.200  N1 = 1.58340  ν1 = 30.23 
r2 = 8.289  d2 = 1.623 
r3 = 26.068  d3 = 0.900  N2 = 1.79271  ν2 = 45.90 
r4 = 5.496  d4 = 1.179 
r5 = 7.356  d5 = 1.921  N3 = 1.84666  ν3 = 23.82 
r6 = 15.373  d6 = 10.224 5.176 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 7.124  d8 = 3.411  N4 = 1.85000  ν4 = 40.04 
r9 = −11.538  d9 = 0.154 
r10 = −8.339  d10 = 1.713  N5 = 1.72418  ν5 = 25.37 
r11 = 5.686  d11 = 0.401 
r12 = 10.731  d12 = 2.078  N6 = 1.75450  ν6 = 51.57 
r13 = −18.326  d13 = 1.000 3.307 6.708 
r14* = 8.148  d14 = 3.002  N7 = 1.52510  ν7 = 56.38 
r15 = 16.995  d15 = 0.795 
r16 = ∞  d16 = 3.400  N8 = 1.54426  ν8 = 69.60 
r17 = ∞ 
[Aspherical Coefficients of 1st Surface (r1)] 
ε = 0.10000 × 10 
A4 = 0.15951 × 10^{−3} 
A6 = 0.14779 × 10^{−6} 
A8 = 0.56026 × 10^{−7} 
[Aspherical Coefficients of 14th Surface (r14)] 
ε = 0.10000 × 10 
A4 = −0.27776 × 10^{−3} 
A6 = 0.23365 × 10^{−5} 
A8 = 0.19731 × 10^{−6} 


[0255]
[0255]
TABLE 9 


Construction Data of Example 9 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of tile Entire Optical System) 
FNO = 2.73 3.10 3.60 (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 52.355  d1 = 1.100  N1 = 1.72677  ν1 = 52.55 
r2 = 6.927  d2 = 3.324 
r3* = 23.902  d3 = 1.940  N2 = 1.58340  ν2 = 30.23 
r4 = −100.448  d4 = 14.827 7.138 1.500 
r5 = ∞ (Aperture Stop)  d5 = 1.500   
r6 = 5.036  d6 = 3.339  N3 = 1.77742  ν3 = 47.95 
r7 = −12.586  d7 = 0.234 
r8 = −10.396  d8 = 0.800  N4 = 1.79850  ν4 = 22.60 
r9 = 16.524  d9 = 0.740 
r10 = −7.142  d10 = 1.200  N5 = 1.58340  ν5 = 30.23 
r11* = −26.834  d11 = 1.000 2.921 5.663 
r12 = 15.086  d12 = 2.096  N6 = 1.48749  ν6 = 70.44 
r13 = −14.941  d13 = 0.500 
r14 = ∞  d14 = 3.400  N7 = 1.54426  ν7 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.24908 × 10^{−3} 
A6 = −0.62198 × 10^{−7} 
A8 = 0.10295 × 10^{−6} 
[Aspherical Coefficients of 11th Surface (r11)] 
ε = 0.10000 × 10 
A4 = 0.39625 × 10^{−2} 
A6 = 0.16585 × 10^{−3} 
A8 = 0.13563 × 10^{−4} 


[0256]
[0256]
TABLE 10 


Construction Data of Example 10 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.75 3.11 3.60 (F numbers) 
Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1* = 17.928  d1 = 1.200  N1 = 1.58340  ν1 = 30.23 
r2 = 9.608  d2 = 1.325 
r3 = 19.410  d3 = 0.900  N2 = 1.80280  ν2 = 44.68 
r4 = 5.204  d4 = 1.288 
r5 = 7.294  d5 = 1.940  N3 = 1.84666  ν3 = 23.82 
r6 = 14.586  d6 = 10.102 5.348 1.500 
r7 = ∞ (Aperture Stop)  d7 = 1.500   
r8 = 6.594  d8 = 4.206  N4 = 1.81063  ν4 = 43.80 
r9 = −10.411  d9 = 0.208 
r10 = −7.270  d10 = 0.600  N5= 1.70098  ν5 = 26.53 
r11 = 5.447  d11 = 0.504 
r12 = 10.684  d12 = 2.062  N6 = 1.75450  ν6 = 51.57 
r13 = −20.769  d13 = 1.000 3.880 6.996 
r14* = 6.351  d14 = 2.209  N7 = 1.52510  ν7 = 56.38 
r15 = 12.184  d15 = 1.055 0.800 1.067 
r16 = ∞  d16 = 3.400  N8 = 1.54426  ν8 = 69.60 
r17 = ∞ 
[Aspherical Coefficients of 1st Surface (r1)] 
ε = 0.10000 × 10 
A4 = 0.19398 × 10^{−3} 
A6 = 0.47895 × 10^{−6} 
A8 = 0.46069 × 10^{−7} 
[Aspherical Coefficients of 14th Surface (r14)] 
ε = 0.10000 × 10 
A4 = −0.37579 × 10^{−3} 
A6 = −0.11089 × 10^{−5} 
A8 = 0.87379 × 10^{−7} 


[0257]
[0257]
TABLE 11 


Construction Data of Example 11 
f = 5.4 mm 7.5 mm 10.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.97 3.27 3.60 (F numbers) 

Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = −112.214 
 d1 = 1.200  N1 = 1.63347  ν1 = 56.87 
r2 = 7.682 
 d2 = 1.473 
r3* = 17.799 
 d3 = 2.175  N2 = 1.58340  ν2 = 30.23 
r4 = 274.206 
 d4 = 16.482  8.078 1.500 
r5 = ∞(Aperture Stop) 
 d5 = 1.500 
r6 = 5.066 
 d6 = 2.164  N3 = 1.84746  ν4 = 40.25 
r7 = −15.255 
 d7 = 0.208 
r8 = −13.752 
 d8 = 0.800  N4 = 1.79850  ν5 = 22.60 
r9 = 7.640 
 d9 = 0.352 
r10* = 8.419 
 d10 = 1.200  N5 = 1.58340  ν6 = 30.23 
r11 = 4.700 
 d11 = 1.000  1.802 2.808 
r12 = 40.534 
 d12 = 2.262  N6 = 1.51838  ν7 = 66.35 
r13 * = −6.756 
 d13 = 1.131  2.007 3.472 
r14 = ∞ 
 d14 = 3.400  N7 = 1.54426  ν8 = 69.60 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.24372 × 10^{−3} 
A6 = −0.10309 × 10^{−6} 
A8 = 0.84837 × 10^{−7} 
[Aspherical Coefficients of 10th Surface (r10)] 
ε = 0.10000 × 10 
A4 = −0.35107 × 10^{−2} 
A6 = −0.17279 × 10^{−3} 
A8 = −0.80824 × 10^{−5} 
[Aspherical Coefficients of 13th Surface (r13)] 
ε = 0.10000 × 10 
A4 = 0.11613 × 10^{−3} 
A6 = −0.34635 × 10^{−4} 
A8 = 0.66386 × 10^{−6} 


[0258]
[0258]
TABLE 12 


Construction Data of Example 12 
f = 5.4 mm 8.0 mm 12.0 mm (Focal Length of the Entire Optical System) 
FNO = 2.55 2.95 3.60 (F numbers) 

Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 64.355 
 d1 = 0.650  N1 = 1.48749  ν1 = 70.44 
r2 = 9.616 
 d2 = 1.136 
r3* = 15.072 
 d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 6.352 
 d4 = 1.939 
r5 = 8.584 
 d5 = 2.060  N3 = 1.84877  ν3 = 32.01 
r6 = 12.547 
 d6 = 15.531  7.207 1.500 
r7 = ∞Aperture Stop) 
 d7 = 1.500 
r8 = 5.666 
 d8 = 3.346  N4 = 1.75450  ν4 = 51.57 
r9 = −8.847 
 d9 = 0.100 
r10 = −7.390 
 d10 = 0.600  N5 = 1.58340  ν5 = 30.23 
r11 = 4.818 
 d11 = 0.400 
r12* = 6.048 
 d12 = 2.459  N6 = 1.52510  ν6 = 56.38 
r13 = 9.906 
 d13 = 1.000  3.334 6.995 
r14 = 11.941 
 d14 = 1.979  N7 = 1.52510  ν7 = 56.38 
r15* = −29.235 
 d15 = 0.500 
r16 = ∞ 
 d16 = 3.400  N8 = 1.54426  ν8 = 69.60 
r17 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.17978 × 10^{−3} 
A6 = −0.30828 × 10^{−6} 
A8 = 0.71904 × 10^{−7} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε 0.10000 × 10 
A4 = −0.18066 × 10^{−2} 
A6 = −0.54257 × 10^{−4} 
A8 = −0.76508 × 10^{−5} 
[Aspherical Coefficients of 15th Surface (r15)] 
ε = 0.10000 × 10 
A4 = 0.29756 × 10^{−3} 
A6 = −0.62953 × 10^{−5} 
A8 = −0.77785 × 10^{−7} 


[0259]
[0259]
TABLE 13 


Construction Data of Example 13 
f = 5.4 mm 8.8 mm 14.0mm (Focal Length of the Entire Optical System) 
FNO = 2.34 2.84 3.60 (F numbers) 

Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 25.623 
 d1 = 0.650  N1 = 1.48749  ν1 = 70.44 
r2 = 9.290 
 d2 = 1.626 
r3* = 19.577 
 d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 5.973 
 d4 = 2.273 
r5 = 7.949 
 d5 = 2.008  N3 = 1.84807  ν3 = 28.75 
r6 = 10.541 
 d6 = 16.801  7.154 1.500 
r7 = ∞(Aperture Stop) 
 d7 = 1.500 
r8 = 5.107 
 d8 = 2.743  N4 = 1.64626  ν4 = 56.17 
r9 = −9.178 
 d9 = 0.100 
r10 = −8.533 
 d10 = 0.600  N5 = 1.58340  ν5 = 30.23 
r11 = 7.962 
 d11 = 0.849 
r12* = 7.572 
 d12 = 1.401  N6 = 1.52510  ν6 = 56.38 
r13 = 8.290 
 d13 = 1.000  4.278 9.371 
r14* = 9.062 
 d14 = 1.423  N7 = 1.58340  ν7 = 30.23 
r15 = 6.924 
 d15 = 0.747 
r16 = 11.941 
 d16 = 1.979  N8 = 1.52510  ν8 = 56.38 
r17* = −29.488 
 d17 = 0.500 
r18 = ∞ 
 d18 = 3.400  N9 = 1.54426  ν9 = 69.60 
r19 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.16055 × 10^{−3} 
A6 = 0.48397 × 10^{−7} 
A8 = 0.67121 × 10^{−7} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.25048 × 10^{−2} 
A6 = −0.87701 × 10^{−4} 
A8 = −0.12082 × 10^{−4} 
[Aspherical Coefficients of 14th Surface (r14)] 
ε = 0.10000 × 10 
A4 = −0.52484 × 10^{31 3} 
A6 = 0.58442 × 10^{−5} 
A8 = 0.87159 × 10^{−8} 
[Aspherical Coefficients of 17th Surface (r17)] 
ε = 0.10000 × 10 
A4 = −0.91828 × 10^{−3} 
A6 = −0.59033 × 10^{−5} 
A8 = 0.27335 × 10^{−6} 


[0260]
[0260]
TABLE 14 


Construction Data of Example 14 
f = 5.4 mm 7.5 mm 13.5 mm (Focal Length of the Entire Optical System) 
FNO = 2.08 2.48 3.60 (F numbers) 

Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 14.018 
 d1 = 0.650  N1 = 1.74388  ν1 = 51.93 
r2 = 6.286 
 d2 = 1.790 
r3* = 17.191 
 d3 = 1.400  N2 = 1.52510  ν2 = 56.38 
r4 = 5.770 
 d4 = 0.907 
r5 = 6.726 
 d5 = 1.953  N3 = 1.84666  ν3 = 23.82 
r6 = 10.531 
 d6 = 9.731  5.843 1.500 
r7 = ∞(Aperture Stop) 
 d7 = 1.500 
r8 = 6.489 
 d8 = 1.774  N4 = 1.85000  ν4 = 40.04 
r9 = 52.968 
 d9 = 0.665 
r10 = −31.304 
 d10 = 0.600  N5 = 1.77185  ν5 = 23.46 
r11 = 6.642 
 d11 = 0.400 
r12* = 11.190 
 d12 = 2.101  N6 = 1.52510  ν6 = 56.38 
r13 = −9.334 
 d13 = 1.000  5.310 15.247 
r14 = −10.861 
 d14 = 1.200  N7 = 1.58340  ν7 = 30.23 
r15* = 16.708 
 d15 = 0.100 
r16 = 12.354 
 d16 = 2.934  N8 = 1.84353  ν8 = 40.59 
r17 = −10.876 
 d17 = 2.914  2.385 0.717 
r18 = ∞ 
 d18 = 3.400  N9 = 1.54426  ν9 = 69.60 
r19 = ∞ 
[Aspherical Coefficients of 3rd Surface (r3)] 
ε = 0.10000 × 10 
A4 = 0.28799 × 10^{−3} 
A6 = 0.40089 × 10^{−5} 
A8 = 0.14823 × 10^{−6} 
[Aspherical Coefficients of 12th Surface (r12)] 
ε = 0.10000 × 10 
A4 = −0.62816 × 10^{−3} 
A6 = −0.22891 × 10^{−4} 
A8 = 0.42945 × 10^{−6} 
[Aspherical Coefficients of 15th Surface (r15)] 
ε = 0.10000 × 10 
A4 = 0.60130 × 10^{−3} 
A6 = −0.42374 × 10^{−5} 
A8 = 0.11268 × 10^{−7} 


[0261]
[0261]
TABLE 15 


Construction Data of Example 15 
f = 5.4 mm 8.4 mm 15.6 mm (Focal Length of the Entire Optical System) 
FNO = 2.57 3.04 4.20 (F numbers) 

Radius of  Axial  Refractive  Abbe 
Curvature  Distance  Index (Nd)  Number (d) 

r1 = 34.564 
 d1 = 1.600  N1 = 1.52510  ν1 = 56.38 
r2 = 7.185 
 d2 = 3.500 
r3* = 10.666 
 d3 = 2.344  N2 = 1.75000  ν2 = 25.14 
r4 = 17.516 
 d4 = 22.572  11.179 1.713 
r5 = ∞ 
 d5 = 1.500 
r6 = 8.000 
 d6 = 2.941  N3 = 1.80420  ν3 = 46.50 
r7 = −8.598 
 d7 = 0.010  N4 = 1.51400  ν4 = 42.83 
r8 = −8.598 
 d8 = 0.600  N5 = 1.70055  ν5 = 30.11 
r9 = 8.182 
 d9 = 0.200 
r10* = 5.244 
 d10 = 3.249  N6 = 1.52510  ν6 = 56.38 
r11* = 6.000 
 d11 = 2.740  5.844 13.277 
r12 = 21.195 
 d12 = 2.000  N7 = 1.48749  ν7 = 70.44 
r13 = −16.672 
 d13 = 1.086 
r14 = ∞ 
 d14 = 3.400  N8 = 1.51680  ν8 = 64.20 
r15 = ∞ 
[Aspherical Coefficients of 3rd Surface (r1)] 
ε = 0.10000 × 10 
A4 = 0.43400 × 10^{−3} 
A6 = −0.55461 × 10^{−5} 
A8 = 0.27915 × 10^{−7} 
[Aspherical Coefficients of 12th Surface (r2)] 
ε = 0.10000 × 10 
A4 = 0.26861 × 10^{−3} 
A6 = 0.25040 × 10^{−5} 
A8 = 0.23353 × 10^{−6} 
[Aspherical Coefficients of 15th Surface (r10)] 
ε = 0.10000 × 10 
A4 = −0.30306 × 10^{−3} 
A6 = −0.13415 × 10^{−4} 
A8 = −0.19911 × 10^{−5} 
[Aspherical Coefficients of 15th Surface (r11] 
ε = 0.10000 × 10 
A4 = 0.19342 × 10^{−2} 
A6 = 0.59893 × 10^{−4} 
A8 = −0.42081 × 10^{−5} 


[0262]
[0262]
TABLE 16 


The variables used in Conditions (1) to (5) in Examples 1 to 5 


 φ1  φ2  φW   
Example 1  0.076171  0.102604  0.185185 
  φPi  hi  φPi/φW × hi  Sum 
Example 1  G2:  −0.04968  1.088763  −0.292107 
 G6:  0.11313  1.264821  0.7726821  0.480575 
 φ1  φ2 φW 
Example 2  0.069512  0.102665  0.185162 
  φPi  hi  φPi/φW × hi  Sum 
Example 2  G2:  −0.06587  1.090648  −0.387944 
 G3:  0.045137  1.299594  0.3167591 
 G5:  −0.16797  1.270288  −1.152222 
 G6:  0.080916  1.2079  0.5277862  −0.69562 
 φ1  φ2 φW 
Example 3  0.07421  0.104252  0.185186 
  φPi  hi  φPi/φW × hi  Sum 
Example 3  G2:  −0.05994  1.070319  −0.346422 
 G3:  −0.16771  1.288669  −1.167062 
 G5:  0.083429  1.23342  0.555676  −0.95781 
 φ1  φ2 
Example 4  0.070779  0.089085  0.185184 
  φPi  hi  φPi/φW × hi  Sum 
Example 4  G3:  0.05212  1.068396  0.3006979 
 G5:  −0.15954  1.348671  −1.161906  −0.86121 
 φ1  φ2  φW 
Example 5  0.115  0.104369  0.185185 
  φPi  hi  φPi/φW × hi  Sum 
Example 5  G2:  −0.04227  1.161585  −0.265113 
 G6:  0.11589  1.553375  0.9721086  0.706996 


[0263]
[0263]
TABLE 17 


The values corresponding to Conditions (1) to (5) in Examples 1 to 5 
 φ1/φ2  φ2/φW  φP/φ1  φP/φ2  ΕφPi/φW × hi 
 
Example 1  0.41  0.55  G2: 0.65  G6: 1.10  0.48 
Example 2  0.38  0.55  G2: 0.95  G5: 1.64  −0.70 
   G3: 0.65  G6: 0.79 
Example 3  0.40  0.56  G2: 0.81  G5: 1.61  −0.96 
   G6: 0.80 
Example 4  0.38  0.48  G3: 0.74  G5: 1.79  −0.86 
Example 5  0.62  0.56  G2: 0.37  G6: 1.11  0.71 


[0264]
[0264]
TABLE 18 


The values corresponding to Conditions (9) to 
(13) and (18) to (2φin Examples 6 to 15 


  φP/φW  φP/φ1  φP/φ2  φP/φ3  M3/M2 

Example 6  G2:  0.25  0.63    0.00 
 G6:  0.55   1.10 
Example 7  G2:  0.27  0.72    0.00 
 G7:  0.25   1.00 
Example 8  G1:  0.15  0.39    0.00 
 G7:  0.20   1.00 
Example 9  G2:  0.16  0.59    0.00 
 G5:  0.32   0.68 
Example 10  G1:  0.14  0.38    0.00 
 G7:  0.24   0.47  1.00 
Example 11  G2:  0.17  0.57   0.56 
 G5:  0.26   0.65 
Example 12  G2:  0.24  0.86   0.00 
 G5:  1.10   2.27 
 G6:  0.22   0.46 
 G7:  0.33    1.00 
Example 13  G2:  0.32  0.97    0.00 
 G5:  0.78   1.64 
 G6:  0.05   0.11 
 G7:  0.08    0.35 
 G8:  0.33    1.40 
Example 14  G2:  0.31271  0.79   −0.18 
 G6:  0.5375   1.19 
 G7:  0.48626    1.38 

  log(β2T/β2W)/logZ  log(β3T/β3W)/logZ 

Example 6  G2:  1.00  0.00 
Example 7  G2:  1.00  0.00 
Example 8  G1:  1.00  0.00 
Example 9  G2:  0.99  0.01 
Example 10  G1:  1.00  0.00 
Example 11  G2:  1.87  −0.87 
Example 12  G2:  0.99  0.01 
Example 13  G2:  1.00  0.00 
Example 14  G2:  0.75  0.25 

  log(β3T/β3W)/log(β2T/β2W) 

Example 6  G2:  0.00 
Example 7  G2:  0.00 
Example 8  G1:  0.00 
Example 9  G2:  0.01 
Example 10  G1:  0.00 
Example 11  G2:  −0.46 
Example 12  G2:  0.01 
Example 13  G2:  0.00 
Example 14  G2:  0.34 

  ∩P/ 0W × h  ΕφPi/φW × hi 

Example 6  G2:  −0.27 
 G6:  0.66  0.39 
Example 7  G2:  −0.28 
 G7:  0.17  −0.12 
Example 8  G1:  −0.15 
 G7:  0.14  −0.01 
Example 9  G2:  0.21 
 G5:  −0.30  −0.09 
Example 10  G1:  −0.14 
 G7:  0.16  0.02 
Example 11  G2:  0.19 
 G5:  −0.26  −0.08 
Example 12  G2:  −0.26 
 G5:  −1.20 
 G6:  0.23 
 G7:  0.16  −1.06 
Example 13  G2:  −0.33 
 G5:  −0.93 
 G6:  0.06 
 G7:  −0.04 
 G8:  0.14  −1.10 
Example 14  G2:  −0.34 
 G6:  0.68 
 G7:  −0.25  0.09 

  φ1/φW  φ2/φW  φ3/φW 

Example 6  G2:  0.40  0.50  0.21 
Example 7  G2:  0.37  0.50  0.25 
Example 8  G1:  0.40  0.52  0.20 
Example 9  G2:  0.27  0.47  0.34 
Example 10  G1:  0.38  0.51  0.24 
Example 11  G2:  0.29  0.40  0.48 
Example 12  G2:  0.29  0.48  0.33 
Example 13  G2:  0.33  0.47  0.23 
Example 14  G2:  0.39  0.45  0.35 

 Cp × (N′N)/φW  
  Object side  Image side 

Example 6  G2:  0.23  −0.50 
 G6:  0.25  0.31 
Example 7  G2:  0.25  −0.54 
 G7:  0.33  −0.10 
Example 8  G1:  0.22  −0.38 
 G7:  0.35  −0.17 
Example 9  G2:  0.13  0.031 
 G5:  −0.44  0.12 
Example 10  G1:  0.18  −0.33 
 G7:  0.45  −0.23 
Example 11  G2:  0.18  −0.01 
 G5:  0.37  −0.67 
Example 12  G2:  0.19  −0.45 
 G5:  −0.43  −0.65 
 G6:  0.47  −0.29 
 G7:  0.24  0.10 
Example 13  G2:  0.15  −0.48 
 G5:  −0.37  −0.40 
 G6:  0.37  −0.34 
 G7:  0.35  −0.46 
 G8:  0.24  0.10 
Example 14  G2:  0.17  −0.49 
 G6:  0.25  0.30 
 G7:  −0.29  −0.19 


[0265]
[0265]
TABLE 19 


The values corresponding to Conditions (7) and (8) in Examples 1 to 5 
 Example 1 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00037 
 0.40Y  −0.00634 
 0.60Y  −0.03585 
 0.80Y  −0.13341 
 1.00Y  −0.40394 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00037 
 0.40Y  −0.00598 
 0.60Y  −0.03057 
 0.80Y  −0.09885 
 1.00Y  −0.25219 
 
 Example 2 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00051 
 0.40Y  −0.00870 
 0.60Y  −0.04931 
 0.80Y  −0.18376 
 1.00Y  −0.55608 
 
 [10th Surface (r10)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  0.00005 
 0.40Y  0.00077 
 0.60Y  0.00408 
 0.80Y  0.01399 
 1.00Y  0.03852 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00072 
 0.40Y  −0.01169 
 0.60Y  −0.06096 
 0.80Y  −0.20787 
 1.00Y  −0.58532 
 
 Example 3 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00050 
 0.40Y  −0.00851 
 0.60Y  −0.04778 
 0.80Y  −0.17765 
 1.00Y  −0.54143 
 
 [10th Surface (r10)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  −0.00000 
 0.20Y  0.00003 
 0.40Y  0.00046 
 0.60Y  0.00259 
 0.80Y  0.00945 
 1.00Y  0.02790 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00065 
 0.40Y  −0.01058 
 0.60Y  −0.05546 
 0.80Y  −0.19007 
 1.00Y  −0.53702 
 
 Example 4 
 [5th Surface (r5)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00008 
 0.40Y  −0.00129 
 0.60Y  −0.00719 
 0.80Y  −0.02684 
 1.00Y  −0.08390 
 
 [6th Surface (r6)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00066 
 0.40Y  −0.01070 
 0.60Y  −0.05580 
 0.80Y  −0.18492 
 1.00Y  −0.48426 
 
 [11th Surface (r11)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00017 
 0.40Y  −0.00282 
 0.60Y  −0.01457 
 0.80Y  −0.04772 
 1.00Y  −0.12247 
 
 Example 5 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00058 
 0.40Y  −0.00938 
 0.60Y  −0.04968 
 0.80Y  −0.17281 
 1.00Y  −0.49672 
 
 [12th Surface (n12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00039 
 0.40Y  −0.00630 
 0.60Y  −0.03215 
 0.80Y  −0.10366 
 1.00Y  −0.26303 
 
The values corresponding to Conditions (15) and (17) in Examples 6 to 15 
 Example 6 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00036 
 0.40Y  −0.00585 
 0.60Y  −0.03124 
 0.80Y  −0.10983 
 1.00Y  −0.31946 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00016 
 0.40Y  −0.00266 
 0.60Y  −0.01382 
 0.80Y  −0.04620 
 1.00Y  −0.12441 
 
 Example 7 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00040 
 0.40Y  −0.00645 
 0.60Y  −0.03442 
 0.80Y  −0.12249 
 1.00Y  −0.36724 
 
 [14th Surface (r14)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00005 
 0.40Y  −0.00072 
 0.60Y  −0.00343 
 0.80Y  −0.00979 
 1.00Y  −0.02004 
 
 Example 8 
 [1st Surface (r1)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00047 
 0.40Y  −0.00762 
 0.60Y  −0.04017 
 0.80Y  −0.13975 
 1.00Y  −0.40512 
 
 [14th Surface (r14)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00007 
 0.40Y  −0.00103 
 0.60Y  −0.00497 
 0.80Y  −0.01421 
 1.00Y  −0.02846 
 
 Example 9 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00034 
 0.40Y  −0.00549 
 0.60Y  −0.02824 
 0.80Y  −0.09332 
 1.00Y  −0.24896 
 
 [11th Surface (r11)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00086 
 0.40Y  −0.01414 
 0.60Y  −0.07574 
 0.80Y  −0.26114 
 1.00Y  −0.14147 
 
 Example 10 
 [1st Surface (r1)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00077 
 0.40Y  −0.01256 
 0.60Y  −0.06639 
 0.80Y  −0.22928 
 1.00Y  −0.65070 
 
 [14th Surface (r14)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00008 
 0.40Y  −0.00129 
 0.60Y  −0.00655 
 0.80Y  −0.02065 
 1.00Y  −0.04955 
 
 Example 11 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00041 
 0.40Y  −0.00663 
 0.60Y  −0.03428 
 0.80Y  −0.11465 
 1.00Y  −0.31309 
 
 [10th Surface (r10)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00016 
 0.40Y  −0.00260 
 0.60Y  −0.01388 
 0.80Y  −0.04736 
 1.00Y  −0.12790 
 
 Example 12 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00058 
 0.40Y  −0.00940 
 0.60Y  −0.04961 
 0.80Y  −0.17667 
 1.00Y  −0.53893 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00011 
 0.40Y  −0.00182 
 0.60Y  −0.00969 
 0.80Y  −0.03330 
 1.00Y  −0.09218 
 
 [15th Surface (r15)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00033 
 0.40Y  −0.00502 
 0.60Y  −0.02364 
 0.80Y  −0.06629 
 1.00Y  −0.13286 
 
 Example 13 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00082 
 0.40Y  −0.01333 
 0.60Y  −0.07171 
 0.80Y  −0.26196 
 1.00Y  −0.82010 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00020 
 0.40Y  −0.00328 
 0.60Y  −0.01759 
 0.80Y  −0.06132 
 1.00Y  −0.17301 
 
 [14th Surface (r14)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00020 
 0.40Y  −0.00311 
 0.60Y  −0.01525 
 0.80Y  −0.04605 
 1.00Y  −0.10564 
 
 [17th Surface (r17)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  0.00068 
 0.40Y  0.01090 
 0.60Y  0.05583 
 0.80Y  0.17801 
 1.00Y  0.43402 
 
 Example 14 
 [3rd Surface (r3)] 
 Height  (X − X0)/{C0(N′N) · f1} 
 
 0.00Y  −0.00000 
 0.20Y  −0.00048 
 0.40Y  −0.00802 
 0.60Y  −0.04370 
 0.80Y  −0.15559 
 1.00Y  −0.44995 
 
 [12th Surface (r12)] 
 Height  (X − X0)/{C0(N′N) · f2} 
 
 0.00Y  0.00000 
 0.20Y  −0.00007 
 0.40Y  −0.00110 
 0.60Y  −0.00579 
 0.80Y  −0.01922 
 1.00Y  −0.04962 
 
 [15th Surface (r15)] 
 Height  (X − X0)/{C0(N′N) · f3} 
 
 0.00Y  0.00000 
 0.20Y  −0.00067 
 0.40Y  −0.01051 
 0.60Y  −0.05178 
 0.80Y  −0.15744 
 1.00Y  −0.36553 
 