CROSSREFERENCE TO RELATED APPLICATIONS
This application is based upon and claims the benefit of priority from the Japanese Patent Application No. 2008191525 filed on Jul. 24, 2008; the entire contents of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a variable focusing lens that includes four lens groups and is provided in, for example, a projection display device, and a projection display device including the variable focusing lens, more particularly, to a projection variable focusing lens and a projection display device that enlarge and project light having image information from a light valve of, for example, a transmissive or reflective liquid crystal display device or a DMD (digital micromirror device) display device onto a screen.
2. Description of the Related Art
In recent years, projection display devices using light valves, such as a liquid crystal display device or a DMD display device, have come into widespread use. In particular, a projection display device has been widely used which uses three light valves corresponding to illumination light components of three primary colors, such as R, G, and B, to modulate the illumination light components, and combines the light components modulated by the three light valves using, for example, a prism, and displays an image on a screen using a projection lens.
As the size of the light valve is reduced, the precision thereof is improved, and personal computers are widely spread, the use of the projection display device for presentation is increased. It is preferable that the projection display device have high user convenience and be easy to install. Therefore, there is an increasing demand for a projection display device having a high performance, a high magnifying power, a small size, and a light weight. In addition, there is an increasing demand for a projection lens having a high performance, a high magnifying power, a small size, and a light weight. Further, there is an increasing demand for a projection lens with a low manufacturing cost.
When a color composition prism for composing the modulated light components from a plurality of light valves or a TIR prism for separating illumination light from projection light is provided in an optical system, the reduction side of the projection lens needs to be substantially telecentric in order to prevent the occurrence of color unevenness in the color composition prism and in order to prevent a reduction in separation efficiency in the TIR prism.
As a projection lens capable of meeting the abovementioned various demands, various types of projection zoom lenses have been known. The zoom lens generally includes two or more variable power lens groups that are moved together when power varies and a focusing lens group. In the zoom lens, a lens driving unit, such as a cam mechanism, is complicated, and it is difficult to reduce the size, weight, and cost of the zoom lens.
JPA2005300619 discloses a projection zoom lens that uses one lens group to perform zooming and uses another lens group to perform focusing.
However, since the projection zoom lens disclosed in JPA2005300619 also has a zoom function, there are restrictions in the movement of the lens groups when power varies. Therefore, there is a large variation in aberration when power varies.
Further, in the projection zoom lens disclosed in JPA2005300619, the number of lenses arranged on the reduction side in the lens group for varying power is small, and it is difficult to obtain a high zoom ratio in an optical system in which the reduction side is substantially telecentric.
SUMMARY OF THE INVENTION
The invention has been made in order to solve the abovementioned problems, and an object of the invention is to provide a projection variable focusing lens and a projection display device that has a reduction side which is telecentric, a high magnifying power, a small size, a light weight, and a low manufacturing cost without being affected by the problems inherent in a zoom lens and is capable of effectively correcting all aberrations, particularly, aberrations occurring when power varies with good balance.
According to an aspect of the invention, a projection variable focusing lens includes a first lens group having a negative refractive power, a second lens group having a positive refractive power, a third lens group, and a fourth lens group having a positive refractive power arranged in this order from a magnification side. When a focal length varies, the second lens group is moved in an optical axis direction. During focusing, the third lens group is moved in the optical axis direction. A reduction side is substantially telecentric.
The ‘variable focusing lens’ is also called a varifocal lens. Unlike the zoom lens, the conjugation length of the variable focusing lens varies when power varies. Therefore, focusing is performed to adjust defocusing.
The second lens group may satisfy the following conditional expression:
1.0<f _{2} /f _{w}<4.0
where f_{w }indicates the focal length of the entire system at a wide angle end, and f_{2 }indicates the focal length of the second lens group.
The second lens group may satisfy the following conditional expression:
0.15<D _{2} /L<0.55
where D_{2 }indicates the largest surface spacing between lenses in the second lens group and L indicates the total length of the lenses.
The second lens group may include two positive lenses.
The third lens group may include a first negative lens, a second positive lens having a convex surface facing the reduction side, and a third positive lens having a convex surface facing the reduction side arranged in this order from the magnification side.
The fourth lens group may include one positive lens having a convex surface facing the magnification side.
The third lens group may satisfy the following conditional expression:
f _{3} /f _{w}<−3.0
where f_{3 }indicates the focal length of the third lens group.
The first lens group may have two lenses including a negative lens that has a concave surface facing the reduction side. Alternatively, the first lens group may include one negative lens having a concave surface facing the reduction side.
The first lens group may include at least one aspheric surface.
The first lens group may have two lenses including a negative lens that has a concave surface facing the reduction side. The second lens group may include two positive lenses. The third lens group may include a first negative lens, a second positive lens having a convex surface facing the reduction side, and a third positive lens having a convex surface facing the reduction side arranged in this order from the magnification side. The fourth lens group may include one positive lens having a convex surface facing the magnification side. The entire system may include eight lenses.
The first lens group may include one negative lens having a concave surface facing the reduction side. The second lens group may include two positive lenses. The third lens group may include a first negative lens, a second positive lens having a convex surface facing the reduction side, and a third positive lens having a convex surface facing the reduction side arranged in this order from the magnification side. The fourth lens group may include one positive lens having a convex surface facing the magnification side. The entire system may include seven lenses.
According to another aspect of the invention, a projection display device includes: at least one light source; at least one light valve; at least one illumination optical unit that guides light emitted from the light source to the light valve; and the projection variable focusing lens. The light valve modulates the light emitted from the light source, and the modulated light is projected onto a screen by the projection variable focusing lens.
The projection variable focusing lens according to the invention has four lens groups including two negative and positive lens groups arranged in this order from the magnification side and a positive lens group arranged closest to the reduction side. When a focal length varies, the second lens group is moved in the optical axis direction. During focusing, the third lens group is moved in the optical axis direction. The reduction side is substantially telecentric.
According to the abovementioned structure, it is possible to provide a projection variable focusing lens that has a reduction side which is telecentric, a high magnifying power, a small size, a light weight, and a low manufacturing cost without being affected by the problems inherent in the zoom lens. In addition, it is possible to effectively correct aberrations occurring when power varies with good balance.
However, in the related art, the zoom lens is used to form a projection lens having a function of changing power. Therefore, when power varies, it is necessary to move two or more lens groups together. In general, it is necessary to move the other lens groups during focusing. Therefore, a large number of lens groups are moved. As a result, it is difficult to reduce the size, weight, and cost of the projection lens.
However, in the invention, a variable focusing lens is used to change the power of a projection lens, and only one lens group is moved to vary the power. Therefore, a complicate lens driving mechanism, such as a cam mechanism, is not needed. As a result, it is possible to reduce the size, weight, and cost of each stage, as compared to the related art. In the case of the zoom lens, there are restrictions in the relative movement of the lens groups when power varies, which results in a large variation in aberration when power varies. However, in the projection variable focusing lens according to the invention, it is possible to remove restrictions in the movement of the lens groups when power varies. Therefore, it is possible to significantly reduce an aberration variation when power varies.
The variable focusing lens has been used for, for example, an imaging lens. When power varies, the conjugation length of the variable focusing lens is changed. Therefore, focus adjustment is needed for focusing, and the focus adjustment is performed whenever an image is captured.
However, in the projection lens, generally, once the projection display device and a screen are set, it is not necessary to change power whenever a projection operation is performed, and only one focus adjustment operation is performed at the beginning. Therefore, the abovementioned problems of the imaging lens do not arise.
Further, in the projection variable focusing lens according to the invention, among four lens groups, the second lens group from the magnification side is used to change power, unlike the projection zoom lens disclosed in JPA2005300619. Therefore, an optical system in which the reduction side is substantially telecentric can obtain a high zoom ratio.
Furthermore, the projection display device according to the invention uses the projection variable focusing lens according to the invention. Therefore, the projection display device can have a high magnifying power, a small size, a light weight, and a low manufacturing cost, and maintain a high optical performance.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 1 of the invention at a wide angle end (wide) and a telephoto end (tele);
FIG. 2 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 2 of the invention at a wide angle end (wide) and a telephoto end (tele);
FIG. 3 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 3 of the invention at a wide angle end (wide) and a telephoto end (tele);
FIG. 4 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 4 of the invention at a wide angle end (wide) and a telephoto end (tele);
FIG. 5 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 5 of the invention at a wide angle end (wide) and a telephoto end (tele);
FIG. 6 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 1;
FIG. 7 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 2;
FIG. 8 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 3;
FIG. 9 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 4;
FIG. 10 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 5; and
FIG. 11 is a diagram schematically illustrating the structure of a projection display device according to an embodiment of the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinafter, exemplary embodiments of the invention will be described with reference to the accompanying drawings. A projection variable focusing lens according to an embodiment of the invention shown in FIG. 1 (which is a representative example of a projection variable focusing lens according to Example 1) includes a first lens group G_{1 }having a negative refractive power, a second lens group G_{2 }having a positive refractive power, a third lens group G_{3}, and a fourth lens group G_{4 }having a positive refractive power arranged in this order from a magnification side. A reduction side is substantially telecentric, and a glass block (which includes a filter unit) 2, which is mainly a color composition prism, and an image display surface 1 of a light valve, such as a liquid crystal display panel, are provided in the rear stage of the fourth lens group. In FIG. 1, X indicates an optical axis.
When power varies (when a focal length varies), the second lens group G_{2 }(which includes a mask (aperture diaphragm) 3) is moved along the optical axis X. During focusing, the third lens group G_{3 }is moved along the optical axis X.
The first lens group G_{1 }includes a first lens L_{1}, which is an aspheric lens (which is preferably made of plastic) having at least one aspheric surface that is concave to the reduction side, and a second lens L_{2}, which is a planoconcave lens or a biconcave lens having a concave surface facing the reduction side (in Example 3, the first lens group G_{1 }includes a first lens L_{1}, which is a biconcave lens, and a second lens L_{2}, which is an aspheric lens having at least one aspheric surface that is concave to the reduction side; in Example 4, the first lens group G_{1 }includes a first lens L_{1}, which is an aspheric lens having at least one aspheric surface that is concave to the reduction side; and in Example 5, the first lens group G_{1 }includes a first lens L_{1}, which is a composite aspheric lens obtained by adding a resin film molded into an aspheric shape to a reductionside surface of a negative meniscus lens (which is preferably made of glass) having a concave surface facing the reduction side)
he first lens group G_{1 }has two lenses including a negative lens having a concave surface facing the reduction side, or only one negative lens having a concave surface facing the reduction side. Therefore, it is possible to reduce the size and cost of a lens system. In particular, the first lens group G_{1 }includes an aspheric surface. Therefore, it is possible to significantly reduce manufacturing costs by decreasing an outside diameter.
The second lens group G_{2 }includes two positive lenses. Therefore, it is possible to reduce the size and cost of a lens system. It is more preferable that the second lens group G_{2 }include a third lens L_{3}, which is a biconvex lens, a mask (or an aperture diaphragm, which is similarly applied to the following description) 3, and a fourth lens L_{4}, which is a biconvex lens. When the mask 3 is provided between the two positive lenses, it is possible to further improve telecentricity on the reduction side.
In the second lens group G_{2}, it is preferable that the two positive lenses all have a refractive index of 1.65 or more in order to correct aberration.
The third lens group G_{3 }includes a negative lens, a positive (or negative) lens having a convex surface facing the reduction side, and a positive lens having a convex surface facing the reduction side arranged in this order from the magnification side. In this way, it is possible to reduce an aberration variation during focusing. It is more preferable that the third lens group G_{3 }include a fifth lens L_{5}, which is a biconcave lens, a sixth lens L_{6}, which is a positive meniscus lens having a convex surface facing the reduction side, and a seventh lens L_{7}, which is a biconvex lens (in Example 4, the sixth lens L_{6 }arranged closest to the reduction side is a positive meniscus lens having a convex surface facing the reduction side).
In the third lens group G_{3}, it is preferable that the second lens and the third lens from the magnification side all have a refractive index of less than 1.65 in order to reduce costs.
The fourth lens group G_{4 }includes only an eighth lens L_{8}, which is a positive meniscus lens having a convex surface facing the magnification side (in Example 4, the fourth lens group G_{4 }includes only the seventh lens L_{7}, which is a biconvex lens).
In the fourth lens group G_{4}, it is preferable that the positive lens have a refractive index of less than 1.65 in order to reduce costs.
In the projection variable focusing lens according to this embodiment, it is possible to vary power by moving only the second lens group G_{2}, and a complicate lens driving mechanism, such as a cam mechanism, is not needed. Therefore, it is possible to reduce the size, weight, and cost of each stage, as compared to the related art. In this embodiment, the total number of lenses in all of the lens groups having the abovementioned structure is seven or eight. A reduction in the number of lenses is achieved using a variable focusing lens, not a zoom lens.
In addition, it is possible to remove restrictions in moving the lens groups together when power varies. Therefore, it is possible to significantly reduce an aberration variation when power varies.
The conjugation length of the ‘variable focusing lens’ is changed when power varies, and the variable focusing lens is out of focus. In this case, focusing is needed. However, one lens group can be moved to vary power. At least two moving groups are sufficient for focusing even considering another focus group.
In contrast to the ‘variable focusing lens’, the ‘zoom lens’ has a constant conjugation length when power varies, and a focusing lens is used to adjust a little variation in the conjugation length. When power varies, two or more moving groups are moved relative to each other by a zoom cam mechanism according to a predetermined rule. When another focus group is considered, three or more lens groups are moved, which is disadvantageous in reducing the size, weight, and cost of an optical lens system.
As described above, since the projection variable focusing lens according to this embodiment is a zoom lens in which a lens closest to the magnification side has a negative power, it is easy to increase an angle of view and it is possible to ensure back focus with an appropriate length.
Further, in the projection variable focusing lens according to this embodiment, it is preferable that all the lenses be single lenses without using cemented lenses having low heat resistance. In this case, it is possible to prevent thermal problems arising in a projection lens having a very high system temperature (particularly, at a position where a beam width is narrow).
Furthermore, in the projection variable focusing lens according to this embodiment, it is preferable that the second lens group G_{2 }satisfy at least one of Conditional expressions 1 and 2 given below:
1.0<f _{2} /f _{w}<4.0, and [Conditional expression 1]
0.15<D _{2} /L<0.55 [Conditional expression 2]
(where f_{w }indicates the focal length of the entire system at a wide angle end, f_{2 }indicates the focal length of the second lens group G_{2}, D_{2 }indicates the largest surface spacing between lenses in the second lens group G_{2}, and L indicates the total length of lenses).
It is preferable that the projection variable focusing lens according to this embodiment satisfy the following Conditional expression 3.
It is preferable that the fourth lens group G_{4 }include only one positive lens having a convex surface facing the magnification side and the third lens group G_{3 }satisfy Conditional expression 3 given below:
f _{3} /f _{w}<−3.0 [Conditional expression 3]
(where f_{3 }indicates the focal length of the third lens group G_{3}).
Next, the technical meaning of the abovementioned Conditional expressions 1 to 3 will be described.
First, Conditional expression 1 defines the range of the ratio between the focal length f_{2 }of the second lens group G_{2}, which is a moving group for varying power, and the focal length f_{1 }of the entire system at the wide angle end, and also defines the power range of the second lens group G_{2}. In addition, Conditional expression 1 defines a range capable of effectively correcting each aberration and reducing the size of a lens system. That is, if the ratio is equal to or less than the lower limit of Conditional expression 1, it is difficult to correct aberration. On the other hand, if the ratio is equal to or greater than the upper limit of Conditional expression 1, the movement of the lens is increased, which results in an increase in the total length of the lenses. The second lens group preferably satisfies the following Conditional expression 1′ and more preferably, the following Conditional expression 1″ in order to more effectively obtain the effects of Conditional expression 1:
1.3<f _{2} /f _{w}<3.0, and [Conditional expression 1′]
1.5<f _{2} /f _{w}<2.5. [Conditional expression 1″]
Conditional expression 2 defines the range of the ratio of the largest surface spacing D_{2 }between the lenses in the second lens group G_{2 }to the total length L of the lenses, and also defines a range capable of effectively correcting each aberration, particularly, an image surface or distortion, and reducing the size of a lens system. That is, if the ratio is equal to or less than the lower limit of Conditional expression 2, it is difficult to correct aberration, particularly, an image surface or distortion. On the other hand, if the ratio is equal to or greater than the upper limit of Conditional expression 2, the movement of the lens is increased, which results in an increase in the total length of the lenses. The second lens group preferably satisfies the following Conditional expression 2′ and more preferably, the following Conditional expression 2″ in order to more effectively obtain the effects of Conditional expression 2:
0.2<D _{2} /L<0.5, and [Conditional expression 2′]
0.25<D _{2} /L<0.4. [Conditional expression 2″]
Conditional expression 3 defines the range of the ratio between the focal length f_{3 }of the third lens group G_{3 }and the focal length f_{w }of the entire system at the wide angle end, and also defines a range capable of effectively correcting aberration. That is, if the ratio is equal to or greater than the upper limit of Conditional expression 3, it is difficult to effectively correct aberration. It is preferable that the third lens group satisfy the following Conditional expression 3′ in order to more effectively obtain the effects of Conditional expression 3:
f _{3} /f _{w}<−5.0. [Conditional expression 3′]
When the following Conditional expression 4 is satisfied, a back focus Bf that is 1.2 times longer than the focal length f_{w }of the entire system at the wide angle end is ensured to obtain good telecentricity and an optical system, such as a prism, for color composition or beam separation is arranged on the reduction side, it is possible to solve problems, such as color unevenness and a reduction in the separation efficiency of illumination light and projection light, due to deterioration of dichroic film characteristics:
Bf/f _{w}>1.2. [Conditional expression 4]
It is preferable that the following Conditional expression 4′ be satisfied in order to more effectively obtain the effects of Conditional expression 4:
Bf/f _{w}>1.45. [Conditional expression 4′]
The projection variable focusing lens according to each of the following examples includes at least one aspheric surface in the first lens group G_{1}. In this way, it is possible to effectively correct distortion. The shape of the aspheric surface is represented by the following aspheric expression:
$\begin{array}{cc}Z=\frac{{Y}^{2}/R}{1+\sqrt{1K\times {Y}^{2}/{R}^{2}}}+\sum _{i=3}^{12}{A}_{i}{Y}^{i}& \left[\mathrm{Expression}\phantom{\rule{0.8em}{0.8ex}}1\right]\end{array}$
(where Z indicates the length of a perpendicular line that drops from a point on an aspheric surface at a distance Y from the optical axis to a tangent plane to the top of the aspheric surface (a plane vertical to the optical axis), Y indicates a distance from the optical axis, R indicates a curvature radius of an aspheric surface near the optical axis, K indicates eccentricity, and A_{i }indicates an aspheric coefficient (i=3 to 12)).
An example of a projection display device provided with the abovementioned projection variable focusing lens will be described with reference to FIG. 11. The projection display device shown in FIG. 11 includes transmissive liquid crystal panels 11 a to 11 c as light valves and uses the projection variable focusing lens according to the abovedescribed embodiment as a projection variable focusing lens 10. An integrator (not shown), such as a flyeye lens, is provided between a light source and a dichroic mirror 12. White light emitted from the light source is incident on the liquid crystal panels 11 a to 11 c corresponding to three color beams (G light, B light, and R light) through an illumination optical unit and then modulated. The modulated light components are composed by a cross dichroic prism 14, and the composed light is projected onto a screen (not shown) by the projection variable focusing lens 10. This device includes the dichroic mirrors 12 and 13 for color separation, the cross dichroic prism 14 for color composition, condenser lenses 16 a to 16 c, and total reflecting mirrors 18 a to 18 c. In this embodiment, the projection display device uses the projection variable focusing lens according to this embodiment. Therefore, the projection display device can have a small size, a high magnifying power, a light weight, and a low manufacturing cost. In addition, the projection display device can maintain a high optical performance.
The use of the projection variable focusing lens according to this embodiment of the invention is not limited to the projection display device using a transmissive liquid crystal display panel, but the projection variable focusing lens according to this embodiment can be used for a display device using a reflective liquid crystal display panel or another light modulating unit, such as a DMD.
EXAMPLES
Next, the projection variable focusing lens according to the invention will be described with reference to detailed examples.
Example 1
As described above, a projection variable focusing lens according to Example 1 has the structure shown in FIG. 1. That is, in the projection variable focusing lens, a first lens group G_{1 }includes a first lens L_{1}, which is a biconcave lens having aspheric surfaces at both sides, and a second lens L_{2}, which is a planoconcave lens having a concave surface facing the reduction side, arranged in this order from the magnification side. In addition, a second lens group G_{2 }includes a third lens L_{3}, which is a biconvex lens, a mask 3, and a fourth lens L_{4}, which is a biconvex lens, arranged in this order from the magnification side. A third lens group G_{3 }includes a fifth lens L_{5}, which is a biconcave lens, a sixth positive lens L_{6}, which is a meniscus lens having a convex surface facing the reduction side, and a seventh lens L_{7}, which is a biconvex lens, arranged in this order from the magnification side. A fourth lens group G_{4 }includes only an eighth lens L_{8}, which is a positive meniscus lens having a convex surface facing the magnification side.
When power varies from the wide angle end to the telephoto end, only the second lens group G_{2 }is moved to the magnification side along the optical axis X.
Focusing is performed by moving the third lens group G_{3 }in the X direction, which is the optical axis.
In Table 1, an upper part shows the curvature radius R of each lens surface according to Example 1 (the focal length of the entire lens system is normalized to 1.0, which is similarly applied to the following tables), the thickness of the center of each lens and an air space D between the lenses (which are normalized, similar to the curvature radius R, which are similarly applied to the following tables), and the refractive index Nd and the Abbe number νd of each lens with respect to the dline. In Table 1 and Tables 2 to 5, which will be described below, numbers corresponding to R, D, Nd, and νd are sequentially increased from the magnification side.
In addition, in Table 1, a middle part shows the values of constants K and A_{3 }to A_{12 }corresponding to the aspheric surfaces. In Table 1, a lower part shows a variable spacing 1 (the gap between the first lens group G_{1 }and the second lens group G_{2}), a variable spacing 2 (the gap between the second lens group G_{2 }and the third lens group G_{3}), and a variable spacing 3 (the gap between the third lens group G_{3 }and the fourth lens group G_{4}) at the wide angle end (wide) and the telephoto end (tele) when a projection distance is 125.50 and 543.27.
TABLE 1 


Surface 





Number 
R 
D 
Nd 
νd 


1 * 
−5.433 
0.201 
1.5101 
56.2 

2 * 
8.778 
0.305 



3 
∞ 
0.071 
1.4875 
70.2 

4 
1.111 
Variable 





spacing D1 



5 
2.526 
0.188 
1.7995 
42.2 

6 
−7.472 
0.380 



7 (mask) 
∞ 
1.216 



8 
6.831 
0.144 
1.6968 
55.5 

9 
−1.996 
Variable 





spacing D2 



10 
−1.239 
0.054 
1.8467 
23.8 

11 
3.651 
0.095 



12 
−1.537 
0.283 
1.6230 
58.2 

13 
−1.321 
0.172 



14 
10.008 
0.241 
1.6031 
60.6 

15 
−1.754 
Variable 





spacing D3 



16 
1.593 
0.228 
1.6230 
58.2 

17 
8.939 
0.730 



18 
∞ 
1.206 
1.5163 
64.1 

19 
∞ 



K 
A_{3} 
A_{4} 
A_{5} 
A_{6} 


1 
1.0000 
−3.4851E−02 
6.4538E−01 
7.6153E−01 
−4.0697E+00 

2 
1.0000 
−3.2949E−02 
9.0247E−01 
−9.3936E−01 
1.9961E+00 


A_{7} 
A_{8} 
A_{9} 
A_{10} 
A_{11} 
A_{12} 

1 
6.6351E+00 
−6.0944E+00 
3.2512E+00 
−7.7827E−01 
0.0000E+00 
0.0000E+00 
2 
−3.8931E+00 
2.7806E+00 
5.9059E−01 
−1.0156E+00 
0.0000E+00 
0.0000E+00 


Variable spacing 1 
1.316 
0.906 
1.316 
0.906 

Variable spacing 2 
0.154 
0.338 
0.146 
0.326 

Variable spacing 3 
0.108 
0.333 
0.116 
0.345 

* aspheric surface 
In addition, Table 6 shows numerical values corresponding to the conditional expressions according to Example 1.
FIG. 6 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 1 at the wide angle end (wide: a projection distance of 125.50) and the telephoto end (tele: a projection distance of 125.50). FIG. 6 and FIGS. 7 to 10 show the spherical aberration of light with respect to the dline, the Fline, and Cline, the astigmatism of a sagittal image surface and a tangential image surface, and the lateral chromatic aberration of light with respect to the dline, the Fline, and the Cline.
As can be seen from FIG. 6, the projection variable focusing lens according to Example 1 has an angle of view 2ω of 53.8 degrees, which is a wide angle, and an F number of 2.04, which is a large value, at the wide angle end. Therefore, all aberrations are effectively corrected.
In addition, as shown in Table 6, the projection variable focusing lens according to Example 1 satisfies all of Conditional expressions 1 to 4, Conditional expressions 1′ to 4′, and Conditional expressions 1″ and 2″.
Example 2
FIG. 2 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 2. The projection variable focusing lens according to Example 2 has substantially the same structure as that according to Example 1 except that a second lens L_{2 }of a first lens group G_{1 }is a biconcave lens.
In Table 2, an upper part shows the curvature radius R of each lens surface according to Example 2, the thickness of the center of each lens and an air space D between the lenses, and the refractive index Nd and the Abbe number νd of each lens with respect to the dline.
In addition, in Table 2, a middle part shows the values of constants K and A_{3 }to A_{12 }corresponding to the aspheric surfaces. In Table 2, a lower part shows the variable spacing 1 (the gap between the first lens group G_{1 }and the second lens group G_{2}), the variable spacing 2 (the gap between the second lens group G_{2 }and the third lens group G_{3}), and the variable spacing 3 (the gap between the third lens group G_{3 }and the fourth lens group G_{4}) at the wide angle end (wide) and the telephoto end (tele) when a projection distance is 125.50 and 543.31.
TABLE 2 


Surface 





Number 
R 
D 
Nd 
νd 


1 * 
−5.433 
0.201 
1.5101 
56.2 

2 * 
8.674 
0.309 



3 
−46.857 
0.071 
1.5163 
64.1 

4 
1.132 
Variable 





spacing D1 



5 
2.771 
0.192 
1.8340 
37.2 

6 
−6.716 
0.489 



7 (mask) 
∞ 
1.052 



8 
5.107 
0.174 
1.7130 
53.9 

9 
−2.001 
Variable 





spacing D2 



10 
−1.299 
0.054 
1.8467 
23.8 

11 
3.009 
0.087 



12 
−1.526 
0.278 
1.6230 
58.2 

13 
−1.307 
0.249 



14 
8.535 
0.235 
1.6031 
60.6 

15 
−1.752 
Variable 





spacing D3 



16 
1.607 
0.223 
1.6031 
60.6 

17 
9.285 
0.685 



18 
∞ 
1.206 
1.5163 
64.1 

19 
∞ 



K 
A_{3} 
A_{4} 
A_{5} 
A_{6} 


1 
1.0000 
−1.8239E−02 
5.9695E−01 
7.8747E−01 
−4.0391E+00 

2 
1.0000 
−1.2482E−02 
8.3537E−01 
−8.8164E−01 
2.0056E+00 


A_{7} 
A_{8} 
A_{9} 
A_{10} 
A_{11} 
A_{12} 

1 
6.6193E+00 
−6.1302E+00 
3.3004E+00 
−7.9733E−01 
0.0000E+00 
0.0000E+00 
2 
−3.9483E+00 
2.8044E+00 
6.8738E−01 
−1.0992E+00 
0.0000E+00 
0.0000E+00 



Wide 
Tele 
Wide 
Tele 


Variable spacing 1 
1.189 
0.789 
1.189 
0.789 

Variable spacing 2 
0.143 
0.318 
0.136 
0.307 

Variable spacing 3 
0.317 
0.541 
0.324 
0.552 

* aspheric surface 
In addition, Table 6 shows numerical values corresponding to the conditional expressions according to Example 2. FIG. 7 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 2 at the wide angle end (wide: a projection distance of 125.50) and the telephoto end (tele: a projection distance of 125.50).
As can be seen from FIG. 7, the projection variable focusing lens according to Example 2 has an angle of view 2ω of 53.6 degrees, which is a wide angle, and an F number of 2.05, which is a large value, at the wide angle end. Therefore, all aberrations are effectively corrected.
In addition, as shown in Table 6, the projection variable focusing lens according to Example 2 satisfies all of Conditional expressions 1 to 4, Conditional expressions 1′ to 4′, and Conditional expressions 1″ and 2″.
Example 3
FIG. 3 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 3. The projection variable focusing lens according to Example 3 has substantially the same structure as that according to Example 1 except that a first lens group G_{1 }includes a first lens L_{1}, which is a biconcave lens, and a second lens L_{2}, which is a meniscus lens having two aspheric surfaces one of which is a concave surface facing the reduction side.
In Table 3, an upper part shows the curvature radius R of each lens surface according to Example 3, the thickness of the center of each lens and an air space D between the lenses, and the refractive index Nd and the Abbe number νd of each lens with respect to the dline.
In addition, in Table 3, a middle part shows the values of constants K and A_{3 }to A_{12 }corresponding to the aspheric surfaces. In Table 3, a lower part shows the variable spacing 1 (the gap between the first lens group G_{1 }and the second lens group G_{2}), the variable spacing 2 (the gap between the second lens group G_{2 }and the third lens group G_{3}), and the variable spacing 3 (the gap between the third lens group G_{3 }and the fourth lens group G_{4}) at the wide angle end (wide) and the telephoto end (tele) when a projection distance is 125.77 and 544.48.
TABLE 3 


Surface 





Number 
R 
D 
Nd 
νd 


1 
−15.274 
0.076 
1.4875 
70.2 

2 
1.182 
0.106 



3 * 
−9.516 
0.174 
1.5101 
56.2 

4 * 
4.285 
Variable 





spacing D1 



5 
2.449 
0.186 
1.7859 
44.2 

6 
−7.705 
0.191 



7 (mask) 
∞ 
1.404 



8 
8.810 
0.146 
1.6968 
55.5 

9 
−1.952 
Variable 





spacing D2 



10 
−1.259 
0.054 
1.8052 
25.4 

11 
3.569 
0.069 



12 
−2.749 
0.278 
1.6968 
55.5 

13 
−1.728 
0.337 



14 
10.852 
0.297 
1.4970 
81.5 

15 
−1.776 
Variable 





spacing D3 



16 
1.869 
0.238 
1.6516 
58.5 

17 
18.494 
0.742 



18 
∞ 
1.209 
1.5163 
64.1 

19 
∞ 



K 
A_{3} 
A_{4} 
A_{5} 
A_{6} 


3 
1.0000 
−4.3801E−02 
1.3771E+00 
−5.0361E−01 
−1.2060E+00 

4 
1.0000 
−1.1271E−02 
1.1502E+00 
−5.8527E−02 
−8.2654E+00 


A_{7} 
A_{8} 
A_{9} 
A_{10} 
A_{11} 
A_{12} 

3 
5.4892E−01 
1.6267E+00 
−1.2006E+00 
2.0370E−01 
0.0000E+00 
0.0000E+00 
4 
−7.9813E−01 
9.2505E−01 
2.8808E+00 
−2.2908E+00 
0.0000E+00 
0.0000E+00 



Wide 
Tele 
Wide 
Tele 


Variable spacing 1 
1.476 
1.049 
1.476 
1.049 

Variable spacing 2 
0.117 
0.283 
0.109 
0.271 

Variable spacing 3 
0.068 
0.329 
0.077 
0.341 

* aspheric surface 
In addition, Table 6 shows numerical values corresponding to the conditional expressions according to Example 3. FIG. 8 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 3 at the wide angle end (wide: a projection distance of 125.77) and the telephoto end (tele: a projection distance of 125.77).
As can be seen from FIG. 8, the projection variable focusing lens according to Example 3 has an angle of view 2ω of 54.0 degrees, which is a wide angle, and an F number of 2.05, which is a large value, at the wide angle end. Therefore, all aberrations are effectively corrected.
In addition, as shown in Table 6, the projection variable focusing lens according to Example 3 satisfies all of Conditional expressions 1 to 4, Conditional expressions 1′ to 4′, and Conditional expressions 1″ and 2″.
Example 4
FIG. 4 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 4. The projection variable focusing lens according to Example 4 has substantially the same structure as that according to Example 1 except that a first lens group G_{1 }includes only a first lens L_{1}, which is a biconcave lens having two aspheric surfaces, a lens (sixth lens L_{6}) arranged closest to the reduction side in a third lens group G_{3 }is a positive meniscus lens having a convex surface facing the reduction side, and a positive lens (seventh lens L_{7}) of a fourth lens group G_{4 }is a biconvex lens. Since the first lens group G_{1 }includes one lens, the lens numbers of the other lenses are decreased by one, as compared to the corresponding lenses according to Example 1.
In Table 4, an upper part shows the curvature radius R of each lens surface according to Example 4, the thickness of the center of each lens and an air space D between the lenses, and the refractive index Nd and the Abbe number νd of each lens with respect to the dline.
In addition, in Table 4, a middle part shows the values of constants K and A_{3 }to A_{12 }corresponding to the aspheric surfaces. In Table 4, a lower part shows the variable spacing 1 (the gap between the first lens group G_{1 }and the second lens group G_{2}), the variable spacing 2 (the gap between the second lens group G_{2 }and the third lens group G_{3}), and the variable spacing 3 (the gap between the third lens group G_{3 }and the fourth lens group G_{4}) at the wide angle end (wide) and the telephoto end (tele) when a projection distance is 125.54 and 597.79.
TABLE 4 


Surface 





Number 
R 
D 
Nd 
νd 


1 * 
−12.726 
0.096 
1.4970 
81.5 

2 * 
1.040 
Variable 





spacing D1 



3 
3.340 
0.225 
1.8040 
46.6 

4 
−5.937 
0.807 



5 (mask) 
∞ 
0.954 



6 
63.755 
0.126 
1.7725 
49.6 

7 
−2.139 
Variable 





spacing D2 



8 
−1.079 
0.060 
1.8467 
23.8 

9 
8.849 
0.064 



10 
−1.613 
0.329 
1.8040 
46.6 

11 
−1.276 
0.268 



12 
−33.242 
0.251 
1.4970 
81.5 

13 
−1.535 
Variable 





spacing D3 



14 
2.434 
0.229 
1.7292 
54.7 

15 
−14.462 
0.764 



16 
∞ 
1.327 
1.5163 
64.1 

17 
∞ 



K 
A_{3} 
A_{4} 
A_{5} 
A_{6} 


1 
1.0000 
4.1975E−02 
1.7138E−01 
−1.2254E−01 
−2.6551E−01 

2 
1.0000 
5.5966E−02 
1.1941E−01 
−2.8023E−01 
1.3480E−01 


A_{7} 
A_{8} 
A_{9} 
A_{10} 
A_{11} 
A_{12} 

1 
7.6985E−02 
5.8373E−01 
−6.3763E−01 
2.0206E−01 
0.0000E+00 
0.0000E+00 
2 
−2.8184E−01 
5.7547E−02 
3.6861E−01 
−3.1856E−01 
0.0000E+00 
0.0000E+00 



Wide 
Tele 
Wide 
Tele 


Variable spacing 1 
1.726 
1.246 
1.726 
1.246 

Variable spacing 2 
0.133 
0.319 
0.119 
0.300 

Variable spacing 3 
0.076 
0.370 
0.090 
0.389 

* aspheric surface 
In addition, Table 6 shows numerical values corresponding to the conditional expressions according to Example 4. FIG. 9 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 4 at the wide angle end (wide: a projection distance of 125.54) and the telephoto end (tele: a projection distance of 125.54).
As can be seen from FIG. 9, the projection variable focusing lens according to Example 4 has an angle of view 2ω of 58.4 degrees, which is a wide angle, and an F number of 2.42, which is a large value, at the wide angle end. Therefore, all aberrations are effectively corrected.
In addition, as shown in Table 6, the projection variable focusing lens according to Example 4 satisfies all of Conditional expressions 1 to 4, Conditional expressions 1′ to 4′, and Conditional expressions 1″ and 2″.
Example 5
FIG. 5 is a diagram schematically illustrating the structure of a projection variable focusing lens according to Example 5. The projection variable focusing lens according to Example 5 has substantially the same structure as that according to Example 1 except that a first lens group G_{1 }includes only a composite aspheric lens L_{1}. The composite aspheric lens L_{1 }is formed by adding a resin l_{1b }to a reductionside surface of a negative meniscusshaped spherical glass lens l_{1a }having a concave surface facing the reduction side. A reductionside surface of the resin film l_{1b }is an aspheric surface. Since the first lens group G_{1 }includes one lens, the lens numbers of the other lenses are decreased by one, as compared to the corresponding lenses according to Example 1.
In Table 5, an upper part shows the curvature radius R of each lens surface according to Example 5, the thickness of the center of each lens and an air space D between the lenses, and the refractive index Nd and the Abbe number νd of each lens with respect to the dline.
In addition, in Table 5, a middle part shows the values of constants K and A_{3 }to A_{12 }corresponding to the aspheric surfaces. In Table 5, a lower part shows the variable spacing 1 (the gap between the first lens group G_{1 }and the second lens group G_{2}), the variable spacing 2 (the gap between the second lens group G_{2 }and the third lens group G_{3}), and the variable spacing 3 (the gap between the third lens group G_{3 }and the fourth lens group G_{4}) at the wide angle end (wide) and the telephoto end (tele) when a projection distance is 125.54 and 543.45.
TABLE 5 


Surface 





Number 
R 
D 
Nd 
νd 


1 
3.890 
0.087 
1.6516 
58.5 

2 
1.056 
0.008 
1.5277 
41.8 

3 * 
0.949 
Variable 





spacing D1 



4 
2.222 
0.202 
1.8040 
46.6 

5 
−11.045 
0.353 



6 (mask) 
∞ 
1.166 



7 
30.918 
0.115 
1.7725 
49.6 

8 
−2.643 
Variable 





spacing D2 



9 
−0.900 
0.054 
1.8467 
23.8 

10 
6.279 
0.080 



11 
−1.347 
0.314 
1.7130 
53.9 

12 
−1.169 
0.011 



13 
14.030 
0.323 
1.4970 
81.5 

14 
−1.198 
Variable 





spacing D3 



15 
2.075 
0.249 
1.7725 
49.6 

16 
1417.836 
0.679 



17 
∞ 
1.206 
1.5163 
64.1 

18 
∞ 



K 
A_{3} 
A_{4} 
A_{5} 
A_{6} 


3 
1.0000 
1.6976E−02 
−1.6264E−01 
9.0641E−02 
2.7356E−01 


A_{7} 
A_{8} 
A_{9} 
A_{10} 
A_{11} 
A_{12} 

3 
−9.5014E−01 
3.5903E−02 
1.6281E+00 
−1.3184E+00 
0.0000E+00 
0.0000E+00 



Wide 
Tele 
Wide 
Tele 


Variable spacing 1 
1.946 
1.484 
1.946 
1.484 

Variable spacing 2 
0.130 
0.273 
0.118 
0.255 

Variable spacing 3 
0.072 
0.392 
0.085 
0.409 

* aspheric surface 
In addition, Table 6 shows numerical values corresponding to the conditional expressions according to Example 5. FIG. 10 is a diagram illustrating all aberrations (spherical aberration, astigmatism, distortion, and lateral chromatic aberration) of the projection variable focusing lens according to Example 5 at the wide angle end (wide: a projection distance of 125.54) and the telephoto end (tele: a projection distance of 125.54).
As can be seen from FIG. 10, the projection variable focusing lens according to Example 5 has an angle of view 2ω of 54.0 degrees, which is a wide angle, and an F number of 2.06, which is a large value, at the wide angle end. Therefore, all aberrations are effectively corrected.
In addition, as shown in Table 6, the projection variable focusing lens according to Example 5 satisfies all of Conditional expressions 1 to 4, Conditional expressions 1′ to 4′, and Conditional expressions 1″ and 2″.

TABLE 6 



Conditional expression 


(1), (1′), (1″) 
(2), (2′), (2″) 
(3), (3′) 
(4), (4′) 


Example 1 
1.85 
0.31 
−9.47 
1.53 
Example 2 
1.78 
0.29 
−11.80 
1.48 
Example 3 
1.87 
0.31 
−8.40 
1.54 
Example 4 
2.08 
0.33 
−12.17 
1.64 
Example 5 
1.92 
0.30 
−10.89 
1.47 
