# Patent

## Title
Projection optical system and projection-type display apparatus

## Abstract

In a projection optical system that projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image, the projection optical system includes a refractive optical system and a reflective optical system having negative refractive power in this order from a reduction side. Further, the following conditional formula (1) is satisfied:

−0.0015≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1).

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2013-193988, filed on Sep. 19, 2013. The above application is hereby expressly incorporated by reference, in its entirety, into the present application.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a projection optical system that uses a refractive optical system and a reflective optical system, and which forms, on a screen, an image of an image displayed on an image display device, and also to a projection-type display apparatus including the projection optical system.
2. Description of the Related Art
As a projection-type display apparatus including a projection optical system that uses a refractive optical system and a reflective optical system, and which forms, on a screen, an image of an image displayed on an image display device, apparatuses disclosed in Japanese Unexamined Patent Publication No. 2007-323047 (Patent Document 1), Japanese Unexamined Patent Publication No. 2007-334052 (Patent Document 2), Specification of Japanese Patent No. 4731808 (Patent Document 3) and Specification of Japanese Patent No. 4889289 (Patent Document 4) are known.
SUMMARY OF THE INVENTION
In the projection optical system and the projection-type display apparatus including the projection optical system, as described above, further reduction in the size and the cost of the apparatus and a shorter projection distance while a magnified video image in sufficient size is displayed on a screen are requested.
In view of the foregoing circumstances, it is an object of the present invention to provide a projection optical system that can display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of an apparatus, and also a projection-type display apparatus including the projection optical system.
A projection optical system of the present invention projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system and a reflective optical system having negative refractive power in this order from a reduction side, and the following conditional formula (1) is satisfied:

−0.0015≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1), where

ωmax: a maximum angle of incidence of a chief ray entering the magnification-side conjugate plane,
θL: an angle between a chief ray from a center of a display surface of the image display device and an optical axis when the chief ray exits from the refractive optical system, and
θM: an angle between the chief ray from the center of the display surface and the optical axis when the chief ray exits from the reflective optical system.
In the projection optical system of the present invention, it is desirable that the refractive optical system and the reflective optical system have a common optical axis.
Further, it is desirable that the refractive optical system and the reflective optical system are rotationally symmetric about the optical axis.
Further, it is desirable that the reflective optical system substantially consists of a mirror having negative refractive power.
It is desirable that the following conditional formula (2) is satisfied:

0.18≦θL/θM   (2).

It is desirable that the following conditional formula (3) is satisfied:

2.0≦tan(ωmax)≦7.5   (3).

It is desirable that the following conditional formula (4) is satisfied:

|cos θ−2 cos φ cos ψ|≦0.6   (4), where

θ: an angle between a chief ray from a most peripheral area on a display surface of the image display device and the optical axis when the chief ray exits from the refractive optical system,
φ: an angle between a normal to the reflective optical system and the optical axis at a point where the chief ray from the most peripheral area on the display surface enters the reflective optical system, and
ψ: an angle between the chief ray and the normal to the reflective optical system at the point where the chief ray from the most peripheral area on the display surface enters the reflective optical system.
It is desirable that the following conditional formula (5) is satisfied:

0.5≦(ZL+ZD)/Hm≦2.1   (5), where

ZL: a total length of the refractive optical system,
ZD: a distance on an optical axis between the refractive optical system and the reflective optical system,
Hm: a maximum effective diameter at a reflection surface of the reflective optical system.
It is desirable that the refractive optical system includes at least one aspheric lens between optical element Lp and the reflective optical system when an optical element (a single lens or a cemented lens) including one of a spherical surface or surfaces arranged closest to a magnification side in the refractive optical system is optical element Lp.
It is desirable that a second lens group, as a whole, has positive refractive power when a lens system (which does not include optical element Lp) arranged between optical element Lp and the reflective optical system is a first lens group in the refractive optical system and a lens system including optical element Lp, and which is arranged toward a reduction side of the optical element Lp, is the second lens group in the refractive optical system.
Further, the first lens group may substantially consist of two lenses of an aspheric lens having negative refractive power and an aspheric lens having positive refractive power in this order from the magnification side. Alternatively, the first lens group may substantially consist of an aspheric lens having negative refractive power.
Further, it is desirable that a most-magnification-side surface of optical element Lp has a convex shape toward the magnification side.
It is desirable that a most-reduction-side surface of optical element Lp has a concave shape facing the reduction side.
Further, it is desirable that optical element Lp has negative refractive power.
Further, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a positive lens with its convex surface facing the magnification side, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Alternatively, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power.
It is desirable that the 2a-th lens group, as a whole, has positive refractive power.
It is desirable that the 2b-th lens group, as a whole, has positive refractive power.
It is desirable that the 2b-th lens group includes at least one aspheric lens.
It is desirable that the following conditional formula (1-1) is satisfied:

−0.0005≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1-1).

Further, it is desirable that the following conditional formula (2-1) is satisfied:

0.24≦θL/θM   (2-1).

It is desirable that the following conditional formula (3-1) is satisfied:

2.3≦tan(ωmax)≦5.0   (3-1).

Further, it is desirable that the following conditional formula (4-1) is satisfied:

|cos θ−2 cos φ cos ψ|≦0.4   (4-1).

Further, it is desirable that the following conditional formula (5-1) is satisfied:

1.0≦(ZL+ZD)/Hm≦1.6   (5-1).

A projection-type display apparatus of the present invention includes a light source, a light valve on which light from the light source is incident, and the aforementioned projection optical system of the present invention, as a projection optical system that projects an optical image of light that has been optically modulated by the light valve onto a screen.
Here, the expression “substantially consisting of” means that lenses substantially without any refractive power, optical elements other than lenses, such as a stop, a mask, a cover glass and a filter, mechanism parts, such as a lens flange, a lens barrel, an imaging device and a hand shake blur correction mechanism, and the like may be included in addition to the lens groups mentioned as composition elements.
The surface shape of the lens and the sign of the refractive power of the lens are considered in a paraxial region when the lens includes an aspherical surface.
Further, the term “chief ray” means a ray crossing the optical axis at an entrance pupil position.
A projection optical system of the present invention projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system and a reflective optical system having negative refractive power in this order from a reduction side, and the following conditional formula (1) is satisfied. Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system.

−0.0015≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1)

The projection-type display apparatus of the present invention includes the projection optical system of the present invention. Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the apparatus.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a cross section illustrating the structure of a projection optical system according to an embodiment of the present invention (common to Example 1);
FIG. 2 is a cross section illustrating the structure of a projection optical system in Example 2 of the present invention;
FIG. 3 is a cross section illustrating the structure of a projection optical system in Example 3 of the present invention;
FIG. 4 is a cross section illustrating the structure of a projection optical system in Example 4 of the present invention;
FIG. 5 is a cross section illustrating the structure of a projection optical system in Example 5 of the present invention;
FIG. 6 is a cross section illustrating the structure of a projection optical system in Example 6 of the present invention;
FIG. 7 is a cross section illustrating the structure of a projection optical system in Example 7 of the present invention;
FIG. 8 is a cross section illustrating the structure of a projection optical system in Example 8 of the present invention;
FIG. 9 is a cross section illustrating the structure of a projection optical system in Example 9 of the present invention;
FIG. 10 is a cross section illustrating the structure of a projection optical system in Example 10 of the present invention;
FIG. 11 is a cross section illustrating the structure of a projection optical system in Example 11 of the present invention;
FIG. 12 is a cross section illustrating the structure of a projection optical system in Example 12 of the present invention;
FIG. 13 is a cross section illustrating the structure of a projection optical system in Example 13 of the present invention;
FIG. 14 is a cross section illustrating the structure of a projection optical system in Example 14 of the present invention;
FIG. 15 is a cross section illustrating the structure of a projection optical system in Example 15 of the present invention;
FIG. 16 is a cross section illustrating the structure of a projection optical system in Example 16 of the present invention;
FIG. 17 is a cross section illustrating the structure of a projection optical system in Example 17 of the present invention;
FIG. 18 is a diagram illustrating distortion performance of the projection optical system in Example 1 of the present invention;
FIG. 19 is a diagram illustrating distortion performance of the projection optical system in Example 2 of the present invention;
FIG. 20 is a diagram illustrating distortion performance of the projection optical system in Example 3 of the present invention;
FIG. 21 is a diagram illustrating distortion performance of the projection optical system in Example 4 of the present invention;
FIG. 22 is a diagram illustrating distortion performance of the projection optical system in Example 5 of the present invention;
FIG. 23 is a diagram illustrating distortion performance of the projection optical system in Example 6 of the present invention;
FIG. 24 is a diagram illustrating distortion performance of the projection optical system in Example 7 of the present invention;
FIG. 25 is a diagram illustrating distortion performance of the projection optical system in Example 8 of the present invention;
FIG. 26 is a diagram illustrating distortion performance of the projection optical system in Example 9 of the present invention;
FIG. 27 is a diagram illustrating distortion performance of the projection optical system in Example 10 of the present invention;
FIG. 28 is a diagram illustrating distortion performance of the projection optical system in Example 11 of the present invention;
FIG. 29 is a diagram illustrating distortion performance of the projection optical system in Example 12 of the present invention;
FIG. 30 is a diagram illustrating distortion performance of the projection optical system in Example 13 of the present invention;
FIG. 31 is a diagram illustrating distortion performance of the projection optical system in Example 14 of the present invention;
FIG. 32 is a diagram illustrating distortion performance of the projection optical system in Example 15 of the present invention;
FIG. 33 is a diagram illustrating distortion performance of the projection optical system in Example 16 of the present invention;
FIG. 34 is a diagram illustrating distortion performance of the projection optical system in Example 17 of the present invention;
FIG. 35 is a diagram illustrating spot performance of the projection optical system in Example 1 of the present invention;
FIG. 36 is a diagram illustrating spot performance of the projection optical system in Example 2 of the present invention;
FIG. 37 is a diagram illustrating spot performance of the projection optical system in Example 3 of the present invention;
FIG. 38 is a diagram illustrating spot performance of the projection optical system in Example 4 of the present invention;
FIG. 39 is a diagram illustrating spot performance of the projection optical system in Example 5 of the present invention;
FIG. 40 is a diagram illustrating spot performance of the projection optical system in Example 6 of the present invention;
FIG. 41 is a diagram illustrating spot performance of the projection optical system in Example 7 of the present invention;
FIG. 42 is a diagram illustrating spot performance of the projection optical system in Example 8 of the present invention;
FIG. 43 is a diagram illustrating spot performance of the projection optical system in Example 9 of the present invention;
FIG. 44 is a diagram illustrating spot performance of the projection optical system in Example 10 of the present invention;
FIG. 45 is a diagram illustrating spot performance of the projection optical system in Example 11 of the present invention;
FIG. 46 is a diagram illustrating spot performance of the projection optical system in Example 12 of the present invention;
FIG. 47 is a diagram illustrating spot performance of the projection optical system in Example 13 of the present invention;
FIG. 48 is a diagram illustrating spot performance of the projection optical system in Example 14 of the present invention;
FIG. 49 is a diagram illustrating spot performance of the projection optical system in Example 15 of the present invention;
FIG. 50 is a diagram illustrating spot performance of the projection optical system in Example 16 of the present invention;
FIG. 51 is a diagram illustrating spot performance of the projection optical system in Example 17 of the present invention;
FIG. 52 is a diagram illustrating evaluation points in an image display device;
FIG. 53 is a diagram illustrating evaluation points in a magnified image on a magnification-side conjugate plane; and
FIG. 54 is a schematic diagram illustrating the configuration of a projection-type display apparatus according to an embodiment of the present invention.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
Embodiments of the present invention will be described in detail with reference to drawings. FIG. 1 is a cross section illustrating the structure of a projection optical system according to an embodiment of the present invention. The example of structure illustrated in FIG. 1 is common to the structure of a projection optical system in Example 1, which will be described later. In FIG. 1, the left side is a reduction side, and the right side is a magnification side.
As illustrated in FIG. 1, this projection optical system projects an image displayed on image display device D arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system substantially consisting of lenses L1 through L12 and reflective optical system R having negative refractive power in this order from a reduction side along optical axis Z.
Image display device D is arranged at a position of so-called full shift or more so that no part of a whole display surface of image display device D crosses optical axis Z.
When this projection optical system is applied to a projection-type display apparatus, it is desirable to arrange a cover glass, a prism, and various filters, such as an infrared-ray-cut filter and a low-pass filter, between image display device D and the refractive optical system based on the configuration of the apparatus. Therefore, FIG. 1 illustrates an example in which parallel-flat-plate-shaped optical member PP, assuming these elements, is arranged between image display device D and the refractive optical system.
The projection optical system is structured in such a manner to satisfy the following conditional formula (1). Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (1-1) is satisfied, more excellent properties are achievable:

−0.0015≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1); and

−0.0005≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1-1), where

ωmax: a maximum angle of incidence of a chief ray entering the magnification-side conjugate plane,
θL: an angle between a chief ray from a center of a display surface of the image display device and an optical axis when the chief ray exits from the refractive optical system, and
θM: an angle between the chief ray from the center of the display surface and the optical axis when the chief ray exits from the reflective optical system.
In the projection optical system, it is desirable that the refractive optical system and reflective optical system R have a common optical axis. Further, it is desirable that the refractive optical system and the reflective optical system are rotationally symmetric about the optical axis. Further, it is desirable that the reflective optical system substantially consists of a mirror having negative refractive power. Accordingly, it is possible to simplify the structure of the projection optical system, and that contributes to reduction in cost.
Further, it is desirable that the following conditional formula (2) is satisfied. Accordingly, it becomes possible to reduce the size and the cost of the optical system. When the following conditional formula (2-1) is satisfied, more excellent properties are achievable:

0.18≦θL/θM   (2); and

0.24≦θL/θM   (2-1).

Further, it is desirable that the following conditional formula (3) is satisfied. When the value does not exceed the upper limit of conditional formula (3), it is possible to reduce the size and the cost of the optical system. When the value is not lower than the lower limit of conditional formula (3), it is possible to display a magnified image in sufficient size on a screen at a short projection distance. When the following conditional formula (3-1) is satisfied, more excellent properties are achievable:

2.0≦tan(ωmax)≦7.5   (3); and

2.3≦tan(ωmax)≦5.0   (3-1).

Further, it is desirable that the following conditional formula (4) is satisfied. Accordingly, it becomes possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (4-1) is satisfied, more excellent properties are achievable:

|cos θ−2 cos φ cos ψ|0.6   (4); and

|cos θ−2 cos φ cos ψ|0.4   (4-1), where

θ: an angle between a chief ray from a most peripheral area on a display surface of the image display device and the optical axis when the chief ray exits from the refractive optical system,
φ: an angle between a normal to the reflective optical system and the optical axis at a point where the chief ray from the most peripheral area on the display surface enters the reflective optical system, and
ψ: an angle between the chief ray and the normal to the reflective optical system at the point where the chief ray from the most peripheral area on the display surface enters the reflective optical system.
Further, it is desirable to satisfy the following conditional formula (5). Accordingly, it becomes possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (5-1) is satisfied, more excellent properties are achievable:

0.5≦(ZL+ZD)/Hm≦2.1   (5); and

1.0≦(ZL+ZD)/Hm≦1.6   (5-1), where

ZL: a total length of the refractive optical system,
ZD: a distance on an optical axis between the refractive optical system and the reflective optical system, and
Hm: a maximum effective diameter at a reflection surface of the reflective optical system.
Further, it is desirable that the refractive optical system includes at least one aspheric lens between optical element Lp and reflective optical system R when an optical element (a single lens or a cemented lens) including one of a spherical surface or surfaces arranged closest to a magnification side in the refractive optical system is optical element Lp. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R. In the embodiment of the present invention, lens L10 corresponds to optical element Lp, and the projection optical system includes two aspheric lenses L11, L12 between optical element Lp and reflective optical system R.
It is desirable that a second lens group, as a whole, has positive refractive power when a lens system (which does not include optical element Lp) arranged between optical element Lp and reflective optical system R is a first lens group in the refractive optical system and a lens system including the optical element Lp, and which is arranged toward a reduction side of the optical element Lp, is the second lens group in the refractive optical system. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R.
Further, the first lens group may substantially consist of two lenses of an aspheric lens having negative refractive power and an aspheric lens having positive refractive power in this order from the magnification side. Alternatively, the first lens group may substantially consist of an aspheric lens having negative refractive power. However, when the first lens group substantially consists of two lenses of a negative aspheric lens and a positive aspheric lens, it is possible to more excellently correct various aberrations generated in reflective optical system R. When the first lens group substantially consists of an aspheric lens having negative refractive power, it is possible to simplify the optical system, and to suppress a level of difficulty in assembly and adjustment. In the embodiment of the present invention, the first lens group substantially consists of two lenses of aspheric lens L12 having negative refractive power and aspheric lens L11 having positive refractive power in this order from the magnification side.
It is desirable that a most-magnification-side surface of optical element Lp has a convex shape toward the magnification side. Further, it is desirable that a most-reduction-side surface of optical element Lp has a concave shape facing the reduction side. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R.
Further, it is desirable that optical element Lp has negative refractive power. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R while displaying a magnified video image in sufficient size on a screen at a short projection distance.
Further, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a positive lens with its convex surface facing the magnification side, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Alternatively, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R.
It is desirable that the 2a-th lens group, as a whole, has positive refractive power. Further, it is desirable that the 2b-th lens group, as a whole, has positive refractive power. Further, it is desirable that the 2b-th lens group includes at least one aspheric lens. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R.
FIG. 1 illustrates an example in which optical member PP is arranged between image display device D and the refractive optical system. Instead of arranging various filters, such as a low-pass filter and a filter that cuts a specific wavelength band, and the like between image display device D and the refractive optical system, the various filters and the like may be arranged between lenses. Alternatively, a coating having a similar action to the various filters and the like may be applied to a lens surface of one of the lenses, or a multi-layer coating for protection, an anti-reflection coating for reducing ghost light or the like, and the like may be applied to a lens surface of one of the lenses.
Next, numerical value examples of the projection optical system of the present invention will be described.
First, a projection optical system in Example 1 will be described. FIG. 1 is a cross section illustrating the structure of the projection optical system in Example 1. In FIG. 1 and FIGS. 2 through 17 corresponding to Examples 2 through 17, which will be described later, optical member PP is also illustrated, and the left side of the diagrams is a reduction side, and the right side of the diagrams is a magnification side.
Table 1 shows basic lens data on the projection optical system in Example 1. Table 2 shows data about specification, and Table 3 shows data about aspherical surface coefficients. Next, the meanings of signs in the tables will be described using the tables in Example 1, as an example. The meanings are basically similar in Examples 2 through 17.
In the lens data of Table 1, column Si shows the surface number of the i-th surface (i=1, 2, 3, . . . ) when the most-reduction-side surface of composition elements is the first surface, and surface numbers sequentially increase toward the magnification side. Column Ri shows the curvature radius of the i-th surface, and column Di shows a distance between the i-th surface and the (i+1)th surface on optical axis Z. Column Ndj shows the refractive index of the j-th optical element (j=1, 2, 3, . . . ) for d-line (wavelength is 587.6 nm). The most reduction-side optical element is the first optical element, and the number j sequentially increases toward the magnification side. The column νdj shows the Abbe number of also the j-th optical element for d-line (wavelength is 587.6 nm).
Here, the sign of a curvature radius is positive when a surface shape is convex toward the reduction side, and negative when a surface shape is convex toward the magnification side. The basic lens data show data including optical member PP.
The data about specification in Table 2 show the value of F-number FNo. and the value of full angle of view 2ω.
In the basic lens data and data about specification, degree is used as the unit of an angle, and mm is used as the unit of a length. Since an optical system is usable by being proportionally enlarged or proportionally reduced, other appropriate units may be used.
In the lens data of Table 1, marks * are attached to the surface numbers of aspherical surfaces. Further, the numerical value of a paraxial curvature radius is shown as a curvature radius of an aspherical surface. The data about aspherical surface coefficients in Table 3 show surface numbers Si of aspherical surfaces and aspherical surface coefficients about the aspherical surfaces. The aspherical surface coefficients are values of coefficients KA, Am (m=4, 6, 8, . . . 20) in an aspherical surface equation represented by the following expression (A):

Zd=C·h2/{1+(1−KA·C2·h2)1/2}+ΣAm·hm   (A), where

Zd: the depth of an aspherical surface (the length of a perpendicular from a point on the aspherical surface at height h to a flat plane that contacts with the vertex of the aspherical surface and is perpendicular to the optical axis),
h: a height (a length from the optical axis),
C: a reciprocal of a paraxial curvature radius, and
KA, Am: aspherical surface coefficients (m=3, 4, 5, . . . 20).







TABLE 1







EXAMPLE 1•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.6987




2
∞
1.0500
1.51633
64.14


3
∞
19.9000


4
24.6586
10.0091
1.65960
48.29


5
−15.6789
1.0000
1.80000
48.00


6
15.7283
0.1999


7
14.1414
4.7519
1.58587
49.98


8
−38.7087
1.9998


9
18.0461
9.0902
1.49007
65.38


10
−12.2005
0.1200


11
−11.5906
1.0002
1.90366
31.31


12
65.2415
3.4718


13
85.7210
4.6078
1.55557
62.86


14
−25.2767
4.9873


15
37.6964
5.3799
1.63028
40.80


16
−57.2505
14.6255


17
−20.3607
2.6358
1.55831
62.76


18
40.3593
1.0481


19
59.8280
7.7872
1.61102
36.90


20
−30.9203
4.6847


21
−17.8928
1.7010
1.75054
49.35


22
−40.0374
14.1767


*23
−13.1426
5.0014
1.49100
57.58


*24
−10.8105
29.9627


*25
−14.3833
6.0000
1.49100
57.58


*26
−15301.9711
25.7890


*27
34.0756
−240.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE













TABLE 2





EXAMPLE 1•SPECIFICATION (d-LINE)


















FNo.
2.50



2ω[°]
156.10

















TABLE 3





EXAMPLE 1•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
23







KA
−4.6412961E−02



A3
−3.2780215E−03



A4
 6.2262301E−04



A5
−5.7798269E−06



A6
−6.4964585E−06



A7
 4.2948136E−07



A8
 1.5028564E−08



A9
−2.7888875E−09



A10
 9.6125863E−11



A11
 1.4890607E−12



A12
−1.1758397E−13



A13
−9.1203310E−16



A14
−6.5840553E−17



A15
 1.2272777E−17



A16
−2.6452600E−19














SURFACE NUMBER
24







KA
1.6532179E−01



A3
−2.1512871E−03 



A4
3.5886722E−04



A5
−3.0768866E−05 



A6
9.3696535E−06



A7
−1.7389268E−06 



A8
1.5561909E−07



A9
−6.8935855E−09 



A10
6.6355189E−11



A11
9.4534688E−12



A12
−4.5745988E−13 



A13
−2.7719524E−15 



A14
8.9862999E−16



A15
−2.9125420E−17 



A16
3.1248281E−19














SURFACE NUMBER
25







KA
−5.0166516E−03



A3
−2.6609567E−03



A4
 5.2802485E−04



A5
−2.7498193E−05



A6
−7.0818516E−07



A7
 6.2838432E−08



A8
 2.9559652E−09



A9
−2.3843579E−10



A10
 3.8266963E−13



A11
 2.3662850E−13



A12
−2.4988875E−15



A13
−1.4401058E−16



A14
 3.6438603E−18



A15
−2.0672982E−20



A16
−6.8018496E−23







SURFACE NUMBER
26







KA
 1.2663467E+05



A3
−9.1565413E−04



A4
 2.8728395E−05



A5
−8.3301551E−07



A6
−1.3025401E−07



A7
 8.8433551E−09



A8
−1.0064131E−10



A9
−2.5674450E−12



A10
−1.2063025E−14



A11
 2.8003831E−15



A12
−3.1931820E−17



A13
−4.6032388E−19



A14
 1.5503710E−20



A15
−1.9170291E−22



A16
 1.0120978E−24







SURFACE NUMBER
27







KA
−3.5372007E+00



A3
 3.6766137E−05



A4
−1.0325833E−06



A5
 8.6090225E−09



A6
−1.3764971E−10



A7
 3.6950491E−12



A8
−2.7956965E−14



A9
−2.8233783E−16



A10
 4.5775758E−18



A11
 3.8203822E−21



A12
−3.8319158E−22



A13
 2.2811185E−24



A14
−1.3780969E−27



A15
−2.6728962E−29



A16
 6.6325098E−32










In Example 1, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group.
FIG. 18 illustrates distortion performance of the projection optical system in Example 1, and FIG. 35 illustrates spot performance of the projection optical system in Example 1. Evaluation points in the diagram illustrating spot performance correspond to point 1 through point 15 in FIG. 52 and FIG. 53, and that is similar also in Examples 2 through 17.
Next, a projection optical system in Example 2 will be described. FIG. 2 is a cross section illustrating the structure of the projection optical system in Example 2. Table 4 shows basic lens data on the projection optical system in Example 2, and Table 5 shows data about specification. Table 6 shows data about aspherical surface coefficients. FIG. 19 is a diagram illustrating distortion performance, and FIG. 36 is a diagram illustrating spot performance.
In Example 2, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group.







TABLE 4







EXAMPLE 2•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7012




2
∞
1.0500
1.51633
64.14


3
∞
20.0002


4
23.7903
6.9435
1.71976
40.01


5
−16.2245
1.2008
1.80001
48.00


6
13.9036
0.1998


7
13.1492
5.0686
1.55294
62.96


8
−42.5195
2.0002


9
18.9943
10.1632
1.48999
65.39


10
−12.5556
0.1491


11
−11.7473
1.5008
1.80001
28.16


12
65.9312
5.2755


13
56.7245
4.8304
1.53701
63.58


14
−32.8901
0.1990


15
41.9824
5.0841
1.58194
39.81


16
−51.2078
13.6442


17
−19.4317
1.4998
1.52280
64.12


18
41.3726
1.4655


19
90.1560
6.8992
1.67458
31.82


20
−29.3643
4.4550


21
−17.0768
1.7007
1.76427
51.57


22
−40.1439
13.3109


*23
−13.5347
4.9990
1.49100
57.58


*24
−10.8237
27.0600


*25
−15.3393
5.0002
1.49100
57.58


*26
126.2269
27.3740


*27
44.1766
−290.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE













TABLE 5





EXAMPLE 2•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
153.10

















TABLE 6





EXAMPLE 2•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
23







KA
−6.1194506E−02



A3
−2.5414362E−03



A4
 5.5231532E−04



A5
−1.5278226E−05



A6
−4.9756216E−06



A7
 4.1820671E−07



A8
 7.3790248E−09



A9
−2.3384664E−09



A10
 9.6482227E−11



A11
 7.3185219E−13



A12
−1.1947420E−13



A13
 3.7688650E−16



A14
−3.3157198E−17



A15
 8.4666890E−18



A16
−1.9786634E−19














SURFACE NUMBER
24







KA
1.6789111E−01



A3
−1.7002545E−03 



A4
3.3988322E−04



A5
−3.5993263E−05 



A6
1.0101722E−05



A7
−1.8489816E−06 



A8
1.6954470E−07



A9
−7.6330064E−09 



A10
6.8605228E−11



A11
1.0760666E−11



A12
−5.0625644E−13 



A13
−3.3851910E−15 



A14
1.0260264E−15



A15
−3.3857834E−17 



A16
3.7240880E−19














SURFACE NUMBER
25







KA
−2.1145789E−02



A3
−3.1164922E−03



A4
 5.3886174E−04



A5
−3.0073789E−05



A6
−6.2682977E−07



A7
 7.3431696E−08



A8
 3.0089777E−09



A9
−2.8755645E−10



A10
 1.0629670E−12



A11
 2.9732423E−13



A12
−3.6042557E−15



A13
−1.8764745E−16



A14
 4.9399102E−18



A15
−2.6630863E−20



A16
−1.2444372E−22







SURFACE NUMBER
26







KA
−1.3092026E+01



A3
−1.3821578E−03



A4
 3.0252589E−05



A5
 3.8048965E−08



A6
−1.6581558E−07



A7
 1.0168569E−08



A8
−1.2622266E−10



A9
−2.7089593E−12



A10
−2.7249480E−14



A11
 3.9321784E−15



A12
−4.6088715E−17



A13
−6.9749411E−19



A14
 2.5446130E−20



A15
−3.4239994E−22



A16
 1.9353451E−24







SURFACE NUMBER
27







KA
−4.3366875E+00



A3
 5.3926804E−05



A4
−1.3391705E−06



A5
 9.8200425E−09



A6
−2.0776567E−10



A7
 6.3809824E−12



A8
−4.9798883E−14



A9
−5.6057817E−16



A10
 9.3161027E−18



A11
 9.8245743E−21



A12
−8.9078606E−22



A13
 5.5840605E−24



A14
−3.3733947E−27



A15
−7.5313252E−29



A16
 1.9838590E−31










Next, a projection optical system in Example 3 will be described. FIG. 3 is a cross section illustrating the structure of the projection optical system in Example 3. Table 7 shows basic lens data on the projection optical system in Example 3, and Table 8 shows data about specification. Table 9 shows data about aspherical surface coefficients. FIG. 20 is a diagram illustrating distortion performance, and FIG. 37 is a diagram illustrating spot performance.
In Example 3, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group.







TABLE 7







EXAMPLE 3•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7009




2
∞
1.0500
1.51633
64.14


3
∞
20.0010


4
25.5726
6.7309
1.73200
39.48


5
−15.5584
1.1999
1.80001
48.00


6
14.3760
0.1991


7
13.3689
5.0218
1.54418
63.30


8
−46.6808
2.0002


9
19.3005
10.4662
1.48999
65.38


10
−12.4734
0.1490


11
−11.7144
1.5000
1.80001
27.02


12
74.6714
5.2910


13
60.8455
4.8649
1.66531
41.40


14
−39.1599
0.2005


15
40.2186
5.3141
1.60466
60.97


16
−61.0762
11.4801


17
−23.9550
1.4997
1.52511
64.03


18
35.2385
1.4771


19
71.7629
5.3887
1.74446
27.78


20
−42.9540
5.5497


21
−15.9111
1.7000
1.71640
55.68


22
−42.0422
11.2507


*23
−14.1095
5.0001
1.49100
57.58


*24
−10.8434
23.5897


*25
−15.7823
5.1561
1.49100
57.58


*26
102.6229
29.9990


*27
54.1512
−345.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE













TABLE 8





EXAMPLE 3•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
149.90

















TABLE 9





EXAMPLE 3•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
23







KA
−2.0639393E−02



A3
−2.2428175E−03



A4
 7.0894582E−04



A5
−3.5395657E−05



A6
−7.5077644E−06



A7
 8.6886666E−07



A8
 1.1665169E−08



A9
−5.7474932E−09



A10
 2.1668961E−10



A11
 6.1721628E−12



A12
−3.7936224E−13



A13
−6.7067101E−15



A14
 1.0982016E−16



A15
 2.9753518E−17



A16
−7.6815219E−19














SURFACE NUMBER
24







KA
1.7672298E−01



A3
−1.8281729E−03 



A4
4.8935302E−04



A5
−4.0200405E−05 



A6
7.8115439E−06



A7
−1.7384392E−06 



A8
1.8293213E−07



A9
−8.1403441E−09 



A10
9.9820032E−12



A11
1.2464099E−11



A12
−3.8041398E−13 



A13
−6.0465040E−15 



A14
8.8171579E−16



A15
−3.1554069E−17 



A16
4.1570146E−19














SURFACE NUMBER
25







KA
−9.1213395E−02



A3
−3.1739315E−03



A4
 6.1510088E−04



A5
−4.2429242E−05



A6
−5.5034644E−07



A7
 1.1268926E−07



A8
 4.2515689E−09



A9
−5.1007821E−10



A10
 3.1856576E−12



A11
 6.0179609E−13



A12
−8.7928372E−15



A13
−4.3662096E−16



A14
 1.2814644E−17



A15
−7.4196538E−20



A16
−3.9318034E−22







SURFACE NUMBER
26







KA
 5.9764602E+00



A3
−1.1980257E−03



A4
 6.5886160E−06



A5
−2.1395820E−08



A6
−1.6486329E−07



A7
 1.5717320E−08



A8
−3.9497973E−10



A9
−1.3833639E−12



A10
 5.4003304E−14



A11
 6.4540563E−15



A12
−1.7110134E−16



A13
−9.2439125E−19



A14
 9.0244609E−20



A15
−1.3067207E−21



A16
 6.2798026E−24







SURFACE NUMBER
27







KA
−6.2052363E+00



A3
 7.2391590E−05



A4
−1.5134281E−06



A5
 8.0683826E−09



A6
−2.6461014E−10



A7
 9.2070275E−12



A8
−7.1848366E−14



A9
−8.7571201E−16



A10
 1.4440586E−17



A11
 1.8591265E−20



A12
−1.4850227E−21



A13
 9.4753676E−24



A14
−5.3295272E−27



A15
−1.3916960E−28



A16
 3.7601655E−31










Next, a projection optical system in Example 4 will be described. FIG. 4 is a cross section illustrating the structure of the projection optical system in Example 4. Table 10 shows basic lens data on the projection optical system in Example 4, and Table 11 shows data about specification. Table 12 shows data about aspherical surface coefficients. FIG. 21 is a diagram illustrating distortion performance, and FIG. 38 is a diagram illustrating spot performance.
In Example 4, Surface 18 through Surface 17 are optical element Lp, Surface 22 through Surface 19 are a first lens group, Surface 18 through Surface 11 are a 2a-th lens group, and Surface 10 through Surface 4 are a 2b-th lens group.







TABLE 10







EXAMPLE 4•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7087




2
∞
1.0500
1.51633
64.14


3
∞
20.0008


4
25.9189
7.5621
1.80001
48.00


5
8.3415
6.0621
1.68841
57.08


6
−225.5059
6.2257


7
23.4804
4.9370
1.57886
61.97


8
−14.0217
0.9494


9
−13.0557
1.5004
1.68892
30.79


10
43.3546
7.4113


11
41.9575
5.8914
1.75513
45.36


12
−44.8569
7.7187


13
120.1457
4.7104
1.61001
37.00


14
−44.2753
1.7754


15
−25.7538
1.5007
1.51499
64.42


16
326.9731
10.7972


17
−16.1641
1.7005
1.49804
65.08


18
−45.0924
8.7789


*19
−12.6516
5.2032
1.49100
57.58


*20
−9.3356
16.1991


*21
−21.0963
5.9848
1.49100
57.58


*22
22.8430
35.1061


*23
57.4912
−425.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE













TABLE 11





EXAMPLE 4•SPECIFICATION (d-LINE)


















FNo.
2.50



2ω[°]
144.80

















TABLE 12





EXAMPLE 4•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
19







KA
−6.7156234E−02



A3
 1.0567713E−03



A4
 1.9219394E−04



A5
−3.5906268E−05



A6
−8.5470585E−07



A7
 5.6451265E−07



A8
−2.0566226E−08



A9
−3.2759567E−09



A10
 2.6972146E−10



A11
−1.4475486E−12



A12
−3.7746164E−13



A13
 4.9580039E−15



A14
 4.9548202E−18



A15
 2.0541125E−17



A16
−5.9640374E−19














SURFACE NUMBER
20







KA
1.0579492E−01



A3
2.5017462E−04



A4
3.4537062E−04



A5
−5.5802286E−05 



A6
7.9112290E−06



A7
−1.1651071E−06 



A8
1.2252480E−07



A9
−6.2224057E−09 



A10
3.7564237E−11



A11
9.0614032E−12



A12
−2.8240213E−13 



A13
−4.6937030E−15 



A14
5.4150234E−16



A15
−1.6898556E−17 



A16
2.0937344E−19







SURFACE NUMBER
21







KA
3.9545077E−01



A3
−2.2688757E−03 



A4
1.5752495E−04



A5
−8.8038289E−06 



A6
7.0147962E−08



A7
9.4251735E−09



A8
9.5959499E−10



A9
−7.0382801E−11 



A10
1.3800570E−13



A11
6.2556412E−14



A12
−5.7014117E−16 



A13
−3.4866746E−17 



A14
8.0807199E−19



A15
−5.2545272E−21 



A16
5.0591645E−24














SURFACE NUMBER
22







KA
−1.4636230E+00



A3
−3.8320839E−03



A4
 1.3504916E−04



A5
 3.3822783E−06



A6
−6.3274316E−07



A7
 3.1103619E−08



A8
−6.2754133E−10



A9
−2.7111426E−13



A10
−3.0866385E−14



A11
 2.0258915E−14



A12
−6.3486489E−16



A13
−3.2260850E−18



A14
 4.5398157E−19



A15
−7.3492347E−21



A16
 3.5784190E−23







SURFACE NUMBER
23







KA
−4.3689790E+00



A3
 2.7225351E−05



A4
−8.7775940E−07



A5
 1.7257081E−08



A6
−7.5182563E−10



A7
 1.7040996E−11



A8
−9.1515104E−14



A9
−2.0808430E−15



A10
 2.8724682E−17



A11
 7.3195980E−20



A12
−3.6670401E−21



A13
 2.4143458E−23



A14
−1.3140987E−26



A15
−4.1509346E−28



A16
 1.2055245E−30










Next, a projection optical system in Example 5 will be described. FIG. 5 is a cross section illustrating the structure of the projection optical system in Example 5. Table 13 shows basic lens data on the projection optical system in Example 5, and Table 14 shows data about specification. Table 15 shows data about aspherical surface coefficients. FIG. 22 is a diagram illustrating distortion performance, and FIG. 39 is a diagram illustrating spot performance.
In Example 5, Surface 23 through Surface 22 are optical element Lp, Surface 25 through Surface 24 are a first lens group, Surface 23 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group.







TABLE 13







EXAMPLE 5•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7064




2
∞
1.0500
1.51633
64.14


3
∞
23.5000


4
24.3572
5.9036
1.48749
70.23


5
−11.7048
0.0397


6
−11.4784
1.1360
1.83400
37.16


7
41.3595
0.2001


*8
17.6321
5.9987
1.58313
59.38


*9
−14.7819
0.2008


10
532.1221
7.4349
1.51633
64.14


11
−11.4305
0.0604


12
−11.2711
1.0506
1.78590
44.20


13
30.5625
0.9942


14
57.7667
14.2840
1.51742
52.43


15
−19.1849
21.2107


16
120.1641
8.1224
1.80518
25.42


17
−55.7119
1.8827


18
36.4802
6.1085
1.80518
25.42


19
167.9520
2.1727


20
−144.0455
1.3991
1.80518
25.42


21
24.6524
14.7685


22
−18.4764
5.4618
1.84666
23.78


23
−60.6146
18.2285


*24
15.0773
7.0000
1.49100
57.58


*25
9.2087
51.3833


*26
113.6259
−562.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 30.2 FROM FIRST SURFACE













TABLE 14





EXAMPLE 5•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
140.20

















TABLE 15





EXAMPLE 5•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
8







KA
1.0000000E+00



A4
−5.8646571E−05 



A6
3.0074427E−07



A8
1.0977627E−09



A10
−3.0481514E−12 














SURFACE NUMBER
9







KA
1.0000000E+00



A4
3.0060642E−05



A6
5.3583142E−08



A8
1.9272085E−09



A10
2.8311516E−11







SURFACE NUMBER
24







KA
−4.8530596E+00



A3
−6.8078736E−04



A4
−1.8886971E−05



A5
−1.3974903E−06



A6
−4.5172871E−08



A7
 1.1636985E−08



A8
 3.2713625E−11



A9
−2.8750701E−11



A10
 4.2833732E−13



A11
 1.4527379E−14



A12
 5.4481976E−17



A13
−1.2091389E−17



A14
−2.3255189E−19



A15
 1.2626231E−20



A16
−1.1360084E−22







SURFACE NUMBER
25







KA
−2.7478619E+00



A3
−8.4342662E−05



A4
−7.0929113E−05



A5
 1.1930934E−06



A6
 1.3015805E−07



A7
−5.7260652E−10



A8
−4.9222461E−10



A9
 2.0850003E−11



A10
−2.1174948E−13



A11
−2.5709636E−15



A12
−2.2162726E−17



A13
 3.8373323E−19



A14
 1.2458051E−19



A15
−3.5196617E−21



A16
 2.7900258E−23







SURFACE NUMBER
26







KA
−1.0143512E+01



A3
−9.9531779E−06



A4
 1.2027936E−07



A5
 5.6799538E−09



A6
−1.2021621E−10



A7
 3.0011813E−12



A8
−1.5049754E−13



A9
 4.5218697E−15



A10
−8.7270730E−17



A11
 1.2285732E−18



A12
−1.2946242E−20



A13
 9.7693647E−23



A14
−4.8799440E−25



A15
 1.4265937E−27



A16
−1.8362336E−30










Next, a projection optical system in Example 6 will be described. FIG. 6 is a cross section illustrating the structure of the projection optical system in Example 6. Table 16 shows basic lens data on the projection optical system in Example 6, and Table 17 shows data about specification. Table 18 shows data about aspherical surface coefficients. FIG. 23 is a diagram illustrating distortion performance, and FIG. 40 is a diagram illustrating spot performance.
In Example 6, Surface 21 through Surface 20 are optical element Lp, Surface 23 through Surface 22 are a first lens group, Surface 21 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group.







TABLE 16







EXAMPLE 6•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7122




2
∞
1.0500
1.51633
64.14


3
∞
23.5000


4
24.2572
5.0038
1.48749
70.23


5
−11.9259
0.0409


6
−11.6867
0.9634
1.83400
37.16


7
41.3064
0.4546


*8
19.1138
5.9124
1.58313
59.38


*9
−14.6324
0.1991


10
167.0780
6.4709
1.48749
70.23


11
−11.7776
0.0600


12
−11.5974
1.0501
1.80400
46.58


13
31.8087
1.3550


14
59.1257
13.8651
1.49533
64.48


15
−18.3239
20.6040


16
126.3462
6.7262
1.79999
25.00


17
−69.2194
3.9097


18
27.4705
8.3848
1.51669
64.36


19
18.8667
16.2428


20
−18.0070
5.5007
1.83419
24.27


21
−134.9902
19.1604


*22
14.0814
7.0001
1.49100
57.58


*23
8.9104
52.1050


*24
119.1422
−562.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 30.2 FROM FIRST SURFACE













TABLE 17





EXAMPLE 6•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
140.00

















TABLE 18





EXAMPLE 6•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
8







KA
1.0000000E+00



A4
−4.2839566E−05 



A6
1.5838606E−07



A8
5.3108137E−09



A10
−1.9739049E−11 







SURFACE NUMBER
9







KA
1.0000000E+00



A4
3.0351035E−05



A6
1.4248812E−07



A8
−7.9831740E−10 



A10
7.3628436E−11














SURFACE NUMBER
22







KA
−4.9675509E+00



A3
−8.3564233E−04



A4
 2.7260068E−06



A5
−1.5162176E−06



A6
−1.1582365E−07



A7
 1.2896963E−08



A8
 1.4178798E−10



A9
−3.0636011E−11



A10
 3.1856151E−13



A11
 1.6763884E−14



A12
 7.8227138E−17



A13
−1.2591173E−17



A14
−2.1397590E−19



A15
 1.1737565E−20



A16
−1.0356158E−22







SURFACE NUMBER
23







KA
−3.1856063E+00



A3
 1.4615400E−04



A4
−8.0637819E−05



A5
 1.0613018E−06



A8
 1.4639739E−07



A7
−7.9152457E−10



A8
−4.8778452E−10



A9
 2.0158050E−11



A10
−1.9044707E−13



A11
−2.6270917E−15



A12
−2.3810326E−17



A13
 4.0749800E−19



A14
 1.1553271E−19



A15
−3.2263399E−21



A16
 2.5278504E−23







SURFACE NUMBER
24







KA
−1.1141359E+01



A3
−1.0024196E−05



A4
 1.2358980E−07



A5
 5.5061450E−09



A6
−1.2298128E−10



A7
 3.2343199E−12



A8
−1.6444853E−13



A9
 4.9846709E−15



A10
−9.6899945E−17



A11
 1.3763157E−18



A12
−1.4673207E−20



A13
 1.1207577E−22



A14
−5.6564215E−25



A15
 1.6666037E−27



A16
−2.1575652E−30










Next, a projection optical system in Example 7 will be described. FIG. 7 is a cross section illustrating the structure of the projection optical system in Example 7. Table 19 shows basic lens data on the projection optical system in Example 7, and Table 20 shows data about specification. Table 21 shows data about aspherical surface coefficients. FIG. 24 is a diagram illustrating distortion performance, and FIG. 41 is a diagram illustrating spot performance.
In Example 7, Surface 23 through Surface 22 are optical element Lp, Surface 27 through Surface 24 are a first lens group, Surface 23 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group.







TABLE 19







EXAMPLE 7•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
1.1436




2
∞
1.0500
1.51633
64.14


3
∞
24.0000


4
26.4352
4.6158
1.48749
70.23


5
−12.2017
0.0408


6
−11.9544
0.8998
1.83400
37.16


7
50.2341
0.2469


*8
19.7081
6.0697
1.58313
59.38


*9
−15.5249
0.3641


10
86.6728
5.7616
1.48749
70.23


11
−11.9472
0.0594


12
−11.7832
1.0508
1.80400
46.58


13
29.8102
0.9315


14
50.9628
16.0000
1.51633
64.14


15
−20.8828
20.1857


16
79.7028
8.4744
1.80000
29.84


17
−66.9751
4.5035


18
41.7057
5.4800
1.80518
25.42


19
233.4703
2.6733


20
−91.1313
1.3999
1.68893
31.07


21
23.7989
14.9364


22
−18.0261
1.9861
1.84666
23.78


23
−82.9595
8.2553


*24
−41.5406
5.4696
1.49100
57.58


*25
−54.9166
10.0230


*26
7.3049
5.9036
1.49100
57.58


*27
5.1475
49.6818


*28
135.0387
−562.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE













TABLE 20





EXAMPLE 7•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
139.70

















TABLE 21





EXAMPLE 7•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
8







KA
 1.0000000E+00



A4
−3.6369620E−05



A6
 2.8442859E−07



A8
−2.2536981E−10



A10
−2.4002750E−12














SURFACE NUMBER
9







KA
1.0000000E+00



A4
2.2149593E−05



A6
−6.7326578E−09 



A8
3.0573301E−09



A10
−3.6453768E−12 







SURFACE NUMBER
24







KA
1.5583500E+00



A3
−1.5401324E−03 



A4
9.6295783E−05



A5
1.5917455E−05



A6
−9.2729971E−07 



A7
−6.5352396E−08 



A8
3.6993206E−09



A9
1.3928520E−10



A10
−7.5961829E−12 



A11
−1.6273741E−13 



A12
8.3948834E−15



A13
9.8648985E−17



A14
−4.7521895E−18 



A15
−2.4171128E−20 



A16
1.0851097E−21







SURFACE NUMBER
25







KA
1.2510904E+00



A3
−2.6851525E−03 



A4
1.0669764E−04



A5
1.9861296E−05



A6
−8.5838808E−07 



A7
−6.9757964E−08 



A8
3.1315071E−09



A9
1.3167122E−10



A10
−6.0404997E−12 



A11
−1.3718034E−13 



A12
6.4062963E−15



A13
7.4185264E−17



A14
−3.5372651E−18 



A15
−1.6271230E−20 



A16
7.9462615E−22














SURFACE NUMBER
26







KA
−5.6235108E+00



A3
−2.9333167E−03



A4
 8.3296856E−05



A5
 4.6023512E−06



A6
−4.5096481E−07



A7
 1.0073123E−09



A8
 8.8563150E−10



A9
−1.2610404E−11



A10
−7.2112729E−13



A11
 5.6478789E−15



A12
 6.4584300E−16



A13
−5.5762994E−18



A14
−3.1653003E−19



A15
 5.8095791E−21



A16
−2.2969300E−23







SURFACE NUMBER
27







KA
−4.0374968E+00



A3
−6.5960709E−04



A4
−4.4331836E−05



A5
 2.2207558E−06



A6
 4.6458610E−08



A7
−1.8244784E−09



A8
−2.9177789E−10



A9
 1.6823917E−11



A10
−2.3813487E−13



A11
−1.9087294E−15



A12
 1.6682888E−17



A13
 1.6807941E−19



A14
 7.7040757E−20



A15
−2.2684215E−21



A16
 1.8118812E−23







SURFACE NUMBER
28







KA
−1.8325942E+01



A3
 4.6594993E−06



A4
 2.7099017E−07



A5
−2.4593862E−09



A6
−9.4890899E−11



A7
 2.2823093E−12



A8
−4.6562219E−14



A9
 1.1671872E−15



A10
−2.1804927E−17



A11
 2.7641493E−19



A12
−2.4781109E−21



A13
 1.5877131E−23



A14
−6.9267939E−26



A15
 1.8238324E−28



A16
−2.1615054E−31










Next, a projection optical system in Example 8 will be described. FIG. 8 is a cross section illustrating the structure of the projection optical system in Example 8. Table 22 shows basic lens data on the projection optical system in Example 8, and Table 23 shows data about specification. Table 24 shows data about aspherical surface coefficients. FIG. 25 is a diagram illustrating distortion performance, and FIG. 42 is a diagram illustrating spot performance.
In Example 8, Surface 24 through Surface 22 are optical element Lp, Surface 26 through Surface 25 are a first lens group, Surface 24 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group.







TABLE 22







EXAMPLE 8•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7027




2
∞
1.0500
1.51633
64.14


3
∞
24.0000


4
25.3362
5.9809
1.51199
64.54


5
−11.2080
0.0409


6
−10.9968
0.8991
1.90366
31.31


7
61.3664
0.2004


8
21.9589
4.9836
1.56104
50.24


9
−15.1724
0.1991


10
34.6386
4.6245
1.51919
51.40


11
−21.5342
0.9936


12
−13.5703
1.0492
1.83400
37.16


13
30.7732
0.8494


14
53.5248
13.5547
1.56564
44.58


15
−21.8172
16.7220


16
149.3213
7.5906
1.80518
25.42


17
−53.7445
9.1930


18
35.5435
6.2231
1.80000
29.64


19
265.5989
2.5746


20
−80.3130
1.3990
1.80518
25.42


21
27.4807
14.6970


*22
−19.7727
0.4010
1.52437
53.67


23
−19.2203
1.7000
1.80518
25.42


24
−64.3321
15.4613


*25
10.3764
7.0009
1.49100
57.58


*26
6.8379
53.6900


*27
120.1798
−516.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE













TABLE 23





EXAMPLE 8•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
139.70

















TABLE 24





EXAMPLE 8•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
22







KA
1.0000000E+00



A3
0.0000000E+00



A4
4.3301170E−05



A5
−3.2557864E−06 



A6
−7.0340177E−08 



A7
7.7847644E−10



A8
1.8653702E−10



A9
7.0752174E−12



A10
2.5778014E−13



A11
−2.0204305E−14 



A12
−3.3943719E−16 



A13
−1.0284233E−16 



A14
−5.0935247E−18 



A15
1.9504046E−19



A16
1.3198964E−21














SURFACE NUMBER
25







KA
−2.0811958E+00



A3
−1.1519904E−03



A4
−4.0862512E−05



A5
−1.0901039E−06



A6
 6.8913160E−08



A7
 1.1016458E−08



A8
−2.0162098E−10



A9
−2.3114343E−11



A10
 5.5827689E−13



A11
 1.0899909E−14



A12
−1.5724241E−16



A13
−7.2553162E−18



A14
−6.1150901E−20



A15
 6.7240125E−21



A16
−6.8609827E−23







SURFACE NUMBER
26







KA
−1.7389678E+00



A3
−9.1409111E−04



A4
−4.5203813E−05



A5
 2.5559318E−06



A6
 5.1169398E−08



A7
−1.1890333E−09



A8
−3.8699943E−10



A9
 2.0163039E−11



A10
−2.7472040E−13



A11
−1.8935931E−15



A12
−8.3881513E−19



A13
 1.2646365E−19



A14
 1.1997609E−19



A15
−3.4318299E−21



A16
 2.7441423E−23







SURFACE NUMBER
27







KA
−1.9228012E+01



A3
 2.4033356E−05



A4
−4.3123308E−07



A5
−7.6485930E−10



A6
 1.1464411E−10



A7
 3.7338832E−12



A8
−2.7061878E−13



A9
 7.3336443E−15



A10
−1.3677378E−16



A11
 2.0250792E−18



A12
−2.3044680E−20



A13
 1.8483775E−22



A14
−9.5824880E−25



A15
 2.8556539E−27



A16
−3.7060729E−30










Next, a projection optical system in Example 9 will be described. FIG. 9 is a cross section illustrating the structure of the projection optical system in Example 9. Table 25 shows basic lens data on the projection optical system in Example 9, and Table 26 shows data about specification. Table 27 shows data about aspherical surface coefficients. FIG. 26 is a diagram illustrating distortion performance, and FIG. 43 is a diagram illustrating spot performance.
In Example 9, Surface 25 through Surface 24 are optical element Lp, Surface 29 through Surface 26 are a first lens group, Surface 25 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group.







TABLE 25







EXAMPLE 9•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.7048




2
∞
1.0500
1.51633
64.14


3
∞
24.0000


4
24.8239
4.3703
1.48749
70.24


5
−16.3683
0.0402


6
−15.9011
1.0000
1.80400
46.58


7
27.7848
0.1990


8
18.6030
5.0117
1.50581
64.78


9
−19.1856
0.1999


10
20.9264
7.1571
1.48749
70.24


11
−12.1402
0.0608


12
−11.9689
1.9396
1.80001
43.85


13
26.3423
0.5600


14
37.9928
4.1565
1.53060
63.82


15
−58.8206
13.2720


16
65.2172
10.0808
1.57193
62.23


17
−41.7832
0.2002


18
62.2668
5.8088
1.79443
32.68


19
−241.9075
13.6843


20
−27.3434
2.0742
1.51000
53.13


21
29.1097
4.5987


22
206.7866
5.5512
1.80000
35.09


23
−51.6637
6.8130


24
−20.1641
1.7002
1.84666
23.78


25
−47.5862
18.7680


*26
−55.7840
5.0042
1.49100
57.58


*27
−36.4526
22.7525


*28
−26.9278
5.0006
1.49100
57.58


*29
19.4847
30.0000


*30
94.4520
−430.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE













TABLE 26





EXAMPLE 9•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
144.80

















TABLE 27





EXAMPLE 9•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
26







KA
 4.2742769E+00



A3
−3.0679255E−03



A4
 1.3199878E−04



A5
−2.1822209E−06



A6
−7.9313815E−07



A7
 1.0887543E−07



A8
−2.6572306E−09



A9
−5.3262036E−10



A10
 3.9437503E−11



A11
−3.9345972E−13



A12
−2.7188425E−14



A13
 5.4193605E−16



A14
−2.5653762E−17



A15
 1.6129763E−18



A16
−2.5222424E−20







SURFACE NUMBER
27







KA
 8.4019028E−01



A3
−1.4161064E−03



A4
−7.6633531E−05



A5
−7.2072345E−06



A6
 3.6477353E−06



A7
−4.1235608E−07



A8
 2.3999573E−08



A9
−8.3236016E−10



A10
 1.1848177E−11



A11
 6.7342354E−13



A12
−3.7650201E−14



A13
−4.6000900E−17



A14
 4.4791608E−17



A15
−1.1105544E−18



A16
 8.3329621E−21







SURFACE NUMBER
28







KA
−3.6940660E+00



A3
 1.2454970E−03



A4
−4.5013280E−04



A5
−9.0926391E−06



A6
 2.9038766E−06



A7
−9.0182168E−08



A8
 7.7883408E−10



A9
−8.9844580E−11



A10
 2.2275225E−12



A11
 1.5425791E−13



A12
−3.6275698E−15



A13
−2.1563571E−16



A14
 9.9890726E−18



A15
−1.5051643E−19



A16
 7.9845950E−22







SURFACE NUMBER
29







KA
−4.9082415E−01



A3
−4.1301737E−03



A4
 9.0454113E−05



A5
 3.2145474E−06



A6
−4.6721060E−07



A7
 2.5360824E−08



A8
−4.1241893E−10



A9
−5.1046458E−12



A10
−1.2247544E−13



A11
 1.7277863E−14



A12
−2.9701064E−16



A13
−3.7764965E−18



A14
 2.1893241E−19



A15
−3.6245785E−21



A16
 2.3488105E−23







SURFACE NUMBER
30







KA
−2.0882647E+00



A3
−8.3116592E−06



A4
 1.5285758E−06



A5
−1.0936649E−08



A6
−1.7665390E−09



A7
 4.3511488E−11



A8
−1.3681297E−13



A9
−6.5213847E−15



A10
 6.6348516E−17



A11
 3.7153014E−19



A12
−9.7647580E−21



A13
 5.2574189E−23



A14
 2.2682052E−26



A15
−1.0773951E−27



A16
 2.6966738E−30










Next, a projection optical system in Example 10 will be described. FIG. 10 is a cross section illustrating the structure of the projection optical system in Example 10. Table 28 shows basic lens data on the projection optical system in Example 10, and Table 29 shows data about specification. Table 30 shows data about aspherical surface coefficients. FIG. 27 is a diagram illustrating distortion performance, and FIG. 44 is a diagram illustrating spot performance.
In Example 10, Surface 27 through Surface 26 are optical element Lp, Surface 31 through Surface 28 are a first lens group, Surface 27 through Surface 16 are a 2a-th lens group, and Surface 15 through Surface 4 are a 2b-th lens group.







TABLE 28







EXAMPLE 10•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.0111




2
∞
1.0500
1.51633
64.14


3
∞
24.0000


4
39.8387
2.7394
1.67790
55.34


5
−45.1095
0.6703


6
−21.3338
1.4820
1.80518
25.42


7
−50.4092
0.1998


8
39.8543
4.2090
1.51633
64.14


9
−12.1664
1.0006
1.77250
49.60


10
40.1232
0.2000


11
22.6870
4.8931
1.57099
50.80


12
−17.3384
0.2006


13
43.0088
6.1940
1.48749
70.23


14
−11.7230
1.1610
1.80610
40.92


15
26.5498
0.5784


16
37.4859
4.9082
1.51633
64.14


17
−30.5336
13.6869


18
95.5747
6.9253
1.72825
28.46


19
−40.4376
0.4014


20
43.7848
4.0166
1.51742
52.43


21
124.1146
7.4964


22
−47.9497
1.5004
1.62299
58.16


23
37.0602
7.5053


*24
−42.6101
4.9120
1.49100
57.58


*25
−28.3253
12.7739


26
−23.2771
2.0003
1.80518
25.42


27
−47.4367
15.1363


*28
−78.2426
5.4470
1.49100
57.58


*29
−61.2421
23.0176


*30
−818.9245
5.0526
1.49100
57.58


*31
25.3056
31.7038


*32
61.9999
−290.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE













TABLE 29





EXAMPLE 10•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
152.70

















TABLE 30





EXAMPLE 10•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
24







KA
4.0207962E+00



A3
−6.2359574E−05 



A4
2.4260210E−05



A5
3.0315217E−06



A6
−8.7417236E−07 



A7
−6.8974126E−10 



A8
1.2266829E−08



A9
−2.1874992E−10 



A10
−8.0518176E−11 



A11
1.5502178E−12



A12
2.8919120E−13



A13
−4.6056801E−15 



A14
−5.6744965E−16 



A15
5.1633933E−18



A16
4.6857766E−19














SURFACE NUMBER
25







KA
−9.6051245E−01



A3
−3.8027998E−04



A4
 1.1179819E−04



A5
−6.2142858E−06



A5
−1.1736404E−06



A7
 1.3257522E−07



A8
 6.1593066E−09



A9
−1.0000797E−09



A10
−4.9879936E−12



A11
 3.6933649E−12



A12
−6.4827940E−14



A13
−6.5924532E−15



A14
 2.0139651E−16



A15
 4.9295873E−18



A16
−1.9084085E−19














SURFACE NUMBER
28







KA
7.0965628E+00



A3
−4.6197923E−03 



A4
1.7413996E−04



A5
3.5622953E−05



A6
−2.1533506E−06 



A7
−1.4851853E−07 



A8
8.8928737E−09



A9
3.5288730E−10



A10
−1.3487677E−11 



A11
−1.0237058E−12 



A12
3.4187251E−14



A13
8.4928668E−15



A14
−3.9240931E−17 



A15
1.7216154E−19



A16
4.2658955E−21







SURFACE NUMBER
29







KA
2.8166231E+00



A3
−4.2844184E−03 



A4
1.3184318E−04



A5
1.3746538E−05



A6
1.9540189E−06



A7
−4.5661487E−07 



A8
2.7686005E−08



A9
−6.2578676E−10 



A10
−8.7688938E−13 



A11
4.5769213E−13



A12
−1.9380766E−14 



A13
4.2420170E−17



A14
2.9958262E−17



A15
−9.7725046E−19 



A16
9.5336091E−21







SURFACE NUMBER
30







KA
3.3497301E+02



A3
−4.8854643E−03 



A4
−5.4760381E−05 



A5
1.4991593E−05



A6
2.6026984E−07



A7
−4.2855670E−08 



A8
6.6724473E−10



A9
1.6824790E−11



A10
−3.4565251E−13 



A11
−4.1952599E−15 



A12
9.6643528E−17



A13
−3.8039529E−18 



A14
1.9401136E−19



A15
−3.4328223E−21 



A16
1.9764393E−23














SURFACE NUMBER
31







KA
−9.8472941E−01



A3
−3.5819758E−03



A4
 3.7884587E−05



A5
 5.8341491E−06



A6
−2.6050838E−07



A7
 6.6284039E−09



A8
−1.7831210E−10



A9
 4.9407516E−12



A10
−1.2459978E−13



A11
 3.1126223E−15



A12
−6.0462218E−17



A13
−2.8060225E−19



A14
 5.3261544E−20



A15
−1.1446516E−21



A16
 7.9423996E−24














SURFACE NUMBER
32







KA
−2.2510641E+00 



A3
−2.4732774E−05 



A4
7.9262476E−07



A5
1.6111326E−09



A6
−8.9009744E−10 



A7
1.8699936E−11



A8
−5.7013185E−14 



A9
−2.2690220E−15 



A10
2.1896828E−17



A11
1.0114568E−19



A12
−2.6031577E−21 



A13
1.3152983E−23



A14
3.1117842E−27



A15
−2.1551088E−28 



A16
5.0042640E−31










Next, a projection optical system in Example 11 will be described. FIG. 11 is a cross section illustrating the structure of the projection optical system in Example 11. Table 31 shows basic lens data on the projection optical system in Example 11, and Table 32 shows data about specification. Table 33 shows data about aspherical surface coefficients. FIG. 28 is a diagram illustrating distortion performance, and FIG. 45 is a diagram illustrating spot performance.
In Example 11, Surface 27 through Surface 26 are optical element Lp, Surface 31 through Surface 28 are a first lens group, Surface 27 through Surface 16 are a 2a-th lens group, and Surface 15 through Surface 4 are a 2b-th lens group.







TABLE 31







EXAMPLE 11•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.0102




2
∞
1.0500
1.51633
64.14


3
∞
24.0000


4
37.1892
2.5247
1.74400
44.78


5
−104.1925
0.8964


6
−23.2256
1.4769
1.69895
30.13


7
−60.3560
0.2009


8
63.8991
4.1462
1.48749
70.23


9
−11.7717
1.0003
1.77250
49.60


10
48.9655
0.2008


11
26.3175
5.2294
1.58267
46.42


12
−17.1244
0.2007


13
39.3962
7.2641
1.48749
70.23


14
−12.1652
1.1006
1.80100
34.97


15
31.2009
0.5937


16
42.1666
8.1904
1.62299
58.16


17
−39.7791
12.5227


18
65.8979
7.7887
1.80000
29.84


19
−57.0081
7.7565


20
58.9087
3.9579
1.58913
61.14


21
825.6641
4.3518


22
−31.8577
1.5001
1.51633
64.14


23
28.7855
6.1834


24
−78.0750
4.3560
1.80518
25.42


25
−34.8737
5.2877


26
−18.9041
2.8155
1.84666
23.78


27
−51.6913
15.8918


*28
−78.3452
4.9999
1.49100
57.58


*29
−39.7185
24.5711


*30
−64.3891
5.0000
1.49100
57.58


*31
15.6633
30.0006


*32
98.2779
−425.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE













TABLE 32





EXAMPLE 11•SPECIFICATION (d-LINE)


















FNo.
2.40



2ω[°]
144.20

















TABLE 33





EXAMPLE 11•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
28







KA
8.3580004E+00



A3
−4.1116274E−03 



A4
1.7197848E−04



A5
1.2682272E−05



A6
−1.8503067E−06 



A7
2.4365158E−08



A8
4.8192812E−09



A9
−2.5340485E−10 



A10
1.3830305E−11



A11
−8.9023525E−13 



A12
1.8296073E−14



A13
1.0057412E−15



A14
−6.6618797E−17 



A15
1.4071485E−18



A16
−9.4814544E−21 







SURFACE NUMBER
29







KA
1.0860865E+00



A3
−2.3075972E−03 



A4
−3.2577874E−05 



A5
−2.7132324E−06 



A6
4.1036319E−06



A7
−5.8838142E−07 



A8
3.7463885E−08



A9
−1.1736101E−09 



A10
9.5961186E−12



A11
9.9510211E−13



A12
−5.0513283E−14 



A13
2.3434680E−19



A14
7.2298905E−17



A15
−2.1835172E−18 



A16
2.0536684E−20














SURFACE NUMBER
30







KA
−8.0863559E+00



A3
 2.7965765E−04



A4
−3.6088477E−04



A5
−6.1940485E−06



A6
 2.1517821E−06



A7
−5.9063317E−08



A8
 2.9531977E−10



A9
−6.9033466E−11



A10
 1.8660754E−12



A11
 1.0275935E−13



A12
−2.5419951E−15



A13
−1.1878350E−16



A14
 5.1585030E−18



A15
−6.7583859E−20



A16
 2.8693193E−22







SURFACE NUMBER
31







KA
−6.1758240E−01



A3
−4.2929557E−03



A4
 8.4814161E−05



A5
 4.6605533E−06



A6
−4.7564118E−07



A7
 2.1336645E−08



A8
−3.3357299E−10



A9
−1.2230526E−12



A10
−2.0079317E−13



A11
 1.4327562E−14



A12
−2.3111377E−16



A13
−2.8978980E−18



A14
 1.9068446E−19



A15
−3.5055118E−21



A16
 2.4174564E−23







SURFACE NUMBER
32







KA
−1.8886101E+00



A3
−8.1732739E−06



A4
 1.3580137E−06



A5
−8.7838123E−09



A6
−1.6535504E−09



A7
 4.0342143E−11



A8
−1.2841316E−13



A9
−5.9391024E−15



A10
 6.0544119E−17



A11
 3.3056836E−19



A12
−8.7549642E−21



A13
 4.7148570E−23



A14
 1.8514268E−26



A15
−9.4818523E−28



A16
 2.3700793E−30










Next, a projection optical system in Example 12 will be described. FIG. 12 is a cross section illustrating the structure of the projection optical system in Example 12. Table 34 shows basic lens data on the projection optical system in Example 12, and Table 35 shows data about specification. Table 36 shows data about aspherical surface coefficients. FIG. 29 is a diagram illustrating distortion performance, and FIG. 46 is a diagram illustrating spot performance.
In Example 12, Surface 24 through Surface 22 are optical element Lp, Surface 28 through Surface 25 are a first lens group, and Surface 24 through Surface 4 are a second lens group.







TABLE 34







EXAMPLE 12•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
9.5189




2
∞
22.8800
1.51633
64.14


3
∞
5.3800


4
39.1045
8.2325
1.80518
25.42


5
2683.6464
0.2000


6
73.2268
3.3349
1.80518
20.42


7
182.5779
0.4000


*8
167.2211
3.7366
1.49100
57.58


*9
164.0477
4.5646


10
33.8582
13.3905
1.49700
81.54


11
−19.0114
1.2001
1.80518
25.42


12
32.5474
5.8328


13
47.9288
6.4582
1.58913
61.14


14
−30.4974
16.2777


15
62.8723
12.7689
1.64769
33.79


16
−20.7981
3.0778
1.80000
29.84


17
−42.4107
0.2007


18
−704.3081
9.9817
1.75520
27.51


19
−68.1613
1.4396


20
−38.6682
1.3000
1.67003
47.23


21
34.2547
11.8778


22
−17.7538
1.4100
1.60311
60.64


23
−43.2599
7.1941
1.80518
25.42


24
−26.2228
14.1293


*25
−11.9944
6.0004
1.49100
57.58


*26
−10.4452
19.8865


*27
−14.1202
7.4467
1.49100
57.58


*28
253.6856
40.6700


*29
115.5274
−603.2000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 929.8 FROM FIRST SURFACE













TABLE 35





EXAMPLE 12•SPECIFICATION (d-LINE)


















FNo.
1.80



2ω[°]
139.50

















TABLE 36





EXAMPLE 12•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
8







KA
−1.8729670E+01



A3
−3.9026395E−05



A4
 2.5081689E−05



A5
 3.7858816E−06



A6
−9.9024780E−07



A7
 1.1938756E−07



A8
−8.2770926E−09



A9
 3.9347907E−10



A10
−1.1809931E−11



A11
−1.0337533E−12



A12
 1.7126594E−13



A13
−8.0739882E−15



A14
 3.2305324E−17



A15
 7.8259687E−18



A16
−1.6769954E−19














SURFACE NUMBER
9







KA
3.7819359E+01



A3
1.0854092E−04



A4
−9.4324243E−06 



A5
9.7864768E−06



A6
−4.8009532E−07 



A7
−1.5109562E−07 



A8
2.5554611E−08



A9
−5.7919116E−10 



A10
−1.8176223E−10 



A11
1.5404820E−11



A12
7.2416280E−14



A13
−6.7967026E−14 



A14
3.7860548E−15



A15
−8.8607650E−17 



A16
7.8537900E−19







SURFACE NUMBER
25







KA
2.4533335E−01



A3
5.0186041E−04



A4
−1.2440749E−04 



A5
6.9122074E−05



A6
−1.8472019E−05 



A7
2.3895483E−06



A8
−1.5110369E−07 



A9
3.3737010E−09



A10
7.4211020E−11



A11
−1.7439111E−12 



A12
−2.6300717E−13 



A13
1.0279311E−14



A14
4.7792073E−16



A15
−6.1522373E−17 



A16
1.0512432E−18



A17
1.8460378E−19



A18
−1.3318964E−20 



A19
3.6090060E−22



A20
−3.6248217E−24 







SURFACE NUMBER
26







KA
1.5214495E−01



A3
7.7045392E−04



A4
−3.8594787E−04 



A5
1.4711447E−04



A6
−2.9170246E−05 



A7
3.2542107E−06



A8
−1.9169657E−07 



A9
2.4325950E−09



A10
4.7727624E−10



A11
−3.5790688E−11 



A12
1.0854735E−12



A13
−2.5918249E−14 



A14
1.9141082E−15



A15
−8.4480869E−17 



A16
−2.1057922E−19 



A17
1.0455659E−19



A18
−1.8044943E−21 



A19
−2.1874301E−23 



A20
5.8532230E−25







SURFACE NUMBER
27







KA
−2.3279202E+00 



A3
−1.3112333E−03 



A4
−1.5483678E−04 



A5
1.1425286E−05



A6
2.2637925E−06



A7
−2.6489603E−07 



A8
6.4495222E−09



A9
1.9350310E−10



A10
−1.9088067E−12 



A11
−6.5926166E−13 



A12
1.5949064E−14



A13
4.5438171E−16



A14
−1.3263628E−17 



A15
−4.1734714E−19 



A16
1.4143953E−20



A17
9.5491702E−23



A18
−6.4078165E−24 



A19
3.8554102E−26



A20
2.8671058E−28














SURFACE NUMBER
28







KA
−2.1156382E+19



A3
−1.7190824E−03



A4
−4.3709076E−05



A5
 1.3310457E−05



A6
−4.6023666E−07



A7
−5.6047951E−09



A8
−4.0074839E−10



A9
 7.1376825E−11



A10
−1.0165856E−12



A11
−9.4856881E−14



A12
 2.7822966E−15



A13
 5.0996261E−17



A14
−2.7412501E−18



A15
 6.1018870E−21



A16
 8.9138916E−22



A17
−4.0484579E−24



A18
−2.3934231E−25



A19
 2.7988883E−27



A20
−4.1314057E−30







SURFACE NUMBER
29







KA
 1.0930970E+00



A3
 2.0500921E−04



A4
−7.5522598E−06



A5
−5.5985360E−08



A6
 8.9414144E−09



A7
−1.5663911E−10



A8
−2.7661297E−12



A9
 1.4653416E−13



A10
−2.2231012E−15



A11
 1.3346813E−17



A12
−3.6886813E−20



A13
 9.1565994E−22



A14
−6.7799680E−24



A15
−1.4084431E−25



A16
 1.6277053E−27



A17
 9.7981637E−30



A18
−2.4320887E−31



A19
 1.4350978E−33



A20
−2.9316381E−36










Next, a projection optical system in Example 13 will be described. FIG. 13 is a cross section illustrating the structure of the projection optical system in Example 13. Table 37 shows basic lens data on the projection optical system in Example 13, and Table 38 shows data about specification. Table 39 shows data about aspherical surface coefficients. FIG. 30 is a diagram illustrating distortion performance, and FIG. 47 is a diagram illustrating spot performance.
In Example 13, Surface 18 through Surface 16 are optical element Lp, Surface 23 through Surface 19 are a first lens group, Surface 18 through Surface 11 are a 2a-th lens group, and Surface 10 through Surface 4 are a 2b-th lens group.







TABLE 37







EXAMPLE 13•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
9.5103




2
∞
22.8800
1.51633
64.14


3
∞
5.3800


4
33.7812
9.3936
1.79544
25.64


5
−1401.6603
0.4007


*6
159.8129
4.3632
1.49100
57.58


*7
116.8669
3.3723


8
25.2038
13.5077
1.49700
81.54


9
−20.0000
1.1991
1.74929
27.62


10
27.0040
5.8682


11
39.0282
8.5701
1.58812
61.61


12
−32.4013
11.4317


13
51.3833
11.0982
1.57758
42.19


14
−15.8531
17.5326
1.61001
41.32


15
40.6474
9.8325


16
−17.8029
1.4091
1.57662
62.05


17
−157.5661
9.2554
1.80518
25.42


18
−30.5930
16.4458


*19
−12.2634
6.1991
1.49100
57.58


*20
−10.3989
19.9757


*21
−14.1305
7.4901
1.49100
57.58


*22
164.3597
43.6714


*23
116.1369
−657.5000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 929.8 FROM FIRST SURFACE













TABLE 38





EXAMPLE 13•SPECIFICATION (d-LINE)


















FNo.
1.80



2ω[°]
139.80

















TABLE 39





EXAMPLE 13•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
6







KA
5.6079681E+01



A3
−3.0172586E−05 



A4
6.6648587E−05



A5
−2.2925425E−05 



A6
7.6878177E−06



A7
−1.5411327E−06 



A8
1.8549282E−07



A9
−1.1869984E−08 



A10
5.3265780E−11



A11
5.8417915E−11



A12
−5.1895274E−12 



A13
2.2664450E−13



A14
−5.4161016E−15 



A15
6.3570357E−17



A16
−2.3637700E−19 







SURFACE NUMBER
7







KA
4.4919516E+01



A3
2.0232701E−04



A4
−4.8331328E−05 



A5
2.6387613E−05



A6
−4.9693371E−06 



A7
7.2148746E−07



A8
−8.8623500E−08 



A9
8.7751911E−09



A10
−5.6805488E−10 



A11
1.1903760E−11



A12
1.2078073E−12



A13
−9.6738296E−14 



A14
1.8727038E−15



A15
4.3099568E−17



A16
−1.5914424E−18 







SURFACE NUMBER
19







KA
2.5868376E−01



A3
5.5917339E−04



A4
−1.5519518E−04 



A5
7.2651815E−05



A6
−1.7936303E−05 



A7
2.3037907E−06



A8
−1.5381578E−07 



A9
4.1841481E−09



A10
6.7336594E−11



A11
−5.4628815E−12 



A12
−1.6420420E−13 



A13
1.9814336E−14



A14
1.1318652E−16



A15
−7.5233481E−17 



A16
1.7097428E−18



A17
1.9508630E−19



A18
−1.3949266E−20 



A19
3.5930473E−22



A20
−3.4276559E−24 







SURFACE NUMBER
20







KA
1.5181721E−01



A3
1.0354464E−03



A4
−4.4828184E−04 



A5
1.5317401E−04



A6
−2.9132927E−05 



A7
3.2585184E−06



A8
−1.9896975E−07 



A9
2.9771466E−09



A10
4.9299833E−10



A11
−3.8787858E−11 



A12
1.1537217E−12



A13
−2.3480232E−14 



A14
1.9178965E−15



A15
−9.2927560E−17 



A16
−9.2616324E−20 



A17
1.1316315E−19



A18
−2.0099967E−21 



A19
−2.3960966E−23 



A20
6.5388306E−25







SURFACE NUMBER
21







KA
−2.1025943E+00 



A3
−5.4358481E−04 



A4
−1.5011214E−04 



A5
6.1317649E−06



A6
2.3532540E−06



A7
−2.6034715E−07 



A8
7.1740969E−09



A9
1.5208492E−10



A10
−2.7272479E−12 



A11
−6.4003421E−13 



A12
1.9351623E−14



A13
4.1796412E−16



A14
−1.7012515E−17 



A15
−4.2159324E−19 



A16
1.7887527E−20



A17
9.0675967E−23



A18
−8.1712742E−24 



A19
5.0082923E−26



A20
4.2841319E−28














SURFACE NUMBER
22







KA
−2.1156382E+19



A3
−1.2390375E−03



A4
−5.2229702E−05



A5
 1.1548327E−05



A6
−4.1120450E−07



A7
−3.3911485E−09



A8
−4.8077604E−10



A9
 7.0992677E−11



A10
−9.5083699E−13



A11
−9.9091098E−14



A12
 2.8085486E−15



A13
 5.7737784E−17



A14
−2.8338197E−18



A15
 9.6802790E−22



A15
 9.7931205E−22



A17
−2.4185449E−24



A18
−2.6776143E−25



A19
 2.5057504E−27



A20
 7.3999405E−31







SURFACE NUMBER
23







KA
 1.0887191E+00



A3
 1.9805169E−04



A4
−7.5305630E−06



A5
−4.8578661E−08



A6
 8.9996496E−09



A7
−1.6355746E−10



A8
−2.7815281E−12



A9
 1.5104119E−13



A10
−2.2866996E−15



A11
 1.3362744E−17



A12
−3.4956150E−20



A13
 9.8640041E−22



A14
−7.4229990E−24



A15
−1.4930115E−25



A18
 1.7247088E−27



A17
 1.0347675E−29



A18
−2.5508970E−31



A19
 1.4948502E−33



A20
−3.0311027E−36










Next, a projection optical system in Example 14 will be described. FIG. 14 is a cross section illustrating the structure of the projection optical system in Example 14. Table 40 shows basic lens data on the projection optical system in Example 14, and Table 41 shows data about specification. Table 42 shows data about aspherical surface coefficients. FIG. 31 is a diagram illustrating distortion performance, and FIG. 48 is a diagram illustrating spot performance.
In Example 14, Surface 19 through Surface 17 are optical element Lp, Surface 23 through Surface 20 are a first lens group, and Surface 19 through Surface 3 are a second lens group.







TABLE 40







EXAMPLE 14•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
26.0500
1.51633
64.14


2
∞
11.9604


3
35.9778
8.6085
1.80518
25.42


4
−154.8133
0.5985


*5
148.3512
3.8119
1.51007
56.24


*6
1465.2411
3.4192


7
30.8141
10.3963
1.48749
70.23


8
−24.6662
1.1990
1.80518
25.42


9
23.6026
5.7251


10
33.7511
6.9859
1.49700
81.54


11
−26.2388
15.2407


12
43.8218
12.8945
1.60342
38.03


13
−17.9859
1.3192
1.80610
33.27


14
−36.5003
0.2009


15
−167.7121
6.8460
1.56883
56.36


16
24.5133
10.8406


17
−15.1471
1.4107
1.56384
60.67


18
−39.7712
6.5466
1.80518
25.42


19
−23.3517
14.7892


*20
−11.2050
5.5005
1.49100
57.58


*21
−9.8885
19.0076


*22
−13.4510
7.2437
1.49100
57.58


*23
−0.1067
42.4438


*24
105.5388
−562.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 709.0 FROM FIRST SURFACE













TABLE 41





EXAMPLE 14•SPECIFICATION (d-LINE)


















FNo.
2.00



2ω[°]
140.00

















TABLE 42





EXAMPLE 14•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
5







KA
6.5766135E+01



A3
5.0795975E−05



A4
−1.4539557E−05 



A5
5.7326791E−06



A6
−9.6620064E−07 



A7
1.2733655E−07



A8
−1.1771777E−08 



A9
8.2316678E−10



A10
−3.0498203E−11 



A11
−2.0343848E−12 



A12
3.4705758E−13



A13
−1.6495176E−14 



A14
5.7602520E−17



A15
1.8371495E−17



A16
−4.2229108E−19 














SURFACE NUMBER
6







KA
−3.3557820E+06



A3
 1.6549633E−04



A4
−1.2388429E−05



A5
 4.8110204E−06



A6
 6.5251044E−08



A7
−1.0249352E−07



A8
 1.5016992E−08



A9
−3.9501197E−10



A10
−1.1048561E−10



A11
 1.0848383E−11



A12
−2.9971685E−14



A13
−4.7325483E−14



A14
 2.8875139E−15



A15
−6.8997086E−17



A16
 5.6348898E−19














SURFACE NUMBER
20







KA
2.3216563E−01



A3
2.1376251E−04



A4
−6.8902504E−05 



A5
8.3269780E−05



A6
−2.5249433E−05 



A7
3.4636962E−06



A8
−2.2310818E−07 



A9
4.1030624E−09



A10
1.6185204E−10



A11
3.2943761E−12



A12
−8.0224409E−13 



A13
2.8220375E−16



A14
2.1568531E−15



A15
−9.8454713E−17 



A16
8.1026974E−20



A17
4.1787310E−19



A18
−3.2242135E−20 



A19
1.0152879E−21



A20
−1.1785269E−23 







SURFACE NUMBER
21







KA
1.5168053E−01



A3
4.5751265E−04



A4
−3.6314202E−04 



A5
1.7636739E−04



A6
−3.8717709E−05 



A7
4.6103336E−06



A8
−2.8168682E−07 



A9
3.0426406E−09



A10
8.0671914E−10



A11
−5.9079226E−11 



A12
1.8450683E−12



A13
−5.5668675E−14 



A14
4.2112037E−15



A15
−1.7373035E−16 



A16
−9.1389725E−19 



A17
2.4492393E−19



A18
−4.2508924E−21 



A19
−5.6710702E−23 



A20
1.5564849E−24







SURFACE NUMBER
22







KA
−2.1185681E+00 



A3
−1.4168490E−03 



A4
−1.2997025E−04 



A5
8.0589444E−06



A6
2.3169271E−06



A7
−2.6082024E−07 



A8
6.8538683E−09



A9
1.1999319E−10



A10
1.2988798E−12



A11
−5.9782089E−13 



A12
9.8184110E−15



A13
3.5839679E−16



A14
−3.3782258E−18 



A15
−4.1301875E−19 



A16
8.4197246E−21



A17
8.5859106E−23



A18
−4.7022379E−24 



A19
6.1175937E−26



A20
−2.8705141E−28 














SURFACE NUMBER
23







KA
−2.5885870E+43



A3
−1.9163843E−03



A4
−3.1954410E−05



A5
 1.3490083E−05



A6
−6.0802460E−07



A7
 1.1962785E−09



A8
−2.2746525E−10



A9
 5.9891347E−11



A10
−1.4087958E−12



A11
−7.5740967E−14



A12
 3.4062567E−15



A13
 2.4977620E−17



A14
−3.3162351E−18



A15
 3.2287212E−20



A16
 9.7984659E−22



A17
−1.3094848E−23



A18
−2.5996999E−25



A19
 5.2010051E−27



A20
−1.9673513E−29







SURFACE NUMBER
24







KA
 1.0510424E+00



A3
 2.5690923E−04



A4
−9.4651289E−06



A5
−9.0558146E−08



A6
 1.2630792E−08



A7
−2.2305821E−10



A8
−4.4849446E−12



A9
 2.4469888E−13



A10
−3.9883739E−15



A11
 2.6675877E−17



A12
−8.4614751E−20



A13
 1.8762077E−21



A14
−1.4559126E−23



A15
−3.3975502E−25



A16
 4.2215174E−27



A17
 2.7262688E−29



A18
−7.3432046E−31



A19
 4.6908597E−33



A20
−1.0374796E−35










Next, a projection optical system in Example 15 will be described. FIG. 15 is a cross section illustrating the structure of the projection optical system in Example 15. Table 43 shows basic lens data on the projection optical system in Example 15, and Table 44 shows data about specification. Table 45 shows data about aspherical surface coefficients. FIG. 32 is a diagram illustrating distortion performance, and FIG. 49 is a diagram illustrating spot performance.
In Example 15, Surface 21 through Surface 20 are optical element Lp, Surface 25 through Surface 22 are a first lens group, Surface 21 through Surface 12 are a 2a-th lens group, and Surface 11 through Surface 5 are a 2b-th lens group.







TABLE 43







EXAMPLE 15•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
0.0958




2
∞
10.6000
1.84666
23.78


3
∞
1.5500
1.51633
64.14


4
∞
4.9000


5
14.6561
3.7457
1.78903
26.14


6
224.0807
0.1990


*7
45.2769
1.9747
1.49100
57.58


*8
55.4989
0.2230


9
9.3094
6.5792
1.49700
81.54


10
−9.7310
1.0992
1.80240
25.55


11
12.5029
3.5528


12
19.0029
2.8979
1.48999
56.88


13
−20.8854
1.1459


14
34.1576
10.7550
1.51456
52.27


15
−35.1796
0.1991


16
62.8567
7.2308
1.80004
25.65


17
−21.0449
0.4473


18
−16.6402
6.5929
1.61752
60.48


19
74.1682
4.4443


20
−8.9472
4.5015
1.72973
33.26


21
−19.5169
9.2447


*22
−5.9583
3.0955
1.49100
57.58


*23
−5.2468
9.0046


*24
−44.9244
4.5009
1.49100
57.58


*25
−0.0781
13.5744


*26
57.7501
−110.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 461.7 FROM FIRST SURFACE













TABLE 44





EXAMPLE 15•SPECIFICATION (d-LINE)


















FNo.
4.00



2ω[°]
146.60

















TABLE 45





EXAMPLE 15•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
7







KA
−4.6392765E+01



A3
−7.0478565E−04



A4
 7.9972373E−04



A5
−6.8306513E−05



A6
−3.3554150E−05



A7
 1.5736232E−05



A8
−1.9261250E−06



A9
−1.0830313E−07



A10
 2.8004572E−08



A11
 1.4510131E−09



A12
−1.8672656E−10



A13
−4.5534704E−11



A14
 3.9684816E−12



A15
 1.5237886E−13



A16
−1.5355110E−14







SURFACE NUMBER
8







KA
−1.7956130E+02



A3
−1.1305315E−04



A4
 5.4684152E−04



A5
 1.7861424E−04



A6
−6.0430901E−05



A7
−4.4997542E−06



A8
 6.5886420E−06



A9
−9.0401925E−07



A10
−1.7580192E−07



A11
 5.0394622E−08



A12
−5.4998562E−10



A13
−9.0064904E−10



A14
 1.0208012E−10



A15
−4.0958032E−12



A16
 5.0163064E−14














SURFACE NUMBER
22







KA
2.3716576E−01



A3
−1.0579370E−02 



A4
2.0387995E−03



A5
1.5249766E−03



A6
−7.8852791E−04 



A7
1.5158835E−04



A8
−1.4814481E−05 



A9
8.2667132E−07



A10
−3.7586489E−08 



A11
2.4173434E−09



A12
8.5914805E−12



A13
−2.9466682E−11 



A14
3.1966324E−12



A15
−4.4109745E−13 



A16
2.1625020E−14



A17
1.0261536E−14



A18
−1.7760618E−15 



A19
1.0667902E−16



A20
−2.2510132E−18 







SURFACE NUMBER
23







KA
1.5246062E−01



A3
5.1331499E−04



A4
−4.9706280E−03 



A5
2.7705955E−03



A6
−8.2845093E−04 



A7
1.8323949E−04



A8
−2.7192802E−05 



A9
1.2388616E−06



A10
2.8897079E−07



A11
−4.5117632E−08 



A12
1.7215740E−09



A13
−3.2848767E−11 



A14
1.8675233E−11



A15
−1.7157086E−12 



A16
−1.9601438E−14 



A17
7.6670049E−15



A18
−2.0417022E−16 



A19
−6.6340849E−18 



A20
2.7355201E−19







SURFACE NUMBER
24







KA
−3.1856395E+00 



A3
−3.1013559E−02 



A4
−3.7060674E−04 



A5
7.7918887E−04



A6
4.2213449E−05



A7
−2.5863509E−05 



A8
1.3681830E−06



A9
1.3375653E−07



A10
−6.4057864E−09 



A11
−1.1905894E−09 



A12
6.6479437E−11



A13
3.8430832E−12



A14
−2.3889387E−13 



A15
−1.1560425E−14 



A16
7.7155480E−16



A17
1.2488066E−17



A18
−1.2455464E−18 



A19
6.7736438E−21



A20
3.7111248E−22














SURFACE NUMBER
25







KA
−2.1156382E+19



A3
−2.7451387E−03



A4
−1.7950739E−03



A5
 1.7288434E−04



A6
 1.3247307E−05



A7
 2.2070499E−07



A8
−4.7314308E−07



A9
 2.8325839E−08



A10
 1.9788122E−09



A11
−2.0092837E−10



A12
−2.1331870E−12



A13
 6.2559028E−13



A14
−1.0814452E−14



A15
−4.9865013E−16



A16
 9.1838832E−18



A17
 4.2227044E−19



A18
−2.5894931E−20



A19
 1.2137733E−21



A20
−2.3623223E−23







SURFACE NUMBER
26







KA
 1.0921890E+00



A3
 8.9836331E−04



A4
−5.8899357E−05



A5
−1.1346015E−06



A6
 2.8167686E−07



A7
−9.3986473E−09



A8
−3.5136649E−10



A9
 3.6240681E−11



A10
−1.1064024E−12



A11
 1.3759930E−14



A12
−8.2027665E−17



A13
 3.4859873E−18



A14
−4.9439235E−20



A15
−2.2026962E−21



A15
 5.0266169E−23



A17
 6.1761378E−25



A18
−3.0508431E−26



A19
 3.6132882E−28



A20
−1.4835427E−30










Next, a projection optical system in Example 16 will be described. FIG. 16 is a cross section illustrating the structure of the projection optical system in Example 16. Table 46 shows basic lens data on the projection optical system in Example 16, and Table 47 shows data about specification. Table 48 shows data about aspherical surface coefficients. FIG. 33 is a diagram illustrating distortion performance, and FIG. 50 is a diagram illustrating spot performance.
In Example 16, Surface 29 through Surface 28 are optical element Lp, Surface 33 through Surface 30 are a first lens group, and Surface 29 through Surface 5 are a second lens group.







TABLE 46







EXAMPLE 16•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
ν dj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
1.5500
1.51680
64.20


2
∞
0.0000


3
∞
10.6000
1.84666
23.78


4
∞
5.7991


5
40.9778
2.5739
1.78111
49.89


6
−105.4155
0.1991


7
24.6916
2.0956
1.74756
53.24


8
141.7015
0.1995


9
26.9099
1.6650
1.77620
26.19


10
16.5703
2.4744
1.69946
56.53


11
226.7436
1.9797


*12
122.2666
4.1250
1.51007
56.24


*13
318.7030
1.2375


14
−107.0069
2.2600
1.84481
29.86


15
16.9691
3.5363
1.48746
64.27


16
−49.0550
3.2975


17
27.7522
1.5008
1.48751
57.34


18
−4594.9840
13.2789


19
38.8081
2.2341
1.66731
32.33


20
161.2215
0.3549


21
46.0541
2.2326
1.74816
33.08


22
338.6393
0.4569


23
−244.7909
2.2650
1.50881
63.43


24
62.9054
3.0902
1.59385
39.18


25
−67.2985
0.5741


26
−42.8970
2.7000
1.73160
53.18


27
−441.1616
6.5765


28
−18.4239
3.3000
1.80991
44.62


29
−42.4857
11.6576


*30
−17.2281
3.4991
1.49100
57.58


*31
−11.4306
16.3210


*32
−13.6384
5.0986
1.49100
57.58


*33
64.8825
25.9045


*34
21.2202
−150.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 314.3 FROM FIRST SURFACE













TABLE 47





EXAMPLE 16•SPECIFICATION (d-LINE)


















FNo.
3.97



2ω[°]
159.60

















TABLE 48





EXAMPLE 16•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
12







KA
−1.1587015E+03



A3
−2.6120665E−05



A4
−1.2696991E−04



A5
 1.9368835E−06



A6
−5.0028444E−06



A7
 2.2995257E−07



A8
 2.1441755E−07



A9
−5.8922525E−09



A10
−8.4981907E−10



A11
−1.1921538E−09



A12
 2.3295231E−11



A13
 3.4382533E−12



A14
 7.6230019E−12



A15
−3.8817751E−13



A16
−8.5102663E−15



A17
 3.4120894E−15



A18
−4.7152682E−15



A19
−3.8078062E−17



A20
 7.5497357E−17














SURFACE NUMBER
13







KA
−6.2744169E+03 



A3
−7.9005711E−05 



A4
−1.0207015E−05 



A5
−2.5931068E−05 



A6
5.6204196E−07



A7
1.9536046E−07



A8
5.3545102E−08



A9
2.1293548E−07



A10
3.3607326E−09



A11
−2.3031204E−08 



A12
−1.7951249E−09 



A13
1.8379720E−10



A14
3.8264717E−10



A15
3.3715107E−11



A16
−1.5400874E−11 



A17
−7.8324681E−14 



A18
−5.0117454E−13 



A19
1.8841489E−14



A20
1.7154792E−14














SURFACE NUMBER
30







KA
−2.9503762E−01



A3
−5.8491507E−05



A4
−7.8146781E−05



A5
 1.2934056E−05



A6
 8.9089980E−07



A7
−1.8450519E−07



A8
 5.9930360E−09



A9
−1.5846249E−10



A10
 2.5029599E−11



A11
−1.0327021E−12



A12
−8.4867084E−14



A13
 6.0251682E−15



A14
 3.0893042E−17



A15
 1.4113052E−18



A16
−5.1330874E−19



A17
−7.4152610E−20



A18
 7.6488837E−21



A19
−2.5272112E−22



A20
 1.8072971E−24














SURFACE NUMBER
31







KA
1.6797579E−01



A3
−1.6611232E−04 



A4
9.4682232E−05



A5
−1.3829502E−05 



A6
4.6355743E−06



A7
−5.3533840E−07 



A8
3.9219226E−08



A9
−1.7717638E−09 



A10
−3.4187551E−11 



A11
6.7006420E−12



A12
3.5926093E−14



A13
−2.2073744E−14 



A14
1.5657581E−16



A15
5.9195497E−17



A16
−2.4024388E−18 



A17
2.1095060E−20



A18
1.3148771E−22



A19
1.3131270E−23



A20
−3.5014132E−25 







SURFACE NUMBER
32







KA
−9.8418190E+00 



A3
−4.0624612E−03 



A4
−9.9250632E−05 



A5
2.4118088E−06



A6
3.7110006E−07



A7
3.5789032E−07



A8
−4.2590496E−08 



A9
8.9262884E−10



A10
7.1518698E−11



A11
−1.6592989E−12 



A12
−1.9885938E−13 



A13
7.3679429E−15



A14
3.3057642E−16



A15
−2.9874900E−17 



A16
8.3135603E−19



A17
−1.5274389E−20 



A18
7.1776388E−22



A19
−2.6263932E−23 



A20
3.2336776E−25














SURFACE NUMBER
33







KA
−2.7572211E+03



A3
−1.9905092E−03



A4
−1.1637874E−04



A5
−2.7098745E−06



A6
 2.5884194E−06



A7
−2.2640692E−07



A8
 6.1093455E−09



A9
 3.4354415E−10



A10
−3.5202993E−11



A11
 7.7541210E−13



A12
 3.5282913E−14



A13
−1.7134594E−15



A14
−1.5495969E−17



A15
 9.4419789E−19



A16
 5.7476033E−20



A17
−1.7457513E−21



A18
−5.2028340E−23



A19
 2.4924611E−24



A20
−2.6080823E−26







SURFACE NUMBER
34







KA
−2.5240145E+00



A3
−1.9286019E−05



A4
 1.7668451E−07



A5
 3.9992188E−09



A6
−2.4527463E−10



A7
 1.5311011E−12



A8
 4.5638539E−14



A9
−4.6896864E−16



A10
 3.5785627E−18



A11
−1.3751802E−19



A12
 1.3911262E−21



A13
−4.0646214E−24



A14
 1.1081513E−25



A15
−1.1139248E−27



A16
−4.6280612E−29



A17
 1.5204343E−30



A18
−1.8772399E−32



A19
 1.0063718E−34



A20
−1.7551965E−37










Next, a projection optical system in Example 17 will be described. FIG. 17 is a cross section illustrating the structure of the projection optical system in Example 17. Table 49 shows basic lens data on the projection optical system in Example 17, and Table 50 shows data about specification. Table 51 shows data about aspherical surface coefficients. FIG. 34 is a diagram illustrating distortion performance, and FIG. 51 is a diagram illustrating spot performance.
In Example 17, Surface 21 through Surface 20 are optical element Lp, Surface 25 through Surface 22 are a first lens group, Surface 21 through Surface 15 are a 2a-th lens group, and Surface 14 through Surface 5 are a 2b-th lens group.







TABLE 49







EXAMPLE 17•LENS DATA (n, ν FOR d-LINE)











Si
Ri
Di
Ndj



(SUR-
(CURVA-
(SUR-
(REFRAC-
νdj


FACE
TURE
FACE
TIVE
(ABBE


NUMBER)
RADIUS)
DISTANCE)
INDEX)
NUMBER)














1
∞
1.5500
1.51680
64.20


2
∞
0.0000


3
∞
10.6000
1.84666
23.78


4
∞
6.0005


5
18.9205
3.2903
1.75345
52.66


6
−169.5404
0.1990


7
28.4640
1.6650
1.84500
22.75


8
14.7639
3.1274
1.82319
45.68


9
−143.2185
0.4787


*10
58.9029
4.1250
1.51007
56.24


*11
59.0005
0.7877


12
−68.7558
2.2600
1.84502
22.75


13
18.4710
1.7129
1.65893
58.55


14
−76.5603
5.8046


15
32.7560
1.3427
1.71841
32.31


16
−179.3248
5.5780


17
40.7001
2.3222
1.83194
23.40


18
−36.2430
0.9991
1.48749
65.48


19
107.6291
4.3351


20
−13.2419
3.3000
1.83484
29.89


21
−68.6753
5.1774


*22
−14.7770
3.5010
1.49100
57.58


*23
−8.3245
13.5225


*24
−11.3030
4.4994
1.49100
57.58


*25
60.9090
30.6513


*26
37.6466
−150.0000
REFLECTION





SURFACE





ENTRANCE PUPIL POSITION: 450.0 FROM FIRST SURFACE













TABLE 50





EXAMPLE 17•SPECIFICATION (d-LINE)


















FNo.
3.78



2ω[°]
147.40

















TABLE 51





EXAMPLE 17•ASPHERICAL SURFACE COEFFICIENT


















SURFACE NUMBER
10







KA
−2.0000001E+02



A3
−2.0608485E−06



A4
−2.2367059E−04



A5
−2.4777364E−07



A6
−2.1566237E−06



A7
 3.5005867E−07



A8
−3.1394773E−07



A9
 1.9989087E−07



A10
−4.3110702E−08



A11
−2.3089218E−09



A12
 3.4509613E−09



A13
−8.7868845E−10



A14
 1.1533089E−10



A15
−8.0572036E−12



A16
 2.3712436E−13







SURFACE NUMBER
11







KA
 9.8589363E+01



A3
−1.1031376E−04



A4
−2.3161674E−04



A5
−5.3127939E−06



A6
−1.4741562E−05



A7
 1.3487739E−05



A8
−3.7148720E−06



A9
 1.3162064E−07



A10
 6.4016856E−08



A11
 1.6986505E−08



A12
−4.0186408E−09



A13
−2.3297468E−09



A14
 8.8545192E−10



A15
−1.1144580E−10



A16
 4.9506701E−12














SURFACE NUMBER
22







KA
9.0926128E−06



A3
−2.8227329E−05 



A4
−2.4729788E−05 



A5
1.5310496E−05



A6
2.5974141E−07



A7
−2.4627082E−07 



A8
−4.9697654E−09 



A9
3.0455089E−09



A10
4.7094904E−11



A11
−3.4004259E−11 



A12
1.9970819E−12



A13
−1.1995782E−13 



A14
1.6375356E−14



A15
−1.0568710E−15 



A16
2.2938782E−17







SURFACE NUMBER
23







KA
1.7871517E−01



A3
−1.8662288E−04 



A4
1.6820070E−04



A5
−1.4740000E−05 



A6
3.6348908E−06



A7
−3.7716615E−07 



A8
3.4224910E−08



A9
−2.7347524E−09 



A10
8.9405987E−11



A11
−3.8618208E−12 



A12
5.6698147E−13



A13
6.7031004E−14



A14
−1.6432750E−14 



A15
1.0214001E−15



A16
−2.1230747E−17 














SURFACE NUMBER
24







KA
−5.9145369E+00



A3
−4.1853991E−03



A4
−2.9526853E−04



A5
−1.9583792E−07



A6
 4.1682669E−06



A7
 1.8217440E−07



A8
−4.2361684E−08



A9
−2.3791647E−09



A10
 4.5146294E−10



A11
−5.0525982E−12



A12
−1.2113652E−12



A13
 2.0487937E−14



A14
 3.1280781E−15



A15
−1.4729329E−16



A16
 1.9269750E−18







SURFACE NUMBER
25







KA
−5.0000001E+02



A3
−2.7819326E−03



A4
−1.3760975E−04



A5
 1.5886030E−06



A6
 4.2566726E−06



A7
−5.5623976E−07



A8
 3.2449967E−08



A9
−1.4404690E−09



A10
 1.4126691E−10



A11
−1.4620887E−11



A12
 9.0638146E−13



A13
−3.4143557E−14



A14
 8.4125438E−16



A15
−1.4197753E−17



A16
 1.3267372E−19







SURFACE NUMBER
26







KA
−3.1118883E+00



A3
 2.0340631E−05



A4
−1.3965350E−05



A5
 2.6181849E−06



A6
−2.4143206E−07



A7
 1.3148226E−08



A8
−4.4574735E−10



A9
 8.8689764E−12



A10
−7.1990857E−14



A11
−6.9016277E−16



A12
 1.3883358E−17



A13
 2.0275535E−19



A14
−7.2527639E−21



A15
 7.2481660E−23



A16
−2.5849556E−25










Table 52 shows values corresponding to conditional formulas (1) through (5) about projection optical systems in Examples 1 through 17. In all of the examples, d-line is reference wavelength, and the following Table 52 shows values at this reference wavelength.

















TABLE 52








EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-



PLE 1
PLE 2
PLE 3
PLE 4
PLE 5
PLE 6
PLE 7
PLE 8
PLE 9
PLE 10





(1/tan(ωmax) − 0.16) ×
−0.001
0.001
0.004
0.008
0.041
0.045
0.046
0.046
0.011
0.003


(θL/θM − 0.27)


θL/θM
0.25
0.28
0.31
0.32
0.47
0.49
0.49
0.49
0.34
0.31


tan(ωmax)
4.73
4.19
3.72
3.15
2.77
2.75
2.73
2.72
3.15
4.12


|cosθ − 2cosφcosψ|
0.21
0.23
0.26
0.30
0.34
0.34
0.34
0.34
0.30
0.24


(ZL + ZD)/Hm
1.23
1.20
1.21
1.27
1.59
1.46
1.36
1.42
1.48
1.34


















EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-
EXAM-



PLE 11
PLE 12
PLE 13
PLE 14
PLE 15
PLE 16
PLE 17





(1/tan(ωmax) − 0.16) ×
0.013
0.005
0.004
0.000
0.002
−0.001
0.001


(θL/θM − 0.27)


θL/θM
0.35
0.30
0.29
0.27
0.28
0.20
0.28


tan(ωmax)
3.09
2.71
2.73
2.75
3.34
5.53
3.41


|cosθ − 2cosφcosψ|
0.31
0.35
0.34
0.34
0.29
0.18
0.28


(ZL + ZD)/Hm
1.48
1.96
1.95
2.07
1.93
1.60
1.74









As the above data show, all of the projection optical systems in Examples 1 through 17 satisfy conditional formulas (1) through (5). It is recognizable that all of the projection optical systems can display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system.
Next, embodiments of a projection-type display apparatus according to the present invention will be described with reference to FIG. 54. FIG. 54 is a schematic diagram illustrating the configuration of a projection-type display apparatus according to an embodiment of the present invention.
A projection-type display apparatus 100 illustrated in FIG. 54 includes the projection optical system 10 according to an embodiment of the present invention, a light source 20, transmission-type display devices 11a through 11c, as light valves corresponding to light of respective colors, and an illumination optical unit 30 for guiding rays from the light source 20 to the light valves. The illumination optical unit 30 includes dichroic mirrors 12 and 13 for color separation, a cross-dichroic prism 14 for color combination, condenser lenses 16a through 16c, and total reflection mirrors 18a through 18c. In FIG. 54, the projection optical system 10 is schematically illustrated. Further, an integrator, such as a fly-eye integrator, is arranged between the light source 20 and the dichroic mirror 12. However, the integrator is not illustrated in FIG. 54.
White light that has been output from the light source 20 is separated into rays of three colors (G light, B light and R light) by the dichroic mirrors 12 and 13 in the illumination optical unit 30. After then, optical paths of the separated rays of respective colors are deflected by the total reflection mirrors 18a through 18c, respectively. Further, the separated rays enter transmission-type display devices 11a through 11c corresponding to the rays of respective colors through condenser lenses 16a through 16c, respectively, and are optically modulated. After the colors are combined by the cross-dichroic prism 14, the light enters the projection optical system 10. The projection optical system 10 projects an optical image of the light that has been optically modulated by the transmission-type display devices 11a through 11c onto a screen, which is not illustrated.
As the transmission-type display devices 11a through 11c, for example, transmission-type liquid crystal display devices or the like may be used. FIG. 54 illustrates an example in which transmission-type display devices are used as light valves. However, light valves provided in the projection-type display apparatus of the present invention are not limited to the transmission-type display devices. Other light modulation means, such as a reflection-type liquid crystal display device or a DMD, may be used.
So far, the present invention has been described by using embodiments and examples. However, the present invention is not limited to the aforementioned embodiments nor examples, and various modifications are possible. For example, a curvature radius, a distance between surfaces, a refractive index, an Abbe number and the like of each lens element are not limited to the values in each of the above numerical value examples, but may be other values.

## Claims

1. A projection optical system that projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image, the projection optical system comprising:
a refractive optical system; and
a reflective optical system having negative refractive power in this order from a reduction side,
wherein the following conditional formula (1) is satisfied:


−0.0015≦(1/tan(ωmax)−0.16)×(θL/θM−0.27)   (1),



where
ωmax: a maximum angle of incidence of a chief ray entering the magnification-side conjugate plane,
θL: an angle between a chief ray from a center of a display surface of the image display device and an optical axis when the chief ray exits from the refractive optical system, and
θM: an angle between the chief ray from the center of the display surface and the optical axis when the chief ray exits from the reflective optical system.

2. The projection optical system, as defined in claim 1, wherein the refractive optical system and the reflective optical system have a common optical axis.

3. The projection optical system, as defined in claim 1, wherein the refractive optical system and the reflective optical system are rotationally symmetric about the optical axis.

4. The projection optical system, as defined in claim 1, wherein the reflective optical system substantially consists of a mirror having negative refractive power.

5. The projection optical system, as defined in claim 1, wherein the following conditional formula (2) is satisfied:


0.18≦θL/θM   (2).

6. The projection optical system, as defined in claim 1, wherein the following conditional formula (3) is satisfied:


2.0≦tan(ωmax)≦7.5   (3).

7. The projection optical system, as defined in claim 1, wherein the following conditional formula (4) is satisfied:


|cos θ−2 cos φ cos ψ|≦0.6   (4), where

θ: an angle between a chief ray from a most peripheral area on a display surface of the image display device and the optical axis when the chief ray exits from the refractive optical system,
φ: an angle between a normal to the reflective optical system and the optical axis at a point where the chief ray from the most peripheral area on the display surface enters the reflective optical system, and
ψ: an angle between the chief ray and the normal to the reflective optical system at the point where the chief ray from the most peripheral area on the display surface enters the reflective optical system.

8. The projection optical system, as defined in claim 1, wherein the following conditional formula (5) is satisfied:


0.5≦(ZL+ZD)/Hm≦2.1   (5), where

ZL: a total length of the refractive optical system,
ZD: a distance on an optical axis between the refractive optical system and the reflective optical system, and
Hm: a maximum effective diameter at a reflection surface of the reflective optical system.

9. The projection optical system, as defined in claim 1, wherein the refractive optical system includes at least one aspheric lens between optical element Lp and the reflective optical system when an optical element including one of a spherical surface or surfaces arranged closest to a magnification side in the refractive optical system is optical element Lp.

10. The projection optical system, as defined in claim 9, wherein a second lens group, as a whole, has positive refractive power when a lens system arranged between the optical element Lp and the reflective optical system is a first lens group in the refractive optical system and a lens system including the optical element Lp, and which is arranged toward a reduction side of the optical element Lp, is the second lens group in the refractive optical system.

11. The projection optical system, as defined in claim 10, wherein the first lens group substantially consists of two lenses of an aspheric lens having negative refractive power and an aspheric lens having positive refractive power in this order from the magnification side.

12. The projection optical system, as defined in claim 10, wherein the first lens group substantially consists of an aspheric lens having negative refractive power.

13. The projection optical system, as defined in claim 9, wherein a most-magnification-side surface of the optical element Lp has a convex shape toward the magnification side.

14. The projection optical system, as defined in claim 9, wherein a most-reduction-side surface of the optical element Lp has a concave shape facing the reduction side.

15. The projection optical system, as defined in claim 9, wherein the optical element Lp has negative refractive power.

16. The projection optical system, as defined in claim 10, wherein the second lens group substantially consists of a 2a-th lens group, in which the optical element Lp, a positive lens with its convex surface facing the magnification side, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element has negative refractive power.

17. The projection optical system, as defined in claim 10, wherein the second lens group substantially consists of a 2a-th lens group, in which the optical element Lp, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element has negative refractive power.

18. The projection optical system, as defined in claim 16, wherein the 2a-th lens group, as a whole, has positive refractive power.

19. The projection optical system, as defined in claim 16, wherein the 2b-th lens group, as a whole, has positive refractive power.

20. A projection-type display apparatus comprising:
a light source;
a light valve on which light from the light source is incident; and
the projection optical system, as defined in claim 1, as a projection optical system that projects an optical image of light that has been optically modulated by the light valve onto a screen.