JP7828112B2 - Projection optical system - Google Patents

Description

The present invention relates to a projection optical system that enlarges and projects an image from an image display element or a light source image from a three-dimensional measuring device, etc.

Portable, compact mobile projectors that use high-intensity LED (Light Emitting Diode) elements as light sources for image display elements such as LCDs (Liquid Crystal Displays) have been commercially available. A compact projection optical system with a reduced overall length is known as a projection optical system that is installed in such mobile projectors and projects an enlarged image (see, for example, Patent Document 1).

In addition, many ultra-short throw projectors that combine multiple lenses and reflecting mirrors have been proposed as being capable of large-screen display at short projection distances (for example, Patent Document 2).Furthermore, a projection device that can convert the aspect ratio of the projected image by adding an anamorphic optical system to these ultra-short throw projectors equipped with reflecting mirrors is known (Patent Document 3).

JP 2011-81072 A Japanese Patent Application Laid-Open No. 2019-164176 JP 2015-114609 A

For example, in applications such as small tabletop projectors that project over a limited range at a shorter projection distance, such as when using a table as a screen, the optical system needs to be made even more compact, and it is desirable to realize a projection optical system that does not use a reflective mirror and positions the optical axis of the optical system at an angle to the projection surface, projecting onto the projection surface at an angle from above or below.

In a front projection projector, which projects an image from the front onto a projection surface, the vertical and horizontal lengths of the image display surface of the image display element (pixel pitch) and the vertical and horizontal lengths of the image enlarged by the optical system and projected onto the projection surface (projection pitch) are similar, and the vertical and horizontal resolution of the image display element is maintained on the projection surface.

However, when an image is projected obliquely using a conventional projection optical system optimized for front projection, the vertical projection pitch of the image projected onto the projection surface becomes longer. Therefore, in order to obtain the same aspect ratio of the projected image as when projected frontally, the usable range of the pixels of the image display element must be reduced vertically, resulting in a problem of reduced vertical resolution.

The present invention aims to solve the above-mentioned problems in the prior art and achieve the following objectives: Specifically, the present invention aims to provide a projection optical system that is suitable for use in an oblique projection ultra-short focus projector, that is compact and has a short overall length without using a reflecting mirror, and that maintains the resolution of the image display element in both the vertical and horizontal directions on the projection surface when projecting an image from an oblique direction.

The projection optical system described in claim 1 is a projection optical system that projects an image formed by an image display element onto a projection surface, and comprises, in order from the projection surface side, a front group having an anamorphic lens that converts the aspect ratio of the projected image on the projection surface, and a rear group that has an image-forming function. The front group consists, in order from the projection surface side, of a first and a second anamorphic lens, and the rear group consists, in order from the projection surface side, of a third lens having positive refractive power, a fourth lens having negative refractive power, a fifth lens having positive refractive power, and a sixth lens having negative refractive power. The projection optical system is characterized by an oblique projection projection optical system in which the optical axis of the projection optical system composed of the front and rear groups is arranged obliquely with respect to the projection surface.

The projection optical system described in claim 2 is the projection optical system described in claim 1, wherein the first and second anamorphic lenses are configured so that the aspect ratio of the converted projected image is similar to the vertical and horizontal pixel pitch corresponding to the image display surface on the image display element and the vertical and horizontal projection pitch of the image corresponding to the image display surface projected onto the projection surface.

It is preferable that the projection optical system described in claim 3 satisfies the following condition in the projection optical system described in claim 1.
1.3<EFLY/EFLX<1.8 (1)
where:
When the optical axis direction of the projection optical system is the Z-axis direction, and in a plane perpendicular to the Z-axis direction, the horizontal direction is the X-axis direction and the vertical direction is the Y-axis direction, EFLX is the focal length of the entire projection optical system in the X-axis direction, and EFLY is the focal length of the entire projection optical system in the Y-axis direction.

A projection optical system described in claim 4 is the projection optical system described in claim 3, wherein the front group comprises a first anamorphic lens having negative power in the X-axis direction and positive power in the Y-axis direction, and a second anamorphic lens having negative power in the X-axis direction and negative power in the Y-axis direction, and it is preferable that the projection optical system satisfies the following conditional expression:
0.9<((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))<1.1(2)
where:
L1R1x is the radius of curvature of the surface of the first anamorphic lens on the projection surface side in the X-axis direction,
L1R2x is the radius of curvature of the surface of the first anamorphic lens on the image display element side in the X-axis direction,
L1R1y is the radius of curvature of the surface of the first anamorphic lens on the projection surface side in the Y-axis direction,
L1R2y is the radius of curvature of the surface of the first anamorphic lens on the image display element side in the Y-axis direction,
L2R1x is the radius of curvature of the surface of the second anamorphic lens on the projection surface side in the X-axis direction,
L2R2x is the radius of curvature of the surface of the second anamorphic lens on the image display element side in the X-axis direction,
L2R1y is the radius of curvature of the surface of the second anamorphic lens on the projection surface side in the Y-axis direction,
L2R2y is the radius of curvature of the surface of the second anamorphic lens on the image display element side in the Y-axis direction,
is.

A projection optical system described in claim 5 is the projection optical system described in claim 3, wherein the front group comprises a first anamorphic lens having negative power in the X-axis direction and positive power in the Y-axis direction, and a second anamorphic lens having positive power in the X-axis direction and negative power in the Y-axis direction, and it is preferable that the projection optical system satisfies the following conditional expression:
-0.2<((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))<0.2 (3)

In the projection optical system described in claim 6, it is preferable that the projection optical system described in claim 4 satisfies the following conditional expression.
0.9<d2/((EFLX+EFLY)/2)<1.4 (4)
where:
d2 is the air gap between the first and second lenses of the front group on the optical axis.

In the projection optical system described in claim 7, it is preferable that the projection optical system described in claim 5 satisfies the following conditional expression.
0.6<d2/((EFLX+EFLY)/2)<1.0 (5)
where:
d2 is the air gap between the first and second lenses of the front group on the optical axis.

It is preferable that the projection optical system described in claim 7 satisfies the following conditional expression in the projection optical system described in claims 1 to 6.
0.515<COSθ<0.777 (6)
Here, θ is the angle between the optical axis direction of the projection optical system and the normal to the projection surface.

The present invention has the effect of realizing a projection optical system that is compact with a short overall length and that maintains the resolution of the image display element in both the vertical and horizontal directions on the projection surface when projecting an image from an oblique direction.

1 is a cross-sectional view showing the configuration of a projection optical system of the present invention, taken along an optical axis and viewed in the X direction. 1 is a cross-sectional view taken along an optical axis in the X direction, showing an optical configuration of a projection optical system according to a first embodiment of the present invention. 1 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to a first embodiment of the present invention. 1A and 1B are diagrams illustrating the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 1 is in focus. FIG. 10 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to a second embodiment of the present invention. FIG. 10 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to a second embodiment of the present invention. 10A and 10B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 2 is in focus; FIG. 10 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to a third embodiment of the present invention. FIG. 10 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to a third embodiment of the present invention. 10A and 10B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 3 is in focus; FIG. 10 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to Example 4 of the present invention. FIG. 10 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to Example 4 of the present invention. 10A and 10B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 4 is in focus; FIG. 10 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to a fifth embodiment of the present invention. FIG. 10 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to a fifth embodiment of the present invention. 13A and 13B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 5 is in focus. FIG. 10 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to Example 6 of the present invention. FIG. 10 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to Example 6 of the present invention. 13A and 13B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 6 is in focus. FIG. 11 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to Example 7 of the present invention. FIG. 11 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to Example 7 of the present invention. 13A and 13B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 7 is in focus; FIG. 13 is a cross-sectional view taken along the optical axis in the X direction, showing the optical configuration of a projection optical system according to Example 8 of the present invention. FIG. 13 is a cross-sectional view taken along the optical axis in the Y direction, showing the optical configuration of a projection optical system according to Example 8 of the present invention. 13A and 13B are diagrams showing the curvature of field in the X direction and the Y direction, respectively, when the projection optical system according to Example 8 is in focus.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a cross-sectional view taken along an optical axis in the X direction, showing the configuration of a projection optical system according to an embodiment of the present invention.
FIG. 2 is a cross-sectional view of an example of the optical configuration of a projection optical system according to an embodiment of the present invention, viewed in the X direction along the optical axis. In FIG. 2, the XYZ coordinate system defines the Z axis as the direction coinciding with the optical axis passing through the center of the projection optical system, and defines the X axis as the horizontal direction and the Y axis as the vertical direction, based on the display surface of the image display element, in a plane perpendicular to the Z axis. In the figure, the Y-Z plane including the Z axis is defined as the X direction along the optical axis, and the X-Z plane including the Z axis is defined as the Y direction along the optical axis (the same coordinate system will be used in each embodiment below). FIG. 3 is a cross-sectional view of the same projection optical system according to the embodiment of the present invention as in FIG. 2, viewed in the Y direction along the optical axis. The optical configurations of FIGS. 2 and 3 correspond to the optical configuration of the first embodiment of the present invention.

As shown in Figure 1, the projection optical system of the present invention is an oblique projection optical system in which the optical axis of the optical system is positioned at an angle to the projection surface (a tabletop surface in this embodiment) so that the projection surface is projected diagonally downward from a predetermined height h. Note that the projection optical system of the present invention is not limited to this example, and may be positioned, for example, so that a wall surface is used as the projection surface and the wall surface is illuminated diagonally upward from below.

2 and 3, a projection optical system according to an embodiment of the present invention comprises, in order from the projection surface side, a front group having an anamorphic lens that converts the aspect ratio of the projected image on the projection surface, and a rear group having an image-forming function. The front group is composed of, in order from the projection surface side, first and second anamorphic lenses, and the rear group is a two-group optical system consisting of, in order from the projection surface side, a third lens having positive refractive power, a fourth lens having negative refractive power, a fifth lens having positive refractive power, and a sixth lens having negative refractive power. An aperture stop S is disposed between the front group GF and the rear group GR. In all of the following examples, in the cross-sectional views of the optical configuration, CG denotes a cover glass, and D denotes the display surface of an image display element disposed on the reduction side of the projection optical system.

In the projection optical system of the present invention, an image display element that forms an image, such as an LCD, a digital mirror device (DMD), or a micro LED display, is arranged on the display surface D (not shown).

In the projection optical system according to an embodiment of the present invention, the front group GF is composed of two anamorphic lenses L1 and L2. Anamorphic lenses L1 and L2 are toroidal lenses with different radii of curvature in the X and Y directions on the surface facing the image element or the surface facing the projection surface, respectively. This results in different focal lengths in the X and Y directions for the entire projection optical system.

In the projection optical system according to the embodiment of the present invention, the rear group GR is made up of four rotationally symmetric lenses, the third lens L3 through the sixth lens L6, which together have an imaging function. The third lens L3 through the sixth lens L6 are each aspherical plastic lenses.

As shown in Figure 1, when an image is projected from an oblique direction onto the projection surface, the vertical (depth) projection pitch of the image projected onto the projection surface is longer than when the image is projected from the front (e.g., directly above) of the projection surface. Therefore, in order to obtain a projection image (e.g., a square) with a similar aspect ratio to the image displayed on the image display element (e.g., a square), when using a conventional rotationally symmetric projection optical system, the usable range of the pixels of the image display element must be reduced vertically (shortened vertically), resulting in a deterioration in vertical resolution compared to front projection.

The projection optical system of the present invention is an oblique projection optical system, in which the radius of curvature of each lens surface of the anamorphic lenses L1 and L2 is configured so that the aspect ratio of the projected image converted by the anamorphic lens constituting the front group GF is similar to the vertical and horizontal pixel pitch corresponding to the image display surface on the image display element and the vertical and horizontal projection pitch of the image corresponding to the image display surface projected onto the projection surface.

In the projection optical system according to an embodiment of the present invention, the front group GF consists of a first lens L1 having negative power in the X-axis direction and positive power in the Y-axis direction, and a second lens L2 having negative power in the X-axis direction and negative power in the Y-axis direction.

In other words, the projection optical system according to an embodiment of the present invention is configured such that the radius of curvature of each lens surface of the anamorphic lenses L1 and L2 is such that the focal length in the X direction of the entire projection optical system is shorter than the focal length in the Y direction. Therefore, even in an oblique projection optical system, there is no need to reduce the usable range of pixels of the image display element in the vertical direction, and there is no difference in resolution between the vertical and horizontal directions.

The projection optical system of the present invention also satisfies the following conditional expression:
1.3<EFLY/EFLX<1.8 (1)
where:
When the optical axis direction of the projection optical system is the Z-axis direction, and in a plane perpendicular to the Z-axis direction, the horizontal direction is the X-axis direction and the vertical direction is the Y-axis direction, EFLX is the focal length of the entire projection optical system in the X-axis direction, and EFLY is the focal length of the entire projection optical system in the Y-axis direction.

Conditional formula (1) is a conditional formula that minimizes the difference in resolution between the vertical and horizontal directions of the projected image.If this range is exceeded, there will be a difference in the vertical and horizontal aspect ratio of the pixels on the projection screen, which is undesirable.

In addition, in the projection optical system of the present invention, it is preferable that the front group comprises a first anamorphic lens having negative power in the X-axis direction and positive power in the Y-axis direction, and a second anamorphic lens having negative power in the X-axis direction and negative power in the Y-axis direction, and that the projection optical system satisfies the following conditional expression:
0.9<((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))<1.1(2)
where:
L1R1x is the radius of curvature of the surface of the first lens of the front group facing the projection surface in the X-axis direction,
L1R2x is the radius of curvature of the surface of the first lens in the front group facing the image display device in the X-axis direction,
L1R1y is the radius of curvature of the surface of the first lens of the front group facing the projection surface in the Y-axis direction,
L1R2y is the radius of curvature of the surface of the first lens in the front group facing the image display device in the Y-axis direction,
L2R1x is the radius of curvature of the surface of the second lens in the front group facing the projection surface in the X-axis direction,
L2R2x is the radius of curvature of the surface of the second lens in the front group facing the image display device in the X-axis direction,
L2R1y is the radius of curvature of the surface of the second lens in the front group facing the projection surface in the Y-axis direction,
L2R2y is the radius of curvature of the surface of the second lens in the front group facing the image display element in the Y-axis direction,
is.

Conditional formula (2) is a conditional formula for reducing the difference in field curvature that occurs in the front group GF in the Y and X directions of the projection optical system, thereby effectively correcting the field curvature that occurs in the entire projection optical system.

In addition, in the projection optical system of the present invention, it is preferable that the front group comprises a first anamorphic lens having negative power in the X-axis direction and positive power in the Y-axis direction, and a second anamorphic lens having positive power in the X-axis direction and negative power in the Y-axis direction, and that the projection optical system satisfies the following conditional expression:
-0.2<((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))<0.2 (3)

Conditional formula (3) is a conditional formula for reducing the difference in field curvature that occurs in the front group GF in the Y and X directions of the projection optical system, thereby effectively correcting the field curvature that occurs in the entire projection optical system and shortening the overall length of the optical system.

Furthermore, it is preferable that the projection optical system of the present invention satisfies the following conditional expression in addition to the above conditional expression (2).
0.9<d2/((EFLX+EFLY)/2)<1.4 (4)
where:
d2 is the air gap between the first and second lenses of the front group on the optical axis.

Conditional formula (4) is a conditional formula for shortening the overall length of the projection optical system, preventing differences in resolution between the vertical and horizontal directions of the image projected by the projection optical system, and minimizing the occurrence of coma aberration. Exceeding conditional formula (4) undesirably increases the overall length of the projection optical system. Conversely, failing conditional formula (4) undesirably reduces the difference in focal length between the X and Y directions of the entire projection optical system, resulting in a difference in the vertical and horizontal aspect ratio of pixels on the projection screen. Furthermore, coma aberration worsens in the diagonal direction, making it impossible to ensure diagonal performance.

Furthermore, it is preferable that the projection optical system of the present invention satisfies the following conditional expression in addition to the above conditional expression (3).
0.6<d2/((EFLX+EFLY)/2)<1.0 (5)
where:
d2 is the air gap between the first and second lenses of the front group on the optical axis.

Conditional formula (5) is a conditional formula for shortening the overall length of the projection optical system, preventing differences in resolution between the vertical and horizontal directions of the image projected by the projection optical system, and minimizing the occurrence of coma aberration. Exceeding conditional formula (5) undesirably increases the overall length of the projection optical system. Conversely, failing conditional formula (5) undesirably reduces the difference in focal length between the X and Y directions of the entire projection optical system, resulting in a difference in the vertical and horizontal aspect ratio of pixels on the projection screen. Furthermore, coma aberration worsens in the diagonal direction, making it impossible to ensure diagonal performance.

It is also preferable that the projection optical system of the present invention satisfies the following conditional expression:
0.515<COSθ<0.777 (6)
Here, θ is the angle between the optical axis direction of the projection optical system and the normal to the projection surface.

The projection optical system of the present invention is an oblique projection optical system, and conditional expression (5) is a projection configuration of the optical system that is suitable for use as a small projector that projects over a limited projection range at a shorter projection distance, for example, when using a table as a screen.

Next, specific numerical examples of the projection optical system of the present invention are shown. The symbols used in each example are as follows:

: focal length of the second lens L2 in the Y-axis direction f3-f5: focal lengths of the third lens L3 to the sixth lens L6, r: paraxial radius of curvature rX: paraxial radius of curvature in the X-axis direction, rY: paraxial radius of curvature in the Y-axis direction, d: lens thickness or air space on the optical axis, nd: refractive index of the lens material for the d-line, νd: Abbe number of the lens material. In each example, a surface with an "*" after the surface number is an aspherical surface.
In each example, a surface having a "+" after its surface number is an anamorphic surface.

The aspherical shape is expressed by the following equation (1), where the optical axis direction is the z direction, the direction perpendicular to the z axis is the y direction, the conic coefficient is K, and the aspherical coefficients are A4, A6, A8, A10, etc.
z=(y ² /r)/[1+{1-(1+K)(y/r) ² } ^1/2 ]+A4y ⁴ +A6y ⁶ +A8y ⁸ +A10y ¹⁰ ...(1)

The anamorphic surface shape is expressed by the following equation (2), where the optical axis direction is the z direction, the horizontal direction in a plane perpendicular to the z axis is the X-axis direction, and the vertical direction is the Y-axis direction, the radius of curvature in the horizontal direction is rX, the radius of curvature in the vertical direction is rY, the conic coefficient in the horizontal direction is KX, the conic coefficient in the vertical direction is KY, the aspherical coefficients in the horizontal direction are A4, A6, A8, A10, etc., and the aspherical coefficients in the vertical direction are B4, B6, B8, B10, etc.
z={(x ² /rX)+(y ² /rY)}/[1+{1-(1+KX)(x/rX) ² -(1+KY)(y/rY) ² } ^1/2 ]+A4x ⁴ +B4y ⁴ +A6x ⁶ +B6y ⁶ +A8x ⁸ +B8y ⁸ +A10x ¹⁰ +B10y ¹⁰ ...(2)

In the aspherical coefficients, E represents a power of 10, for example, 2.3×10 ⁻² is expressed as 2.3E-002. The symbols for these specification values are also common to the numerical data in the examples described below. The symbols for these specification values are also common to the numerical data in the examples described below.

Next, the projection optical system according to the first embodiment will be described.
Fig. 2 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of the projection optical system according to Example 1. Fig. 3 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of the projection optical system according to Example 1.

Figure 4 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 1 is focused. The field curvature is shown as a value at a wavelength of 550 nm.

In terms of field curvature, S indicates the sagittal image surface and T indicates the tangential image surface. Also, X and Y in the diagram indicate the image height. Note that the symbols in the aberration diagrams are the same in the examples described below.

2 and 3, the projection optical system of Example 1 is an optical system with a two-group configuration consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also disposed between the front group GF and the rear group GR.

The front group GF consists of a first lens L1 having negative power in the X-axis direction and positive power in the Y-axis direction, and a second lens L2 having negative power in the X-axis direction and negative power in the Y-axis direction.

The surface shape of the first lens L1 and the second lens L2 on the projection surface side is a rotationally symmetric aspherical shape, and the surface shape of the first lens L1 and the second lens L2 on the image display element side is a toroidal surface.

The rear group GR is made up of four lenses, from the third lens L3 to the sixth lens L6, and has an imaging function as a whole. The third lens L3 to the sixth lens L6 are each rotationally symmetric aspherical plastic lenses.

The overall specifications of the projection optical system of Example 1 are shown below.
FnoX: 1.15
FnoY: 1.11
EFLX: 5.361mm
EFLY: 8.399mm
f1X: -172.929mm
f1Y: 25.280mm
f2X: -51.173mm
f2Y: -11.937mm
f3: 4.638mm
f4:-7.105mm
f5: 5.736mm
f6:-15.094mm

The surface data of the projection optical system of Example 1 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 1 is shown below.
Front page
K=0.000E+00
A4=-3.885E-05, A6=-7.917E-07, A8=1.227E-08, A10=-1.955E-10
2nd side
KY=-2.000E+01
KX=-1.044E-02
A4=0.000E+00
Third page
K=0.000E+00
A4=1.060E-03, A6=-4.232E-04, A8=1.207E-04, A10=-1.929E-05, A12=1.533E-06, A14=-4.863E-08,
4th page
KY=2.879E-01
KX=2.001E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-5.244E-04, A6=4.850E-05, A8=3.116E-05, A10=4.091E-06, A12=-6.899E-07, A14=9.438E-08
Page 7
K=0.000E+00
A4=6.589E-03, A6=-2.975E-04, A8=-1.506E-04, A10=3.210E-05, A12=4.808E-06, A14=-1.183E-06
8th page
K=0.000E+00
A4=3.165E-03, A6=-2.522E-03, A8=-1.510E-04, A10=1.711E-05, A12=1.232E-05, A14=-1.023E-06
9th page
K=0.000E+00
A4=5.300E-03, A6=-2.564E-03, A8=3.057E-04, A10=-4.784E-05, A12=6.491E-06, A14=4.302E-07
Page 10
K=0.000E+00
A4=1.494E-02, A6=-3.439E-03, A8=4.804E-04, A10=-2.679E-05, A12=1.218E-06, A14=-4.693E-07
Page 11
K=-1.549E+00
A4=3.074E-04, A6=-5.260E-04, A8=3.452E-05, A10=-2.193E-06, A12=1.153E-06, A14=1.536E-07, A16=-7.210E-08
Page 12
K=-5.915E+00
A4=-3.545E-03, A6=1.151E-04, A8=-3.803E-04, A10=-1.699E-05, A12=9.939E-06, A14=1.468E-06, A16=-4.154E-07
Page 13
K=-3.713E+00
A4=-1.162E-03, A6=-1.078E-03, A8=-1.494E-04, A10=-1.713E-05, A12=1.741E-05, A14=-3.236E-06, A16=1.883E-07

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 1 are shown below.
(1) EFLY/EFLX=1.567
(2) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=1.030
(4) d2/((EFLX+EFLY)/2)=1.079
(6) COSθ=0.555

Next, a projection optical system according to a second embodiment will be described.
5 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of the projection optical system according to Example 2. Also, FIG. 6 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of the projection optical system according to Example 2.

Figure 7 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 2 is focused. The field curvature is shown as a value at a wavelength of 550 nm.

As shown in Figures 5 and 6, the projection optical system of Example 2 is a two-group optical system consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also located between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of the second embodiment are shown below.
FnoX: 1.15
FnoY: 1.08
EFLX: 5.384mm
EFLY: 8.606mm
f1X: -174.689mm
f1Y: 23.983mm
f2X: -51.173mm
f2Y: -11.937mm
f3: 4.638mm
f4:-7.105mm
f5: 5.736mm
f6:-15.094mm
The surface data of the projection optical system of Example 2 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 2 is shown below.
Front page
K=0.000E+00
A4= -1.059E-05, A6= -3.542E-06, A8= 9.224E-08, A10= -1.036E-09
2nd side
KY=-2.000E+01
KX= -7.198E-02
A4=0.000E+00
Third page
K=0.000E+00
A4=1.060E-03, A6=-4.232E-04, A8=1.207E-04, A10=-1.929E-05, A12=1.533E-06, A14=-4.863E-08,
4th page
KY=2.879E-01
KX=2.001E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-5.244E-04, A6=4.850E-05, A8=3.116E-05, A10=4.091E-06, A12=-6.899E-07, A14=9.438E-08
Page 7
K=0.000E+00
A4=6.589E-03, A6=-2.975E-04, A8=-1.506E-04, A10=3.210E-05, A12=4.808E-06, A14=-1.183E-06
8th page
K=0.000E+00
A4=3.165E-03, A6=-2.522E-03, A8=-1.510E-04, A10=1.711E-05, A12=1.232E-05, A14=-1.023E-06
9th page
K=0.000E+00
A4=5.300E-03, A6=-2.564E-03, A8=3.057E-04, A10=-4.784E-05, A12=6.491E-06, A14=4.302E-07
Page 10
K=0.000E+00
A4=1.494E-02, A6=-3.439E-03, A8=4.804E-04, A10=-2.679E-05, A12=1.218E-06, A14=-4.693E-07
Page 11
K=-1.549E+00
A4=3.074E-04, A6=-5.260E-04, A8=3.452E-05, A10=-2.193E-06, A12=1.153E-06, A14=1.536E-07, A16=-7.210E-08
Page 12
K=-5.915E+00
A4=-3.545E-03, A6=1.151E-04, A8=-3.803E-04, A10=-1.699E-05, A12=9.939E-06, A14=1.468E-06, A16=-4.154E-07
Page 13
K=-3.713E+00
A4=-1.162E-03, A6=-1.078E-03, A8=-1.494E-04, A10=-1.713E-05, A12=1.741E-05, A14=-3.236E-06, A16=1.883E-07

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 2 are shown below.
(1) EFLY/EFLX=1.598
(2) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=1.016
(4) d2/((EFLX+EFLY)/2)=1.061
(6) COSθ=0.555

Next, a projection optical system according to a third embodiment will be described.
8 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of the projection optical system according to Example 3. Also, FIG. 9 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of the projection optical system according to Example 3.

Figure 10 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 3 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

As shown in Figures 8 and 9, the projection optical system of Example 3 is a two-group optical system consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also located between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of Example 3 are shown below.
FnoX: 1.15
FnoY: 1.13
EFLX: 5.275mm
EFLY: 7.491mm
f1X: -504.629mm
f1Y: 29.940mm
f2X: -35.684mm
f2Y: -13.214mm
f3: 4.604mm
f4:-7.593mm
f5: 5.652mm
f6:-15.322mm
The surface data of the projection optical system of Example 3 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 3 is shown below.
Front page
K=0.000E+00
A4=-2.974E-05, A6=-8.604E-07, A8=1.032E-08, A10=-1.205E-10
2nd side
KY=-7.193E+00
KX=2.913E-01
A4=0.000E+00
Third page
K=0.000E+00
A4=7.985E-04, A6=-4.046E-04, A8=1.269E-04, A10=-1.975E-05, A12=1.455E-06, A14=-4.174E-08,
4th page
KY=1.728E-01
KX=2.000E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-4.247E-05, A6=1.043E-05, A8=2.920E-05, A10=4.167E-06, A12=-6.460E-07, A14=1.016E-07
Page 7
K=0.000E+00
A4=6.603E-03, A6=-2.802E-04, A8=-1.492E-04, A10=3.214E-05, A12=4.80717E-06, A14=-1.182E-06
8th page
K=0.000E+00
A4=2.748E-03, A6=-2.544E-03, A8=-1.495E-04, A10=1.701E-05, A12=1.20273E-05, A14=-1.193E-06
9th page
K=0.000E+00
A4=7.815E-03, A6=-2.504E-03, A8=3.353E-04, A10=-4.200E-05, A12=6.41076E-06, A14=5.433E-08
Page 10
K=0.000E+00
A4=1.451E-02, A6=-3.212E-03, A8=4.849E-04, A10=-2.917E-05, A12=1.73785E-06, A14=-1.344E-07
Page 11
K=-1.516E+00
A4=-6.349E-06, A6=-5.771E-04, A8=3.458E-05, A10=-1.015E-06, A12=1.22408E-06, A14=1.642E-07, A16=-5.188E-08
Page 12
K=-4.935E+00
A4=-3.270E-03, A6=1.308E-04, A8=-3.769E-04, A10=-1.602E-05, A12=1.00862E-05, A14=1.494E-06, A16=-3.992E-07
Page 13
K=-3.166E+00
A4=6.552E-05, A6=-1.097E-03, A8=-1.697E-04, A10=-1.835E-05, A12=1.75976E-05, A14=-3.199E-06, A16=1.761E-07

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 3 are shown below.
(1)EFLY/EFLX=1.420
(2) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=1.018
(4) d2/((EFLX+EFLY)/2)=1.190
(6) COSθ=0.555

Figure 11 is a cross-sectional view taken along the optical axis in the X direction, showing an example of the optical configuration of a projection optical system according to Example 4. Figure 12 is a cross-sectional view taken along the optical axis in the Y direction, showing an example of the optical configuration of a projection optical system according to Example 4.

Figure 13 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 4 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

11 and 12, the projection optical system of Example 4 is an optical system with a two-group configuration consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also disposed between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of Example 4 are shown below.
FnoX: 1.16
FnoY: 1.12
EFLX: 4.739mm
EFLY: 7.941mm
f1X: -44.689mm
f1Y: 34.987mm
f2X: -915.655mm
f2Y: -17.882mm
f3: 4.801mm
f4: -6.158mm
f5:5.350mm
f6:-29.628mm
The surface data of the projection optical system of Example 4 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 4 is shown below.
Front page
K=0.000E+00
A4= -4.289E-05, A6= -1.020E-07, A8= 8.440E-09, A10= -1.131E-10
2nd side
KY= -3.984E+00
KX= 6.083E-02
A4=0.000E+00
Third page
K=0.000E+00
A4= 8.775E-04, A6= -3.293E-04, A8=1.183E-04, A10= -1.970E-05, A12= 1.521E-06, A14= -4.507E-08,
4th page
KY=1.028E+00
KX=2.000E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4= -1.898E-04, A6=2.533E-06, A8= 4.170E-05, A10=4.630E-06, A12= -6.218E-07, A14= 6.391E-08
Page 7
K=0.000E+00
A4= 8.209E-03, A6= -2.687E-04, A8= -1.509E-04, A10= 3.143E-05, A12= 3.579E-06, A14= -1.194E-06
8th page
K=0.000E+00
A4=4.090E-03, A6= -2.497E-03, A8= -1.747E-04, A10= -2.276E-06, A12= 9.507E-06, A14= 3.120E-07
9th page
K=0.000E+00
A4=3.814E-03, A6= -2.647E-03, A8=3.131E-04, A10=-4.642E-05, A12=7.865E-06, A14=2.832E-07
Page 10
K=0.000E+00
A4=1.814E-02, A6=-2.534E-03, A8=3.477E-04, A10=-8.366E-05, A12=1.663E-05, A14=-1.088E-06
Page 11
K=-1.958E+00
A4=-3.382E-04, A6=-6.658E-04, A8=5.339E-05, A10=9.428E-07, A12=1.804E-07, A14=-7.987E-09, A16=-1.888E-08
Page 12
K=-3.698E+00
A4=3.354E-04, A6=6.850E-04, A8=-1.057E-03, A10=9.837E-05, A12=4.267E-06, A14=1.347E-06, A16=-5.029E-07
Page 13
K=-3.926E+00
A4=6.008E-03, A6=-3.452E-03, A8=-1.281E-04, A10=4.366E-05, A12=1.726E-05, A14=-5.059E-06, A16=3.345E-07

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 4 are shown below.
(1) EFLY/EFLX=1.676
(2) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=0.952
(4) d2/((EFLX+EFLY)/2)=1.314
(6) COSθ=0.555

Next, a projection optical system according to a fifth embodiment will be described.
14 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of a projection optical system according to Example 5. Also, FIG. 15 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of a projection optical system according to Example 5.

Figure 16 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 5 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

14 and 15, the projection optical system of Example 5 is an optical system with a two-group configuration consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also disposed between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of Example 5 are shown below.
FnoX: 1.14
FnoY: 1.12
EFLX: 5.313mm
EFLY: 9.225mm
f1X: -139.014mm
f1Y: 27.970mm
f2X: -59.784mm
f2Y: -11.438mm
f3: 4.669mm
f4:-6.270mm
f5: 5.305mm
f6:-24.411mm
The surface data of the projection optical system of Example 5 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 5 is shown below.
Front page
K=0.000E+00
A4=-2.016E-05, A6=-8.971E-07, A8=4.661E-09, A10=-1.158E-10
2nd side
KY=-1.278E+01
KX=-6.657E-02
A4=0.000E+00
Third page
K=0.000E+00
A4=3.691E-04, A6=-3.344E-04, A8=1.208E-04, A10=-1.986E-05, A12=1.486E-06, A14=-4.151E-08,
4th page
KY=-7.180E-01
KX=1.644E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=3.571E-04, A6=-2.940E-06, A8=3.247E-05, A10=3.822E-06, A12=-6.739E-07, A14=6.220E-08
Page 7
K=0.000E+00
A4=7.914E-03, A6=-2.620E-04, A8=-1.487E-04, A10=3.176E-05, A12=4.394E-06, A14=-1.374E-06
8th page
K=0.000E+00
A4=3.648E-03, A6=-2.607E-03, A8=-2.046E-04, A10=-3.365E-06, A12=9.443E-06, A14=3.191E-07
9th page
K=0.000E+00
A4=4.223E-03, A6=-2.705E-03, A8=2.874E-04, A10=-5.180E-05, A12=6.796E-06, A14=9.537E-08
Page 10
K=0.000E+00
A4=1.675E-02, A6=-2.615E-03, A8=3.375E-04, A10=-8.595E-05, A12=1.563E-05, A14=-1.116E-06
Page 11
K=-1.885E+00
A4=-6.596E-04, A6=-7.223E-04, A8=5.655E-05, A10=1.272E-06, A12=9.474E-07, A14=5.559E-09, A16=-3.906E-08
Page 12
K=-3.967E+00
A4=-3.349E-03, A6=-2.023E-04, A8=-1.091E-03, A10=1.263E-04, A12=4.039E-06, A14=6.799E-07, A16=-5.338E-07
Page 13
K=-3.474E+00
A4=4.034E-03, A6=-3.626E-03, A8=-2.200E-04, A10=3.939E-05, A12=1.647E-05, A14=-4.162E-06, A16=2.599E-07

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 5 are shown below.
(1) EFLY/EFLX=1.736
(2) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=1.080
(4) d2/((EFLX+EFLY)/2)=1.168
(6) COSθ=0.555

Next, a projection optical system according to Example 6 will be described.
17 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of a projection optical system according to Example 6. Also, FIG. 18 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of a projection optical system according to Example 6.

Figure 19 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 6 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

In terms of field curvature, S indicates the sagittal image surface and T indicates the tangential image surface. Also, X and Y in the diagram indicate the image height. Note that the symbols in the aberration diagrams are the same in the examples described below.

As shown in Figures 17 and 18, the projection optical system of Example 6 is a two-group optical system consisting of, in order from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also located between the front group GF and the rear group GR.

The front group GF consists of a first lens L1 that has negative power in the X-axis direction and positive power in the Y-axis direction, and a second lens L2 that has positive power in the X-axis direction and negative power in the Y-axis direction and has a concave surface facing the projection surface.

The surface shape of the first lens L1 and the second lens L2 on the projection surface side is a rotationally symmetric aspherical shape, and the surface shape of the first lens L1 and the second lens L2 on the image display element side is a toroidal surface.

The rear group GR is made up of four lenses, from the third lens L3 to the sixth lens L6, and has an imaging function as a whole. The third lens L3 to the sixth lens L6 are each rotationally symmetric aspherical plastic lenses.

The overall specifications of the projection optical system of Example 6 are shown below.
FnoX: 1.83
F no Y: 1.78
EFLX: 5.236mm
EFLY: 8.352mm
f1X:-33.490mm
f1Y: 26.198mm
f2X: 88.129mm
f2Y: -15.966mm
f3: 4.502mm
f4:-5.851mm
f5: 2.693mm
f6:-17.512mm

The surface data of the projection optical system of Example 6 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 6 is shown below.
Front page
K=0.000E+00
A4=-1.224E-04, A6=8.124E-06, A8=-1.495E-07, A10=9.406E-10
2nd side
KY=-1.030E+01
KX=8.590E-01
A4=0.000E+00
Third page
K=0.000E+00
A4=5.991E-03, A6=-1.281E-03, A8=5.466E-05, A10=1.004E-05, A12=-9.709E-07
4th page
KY=0.000E+00
KX=0.000E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-1.193E-02, A6=8.824E-04, A8=-6.987E-05, A10=-1.733E-06, A12=1.242E-05
Page 7
K=0.000E+00
A4=5.999E-04, A6=8.717E-05, A8=-3.101E-05, A10=8.288E-05, A12=1.712E-09
8th page
K=0.000E+00
A4=1.377E-02, A6=-1.960E-03, A8=4.823E-04, A10=-4.601E-05, A12=4.233E-10
9th page
K=0.000E+00
A4=1.076E-04, A6=-7.373E-04, A8=-1.537E-04, A10=6.660E-05, A12=-3.543E-10
Page 10
K=0.000E+00
A4=8.591E-03, A6=-3.949E-03, A8=41.473E-03, A10=-6.689E-05, A12=8.884E-12
Page 11
K=-1.939E+00
A4=2.746E-03, A6=5.097E-04, A8=9.993E-06, A10=6.938E-05, A12=1.940E-09
Page 12
K=-4.185E+00
A4=-6.139E-04, A6=2.234E-06, A8=-4.482E-04, A10=-1.785E-05, A12=3.406E-06
Page 13
K=-3.491E+00
A4=-1.433E-03, A6=-6.738E-04, A8=-1.528E-04, A10=-3.630E-05, A12=6.775E-06

The values corresponding to the conditional expressions (1) to (6) of the projection optical system of Example 6 are shown below.
(1) EFLY/EFLX=1.600
(3) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=0.013
(5) d2/((EFLX+EFLY)/2)=0.908
(6) COSθ=0.555

Next, a projection optical system according to Example 7 will be described.
20 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of a projection optical system according to Example 7. Also, FIG. 21 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of a projection optical system according to Example 7.

Figure 22 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 7 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

As shown in Figures 20 and 21, the projection optical system of Example 7 is an optical system with a two-group configuration consisting of, from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also located between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of Example 7 are shown below.
FnoX: 1.81
F no Y: 1.77
EFLX: 5.237mm
EFLY: 7.934mm
f1X: -30.885mm
f1Y: 25.560mm
f2X: 59.025mm
f2Y: -17.077mm
f3: 4.462mm
f4:-5.736mm
f5: 2.708mm
f6:-16.136mm
The surface data of the projection optical system of Example 7 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 7 is shown below.
Front page
K=0.000E+00
A4=-1.968E-04, A6=1.738E-05, A8=-2.778E-07, A10= -6.540E-
2nd side
KY=-1.399E+01
KX= 1.109E+00
A4=0.000E+00
Third page
K=0.000E+00
A4=4.612E-03, A6=-1.262E-03, A8=3.448E-05, A10=9.295E-06, A12=-1.662E-06
4th page
KY=0.000E+00
KX=2.001E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-1.243E-02, A6=5.212E-04, A8=-1.265E-04, A10=-1.629E-05, A12=1.521E-05
Page 7
K=0.000E+00
A4=-4.285E-03, A6=-4.133E-05, A8=-1.416E-04, A10=8.223E-05, A12=-1.238E-07
8th page
K=0.000E+00
A4=9.609E-03, A6=-1.707E-03, A8=6.001E-04, A10=8.203E-06, A12=-8.577E-09
9th page
K=0.000E+00
A4=8.421E-04, A6=-1.953E-03, A8=-2.983E-04, A10=1.439E-04, A12=-6.111E-09
Page 10
K=0.000E+00
A4=8.010E-03, A6=-5.037E-03, A8=1.511E-03, A10=-6.502E-05, A12=2.227E-09
Page 11
K=-1.995E+00
A4=3.195E-03, A6=1.154E-03, A8=1.936E-04, A10=9.913E-05, A12=6.694E-09
Page 12
K=-4.100E+00
A4=-4.848E-04, A6=7.805E-05, A8=-4.088E-04, A10=-1.188E-05, A12=-3.934E-08
Page 13
K=-3.523E+00
A4=-1.730E-03, A6=-7.319E-04, A8=-1.644E-04, A10=-3.824E-05, A12=5.338E-06

The values corresponding to the conditional expressions (1) to (5) of the projection optical system of Example 7 are shown below.
(1) EFLY/EFLX=1.520
(3) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=0.139
(5) d2/((EFLX+EFLY)/2)=0.820
(6) COSθ=0.555

Next, a projection optical system according to an eighth embodiment will be described.
Fig. 23 is a cross-sectional view taken along the optical axis in the X direction showing an example of the optical configuration of a projection optical system according to Example 8. Fig. 24 is a cross-sectional view taken along the optical axis in the Y direction showing an example of the optical configuration of a projection optical system according to Example 8.

Figure 25 shows (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system of Example 8 is in focus. The field curvature is shown as a value at a wavelength of 550 nm.

As shown in Figures 23 and 24, the projection optical system of Example 8 is an optical system with a two-group configuration consisting of, from the projection surface side, a front group GF that converts the aspect ratio of the projected image on the projection surface, and a rear group GR that has an image-forming function. An aperture stop S is also located between the front group GF and the rear group GR.

The configuration of the front group GF and the rear group GR is the same as that of the projection optical system in Example 1, so detailed explanation will be omitted.

The overall specifications of the projection optical system of Example 8 are shown below.
FnoX: 1.80
F no Y: 1.75
EFLX: 5.249mm
EFLY: 7.446mm
f1X: -28.393mm
f1Y: 24.599mm
f2X: 57.182mm
f2Y: -16.393mm
f3: 4.108mm
f4:-5.774mm
f5: 2.814mm
f6:-12.401mm
The surface data of the projection optical system of Example 8 is shown below (unit: mm).

The aspherical data of the projection optical system of Example 8 is shown below.
Front page
K=0.000E+00
A4=-2.990E-04, A6=2.714E-05, A8=-4.905E-07, A10=-4.695E-09
2nd side
KY=1.997E+00
KX=1.444E+00
A4=0.000E+00
Third page
K=0.000E+00
A4=7.985E-04, A6=-4.046E-04, A8=1.269E-04, A10=-1.975E-05, A12=1.455E-06, A14=-4.174E-08,
4th page
KY=-2.000E+01
KX=0.000E+00
A4=0.000E+00
Page 6
K=0.000E+00
A4=-1.186E-02, A6=5.831E-04, A8=-1.729E-04, A10=-2.415E-05, A12=1.336E-05
Page 7
K=0.000E+00
A4=-5.266E-03, A6=3.315E-05, A8=-1.429E-04, A10=1.009E-04, A12=4.433E-08
8th page
K=0.000E+00
A4=7.547E-03, A6=-2.423E-03, A8=1.877E-03, A10=-1.602E-04, A12=-4.170E-09
9th page
K=0.000E+00
A4=5.434E-03, A6=1.831E-03, A8=-1.514E-03, A10=1.015E-03, A12=-2.515E-09
Page 10
K=0.000E+00
A4=1.875E-03, A6=-7.621E-03, A8=2.628E-03, A10=3.474E-04, A12=5.780E-09
Page 11
K=-2.544E+00
A4=7.415E-03, A6=2.152E-03, A8=1.842E-04, A10=3.448E-04, A12=-1.256E-08
Page 12
K=-3.976E+00
A4=-2.650E-04, A6=1.492E-04, A8=-4.037E-04, A10=-6.523E-06, A12=2.921E-06
Page 13
K=-3.910E+00
A4=-2.295E-03, A6=-7.227E-04, A8=-1.717E-04, A10=-4.166E-05, A12=3.391E-06

The values corresponding to the conditional expressions (1) to (5) of the projection optical system of Example 8 are shown below.
(1) EFLY/EFLX=1.423
(3) ((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))=-0.111
(5) d2/((EFLX+EFLY)/2)=0.679
(5) COSθ=0.555

GF Front group GR Rear group L1 First lens (anamorphic lens)
L2 Second lens (anamorphic lens)
L3 Third lens L4 Fourth lens L5 Fifth lens L6 Sixth lens CG Cover glass D Display surface of image display element S Aperture diaphragm

Claims (3)

A projection optical system that projects an image formed by an image display element onto a projection surface,
The lens comprises , in order from the projection surface side, a front group having an anamorphic lens that converts the aspect ratio of the projected image on the projection surface, and a rear group having an image-forming function.
the front group comprises a first anamorphic lens having negative power in the X-axis direction and positive power in the Y-axis direction, and a second anamorphic lens having positive power in the X-axis direction and negative power in the Y-axis direction ;
the rear group comprises, in order from the projection surface side, a third lens having positive refractive power, a fourth lens having negative refractive power, a fifth lens having positive refractive power, and a sixth lens having negative refractive power;
a projection optical system for oblique projection in which the optical axis of the projection optical system composed of the front group and the rear group is disposed obliquely with respect to the projection surface,
A projection optical system characterized by satisfying the following conditional expression:
1.3<EFLY/EFLX<1.8 (1)
-0.2<((1/L1R1y+1/L1R2y)+(1/L2R1y+1/L2R2y))/((1/L1R1x+1/L1R2x)+(1/L2R1x+1/L2R2x))<0.2 (3)
0.515<COSθ<0.777 (6)
where:
When the optical axis direction of the projection optical system is the Z-axis direction, and in a plane perpendicular to the Z-axis direction, the horizontal direction is the X-axis direction and the vertical direction is the Y-axis direction, EFLX is the focal length of the entire projection optical system in the X-axis direction, and EFLY is the focal length of the entire projection optical system in the Y-axis direction.
Also,
L1R1x is the radius of curvature of the surface of the first anamorphic lens on the projection surface side in the X-axis direction,
L1R2x is the radius of curvature of the surface of the first anamorphic lens on the image display element side in the X-axis direction,
L1R1y is the radius of curvature of the surface of the first anamorphic lens on the projection surface side in the Y-axis direction,
L1R2y is the radius of curvature of the surface of the first anamorphic lens on the image display element side in the Y-axis direction,
L2R1x is the radius of curvature of the surface of the second anamorphic lens on the projection surface side in the X-axis direction,
L2R2x is the radius of curvature of the surface of the second anamorphic lens on the image display element side in the X-axis direction,
L2R1y is the radius of curvature of the surface of the second anamorphic lens on the projection surface side in the Y-axis direction,
L2R2y is the radius of curvature of the surface of the second anamorphic lens on the image display element side in the Y-axis direction,
θ is the angle between the optical axis direction of the projection optical system and the normal to the projection surface. The projection optical system of claim 1, wherein the first and second anamorphic lenses are configured so that the aspect ratio of the converted projected image is similar to the vertical and horizontal pixel pitches corresponding to the image display surface on the image display element and the vertical and horizontal projection pitches of the image corresponding to the image display surface projected onto the projection surface. 2. The projection optical system according to claim 1, wherein the following condition is satisfied:
0.6<d2/((EFLX+EFLY)/2)<1.0 (5)
where:
d2 is the air gap between the first and second lenses of the front group on the optical axis.