Projection Optics

Abstract

Provided is a projection optical system that has a short total length, that is compact, and that, if an image is to be projected from an oblique direction, maintains the resolution of an image display element in vertical and horizontal directions on a projection plane. The projection optical system is for oblique projection and comprises, in order from a projection plane side, a front group having an anamorphic lens for converting the aspect ratio of a projected image that is on the projection plane; and a rear group that has a focusing action. The front group comprises, in order from the projection plane side, a first anamorphic lens, and a second anamorphic lens which is concave on the projection plane side. The optical axis of the projection optical system, which is constituted of the front group and the rear group, is disposed inclined with respect to the projection plane.

Description

[Technical Field]

[0001] 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 or the like. [Background technology]

[0002] Portable, compact mobile projectors that use high-brightness LED (Light Emitting Diode) elements as light sources for image display elements such as LCDs (Liquid Crystal Displays) have been put to practical use. As a projection optical system that is mounted in such mobile projectors and projects an enlarged image, a compact projection optical system with a reduced overall length is known (for example, Patent Document 1).

[0003] Additionally, many ultra-short throw projectors that combine multiple lenses and reflecting mirrors have been proposed as being capable of large-screen display at a short projection distance (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). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2011-81072 [Patent Document 2] Japanese Patent Application Publication No. 2019-164176 [Patent Document 3] Japanese Patent Application Laid-Open No. 2015-114609 Summary of the Invention [Problem to be solved by the invention]

[0005] For example, in applications such as small tabletop projectors that project onto a limited projection range at a shorter projection distance, such as when using a tabletop as a screen, it is necessary to further miniaturize the optical system, 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.

[0006] 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.

[0007] 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 in front projection, the usable range of the pixels of the image display element must be reduced vertically, resulting in a problem of a deterioration in vertical resolution.

[0008] The present invention aims to solve the above-mentioned problems in the prior art and to achieve the following object: That is, 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. [Means for solving the problem]

[0009] 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 is equipped with, 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, wherein the front group consists of, in order from the projection surface side, a first and a second anamorphic lens, and the rear group consists 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, and is characterized by being an oblique projection projection optical system in which the optical axis of the projection optical system composed of the front group and the rear group is arranged obliquely with respect to the projection surface.

[0010] 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 projection 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.

[0011] It is preferable that the projection optical system described in claim 3 is the projection optical system described in claim 1, and 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 the horizontal direction is the X-axis direction and the vertical direction is the Y-axis direction in a plane perpendicular to the Z-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.

[0012] The 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 preferably 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.

[0013] The 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 preferably 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)

[0014] It is preferable that the projection optical system described in claim 6 is the projection optical system described in claim 4, and 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 in the front group on the optical axis is.

[0015] It is preferable that the projection optical system described in claim 7, in addition to 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 in the front group on the optical axis is.

[0016] It is preferable that the projection optical system described in claim 7, in the projection optical systems described in claims 1 to 6, 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. is. [Effects of the Invention]

[0017] According to the present invention, it is possible to realize a projection optical system that is compact with a short overall length and that maintains the resolution of the image display element in the vertical and horizontal directions on the projection surface when projecting an image from an oblique direction. [Brief explanation of the drawings]

[0018] [Figure 1] 1 is a cross-sectional view showing the configuration of a projection optical system of the present invention, viewed in the X direction along the optical axis. [Figure 2] 1 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 first embodiment of the present invention. [Figure 3] 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. [Figure 4] 1A and 1B are diagrams showing 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. [Figure 5]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 2 of the present invention. [Figure 6] 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 2 of the present invention. [Figure 7] 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. [Figure 8] 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 3 of the present invention. [Figure 9] 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 3 of the present invention. [Figure 10] 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. [Figure 11] 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. [Figure 12] 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. [Figure 13] 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. [Figure 14] 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. [Figure 15] 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. [Figure 16] 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. [Figure 17] 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. [Figure 18] 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. [Figure 19]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. [Figure 20] 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. [Figure 21] 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. [Figure 22] 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. [Figure 23] 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. [Figure 24] 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. [Figure 25] 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. DETAILED DESCRIPTION OF THE INVENTION

[0019] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a cross-sectional view taken along the optical axis and viewed 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 YZ plane including the Z axis is defined as the X direction along the optical axis, and the XZ 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 a first embodiment of the present invention.

[0020] 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 disposed obliquely with respect to the projection surface (a tabletop surface in this embodiment) so that the projection surface is projected obliquely 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 disposed, for example, so that a wall surface is used as the projection surface and the wall surface is irradiated obliquely upward from below.

[0021] As shown in Figures 2 and 3, a projection optical system according to an embodiment of the present invention includes, in order from the projection surface side, a front group having an anamorphic lens that converts the aspect ratio of a 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. 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.

[0022] An image display element (not shown) that forms an image, such as an LCD, a digital mirror device (DMD), or a micro LED display, is disposed on the display surface D in the projection optical system of the present invention.

[0023] In the projection optical system according to the embodiment of the present invention, the front group GF is composed of two anamorphic lenses L1 and L2. The 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 sensor or the surface facing the projection surface, respectively. This causes the focal lengths of the entire projection optical system to differ in the X and Y directions.

[0024] 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 form an image. The third lens L3 through the sixth lens L6 are aspherical plastic lenses.

[0025] As shown in Figure 1, when an image is projected obliquely onto the projection surface, the projection pitch in the vertical direction (depth direction) of the image projected onto the projection surface is longer than when the image is projected from the front (for example, directly above) of the projection surface. Therefore, in order to obtain a projection image (for example, a square) with a similar aspect ratio to the image displayed on the image display element (for example, a square), when a conventional rotationally symmetric projection optical system is used, the usable range of the pixels of the image display element must be reduced in the vertical direction (shortened in the vertical direction), which results in a deterioration in vertical resolution compared to front projection.

[0026] The projection optical system of the present invention is an oblique projection optical system, in which the radii of curvature of the lens surfaces of the anamorphic lenses L1 and L2 are 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 pitches corresponding to the image display surface on the image display element and the vertical and horizontal projection pitches of the image projected onto the projection surface corresponding to the image display surface.

[0027] In a projection optical system according to an embodiment of the present invention, the front group GF is composed 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.

[0028] That is, the projection optical system according to the 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.

[0029] 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 the horizontal direction is the X-axis direction and the vertical direction is the Y-axis direction in a plane perpendicular to the Z-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.

[0030] Condition (1) is a condition that minimizes the difference in resolution between the vertical and horizontal directions of the projected image. If this range is exceeded, a difference will occur in the aspect ratio of the pixels in the projection image, which is not desirable.

[0031] 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 in 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 in 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 element 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.

[0032] Condition (2) is a condition 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 field curvature that occurs in the entire projection optical system.

[0033] 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)

[0034] Conditional expression (3) is a condition for reducing the difference in field curvature that occurs in the front group GF in the Y direction and the X direction of the projection optical system, thereby effectively correcting field curvature that occurs in the entire projection optical system, and for shortening the overall length of the optical system.

[0035] 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 in the front group on the optical axis is.

[0036] Condition (4) is a condition that shortens the overall length of the projection optical system, prevents differences in resolution between the vertical and horizontal directions of the image projected by the projection optical system, and minimizes the occurrence of coma aberration. Exceeding condition (4) undesirably increases the overall length of the projection optical system. Also, failing condition (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 performance in the diagonal direction.

[0037] Furthermore, it is preferable that the projection optical system of the present invention satisfy 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 in the front group on the optical axis is.

[0038] Condition (5) is a condition that shortens the overall length of the projection optical system, prevents differences in resolution between the vertical and horizontal directions of the image projected by the projection optical system, and minimizes the occurrence of coma aberration. Exceeding condition (5) undesirably increases the overall length of the projection optical system. Also, failing condition (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 performance in the diagonal direction.

[0039] 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. is.

[0040] The projection optical system of the present invention is an oblique projection optical system, and conditional formula (5) indicates a projection configuration of the optical system that is suitable for use as a small projector that projects light over a limited projection range at a shorter projection distance, for example, when a table is used as a screen. [Example]

[0041] Next, specific numerical examples of the projection optical system of the present invention will be shown. The symbols used in each example are as follows.

[0042] EFLX: Focal length of the entire projection optical system in the X-axis direction EFLY: Focal length of the entire projection optical system in the Y-axis direction FnoX: F-number in the X-axis direction FnoY: F-number in the Y-axis direction f1X: Focal length of the first lens L1 in the X-axis direction f1Y: focal length of the first lens L1 in the Y-axis direction f2X: Focal length of the second lens L2 in the X-axis direction f2Y: Focal length of the second lens L2 in the Y-axis direction f3 to f5: focal length 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 gap 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 asterisk (*) after the surface number is an aspherical surface. In each embodiment, a surface having a "+" after the surface number is an anamorphic surface.

[0043] 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)

[0044] The shape of the anamorphic surface is expressed by the following equation (2), where the optical axis direction is the z direction, the horizontal direction within a plane perpendicular to the z axis is the X-axis direction, and the vertical direction is the Y-axis direction, and 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..., and the aspherical coefficients in the vertical direction are B4, B6, B8, B10.... 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)

[0045] In the aspherical coefficients, E indicates 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 later. The symbols for these specification values ​​are also common to the numerical data in the examples described later. [Example]

[0046] 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.

[0047] 4A and 4B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 1 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0048] Regarding the curvature of field, S indicates the sagittal image surface and T indicates the tangential image surface. In the diagrams, X and Y indicate the image height. The symbols in the aberration diagrams are common to the examples described below.

[0049] 2 and 3, the projection optical system according to 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 disposed between the front group GF and the rear group GR.

[0050] The front group GF is made up 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.

[0051] The surfaces of the first lens L1 and the second lens L2 on the projection surface side are rotationally symmetric aspherical, and the surfaces of the first lens L1 and the second lens L2 on the image display element side are toroidal.

[0052] The rear group GR is made up of four lenses, from the third lens element L3 to the sixth lens element L6, and functions as a whole to form an image. The third lens element L3 to the sixth lens element L6 are each rotationally symmetric aspherical plastic lenses.

[0053] The overall specifications of the projection optical system of the first embodiment 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

[0054] The surface data of the projection optical system of Example 1 is shown below (unit: mm).

[0055] [Table 1]

[0056] 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 3rd 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, Side 4 KY=2.879E-01 KX=2.001E+00 A4=0.000E+00 Side 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 Page 8 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 Page 9 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

[0057] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the first embodiment 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 [Example]

[0058] Next, a projection optical system according to a second embodiment will be described. Fig. 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. 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.

[0059] 7A and 7B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 2 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0060] 5 and 6, the projection optical system according to Example 2 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 disposed between the front group GF and the rear group GR.

[0061] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0062] 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).

[0063] [Table 2]

[0064] 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 3rd 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, Side 4 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 Page 8 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 Page 9 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

[0065] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the second embodiment 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 [Example]

[0066] Next, a projection optical system according to a third embodiment will be described. Fig. 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. 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.

[0067] 10A and 10B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 3 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0068] 8 and 9, the projection optical system according to Example 3 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 disposed between the front group GF and the rear group GR.

[0069] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0070] The overall specifications of the projection optical system of the third embodiment 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).

[0071] [Table 3]

[0072] 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 3rd 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, Page 4 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 Page 8 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 Page 9 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 Side 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

[0073] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the third embodiment 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 [Example]

[0074] Fig. 11 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 4. Fig. 12 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 4.

[0075] 13A and 13B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 4 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0076] 11 and 12, the projection optical system according to 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 disposed between the front group GF and the rear group GR.

[0077] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0078] The overall specifications of the projection optical system of the fourth embodiment 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).

[0079] [Table 4]

[0080] 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 Page 2 KY = -3.984E+00 KX = 6.083E-02 A4=0.000E+00 Page 3 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, Page 4 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 Page 8 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 Page 9 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 Side 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

[0081] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the fourth embodiment 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 [Example]

[0082] Next, a projection optical system according to a fifth embodiment will be described. Fig. 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. 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.

[0083] 16A and 16B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 5 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0084] 14 and 15, the projection optical system according to 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 disposed between the front group GF and the rear group GR.

[0085] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0086] The overall specifications of the projection optical system of the fifth embodiment 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).

[0087] [Table 5]

[0088] The aspheric surface 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 3rd 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, Side 4 KY=-7.180E-01 KX=1.644E+00 A4=0.000E+00 Side 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 Side 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 Side 8 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 Side 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 Side 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

[0089] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the fifth embodiment 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 [Example]

[0090] Next, a projection optical system according to a sixth embodiment will be described. Fig. 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. 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.

[0091] 19A and 19B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 6 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0092] Regarding the curvature of field, S indicates the sagittal image surface and T indicates the tangential image surface. In the diagrams, X and Y indicate the image height. The symbols in the aberration diagrams are common to the examples described below.

[0093] 17 and 18, the projection optical system according to Example 6 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 disposed between the front group GF and the rear group GR.

[0094] 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 side.

[0095] The surfaces of the first lens L1 and the second lens L2 on the projection surface side are rotationally symmetric aspherical, and the surfaces of the first lens L1 and the second lens L2 on the image display element side are toroidal.

[0096] The rear group GR is made up of four lenses, from the third lens element L3 to the sixth lens element L6, and functions as a whole to form an image. The third lens element L3 to the sixth lens element L6 are each rotationally symmetric aspherical plastic lenses.

[0097] The overall specifications of the projection optical system of Example 6 are shown below. FnoX:1.83 FnoY: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

[0098] The surface data of the projection optical system of Example 6 is shown below (unit: mm).

[0099] [Table 6]

[0100] 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 3rd 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 Side 4 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 Page 8 K=0.000E+00 A4=1.377E-02, A6=-1.960E-03, A8=4.823E-04, A10=-4.601E-05, A12=4.233E-10 Page 9 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

[0101] The values ​​corresponding to the conditional expressions (1) to (6) of the projection optical system of the sixth embodiment 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 [Example]

[0102] Next, a projection optical system according to a seventh embodiment will be described. Fig. 20 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 7. Fig. 21 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 7.

[0103] 22A and 22B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 7 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0104] 20 and 21, the projection optical system according to Example 7 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 disposed between the front group GF and the rear group GR.

[0105] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0106] The overall specifications of the projection optical system of Example 7 are shown below. FnoX:1.81 FnoY: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).

[0107] [Table 7]

[0108] 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 3rd 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 Side 4 KY=0.000E+00 KX=2.001E+00 A4=0.000E+00 Side 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 Page 8 K=0.000E+00 A4=9.609E-03, A6=-1.707E-03, A8=6.001E-04, A10=8.203E-06, A12=-8.577E-09 Page 9 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

[0109] 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 [Example]

[0110] 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.

[0111] 25A and 25B are diagrams showing (A) the field curvature in the X direction and (B) the field curvature in the Y direction when the projection optical system according to Example 8 is in focus. The field curvatures are shown as values ​​at a wavelength of 550 nm.

[0112] 23 and 24, the projection optical system according to Example 8 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 disposed between the front group GF and the rear group GR.

[0113] The configurations of the front group GF and the rear group GR are the same as those of the projection optical system according to the first embodiment, so detailed description thereof will be omitted.

[0114] The overall specifications of the projection optical system of Example 8 are shown below. FnoX:1.80 FnoY: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).

[0115] [Table 8]

[0116] 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 3rd 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, Side 4 KY=-2.000E+01 KX=0.000E+00 A4=0.000E+00 Side 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 Side 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 Side 8 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 Side 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 Side 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

[0117] 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 [Explanation of symbols]

[0118] GF front group GR rear group L1 First lens (anamorphic lens) L2 Second lens (anamorphic lens) L3 Third lens L4 4th lens L5 Fifth lens L6 6th lens CG cover glass D Display surface of image display element S aperture stop

Claims

1. 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 includes 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 is.

2. 2. The projection optical system according to claim 1, wherein the first and second anamorphic lenses are configured so that the aspect ratio of the converted projection 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.

3. 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 in the front group on the optical axis is.

Images