Optical system, image projection device, and imaging device

Abstract

Disclosed herein is an optical system having a reduction conjugate point on a reduction side and an enlargement conjugate point on an enlargement side, and having therein intermediate image formation positions that are respectively conjugate to the reduction conjugate point and the enlargement conjugate point. The optical system comprises: a first sub-optical system having a plurality of lenses and an aperture that are rotationally symmetric with respect to the optical axis; and a second sub-optical system including a prism. The prism has, in order from the reduction side to the enlargement side, a first transmission surface, a first reflection surface, a second reflection surface, and a second transmission surface. Regarding effective regions of optical surfaces, the distance FL1 between the farthest point on the first reflection surface from a perpendicular line of an optical axis passing through the surface apex of an optical surface on the most enlargement side of the first sub-optical system and the perpendicular line, is smaller than the distance FL2 between the farthest point on the second transmission surface from the perpendicular line and the perpendicular line.

Description

Optical system, image projection device, and imaging device

[0001] The present disclosure relates to an optical system using a prism, and also to an image projection device and an imaging device using such an optical system.

[0002] Patent Documents 1 to 3 disclose optical systems that use a prism to enable short-focus and large-screen projection or imaging.

[0003] JP 2020-194115 A JP 2021-117276 A JP 2020-024377 A

[0004] The present disclosure provides an optical system that enables short-focus, large-screen projection or imaging in an oblique direction, and also provides an image projection device and an imaging device that use such an optical system.

[0005] One aspect of the present disclosure is an optical system having a reduction conjugate point on a reduction side and an enlargement conjugate point on an enlargement side, and having an intermediate imaging position therein that is conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, the optical system comprising: a first sub-optical system having a plurality of lenses that are rotationally symmetric with respect to an optical axis along the Z direction and a stop between the plurality of lenses; and a second sub-optical system arranged on the enlargement side of the first sub-optical system and including a prism having a plurality of optical surfaces, the prism having, as the plurality of optical surfaces, a first transmitting surface, a first reflecting surface, a second reflecting surface, and a second transmitting surface, in that order from the reduction side to the enlargement side, and a light ray travels within the prism in a YZ plane that includes the Z direction and a Y direction perpendicular to the Z direction, the intermediate imaging position of the light ray closest to the optical axis is arranged between the first transmitting surface and the first reflecting surface, the first reflecting surface has a stronger positive power than the second reflecting surface, and in the YZ plane with respect to the effective areas of the plurality of optical surfaces: The distance FL1 is between the point on the first reflecting surface farthest from the perpendicular to the optical axis passing through the vertex of the optical surface on the most magnified side of the first sub-optical system and the perpendicular, and the distance FL2 is between the point on the second transmitting surface farthest from the perpendicular and the perpendicular, and the distance FL2 is smaller than the distance FL1.

[0006] Another aspect of the present disclosure is an optical system having a reduction conjugate point on a reduction side and an enlargement conjugate point on an enlargement side, and having intermediate image positions therein that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, and the reduction conjugate point has an image-forming relationship in a rectangular area having a first direction and a second direction, the optical system comprising: a first sub-optical system including a plurality of lenses through which a light beam passes and an aperture stop between two lenses of the plurality of lenses; and a second sub-optical system provided on the enlargement side of the first sub-optical system and including a prism, the prism including: a first transmitting surface located on the reduction side; a second transmitting surface located on the enlargement side; and a first reflecting surface and a second reflecting surface in this order along an optical path from the first transmitting surface to the second transmitting surface, When a plane including the position where the chief ray of a first light beam that passes through the point in the rectangular area closest to the optical axis of the first sub-optical system is reflected on the first reflecting surface and the optical axis of the first sub-optical system is defined as a Y-section, and a ray that passes through the point farthest from the optical axis of the first sub-optical system on the line where the Y-section and the rectangular area intersect is defined as a second light beam, on the second reflecting surface, the first footprint area of ​​the first light beam overlaps with the second footprint area of ​​the second light beam.

[0007] An image projection device according to another aspect of the present disclosure includes the optical system described above, and an image forming element that generates an image to be projected onto a screen via the optical system.

[0008] An imaging device according to another aspect of the present disclosure includes the optical system described above and an imaging element that receives an optical image formed by the optical system and converts the optical image into an electrical image signal.

[0009] The optical system according to the present disclosure facilitates the manufacture of prisms, enables miniaturization of prisms having free-form surfaces, and enables projection or imaging in an oblique direction toward a magnification conjugate point.

[0010] Layout diagram showing an optical system 1 according to Example 1. FIG. 2(A) is a perspective view showing the three-dimensional shape of each optical surface of the prism PM. FIG. 2(B) shows a portion of a light ray traveling inside the prism PM. FIG. 3(A) is a cross-sectional view of the prism PM along the YZ plane. FIG. 3(B) shows a portion of a light ray traveling inside the prism PM. FIG. 4(A) is a top view of the prism PM as seen from the Y direction. FIG. 4(B) shows a portion of a light ray traveling inside the prism PM. FIG. 5(A) is a YZ cross-sectional view explaining the definitions of a first point on the first transmitting surface T1, a second point on the second reflecting surface R2, and the angle of incidence of a light ray at the second reflecting surface R2. FIG. 5(B) is a YZ cross-sectional view explaining the definitions of distances PL1 and PL2. Layout diagram showing an optical system 1 according to Example 2. Layout diagram showing an optical system 1 according to Example 2. Layout diagram showing an optical system 1 according to Example 3. 11A shows a state in which the image projection device 100 is installed on the underside of the ceiling CE. FIG. 11B shows a state in which the image projection device 100 is installed on the upper surface of the ceiling CE. A diagram explaining the definition of variables in equation (6). FIG. 12A shows a YZ cross-sectional view. FIG. 12B shows a ZX cross-sectional view. A layout diagram showing the optical system 1 according to Example 4. FIG. 14A is a front perspective view showing the three-dimensional shape of each optical surface of the prism PM. FIG. 14B is a rear perspective view showing the three-dimensional shape of each optical surface of the prism PM. FIG. 14C is a side view showing the three-dimensional shape of the prism PM. FIG. 15A is a side view showing the relative positions of the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3. FIG. 15B is a side view showing a portion of a light ray traveling inside the prism PM. 16A is a top view seen from the Y direction showing the relative positions of the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3. FIG. 16B is a top view showing a portion of a light beam traveling inside the prism PM. FIG. 16B is a YZ cross-sectional view showing the state in which the first light beam LF1 and the second light beam LF2 travel through the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3 in this order. FIG. 16C is an explanatory diagram showing the relationship between the first footprint area FP1 of the first light beam LF1 and the second footprint area FP2 of the second light beam LF2 on the second reflecting surface R2.10 is an explanatory diagram showing the relationship between a third footprint region FP3 of the first light beam LF1 and a fourth footprint region FP4 of the second light beam LF2 on the third reflecting surface R3. A graph showing the second derivative value of the change in sag amount in the Y cross section on the first reflecting surface R1. A lateral aberration diagram of the optical system 1 according to Example 4. A lateral aberration diagram of the optical system 1 according to Example 4. A lateral aberration diagram of the optical system 1 according to Example 4. A layout diagram showing the optical system 1 according to Example 5. A lateral aberration diagram of ... diagram corresponding to FIG. 9 of the basic application (Japanese Patent Application No. 2023-198654), showing the shapes of the footprints on the first reflecting surface R1 and the second reflecting surface R2. A block diagram showing an example of an image projection device according to the present disclosure. A block diagram showing an example of an imaging device according to the present disclosure.

[0011] Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. However, more detailed explanation than necessary may be omitted. For example, detailed explanation of well-known matters or redundant explanation of substantially the same configuration may be omitted. This is to avoid unnecessary redundancy in the following explanation and to facilitate understanding by those skilled in the art.

[0012] The applicant provides the accompanying drawings and the following description to enable those skilled in the art to fully understand the present disclosure, and does not intend for them to limit the subject matter described in the claims.

[0013] Below, various embodiments of the optical system according to the present disclosure will be described. In each embodiment, a case will be described in which the optical system is used in a projector (an example of an image projection device) that projects image light of an original image SA, which is obtained by spatially modulating incident light using an image forming element such as a liquid crystal display or a DMD (digital micromirror device) based on an image signal, onto a screen. That is, the optical system according to the present disclosure can be used to enlarge and project onto the screen an original image SA on an image forming element arranged on the reduction side by placing a screen (not shown) on an extension of the enlargement side. However, the projection surface is not limited to a screen. Projection surfaces also include walls, ceilings, floors, and windows inside homes, stores, and vehicles and aircraft used for transportation.

[0014] In addition, the optical system according to the present disclosure can also be used to collect light emitted from an object located on the extension of the magnification side and form an optical image of the object on the imaging surface of an imaging element located on the reduction side.

[0015] First Embodiment An optical system according to a first embodiment of the present disclosure will be described below with reference to FIGS.

[0016] Example 1 Fig. 1 is a layout diagram showing an optical system 1 according to Example 1. The optical system 1 includes a first sub-optical system including an aperture stop ST and a second sub-optical system including a prism PM. In Fig. 1, a reduction conjugate point, which is an image formation position on the reduction side, is located to the right of the optical axis OA, and a magnification conjugate point, which is an image formation position on the magnification side, is located to the lower left of the optical axis OA. The second sub-optical system is located on the magnification side of the first sub-optical system.

[0017] Furthermore, an intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point is located within the optical system 1. At this intermediate image position, both a Y-direction intermediate image IMy and an X-direction intermediate image IMx exist within the prism PM. The Y-direction intermediate image IMy is shown in FIG. 1, but the X-direction intermediate image IMx is not shown.

[0018] The first sub-optical system includes, from the reduction side to the magnification side, an optical element PA and lens elements L1 to L7. The optical element PA represents an optical element such as a TIR (total internal reflection) prism, a color separation or color synthesis prism, an optical filter, a parallel plate glass, a quartz low-pass filter, or an infrared cut filter. A reduction conjugate point is set at a predetermined distance from the reduction-side end face of the optical element PA, where the original image SA is placed (surface 23). Note that for the surface numbers, refer to the numerical examples described below.

[0019] The optical element PA has two parallel, flat transmitting surfaces (surfaces 21 and 22). Lens element L1 has a biconvex shape (surfaces 19 and 20). Lens element L2 has a biconvex shape (surfaces 17 and 18). Lens element L3 has a biconcave shape (surfaces 15 and 16). Lens element L4 has a biconvex shape (surfaces 13 and 14). Lens element L5 has a biconvex shape (surfaces 9 and 10). Lens element L6 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 7 and 8). Lens element L7 has a biconcave shape (surfaces 5 and 6). These lens elements L1 to L7 are rotationally symmetric lenses having surface shapes that are rotationally symmetric about the optical axis OA of the first sub-optical system, and portions through which light rays do not pass may be removed as necessary.

[0020] The second sub-optical system includes a prism PM made of a transparent medium, such as glass or synthetic resin. The prism PM has multiple optical surfaces: a first transmitting surface T1 located on the reduction side, a second transmitting surface T2 located on the magnification side, and two reflecting surfaces, a first reflecting surface R1 and a second reflecting surface R2, located on the optical path between the first transmitting surface T1 and the second transmitting surface T2. The first transmitting surface T1 has a free-form curved surface with a convex surface facing the reduction side (Surface 4). The first reflecting surface R1 has a free-form curved surface with a concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (Surface 3). The second reflecting surface R2 has a free-form curved surface with a convex surface facing the direction in which light rays incident on the second reflecting surface R2 are reflected (Surface 2). The second transmitting surface T2 has a free-form curved surface with a convex surface facing the magnification side (Surface 1).

[0021] The aperture stop ST defines the range through which the light beam passes through the optical system 1, and is positioned between the reduction conjugate point and the intermediate image position described above. As an example, the aperture stop ST is located between the lens element L4 and the lens element L5 (surface 12).

[0022] Fig. 2(A) is a perspective view showing the three-dimensional shape of each optical surface of the prism PM, and Fig. 2(B) shows a portion of a light beam traveling inside the prism PM. Fig. 3(A) is a cross-sectional view of the prism PM along the YZ plane, and Fig. 3(B) shows a portion of a light beam traveling inside the prism PM. Fig. 4(A) is a top view of the prism PM as seen from the Y direction, and Fig. 4(B) shows a portion of a light beam traveling inside the prism PM.

[0023] Fig. 5A is a YZ cross-sectional view illustrating the definitions of the first point on the first transmitting surface T1, the second point on the second reflecting surface R2, and the angle of incidence of the light ray on the second reflecting surface R2. Fig. 5B is a YZ cross-sectional view illustrating the definitions of the distances PL1 and PL2. Details will be described later.

[0024] 6 is a diagram of lateral aberration of the optical system 1 according to Example 1. Each graph corresponds to the normalized coordinates (X, Y) of the first rectangular effective area at the reduction conjugate point, where (X, Y) = (1.00, 1.00), (1.00, 0.56), (1.00, 0.12), (0.00, 1.00), (0.00, 0.56), and (0.00, 0.12), respectively. The solid line represents a wavelength of 550.0000 nm, the dashed line represents a wavelength of 610.0000 nm, and the dashed-dotted line represents a wavelength of 455.0000 nm. These graphs demonstrate that the optical system 1 according to Example 1 exhibits excellent optical performance.

[0025] Example 2 Fig. 7 is a layout diagram showing an optical system 1 according to Example 2. This optical system 1 has a configuration similar to that of Example 1, and therefore a description that overlaps with Example 1 will be omitted. The optical system 1 includes a first sub-optical system including an aperture stop ST and a second sub-optical system including a prism PM. In Fig. 7, a reduction conjugate point, which is an image formation position on the reduction side, is located to the right of the optical axis OA, and a magnification conjugate point, which is an image formation position on the magnification side, is located to the lower left of the optical axis OA. The second sub-optical system is provided on the magnification side of the first sub-optical system.

[0026] Furthermore, an intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point is located within the optical system 1. At this intermediate image position, both a Y-direction intermediate image IMy and an X-direction intermediate image IMx exist within the prism PM. The Y-direction intermediate image IMy is shown in FIG. 7, but the X-direction intermediate image IMx is not shown.

[0027] The first sub-optical system includes, in order from the reduction side to the enlargement side, an optical element PA and lens elements L1 to L7. A reduction conjugate point is set at a position a predetermined distance from the reduction-side end face of the optical element PA, and the original image SA is placed at this point (surface 23). Note that for the surface numbers, refer to the numerical examples described later.

[0028] The optical element PA has two parallel, flat, transmitting surfaces (surfaces 21 and 22). Lens element L1 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 19 and 20). Lens element L2 has a biconvex shape (surfaces 17 and 18). Lens element L3 has a biconcave shape (surfaces 15 and 16). Lens element L4 has a biconvex shape (surfaces 13 and 14). Lens element L5 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 9 and 10). Lens element L6 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 7 and 8). Lens element L7 has a biconcave shape (surfaces 5 and 6). These lens elements L1 to L7 are rotationally symmetric lenses with surface shapes that are rotationally symmetric about the optical axis OA, and portions through which light rays do not pass may be removed if necessary.

[0029] The prism PM has a first transmitting surface T1 located on the reduction side, a second transmitting surface T2 located on the magnification side, and two reflecting surfaces, a first reflecting surface R1 and a second reflecting surface R2, located on the optical path between the first transmitting surface T1 and the second transmitting surface T2. The first transmitting surface T1 has a free-form curved surface shape with its convex surface facing the reduction side (surface 4). The first reflecting surface R1 has a free-form curved surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 3). The second reflecting surface R2 has a free-form curved surface shape with its convex surface facing the direction in which light rays incident on the second reflecting surface R2 are reflected (surface 2). The second transmitting surface T2 has a free-form curved surface shape with its convex surface facing the magnification side (surface 1).

[0030] 8 is a diagram showing lateral aberration of the optical system 1 according to Example 2. The graphs correspond to the normalized coordinates (X, Y) of the first rectangular effective area at the reduction conjugate point, respectively, of (1.00, 1.00), (1.00, 0.56), (1.00, 0.12), (0.00, 1.00), (0.00, 0.56), and (0.00, 0.12). These graphs show that the optical system 1 according to Example 2 exhibits excellent optical performance.

[0031] Example 3 Fig. 9 is a layout diagram showing an optical system 1 according to Example 3. This optical system 1 has a configuration similar to that of Example 1, and therefore a description that overlaps with Example 1 will be omitted. The optical system 1 includes a first sub-optical system including an aperture stop ST and a second sub-optical system including a prism PM. In Fig. 9, a reduction conjugate point, which is an image formation position on the reduction side, is located to the right of the optical axis OA, and a magnification conjugate point, which is an image formation position on the magnification side, is located to the lower left of the optical axis OA. The second sub-optical system is provided on the magnification side of the first sub-optical system.

[0032] Furthermore, an intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point is located inside the optical system 1. At this intermediate image position, both a Y-direction intermediate image IMy and an X-direction intermediate image IMx exist inside the prism PM. The Y-direction intermediate image IMy is shown in FIG. 9, but the X-direction intermediate image IMx is not shown.

[0033] The first sub-optical system includes, in order from the reduction side to the enlargement side, an optical element PA and lens elements L1 to L7. A reduction conjugate point is set at a position a predetermined distance from the reduction-side end face of the optical element PA, and the original image SA is placed at this point (surface 23). Note that for the surface numbers, refer to the numerical examples described later.

[0034] The optical element PA has two parallel, flat, transmitting surfaces (surfaces 21 and 22). Lens element L1 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 19 and 20). Lens element L2 has a biconvex shape (surfaces 17 and 18). Lens element L3 has a biconcave shape (surfaces 15 and 16). Lens element L4 has a biconvex shape (surfaces 13 and 14). Lens element L5 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 9 and 10). Lens element L6 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 7 and 8). Lens element L7 has a biconcave shape (surfaces 5 and 6). These lens elements L1 to L7 are rotationally symmetric lenses with surface shapes that are rotationally symmetric about the optical axis OA, and portions through which light rays do not pass may be removed if necessary.

[0035] The prism PM has a first transmitting surface T1 located on the reduction side, a second transmitting surface T2 located on the magnification side, and two reflecting surfaces, a first reflecting surface R1 and a second reflecting surface R2, located on the optical path between the first transmitting surface T1 and the second transmitting surface T2. The first transmitting surface T1 has a free-form curved surface shape with its convex surface facing the reduction side (surface 4). The first reflecting surface R1 has a free-form curved surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 3). The second reflecting surface R2 has a free-form curved surface shape with its convex surface facing the direction in which light rays incident on the second reflecting surface R2 are reflected (surface 2). The second transmitting surface T2 has a free-form curved surface shape with its convex surface facing the magnification side (surface 1).

[0036] 10 is a diagram showing lateral aberration of the optical system 1 according to Example 3. The graphs correspond to the normalized coordinates (X, Y) of the first rectangular effective area at the reduction conjugate point, respectively, of (1.00, 1.00), (1.00, 0.56), (1.00, 0.12), (0.00, 1.00), (0.00, 0.56), and (0.00, 0.12). These graphs show that the optical system 1 according to Example 3 exhibits excellent optical performance.

[0037] Example 4 Fig. 13 is a layout diagram showing an optical system 1 according to Example 4. The optical system 1 includes a first sub-optical system including an aperture stop ST and a second sub-optical system including a prism PM. In Fig. 13, a reduction conjugate point, which is an image formation position on the reduction side, is located to the left of the optical axis OA, and a magnification conjugate point, which is an image formation position on the magnification side, is located diagonally above the prism PM. The second sub-optical system is located on the magnification side of the first sub-optical system.

[0038] Furthermore, an intermediate imaging position that is conjugate to the reduction conjugate point and the enlargement conjugate point is located within the optical system 1. At this intermediate imaging position, both a Y-direction intermediate image IMy and an X-direction intermediate image IMx exist within the prism PM. The Y-direction intermediate image IMy is shown in FIG. 13, but the X-direction intermediate image IMx is not shown.

[0039] The first sub-optical system includes, in order from the reduction side to the magnification side, an optical element PA and lens elements L1 to L10. The optical element PA represents an optical element such as a TIR (total internal reflection) prism, a color separation or color synthesis prism, an optical filter, a parallel plate glass, a quartz low-pass filter, or an infrared cut filter. A reduction conjugate point is set at a position a predetermined distance from the reduction-side end face of the optical element PA1, where the original image SA is placed (surface 0). Note that for the surface numbers, refer to the numerical examples described below.

[0040] Optical element PA has two parallel, flat, transmissive surfaces (surfaces 1 and 2). Lens element L1 has a biconvex shape (surfaces 3 and 4). Lens element L2 has a biconvex shape (surfaces 5 and 6). Lens element L3 has a biconcave shape (surfaces 7 and 8). Lens element L4 has a biconcave shape (surfaces 9 and 10). Lens element L5 has a biconvex shape (surfaces 11 and 12). Lens element L6 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 15 and 16). Lens element L7 has a biconvex shape (surfaces 17 and 18). Lens element L8 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 19 and 20). Lens element L9 has a biconcave shape (surfaces 21 and 22). Lens element L10 has a negative meniscus shape with the convex surface facing the reduction side (surfaces 23 and 24). These lens elements L1 to L10 are rotationally symmetric lenses having a surface shape that is rotationally symmetric about the optical axis OA of the first sub-optical system, and portions through which light rays do not pass may be removed as necessary.

[0041] The second sub-optical system includes a prism PM made of a transparent medium, such as glass or synthetic resin. The prism PM has a plurality of optical surfaces: a first transmitting surface T1 located on the reduction side, a second transmitting surface T2 located on the magnification side, and three reflecting surfaces R1, R2, and R3 located on the optical path between the first transmitting surface T1 and the second transmitting surface T2. The first transmitting surface T1 has a free-form surface shape with a convex surface facing the reduction side (surface 25). The first reflecting surface R1 has a free-form surface shape with a convex surface and a concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 26). The second reflecting surface R2 has a free-form surface shape with a concave surface facing in the direction in which light rays incident on the second reflecting surface R2 are reflected (surface 27). The third reflecting surface R3 has a free-form surface shape with a convex surface facing in the direction in which light rays incident on the third reflecting surface R3 are reflected (surface 28). The second transmitting surface T2 has a free-form curved shape with a convex surface facing the magnification side (surface 29).

[0042] The aperture stop ST defines the range through which the light beam passes through the optical system 1, and is positioned between the reduction conjugate point and the intermediate image position described above. As an example, the aperture stop ST is located between the lens element L5 and the lens element L6 (surface 13).

[0043] FIG. 14(A) is a front perspective view showing the three-dimensional shape of each optical surface of the prism PM. FIG. 14(B) is a rear perspective view showing the three-dimensional shape of each optical surface of the prism PM. FIG. 14(C) is a side view showing the three-dimensional shape of the prism PM. FIG. 15(A) is a side view showing the relative positions of the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3. FIG. 15(B) is a side view showing a portion of a light ray traveling inside the prism PM. FIG. 16(A) is a top view from the Y direction showing the relative positions of the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3. FIG. 16(B) is a top view showing a portion of a light ray traveling inside the prism PM.

[0044] Fig. 17 is a YZ cross-sectional view showing the first and second light beams LF1 and LF2 traveling through the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, the second reflecting surface R2, and the third reflecting surface R3 in this order. Figs. 18A and 18B are explanatory diagrams showing the relationship between the first footprint area FP1 of the first light beam LF1 and the second footprint area FP2 of the second light beam LF2 on the second reflecting surface R2. Fig. 19 is an explanatory diagram showing the relationship between the third footprint area FP3 of the first light beam LF1 and the fourth footprint area FP4 of the second light beam LF2 on the third reflecting surface R3. Fig. 20 is a graph showing the second derivative value of the change in sag amount in the Y cross-section on the first reflecting surface R1. These will be described in detail later.

[0045] 21 to 23 are lateral aberration diagrams of the optical system 1 according to Example 4. Each graph corresponds to the coordinates (X, Y) of the first rectangular region at the reduction conjugate point: (0.00, 75.9), (0.00, 67.2), (0.00, 38.2), (54.6, 75.9), (54.7, 67.2), (54.6, 38.4), (70.6, 75.9), (70.6, 67.3), and (70.6, 38.6), respectively. The solid line represents a wavelength of 550.0000 nm, the dashed line represents a wavelength of 610.0000 nm, and the dash-dot line represents a wavelength of 455.0000 nm. These graphs demonstrate that the optical system 1 according to Example 4 exhibits excellent optical performance.

[0046] Example 5 Fig. 24 is a layout diagram showing an optical system 1 according to Example 5. This optical system 1 has a configuration similar to that of Example 4, and a description that overlaps with Example 4 will be omitted. The optical system 1 includes a first sub-optical system including an aperture stop ST and a second sub-optical system including a prism PM. In Fig. 24, a reduction conjugate point, which is an image formation position on the reduction side, is located to the left of the optical axis OA, and a magnification conjugate point, which is an image formation position on the magnification side, is located diagonally above the prism PM. The second sub-optical system is provided on the magnification side of the first sub-optical system.

[0047] Furthermore, an intermediate imaging position that is conjugate to the reduction conjugate point and the enlargement conjugate point is located within the optical system 1. At this intermediate imaging position, both a Y-direction intermediate image IMy and an X-direction intermediate image IMx exist within the prism PM. The Y-direction intermediate image IMy is shown in FIG. 24, but the X-direction intermediate image IMx is not shown.

[0048] The first sub-optical system includes, in order from the reduction side to the enlargement side, an optical element PA and lens elements L1 to L10. A reduction conjugate point is set at a position a predetermined distance from the reduction-side end face of the optical element PA, and the original image SA is placed at this point (surface 0). Note that for the surface numbers, refer to the numerical examples described later.

[0049] Optical element PA has two parallel, flat, transmissive surfaces (surfaces 1 and 2). Lens element L1 has a biconvex shape (surfaces 3 and 4). Lens element L2 has a biconvex shape (surfaces 5 and 6). Lens element L3 has a biconcave shape (surfaces 7 and 8). Lens element L4 has a biconcave shape (surfaces 9 and 10). Lens element L5 has a biconvex shape (surfaces 11 and 12). Lens element L6 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 15 and 16). Lens element L7 has a biconvex shape (surfaces 17 and 18). Lens element L8 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 19 and 20). Lens element L9 has a biconcave shape (surfaces 21 and 22). Lens element L10 has a negative meniscus shape with the convex surface facing the reduction side (surfaces 23 and 24). These lens elements L1 to L10 are rotationally symmetric lenses having a surface shape that is rotationally symmetric about the optical axis OA of the first sub-optical system, and portions through which light rays do not pass may be removed as necessary.

[0050] The prism PM has multiple optical surfaces: a first transmitting surface T1 located on the reduction side, a second transmitting surface T2 located on the magnification side, and three reflecting surfaces R1, R2, and R3 located on the optical path between the first transmitting surface T1 and the second transmitting surface T2. The first transmitting surface T1 has a free-form surface shape with a convex surface facing the reduction side (surface 25). The first reflecting surface R1 has a free-form surface shape with a convex surface and a concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 26). The second reflecting surface R2 has a free-form surface shape with a concave surface facing in the direction in which light rays incident on the second reflecting surface R2 are reflected (surface 27). The third reflecting surface R3 has a free-form surface shape with a convex surface facing in the direction in which light rays incident on the third reflecting surface R3 are reflected (surface 28). The second transmitting surface T2 has a free-form surface shape with a convex surface facing in the direction in which light rays incident on the third reflecting surface R3 are reflected (surface 29).

[0051] 25 to 27 are lateral aberration diagrams of the optical system 1 according to Example 5. The graphs correspond to the coordinates (X, Y) of the first rectangular region at the reduction conjugate point, respectively, of (0.00, 75.9), (0.00, 67.2), (0.00, 38.2), (54.6, 75.9), (54.7, 67.2), (54.6, 38.4), (70.6, 75.9), (70.6, 67.3), and (70.6, 38.6). These graphs show that the optical system 1 according to Example 5 exhibits excellent optical performance.

[0052] FIG. 28 corresponds to FIG. 9 attached to the priority application (Japanese Patent Application No. 2023-198654) of the present application, and is an explanatory diagram showing the shapes of the footprints on the first reflecting surface R1 and the second reflecting surface R2 according to Examples 1 to 3 of the basic application. In Examples 1 to 3 of the basic application, the first chief ray passes through a position near the bottom of the first reflecting surface R1 and then passes through a position near the top of the second reflecting surface R2. The second chief ray passes through a position near the top of the first reflecting surface R1 and then passes through a position near the center of the second reflecting surface R2. The footprint of the first chief ray tends to be larger than the footprint of the second chief ray, and this tendency is particularly pronounced for the second reflecting surface R2. In particular, focusing on the second reflecting surface R2 in Example 2, it can be seen that footprint A, located at the center of the first chief ray, overlaps with footprint B, located at the center of the second chief ray.

[0053] Next, conditions that can be satisfied by the optical system according to this embodiment will be described. Note that, although multiple conditions are specified for the optical system according to each example, it is possible to satisfy all of these multiple conditions, or to satisfy individual conditions to obtain the corresponding effects.

[0054] The optical system according to this embodiment is an optical system having a reduction conjugate point on the reduction side and an enlargement conjugate point on the enlargement side, and having an intermediate imaging position therein that is conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, and comprising: a first sub-optical system having a plurality of lenses that are rotationally symmetric with respect to an optical axis OA along the Z direction and a stop between the plurality of lenses; and a second sub-optical system arranged on the enlargement side of the first sub-optical system and including a prism PM having a plurality of optical surfaces, wherein the prism PM has, as the plurality of optical surfaces, a first transmitting surface T1, a first reflecting surface R1, a second reflecting surface R2, and a second transmitting surface T2, in that order from the reduction side to the enlargement side, and a light ray travels within the prism PM in a YZ plane that includes the Z direction and a Y direction perpendicular to the Z direction; the intermediate imaging position of the light ray closest to the optical axis OA is arranged between the first transmitting surface T1 and the first reflecting surface R1; and the first reflecting surface R1 has a stronger positive power than the second reflecting surface R2. With respect to the effective area of ​​the plurality of optical surfaces, in the YZ plane, a distance FL1 is between the point on the first reflecting surface R1 farthest from the perpendicular to the optical axis OA passing through the vertex of the optical surface on the most enlarged side of the first sub-optical system and the perpendicular, and a distance FL2 is between the point on the second transmitting surface T2 farthest from the perpendicular and the perpendicular, and the distance FL2 is smaller than the distance FL1.

[0055] As shown in FIG. 5A , the prism PM has, in order from the reduction side to the magnification side, a first transmitting surface T1, a first reflecting surface R1, a second reflecting surface R2, and a second transmitting surface T2. Here, a distance FL1 between the point on the first reflecting surface R1 farthest from a perpendicular to the optical axis OA passing through the apex of the optical surface closest to the magnification side of the first sub-optical system and the perpendicular and a distance FL2 between the point on the second transmitting surface T2 farthest from the perpendicular can be defined. As shown in the figure, a predetermined distance is required between the first transmitting surface T1 and the first reflecting surface R1 in order for the first reflecting surface R1 to reflect multiple light beams incident from the first sub-optical system to the second reflecting surface R2. In this case, by designing the distance FL2 to be smaller than the distance FL1, the optical system can be shortened in the Z direction, thereby reducing the size of the prism PM.

[0056] In the optical system of this embodiment, in the YZ plane, a distance PL1 parallel to the Z direction between a point on the first transmitting surface T1 closest to the perpendicular line and a point on the first reflecting surface R1 farthest from the perpendicular line, and a distance PL2 parallel to the Z direction between a point on the second reflecting surface R2 closest to the perpendicular line and a point on the second transmitting surface T2 farthest from the perpendicular line may be smaller than the distance PL1.

[0057] 5B, the distance PL2 is smaller than the distance PL1, which allows the prism to be made smaller in the Z direction. Furthermore, when shift projection in the Y direction is performed, the second transmitting surface T2 tends to be larger in the Y direction. Therefore, by reducing the size of the second transmitting surface T2 in the Z direction, it is possible to prevent the prism from becoming larger in the Y direction.

[0058] In the optical system according to the present embodiment, when a YZ coordinate (yt1, zt1) of a first point on the first transmitting surface through which a chief ray PR of the light beam closest to the optical axis OA passes and a YZ coordinate (yr2, zr2) of a second point on the second reflecting surface R2 at which the chief ray PR of the light beam closest to the optical axis OA is reflected are compared, an interval |zr2-zt1| of the Z coordinates may be smaller than an interval |yr2-yt1| of the Y coordinates, where |x| represents the absolute value of x.

[0059] For ease of understanding, Fig. 5A shows only the light beam closest to the optical axis OA and its chief ray PR among all light rays passing through or reflected from the effective area of ​​the optical surface. In this case, the YZ coordinates (yt1, zt1) of a first point on the first transmitting surface T1 through which the chief ray PR passes can be defined. Also, the YZ coordinates (yr2, zr2) of a second point on the second reflecting surface R2 from which the chief ray PR is reflected can be defined.

[0060] The arrangement of the first transmitting surface T1 and the second reflecting surface R2 is designed so that, when the YZ coordinates of both are compared, |zr2 - zt1| is smaller than the Y coordinate interval |yr2 - yt1|. In FIG. 5A, the Z coordinate zt1 of the first point is located on the +Z side (the right side of FIG. 5A) of the Z coordinate zr2 of the second point. However, the Z coordinate zt1 of the first point may also be located on the -Z side (the left side of FIG. 5A) of the Z coordinate zr2 of the second point. Furthermore, the Z coordinate zt1 of the first point and the Z coordinate zr2 of the second point may be the same, in which case it is sufficient that the Z coordinate interval |zr2 - zt1| (= 0) is smaller than the Y coordinate interval |yr2 - yt1|.

[0061] 5B , a distance PL1 parallel to the optical axis OA of the first sub-optical system can be defined between the point on the first transmitting surface T1 closest to the perpendicular to the optical axis OA that passes through the apex (the intersection of the optical surface and the optical axis) of the optical surface (the enlargement-side surface of lens element L7) that is closest to the enlargement side of the first sub-optical system, and the point on the first reflecting surface R1 farthest from that perpendicular. Also, a distance PL2 parallel to the optical axis OA of the first sub-optical system can be defined between the point on the second reflecting surface R2 closest to the perpendicular and the point on the second transmitting surface T2 farthest from the perpendicular. In this case, the arrangements of the first transmitting surface T1, the first reflecting surface R1, the second reflecting surface R2, and the second transmitting surface T2 are designed so that the distance PL2 is smaller than the distance PL1.

[0062] With this configuration, the first transmitting surface T1 and the second reflecting surface R2 can be maintained approximately perpendicular to the optical axis OA, making it easy to manufacture the prism PM. Conversely, if the first transmitting surface T1 and the second reflecting surface R2 are tilted too much with respect to the optical axis OA, it becomes difficult to manufacture the prism PM. Furthermore, because the first transmitting surface T1 and the second reflecting surface R2 are close to each other in the Z direction and the distance PL2 is smaller than the distance PL1, it is possible to miniaturize a prism having a free-form surface.

[0063] The optical system according to this embodiment may satisfy the following expressions (1) and (2): 0.5<PL2 / PL1<0.8 (1) |(zr2-zt1) / (yr2-yt1)|<1.0 (2)

[0064] According to this configuration, by satisfying the formulas (1) and (2), the prism PM can be manufactured more easily, and the prism having a free-form surface can be further miniaturized.

[0065] The optical system according to this embodiment may satisfy the following formula (3): 0.5<αr2<3.0 (3) where αr2: the angle (unit: °) between the normal to the second reflecting surface R2 at the position where the chief ray PR of the light beam closest to the optical axis OA is incident and the normal to the conjugate plane including the reduction conjugate point.

[0066] As shown in FIG. 5A , the chief ray PR of the light beam closest to the optical axis OA is reflected by the first reflecting surface R1 and then incident on the second reflecting surface R2 at a second point (yr2, zr2). In this case, a normal NA at the second point (yr2, zr2) can be defined. Meanwhile, a normal NR of the conjugate plane including the reduction conjugate point can be defined. This normal NR can generally be set parallel to the optical axis OA of the optical system. Therefore, by making the angle αr2 between the normal NA and the normal NR satisfy Equation (3), it becomes possible to miniaturize the prism while achieving oblique projection or imaging of a large-screen image perpendicular to the optical axis OA at the enlargement conjugate point.

[0067] The optical system according to this embodiment may satisfy the following formula (4): 0.0<rt1x / rt1y<0.8 (4) where, rt1x: partial radius of curvature in the x direction of the first transmitting surface T1 at the first point, and rt1y: partial radius of curvature in the y direction of the first transmitting surface T1 at the first point.

[0068] 5A, the YZ coordinate (yt1, zt1) of the first point through which the principal ray PR passes has a partial radius of curvature rt1x in the x direction and a partial radius of curvature rt1y in the y direction. In this case, by both of them satisfying Expression (4), it is possible to achieve oblique projection or imaging at the magnification conjugate point while suppressing astigmatism at the magnification conjugate point.

[0069] The optical system according to this embodiment may satisfy the following formula (5): 15<αi2m<30 (5), where αi2m: the angle of incidence (unit: degrees) at which the chief ray PR of the light beam closest to the optical axis OA is incident on the second reflecting surface R2.

[0070] 5A, the chief ray PR of the light beam closest to the optical axis OA is reflected by the first reflecting surface R1 and then incident on the second reflecting surface R2 at a second point (yr2, zr2). In this case, the angle of incidence of the chief ray PR on the second reflecting surface R2 can be defined as the angle of incidence αi2m between the normal NA at the second point and the traveling direction of the chief ray PR. Therefore, when the angle of incidence αi2m satisfies equation (5), it is possible to achieve oblique projection or imaging of a large-screen image perpendicular to the optical axis OA at an enlargement conjugate point while suppressing field curvature at the enlargement conjugate point.

[0071] In the optical system of this embodiment, in the Z direction, the optical system is positioned between a reduction conjugate plane formed at the position of the reduction conjugate point and an expansion conjugate plane formed at the position of the expansion conjugate point, and the reduction conjugate plane and the expansion conjugate plane may be parallel to each other.

[0072] With this configuration, the light rays that project a large-screen image perpendicular to the optical axis OA obliquely onto the screen do not pass through the periphery of the optical system, making it possible to install any desired components around the optical system, for example, to hide the optical system from the view of the audience.

[0073] The optical system according to this embodiment may satisfy the following formula (6): |(SF / V)×(H / D)|>2.7 ... (6) where, D: distance between the magnified conjugate point and the optical system, V: length in a first direction parallel to a perpendicular direction to the magnified conjugate point that is perpendicular to the optical axis, of an effective area onto which all light rays are projected or imaged on a conjugate plane including the magnified conjugate point, H: length in a second direction perpendicular to the perpendicular direction, of an effective area onto which all light rays are projected or imaged on a conjugate plane including the magnified conjugate point, SF: perpendicular distance from the optical axis to the center of the length in the first direction of the effective area.

[0074] For example, as shown in FIG. 11A , when an optical system is mounted on an image projection device 100 and obliquely projects an image toward a screen SR (magnified conjugate point), the image projection device 100 is typically installed below the ceiling CE. The audience views the image projected onto the screen SR, but they are also aware of the presence of the image projection device 100. In contrast, as shown in FIG. 11B , the image projection device 100 can be installed above the ceiling CE and obliquely projects an image toward the screen SR. In this case, the image projection device 100 is hidden by the ceiling CE, making it difficult for the audience to recognize the presence of the image projection device 100, allowing them to immerse themselves in viewing the image. To achieve the arrangement shown in FIG. 11B , an optical system capable of projecting an image at a large angle relative to the screen SR, which is perpendicular to the optical axis OA, is required.

[0075] 11A and 11B show an example in which the image projection device 100 is installed on the ceiling CE side and projects an image downward, but alternatively, the image projection device 100 may be installed on the floor side and project an image obliquely upward. Also, the image projection device 100 may be installed on a side wall (right or left wall) of a room and project an image obliquely horizontally (left or right).

[0076] 12A and 12B are diagrams illustrating the definitions of the variables in equation (6), with FIG. 12A showing a YZ cross-sectional view and FIG. 12B showing a ZX cross-sectional view. The optical system can satisfy equation (6) by defining D as the distance between the screen SR and the optical system of the image projection device 100, H as the length of the effective area on the screen SR onto which all light rays are projected in a second direction perpendicular to the direction perpendicular to the magnified conjugate point perpendicular to the optical axis OA, V as the length of the effective area on the screen SR onto which all light rays are projected in a first direction parallel to the vertical direction, and SF as the vertical distance from the optical axis OA to the center of the length of the effective area in the first direction. This configuration allows for a configuration in which the projection distance D to the screen SR is short (so-called short focus projection) and the vertical distance SF is large (so-called super shift projection).

[0077] In the optical system according to this embodiment, a first footprint area on the second reflecting surface of a first light beam that is closest to the optical axis on the first transmitting surface may overlap with a second footprint area on the second reflecting surface of a second light beam that is farthest from the optical axis on the first transmitting surface.

[0078] As shown in FIG. 5B , the first light beam LF1 closest to the optical axis OA on the first transmitting surface T1 forms a first footprint area FP1 on the second reflecting surface R2. The second light beam LF2 farthest from the optical axis OA on the first transmitting surface T1 forms a second footprint area FP2 on the second reflecting surface R2. In this case, by performing an optical design such that the entire first footprint area FP1 overlaps the second footprint area FP2 on the second reflecting surface R2, the area for the second footprint area FP2 can be reduced, thereby reducing the size of the second reflecting surface R2 and preventing the prism PM from becoming larger in the Y direction. Even if only a portion of the first footprint area FP1 overlaps the second footprint area FP2 on the second reflecting surface R2, the area of ​​the second footprint area FP2 overlapping the first footprint area FP1 can be reduced, thereby reducing the size of the second reflecting surface R2 and preventing the prism PM from becoming larger in the Y direction.

[0079] The optical system according to this embodiment has a reduction conjugate point on the reduction side and an enlargement conjugate point on the enlargement side, and has intermediate imaging positions therein that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, and the reduction conjugate point has an imaging relationship in a rectangular area having a first direction and a second direction, and comprises: a first sub-optical system including a plurality of lenses through which a light beam passes and an aperture stop between two lenses of the plurality of lenses; and a second sub-optical system that is provided on the enlargement side of the first sub-optical system and includes a prism PM, and the prism PM includes: a first transmitting surface T1 located on the reduction side; a second transmitting surface T2 located on the enlargement side; and a first reflecting surface R2 and a second reflecting surface R2, in this order of the optical path from the first transmitting surface T1 to the second transmitting surface T2, When the Y-section is a plane including the position where the chief ray of the first light beam LF1, which passes through the point in the rectangular area closest to the optical axis OA of the first sub-optical system, is reflected by the first reflecting surface R1, and the optical axis OA of the first sub-optical system, and the second light beam LF2 is a ray that passes through the point farthest from the optical axis OA of the first sub-optical system on the line where the Y-section and the rectangular area intersect, on the second reflecting surface R2, the first footprint area FP1 of the first light beam LF1 overlaps with the second footprint area FP2 of the second light beam LF2.

[0080] As shown in Figure 17, the prism PM has, as its optical surfaces, a first transmitting surface T1, a first reflecting surface R1, a second reflecting surface R2, a third reflecting surface R3, and a second transmitting surface T2, in that order from the reduction side to the enlargement side. Here, a prism PM having three reflecting surfaces R1 to R3 is illustrated, but the prism PM may have one, two, or four or more reflecting surfaces. A first light beam LF1 passing through a point closest to the optical axis OA forms a first footprint area FP1 on the second reflecting surface R2. A second light beam LF2 passing through a point farthest from the optical axis OA forms a second footprint area FP2 on the second reflecting surface R2. 18A, by performing an optical design such that the entire first footprint region FP1 overlaps the second footprint region FP2 on the second reflecting surface R2, the area for the second footprint region FP2 can be reduced, thereby reducing the size of the second reflecting surface R2 and also preventing the prism PM from increasing in size in the Y direction. Also, even if only a portion of the first footprint region FP1 overlaps the second footprint region FP2 on the second reflecting surface R2, the area of ​​the second footprint region FP2 that overlaps with the first footprint region FP1 can be reduced, thereby reducing the size of the second reflecting surface R2 and also preventing the prism PM from increasing in size in the Y direction.

[0081] In the optical system according to this embodiment, when the position at which the chief ray of the first light beam LF1 is reflected is defined as Y1, the first reflecting surface R1 may have a curved surface shape that imparts positive power at Y1.

[0082] 17 , the first reflecting surface R1 has a curved surface that imparts a positive power P1 at a position Y1 where the chief ray of the first light beam LF1 passing through the point closest to the optical axis OA is reflected. This allows the size of the first footprint region FP1 formed by the first light beam LF1 on the second reflecting surface R2 to be reduced. As a result, the prism PM can be made smaller.

[0083] In the optical system according to this embodiment, the first reflecting surface R1 may have a curved surface shape such that, when the position at which the chief ray of the second light beam FL2 is reflected is Y2, the power imparted at Y2 is smaller than the positive power imparted at Y1.

[0084] 17 , at position Y2 where the chief ray of second light beam LF2 passing through the point farthest from the optical axis OA is reflected, first reflecting surface R1 has positive or negative power P2 that is smaller than the positive power P1 associated with first light beam LF1. As a result, the size of second footprint area FP2 formed by second light beam LF2 on second reflecting surface R2 is larger than the size of first footprint area FP1. As a result, optical performance can be ensured even at a low throw ratio.

[0085] In the optical system according to this embodiment, the first reflecting surface R1 may have a curved surface shape to which negative power is imparted in the Y2 direction.

[0086] As shown in FIG. 17 , the first reflecting surface R1 has a negative power P2 at position Y2. This causes the size of the second footprint area FP2 formed by the second light beam LF2 on the second reflecting surface R2 to be larger than the first footprint area FP1. As a result, optical performance can be ensured even at a low throw ratio. Regarding the curved surface shape of the first reflecting surface R1, as shown in FIG. 20 , for example, the range in which the second derivative value of the sag amount change in the Y cross section is positive indicates negative power P2, and the range in which the second derivative value is negative indicates positive power P1. Such a curved surface shape can be designed as a free-form surface shape defined by (Equation 2) and (Equation 3) described below.

[0087] The optical system according to this embodiment may have a third reflecting surface R3 on the optical path between the second reflecting surface R2 and the second transmitting surface T1.

[0088] 17, the prism PM has three reflecting surfaces R1 to R3 on the optical path between the first transmitting surface T1 and the second transmitting surface T2, which results in both a compact prism and a low throw ratio.

[0089] In the optical system according to this embodiment, the second reflecting surface R2 may have a concave shape with respect to the inside of the prism, and the third reflecting surface R3 may have a convex shape with respect to the inside of the prism.

[0090] As shown in Figure 17, the second reflecting surface R2 has a concave shape relative to the interior of the prism, and therefore functions to converge the light beam. On the other hand, the third reflecting surface R3 has a convex shape relative to the interior of the prism, and therefore functions to diverge the light beam. As a result, the prism can be made compact and have a low throw ratio.

[0091] In the optical system according to this embodiment, the first footprint area FP1 may be located within a central 70% range of the second footprint area FP2 in the Y cross section.

[0092] 18A, the longitudinal size of the second footprint area FP2 is A, and the first footprint area FP1 is included within a range of -A x 35% to +A x 35% from the center of the second footprint area FP2. This allows the size of the second reflecting surface R2 to be reduced, thereby enabling the prism to be made more compact.

[0093] In the optical system according to this embodiment, in the Y cross section, the size ratio of the second footprint area FP to the first footprint area FP may be 20% or less.

[0094] 18B, the longitudinal size of the second footprint area FP2 is set to A × 20% or less, where A is the longitudinal size of the first footprint area FP1, which allows the size of the second reflecting surface R2 to be reduced, thereby enabling the prism to be made more compact.

[0095] The optical system of this embodiment has a third reflecting surface R3 on the optical path between the second reflecting surface R2 and the second transmitting surface T2, and on the third reflecting surface R3, the third footprint area FP3 of the first light beam LF1 is located closer to the optical axis OA of the first sub-optical system than the fourth footprint area FP4 of the second light beam LF2, and in the Y cross section, the size ratio of the third footprint area FP3 to the fourth footprint area FP4 may be 20% or less.

[0096] 19 , the first light beam LF1 passing through the point closest to the optical axis OA forms a third footprint area FP3 on the third reflecting surface R3. The second light beam LF2 passing through the point farthest from the optical axis OA forms a fourth footprint area FP4 on the third reflecting surface R3. In this case, the third footprint area FP3 is located closer to the optical axis OA than the fourth footprint area FP4, and the longitudinal size of the fourth footprint area FP4 is set to B × 20% or less. This allows the size of the second reflecting surface R2 to be reduced, thereby enabling the prism to be made more compact.

[0097] In the optical system of this embodiment, the prism PM may have a shape such that, when the prism PM is viewed from the first sub-optical system, the second reflecting surface R2 is located between the first transmitting surface T1 and the second transmitting surface T2 in the Y cross section.

[0098] 14A to 14C, the first transmitting surface T1, the second reflecting surface R2, and the second transmitting surface T2 are arranged in front of the prism PM, and the first reflecting surface R1 and the second reflecting surface R2 are arranged behind the prism PM. When this optical system is used in an image projection device, rear projection can be achieved in which image light from an image forming element is incident on the first transmitting surface T1 and exits obliquely upward from the second transmitting surface T2.

[0099] Numerical examples of the optical systems according to Examples 1 to 3 will be described below. In each numerical example, all length units in the tables are "mm" and all angle of view units are "°". Each numerical example also shows the object height (XY polynomial surface, spherical surface, aspherical surface), radius of curvature, surface spacing, d-line refractive index, d-line Abbe number, material, refraction / reflection, decentering type, and Y decentering amount. The quantities in each numerical example are calculated based on a wavelength of 550 nm. In each numerical example, the shape of the aspherical surface is defined by the following equation. Note that only non-zero aspherical coefficients other than the Conic coefficient k are shown.

[0100]

[0101] Here, z: sag amount of the surface parallel to the z axis, r: distance in the radial direction (=√(x ２ +y２ ) c: curvature at the vertex of the surface k: Conic coefficient A to H: 4th to 18th order coefficients of r.

[0102] The shape of the free-form surface is defined by the following equation using a local orthogonal coordinate system (x, y, z) with the vertex of the surface as the origin.

[0103]

[0104]

[0105] Here, z: Sag amount of the surface parallel to the z axis r: Radial distance (=√(x ２ +y ２ )) c: curvature at the surface vertex k: conic coefficient C ｊ :monomial x ｍ y ｎ is the coefficient of .

[0106] In the following data, the i-th order x term and j-th order y term, which are free-form surface coefficients in a polynomial, are written as x**i*y**j. For example, "X**2*Y" indicates the free-form surface coefficients of the quadratic x and linear y terms in the polynomial.

[0107] (Numerical Example 1) For the optical system of Numerical Example 1 (corresponding to Example 1), lens data is shown in Table 1, aspherical lens shape data is shown in Table 2, and free-form surface shape data of the prism is shown in Table 3. Note that "DAR (Decenter and Return)" in Table 1 refers to coordinate conversion between global coordinates and local coordinates during numerical calculation. The same applies to the other numerical examples.

[0108]

[0109]

[0110]

[0111] Numerical Example 2 For the optical system of Numerical Example 2 (corresponding to Example 2), lens data is shown in Table 4, aspherical lens shape data is shown in Table 5, and free-form surface shape data of the prism is shown in Table 6.

[0112]

[0113]

[0114]

[0115] Numerical Example 3 For the optical system of Numerical Example 3 (corresponding to Example 3), lens data is shown in Table 7, aspherical lens shape data is shown in Table 8, and free-form surface shape data of the prism is shown in Table 9.

[0116]

[0117]

[0118]

[0119] Table 10 below shows the corresponding values ​​of each of the formulas (1) to (6) in each of the numerical examples 1 to 3. Regarding formula (6), when a large-screen image perpendicular to the optical axis OA is projected obliquely onto a screen, the image-forming element is often also shifted in the Y direction from the optical axis PA as necessary. Here, examples are shown in which the shift amounts of the image-forming element in the Y direction are -7.182 mm and -9.018 mm, respectively. In other words, in FIG. 1, the center position of the original image SA on the image-forming element is shifted downward by 7.182 mm and 9.018 mm relative to the optical axis OA.

[0120]

[0121] Numerical Example 4 For the optical system of Numerical Example 4 (corresponding to Example 4), lens data is shown in Table 11, aspherical lens shape data is shown in Table 12, and free-form surface shape data of the prism is shown in Table 13.

[0122]

[0123]

[0124]

[0125] Numerical Example 5 With regard to the optical system of Numerical Example 5 (corresponding to Example 5), lens data is shown in Table 14, aspherical lens shape data is shown in Table 15, and free-form surface shape data of the prism is shown in Table 16.

[0126]

[0127]

[0128]

[0129] (Embodiment 2) Hereinafter, embodiment 2 of the present disclosure will be described with reference to FIG. 29 . FIG. 29 is a block diagram showing an example of an image projection device according to the present disclosure. The image projection device 100 includes the optical system 1 disclosed in embodiment 1, an image forming element 101, a light source 102, a control unit 110, and the like. The image forming element 101 is configured with a liquid crystal, a DMD, or the like, and generates an image to be projected onto the screen SR via the optical system 1. The light source 102 is configured with an LED (light-emitting diode), a laser, or the like, and supplies light to the image forming element 101. The control unit 110 is configured with a CPU, an MPU, or the like, and controls the entire device and each component. The optical system 1 may be configured as an interchangeable lens that can be detachably attached to the image projection device 100, or as a built-in lens integrated into the image projection device 100.

[0130] The image projection device 100 described above is capable of short-focus and large-screen projection with a small device due to the optical system 1 according to the first embodiment.

[0131] (Embodiment 3) Hereinafter, embodiment 3 of the present disclosure will be described with reference to FIG. 30 . FIG. 30 is a block diagram showing an example of an imaging device according to the present disclosure. The imaging device 200 includes the optical system 1 disclosed in embodiment 1, an imaging element 201, a control unit 210, and the like. The imaging element 201 is configured as a CCD (charge-coupled device) image sensor, a CMOS image sensor, or the like, and receives an optical image of an object OBJ formed by the optical system 1 and converts it into an electrical image signal. The control unit 110 is configured as a CPU, an MPU, or the like, and controls the entire device and each component. The optical system 1 may be configured as an interchangeable lens that can be detachably attached to the imaging device 200, or as a built-in lens integrated into the imaging device 200.

[0132] The imaging device 200 described above is capable of capturing images with a short focus and a large screen using the optical system 1 according to the first embodiment.

[0133] As described above, the embodiments have been described as disclosure of the technology in the present disclosure, and the accompanying drawings and detailed description have been provided for this purpose.

[0134] Therefore, the components shown in the accompanying drawings and detailed description may include not only essential components for solving the problem, but also components that are not essential for solving the problem in order to illustrate the above technology. Therefore, the fact that these non-essential components are shown in the accompanying drawings or detailed description should not be interpreted as immediately indicating that these non-essential components are essential.

[0135] Furthermore, since the above-described embodiments are intended to illustrate the technology of the present disclosure, various modifications, substitutions, additions, omissions, etc. may be made within the scope of the claims or their equivalents.

[0136] The present disclosure is applicable to image projection devices such as projectors and head-up displays, as well as imaging devices such as digital still cameras, digital video cameras, surveillance cameras in surveillance systems, web cameras, and vehicle-mounted cameras. In particular, the present disclosure is applicable to imaging optical systems that require high image quality, such as projectors, digital still camera systems, and digital video camera systems.

Claims

1. An optical system having a reduction conjugate point on the reduction side and an enlargement conjugate point on the enlargement side, and having intermediate imaging positions internally that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, A first sub-optical system having a plurality of lenses arranged along the optical axis in the Z direction, and an aperture diaphragm between two of the plurality of lenses, The system comprises a second sub-optical system, which is positioned on the magnifying side of the first sub-optical system and includes a prism having multiple optical surfaces, The prism has, as the plurality of optical surfaces, The first transparent surface located on the reduced side, The second transparent surface located on the enlarged side, In the Y direction perpendicular to the Z direction, a plurality of reflective surfaces, including a first reflective surface and a second reflective surface, are arranged between the first and second transmissive surfaces, in the order of the optical path from the first transmissive surface to the second transmissive surface. It has, Inside the prism, the light beam propagates in the YZ plane, including the Z and Y directions. The intermediate imaging position of the first light beam closest to the optical axis is located between the first transmission surface and the first reflection surface. The second transmission surface has a shape with a convex surface facing the magnification side, and the reflective surface on the magnification side of the group of reflective surfaces has a convex shape with respect to the inside of the prism. The first reflective surface has a stronger positive power than the second reflective surface. With respect to the effective region of the plurality of optical surfaces, in the YZ plane, An optical system in which, in terms of the distance FL1 between the point on the first reflecting surface furthest from the perpendicular to the optical axis passing through the top of the optical surface on the most magnified side of the first sub-optical system and the perpendicular, and the distance FL2 between the point on the second transmitting surface furthest from the perpendicular and the perpendicular, the distance FL2 is smaller than the distance FL1.

2. The optical system according to claim 1, wherein, in the YZ plane, the distance PL1 parallel to the Z direction between the point of the first transmissive surface closest to the perpendicular and the point of the first reflective surface furthest from the perpendicular, and the distance PL2 parallel to the Z direction between the point of the second reflective surface closest to the perpendicular and the point of the second transmissive surface furthest from the perpendicular, wherein the distance PL2 is smaller than the distance PL1.

3. The optical system according to claim 1 or 2, wherein when comparing the YZ coordinates (yt1, zt1) of a first point through which the principal ray of the first luminous beam passes on the first transmitting surface and the YZ coordinates (yr2, zr2) of a second point reflected by the principal ray of the first luminous beam on the second reflecting surface, the interval of the Z coordinates |zr2 - zt1| is smaller than the interval of the Y coordinates |yr2 - yt1|.

4. The optical system according to claim 2, satisfying the following formulas (1) and (2). 0.5<PL2 / PL1<0.8...(1) |(zr2-zt1) / (yr2-yt1)|<1.0...(2)

5. The optical system according to claim 1, satisfying the following formula (3). 0.5<αr2<3.0…(3) Here, αr²: The angle between the normal at the position of the second reflecting surface into which the principal ray of the first luminous beam is incident, and the normal of the conjugate surface containing the reduced conjugate point (unit: °). That is the case.

6. The optical system according to claim 1, satisfying the following formula (4). 0.0<rt1x / rt1y<0.8...(4) Here, rt1x: Partial radius of curvature in the x-direction of the first transmissive surface at the first point through which the principal ray of the first luminous beam passes. rt1y: Partial radius of curvature in the y direction of the first transmissive surface at the first point through which the principal ray of the first luminous beam passes. That is the case.

7. The optical system according to claim 1, satisfying the following formula (5). 15<αi2m<30…(5) Here, αi2m: The angle of incidence (in degrees) at which the principal ray of the first luminous beam enters the second reflective surface. That is the case.

8. The optical system according to claim 1, wherein in the Z direction, the optical system is positioned between a reduced conjugate plane formed at the position of the reduced conjugate point and an enlarged conjugate plane formed at the position of the enlarged conjugate point, and the reduced conjugate plane and the enlarged conjugate plane are parallel to each other.

9. The optical system according to claim 1, satisfying the following formula (6). |(SF / V)×(H / D)|>2.7...(6) Here, D: Distance between the enlarged conjugate point and the optical system V: The length of the effective region on the conjugate plane including the enlarged conjugate point where all rays are projected or imaged, in a first direction parallel to the direction perpendicular to the enlarged conjugate point and perpendicular to the optical axis. H: Length of the second direction perpendicular to the vertical direction of the effective area on the conjugate plane including the enlarged conjugate point where all rays are projected or imaged. SF: The vertical distance from the optical axis to the center of the length of the first direction of the effective area. That is the case.

10. The optical system according to claim 1, wherein, in the first transmission surface, the first footprint region of the first light beam on the second reflection surface overlaps with the second footprint region of the second light beam furthest from the optical axis on the first transmission surface.

11. An optical system having a reduction conjugate point on the reduction side and an enlargement conjugate point on the enlargement side, and having intermediate imaging positions internally that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, A first sub-optical system comprising a plurality of lenses arranged along the optical axis in the Z direction, and an aperture diaphragm between two of the plurality of lenses, The system comprises a second sub-optical system, which is positioned on the magnifying side of the first sub-optical system and includes a prism having multiple optical surfaces, The prism has, as the plurality of optical surfaces, The first transparent surface located on the reduced side, The second transparent surface located on the enlarged side, In the Y direction perpendicular to the Z direction, a group of reflective surfaces including the first and second reflective surfaces are arranged between the first and second transmissive surfaces, in the order of the optical path from the first transmissive surface to the second transmissive surface, It has, Inside the prism, the light beam propagates in the YZ plane, including the Z and Y directions. The intermediate imaging position of the first light beam closest to the optical axis is located between the first transmission surface and the first reflection surface. The second transmission surface has a shape with a convex surface facing the magnification side, and the reflective surface on the magnification side of the group of reflective surfaces has a convex shape with respect to the inside of the prism. The reduced conjugate point is an optical system in which, when the plane containing the position where the principal ray of the first luminous beam is reflected by the first reflecting surface in a rectangular region having a first direction and a second direction, and the optical axis of the first sub-optical system, is defined as the Y cross-section, and the luminous beam furthest from the optical axis of the first sub-optical system on the line where the Y cross-section and the rectangular region intersect is defined as the second luminous beam, the first footprint region of the first luminous beam overlaps the second footprint region of the second luminous beam on the second reflecting surface.

12. The optical system according to claim 11, wherein the first reflective surface has a curved shape that imparts positive power at Y1, where Y1 is the position where the principal ray of the first luminous beam is reflected.

13. The optical system according to claim 12, wherein the first reflective surface has a curved shape such that, when Y2 is the position where the principal ray of the second luminous beam is reflected, the power applied at Y2 is less than the positive power applied at Y1.

14. The optical system according to claim 13, wherein the first reflective surface has a curved shape to which negative power is applied in Y2.

15. A third reflective surface is located in the optical path between the second reflective surface and the second transmissive surface, The optical system according to claim 12, wherein the second reflective surface has a concave shape with respect to the interior of the prism, and the third reflective surface is the most magnified reflective surface of the group of reflective surfaces.

16. The optical system according to claim 12, wherein in the Y cross-section, the first footprint region is located within the central 70% of the second footprint region.

17. The optical system according to claim 16, wherein in the Y cross-section, the size ratio of the second footprint region to the first footprint region is 20% or less.

18. A third reflective surface is located in the optical path between the second reflective surface and the second transmissive surface, wherein the third footprint region of the first luminous beam is located closer to the optical axis of the first sub-optical system than the fourth footprint region of the second luminous beam. The optical system according to claim 12, wherein in the Y cross-section, the size ratio of the third footprint region to the fourth footprint region is 20% or less.

19. The optical system according to claim 1 or 11, An image projection device comprising an image forming element that generates an image to be projected onto a screen via the optical system.

20. The optical system according to claim 1 or 11, An imaging device comprising: an image sensor that receives an optical image formed by the optical system and converts it into an electrical image signal.