Optical system, image projection device and imaging device

Abstract

This optical system is provided with a first sub-optical system including an aperture stop, and a second sub-optical system including a prism. The prism has a first transmission surface located on the reduction side, a second transmission surface located on the enlargement side, and at least one reflection surface located between the first transmission surface and the second transmission surface. The first sub-optical system includes a plurality of rotationally symmetrical lens elements. When an axis passing through at least two centers of the rotationally symmetrical lens elements is defined as a reference optical axis, at least one optical surface of the prism is formed such that, within a plane perpendicular to the reference optical axis, a maximum angle θmax and a minimum angle θmin of an angle at which a principal ray of light rays having an image formation relationship on a concentric circle centered at an intersection point of the reference optical axis and a reduction conjugate point of a rectangular region intersects with a normal to the surface at a position at which the principal ray is incident on the optical surface satisfy the following expression. 45° > |θmax|-|θmin| > 0.014°

Description

[Technical Field]

[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. [Background technology]

[0002] Patent Documents 1 to 3 disclose projection optical systems that include an optical element in which a transmitting surface and a reflecting surface are integrated, and mention that either the transmitting surface or the reflecting surface may be aspherical. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2020-020860 [Patent Document 2] Japanese Patent Publication No. 2020-024377 [Patent Document 3] International Publication No. 2019 / 151252 Summary of the Invention [Problem to be solved by the invention]

[0004] The present disclosure provides an optical system that enables short-focus, large-screen projection or imaging using a small prism, and also provides an image projection device and an imaging device that use such an imaging optical system. [Means for solving the problem]

[0005] One aspect of the present disclosure relates to an optical system having a reduction-side conjugate point and an enlargement-side conjugate point, and having an internal intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point. The reduction conjugate point has an imaging relationship with a rectangular area having a long direction and a short direction. The optical system includes a first sub-optical system including an aperture stop that defines the range through which a light beam passes through the optical system, and a second sub-optical system located on the enlargement side of the first sub-optical system and including a prism formed of a transparent medium. The prism has a first transmitting surface located on the reduction side, a second transmitting surface located on the enlargement side, and at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface. The aperture stop is positioned between the reduction conjugate point and the intermediate image position. Part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located furthest to the reduction side of the at least one reflecting surface. The first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected. The first sub-optical system includes a plurality of rotationally symmetric lens elements. When an axis passing through the centers of at least two of the rotationally symmetric lens elements is defined as a reference optical axis, at least one optical surface among the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism is formed so that, in a plane perpendicular to the reference optical axis, a maximum angle θmax and a minimum angle θmin of an angle at which a chief ray of a light ray having an image-forming relationship on a concentric circle centered at an intersection point between the reference optical axis and a reduction conjugate point of the rectangular area intersects with a normal to the surface at a position where the chief ray is incident on the optical surface satisfies the following formula (1): 45°>|θmax|-|θmin|>0.014° …(1)

[0006] Another aspect of the present disclosure relates to an optical system having a reduction-side conjugate point and an enlargement-side conjugate point, and having an internal intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point. The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction. The optical system includes a first sub-optical system including an aperture stop that defines the range through which a light beam passes through the optical system, and a second sub-optical system located on the enlargement side of the first sub-optical system and including a prism formed of a transparent medium. The prism has a first transmitting surface located on the reduction side, a second transmitting surface located on the enlargement side, and at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface. The aperture stop is positioned between the reduction conjugate point and the intermediate image position. Part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located furthest to the reduction side of the at least one reflecting surface. The first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected. The first sub-optical system includes a plurality of rotationally symmetric lens elements. When an axis passing through the centers of at least two of the rotationally symmetric lens elements is defined as a reference optical axis, at least one optical surface among the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism satisfies the following formula (5): 10>ΔSmax / r>0.001 …(5) where: ΔSmax: the maximum sag difference in the amount of sag in the direction along the reference optical axis on the optical surface through which the principal ray passes r: radius of the concentric circle is.

[0007] Another aspect of the present disclosure relates to an optical system having a reduction-side conjugate point and an enlargement-side conjugate point, and having an internal intermediate image position that is conjugate to the reduction conjugate point and the enlargement conjugate point. The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction. The optical system includes a first sub-optical system including an aperture stop that defines the range through which a light beam passes through the optical system, and a second sub-optical system located on the enlargement side of the first sub-optical system and including a prism formed of a transparent medium. The prism has a first transmitting surface located on the reduction side, a second transmitting surface located on the enlargement side, and at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface. The aperture stop is positioned between the reduction conjugate point and the intermediate image position. Part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located furthest to the reduction side of the at least one reflecting surface. The first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected. The first sub-optical system includes a plurality of rotationally symmetric lens elements. A maximum optical path length difference ΔLmax of an optical path of the chief ray passing through the inside of the prism satisfies the following formula (9) using the radius r of the concentric circle. 3>ΔLmax / r>0.005 …(9)

[0008] 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.

[0009] 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. [Effects of the Invention]

[0010] The optical system according to the present disclosure can shorten the overall length of the optical system while maintaining the size of the optical system located on the magnification side, including the reflective surface. Furthermore, it is possible to maintain good optical performance, including distortion, over a wide imaging range of the magnification-side conjugate point. Furthermore, it is possible to shorten the distance between the magnification-side conjugate point and the optical system. This enables short-focus, large-screen projection or imaging using a compact prism. [Brief explanation of the drawings]

[0011] [Figure 1] Layout diagram showing the optical system according to Example 1 [Figure 2] 2A is a Y-sectional view showing the optical path through which the principal ray of the reference light ray Ref passes in the prism PM according to the first embodiment. FIG. 2B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the first embodiment. [Figure 3] An explanatory diagram showing the imaging position of the reduction conjugate point that determines the effective size of the optical surface. [Figure 4] Fig. 4(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 1. Fig. 4(B) shows the light flux distribution at the first reflecting surface R1. Fig. 4(C) shows the light flux distribution at the second reflecting surface R2. Fig. 4(D) shows the light flux distribution at the second transmitting surface T2. [Figure 5] Layout diagram showing an optical system according to Example 2 [Figure 6] 6A is a Y-sectional view showing the optical path through which the principal ray of the reference light beam Ref passes in the prism PM according to the second embodiment. FIG. 6B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the second embodiment. [Figure 7] Fig. 7(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 2. Fig. 7(B) shows the light flux distribution at the first reflecting surface R1. Fig. 7(C) shows the light flux distribution at the second reflecting surface R2. Fig. 7(D) shows the light flux distribution at the second transmitting surface T2. [Figure 8] Layout diagram showing an optical system according to Example 3 [Figure 9]9A is a Y-sectional view showing the optical path through which the principal ray of the reference light ray Ref passes in the prism PM according to Example 3. FIG. 9B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 3. [Figure 10] Fig. 10(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 3. Fig. 10(B) shows the light flux distribution at the first reflecting surface R1. Fig. 10(C) shows the light flux distribution at the second transmitting surface T2. [Figure 11] Layout diagram showing an optical system according to Example 4 [Figure 12] 12A is a Y-sectional view showing the optical path through which the principal ray of the reference light ray Ref passes in the prism PM according to Example 4. FIG. 12B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 4. [Figure 13] Fig. 13(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 4. Fig. 13(B) shows the light flux distribution at the first reflecting surface R1. Fig. 13(C) shows the light flux distribution at the second transmitting surface T2. [Figure 14] Layout diagram showing an optical system according to Example 5 [Figure 15] 15A is a Y-sectional view showing the optical path through which the principal ray of the reference light beam Ref passes in the prism PM according to Example 5. FIG. 15B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 5. [Figure 16] Fig. 16(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 5. Fig. 16(B) shows the light flux distribution at the first reflecting surface R1. Fig. 16(C) shows the light flux distribution at the second reflecting surface R2. Fig. 16(D) shows the light flux distribution at the second transmitting surface T2. [Figure 17] Layout diagram showing an optical system according to Example 6 [Figure 18] 18A is a Y-sectional view showing the optical path through which the principal ray of the reference light beam Ref passes in the prism PM according to Example 6. FIG. 18B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 6. [Figure 19]Fig. 19(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 6. Fig. 19(B) shows the light flux distribution at the first reflecting surface R1. Fig. 19(C) shows the light flux distribution at the second reflecting surface R2. Fig. 19(D) shows the light flux distribution at the second transmitting surface T2. [Figure 20] Layout diagram showing an optical system according to Example 7 [Figure 21] 21A is a Y-sectional view showing the optical path through which the principal ray of the reference light ray Ref passes in the prism PM according to Example 7. FIG. 21B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 7. [Figure 22] Fig. 22(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 7. Fig. 22(B) shows the light flux distribution at the first reflecting surface R1. Fig. 22(C) shows the light flux distribution at the second transmitting surface T2. [Figure 23] Layout diagram showing an optical system according to Example 8 [Figure 24] 24A is a Y-sectional view showing the optical path through which the principal ray of the reference light beam Ref passes in the prism PM according to Example 8. FIG. 24B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 8. [Figure 25] Fig. 25(A) shows the light flux distribution at the first transmitting surface T1 of the prism PM according to Example 8. Fig. 25(B) shows the light flux distribution at the first reflecting surface R1. Fig. 25(C) shows the light flux distribution at the second reflecting surface R2. [Figure 26] 26A is a layout diagram showing an optical system according to Example 9. FIG. 26B is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 9. [Figure 27] Fig. 27(A) is a layout diagram showing an optical system 1 according to Example 10. Fig. 27(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to Example 10. [Figure 28] FIG. 10 is an explanatory diagram illustrating an example of an image region at a contracted conjugate point; [Figure 29] Fig. 29(A) is a side view for explaining the definition of the reference ray Ref. Fig. 29(B) is a perspective view thereof. [Figure 30]30A is an XY cross-sectional view showing the distribution of the chief ray of light at the reduction conjugate point, and FIG. 30B is a layout diagram showing the optical system 1 according to Example 5. [Figure 31] Figure 31(A) is an XY cross-sectional view showing the distribution of the chief ray of a light beam at a reduction conjugate point. Figure 31(B) is a conceptual explanatory diagram showing how the chief ray of a light beam at a rotationally symmetric prism optical surface is incident on the optical surface. Figure 31(C) is a conceptual explanatory diagram showing how the chief ray of a light beam at a free-form prism optical surface is incident on the optical surface. [Figure 32] 32(A) is an explanatory diagram showing the arrangement of concentric circles (radius r) and rectangular regions at contraction conjugate points when there is no optical shift. FIG. 32(B) is an explanatory diagram showing the arrangement of concentric circles (radius r) and rectangular regions at contraction conjugate points when there is an optical shift. [Figure 33] An explanatory diagram showing the concepts of rotationally symmetric optical surfaces (spherical, aspherical, etc.) and rotationally asymmetric optical surfaces (free-form surfaces, etc.) [Figure 34] An explanatory diagram showing the concept of a rotationally symmetric optical element (without decentering) and a rotationally asymmetric optical element (with decentering). [Figure 35] 8A to 8C are cross-sectional views in the Y direction showing various examples of the stepped structure of the prism PM according to Examples 1 to 8. [Figure 36] Graph showing the shapes of rectangular regions and concentric circles at contracted conjugate points in each of Numerical Examples 1 to 8 [Figure 37] Graphs showing the cross-sectional shapes and coordinate origins of the respective optical surfaces based on the coordinate system of the first transmitting surface T1 in Numerical Examples 1 to 4. [Figure 38] Graphs showing the cross-sectional shapes and coordinate origins of the optical surfaces based on the coordinate system of the first transmitting surface T1 in Numerical Examples 5 to 8. [Figure 39] Graphs showing distortion shapes at the magnification-side conjugate point caused by distortion aberration in the optical systems according to Numerical Examples 1 to 8. [Figure 40] FIG. 1 is a block diagram illustrating an example of an image projection device according to the present disclosure. [Figure 41] FIG. 1 is a block diagram illustrating an example of an imaging device according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0012] 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.

[0013] 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.

[0014] 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 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 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.

[0015] 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.

[0016] (Embodiment 1) The optical system according to the first embodiment of the present disclosure will be described below with reference to FIGS.

[0017] Example 1 FIG. 1 is a layout diagram showing an optical system 1 according to a first embodiment. 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 imaging position on the reduction side, is located on the lower side, and a magnification conjugate point, which is an imaging position on the magnification side, is located on the upper side. The second sub-optical system is located on the magnification side of the first sub-optical system.

[0018] FIG. 28 is an explanatory diagram showing an example of an image area at the reduction conjugate point. The image area at the reduction conjugate point is defined as a rectangular area having a longitudinal direction (X direction) and a transverse direction (Y direction), and has an optically conjugate imaging relationship with the image area at the expansion conjugate point. Light rays travel along the normal direction (Z direction) of this rectangular area. This rectangular area has, for example, an aspect ratio of 3:2, 4:3, 16:9, 16:10, or 256:135, and corresponds to the image display area of ​​an image forming element in the case of an image projection device, or the imaging area of ​​an imaging element in the case of an imaging device.

[0019] Furthermore, an intermediate image position that is conjugate to each of the reduction conjugate point and the enlargement conjugate point is located inside the optical system 1. This intermediate image position is shown as a Y-direction intermediate image IMy in Fig. 1, but the X-direction intermediate image IMx is not shown.

[0020] The first sub-optical system includes, from the reduction side to the magnification side, an optical element PA and lens elements L1 to L18. The optical element PA represents an optical element such as a TIR (total internal reflection) prism, a prism for color separation or color synthesis, an optical filter, a parallel plate glass, a quartz low-pass filter, or an infrared cut filter. The reduction-side end face of the optical element PA is set at the reduction conjugate point, where the original image SA is placed (surface 1). Note that for the surface numbers, refer to the numerical examples described later.

[0021] The optical element PA has two parallel, flat transmitting surfaces (surfaces 2 and 3). Lens element L1 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 6 and 7). Lens element L3 has a biconvex shape (surfaces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. Lens element L5 has a biconvex shape (surfaces 10 and 11). Lens element L6 has a biconcave shape (surfaces 11 and 12). Lens elements L5 and L6 are cemented together to form a compound lens. Lens element L7 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 13 and 14). Lens element L8 has a biconvex shape (surfaces 14 and 15). Lens elements L7 and L8 are cemented together to form a compound lens.

[0022] 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 lens element L8 and lens element L9 (surface 16).

[0023] Lens element L9 has a biconvex shape (surfaces 17, 18). Lens element L10 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 18, 19). Lens elements L9 and L10 are cemented together to form a compound lens. Lens element L11 has a biconcave shape (surfaces 20, 21). Lens element L12 has a biconvex shape (surfaces 21, 22). Lens elements L11 and L12 are cemented together to form a compound lens. Lens element L13 has a biconvex shape (surfaces 23, 24). Lens element L14 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 25, 26). Lens element L15 has a biconcave shape (surfaces 27, 28). Lens element L16 has a biconvex shape (surfaces 28, 29). Lens elements L15 and L16 are cemented together to form a compound lens. Lens element L17 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 30 and 31). Lens element L18 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 32 and 33). By using the above lens element configuration for the first sub-optical system, it is possible to suppress the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0024] 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 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 shape with its concave surface facing the reduction side (surface 34). The first reflecting surface R1 has a free-form shape with its concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 35). The second reflecting surface R2 has a planar shape (surface 36). The second transmitting surface T2 has a free-form shape with its convex surface facing the magnification side (surface 37).

[0025] Prism PM integrates the first transmitting surface T1, the second transmitting surface T2, the first reflecting surface R1, and the second reflecting surface R2, eliminating assembly and adjustment between optical components and reducing costs. Furthermore, the optical surfaces of prism PM, such as the first transmitting surface T1, the second transmitting surface T2, and the first reflecting surface R1, lack an axis of rotational symmetry; that is, they are formed as free-form surfaces with different curvatures along the X and Y axes. Using free-form surfaces that can define different curvatures along the X and Y axes for the prism's optical surfaces increases the flexibility for correcting distortion, potentially shortening the overall length of the first sub-optical system. This also reduces the weight of the head of optical system 1, allowing for a more balanced center of gravity and simplifying the design of the coupling that holds the optical system's lens barrel to the optical system housing.

[0026] 29(A) is a side view illustrating the definition of the reference ray Ref, and FIG. 29(B) is a perspective view thereof. The reference ray Ref is defined as the ray that forms an image at the position closest to the optical system among the magnification-side conjugate points on the screen SC.

[0027] FIG. 2(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the first embodiment. FIG. 2(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the first embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above the support stand at a relatively short horizontal distance, for example, 0.7 m. Light generated by the optical system 1 is projected diagonally forward and upward, achieving a short-focus, large-screen projection.

[0028] 3 is an explanatory diagram showing the imaging positions of the reduction conjugate points that determine the effective size of the optical surface. The original image SA located at the reduction conjugate points has a rectangular area, and as an example, the relative X coordinate of the imaging position is set in the range of -1.0 to 1.0 at intervals of 0.5, and the relative Y coordinate is set in the range of 0.0 to 1.0 at intervals of 0.25, for a total of 25 coordinates.

[0029] Figure 4 shows the passing positions and shapes of light beams corresponding to the respective imaging positions shown in Figure 3, with Figure 4(A) showing the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 1. Figure 4(B) shows the light beam distribution at the first reflecting surface R1. Figure 4(C) shows the light beam distribution at the second reflecting surface R2. Figure 4(D) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective range of the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective range of the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective range of the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective range of the first reflecting surface R1 when measured parallel to the Y cross section, M2X is the X effective range of the second reflecting surface R2 when measured parallel to the X cross section, M2Y is the Y effective range of the second reflecting surface R2 when measured parallel to the Y cross section, T2X is the X effective range of the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective range of the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the luminous flux distribution touches the rectangular region of the X and Y coordinates. Here, the X and Y coordinates are based on the coordinate system that forms each optical surface.

[0030] Example 2 FIG. 5 is a layout diagram showing an optical system 1 according to a second embodiment. This optical system 1 has a similar configuration to that of the first embodiment, but has an intermediate image in the first sub-optical system as well, and has two intermediate image positions as an optical system. The first sub-optical system includes lens elements L1 to L28, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with those of the first embodiment will be omitted.

[0031] Lens element L1 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 4 and 5). Lens element L2 has a biconvex shape (surfaces 6 and 7). Lens element L3 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 8 and 9). Lens element L4 has a biconvex shape (surfaces 10 and 11). Lens element L5 has a biconvex shape (surfaces 12 and 13). Lens element L6 has a biconcave shape (surfaces 13 and 14). Lens elements L5 and L6 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L6 and L7 (surface 15).

[0032] Lens element L7 has a biconcave shape (surfaces 16, 17). Lens element L8 has a biconvex shape (surfaces 17, 18). Lens elements L7 and L8 are cemented together to form a compound lens. Lens element L9 has a positive meniscus shape with the convex surface facing the magnification side (surfaces 19, 20). Lens element L10 has a biconvex shape (surfaces 21, 22). Lens element L11 has a negative meniscus shape with the convex surface facing the magnification side (surfaces 23, 24). Lens element L12 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 25, 26). Lens element L13 has a biconcave shape (surfaces 27, 28). Lens element L14 has a biconvex shape (surfaces 29, 30). Lens element L15 has a biconvex shape (surfaces 31, 32). Lens element L16 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 33, 34). Lens element L17 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 35, 36). Lens element L18 has a biconvex shape (surfaces 36, 37). Lens elements L17 and L18 are cemented together to form a compound lens. Lens element L19 has a biconcave shape (surfaces 38, 39). Lens element L20 has a biconcave shape (surfaces 40, 41). Lens element L21 has a biconvex shape (surfaces 42, 43). Lens element L22 has a biconvex shape (surfaces 44, 45). Lens element L23 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 46, 47). Lens element L24 has a biconvex shape (surfaces 48, 49). Lens element L25 has a biconvex shape (surfaces 50, 51). Lens element L26 has a biconcave shape (surfaces 52, 53). Lens element L27 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 54, 55). Lens element L28 has a biconcave shape (surfaces 56, 57). By using the above lens element configuration for the first sub-optical system, it is possible to suppress the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0033] 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 shape with its concave surface facing the reduction side (surface 58). The first reflecting surface R1 has a free-form shape with its concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 59). The second reflecting surface R2 has a flat shape (surface 60). The second transmitting surface T2 has a free-form shape with its convex surface facing the magnification side (surface 61).

[0034] FIG. 6(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the second embodiment. FIG. 6(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the second embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed horizontally in front of the support stand at a relatively short horizontal distance, for example, 0.2 m. Light generated by the optical system 1 is projected diagonally downward and forward, achieving a short-focus and large-screen projection.

[0035] 7 shows the passing positions and shapes of light beams corresponding to the respective imaging positions shown in FIG. 3, with FIG. 7(A) showing the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 2. FIG. 7(B) shows the light beam distribution at the first reflecting surface R1. FIG. 7(C) shows the light beam distribution at the second reflecting surface R2. FIG. 7(D) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective range of the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective range of the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective range of the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective range of the first reflecting surface R1 when measured parallel to the Y cross section, M2X is the X effective range of the second reflecting surface R2 when measured parallel to the X cross section, M2Y is the Y effective range of the second reflecting surface R2 when measured parallel to the Y cross section, T2X is the X effective range of the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective range of the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the luminous flux distribution touches the rectangular region of the X and Y coordinates. Here, the X and Y coordinates are based on the coordinate system that forms each optical surface.

[0036] Example 3 8 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, but the first sub-optical system includes lens elements L1 to L10, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0037] Lens element L1 has a biconvex shape (surfaces 4 and 5). Lens element L2 has a biconvex shape (surfaces 6 and 7). Lens element L3 has a biconcave shape (surfaces 7 and 8). Lens element L4 has a biconvex shape (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L4 and L5 (surface 10).

[0038] Lens element L5 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 11 and 12). Lens element L6 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 12 and 13). Lens elements L5 and L6 are cemented together to form a compound lens. Lens element L7 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 14 and 15). Lens element L8 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 16 and 17). Lens element L9 has a biconvex shape (surfaces 18 and 19). Lens element L10 has a biconcave shape (surfaces 19 and 20). Lens elements L9 and L10 are cemented together to form a compound lens. By using the above lens element configuration for the first sub-optical system, it is possible to reduce the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0039] 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 a first reflecting surface R1 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 shape with a concave surface facing the reduction side (surface 21). The first reflecting surface R1 has a free-form curved shape with a concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 22). The second transmitting surface T2 has a free-form curved shape with a convex surface facing the magnification side (surface 23).

[0040] FIG. 9(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the third embodiment. FIG. 9(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the third embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above and behind the support stand at a relatively short horizontal distance, for example, 0.8 m. Light generated by the optical system 1 is projected diagonally upward and backward, achieving a short-focus, large-screen projection.

[0041] 10 shows the passing positions and shapes of light beams corresponding to the imaging positions shown in FIG. 3 . FIG. 10(A) shows the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 3. FIG. 10(B) shows the light beam distribution at the first reflecting surface R1. FIG. 10(C) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective area of ​​the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective area of ​​the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective area of ​​the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective area of ​​the first reflecting surface R1 when measured parallel to the Y cross section, T2X is the X effective area of ​​the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective area of ​​the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the light flux distribution touches the rectangular area defined by the X and Y coordinates, where the X and Y coordinates are based on the coordinate system that defines each optical surface.

[0042] Example 4 11 is a layout diagram showing an optical system 1 according to Example 4. This optical system 1 has a configuration similar to that of Example 1, but the first sub-optical system includes lens elements L1 to L10, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0043] Lens element L1 has a biconvex shape (surfaces 4 and 5). Lens element L2 has a biconvex shape (surfaces 6 and 7). Lens element L3 has a biconcave shape (surfaces 7 and 8). Lens element L4 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L4 and L5 (surface 10).

[0044] Lens element L5 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 11 and 12). Lens element L6 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 12 and 13). Lens elements L5 and L6 are cemented together to form a compound lens. Lens element L7 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 14 and 15). Lens element L8 has a biconvex shape (surfaces 16 and 17). Lens element L9 has a biconvex shape (surfaces 18 and 19). Lens element L10 has a biconcave shape (surfaces 19 and 20). Lens elements L9 and L10 are cemented together to form a compound lens. By using the above lens element configuration for the first sub-optical system, it is possible to reduce the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0045] 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 a first reflecting surface R1 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 shape with a concave surface facing the reduction side (surface 21). The first reflecting surface R1 has a free-form curved shape with a concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 22). The second transmitting surface T2 has a free-form curved shape with a convex surface facing the magnification side (surface 23).

[0046] FIG. 12(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the fourth embodiment. FIG. 12(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the fourth embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above and behind the support stand at a relatively short horizontal distance, for example, 0.6 m. Light generated by the optical system 1 is projected diagonally upward and backward, achieving a short-focus, large-screen projection.

[0047] 13 shows the passing positions and shapes of light beams corresponding to the imaging positions shown in FIG. 3 . FIG. 13(A) shows the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 4. FIG. 13(B) shows the light beam distribution at the first reflecting surface R1. FIG. 13(C) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective area of ​​the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective area of ​​the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective area of ​​the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective area of ​​the first reflecting surface R1 when measured parallel to the Y cross section, T2X is the X effective area of ​​the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective area of ​​the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the light flux distribution touches the rectangular area defined by the X and Y coordinates, where the X and Y coordinates are based on the coordinate system that defines each optical surface.

[0048] Example 5 14 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 1, but the first sub-optical system includes lens elements L1 to L14, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0049] Lens element L1 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 6 and 7). Lens element L3 has a biconvex shape (surfaces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. Lens element L5 has a biconcave shape (surfaces 10 and 11). Lens element L6 has a biconvex shape (surfaces 11 and 12). Lens elements L5 and L6 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L6 and L7 (surface 13).

[0050] Lens element L7 has a biconvex shape (surfaces 14, 15). Lens element L8 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 16, 17). Lens element L9 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 17, 18). Lens elements L8 and L9 are cemented together to form a compound lens. Lens element L10 has a biconvex shape (surfaces 19, 20). Lens element L11 has a biconvex shape (surfaces 21, 22). Lens element L12 has a biconcave shape (surfaces 22, 23). Lens elements L11 and L12 are cemented together to form a compound lens. Lens element L13 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 24, 25). Lens element L14 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 26, 27). By adopting the above lens element configuration, the first sub-optical system can suppress the spread of light rays between the first sub-optical system and the second sub-optical system while maintaining good optical performance.

[0051] 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 shape with its concave surface facing the reduction side (surface 28). The first reflecting surface R1 has a free-form shape with its concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 29). The second reflecting surface R2 has a flat shape (surface 30). The second transmitting surface T2 has a free-form shape with its convex surface facing the magnification side (surface 31).

[0052] FIG. 15(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the fifth embodiment. FIG. 15(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the fifth embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above the support stand at a relatively short horizontal distance, for example, 0.6 m. Light generated by the optical system 1 is projected diagonally forward and upward, achieving a short-focus, large-screen projection.

[0053] Figure 16 shows the passing positions and shapes of light beams corresponding to the respective imaging positions shown in Figure 3, with Figure 16(A) showing the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 5. Figure 16(B) shows the light beam distribution at the first reflecting surface R1. Figure 16(C) shows the light beam distribution at the second reflecting surface R2. Figure 16(D) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective range of the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective range of the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective range of the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective range of the first reflecting surface R1 when measured parallel to the Y cross section, M2X is the X effective range of the second reflecting surface R2 when measured parallel to the X cross section, M2Y is the Y effective range of the second reflecting surface R2 when measured parallel to the Y cross section, T2X is the X effective range of the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective range of the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the luminous flux distribution touches the rectangular region of the X and Y coordinates. Here, the X and Y coordinates are based on the coordinate system that forms each optical surface.

[0054] Example 6 17 is a layout diagram showing an optical system 1 according to Example 6. This optical system 1 has a similar configuration to Example 1, but the first sub-optical system includes lens elements L1 to L13, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0055] Lens element L1 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 6 and 7). Lens element L3 has a biconvex shape (surfaces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. Lens element L5 has a biconcave shape (surfaces 10 and 11). Lens element L6 has a biconvex shape (surfaces 11 and 12). Lens elements L5 and L6 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L6 and L7 (surface 13).

[0056] Lens element L7 has a biconvex shape (surfaces 14, 15). Lens element L8 has a negative meniscus shape with the convex surface facing the magnification side (surfaces 16, 17). Lens element L9 has a biconvex shape (surfaces 18, 19). Lens element L10 has a biconvex shape (surfaces 20, 21). Lens element L11 has a biconcave shape (surfaces 21, 22). Lens elements L10 and L11 are cemented together to form a compound lens. Lens element L12 has a negative meniscus shape with the convex surface facing the reduction side (surfaces 23, 24). Lens element L13 has a biconvex shape (surfaces 25, 26). By using the above lens element configuration for the first sub-optical system, it is possible to reduce the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0057] 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 shape with its concave surface facing the reduction side (surface 27). The first reflecting surface R1 has a free-form shape with its concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 28). The second reflecting surface R2 has a flat shape (surface 29). The second transmitting surface T2 has a free-form shape with its convex surface facing the magnification side (surface 30).

[0058] FIG. 18(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the sixth embodiment. FIG. 18(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the sixth embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed horizontally in front of the support stand at a relatively short horizontal distance, for example, 0.6 m. Light generated by the optical system 1 is projected diagonally downward and forward, achieving a short-focus and large-screen projection.

[0059] Figure 19 shows the passing positions and shapes of light beams corresponding to the respective imaging positions shown in Figure 3, with Figure 19(A) showing the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 6. Figure 19(B) shows the light beam distribution at the first reflecting surface R1. Figure 19(C) shows the light beam distribution at the second reflecting surface R2. Figure 19(D) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective range of the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective range of the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective range of the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective range of the first reflecting surface R1 when measured parallel to the Y cross section, M2X is the X effective range of the second reflecting surface R2 when measured parallel to the X cross section, M2Y is the Y effective range of the second reflecting surface R2 when measured parallel to the Y cross section, T2X is the X effective range of the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective range of the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the luminous flux distribution touches the rectangular region of the X and Y coordinates. Here, the X and Y coordinates are based on the coordinate system that forms each optical surface.

[0060] Example 7 20 is a layout diagram showing an optical system 1 according to Example 7. This optical system 1 has a configuration similar to that of Example 1, but the first sub-optical system includes lens elements L1 to L14, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0061] Lens element L1 has a positive meniscus shape with its convex surface facing the reduction side (surfaces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 6 and 7). Lens element L3 has a biconvex shape (surfaces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 8 and 9). Lens elements L2 to L4 are cemented together to form a compound lens. Lens element L5 has a biconcave shape (surfaces 10 and 11). Lens element L6 has a biconvex shape (surfaces 11 and 12). Lens elements L5 and L6 are cemented together to form a compound lens. An aperture stop ST is located between lens elements L4 and L5 (surface 13).

[0062] Lens element L7 has a biconvex shape (surfaces 14, 15). Lens element L8 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 16, 17). Lens element L9 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 17, 18). Lens elements L8 and L9 are cemented together to form a compound lens. Lens element L10 has a biconvex shape (surfaces 19, 20). Lens element L11 has a biconvex shape (surfaces 21, 22). Lens element L12 has a biconcave shape (surfaces 22, 23). Lens elements L11 and L12 are cemented together to form a compound lens. Lens element L13 has a negative meniscus shape with its convex surface facing the reduction side (surfaces 24, 25). Lens element L14 has a positive meniscus shape with its convex surface facing the magnification side (surfaces 26, 27). By adopting the above lens element configuration, the first sub-optical system can suppress the spread of light rays between the first sub-optical system and the second sub-optical system while maintaining good optical performance.

[0063] 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 a first reflecting surface R1 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 shape with its concave surface facing the reduction side (surface 28). The first reflecting surface R1 has a free-form curved shape with its concave surface facing in the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 29). The second transmitting surface T2 has a free-form curved shape with its convex surface facing the magnification side (surface 30).

[0064] FIG. 21(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to Example 7. FIG. 21(B) is an explanatory diagram showing how an image projection device using the optical system 1 according to Example 7 is used. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above and behind the support stand at a relatively short horizontal distance, for example, 0.6 m. Light generated by the optical system 1 is projected diagonally upward and backward, achieving a short-focus, large-screen projection.

[0065] 22 shows the passing positions and shapes of light beams corresponding to the imaging positions shown in FIG. 3 . FIG. 22(A) shows the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 7. FIG. 22(B) shows the light beam distribution at the first reflecting surface R1. FIG. 22(C) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective area of ​​the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective area of ​​the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective area of ​​the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective area of ​​the first reflecting surface R1 when measured parallel to the Y cross section, T2X is the X effective area of ​​the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective area of ​​the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the light flux distribution touches the rectangular area defined by the X and Y coordinates, where the X and Y coordinates are based on the coordinate system that defines each optical surface.

[0066] Example 8 23 is a layout diagram showing an optical system 1 according to Example 8. This optical system 1 has a configuration similar to that of Example 1, but the first sub-optical system includes lens elements L1 to L3 and a prism PF, and the second sub-optical system including a prism PM projects in an oblique direction in the case of an image projection device. Below, explanations that overlap with Example 1 will be omitted.

[0067] Lens element L1 has a biconvex shape (surfaces 2 and 3). Lens element L2 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 4 and 5). Lens element L3 has a negative meniscus shape with its convex surface facing the magnification side (surfaces 6 and 7). An aperture stop ST is located between lens element L3 and the prism PF (surface 8). By using the above lens element configuration for the first sub-optical system, it is possible to suppress the spread of light rays between the first and second sub-optical systems while maintaining good optical performance.

[0068] Like prism PM, prism PF is formed of a transparent medium, such as glass or synthetic resin. Prism PF has a transmitting surface Q1 located on the reduction side, a transmitting surface Q2 located on the magnification side, and three reflecting surfaces K1, K2, and K3 located on the optical path between transmitting surface Q1 and transmitting surface Q2. Transmitting surface Q1 has a free-form curved surface with a concave surface facing the reduction side (surface 9). Reflecting surface K1 has a free-form curved surface with a concave surface facing both the reduction side and the magnification side (surface 10). Reflecting surface K2 has a free-form curved surface with a convex surface facing both the reduction side and the magnification side (surface 11). Reflecting surface K3 has a free-form curved surface with a concave surface facing both the reduction side and the magnification side (surface 12). Transmitting surface Q2 has a free-form curved surface with a convex surface facing the reduction side (surface 13).

[0069] 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 shape with its convex surface facing the reduction side (surface 14). The first reflecting surface R1 has a free-form curved shape with its concave surface facing both the reduction side and the magnification side (surface 15). The second reflecting surface R2 has a free-form curved shape with its convex surface facing in the direction in which light rays incident on the second reflecting surface R2 are reflected (surface 16). The second transmitting surface T2 has a free-form curved shape with its convex surface facing the magnification side (surface 17).

[0070] FIG. 24(A) is a Y-sectional view showing the optical path of the principal ray of the reference light beam Ref in the prism PM according to the eighth embodiment. FIG. 24(B) is an explanatory diagram showing a usage mode of an image projection device using the optical system 1 according to the eighth embodiment. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed vertically above and behind the support stand at a relatively short horizontal distance, for example, 0.2 m. Light generated by the optical system 1 is projected diagonally upward and rearward, achieving a short-focus, large-screen projection.

[0071] Figure 25 shows the passing positions and shapes of light beams corresponding to the respective imaging positions shown in Figure 3, with Figure 25(A) showing the light beam distribution at the first transmitting surface T1 of the prism PM according to Example 8. Figure 25(B) shows the light beam distribution at the first reflecting surface R1. Figure 25(C) shows the light beam distribution at the second reflecting surface R2. Figure 25(D) shows the light beam distribution at the second transmitting surface T2. Here, T1X is the X effective range of the first transmitting surface T1 when measured parallel to the X cross section, T1Y is the Y effective range of the first transmitting surface T1 when measured parallel to the Y cross section, M1X is the X effective range of the first reflecting surface R1 when measured parallel to the X cross section, M1Y is the Y effective range of the first reflecting surface R1 when measured parallel to the Y cross section, M2X is the X effective range of the second reflecting surface R2 when measured parallel to the X cross section, M2Y is the Y effective range of the second reflecting surface R2 when measured parallel to the Y cross section, T2X is the X effective range of the second transmitting surface T2 when measured parallel to the X cross section, and T2Y is the Y effective range of the second transmitting surface T2 when measured parallel to the Y cross section. The effective range of each optical surface is determined by the position where the outermost part of the luminous flux distribution touches the rectangular region of the X and Y coordinates. Here, the X and Y coordinates are based on the coordinate system that forms each optical surface.

[0072] Example 9 26A is a layout diagram showing an optical system 1 according to Example 9. This optical system 1 has the same optical design as Example 5, but a plane mirror MR1 is interposed between lens elements L7 and L8 to bend the reference optical axis A at a right angle in the YZ plane. The reference ray Ref is also bent in the YZ plane via the plane mirror MR1.

[0073] FIG. 26(B) is an explanatory diagram showing a usage state of an image projection device using the optical system 1 according to Example 9. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed parallel to the ZX plane at a relatively short horizontal distance, for example, 0.6 m, from the support stand. Light generated by the optical system 1 is projected obliquely, achieving short-focus and large-screen projection.

[0074] Example 10 27A is a layout diagram showing an optical system 1 according to Example 10. This optical system 1 has the same optical design as Example 5, but a plane mirror MR2 is interposed between lens elements L7 and L8 to bend the reference optical axis A at a right angle within the ZX plane. The reference ray Ref is also bent within the ZX plane via the plane mirror MR2.

[0075] FIG. 27(B) is an explanatory diagram showing a usage state of an image projection device using the optical system 1 according to Example 10. The image projection device including the optical system 1 is placed horizontally on a support stand such as a table or on the floor. A screen SC is installed parallel to the YZ plane at a relatively short horizontal distance, for example, 0.6 m, from the support stand. Light generated by the optical system 1 is projected obliquely, achieving short-focus and large-screen projection.

[0076] The first sub-optical system included in Examples 1 to 7 and Examples 9 to 10 is configured to include three or more convex lenses between the aperture stop and the reduction-side conjugate point, and between the aperture stop and the intermediate imaging position. This is because, when an image-forming element is disposed on the reduction conjugate point side, it is desirable to make the reduction conjugate point side an approximately telecentric optical system in order to uniformly guide light from the image-forming element to the first sub-optical system. Also, when guiding light to the second sub-optical system, making the magnification conjugate point side of the first sub-optical system an approximately telecentric optical system reduces the spread of light rays entering the second sub-optical system, which has the effect of reducing the size of the second sub-optical system.

[0077] Furthermore, the optical element with power located closest to the reduction conjugate point in the first sub-optical system does not spread the light rays on the reduction conjugate point side, so if a positive lens is located there, the approximate telecentric effect can be further enhanced.

[0078] The second reflecting surface of the prisms PM included in Examples 1 and 2, Examples 5 and 6, and Examples 9 and 10 is not limited to a flat surface, and may be configured as a curved reflecting surface. By using a curved reflecting surface, the degree of freedom in the direction of the magnification-side conjugate point increases, and good shape precision of the reflecting surface can be maintained during processing of the prism PM. Furthermore, a flat reflecting mirror formed by aluminum deposition or the like on a glass substrate that has been flattened by polishing or the like can be bonded to the outside of the second reflecting surface of the prism PM and used as a substitute for the second reflecting surface. In this case, high flatness precision can be achieved as the second reflecting surface, and good shape precision can be maintained after processing of the prism PM.

[0079] Examples 1 and 2, 5 and 6, and 8 to 10 have a second reflecting surface, and the convex surfaces of the first reflecting surface and the second transmitting surface are both arranged facing the magnification conjugate point. This configuration makes it possible to effectively correct distortion while further reducing the height of the prism PM. In this case, it is desirable that the normal to the second reflecting surface faces the magnification conjugate point.

[0080] The light beam distribution of the optical surface located on the magnification side of the intermediate imaging position within the prism PM included in the second sub-optical system is distributed so that the light beam size of the reference light ray Ref, which forms an image at the position closest to the optical system among the magnification-side conjugate points on the screen SC, is smallest. This is because by increasing the light beam size in proportion to the distance between the light beam passing through the prism PM and the magnification-side conjugate point, distortion on the magnification side and reduction side can be maintained effectively. Furthermore, by making the light beam distribution of each optical surface located on the magnification side of the intermediate imaging position within the prism PM approximately elliptical with the major axis in the direction projected onto the XY plane in the direction in which each light beam travels, distortion on the magnification conjugate point side can be effectively corrected.

[0081] Prism PM has a reflecting surface formed on a part of a lens element or the like having an optical surface with a free-form curved shape, and has at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface, thereby achieving the same effect as prism PM.

[0082] Prism PM has a reflecting surface formed on a part of a lens element or the like having a decentered optical surface, and has at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface, thereby achieving the same effect as prism PM.

[0083] Prism PM has a reflecting surface formed on a part of a lens element or the like having an optical surface with a decentered free-form curved shape, and has at least one reflecting surface located on the optical path between the first transmitting surface and the second transmitting surface, thereby achieving the same effect as prism PM. In each embodiment, a reference optical axis A is defined as an axis passing through the centers of at least two of the lens elements, and the prism PM is disposed so as to intersect with the reference optical axis A.

[0084] 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.

[0085] 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 image positions therein that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction, a first sub-optical system including an aperture stop that defines a range through which a light beam passes through the optical system; a second sub-optical system provided on the magnification side of the first sub-optical system and including a prism formed of a transparent medium; the prism has a first transmitting surface located on a reduction side, a second transmitting surface located on a magnification side, and at least one reflecting surface located on an optical path between the first transmitting surface and the second transmitting surface; the aperture stop is positioned between the reduction conjugate point and the intermediate image position; a part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located on the most reduction side of the at least one reflecting surface, the first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements; When an axis passing through at least two centers of the rotationally symmetric lens element is defined as a reference optical axis A, at least one optical surface of the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism may be formed so that, in a plane perpendicular to the reference optical axis A, the maximum angle θmax and the minimum angle θmin of the angle at which a chief ray of a light ray having an imaging relationship on a concentric circle centered at the intersection point between the reference optical axis A and the reduction conjugate point of the rectangular area intersects with a normal to the surface at a position where the chief ray is incident on the optical surface satisfies the following formula (1): 45°>|θmax|-|θmin|>0.014° …(1)

[0086] FIG. 30(A) is an XY cross-sectional view showing the distribution of the chief ray of a light beam at the reduction conjugate point. FIG. 30(B) is a layout diagram showing an optical system 1 according to Example 5 as an example. The reduction conjugate point has an imaging relationship in a rectangular area having a longitudinal direction and a lateral direction. The chief ray of the light beam has an imaging relationship on concentric circles centered on the intersection of the reference optical axis A and the reduction conjugate point. Furthermore, the angle at which the chief ray of the light beam intersects with the normal to the surface at the position where it is incident on the optical surface varies between a maximum angle and a minimum angle. In this case, the shape of the optical surface is designed so that the difference between the absolute value of the maximum angle and the absolute value of the minimum angle satisfies formula (1).

[0087] This configuration allows the overall length of the optical system to be shortened while maintaining the size of the optical system located on the magnification side, including the reflective surface. Furthermore, good optical performance, including distortion, can be maintained over a wide imaging range at the magnification-side conjugate point. Furthermore, the distance between the magnification-side conjugate point and the optical system can be shortened. This allows for a compact prism to be used to miniaturize the second sub-optical system and enable short-focus, large-screen projection or imaging. Exceeding the upper limit of formula (1) is undesirable because it increases the number of obliquely incident light rays, which are incident on the reflective surface at an acute angle, widens the luminous flux area, and significantly impacts the shape accuracy of the optical surface. Furthermore, distortion is over-corrected, making it difficult to maintain good optical performance. Falling below the lower limit of formula (1) makes it impossible to utilize optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, making it difficult to shorten the overall length of the optical system and narrowing the imaging range with good optical performance at the magnification-side conjugate point.

[0088] Fig. 31(A) is an XY cross-sectional view showing the distribution of the chief ray of a light beam at a reduction conjugate point. Fig. 31(B) is a conceptual explanatory diagram showing how the chief ray of a light beam at a rotationally symmetric prism optical surface is incident on the optical surface. Fig. 31(C) is a conceptual explanatory diagram showing how the chief ray of a light beam at a free-form prism optical surface is incident on the optical surface.

[0089] It can be seen that for the rotationally symmetric prism optical surface shown in Figure 31(B), the angle at which the chief ray of a light ray intersects with the normal to the optical surface is always constant. Therefore, |θmax|-|θmin| in equation (1) is zero. On the other hand, for the free-form prism optical surface shown in Figure 31(C), the angle at which the chief ray of a light ray intersects with the normal to the optical surface is not constant, but varies between a maximum angle and a minimum angle. It can be seen that |θmax|-|θmin| in equation (1) is greater than zero.

[0090] Fig. 32(A) is an explanatory diagram showing the arrangement of concentric circles (radius r) and rectangular areas at the contraction conjugate point when there is no optical shift. Fig. 32(B) is an explanatory diagram showing the arrangement of concentric circles (radius r) and rectangular areas at the contraction conjugate point when there is an optical shift. The position of the concentric circle through which the chief ray of light passes can be defined according to the optical shift.

[0091] Figure 33 is an explanatory diagram showing the concepts of rotationally symmetric optical surfaces (spherical, aspherical, etc.) and rotationally asymmetric optical surfaces (free-form surfaces, etc.). For example, an image sensor, DMD, etc. are installed at a reduction conjugate point, and have an imaging relationship in a rectangular area having a long side direction and a short side direction. Assume an orientation D1 along the short side direction of the rectangular area and an orientation D2 along the diagonal direction of the rectangular area.

[0092] In a rotationally symmetric optical surface, the cross-sectional shape along the direction D1 matches the cross-sectional shape along the direction D2. On the other hand, in a rotationally asymmetric optical surface, the cross-sectional shape along the direction D1 does not match the cross-sectional shape along the direction D2.

[0093] Figure 34 is an explanatory diagram showing the concepts of a rotationally symmetric optical element (without decentering) and a rotationally asymmetric optical element (with decentering). As in Figure 33, for example, an image sensor or DMD is installed at a reduction conjugate point, and an imaging relationship is formed in a rectangular area having a long side direction and a short side direction. Assume an orientation D1 along the short side direction of the rectangular area and an orientation D2 along the diagonal direction of the rectangular area.

[0094] In a rotationally symmetric optical element, the optical axes of the left side surface S1 and the right side surface S2 are aligned, and the optical action along the direction D1 and the optical action along the direction D2 are aligned. On the other hand, in a rotationally asymmetric optical element, the optical axes of the left side surface S1 and the right side surface S2 are shifted from each other, and the optical action along the direction D1 and the optical action along the direction D2 are not aligned.

[0095] In the optical system according to this embodiment, the optical surface is the second transmitting surface, The following formula (2) may be satisfied. 20°>|θmax|-|θmin|>0.020° …(2)

[0096] Furthermore, the optical system may satisfy the following formula: 17°>|θmax|-|θmin|>0.024° …(2a)

[0097] In the optical system according to this embodiment, the optical surface is the first transmitting surface, The following formula (3) may be satisfied. 10°>|θmax|-|θmin|>0.020° …(3)

[0098] Furthermore, the optical system may satisfy the following formula: 5.5°>|θmax|-|θmin|>0.050° …(3a)

[0099] In the optical system according to this embodiment, the optical surface is the first reflecting surface, The following formula (4) may be satisfied. 2°>|θmax|-|θmin|>0.014° …(4)

[0100] Furthermore, the optical system may satisfy the following formula: 1.50°>|θmax|-|θmin|>0.100° …(4a)

[0101] Furthermore, the optical system may satisfy the following formula: 1.25°>|θmax|-|θmin|>0.200° …(4b)

[0102] Furthermore, the optical system may satisfy the following formula: 1.00°>|θmax|-|θmin|>0.300° …(4c)

[0103] 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 intermediate image positions therein that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction, a first sub-optical system including an aperture stop that defines a range through which a light beam passes through the optical system; a second sub-optical system provided on the magnification side of the first sub-optical system and including a prism formed of a transparent medium; the prism has a first transmitting surface located on a reduction side, a second transmitting surface located on a magnification side, and at least one reflecting surface located on an optical path between the first transmitting surface and the second transmitting surface; the aperture stop is positioned between the reduction conjugate point and the intermediate image position; a part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located on the most reduction side of the at least one reflecting surface, the first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements; When an axis passing through at least two centers of the rotationally symmetric lens element is defined as a reference optical axis A, and in a plane perpendicular to the reference optical axis A, chief rays of light have an imaging relationship on concentric circles centered on an intersection point between the reference optical axis A and a reduction conjugate point of the rectangular area, at least one optical surface among the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism may satisfy the following formula (5): 10>ΔSmax / r>0.001 …(5) where: ΔSmax: the maximum sag difference in the amount of sag in the direction along the reference optical axis A on the optical surface through which the principal ray passes r: radius of the concentric circle is.

[0104] The optical system according to this embodiment may satisfy the following formula (6) when the optical surface through which the chief ray passes is the second transmitting surface. 10>ΔSmax / r>0.001 …(6)

[0105] The optical system according to this embodiment may satisfy the following formula (7) when the optical surface through which the chief ray passes is the first transmitting surface. 3>ΔSmax / r>0.001 …(7)

[0106] The optical system according to this embodiment may satisfy the following formula (8) when the optical surface through which the chief ray passes is the first reflecting surface. 1>ΔSmax / r>0.001 …(8)

[0107] Furthermore, the optical system may satisfy the following formula: 0.8>ΔSmax / r>0.002 …(8a)

[0108] Furthermore, the optical system may satisfy the following formula: 0.6>ΔSmax / r>0.004 …(8b)

[0109] Furthermore, the optical system may satisfy the following formula: 0.4>ΔSmax / r>0.006 …(8c)

[0110] 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 intermediate image positions therein that are conjugate to the reduction conjugate point and the enlargement conjugate point, respectively, The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction, a first sub-optical system including an aperture stop that defines a range through which a light beam passes through the optical system; a second sub-optical system provided on the magnification side of the first sub-optical system and including a prism formed of a transparent medium; the prism has a first transmitting surface located on a reduction side, a second transmitting surface located on a magnification side, and at least one reflecting surface located on an optical path between the first transmitting surface and the second transmitting surface; the aperture stop is positioned between the reduction conjugate point and the intermediate image position; a part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located on the most reduction side of the at least one reflecting surface, the first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements; When an axis passing through at least two centers of the rotationally symmetric lens element is defined as a reference optical axis A, and in a plane perpendicular to the reference optical axis A, chief rays of light have an image-forming relationship on concentric circles whose centers are the intersections of the reference optical axis A and the reduction conjugate points of the rectangular area, a maximum optical path length difference ΔLmax of optical paths of the chief rays passing through the inside of the prism may satisfy the following formula (9) using a radius r of the concentric circles: 3>ΔLmax / r>0.005 …(9)

[0111] Furthermore, the optical system may satisfy the following formula: 2.5>ΔLmax / r>0.002 …(9a)

[0112] Furthermore, the optical system may satisfy the following formula: 2.0>ΔLmax / r>0.004 …(9b)

[0113] Furthermore, the optical system may satisfy the following formula: 1.5>ΔLmax / r>0.006 …(9c)

[0114] The maximum optical path length Lmax of the optical path of the chief ray passing through the inside of the prism may satisfy the following formula (10) using the radius r of the concentric circle. 30>Lmax / r>2 …(10)

[0115] This configuration allows the use of a small prism to miniaturize the second sub-optical system, while enabling short-focus, large-screen projection or imaging. Exceeding the upper limit of formula (10) makes it difficult to miniaturize the optical system located on the magnification side. In particular, the effective range of the second transmitting surface becomes larger. A larger prism requires longer molding times, resulting in increased costs. Falling below the lower limit of formula (10) makes it difficult to form the necessary optical surfaces to maintain good optical performance, including distortion.

[0116] The optical system according to this embodiment may satisfy the following formula (11). 2.00>SP / LP>0.10 …(11) where: SP: the distance between the reduction conjugate point and the aperture stop along the chief ray path of a reference ray Ref, which is defined as the ray that forms an image at the position closest to the optical system among the expansion conjugate points. LP: the distance between the aperture stop and the enlarged end of the first sub-optical system along the chief ray path of the reference ray Ref is.

[0117] With this configuration, good optical performance, including distortion, can be maintained over a wide imaging range at the magnification-side conjugate point, while the distance between the magnification-side conjugate point and the optical system can be shortened. If the upper limit of formula (11) is exceeded, it becomes impossible to utilize optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, making it difficult to shorten the overall length of the optical system and narrowing the imaging range with good optical performance at the magnification-side conjugate point. If the lower limit of formula (11) is exceeded, distortion will be over-corrected, making it difficult to maintain good optical performance.

[0118] The optical system according to this embodiment may satisfy the following formula (12), where a Y cross section is a surface including a position where a chief ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is a cross section that includes the reference optical axis A and is perpendicular to the Y cross section. 0.20>(XM1-RefM1) / r>-3.00 …(12) where: XM1: Y coordinate in the first reflecting surface coordinate system of the chief ray at the X end of the first reflecting surface R1 RefM1: Y coordinate of the reference ray Ref at the first reflecting surface R1 in the first reflecting surface coordinate system r: radius of the concentric circle is.

[0119] This configuration reduces the spread of light rays between the first and second sub-optical systems, making it possible to reduce the size of the optical system located on the magnification side, including the reflecting surface. Furthermore, it is possible to make the light rays at the reduction-side conjugate point nearly telecentric. Exceeding the upper limit of formula (12) makes it difficult to reduce the spread of light rays between the first and second sub-optical systems, and the optical system located on the magnification side, including the reflecting surface, becomes larger. If the lower limit of formula (12) is not reached, light is focused at the reduction-side conjugate point via oblique incidence. Therefore, if an image-forming element such as a DMD is located on the reduction side, it becomes difficult to capture light rays evenly, making it difficult to maintain good optical performance with uniform brightness.

[0120] The optical system according to this embodiment may satisfy the following formula (13), where a Y cross section is a surface including a position where a chief ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is a cross section that includes the reference optical axis A and is perpendicular to the Y cross section. 1.90>M1X / M1Y>1.00 …(13) where: M1X: The X-effective range of the first reflecting surface when measured parallel to the X-section M1Y: The Y effective range of the first reflecting surface when measured parallel to the Y cross section is.

[0121] This configuration allows the overall length of the optical system to be shortened while maintaining the size of the optical system located on the magnification side, including the reflective surface. Furthermore, good optical performance, including distortion, can be maintained over a wide imaging range at the magnification-side conjugate point. The distance between the magnification-side conjugate point and the optical system can also be shortened. Exceeding the upper limit of equation (13) makes it impossible to utilize optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, making it difficult to shorten the overall length of the optical system and narrowing the imaging range with good optical performance at the magnification-side conjugate point. Falling below the lower limit of equation (13) results in overcorrection of distortion, making it difficult to maintain good optical performance. Furthermore, the inclination of the optical surface in the peripheral X direction increases, making processing difficult.

[0122] The optical system according to this embodiment may satisfy the following formula (14), where a Y cross section is a surface including a position where a chief ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is a cross section that includes the reference optical axis A and is perpendicular to the Y cross section. 6.00>T2X / T2Y>2.00 …(14) where: T2X: X coverage of the second transmitting surface when measured parallel to the X cross section T2Y: Y effective range of the second transmitting surface when measured parallel to the Y cross section is.

[0123] With this configuration, the overall length of the optical system can be shortened while maintaining the size of the optical system located on the magnification side, including the reflective surface. Furthermore, good optical performance, including distortion, can be maintained over a wide imaging range at the magnification-side conjugate point. The distance between the magnification-side conjugate point and the optical system can also be shortened. Exceeding the upper limit of equation (14) results in overcorrection of distortion, making it difficult to maintain good optical performance. Furthermore, the inclination of the optical surface at the periphery in the X direction increases, making processing difficult. Falling below the lower limit of equation (14) makes it impossible to utilize optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, making it difficult to shorten the overall length of the optical system and narrowing the imaging range with good optical performance at the magnification-side conjugate point.

[0124] In the optical system according to this embodiment, a Y cross section is a surface including a position where a chief ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is a cross section that includes the reference optical axis A and is perpendicular to the Y cross section, and the optical surfaces having a finite radius of curvature among the optical surfaces may have a shape that is symmetrical only with respect to the Y cross section.

[0125] With this configuration, there is no distortion in the left and right direction (X direction), and good imaging performance can be maintained.

[0126] In the optical system according to this embodiment, a Y cross section is defined as a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is defined as a cross section that includes the reference optical axis A and is perpendicular to the Y cross section, In the Y cross section, a plurality of chief rays may be included between the position where the chief ray of the reference ray Ref is reflected by the first reflecting surface and the coordinate origin position of the first reflecting surface.

[0127] This configuration allows the overall length of the optical system to be shortened while maintaining the size of the optical system located on the magnification side, including the reflecting surface. Furthermore, it is possible to maintain good optical performance, including distortion, over a wide imaging range at the magnification-side conjugate point. Furthermore, it is possible to shorten the distance between the magnification-side conjugate point and the optical system.

[0128] In the optical system according to this embodiment, a Y cross section is defined as a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is defined as a cross section that includes the reference optical axis A and is perpendicular to the Y cross section, At least two of the optical surfaces may be decentered relative to each other in the Y cross section.

[0129] With this configuration, by constructing a prism with decentered optical surfaces, the degree of freedom increases due to the difference in curvature between the Y cross section and the X cross section, making it possible to utilize the higher-order terms of free-form surfaces. The overall length of the optical system can be shortened while maintaining the size of the optical system located on the magnification side. Furthermore, good optical performance, including distortion, can be maintained over the wide imaging range of the magnification-side conjugate point. The distance between the magnification-side conjugate point and the optical system can also be shortened. The optical surface is not limited to a free-form surface defined by an XY polynomial; even aspherical or spherical surfaces with rotationally symmetric optical surfaces can be decentered relative to each other in the Y cross section to obtain optical effects due to different curvatures in the X and Y directions.

[0130] In the optical system according to this embodiment, a Y cross section is defined as a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is defined as a cross section that includes the reference optical axis A and is perpendicular to the Y cross section, The second transmitting surface may be disposed on the opposite side of the coordinate origin of the first reflecting surface with respect to the chief ray of the reference optical axis A in the Y cross section.

[0131] With this configuration, interference between the first sub-optical system and the magnification-side light beam can be avoided, and a compact optical system can be configured.

[0132] In the optical system according to this embodiment, a Y cross section is defined as a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X cross section is defined as a cross section that includes the reference optical axis A and is perpendicular to the Y cross section, The coordinate system of the first reflecting surface may be tilted in a direction along the intermediate image in the Y cross section.

[0133] With this configuration, the distance between the intermediate image position and the first reflecting surface can be appropriately set. Also, the overall length of the optical system can be shortened while maintaining the size of the optical system located on the magnification side, including the reflecting surface. Furthermore, good optical performance, including distortion, can be maintained over a wide imaging range of the magnification-side conjugate point. Furthermore, the distance between the magnification-side conjugate point and the optical system can be shortened.

[0134] In the optical system according to this embodiment, the coordinate origin of at least one of the optical surfaces may be set on the reference optical axis A.

[0135] With this configuration, by aligning the origin coordinates of the optical surface with the reference optical axis A, the optical system, lens barrel, and housing can be designed efficiently.

[0136] In the optical system according to this embodiment, the first reflecting surface and the second transmitting surface may both be arranged so that their convex surfaces face toward the enlargement side.

[0137] This configuration ensures a space between the magnification-side conjugate point and the optical system, increasing the flexibility of the optical system installation. It also helps to reduce the height of the housing that makes up the optical system. Furthermore, it allows the aperture to be made smaller.

[0138] A flat surface perpendicular to the reference optical axis A may be provided on a part of the outer periphery of the prism.

[0139] According to this configuration, the flat surface serves as a reference for assembling the optical system, and the accuracy of attachment and assembly can be improved.

[0140] 35(A) to 35(H) are cross-sectional views in the Y direction showing various examples of the stepped structure of the prism PM according to Examples 1 to 8. The various lens elements and prisms that make up the optical system 1 are generally attached to the inside of a lens barrel (not shown) using adhesives, metal fittings, etc. In this case, a highly accurate attachment structure is required to faithfully reproduce the various dimensions of the optical design.

[0141] For example, an end face PMa, which serves as an attachment reference, is provided on a portion of the outer periphery of the prism PM. This end face PMa can be formed as a flat surface perpendicular to the reference optical axis Ref. Meanwhile, the lens barrel is provided with a flat surface corresponding to the shape of the end face PMa. When mounting, the end face PMa of the prism PM fits into the flat surface of the lens barrel, allowing the prism PM to be fixed to the lens barrel with high precision and stability.

[0142] Furthermore, the second transmitting surface T2 of the prisms PM according to Examples 1 to 10 may be provided with a protective film made of a dielectric, glass, polymer, etc. With this configuration, the second transmitting surface T2 exposed to the outside can be protected from scratches and dirt.

[0143] Numerical examples of the optical systems according to Examples 1 to 10 are described below. In each numerical example, all lengths in the tables are in millimeters, and all angles of view are in degrees. Each numerical example also shows the radius of curvature, surface spacing, Nd (refractive index for the d-line), vd (Abbe number for the d-line), N550 (refractive index at a wavelength of 550 nm), and decentering data (the displacements X, Y, and Z of the prism surface relative to the previous surface in the optical system, and the normal directions α, β, and γ of the prism surface relative to the previous surface). The quantities in each numerical example are calculated based on a wavelength of 550 nm. The term "variable" in the surface spacing means that it can be changed according to the image size (e.g., 100 inches, 80 inches, or 60 inches) at the magnification conjugate point, as shown in the table below. In each numerical example, the shape of the aspherical surface is defined by the following equation. Only non-zero aspherical coefficients are listed, except for the Conic coefficient k.

[0144]

number

[0145] where: z: Sag amount of the surface parallel to the z axis, r: Radial distance (=√(x 2 +y 2 ))、 c: Curvature at the vertex of the surface k: Conic coefficient, A~H: 4th to 18th order coefficients of r is.

[0146] In addition, the free-form surface shape is expressed in a local Cartesian coordinate system (x, y, z) with the vertex of the surface as the origin. It is defined by the following formula using

[0147]

number

[0148]

number

[0149] 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 a polynomial.

[0150] (Numerical Example 1) For the optical system of Numerical Example 1 (corresponding to Example 1), lens data is shown in Table 1, aspheric lens shape data is shown in Table 2, and free-form surface shape data of the prism is shown in Table 3. Table 4 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0151] [Table 1]

[0152] [Table 2]

[0153] [Table 3]

[0154] [Table 4]

[0155] (Numerical Example 2) For the optical system of Numerical Example 2 (corresponding to Example 2), lens data is shown in Table 5, aspheric lens shape data is shown in Table 6, and free-form surface shape data of the prism is shown in Table 7. Table 8 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0156] [Table 5]

[0157] [Table 6]

[0158] [Table 7]

[0159] [Table 8]

[0160] (Numerical Example 3) For the optical system of Numerical Example 3 (corresponding to Example 3), lens data is shown in Table 9, aspheric lens shape data is shown in Table 10, and free-form surface shape data of the prism is shown in Table 11. Table 12 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0161] [Table 9]

[0162] [Table 10]

[0163] [Table 11]

[0164] [Table 12]

[0165] (Numerical Example 4) For the optical system of Numerical Example 4 (corresponding to Example 4), lens data is shown in Table 13, aspheric lens shape data is shown in Table 14, and free-form surface shape data of the prism is shown in Table 15. Table 16 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0166] [Table 13]

[0167] [Table 14]

[0168] [Table 15]

[0169] [Table 16]

[0170] (Numerical Example 5) For the optical system of Numerical Example 5 (corresponding to Example 5), lens data is shown in Table 17, aspheric lens shape data is shown in Table 18, and free-form surface shape data of the prism is shown in Table 19. Table 20 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0171] [Table 17]

[0172] [Table 18]

[0173] [Table 19]

[0174] [Table 20]

[0175] (Numerical Example 6) For the optical system of Numerical Example 6 (corresponding to Example 6), lens data is shown in Table 21, aspheric lens shape data is shown in Table 22, and free-form prism shape data is shown in Table 23. Table 24 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0176] [Table 21]

[0177] [Table 22]

[0178] [Table 23]

[0179] [Table 24]

[0180] (Numerical Example 7) For the optical system of Numerical Example 7 (corresponding to Example 7), lens data is shown in Table 25, aspheric lens shape data is shown in Table 26, and free-form surface shape data of the prism is shown in Table 27. Table 28 shows the origin positions of the coordinate systems of each optical surface based on the coordinate system of the first transmitting surface of the prism.

[0181] [Table 25]

[0182] [Table 26]

[0183] [Table 27]

[0184] [Table 28]

[0185] (Numerical Example 8) For the optical system of Numerical Example 8 (corresponding to Example 8), lens data is shown in Table 29, and free-form surface shape data of the prism is shown in Table 30. The origin position of each optical surface coordinate system based on the coordinate system of the first transmitting surface of the prism is shown in Table 31. In Example 8 only, the lens data are absolute coordinates based on the first surface.

[0186] [Table 29]

[0187] [Table 30]

[0188] [Table 31]

[0189] Tables 32 to 37 below show the corresponding values ​​of the conditional expressions (1) to (14) in Numerical Examples 1 to 8, respectively.

[0190] [Table 32]

[0191] [Table 33]

[0192] [Table 34]

[0193] [Table 35]

[0194] [Table 36]

[0195] [Table 37]

[0196] 36(A) to 36(H) are graphs showing the shapes of the rectangular regions and concentric circles at the contracted conjugate points in each of Numerical Examples 1 to 8.

[0197] 37(A) to (D) and 38(E) to (H) are graphs showing the cross-sectional shapes and coordinate origins of the optical surfaces in Numerical Examples 1 to 8, with the coordinate system of the first transmitting surface T1 as the reference.

[0198] 39(A) to 39(H) are graphs showing the distortion shapes at the magnification-side conjugate point caused by distortion aberration of the optical systems according to Numerical Examples 1 to 8. In each graph, the image size at the magnification conjugate point is 148 inches in Example 1, 110 inches in Example 2, 100 inches in Example 3, 100 inches in Example 4, 150 inches in Example 5, 80 inches in Example 6, 150 inches in Example 7, and 50 inches in Example 8. It can be seen from these graphs that distortion at the magnification-side conjugate point of the optical systems 1 according to Examples 1 to 8 is appropriately corrected.

[0199] (Embodiment 2) A second embodiment of the present disclosure will be described below with reference to FIG. 40. FIG. 40 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 the first embodiment, an image forming element 101, a light source 102, and a control unit 110. The image forming element 101 is configured with a liquid crystal, a DMD, or the like, and generates an image to be projected onto a screen SC 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 or 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.

[0200] 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.

[0201] (Embodiment 3) Hereinafter, a third embodiment of the present disclosure will be described with reference to FIG. 41. FIG. 41 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 the first embodiment, 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.

[0202] 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.

[0203] 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.

[0204] 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.

[0205] 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. [Industrial Applicability]

[0206] 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 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 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, The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction, a first sub-optical system including an aperture stop that defines a range through which a light beam passes through the optical system; a second sub-optical system provided on the magnification side of the first sub-optical system and including a prism made of a transparent medium; the prism has a first transmitting surface located on a reduction side, a second transmitting surface located on a magnification side, and at least one reflecting surface located on an optical path between the first transmitting surface and the second transmitting surface; the aperture stop is positioned between the reduction conjugate point and the intermediate image position; a part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located on the most reduction side of the at least one reflecting surface, the first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements; an optical system in which, when an axis passing through at least two centers of the rotationally symmetric lens elements is defined as a reference optical axis, i) the prism is arranged to intersect with the reference optical axis, and ii) at least one rotationally asymmetric optical surface among the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism is formed so that, in a plane perpendicular to the reference optical axis, a maximum angle θmax and a minimum angle θmin of an angle at which a chief ray of a light beam having an image-forming relationship on a concentric circle centered at an intersection point between the reference optical axis and a reduction conjugate point of the rectangular area intersects with a normal to the surface at a position where the chief ray is incident on the rotationally asymmetric optical surface satisfies the following formula (1): 45°>|θmax|−|θmin|>0.014°…(1)

2. the rotationally asymmetric optical surface is the second transmitting surface, The optical system according to claim 1 , which satisfies the following formula (2a): 17°>|θmax|−|θmin|>0.024°…(2a)

3. the rotationally asymmetric optical surface is the first transmitting surface, The optical system according to claim 1 , which satisfies the following formula (3a): 5.5°>|θmax|−|θmin|>0.050°…(3a)

4. the rotationally asymmetric optical surface is the first reflecting surface, The optical system according to claim 1 , which satisfies the following formula (4a): 1.5°>|θmax|-|θmin|>0.100°…(4a)

5. 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, The reduction conjugate point has an imaging relationship in a rectangular area having a long direction and a short direction, a first sub-optical system including an aperture stop that defines a range through which a light beam passes through the optical system; a second sub-optical system provided on the magnification side of the first sub-optical system and including a prism made of a transparent medium; the prism has a first transmitting surface located on a reduction side, a second transmitting surface located on a magnification side, and at least one reflecting surface located on an optical path between the first transmitting surface and the second transmitting surface; the aperture stop is positioned between the reduction conjugate point and the intermediate image position; a part or all of the intermediate image formed at the intermediate image position is positioned between the first transmitting surface and a first reflecting surface located on the most reduction side of the at least one reflecting surface, the first reflecting surface has a shape with a concave surface facing in a direction in which a light ray incident on the first reflecting surface is reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements; an optical system in which, when an axis passing through at least two centers of the rotationally symmetric lens elements is taken as a reference optical axis, i) the prism is arranged to intersect with the reference optical axis, and ii) in a plane perpendicular to the reference optical axis, when chief rays of light have an imaging relationship on concentric circles whose centers are the intersection points of the reference optical axis and the reduction conjugate point of the rectangular area, at least one rotationally asymmetric optical surface among the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism satisfies the following formula (5): 10>ΔSmax / r>0.001...(5) where: ΔSmax: maximum sag difference in the amount of sag in the direction along the reference optical axis on the rotationally asymmetric optical surface through which the principal ray passes r: radius of the concentric circle is.

6. 6. The optical system according to claim 5, wherein when the optical surface having a rotationally asymmetric shape through which the chief ray passes is the second transmitting surface, the following formula (6) is satisfied: 10>ΔSmax / r>0.001...(6)

7. 6. The optical system according to claim 5, wherein when the optical surface having a rotationally asymmetric shape through which the chief ray passes is the first transmitting surface, the following formula (7) is satisfied: 3>ΔSmax / r>0.001...(7)

8. 6. The optical system according to claim 5, wherein when the optical surface having a rotationally asymmetric shape through which the chief ray passes is the first reflecting surface, the following formula (8a) is satisfied: 0.8>ΔSmax / r>0.002...(8a)

9. 2. The optical system according to claim 1, wherein, when an axis passing through at least two centers of the rotationally symmetric lens elements is defined as a reference optical axis, in a plane perpendicular to the reference optical axis, chief rays of light have an image-forming relationship on concentric circles whose centers are the intersection points of the reference optical axis and the reduction conjugate points of the rectangular area, a maximum optical path length difference ΔLmax of optical paths along which the chief rays pass inside the prism satisfies the following formula (9a) using a radius r of the concentric circles: 2.5>ΔLmax / r>0.002...(9a)

10. 10. The optical system according to claim 9, wherein a maximum optical path length Lmax of an optical path through which the chief ray passes inside the prism satisfies the following formula (10) using a radius r of the concentric circle: 30>Lmax / r>2...(10)

11. 10. The optical system according to claim 1, 5, or 9, which satisfies the following formula (11): 2.00>SP / LP>0.10...(11) where: SP: the distance between the reduction conjugate point and the aperture stop along the chief ray path of a reference ray defined as a ray that forms an image at the position closest to the optical system among the expansion conjugate points LP: the distance between the aperture stop and the magnification end of the first sub-optical system along the chief ray path of the reference ray is.

12. 10. The optical system according to claim 1, wherein a Y cross section is a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface, and an X cross section is a cross section that includes the reference optical axis and is perpendicular to the Y cross section, and the optical system satisfies the following formula (12): 0.20>(XM1-RefM1) / r>-3.00...(12) where: XM1: Y coordinate in the first reflecting surface coordinate system of the chief ray at the X end of the first reflecting surface RefM1: Y coordinate in the first reflecting surface coordinate system on the first reflecting surface of the reference ray defined as the ray that forms an image at the position closest to the optical system among the enlarged conjugate points r: radius of the concentric circle is.

13. 10. The optical system according to claim 1, wherein a plane including a position where a chief ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis and perpendicular to the Y cross section is defined as an X cross section, and the following formula (13) is satisfied: 1.90>M1X / M1Y>1.00...(13) where: M1X: X-effective range of the first reflecting surface when measured parallel to the X-section M1Y: Y effective range of the first reflecting surface when measured parallel to the Y cross section is.

14. 10. The optical system according to claim 1, wherein a plane including a position where a chief ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis and perpendicular to the Y cross section is defined as an X cross section, and the optical system satisfies the following formula (14): 6.00>T2X / T2Y>2.00...(14) where: T2X: X-effective range of the second transmitting surface when measured parallel to the X-section T2Y: Y effective range of the second transmitting surface when measured parallel to the Y cross section is.

15. 6. The optical system according to claim 1, wherein a Y-section is a plane including a position where a chief ray passing through the center of the longitudinal direction of the rectangular area is reflected by the first reflecting surface, and an X-section is a cross section that includes the reference optical axis and is perpendicular to the Y-section, and among the rotationally asymmetric shaped optical surfaces, the rotationally asymmetric shaped optical surfaces having a finite radius of curvature have a shape that is symmetric only with respect to the Y-section.

16. a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis and perpendicular to the Y cross section is defined as an X cross section, 10. An optical system according to claim 1, wherein in the Y cross section, a plurality of chief rays are included between the position where the chief ray of a reference ray, which is defined as a ray that forms an image at a position closest to the optical system among the magnified conjugate points, is reflected by the first reflecting surface and the coordinate origin position of the first reflecting surface.

17. a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis A and perpendicular to the Y cross section is defined as an X cross section, The optical system according to claim 1 , wherein at least two of the rotationally asymmetric optical surfaces are decentered from each other in the Y cross section.

18. a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis and perpendicular to the Y cross section is defined as an X cross section, 10. The optical system according to claim 1, wherein the second transmitting surface is disposed on the opposite side of the coordinate origin of the first reflecting surface with respect to a chief ray of the reference optical axis in the Y cross section.

19. a plane including a position where a principal ray passing through the center of the longitudinal direction of the rectangular region is reflected by the first reflecting surface is defined as a Y cross section, and a cross section including the reference optical axis and perpendicular to the Y cross section is defined as an X cross section, 10. The optical system according to claim 1, wherein the coordinate system of said first reflecting surface is tilted in a direction along the intermediate image in the Y cross section.

20. The optical system according to claim 1 , wherein the coordinate origin of at least one of the rotationally asymmetric optical surfaces is set on the reference optical axis.

21. 10. The optical system according to claim 1, wherein the first reflecting surface and the second transmitting surface are both arranged so as to be convex toward the magnification conjugate point.

22. 10. The optical system according to claim 1, wherein a flat surface perpendicular to the reference optical axis is provided on a part of the outer periphery of the prism.

23. an optical system according to any one of claims 1 to 22; an image forming element that generates an image to be projected onto a screen via the optical system.

24. an optical system according to any one of claims 1 to 22; an imaging element that receives the optical image formed by the optical system and converts it into an electrical image signal;

Images