Optical system, image projection device, and image pickup device

Abstract

Provided are an optical system, an image projection device, and an image pickup device. The optical system includes 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 on a reduction side, a second transmission surface on an enlargement side, and at least one reflection surface between the first transmission surface and the second transmission surface. The first sub optical system includes a plurality of rotationally symmetric lens elements. When an axis passing through the center of at least two of the rotationally symmetric lens elements is set as a reference optical axis, at least one optical surface of the prism is formed so that, in a plane perpendicular to the reference optical axis, a chief ray of a light ray having an imaging relationship on a concentric circle centered on an intersection of the reference optical axis and a reduction conjugate point of a rectangular region, a maximum angle θmax at which the chief ray intersects a normal line of the optical surface at a position of incidence to the optical surface, and a minimum angle θmin satisfy the following equation: 5°>|θmax|−|θmin|>0.014°.

Description

Technical Field

[0001] This disclosure relates to optical systems using prisms. Furthermore, this disclosure relates to image projection devices and camera devices using such optical systems. Background Technology

[0002] Patent documents 1-3 disclose projection optical systems that integrate optical elements with a transmission surface and a reflection surface, and mention that either the transmission surface or the reflection surface can be an aspherical surface.

[0003] Prior art literature

[0004] Patent documents

[0005] Patent Document 1: Japanese Patent Application Publication No. 2020-020860

[0006] Patent Document 2: Japanese Patent Application Publication No. 2020-024377

[0007] Patent Document 3: International Publication No. 2019 / 151252 Summary of the Invention

[0008] The problem the invention aims to solve

[0009] This disclosure provides an optical system that uses a small prism to achieve short-focus, large-screen projection or imaging. Furthermore, this disclosure provides an image projection device and an imaging device using such an imaging optical system.

[0010] Technical solutions for solving the problem

[0011] One aspect of this disclosure relates to an optical system having a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and having an intermediate imaging position internally conjugate to both the reduction and magnification conjugate points. The reduction conjugate points have an imaging relationship within a rectangular region having a long side direction and a short side direction. The optical system comprises a first sub-optical system including an aperture stop that defines the range through which a light beam passes in the optical system, and a second sub-optical system disposed further on the magnification side than the first sub-optical system and comprising a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface in the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and a first reflecting surface, the first reflecting surface being the one most closely positioned on the reduction side of the at least one reflecting surface. The first reflecting surface has a shape such that the concave surface is oriented in the direction of reflection of light incident on the first reflecting surface. The first sub-optical system comprises a plurality of rotationally symmetric lens elements. When the axis passing through the center of at least two of the rotationally symmetric lens elements is taken as the reference optical axis, at least one of the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism is formed such that the maximum angle θmax and the minimum angle θmin of the principal ray of the light ray having an imaging relationship on a concentric circle centered at the intersection of the reference optical axis and the reduced conjugate point of the rectangular region, at the position of incident on the optical surface, intersect the normal of the surface, satisfy the following equation (1).

[0012] 45°>|θmax|-|θmin|>0.014° (1)

[0013] Furthermore, one aspect of this disclosure relates to an optical system having a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and having an intermediate imaging position internally conjugate to both the reduction conjugate point and the magnification conjugate point. The reduction conjugate point has an imaging relationship within a rectangular region having a long side direction and a short side direction. The optical system comprises a first sub-optical system including an aperture stop that defines the range through which a light beam passes in the optical system, and a second sub-optical system disposed further on the magnification side than the first sub-optical system and comprising a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface in the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and the first reflecting surface, which is the reflecting surface located most close to the reduction side among the at least one reflecting surface. The first reflecting surface has a shape such that the concave surface is oriented in the direction in which light incident on the first reflecting surface is reflected. The first sub-optical system comprises a plurality of rotationally symmetric lens elements. When the axis passing through the center of at least two of the rotationally symmetric lens elements is taken as the reference optical axis, at least one of the first transmitting surface, the second transmitting surface, and the at least one reflecting surface of the prism satisfies the following equation (5).

[0014] 10>ΔSmax / r>0.001 (5)

[0015] Here,

[0016] ΔSmax: The maximum sag difference in the direction along the reference optical axis of the optical surface through which the principal ray passes;

[0017] r: the radius of the concentric circles.

[0018] Furthermore, one aspect of this disclosure relates to an optical system having a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and having an intermediate imaging position internally conjugate to both the reduction conjugate point and the magnification conjugate point. The reduction conjugate point has an imaging relationship within a rectangular region having a long side direction and a short side direction. The optical system comprises a first sub-optical system including an aperture stop that defines the range through which a light beam passes in the optical system, and a second sub-optical system disposed further on the magnification side than the first sub-optical system and comprising a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface in the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and the first reflecting surface, which is the reflecting surface located most close to the reduction side among the at least one reflecting surface. The first reflecting surface has a shape such that the concave surface is oriented in the direction in which light rays incident on the first reflecting surface are reflected. The first sub-optical system comprises a plurality of rotationally symmetric lens elements. The maximum optical path length difference ΔLmax of the principal ray passing through the interior of the prism satisfies the following equation (9) using the radius r of the concentric circles.

[0019] 3>ΔLmax / r>0.005 (9)

[0020] Furthermore, another aspect of this disclosure relates to an image projection apparatus comprising the aforementioned optical system and an image forming element for generating an image projected onto a screen via the optical system.

[0021] Furthermore, another aspect of this disclosure relates to a camera device comprising the aforementioned optical system and a camera element that receives the optical image formed by the optical system and converts it into an electrical image signal.

[0022] Invention Effects

[0023] According to the optical system disclosed herein, the overall length of the optical system can be shortened while keeping the optical system, including the reflective surface disposed on the magnification side, small. Furthermore, good optical performance, including distortion, can be ensured over a wider imaging range at the magnification-side conjugate point. In addition, the distance between the magnification-side conjugate point and the optical system can be shortened. Therefore, short-focal-point and large-screen projection or imaging can be achieved using a small prism. Attached Figure Description

[0024] Figure 1 This is a configuration diagram showing the optical system involved in Embodiment 1.

[0025] Figure 2(A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 1. Figure 2 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 1 is used.

[0026] Figure 3 This is an explanatory diagram showing the imaging position of the reduced conjugate point that determines the effective size of the optical surface.

[0027] Figure 4 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 1. Figure 4 (B) shows the beam distribution at the first reflecting surface R1. Figure 4 (C) shows the beam distribution at the second reflecting surface R2. Figure 4 (D) shows the beam distribution at the second transmission surface T2.

[0028] Figure 5 This is a configuration diagram showing the optical system involved in Embodiment 2.

[0029] Figure 6 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism pM involved in Embodiment 2. Figure 6 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 2 is used.

[0030] Figure 7 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 2. Figure 7 (B) shows the beam distribution at the first reflecting surface R1. Figure 7 (C) shows the beam distribution at the second reflecting surface R2. Figure 7 (D) shows the beam distribution at the second transmission surface T2.

[0031] Figure 8 This is a configuration diagram of the optical system involved in Embodiment 3.

[0032] Figure 9 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 3. Figure 9 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 3 is used.

[0033] Figure 10 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 3. Figure 10 (B) shows the beam distribution at the first reflecting surface R1. Figure 10 (C) shows the beam distribution at the second transmission surface T2.

[0034] Figure 11 This is a configuration diagram of the optical system involved in Embodiment 4.

[0035] Figure 12 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 4. Figure 12 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 4 is used.

[0036] Figure 13 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 4. Figure 13 (B) shows the beam distribution at the first reflecting surface R1. Figure 13 (C) shows the beam distribution at the second transmission surface T2.

[0037] Figure 14 This is a configuration diagram showing the optical system involved in Embodiment 5.

[0038] Figure 15 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 5. Figure 15 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 5 is used.

[0039] Figure 16 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 5. Figure 16 (B) shows the beam distribution at the first reflecting surface R1. Figure 16 (C) shows the beam distribution at the second reflecting surface R2. Figure 16 (D) shows the beam distribution at the second transmission surface T2.

[0040] Figure 17 This is a configuration diagram showing the optical system involved in Embodiment 6.

[0041] Figure 18 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 6. Figure 18 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 6 is used.

[0042] Figure 19 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 6. Figure 19(B) shows the beam distribution at the first reflecting surface R1. Figure 19 (C) shows the beam distribution at the second reflecting surface R2. Figure 19 (D) shows the beam distribution at the second transmission surface T2.

[0043] Figure 20 This is a configuration diagram showing the optical system involved in Embodiment 7.

[0044] Figure 21 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 7. Figure 21 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 7 is used.

[0045] Figure 22 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Embodiment 7. Figure 22 (B) shows the beam distribution at the first reflecting surface R1. Figure 22 (C) shows the beam distribution at the second transmission surface T2.

[0046] Figure 23 This is a configuration diagram showing the optical system involved in Embodiment 8.

[0047] Figure 24 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 8. Figure 24 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 8 is used.

[0048] Figure 25 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 8. Figure 25 (B) shows the beam distribution at the first reflecting surface R1. Figure 25 (C) shows the beam distribution at the second reflecting surface R2. Figure 25 (D) shows the beam distribution at the second transmission surface T2.

[0049] Figure 26 (A) is a configuration diagram showing the optical system involved in Embodiment 9. Figure 26 (B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 9 is used.

[0050] Figure 27 (A) is a configuration diagram showing the optical system 1 according to Embodiment 10. Figure 27(B) is an explanatory diagram showing how the image projection device using the optical system 1 according to Embodiment 10 is used.

[0051] Figure 28 This is an illustrative diagram showing an example of a reduced image region at a conjugate point.

[0052] Figure 29 (A) is a side view illustrating the definition of the reference ray Ref. Figure 29 (B) is its three-dimensional diagram.

[0053] Figure 30 (A) is an XY cross-sectional view showing the distribution of the principal rays at the conjugate point of contraction. Figure 30 (B) is a configuration diagram showing the optical system 1 according to Embodiment 5.

[0054] Figure 31 (A) is an XY cross-sectional view showing the distribution of the principal rays at the conjugate point of contraction. Figure 31 (B) is a conceptual illustration showing the pattern of the principal ray of a light ray incident on the optical surface of a rotationally symmetric prism. Figure 31 (C) is a conceptual illustration showing the pattern of the principal ray of light incident on the optical surface of a freeform prism.

[0055] Figure 32 (A) is an illustrative diagram showing the configuration of concentric circles (radius r) and the rectangular region at the narrowed conjugate point without optical offset. Figure 32 (B) is an explanatory diagram showing the configuration of concentric circles (radius r) and the rectangular region at the narrowed conjugate point in the case of optical offset.

[0056] Figure 33 This is an explanatory diagram illustrating the concepts of rotationally symmetric optical surfaces (spherical, aspherical, etc.) and rotationally asymmetric optical surfaces (freeform surfaces, etc.).

[0057] Figure 34 This is an explanatory diagram illustrating the concepts of rotationally symmetric optical elements (without eccentricity) and rotationally asymmetric optical elements (with eccentricity).

[0058] Figure 35 This is a Y-direction cross-sectional view showing various examples of the stepped structure of the prism PM according to Embodiments 1 to 8.

[0059] Figure 36 It is a diagram showing the rectangular region and the shape of the concentric circles at the reduced conjugate point in each of the numerical embodiments 1 to 8.

[0060] Figure 37It is a graph showing the cross-sectional shape of each optical surface and the origin of the coordinate system based on the coordinate system of the first transmission surface T1 in each of the numerical embodiments 1 to 4.

[0061] Figure 38 It is a graph showing the cross-sectional shape of each optical surface and the origin of the coordinate system based on the coordinate system of the first transmission surface T1 in each of the numerical embodiments 5 to 8.

[0062] Figure 39 This is a graph showing the distortion shape at the conjugate point on the magnification side caused by the distortion aberration of the optical system involved in each of the numerical embodiments 1 to 8.

[0063] Figure 40 This is a block diagram illustrating an example of an image projection apparatus related to this disclosure.

[0064] Figure 41 This is a block diagram illustrating an example of the camera device involved in this disclosure. Detailed Implementation

[0065] Hereinafter, embodiments will be described in detail with appropriate reference to the accompanying drawings. However, sometimes necessary detailed descriptions are omitted. For example, detailed descriptions of well-known matters or repetitive descriptions of substantially the same structures are sometimes omitted. This is to avoid unnecessarily redundancy in the following description and to facilitate understanding by those skilled in the art.

[0066] Furthermore, the accompanying drawings and the following description provided by the applicant to enable those skilled in the art to fully understand this disclosure are not intended to limit the subject matter of the technical solutions described herein.

[0067] Hereinafter, various embodiments of the optical system disclosed herein will be described. In each embodiment, the optical system will be described as a projector (an example of an image projection device) that projects an original image SA, based on an image signal spatially modulated by an image forming element such as a liquid crystal or a DMD (digital micromirror device), onto a screen. That is, the optical system disclosed herein has a screen (not shown) arranged on the extension line of the magnification side, and can be used to magnify the original image SA arranged on the image forming element on the reduction side and project it onto the screen. However, the projection surface is not limited to a screen. Walls, ceilings, floors, windows, etc., inside residences, shops, or vehicles used as means of transportation, aircraft, etc., are also included in the projection surface.

[0068] Furthermore, the optical system disclosed herein can also be used to focus light emitted from an object located on the extension line of the magnification side and form an optical image of the object on the imaging surface of the imaging element disposed on the reduction side.

[0069] (Implementation Method 1)

[0070] The following uses Figures 1 to 39 The optical system according to Embodiment 1 of this disclosure will be described.

[0071] (Example 1)

[0072] Figure 1 This is a configuration diagram showing the optical system 1 according to Embodiment 1. The optical system 1 includes a first sub-optical system comprising an aperture stop ST and a second sub-optical system comprising a prism PM. Figure 1 In the image, the imaging position on the reduction side, i.e., the reduction conjugate point, is located on the lower side, while the imaging position on the magnification side, i.e., the magnification conjugate point, is located on the upper side. The second sub-optical system is positioned further on the magnification side than the first sub-optical system.

[0073] Figure 28 This is an explanatory diagram showing an example of the image region at the point of reduction. The image region at the point of reduction is defined as a rectangular region having a long side (X direction) and a short side (Y direction), which has an optically conjugate imaging relationship with the image region at the point of magnification. Light travels along the normal direction (Z direction) of this rectangular region. As an example, this rectangular region has aspect ratios such as 3:2, 4:3, 16:9, 16:10, and 256:135. In the case of an image projection device, this corresponds to the image display area of ​​the image forming element; in the case of a camera device, it corresponds to the imaging area of ​​the camera element.

[0074] Furthermore, the intermediate imaging position, conjugate to both the reduction and magnification conjugate points, is located inside the optical system 1. This intermediate imaging position is... Figure 1 The image is shown as IMY in the Y direction, but the image as IMY in the X direction is omitted from the diagram.

[0075] The first sub-optical system comprises optical element PA and lens elements L1 to L18 sequentially from the reduction side to the magnification side. Optical element PA represents optical elements such as a TIR (total internal reflection) prism, a prism for color decomposition and color synthesis, an optical filter, a parallel plate glass, a quartz low-pass filter, and an infrared cutoff filter. The reduction-side end face of optical element PA is set at the reduction conjugate point, where the original image SA (plane 1) is located. For plane numbering, refer to the numerical embodiment described later.

[0076] Optical element PA has two parallel and flat transmission surfaces (surfaces 2 and 3). Lens element L1 has a positive meniscus shape with the convex surface facing the reduction side (surfaces 4 and 5). Lens element L2 has a negative meniscus shape with the 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 the convex surface facing the magnification side (surfaces 8 and 9). Lens elements L2 to L4 are joined 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 joined together to form a compound lens. Lens element L7 has a negative meniscus shape with the 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 joined together to form a compound lens.

[0077] The aperture stop ST defines the range through which the light beam passes in the optical system 1, and is positioned between the conjugate point of narrowing and the aforementioned intermediate imaging position. As an example, the aperture stop ST is located between lens element L8 and lens element L9 (plane 16).

[0078] Lens element L9 has a biconvex shape (faces 17, 18). Lens element L10 has a negative meniscus shape with the convex surface facing the magnifying side (faces 18, 19). Lens elements L9 and L10 are joined together to form a compound lens. Lens element L11 has a biconcave shape (faces 20, 21). Lens element L12 has a biconvex shape (faces 21, 22). Lens elements L11 and L12 are joined together to form a compound lens. Lens element L13 has a biconvex shape (faces 23, 24). Lens element L14 has a positive meniscus shape with the convex surface facing the reducing side (faces 25, 26). Lens element L15 has a biconcave shape (faces 27, 28). Lens element L16 has a biconvex shape (faces 28, 29). Lens elements L15 and L16 are joined together to form a compound lens. Lens element L17 has a positive meniscus shape with the convex surface facing the reducing side (faces 30, 31). Lens element L18 has a positive meniscus shape (faces 32, 33) with the convex surface facing the magnification side. By employing the above-described lens element structure, the first sub-optical system is able to suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0079] The second sub-optical system includes a prism PM formed of a transparent medium such as glass or synthetic resin. The prism PM has a first transmission surface T1 on the reduction side, a second transmission surface T2 on the magnification side, and two first reflecting surfaces R1 and a second reflecting surface R2 located in the optical path between the first and second transmission surfaces T1 and T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the reduction side (surface 34). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light incident on the first reflecting surface R1 is reflected (surface 35). The second reflecting surface R2 has a planar shape (surface 36). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnification side (surface 37).

[0080] Since the prism PM integrates the first transmission surface T1, the second transmission surface T2, the first reflection surface R1, and the second reflection surface R2, it can reduce the assembly and adjustment between optical components and suppress costs. Furthermore, the optical surfaces of the prism PM, which have optical power, such as the first transmission surface T1, the second transmission surface T2, and the first reflection surface R1, are formed without an axis of rotational symmetry; that is, they are formed as freeform surfaces with different curvatures along the X and Y axes. By using freeform surfaces with different curvatures along the X and Y axes for the optical surfaces of the prism, the degree of freedom for distortion correction is significantly improved, thus also resulting in a reduction in the overall length of the first sub-optical system. In addition, it also reduces the weight of the head of the optical system 1, allows for a well-balanced configuration of the optical system's center of gravity, and simplifies the structure of the joint where the lens barrel of the optical system is held in the housing of the optical system.

[0081] Figure 29 (A) is a side view illustrating the definition of the reference ray Ref. Figure 29 (B) is its stereoscopic view. The reference ray Ref is defined as the ray that images the image at the position closest to the optical system among the magnified conjugate points on the screen SC.

[0082] Figure 2 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 1. Figure 2 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 1. The image projection device, including the optical system 1, is horizontally arranged on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.7m. Light generated from the optical system 1 is projected diagonally upwards and forwards, achieving a short focal point and large image projection.

[0083] Figure 3This is an explanatory diagram showing the imaging position of the reduced conjugate point that determines the effective size of the optical surface. The original image SA located at the reduced conjugate point has a rectangular area. As an example, the relative X coordinate of the imaging position is set in intervals of 0.5 within the range of -1.0 to 1.0, and the relative Y coordinate is set in intervals of 0.25 within the range of 0.0 to 1.0, for a total of 25 coordinates.

[0084] Figure 4 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 4 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 1. Figure 4 (B) shows the beam distribution at the first reflecting surface R1. Figure 4 (C) shows the beam distribution at the second reflecting surface R2. Figure 4 (D) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, M2X is the effective X range of the second reflection surface R2 when measured parallel to the X-section, M2Y is the effective Y range of the second reflection surface R2 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular region of the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular region. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0085] (Example 2)

[0086] Figure 5 This is a configuration diagram showing the optical system 1 according to Embodiment 2. This optical system 1 has the same structure as Embodiment 1, but also has an intermediate image within the first sub-optical system, thus having two intermediate imaging 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. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0087] Lens element L1 has a positive meniscus shape with its convex surface facing the magnifying side (faces 4 and 5). Lens element L2 has a biconvex shape (faces 6 and 7). Lens element L3 has a negative meniscus shape with its convex surface facing the reducing side (faces 8 and 9). Lens element L4 has a biconvex shape (faces 10 and 11). Lens element L5 has a biconvex shape (faces 12 and 13). Lens element L6 has a biconcave shape (faces 13 and 14). Lens elements L5 and L6 are joined together to form a compound lens. The aperture stop ST is located between lens elements L6 and L7 (face 15).

[0088] Lens element L7 has a biconcave shape (faces 16, 17). Lens element L8 has a biconvex shape (faces 17, 18). Lens elements L7 and L8 are joined together to form a compound lens. Lens element L9 has a positive meniscus shape with the convex surface facing the magnifying side (faces 19, 20). Lens element L10 has a biconvex shape (faces 21, 22). Lens element L11 has a negative meniscus shape with the convex surface facing the magnifying side (faces 23, 24). Lens element L12 has a positive meniscus shape with the convex surface facing the reducing side (faces 25, 26). Lens element L13 has a biconcave shape (faces 27, 28). Lens element L14 has a biconvex shape (faces 29, 30). Lens element L15 has a biconvex shape (faces 31, 32). Lens element L16 has a positive meniscus shape with the convex surface facing the magnifying side (faces 33, 34). Lens element L17 has a negative meniscus shape with its convex surface facing the reduction side (faces 35, 36). Lens element L18 has a biconvex shape (faces 36, 37). Lens elements L17 and L18 are joined together to form a compound lens. Lens element L19 has a biconcave shape (faces 38, 39). Lens element L20 has a biconcave shape (faces 40, 41). Lens element L21 has a biconvex shape (faces 42, 43). Lens element L22 has a biconvex shape (faces 44, 45). Lens element L23 has a negative meniscus shape with its convex surface facing the magnification side (faces 46, 47). Lens element L24 has a biconvex shape (faces 48, 49). Lens element L25 has a biconvex shape (faces 50, 51). Lens element L26 has a biconcave shape (faces 52, 53). Lens element L27 has a positive meniscus shape with its convex surface facing the reduction side (faces 54, 55). Lens element L28 has a biconcave shape (faces 56, 57). By employing the above-described lens element structure, the first sub-optical system is able to suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0089] The prism PM has a first transmission surface T1 located on the shrinking side, a second transmission surface T2 located on the magnifying side, and two first reflecting surfaces R1 and a second reflecting surface R2 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the shrinking side (surface 58). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction of reflection of light rays incident on the first reflecting surface R1 (surface 59). The second reflecting surface R2 has a planar shape (surface 60). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 61).

[0090] Figure 6 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 2. Figure 6 (B) is an explanatory diagram showing the usage of the image projection device using the optical system 1 according to Embodiment 2. The image projection device, including the optical system 1, is horizontally arranged on a support platform such as a table or on the floor. The screen SC is positioned horizontally in front of the support platform at a relatively short horizontal distance, for example, 0.2m. Light generated from the optical system 1 is projected diagonally downwards and forwards, achieving a short focal point and large screen projection.

[0091] Figure 7 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 7 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 2. Figure 7 (B) shows the beam distribution at the first reflecting surface R1. Figure 7 (C) shows the beam distribution at the second reflecting surface R2. Figure 7(D) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, M2X is the effective X range of the second reflection surface R2 when measured parallel to the X-section, M2Y is the effective Y range of the second reflection surface R2 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular region of the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular region. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0092] (Example 3)

[0093] Figure 8 This is a configuration diagram showing the optical system 1 according to Embodiment 3. This optical system 1 has the same structure as Embodiment 1, but the first sub-optical system includes lens elements L1 to L10, and the second sub-optical system includes a prism PM, which projects in an oblique direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0094] Lens element L1 has a biconvex shape (faces 4 and 5). Lens element L2 has a biconvex shape (faces 6 and 7). Lens element L3 has a biconcave shape (faces 7 and 8). Lens element L4 has a biconvex shape (faces 8 and 9). Lens elements L2 to L4 are joined together to form a compound lens. The aperture stop ST is located between lens elements L4 and L5 (face 10).

[0095] Lens element L5 has a positive meniscus shape with its convex surface facing the magnifying side (faces 11, 12). Lens element L6 has a negative meniscus shape with its convex surface facing the magnifying side (faces 12, 13). Lens elements L5 and L6 are joined together to form a compound lens. Lens element L7 has a negative meniscus shape with its convex surface facing the magnifying side (faces 14, 15). Lens element L8 has a positive meniscus shape with its convex surface facing the reducing side (faces 16, 17). Lens element L9 has a biconvex shape (faces 18, 19). Lens element L10 has a biconcave shape (faces 19, 20). Lens elements L9 and L10 are joined together to form a compound lens. By employing the above-described lens element structure, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0096] The prism PM has a first transmission surface T1 located on the narrowing side, a second transmission surface T2 located on the magnifying side, and a first reflecting surface R1 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the narrowing side (surface 21). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 22). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 23).

[0097] Figure 9 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 3. Figure 9 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 3. The image projection device, including the optical system 1, is horizontally disposed on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.8 m, separating it from the rear side. Light generated from the optical system 1 is projected obliquely upward from the rear, achieving a short focal point and large image projection.

[0098] Figure 10 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 10 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 3. Figure 10 (B) shows the beam distribution at the first reflecting surface R1. Figure 10(C) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular area of ​​the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular area. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0099] (Example 4)

[0100] Figure 11 This is a configuration diagram showing the optical system 1 according to Embodiment 4. This optical system 1 has the same structure as Embodiment 1, but the first sub-optical system includes lens elements L1 to L10, and the second sub-optical system includes a prism PM, which projects in an inclined direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0101] Lens element L1 has a biconvex shape (faces 4 and 5). Lens element L2 has a biconvex shape (faces 6 and 7). Lens element L3 has a biconcave shape (faces 7 and 8). Lens element L4 has a meniscus shape with the convex surface facing the narrowing side (faces 8 and 9). Lens elements L2 to L4 are joined together to form a compound lens. The aperture stop ST is located between lens elements L4 and L5 (face 10).

[0102] Lens element L5 has a positive meniscus shape with its convex surface facing the magnification side (faces 11, 12). Lens element L6 has a negative meniscus shape with its convex surface facing the magnification side (faces 12, 13). Lens elements L5 and L6 are joined together to form a compound lens. Lens element L7 has a negative meniscus shape with its convex surface facing the magnification side (faces 14, 15). Lens element L8 has a biconvex shape (faces 16, 17). Lens element L9 has a biconvex shape (faces 18, 19). Lens element L10 has a biconcave shape (faces 19, 20). Lens elements L9 and L10 are joined together to form a compound lens. By employing the above-described lens element structure, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0103] The prism PM has a first transmission surface T1 located on the narrowing side, a second transmission surface T2 located on the magnifying side, and a first reflecting surface R1 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the narrowing side (surface 21). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 22). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 23).

[0104] Figure 12 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 4. Figure 12 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 4. The image projection device, including the optical system 1, is horizontally arranged on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.6 m, separating it from the rear side. Light generated from the optical system 1 is projected obliquely upward from the rear, achieving a short focal point and large image projection.

[0105] Figure 13 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 13 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 4. Figure 13 (B) shows the beam distribution at the first reflecting surface R1. Figure 13 (C) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular area of ​​the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular area. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0106] (Example 5)

[0107] Figure 14This is a configuration diagram showing the optical system 1 according to Embodiment 5. This optical system 1 has the same structure as Embodiment 1, but the first sub-optical system includes lens elements L1 to L14, and the second sub-optical system includes a prism PM, which projects in an oblique direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0108] Lens element L1 has a positive meniscus shape with its convex surface facing the narrowing side (faces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the narrowing side (faces 6 and 7). Lens element L3 has a biconvex shape (faces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnifying side (faces 8 and 9). Lens elements L2 to L4 are joined together to form a compound lens. Lens element L5 has a biconcave shape (faces 10 and 11). Lens element L6 has a biconvex shape (faces 11 and 12). Lens elements L5 and L6 are joined together to form a compound lens. The aperture stop ST is located between lens elements L6 and L7 (face 13).

[0109] Lens element L7 has a biconvex shape (faces 14, 15). Lens element L8 has a negative meniscus shape with the convex surface facing the magnifying side (faces 16, 17). Lens element L9 has a positive meniscus shape with the convex surface facing the magnifying side (faces 17, 18). Lens elements L8 and L9 are joined together to form a compound lens. Lens element L10 has a biconvex shape (faces 19, 20). Lens element L11 has a biconvex shape (faces 21, 22). Lens element L12 has a biconcave shape (faces 22, 23). Lens elements L11 and L12 are joined together to form a compound lens. Lens element L13 has a negative meniscus shape with the convex surface facing the reducing side (faces 24, 25). Lens element L14 has a positive meniscus shape with the convex surface facing the magnifying side (faces 26, 27). By employing the above-described lens element structures, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0110] The prism PM has a first transmission surface T1 located on the narrowing side, a second transmission surface T2 located on the magnifying side, and two first reflecting surfaces R1 and a second reflecting surface R2 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the narrowing side (surface 28). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 29). The second reflecting surface R2 has a planar shape (surface 30). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 31).

[0111] Figure 15(A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 5. Figure 15 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 5. The image projection device, including the optical system 1, is horizontally disposed on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.6 m. Light generated from the optical system 1 is projected diagonally upwards and forwards, achieving a short focal point and large image projection.

[0112] Figure 16 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 16 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 5. Figure 16 (B) shows the beam distribution at the first reflecting surface R1. Figure 16 (C) shows the beam distribution at the second reflecting surface R2. Figure 16 (D) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, M2X is the effective X range of the second reflection surface R2 when measured parallel to the X-section, M2Y is the effective Y range of the second reflection surface R2 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular region of the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular region. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0113] (Example 6)

[0114] Figure 17 This is a configuration diagram showing the optical system 1 according to Embodiment 6. This optical system 1 has the same structure as Embodiment 1, but the first sub-optical system includes lens elements L1 to L13, and the second sub-optical system includes a prism PM, which projects in an oblique direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0115] Lens element L1 has a positive meniscus shape with its convex surface facing the narrowing side (faces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the narrowing side (faces 6 and 7). Lens element L3 has a biconvex shape (faces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnifying side (faces 8 and 9). Lens elements L2 to L4 are joined together to form a compound lens. Lens element L5 has a biconcave shape (faces 10 and 11). Lens element L6 has a biconvex shape (faces 11 and 12). Lens elements L5 and L6 are joined together to form a compound lens. The aperture stop ST is located between lens elements L6 and L7 (face 13).

[0116] Lens element L7 has a biconvex shape (faces 14, 15). Lens element L8 has a negative meniscus shape with the convex surface facing the magnifying side (faces 16, 17). Lens element L9 has a biconvex shape (faces 18, 19). Lens element L10 has a biconvex shape (faces 20, 21). Lens element L11 has a biconcave shape (faces 21, 22). Lens elements L10 and L11 are joined together to form a compound lens. Lens element L12 has a negative meniscus shape with the convex surface facing the reducing side (faces 23, 24). Lens element L13 has a biconvex shape (faces 25, 26). By employing the above-described lens element structures, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0117] The prism PM has a first transmission surface T1 located on the shrinking side, a second transmission surface T2 located on the magnifying side, and two first reflecting surfaces R1 and a second reflecting surface R2 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the shrinking side (surface 27). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 28). The second reflecting surface R2 has a planar shape (surface 29). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 30).

[0118] Figure 18 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 6. Figure 18 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 6. The image projection device, including the optical system 1, is horizontally disposed on a support platform such as a table or on the floor. The screen SC is positioned horizontally in front of the support platform at a relatively short horizontal distance, for example, 0.6 m. Light generated from the optical system 1 is projected diagonally downwards and forwards, achieving a short focal point and large image projection.

[0119] Figure 19 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 19 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 6. Figure 19 (B) shows the beam distribution at the first reflecting surface R1. Figure 19 (C) shows the beam distribution at the second reflecting surface R2. Figure 19 (D) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, M2X is the effective X range of the second reflection surface R2 when measured parallel to the X-section, M2Y is the effective Y range of the second reflection surface R2 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular region of the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular region. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0120] (Example 7)

[0121] Figure 20 This is a configuration diagram showing the optical system 1 according to Embodiment 7. This optical system 1 has the same structure as Embodiment 1, but the first sub-optical system includes lens elements L1 to L14, and the second sub-optical system includes a prism PM, which projects in an inclined direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0122] Lens element L1 has a positive meniscus shape with its convex surface facing the narrowing side (faces 4 and 5). Lens element L2 has a negative meniscus shape with its convex surface facing the narrowing side (faces 6 and 7). Lens element L3 has a biconvex shape (faces 7 and 8). Lens element L4 has a negative meniscus shape with its convex surface facing the magnifying side (faces 8 and 9). Lens elements L2 to L4 are joined together to form a compound lens. Lens element L5 has a biconcave shape (faces 10 and 11). Lens element L6 has a biconvex shape (faces 11 and 12). Lens elements L5 and L6 are joined together to form a compound lens. The aperture stop ST is located between lens elements L4 and L5 (face 13).

[0123] Lens element L7 has a biconvex shape (faces 14, 15). Lens element L8 has a negative meniscus shape with the convex surface facing the magnifying side (faces 16, 17). Lens element L9 has a positive meniscus shape with the convex surface facing the magnifying side (faces 17, 18). Lens elements L8 and L9 are joined together to form a compound lens. Lens element L10 has a biconvex shape (faces 19, 20). Lens element L11 has a biconvex shape (faces 21, 22). Lens element L12 has a biconcave shape (faces 22, 23). Lens elements L11 and L12 are joined together to form a compound lens. Lens element L13 has a negative meniscus shape with the convex surface facing the reducing side (faces 24, 25). Lens element L14 has a positive meniscus shape with the convex surface facing the magnifying side (faces 26, 27). By employing the above-described lens element structures, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0124] The prism PM has a first transmission surface T1 located on the narrowing side, a second transmission surface T2 located on the magnifying side, and a first reflecting surface R1 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its concave surface facing the narrowing side (surface 28). The first reflecting surface R1 has a freeform surface shape with its concave surface facing the direction in which light rays incident on the first reflecting surface R1 are reflected (surface 29). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 30).

[0125] Figure 21 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 7. Figure 21 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 7. The image projection device, including the optical system 1, is horizontally arranged on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.6 m, separating it from the rear side. Light generated from the optical system 1 is projected obliquely upward from the rear, achieving a short focal point and large image projection.

[0126] Figure 22 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 22 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Embodiment 7. Figure 22 (B) shows the beam distribution at the first reflecting surface R1. Figure 22(C) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular area of ​​the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular area. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0127] (Example 8)

[0128] Figure 23 This is a configuration diagram showing the optical system 1 according to Embodiment 8. This optical system 1 has the same structure as Embodiment 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 inclined direction in the case of an image projection device. Hereinafter, descriptions repeated in Embodiment 1 will be omitted.

[0129] Lens element L1 has a biconvex shape (faces 2 and 3). Lens element L2 has a negative meniscus shape with the convex surface facing the magnification side (faces 4 and 5). Lens element L3 has a negative meniscus shape with the convex surface facing the magnification side (faces 6 and 7). The aperture stop ST is located between lens element L3 and prism PF (face 8). By employing the above-described lens element structure, the first sub-optical system can suppress light diffusion between the first and second sub-optical systems while maintaining good optical performance.

[0130] Prism PF, like prism PM, is formed from a transparent medium such as glass or synthetic resin. Prism PF has a transmission surface Q1 on the narrowing side, a transmission surface Q2 on the magnifying side, and three reflecting surfaces K1, K2, and K3 located in the optical path between transmission surfaces Q1 and Q2. Transmission surface Q1 has a freeform surface shape with its concave side facing the narrowing side (surface 9). Reflecting surface K1 has a freeform surface shape with its concave side facing both the narrowing and magnifying sides (surface 10). Reflecting surface K2 has a freeform surface shape with its convex side facing both the narrowing and magnifying sides (surface 11). Reflecting surface K3 has a freeform surface shape with its concave side facing both the narrowing and magnifying sides (surface 12). Transmission surface Q2 has a freeform surface shape with its convex side facing the narrowing side (surface 13).

[0131] The prism PM has a first transmission surface T1 located on the narrowing side, a second transmission surface T2 located on the magnifying side, and two first reflecting surfaces R1 and a second reflecting surface R2 located in the optical path between the first transmission surface T1 and the second transmission surface T2. The first transmission surface T1 has a freeform surface shape with its convex surface facing the narrowing side (surface 14). The first reflecting surface R1 has a freeform surface shape with its concave surface facing both the narrowing and magnifying sides (surface 15). The second reflecting surface R2 has a freeform surface shape with its convex surface facing the direction in which light incident on the second reflecting surface R2 is reflected (surface 16). The second transmission surface T2 has a freeform surface shape with its convex surface facing the magnifying side (surface 17).

[0132] Figure 24 (A) is a Y-sectional view showing the optical path through which the principal ray of the reference ray Ref passes in the prism PM involved in Embodiment 8. Figure 24 (B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 8. The image projection device, including the optical system 1, is horizontally arranged on a support platform such as a table or on the floor. The screen SC is positioned vertically above the support platform at a relatively short horizontal distance, for example, 0.2 m, from the rearward side. Light generated from the optical system 1 is projected obliquely upward and backward, achieving a short focal point and large image projection.

[0133] Figure 25 Showing with Figure 3 The diagram shows the beam's position and shape corresponding to each imaging location. Figure 25 (A) shows the beam distribution at the first transmission surface T1 of the prism PM involved in Example 8. Figure 25 (B) shows the beam distribution at the first reflecting surface R1. Figure 25 (C) shows the beam distribution at the second reflecting surface R2. Figure 25(D) shows the beam distribution at the second transmission surface T2. Here, T1X is the effective X range of the first transmission surface T1 when measured parallel to the X-section, T1Y is the effective Y range of the first transmission surface T1 when measured parallel to the Y-section, M1X is the effective X range of the first reflection surface R1 when measured parallel to the X-section, M1Y is the effective Y range of the first reflection surface R1 when measured parallel to the Y-section, M2X is the effective X range of the second reflection surface R2 when measured parallel to the X-section, M2Y is the effective Y range of the second reflection surface R2 when measured parallel to the Y-section, T2X is the effective X range of the second transmission surface T2 when measured parallel to the X-section, and T2Y is the effective Y range of the second transmission surface T2 when measured parallel to the Y-section. Furthermore, the effective range of each optical surface within the rectangular region of the X and Y coordinates is determined by the position where the outermost part of the beam distribution connects to the rectangular region. Here, the X and Y coordinates form the coordinate system of each optical surface as a reference.

[0134] (Example 9)

[0135] Figure 26 (A) is a configuration diagram showing the optical system 1 according to Embodiment 9. The optical system 1 is the same optical design as that of Embodiment 5, but with the plane mirror MR1 positioned between lens elements L7 and L8, so that the reference optical axis A is bent at a right angle in the YZ plane. The reference ray Ref is also bent in the YZ plane via the plane mirror MR1.

[0136] Figure 26 (B) is an explanatory diagram illustrating the use of the image projection device employing the optical system 1 according to Embodiment 9. The image projection device, including the optical system 1, is horizontally disposed on a support platform such as a table or on the floor. The screen SC is disposed parallel to the ZX plane at a position that is a relatively short horizontal distance away from the support platform, for example, 0.6 m. The light generated from the optical system 1 is projected in an oblique direction, achieving a short focal point and large image projection.

[0137] (Example 10)

[0138] Figure 27 (A) is a configuration diagram showing the optical system 1 according to Embodiment 10. The optical system 1 is the same optical design as that of Embodiment 5, but with the plane mirror MR2 positioned between lens elements L7 and L8, so that the reference optical axis A is bent at a right angle in the ZX plane. The reference ray Ref is also bent in the ZX plane via the plane mirror MR2.

[0139] Figure 27(B) is an explanatory diagram showing the use of the image projection device employing the optical system 1 according to Embodiment 10. The image projection device, including the optical system 1, is horizontally arranged on a support such as a table or on the floor. The screen SC is positioned parallel to the YZ plane at a relatively short horizontal distance from the support, for example, 0.6 m. Light generated from the optical system 1 is projected in an oblique direction, achieving a short focal point and large image projection.

[0140] The first sub-optical system included in Examples 1-7 and Examples 9-10 has a structure in which three or more convex lenses are included between the aperture stop and the conjugate point on the narrowing side, and between the aperture stop and the intermediate imaging position. This is to uniformly guide the light from the image forming element to the first sub-optical system when the image forming element is arranged on the narrowing conjugate point side. It is preferable to set the narrowing conjugate point side as approximately telecentric in the optical system. Furthermore, when guiding the light to the second sub-optical system, the magnification conjugate point side of the first sub-optical system is also set as approximately telecentric. This has the effect of suppressing the diffusion of light incident on the second sub-optical system and making the size of the second sub-optical system smaller.

[0141] Furthermore, in order to prevent the light rays from spreading on the side closest to the narrowing conjugate point, the optical element with optical power arranged in the first sub-optical system can be further improved by equipping it with a positive lens, which has a near-telecentric effect.

[0142] The second reflecting surface of the prism PM included in Examples 1-2, 5-6, and 9-10 is not limited to a plane and can also be composed of a reflecting surface with curvature. By making it a reflecting surface with curvature, the directional freedom of the conjugate point on the magnification side can be improved, and the shape accuracy of the reflecting surface can be well ensured during the processing of the prism PM. Furthermore, a planar mirror obtained by performing aluminum evaporation or the like on a glass substrate that has been flattened by grinding or the like can be bonded to the outside of the second reflecting surface of the prism PM, instead of the second reflecting surface. In this case, high planar accuracy can be obtained as the second reflecting surface, and the shape accuracy can be well ensured after the processing of the prism PM.

[0143] Examples 1-2, 5-6, and 8-10 have a second reflecting surface, and the convex surfaces of both the first reflecting surface and the second transmitting surface are arranged towards the magnification conjugate point. By adopting this structure, distortion can be effectively corrected while achieving further reduction in the height of the prism PM. In this case, the normal of the second reflecting surface is preferably oriented towards the magnification conjugate point.

[0144] The beam distribution of the optical surface located on the magnification side, which is situated at the intermediate imaging position within the prism PM, in the second sub-optical system is arranged such that the beam size of the reference ray Ref, which images the point closest to the optical system among the magnification-side conjugate points on the screen SC, is minimized. This ensures good performance of both magnification-side and reduction-side distortion by increasing the beam size proportionally to the distance from the beam passing through the prism PM and to the magnification-side conjugate point. Furthermore, by setting the beam distribution of each optical surface located on the magnification side, which is situated at the intermediate imaging position within the prism PM, to an approximately elliptical shape with a major axis in the direction of projection into the XY plane in the direction of beam propagation, a good effect of correcting distortion on the magnification-side conjugate point can be achieved.

[0145] The prism PM achieves the same effect as the prism PM by adopting a structure in which a part of a lens element or the like with a free-form optical surface forms a reflecting surface and has at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface.

[0146] The prism PM achieves the same effect as the prism PM by adopting a structure in which a part of a lens element or the like with an eccentric optical surface forms a reflecting surface and has at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface.

[0147] The prism PM achieves the same effect as the prism PM by adopting a structure in which a part of a lens element or the like, having an optical surface with an eccentric freeform shape, forms a reflecting surface and has at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface.

[0148] Next, the conditions that the optical system according to this embodiment can satisfy will be explained. Furthermore, while multiple conditions are specified for the optical system according to each embodiment, it is possible to satisfy all of these multiple conditions, or to satisfy only some of them, thereby obtaining corresponding effects.

[0149] Alternatively, the optical system of this embodiment may have a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and internally have intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduction conjugate point has an imaging relationship in a rectangular region having a long side direction and a short side direction. The optical system comprises: a first sub-optical system including an aperture stop that defines the range through which the light beam passes in the optical system; and a second sub-optical system disposed further on the magnification side than the first sub-optical system, including a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface on the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position, and part or all of the intermediate image formed at the intermediate imaging position is fixed. Located between the first transmission surface and the first reflection surface, the first reflection surface is the reflection surface located on the narrowing side of the at least one reflection surface, the first reflection surface has a shape such that the concave surface is oriented toward the direction in which light rays incident on the first reflection surface are reflected, the first sub-optical system includes a plurality of rotationally symmetric lens elements, and when the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis A, at least one optical surface of the prism, the first transmission surface, the second transmission surface and the at least one reflection surface, is formed such that the maximum angle θmax and the minimum angle θmin of the principal ray of the light ray having an imaging relationship with the normal of the surface at the position of incident on the optical surface in a plane perpendicular to the reference optical axis A, and the ray having an imaging relationship with the concentric circle centered at the intersection of the reference optical axis A and the narrowing conjugate point of the rectangular region, satisfy the following equation (1).

[0150] 45°>|θmax|-|θmin|>0.014° (1)

[0151] Figure 30 (A) is an XY cross-sectional view showing the distribution of the principal rays at the conjugate point of contraction. Figure 30 (B) is a configuration diagram of the optical system 1 according to Embodiment 5, shown as an example. The conjugate point of reduction has an imaging relationship in a rectangular region having a long side direction and a short side direction. The principal ray of the light has an imaging relationship on a concentric circle centered on the intersection of the reference optical axis A and the conjugate point of reduction. Furthermore, the angle at which the principal ray of the light intersects the normal of the optical surface at the position of incident on the optical surface varies between the maximum angle and the minimum angle. At this time, the shape of the optical surface is designed such that the difference between the absolute value of the maximum angle and the absolute value of the minimum angle satisfies Equation (1).

[0152] According to this structure, the overall length of the optical system can be shortened while keeping the optical system, including the reflective surface, located on the magnification side small. Furthermore, good optical performance, including distortion, can be ensured within a wider imaging range at the magnification side conjugate point. In addition, the distance between the magnification side conjugate point and the optical system can be shortened. Therefore, the second sub-optical system can be miniaturized using a small prism, and projection or imaging with a short focal point and a large image can be achieved. If the upper limit of Equation (1) is exceeded, the oblique incident light rays with acute angles of incidence at the reflective surface increase, the beam area widens, and the influence of the shape accuracy of the optical surface becomes greater, which is not preferable. In addition, distortion becomes overcorrected, and it becomes difficult to maintain good optical performance. If the lower limit of Equation (1) is lower, it is not possible to effectively utilize the optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, shortening the overall length of the optical system becomes more difficult, and the imaging range with good optical performance at the magnification side conjugate point becomes narrower.

[0153] Figure 31 (A) is an XY cross-sectional view showing the distribution of the principal rays at the conjugate point of contraction. Figure 31 (B) is a conceptual illustration showing the pattern of the principal ray of a light ray incident on the optical surface of a rotationally symmetric prism. Figure 31 (C) is a conceptual illustration showing the pattern of the principal ray of light incident on the optical surface of a freeform prism.

[0154] exist Figure 31 In the rotationally symmetric prism optical surface shown in (B), it can be seen that the angle at which the principal ray intersects the normal of the optical surface is always fixed. Therefore, |θmax|-|θmin| in equation (1) becomes zero. On the other hand, in Figure 31 In the freeform prism optical surface shown in (C), the angle at which the principal ray intersects the normal of the optical surface is not fixed, but varies between the maximum and minimum angles. It can be seen that |θmax|-|θmin| in equation (1) is greater than zero.

[0155] Figure 32 (A) is an illustrative diagram showing the configuration of concentric circles (radius r) and the rectangular region at the narrowed conjugate point without optical offset. Figure 32 (B) is an explanatory diagram showing the configuration of concentric circles (radius r) and the rectangular region at the narrowed conjugate point with optical offset. The position of the concentric circles through which the principal ray passes can be defined in conjunction with the optical offset.

[0156] Figure 33This is an explanatory diagram illustrating the concepts of rotationally symmetric optical surfaces (spherical, aspherical, etc.) and rotationally asymmetric optical surfaces (freeform surfaces, etc.). For example, a camera sensor or DMD is positioned at a conjugate point of reduction and has an imaging relationship in a rectangular region having a long side direction and a short side direction. Assume an orientation D1 along the short side direction of the rectangular region and an orientation D2 along the diagonal direction of the rectangular region.

[0157] In a rotationally symmetric optical surface, the cross-sectional shape along azimuth D1 is the same as the cross-sectional shape along azimuth D2. On the other hand, in a rotationally asymmetric optical surface, the cross-sectional shape along azimuth D1 is different from the cross-sectional shape along azimuth D2.

[0158] Figure 34 This is an illustrative diagram showing the concepts of rotationally symmetric optical elements (without eccentricity) and rotationally asymmetric optical elements (with eccentricity). Figure 33 Similarly, for example, a camera sensor or DMD is positioned at a reduced conjugate point, and has an imaging relationship in a rectangular region having a long side direction and a short side direction. Assume an orientation D1 along the short side direction of the rectangular region and an orientation D2 along the diagonal direction of the rectangular region.

[0159] In a rotationally symmetric optical element, the optical axes of the left side S1 and the right side S2 are aligned, and the optical effects along orientation D1 and along orientation D2 are the same. On the other hand, in a rotationally asymmetric optical element, the optical axes of the left side S1 and the right side S2 are offset from each other, and the optical effects along orientation D1 and along orientation D2 are not the same.

[0160] In the optical system involved in this embodiment, the optical surface may also be the second transmission surface, satisfying the following equation (2).

[0161] 20°>|θmax|-|θmin|>0.020° (2)

[0162] Furthermore, the optical system can satisfy the following equation.

[0163] 17°>|θmax|-|θmin|>0.024° (2a)

[0164] In the optical system involved in this embodiment, the optical surface may also be the first transmission surface, satisfying the following equation (3).

[0165] 10°>|θmax|-|θmin|>0.020° (3)

[0166] Furthermore, the optical system can also satisfy the following equation.

[0167] 5.5°>|θmax|-|θmin|>0.050° (3a)

[0168] In the optical system involved in this embodiment, the optical surface may also be the first reflecting surface, satisfying the following equation (4).

[0169] 2°>|θmax|-|θmin|>0.014° (4)

[0170] Furthermore, the optical system can also satisfy the following equation.

[0171] 1.50°>|θmax|-|θmin|>0.100° (4a)

[0172] Furthermore, the optical system can also satisfy the following equation.

[0173] 1.25°>|θmax|-|θmin|>0.200° (4b)

[0174] Furthermore, the optical system can also satisfy the following equation.

[0175] 1.00°>|θmax|-|θmin|>0.300° (4c)

[0176] Alternatively, the optical system of this embodiment may have a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and internally have intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduction conjugate point has an imaging relationship in a rectangular region having a long side direction and a short side direction. The optical system comprises: a first sub-optical system including an aperture stop that defines the range through which a light beam passes in the optical system; and a second sub-optical system disposed further on the magnification side than the first sub-optical system, including a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface on the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position, forming... Part or all of the intermediate image at the intermediate imaging position is positioned between the first transmission surface and the first reflection surface, the first reflection surface being the reflection surface located closest to the reduction side among the at least one reflection surface, the first reflection surface having a shape such that the concave surface is oriented toward the direction in which light incident on the first reflection surface is reflected, the first sub-optical system comprising a plurality of rotationally symmetric lens elements, wherein when the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis A, and in a plane perpendicular to the reference optical axis A, the principal ray of the light has an imaging relationship on a concentric circle centered at the intersection of the reference optical axis A and the reduction conjugate point of the rectangular region, at least one optical surface of the prism, the first transmission surface, the second transmission surface, and the at least one reflection surface satisfies the following equation (5).

[0177] 10>ΔSmax / r>0.001 (5)

[0178] Here,

[0179] ΔSmax: The maximum sag difference in the direction along the reference optical axis A of the optical surface through which the principal ray passes;

[0180] r: the radius of the concentric circles.

[0181] The optical system described in this embodiment can also satisfy the following equation (6) when the optical surface through which the main ray passes is the second transmission surface.

[0182] 10>ΔSmax / r>0.001 (6)

[0183] The optical system described in this embodiment can also satisfy the following equation (7) when the optical surface through which the main ray passes is the first transmission surface.

[0184] 3>ΔSmax / r>0.001 (7)

[0185] The optical system described in this embodiment can also satisfy the following equation (8) when the optical surface through which the main ray passes is the first reflecting surface.

[0186] 1>ΔSmax / r>0.001 (8)

[0187] Furthermore, the optical system can also satisfy the following equation.

[0188] 0.8 > ΔSmax / r > 0.002 (8a)

[0189] Furthermore, the optical system can also satisfy the following equation.

[0190] 0.6 > ΔSmax / r > 0.004 (8b)

[0191] Furthermore, the optical system can also satisfy the following equation.

[0192] 0.4 > ΔSmax / r > 0.006 (8c)

[0193] Alternatively, the optical system of this embodiment may have a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and internally have intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduction conjugate point has an imaging relationship in a rectangular region having a long side direction and a short side direction. The optical system comprises: a first sub-optical system including an aperture stop that defines the range through which a light beam passes in the optical system; and a second sub-optical system disposed further on the magnification side than the first sub-optical system, including a prism formed of a transparent medium. The prism has a first transmission surface on the reduction side, a second transmission surface on the magnification side, and at least one reflecting surface on the optical path between the first and second transmission surfaces. The aperture stop is positioned between the reduction conjugate point and the intermediate imaging position and is formed in... Part or all of the intermediate image at the intermediate imaging position is positioned between the first transmission surface and the first reflection surface, the first reflection surface being the one located closest to the narrowing side among the at least one reflection surface, the first reflection surface having a shape such that the concave surface is oriented toward the direction in which light incident on the first reflection surface is reflected, the first sub-optical system comprising a plurality of rotationally symmetric lens elements, wherein when the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis A, in a plane perpendicular to the reference optical axis A, the principal ray of the light has an imaging relationship on a concentric circle centered at the intersection of the reference optical axis A and the narrowing conjugate point of the rectangular region, the maximum optical path length difference ΔLmax of the optical path through the interior of the prism satisfies the following equation (9) using the radius r of the concentric circle.

[0194] 3>ΔLmax / r>0.005 (9)

[0195] Furthermore, the optical system can also satisfy the following equation.

[0196] 2.5>ΔLmax / r>0.002 (9a)

[0197] Furthermore, the optical system can also satisfy the following equation.

[0198] 2.0>ΔLmax / r>0.004 (9b)

[0199] Furthermore, the optical system can also satisfy the following equation.

[0200] 1.5>ΔLmax / r>0.006 (9c)

[0201] The maximum optical path length Lmax of the principal ray passing through the interior of the prism can also be satisfied by using the radius r of the concentric circles, as shown in equation (10).

[0202] 30>Lmax / r>2 (10)

[0203] With this structure, the second sub-optical system can be miniaturized using a small prism, enabling projection or imaging with a short focal length and a large image. If the upper limit of equation (10) is exceeded, miniaturization of the optical system configured on the magnification side becomes difficult. In particular, the effective range of the second transmission surface becomes larger. If the prism becomes larger, the forming time becomes longer, leading to increased costs. If the lower limit of equation (10) is exceeded, it becomes difficult to form the optical surface required to ensure good optical performance including distortion.

[0204] The optical system involved in this embodiment can also satisfy the following equation (11).

[0205] 2.00>SP / LP>0.10 (11)

[0206] Here,

[0207] SP: The distance between the narrowing conjugate point and the aperture stop of the principal ray path of the reference ray Ref, which is defined as the ray that images at the position closest to the optical system among the magnification conjugate points;

[0208] LP: The distance between the aperture stop along the principal ray path of the reference ray Ref and the magnification side end of the first sub-optical system.

[0209] According to this structure, within a wider imaging range of the magnification-side conjugate point, good optical performance, including distortion, can be ensured, and the distance between the magnification-side conjugate point and the optical system can be shortened. If the upper limit of Equation (11) is exceeded, it is impossible to effectively utilize optical surfaces with different curvatures in the X and Y directions perpendicular to the reference optical axis A, making it more difficult to shorten the overall length of the optical system, and the imaging range with good optical performance at the magnification-side conjugate point becomes narrower. If the lower limit of Equation (11) is lower, it becomes overcorrected for distortion, and maintaining good optical performance becomes difficult.

[0210] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the position of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section, satisfying the following equation (12).

[0211] 0.20>(XM1-RefM1) / r>-3.00 (12)

[0212] Here,

[0213] XM1: The Y coordinate of the principal ray at the X end of the first reflecting surface R1 in the coordinate system of the first reflecting surface;

[0214] RefM1: The Y-coordinate in the coordinate system of the first reflecting surface R1 of the reference ray Ref;

[0215] r: the radius of the concentric circles.

[0216] With this structure, the diffusion of light between the first and second sub-optical systems can be suppressed, and the optical system including the reflective surface arranged on the magnification side can be reduced. Furthermore, the light rays at the conjugate point on the reduction side can be set approximately telecentrically. If the upper limit of equation (12) is exceeded, it becomes difficult to suppress the diffusion of light between the first and second sub-optical systems, and the optical system including the reflective surface arranged on the magnification side becomes larger. If the lower limit of equation (12) is below, it results in oblique incidence and imaging at the conjugate point on the reduction side. Therefore, if an image forming element such as a DMD is arranged on the reduction side, it becomes difficult to uniformly capture light, and it is impossible to ensure good optical performance with uniform brightness.

[0217] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the position of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section, satisfying the following equation (13).

[0218] 1.90>M1X / M1Y>1.00 (13)

[0219] Here,

[0220] M1X: The effective X range of the first reflecting surface when measured parallel to the X profile;

[0221] M1Y: The effective Y range of the first reflecting surface when measured in parallel with respect to the Y profile.

[0222] According to this structure, the overall length of the optical system can be shortened while keeping the optical system, including the reflective surface, located on the magnification side small. Furthermore, good optical performance, including distortion, can be ensured over a wider imaging range at the magnification side conjugate point. In addition, the distance between the magnification side conjugate point and the optical system can be shortened. If the upper limit of Equation (13) is exceeded, it is not possible to effectively utilize the 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 the imaging range with good optical performance at the magnification side conjugate point becomes narrower. If the lower limit of Equation (13) is lower, it becomes overcorrected for distortion, and it becomes difficult to maintain good optical performance. In addition, the tilt of the optical surface at the periphery in the X direction becomes larger, making processing difficult.

[0223] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the position of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section, satisfying the following equation (14).

[0224] 6.00>T2X / T2Y>2.00 (14)

[0225] Here,

[0226] T2X: The effective range of the second transmission surface when measured in parallel with respect to the X profile;

[0227] T2Y: The effective Y range of the second transmission surface when measured in parallel with respect to the Y profile.

[0228] According to this structure, the overall length of the optical system can be shortened while keeping the optical system, including the reflective surface, located on the magnification side small. Furthermore, good optical performance, including distortion, can be ensured over a wider imaging range at the magnification side conjugate point. In addition, the distance between the magnification side conjugate point and the optical system can be shortened. If the upper limit of Equation (14) is exceeded, the distortion becomes overcorrected, and it becomes difficult to maintain good optical performance. Furthermore, the tilt of the optical surface at the periphery in the X direction becomes larger, making processing difficult. If the lower limit of Equation (14) is below, it is not possible to effectively utilize the 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 the imaging range with good optical performance at the magnification side conjugate point becomes narrower.

[0229] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the location of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section. The optical planes among the optical planes having a finite radius of curvature are symmetrical only about the Y-section.

[0230] With this structure, there is no distortion in the left and right (X direction), which ensures good imaging performance.

[0231] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the position of the first reflecting surface can be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section can be designated as the X-section. In the Y-section, a plurality of principal rays are contained between the position of the principal ray of the reference ray Ref reflected at the first reflecting surface and the position of the origin of the coordinates of the first reflecting surface.

[0232] With this structure, the overall length of the optical system can be shortened while keeping the optical system, including the reflective surface, positioned on the magnification side small. Furthermore, good optical performance, including distortion, can be ensured over a wider imaging range at the magnification-side conjugate point. Additionally, the distance between the magnification-side conjugate point and the optical system can be reduced.

[0233] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the location of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section, wherein at least two of the optical planes are eccentric to each other within the Y-section.

[0234] Based on this structure, by constructing a prism by eccentrically centering the optical surfaces, the degree of freedom based on the curvature difference between the Y-section and the X-section is increased, enabling efficient utilization of higher-order terms of the freeform surface. This allows for maintaining a small optical system configuration on the magnification side while shortening the overall length of the optical system. Furthermore, good optical performance, including distortion, can be ensured over a wider imaging range at the conjugate point on the magnification side. Additionally, the distance between the conjugate point on the magnification side and the optical system can be shortened. The optical surfaces are not limited to freeform surfaces defined by the XY polynomial; even aspherical or spherical surfaces with rotational symmetry can achieve optical effects based on different curvatures in the X and Y directions by mutually eccentricating them within the Y-section.

[0235] In the optical system of this embodiment, the plane containing the principal ray passing through the center of the long side of the rectangular region and reflected by the first reflecting surface may be designated as a Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as an X-section. The second transmission surface is located in the Y-section and is positioned on the opposite side of the origin of the coordinate system of the first reflecting surface relative to the principal ray of the reference optical axis A.

[0236] With this structure, interference between the first sub-optical system and the magnifying side light can be avoided, thus forming a small optical system.

[0237] In the optical system of this embodiment, the plane containing the center of the principal ray passing through the long side of the rectangular region and reflected at the location of the first reflecting surface may be designated as the Y-section, and the plane containing the reference optical axis A and perpendicular to the Y-section may be designated as the X-section. The coordinate system of the first reflecting surface is tilted in the Y-section along the direction of the intermediate imaging.

[0238] With this structure, the distance between the intermediate imaging position and the first reflecting surface can be appropriately set. Furthermore, the overall length of the optical system can be shortened while keeping the optical system, including the reflecting surface, positioned on the magnification side small. Consequently, good optical performance, including distortion, can be ensured over a wider imaging range at the magnification-side conjugate point. Additionally, the distance between the magnification-side conjugate point and the optical system can be shortened.

[0239] In the optical system of this embodiment, the origin of the coordinates of at least one of the optical surfaces may be set on the reference optical axis A.

[0240] With this structure, by aligning the origin coordinates of the optical surface with the reference optical axis A, the design of the optical system, lens barrel, and housing can be implemented efficiently.

[0241] In the optical system described in this embodiment, both the first reflecting surface and the second transmitting surface may be configured such that their convex surfaces face the magnification side.

[0242] This structure ensures sufficient space between the conjugate point on the magnification side and the optical system, increasing the design freedom of the optical system. Furthermore, it facilitates a lower profile for the housing constituting the optical system. Consequently, it allows for a smaller opening.

[0243] Alternatively, a planar portion perpendicular to the reference optical axis A may be provided on a portion of the outer periphery of the prism.

[0244] Based on this structure, the flat portion becomes a reference for assembling the optical system, which can improve the installation and assembly accuracy.

[0245] Figure 35 (A) to (H) are Y-direction cross-sectional views showing various examples of the stepped structure of the prism PM according to Examples 1 to 8. Generally, various lens elements and various prisms constituting the optical system 1 are mounted inside the lens barrel (not shown) using adhesives, molds, etc. At this time, a high-precision mounting structure is required in order to faithfully reproduce the various dimensions of the optical design.

[0246] A portion of the outer periphery of the prism PM is provided, for example, with an end face PMa serving as a mounting reference. This end face Pma can be formed as a planar portion perpendicular to the reference optical axis Ref. On the other hand, a planar portion corresponding to the shape of the end face PMa is provided in the lens barrel. During installation, the end face PMa of the prism PM matches the planar portion of the lens barrel, thereby allowing the prism PM to be fixed relative to the lens barrel with high precision and stability.

[0247] Furthermore, a protective film comprising a dielectric, glass, polymer, or the like can be applied to the second transmission surface T2 of the prism PM described in Examples 1-10. With this structure, the exposed second transmission surface T2 can be protected from scratches and dirt.

[0248] The following describes numerical embodiments of the optical systems involved in Examples 1 to 10. In each numerical embodiment, the unit of length in the tables is "mm", and the unit of angle of view is "0". Furthermore, in each numerical embodiment, the radius of curvature, surface spacing, Nd (refractive index relative to the d-line), vd (Abbe number relative to the d-line), N550 (refractive index at a wavelength of 550 nm), and eccentricity data (the displacement X, Y, Z of the prism surface relative to the previous surface and the normal direction α, β, γ of the prism surface relative to the previous surface) are shown. Furthermore, each quantity in each numerical embodiment is calculated based on a wavelength of 550 nm. Additionally, the term "variable" in surface spacing means that, as shown in the table below, it can vary depending on the image size (100 inches), 80", 60", etc., at the magnified conjugate point. Furthermore, in each numerical embodiment, the shape of the aspherical surface is defined by the following formula. Additionally, only coefficients that are not zero are listed for the aspherical coefficients, except for the conic coefficient k.

[0249] [Mathematical Expression 1]

[0250]

[0251] Here,

[0252] z: The amount of sag of the plane parallel to the z-axis;

[0253] r: Distance in the radial direction

[0254] c: Curvature at the vertex of the face;

[0255] k: Conic coefficient;

[0256] A~H: The 4th to 18th order coefficients of r.

[0257] Furthermore, the shape of a freeform surface is defined by the following formula, which uses a local orthogonal coordinate system (x, y, z) with its vertex as the origin.

[0258] [Mathematical Expression 2]

[0259]

[0260] [Mathematical Expression 3]

[0261]

[0262] Here,

[0263] z: The amount of sag of the plane parallel to the z-axis;

[0264] r: Distance in the radial direction

[0265] c: Curvature at the vertex of the face;

[0266] k: Conic coefficient;

[0267] C j Monomial x m y n The coefficient.

[0268] Furthermore, in the following data, the freeform coefficients of the polynomial, i.e., the i-th degree term of x and the j-th degree term of y, will be recorded as x**i*y**j. For example, "X**2*Y" represents the freeform coefficients of the 2nd degree term of x and the 1st degree term of y in the polynomial.

[0269] (Numerical Example 1)

[0270] Regarding the optical system of Numerical Example 1 (corresponding to Example 1), lens data is shown in Table 1, aspherical shape data of the lens is shown in Table 2, and freeform surface shape data of the prism is shown in Table 3. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 4.

[0271] [Table 1]

[0272] ■ Lens Data

[0273]

[0274]

[0275]

[0276] [Table 1 (continued)]

[0277]

[0278]

[0279] [Table 1 (continued)]

[0280]

[0281] [Table 2]

[0282] ■Astrospherical shape

[0283] Y-radius of curvature 23.640 163.544 244.665 60.187 -2112.796 -52.924 Conical constant -5.4882E-01 0.0000E+00 0.0000E+00 -1.2412E+01 0.0000E+00 0.0000E+00 4 times -2.7759E-07 9.8198E-06 1.5164E-05 1.8620E-06 -6.6077E-06 6.9971E-06 6 times -2.1728E-08 -2.7176E-08 -1.4803E-08 -5.4549E-09 3.4714E-09 1.5470E-09 8 times 1.9017E-11 -1.0097E-10 1.6813E-11 -6.2680E-13 1.3479E-11 -1.0952E-11 10 times -1.2832E-13 1.5850E-13 -9.7800E-15 2.2122E-15 1.7449E-14 -2.1705E-14 12 times -3.4297E-16 -1.9899E-16 -1.7306E-18 5.0329E-18 1.0165E-17 2.3433E-17 14 times 1.5056E-18 -5.0616E-18 -4.9402E-21 3.1670E-20 9.8031E-21 2.0946E-19 16 times -5.1930E-21 1.3672E-20 4.2862E-23 3.7710E-23 2.2477E-23 0.0000E+00 18 times 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

[0284] [Table 3]

[0285] ■Freeform surface shape

[0286]

[0287]

[0288]

[0289] [Table 4]

[0290] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0291] 34 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 35 First reflecting surface 0.000 -77.942 -25.580 -23.522 0.000 0.000 36 Second reflecting surface 0.000 15.680 0.964 0.000 0.000 0.000 37 Second transmission surface 0.000 30.870 17.489 36.388 0.000 0.000

[0292] (Numerical Example 2)

[0293] Regarding the optical system of Numerical Example 2 (corresponding to Example 2), lens data is shown in Table 5, aspherical shape data of the lens is shown in Table 6, and freeform surface shape data of the prism is shown in Table 7. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 8.

[0294] [Table 5]

[0295] ■Transparent Data

[0296]

[0297]

[0298] [Table 5 (continued)]

[0299]

[0300]

[0301]

[0302] [Table 5 (continued)]

[0303]

[0304] [Table 6]

[0305] ■Astrospherical shape

[0306] Y-radius of curvature -948.096 -80.612 28.451 -214.531 -400.743 144.830 Conical constant 0.0000E+00 0.0000E+00 -3.2292E-01 0.0000E+00 0.0000E+00 0.0000E+00 4 times -7.5152E-07 5.2645E-07 -1.1772E-05 2.3860E-05 2.0560E-05 4.8255E-06 6 times -5.8790E-09 -2.3210E-09 5.1972E-09 -3.6426E-08 -2.1909E-08 -1.4037E-08 8 times -8.3198E-12 -1.1065E-11 1.3692E-11 7.6424E-11 2.1111E-11 2.8128E-11 10 times -7.9640E-14 -6.6064E-14 -1.3987E-15 6.4978E-14 -1.1991E-14 5.3867E-15 12 times 0.0000E+00 0.0000E+00 -1.7480E-16 -3.3727E-16 4.4943E-18 -5.3792E-17 14 times 0.0000E+00 0.0000E+00 3.3071E-19 -1.0666E-18 -5.8270E-22 -2.8504E-20 16 times 0.0000E+00 0.0000E+00 -2.0987E-22 2.1447E-21 1.2992E-24 1.1835E-22 18 times 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

[0307] [Table 7]

[0308] ■Freeform surface shape

[0309]

[0310]

[0311]

[0312] [Table 8]

[0313] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0314] 58 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 59 First reflecting surface 0.000 -70.875 -37.049 -42.543 0.000 0.000 60 Second reflecting surface 0.000 -46.924 -51.861 -45.142 0.000 0.000 61 Second transmission surface 0.000 -10.925 39.827 -39.996 0.000 0.000

[0315] (Numerical Example 3)

[0316] Regarding the optical system of numerical embodiment 3 (corresponding to embodiment 3), the lens data is shown in Table 9, the aspherical shape data of the lens is shown in Table 10, and the freeform surface shape data of the prism is shown in Table 11. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 12.

[0317] [Table 9]

[0318] ■Transparent Data

[0319]

[0320]

[0321] [Table 9 (continued)]

[0322]

[0323]

[0324] [Table 9 (continued)]

[0325]

[0326] [Table 10]

[0327] ■Astrospherical shape

[0328] Y-radius of curvature 18.685 -67.394 Conical constant 0.0000E+00 0.0000E+00 4 times -8.0524E-06 1.7615E-05 6 times 0.0000E+00 0.0000E+00 8 times 0.0000E+00 0.0000E+00 10 times 0.0000E+00 0.0000E+00 12 times 0.0000E+00 0.0000E+00 14 times 0.0000E+00 0.0000E+00 16 times 0.0000E+00 0.0000E+00 18 times 0.0000E+00 0.0000E+00

[0329] [Table 11]

[0330] ■Freeform surface shape

[0331]

[0332]

[0333]

[0334] [Table 12]

[0335] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0336] 21 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 22 First reflecting surface 0.000 0.000 23.308 0.000 0.000 0.000 23 Second transmission surface 0.000 0.000 -1.024 0.000 0.000 0.000

[0337] (Numerical Example 4)

[0338] Regarding the optical system of numerical embodiment 4 (corresponding to embodiment 4), lens data is shown in Table 13, aspherical shape data of the lens is shown in Table 14, and freeform surface shape data of the prism is shown in Table 15. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 16.

[0339] [Table 13]

[0340] ■ Lens Data

[0341]

[0342] [Table 13 (continued)]

[0343]

[0344]

[0345] [Table 13 (continued)]

[0346]

[0347] [Table 14]

[0348] ■Astrospherical shape

[0349]

[0350]

[0351] [Table 15]

[0352] ■Freeform surface shape

[0353]

[0354]

[0355]

[0356] [Table 16]

[0357] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0358] 21 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 22 First reflecting surface 0.000 0.000 25.000 0.000 0.000 0.000 23 Second transmission surface 0.000 0.000 0.353 0.000 0.000 0.000

[0359] (Numerical Example 5)

[0360] Regarding the optical system of numerical embodiment 5 (corresponding to embodiment 5), lens data is shown in Table 17, aspherical shape data of the lens is shown in Table 18, and freeform surface shape data of the prism is shown in Table 19. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 20.

[0361] [Table 17]

[0362] ■ Lens Data

[0363]

[0364]

[0365] [Table 17 (continued)]

[0366]

[0367]

[0368] [Table 17 (continued)]

[0369]

[0370] [Table 18]

[0371] ■Astrospherical shape

[0372]

[0373]

[0374] [Table 19]

[0375] ■Freeform surface shape

[0376]

[0377]

[0378] [Table 20]

[0379] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0380] 28 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 29 First reflecting surface 0.000 -77.380 -24.290 -23.450 0.000 0.000 30 Second reflecting surface 0.000 17.368 2.323 0.000 0.000 0.000 31 Second transmission surface 0.000 28.898 19.213 36.600 0.000 0.000

[0381] (Numerical Example 6)

[0382] Regarding the optical system of numerical embodiment 6 (corresponding to embodiment 6), lens data is shown in Table 21, aspherical shape data of the lens is shown in Table 22, and freeform surface shape data of the prism is shown in Table 23. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 24.

[0383] [Table 21]

[0384] ■ Lens Data

[0385]

[0386]

[0387] [Table 21 (continued)]

[0388]

[0389]

[0390] [Table 21 (continued)]

[0391]

[0392] [Table 22]

[0393] ■Astrospherical shape

[0394] Y-radius of curvature 17.060 80.120 -768.012 44.630 Conical constant -4.3827E-01 0.0000E+00 0.0000E+00 1.7682E+00 4 times 4.4126E-06 2.3059E-05 5.7493E-05 1.9949E-05 6 times -1.4161E-08 -1.3206E-08 -1.5100E-07 -6.9656E-08 8 times 1.5349E-11 -9.5211E-10 3.9099E-10 1.9160E-10 10 times 6.9128E-14 3.4350E-12 -5.9278E-13 2.8521E-13 12 times -1.2152E-14 6.7620E-15 3.6158E-16 -1.4532E-15 14 times 9.0561E-17 -2.3105E-16 2.1397E-19 6.0833E-19 16 times -3.0077E-19 7.0088E-19 -2.6529E-22 2.7249E-21 18 times 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00

[0395] [Table 23]

[0396] ■Freeform surface shape

[0397]

[0398]

[0399]

[0400] [Table 24]

[0401] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0402]

[0403]

[0404] (Numerical Example 7)

[0405] Regarding the optical system of Numerical Example 7 (corresponding to Example 7), lens data is shown in Table 25, aspherical shape data of the lens is shown in Table 26, and freeform surface shape data of the prism is shown in Table 27. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 28.

[0406] [Table 25]

[0407] ■ Lens Data

[0408]

[0409]

[0410] [Table 25 (continued)]

[0411]

[0412]

[0413] [Table 25 (continued)]

[0414]

[0415] [Table 26]

[0416] ■Astrospherical shape

[0417] Y-radius of curvature 23.930 173.550 467.714 126.596 -964.988 -178.108 Conical constant -4.7040E-01 0.0000E+00 0.0000E+00 -1.9862E+01 0.0000E+00 0.0000E+00 4 times 4.3332E-07 7.3910E-06 1.4181E-05 3.1555E-06 -1.3757E-07 3.4295E-07 6 times -5.2299E-09 -1.3721E-08 -1.5031E-08 -5.3284E-09 1.2908E-09 1.6866E-09 8 times 4.0353E-12 -7.4701E-11 1.6141E-11 3.4047E-12 3.3829E-12 4.6620E-13 10 times -1.1308E-13 1.3079E-13 -1.0558E-14 3.1724E-15 3.2851E-15 -2.9710E-16 12 times -1.9308E-16 -2.9973E-16 1.7820E-18 -6.7184E-18 -4.9206E-19 3.8858E-18 14 times 1.5390E-18 -5.4098E-18 1.9746E-21 7.3850E-21 -5.4858E-22 2.3066E-21 16 times -6.2475E-21 1.3204E-20 8.6988E-25 1.0627E-24 2.9560E-24 -7.4248E-25 18 times 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -7.6209E-28 -7.0748E-27

[0418] [Table 27]

[0419] ■Freeform surface shape

[0420]

[0421]

[0422]

[0423] [Table 28]

[0424] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0425] 28 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 29 First reflecting surface 0.000 -77.380 -24.290 -23.450 0.000 0.000 30 Second reflecting surface 0.000 28.898 -14.567 -36.600 0.000 0.000

[0426] (Numerical Example 8)

[0427] Regarding the optical system of numerical embodiment 8 (corresponding to embodiment 8), lens data is shown in Table 29, and freeform surface shape data of the prism is shown in Table 30. The origin positions of the coordinate systems of each optical surface, with the first transmission surface coordinate system of the prism as the reference, are shown in Table 31. Only the lens data of embodiment 8 are used as the absolute coordinates of the first surface reference.

[0428] [Table 29]

[0429] ■ Lens Data

[0430]

[0431] [Table 29 (continued)]

[0432]

[0433]

[0434] [Table 29 (continued)]

[0435]

[0436] [Table 30]

[0437] ■Freeform surface shape

[0438]

[0439]

[0440]

[0441] [Table 30 (continued)]

[0442]

[0443]

[0444]

[0445] [Table 30 (continued)]

[0446]

[0447]

[0448]

[0449] [Table 31]

[0450] ■ The origin of each optical surface coordinate system based on the first transmission surface coordinate system

[0451] 15 First transmission surface 0.000 0.000 0.000 0.000 0.000 0.000 16 First reflecting surface 0.000 -25.903 -0.714 25.575 0.000 0.000 17 Second reflecting surface 0.000 -25.597 -0.075 15.567 0.000 0.000 18 Second transmission surface 0.000 14.355 -18.242 -25.848 0.000 0.000

[0452] Tables 32 to 37 below show the corresponding values ​​of each conditional expression (1) to (14) in each of the numerical examples 1 to 8.

[0453] [Table 32]

[0454]

[0455]

[0456] [Table 32 (continued)]

[0457]

[0458]

[0459] [Table 33]

[0460]

[0461] [Table 33 (continued)]

[0462]

[0463]

[0464] [Table 34]

[0465]

[0466] [Table 34 (continued)]

[0467]

[0468] [Table 35]

[0469]

[0470] [Table 35 (continued)]

[0471] Reduced conjugate point ~ aperture stop 104.583 85.613 104.583 9.263 Aperture stop ~ End of first sub-optical system 154.861 113.122 154.860 52.684 Compare 0.675 0.757 0.675 0.176

[0472] [Table 36]

[0473]

[0474]

[0475] [Table 36 (continued)]

[0476] Y coordinate of reference ray Ref 87.008 64.382 86.942 31.587 The Y coordinate of the outermost ray. 85.687 61.432 85.650 30.737 Difference -1.322 -2.950 -1.292 -0.850 r 7.374 5.659 7.374 3.592 Difference / r -0.179 -0.521 -0.175 -0.237

[0477] [Table 37]

[0478]

[0479] [Table 37 (continued)]

[0480]

[0481]

[0482] Figure 36 (A) to (H) are diagrams showing the rectangular regions and the shapes of concentric circles at the reduced conjugate points in each of the numerical embodiments 1 to 8.

[0483] Figure 37 (A)~(D) and Figure 38(E) to (H) are diagrams showing the cross-sectional shape of each optical surface and the origin of the coordinate system based on the coordinate system of the first transmission surface T1 in each of the numerical embodiments 1 to 8.

[0484] Figure 39 Figures (A) to (H) are graphs showing the distortion shape at the magnification-side conjugate point caused by aberrations in the optical systems of 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. According to these graphs, the distortion at the magnification-side conjugate point of the optical system 1 according to Examples 1 to 8 is appropriately corrected.

[0485] (Implementation Method 2)

[0486] The following uses Figure 40 To illustrate Embodiment 2 of this disclosure. Figure 40 This is a block diagram illustrating an example of the image projection apparatus disclosed herein. The image projection apparatus 100 includes an optical system 1, an image forming element 101, a light source 102, and a control unit 110, as disclosed in Embodiment 1. The image forming element 101 is composed of a liquid crystal, a DMD, or the like, and generates an image projected onto a screen SC via the optical system 1. The light source 102 is composed of an LED (light-emitting diode), a laser, or the like, and supplies light to the image forming element 101. The control unit 110 is composed of a CPU or an MPU, and controls the entire apparatus and its components. The optical system 1 may be configured as a replaceable lens that can be detachably mounted to the image projection apparatus 100, or it may be configured as an embedded lens integrated into the image projection apparatus 100.

[0487] The image projection device 100 described above, through the optical system 1 according to Embodiment 1, can achieve short-focus and large-screen projection with a small device.

[0488] (Implementation Method 3)

[0489] The following uses Figure 41 To illustrate Embodiment 3 of this disclosure. Figure 41This is a block diagram illustrating an example of the imaging device involved in this disclosure. The imaging device 200 includes the optical system 1, imaging element 201, and control unit 210 disclosed in Embodiment 1. The imaging element 201 is composed of a CCD (charge-coupled device) image sensor, a CMOS image sensor, etc., and receives the optical image of the object OBJ formed by the optical system 1 and converts it into an electrical image signal. The control unit 110 is composed of a CPU or MPU, etc., and controls the entire device and its components. The optical system 1 can be configured as a replaceable lens that can be detachably mounted to the imaging device 200, or it can be configured as an embedded lens integrated into the imaging device 200.

[0490] The above-described camera device 200, through the optical system 1 described in Embodiment 1, can achieve short-focus and large-screen imaging with a small device.

[0491] As described above, embodiments have been explained as a disclosure of the technology in this disclosure. For this purpose, accompanying drawings and detailed descriptions have been provided.

[0492] Therefore, the constituent elements described in the added drawings and detailed descriptions include not only those necessary for solving the problem, but also those not necessary for solving the problem, in order to illustrate the above-described technology. Therefore, one should not conclude that these non-essential constituent elements are essential simply because they are described in the added drawings or detailed descriptions.

[0493] Furthermore, the above-described embodiments are for illustrating the technology in this disclosure, and therefore various changes, substitutions, additions, omissions, etc., can be made within the scope of the claims or their equivalents.

[0494] Industrial availability

[0495] This disclosure can be applied 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, web cameras, and vehicle-mounted cameras in surveillance systems. In particular, this disclosure can be applied 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 a magnification conjugate point on a magnification side, and having internal intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduced conjugate points have an imaging relationship within a rectangular region having both long and short side directions. The optical system includes: The first sub-optical system includes an aperture stop that defines the range through which a light beam passes in the optical system; and The second sub-optical system, positioned further to the magnification side than the first sub-optical system, includes a prism formed of a transparent medium. The prism has a first transmission surface located on the narrowing side, a second transmission surface located on the magnifying side, and at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface. The aperture stop is positioned between the narrowing conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and the first reflection surface, wherein the first reflection surface is the reflection surface located at the position closest to the reduction side among the at least one reflection surface. The first reflecting surface has a shape in which the concave surface is oriented in the direction in which light rays incident on the first reflecting surface are reflected. The first sub-optical system comprises multiple rotationally symmetric lens elements. When the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis, at least one of the first transmission surface, the second transmission surface, and the at least one reflecting surface of the prism is formed such that: in a plane perpendicular to the reference optical axis, the principal rays of light rays having an imaging relationship on a concentric circle centered at the intersection of the reference optical axis and the reduced conjugate point of the rectangular region, at the position incident on the rotationally asymmetric optical surface, have a maximum angle θmax and a minimum angle θmin intersecting the normal of the surface at the following equation (1). 45°>|θmax|-|θmin|>0.014° (1).

2. The optical system according to claim 1, wherein, The rotationally asymmetric optical surface is the second transmission surface. Satisfy the following equation (2a), 17°>|θmax|-|θmin|>0.024° (2a).

3. The optical system according to claim 1, wherein, The rotationally asymmetric optical surface is the first transmission surface. Satisfy the following equation (3a), 5.5°>|θmax|-|θmin|>0.050° (3a).

4. The optical system according to claim 1, wherein, The rotationally asymmetric optical surface is the first reflecting surface. Satisfy the following equation (4a), 1.5°>|θmax|-|θmin|>0.100° (4a).

5. An optical system having a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and having internally intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduced conjugate points have an imaging relationship within a rectangular region having both long and short side directions. The optical system includes: The first sub-optical system includes an aperture stop that defines the range through which a light beam passes in the optical system; and The second sub-optical system, positioned further to the magnification side than the first sub-optical system, includes a prism formed of a transparent medium. The prism has a first transmission surface located on the narrowing side, a second transmission surface located on the magnifying side, and at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface. The aperture stop is positioned between the narrowing conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and the first reflection surface, wherein the first reflection surface is the reflection surface located at the position closest to the reduction side among the at least one reflection surface. The first reflecting surface has a shape in which the concave surface is oriented in the direction in which light rays incident on the first reflecting surface are reflected. The first sub-optical system comprises multiple rotationally symmetric lens elements. When the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis, and the principal rays of light in a plane perpendicular to the reference optical axis have an imaging relationship on a concentric circle centered at the intersection of the reference optical axis and the reduced conjugate point of the rectangular region, at least one of the first transmission surface, the second transmission surface, and the at least one reflecting surface of the prism satisfies the following equation (5). 10>ΔSmax / r>0.001 (5) Here, ΔSmax: The maximum sag difference along the reference optical axis in the direction of sag of the rotationally asymmetric optical surface through which the principal ray passes; r: the radius of the concentric circles.

6. The optical system according to claim 5, wherein, When the rotationally asymmetric optical surface through which the principal ray passes is the second transmission surface, the following equation (6) is satisfied. 10>ΔSmax / r>0.001 (6).

7. The optical system according to claim 5, wherein, When the rotationally asymmetric optical surface through which the principal ray passes is the first transmission surface, the following equation (7) is satisfied. 3>ΔSmax / r>0.001 (7).

8. The optical system according to claim 5, wherein, When the rotationally asymmetric optical surface through which the principal ray passes is the first reflecting surface, the following equation (8a) is satisfied. 0.8>ΔSmax / r>0.002 (8a).

9. The optical system according to claim 1 or 5, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the position where it is reflected by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section. The rotationally asymmetric optical surface with a finite radius of curvature among the rotationally asymmetric optical surfaces is a shape that is symmetrical only about the Y-section.

10. The optical system according to claim 1 or 5, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the point of reflection by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section. At least two of the rotationally asymmetric optical surfaces are mutually eccentric within the Y-section.

11. The optical system according to claim 1 or 5, wherein, The origin of the coordinates of at least one of the rotationally asymmetric optical surfaces is set on the reference optical axis.

12. An optical system having a reduction conjugate point on a reduction side and a magnification conjugate point on a magnification side, and having internally intermediate imaging positions conjugate to both the reduction conjugate point and the magnification conjugate point. The reduced conjugate points have an imaging relationship within a rectangular region having both long and short side directions. The optical system includes: The first sub-optical system includes an aperture stop that defines the range through which a light beam passes in the optical system; and The second sub-optical system, positioned further to the magnification side than the first sub-optical system, includes a prism formed of a transparent medium. The prism has a first transmission surface located on the narrowing side, a second transmission surface located on the magnifying side, and at least one reflecting surface located in the optical path between the first transmission surface and the second transmission surface. The aperture stop is positioned between the narrowing conjugate point and the intermediate imaging position. Part or all of the intermediate image formed at the intermediate imaging position is positioned between the first transmission surface and the first reflection surface, wherein the first reflection surface is the reflection surface located at the position closest to the reduction side among the at least one reflection surface. The first reflecting surface has a shape in which the concave surface is oriented in the direction in which light rays incident on the first reflecting surface are reflected. The first sub-optical system comprises multiple rotationally symmetric lens elements. When the axis passing through the center of at least two of the rotationally symmetric lens elements is set as the reference optical axis, in a plane perpendicular to the reference optical axis, if the principal ray of a light ray has an imaging relationship on a concentric circle centered at the intersection of the reference optical axis and the narrowed conjugate point of the rectangular region, the maximum optical path length difference ΔLmax of the light path through the interior of the prism satisfies the following equation (9a) using the radius r of the concentric circle. 2.5>ΔLmax / r>0.002 (9a).

13. The optical system according to claim 12, wherein, The maximum optical path length Lmax of the principal ray passing through the interior of the prism satisfies the following equation (10) using the radius r of the concentric circles. 30>Lmax / r>2 (10).

14. The optical system according to any one of claims 1, 5, and 12, wherein, Satisfy the following equation (11), 2.00 > SP / LP > 0.10 (11) Here, SP: The distance between the narrowing conjugate point and the aperture stop of the principal ray path of the reference ray defined as the ray that images at the position closest to the optical system among the magnification conjugate points; LP: The distance between the aperture stop along the main ray path of the reference ray and the magnification side end of the first sub-optical system.

15. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the position where it is reflected by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section, satisfying the following equation (12). 0.20>(XM1-RefM1) / r>-3.00 (12) Here, XM1: The Y coordinate of the principal ray at the X end of the first reflecting surface in the coordinate system of the first reflecting surface; RefM1: The Y-coordinate in the coordinate system of the first reflecting surface at the first reflecting surface of the reference ray; r: the radius of the concentric circles.

16. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the position where it is reflected by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section, satisfying the following equation (13). 1.90 > M1X / M1Y > 1.00 (13) Here, M1X: The effective X range of the first reflecting surface when measured in parallel with respect to the X profile; M1Y: The effective Y range of the first reflecting surface when measured in parallel with respect to the Y profile.

17. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the position where it is reflected by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section, satisfying the following equation (14). 6.00 > T2X / T2Y > 2.00 (14) Here, T2X: The effective range of the second transmission surface when measured in parallel with respect to the X profile; T2Y: The effective Y range of the second transmission surface when measured in parallel with respect to the Y profile.

18. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the point of reflection by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section. In this Y-section, between the position of the principal ray of the reference ray reflected by the first reflecting surface and the position of the origin of the coordinates of the first reflecting surface, there are multiple principal rays.

19. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the point of reflection by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section. The second transmission surface is positioned in the Y-section, relative to the principal ray of the reference optical axis, on the opposite side of the origin of the coordinate system of the first reflection surface.

20. The optical system according to any one of claims 1, 5, and 12, wherein, The plane containing the center of the principal ray passing through the long side of the rectangular region at the point of reflection by the first reflecting surface is designated as the Y-section, and the plane containing the reference optical axis and perpendicular to the Y-section is designated as the X-section. The coordinate system of the first reflecting surface is tilted in the Y-section along the direction of the intermediate imaging.

21. The optical system according to any one of claims 1, 5, and 12, wherein, The first reflecting surface and the second transmitting surface are configured such that both are convex surfaces facing the magnified conjugate point.

22. The optical system according to any one of claims 1, 5, and 12, wherein, A planar portion perpendicular to the reference optical axis is provided on a portion of the outer periphery of the prism.

23. An image projection device, comprising: The optical system according to any one of claims 1 to 22; and An image forming element generates an image that is projected onto a screen via the optical system.

24. A camera device, comprising: The optical system according to any one of claims 1 to 22; and The camera element receives the optical image formed by the optical system and converts it into an electrical image signal.

Images