JP5867577B2 - Image projection device - Google Patents

Description

The present invention relates to a Film image projection device.

  A plurality of methods have been devised and put into practical use for image projection apparatuses (so-called projectors) that project an enlarged image of an image display element. For example, after light from a light source is transmitted through a liquid crystal display element, an image (light) obtained through the liquid crystal display element is screened (projection surface) via a projection optical system including a plurality of lenses. An image projection apparatus that projects an image on an enlarged scale is known (see, for example, Patent Document 1).

JP 2008-134350 A

  In such an image projection apparatus, it is desired to reduce the overall size including the position of the screen (projection surface). In order to satisfy such a requirement, it is preferable to adopt an oblique projection method that allows the screen position to be close to the image projection apparatus itself. However, in the case of the oblique projection method, a large distortion (trapezoidal distortion) occurs in the image projected on the screen, and it is required to reduce this.

In a first aspect of the present invention, the video projection equipment is a video display device, an image projection apparatus comprising an optical system for image projection device is used in a state of being installed at a predetermined installation surface, The image displayed on the image display element is enlarged and projected from the oblique direction on the same surface as the installation surface or on a surface substantially parallel to the installation surface, and the optical system for the image projection device follows the optical axis. And a plurality of free-form surface lenses formed in a rotationally symmetric manner with respect to the central axis, and a plurality of free-form surface lenses formed in a rotationally symmetric manner with respect to the central axis. A free-form surface lens group, and a free-form surface mirror having a reflection surface formed in a non-rotationally symmetrical manner with respect to the central axis until the image display element is reflected from the projection lens group by the free-form surface mirror Translation in the direction perpendicular to the optical axis Therefore, it is possible to correct the trapezoidal distortion generated in the image projected on the projection surface, and in the free-form surface lens group, the mirror-side free-form surface lens closest to the free-form surface mirror, and the mirror-side free-form lens A cross section including the optical axis in at least one of the element-side free-form surface lenses arranged next to the curved lens has a meniscus shape with a concave surface facing the image display element side, and is reflected by the free-form surface mirror The angle formed between the principal ray from the center of the image display element and the optical axis is α, the distance from the optical axis to the center of the image display element is h, and the focal length of the projection lens group is f. Then, the following expression 0.14 ≦ | {sin ⁻¹ (h / f)} / α | ≦ 0.20
It satisfies the following conditions.

In a second aspect of the present invention, the video projection equipment is a video display device, an image projection apparatus comprising an optical system for image projection device is used in a state of being installed at a predetermined installation surface, The image displayed on the image display element is enlarged and projected from the oblique direction on the same surface as the installation surface or on a surface substantially parallel to the installation surface, and the optical system for the image projection device follows the optical axis. And a plurality of free-form surface lenses formed in a rotationally symmetric manner with respect to the central axis, and a plurality of free-form surface lenses formed in a rotationally symmetric manner with respect to the central axis. A free-form surface lens group, and a free-form surface mirror having a reflection surface formed in a non-rotationally symmetrical manner with respect to the central axis until the image display element is reflected from the projection lens group by the free-form surface mirror Translation in the direction perpendicular to the optical axis Therefore, it is possible to correct the trapezoidal distortion generated in the image projected on the projection surface, and in the free-form surface lens group, the mirror-side free-form surface lens closest to the free-form surface mirror, and the mirror-side free-form lens A cross section including the optical axis in at least one of the element-side free-form curved lenses arranged next to the curved lens has a meniscus shape with a concave surface facing the image display element, and the focal length of the projection lens group Is f, and the total length of the optical system for the image projection apparatus is TL, the following equation 15 ≦ | TL / f | ≦ 20
It satisfies the following conditions.

It is a sectional side view of the optical system for video projectors concerning the 1st example. It is a plane sectional view of the optical system for image projection devices concerning the 1st example. It is a 1st lateral aberration figure of the optical system for image projection apparatuses which concerns on 1st Example. It is a 2nd lateral aberration figure of the optical system for image projection apparatuses which concerns on 1st Example. It is a 3rd lateral aberration figure of the optical system for image projection apparatuses which concerns on 1st Example. It is a 4th lateral aberration figure of the optical system for image projectors concerning the 1st example. It is a sectional side view of the optical system for image projection apparatuses which concerns on 2nd Example. It is a plane sectional view of the optical system for image projection devices concerning the 2nd example. It is a 1st lateral aberration figure of the optical system for image projection apparatuses which concerns on 2nd Example. It is a 2nd lateral aberration figure of the optical system for image projection apparatuses which concerns on 2nd Example. It is a 3rd lateral aberration figure of the optical system for image projection apparatuses concerning 2nd Example. It is a 4th lateral aberration figure of the optical system for image projection apparatuses concerning the 2nd example. It is a sectional side view of the optical system for image projection apparatuses which concerns on 3rd Example. It is a plane sectional view of the optical system for image projection devices concerning the 3rd example. It is a 1st lateral aberration figure of the optical system for image projection apparatuses which concerns on 3rd Example. It is a 2nd lateral aberration figure of the optical system for image projection apparatuses which concerns on 3rd Example. It is a 3rd lateral aberration figure of the optical system for image projection apparatuses concerning 3rd Example. It is a 4th lateral aberration figure of the optical system for image projection apparatuses concerning 3rd Example. It is a sectional side view of the optical system for image projection apparatuses which concerns on 4th Example. It is a plane sectional view of the optical system for video projection devices concerning the 4th example. It is a 1st lateral aberration figure of the optical system for image projection apparatuses which concerns on 4th Example. It is a 2nd lateral aberration figure of the optical system for image projection apparatuses which concerns on 4th Example. It is a 3rd lateral aberration figure of the optical system for image projection apparatuses concerning 4th Example. It is a 4th lateral aberration figure of the optical system for image projection apparatuses concerning the 4th example. It is a sectional side view of the optical system for image projection apparatuses which concerns on 5th Example. It is a plane sectional view of the optical system for image projection devices concerning the 5th example. It is a 1st lateral aberration figure of the optical system for image projection apparatuses which concerns on 5th Example. It is a 2nd lateral aberration figure of the optical system for image projection apparatuses concerning 5th Example. It is a 3rd lateral aberration figure of the optical system for image projection apparatuses concerning 5th Example. It is a 4th lateral aberration figure of the optical system for image projection apparatuses concerning 5th Example. It is a perspective view of a video projection device. It is sectional drawing of an image projection apparatus. It is a schematic diagram explaining the inclination of a free-form surface lens group.

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. First, a definition method of “optical axis of optical system” and “center axis of lens (group)” used in the present embodiment will be described. In the present embodiment, information such as the position, shape, and light beam position of each lens surface is not represented by a single representative coordinate system, but a right-handed xyz orthogonal coordinate (hereinafter referred to as a coordinate system unique to each lens surface). , Referred to as a local coordinate system), and the information is shared between adjacent (front and rear) local coordinate systems to represent the entire optical system.

Regarding the “center axis of the lens (group)” (hereinafter sometimes simply referred to as the center axis), it is considered that the origin of the local coordinate system of each surface of the lens (group) is connected by a straight line, (Group) center axis ". In this embodiment, the z axis of each coordinate system is parallel to the central axis. That is, the coordinate axis in the central axis direction in which the direction from the image display element DS toward the free-form surface mirror M is positive is the z-axis, and the coordinate axis perpendicular to the z-axis in the yz section described later is the y-axis. The coordinate axis perpendicular to the axis is the x axis. However, the z axis does not necessarily have to be parallel to the central axis. For the mirror surface, the z axis of the local coordinate system of this surface is defined as the central axis.

  With respect to the “optical axis of the optical system” (hereinafter sometimes simply referred to as the optical axis), it passes through the central axis of the rotationally symmetric reference projection lens group G1 from the object surface (display surface of the video display element DS). It is defined as a single straight line that is reflected by the free-form curved mirror M (following the law of reflection) and reaches the image plane I (projection plane R). That is, in the present embodiment, the central axis of the reference projection lens group G1 coincides with the optical axis.

  In this embodiment, the central axis of the free-form surface lens group G2 is defined by the method as described above. However, if the origins of the local coordinate systems are not on the same straight line, they may be defined as follows. good. That is, the origin of the local coordinate system on the foremost surface (surface closest to the image display element DS) of the free-form surface lens group G2 and the origin of the local coordinate system on the last surface (most image-side surface) of the free-form surface lens group G2. Connected with a straight line, this straight line is defined as the central axis. At this time, the z axis of each local coordinate system in the free-form surface lens group G2 is not necessarily parallel to the central axis.

  Now, the image projection apparatus PRJ of this embodiment is shown in FIGS. FIG. 31 is a perspective view of the image projection device PRJ, and FIG. 32 is a cross-sectional view of the image projection device PRJ. 31 and 32 includes a cylindrical box-shaped housing BD having a window W on the front surface, an image display element DS housed in each of the housings BD, and an image projection. And an apparatus optical system PL. Such an image projection device PRJ is used in a state where it is installed on a predetermined installation surface Q such as the upper surface of a table (or desk) or a wall surface in the vicinity of a whiteboard, and light from a light source (not shown). Is incident on the image display element DS through the polarizing prism, and then the image (light) obtained by reflecting on the image display element DS is transmitted through the optical system PL and the window W for the image projection apparatus, which will be described in detail later. Thus, the image projection apparatus PRJ (housing BD) is configured to be enlarged and projected from an oblique direction onto a projection plane R set on the same plane as the installation plane Q.

  As the light source (not shown), for example, a lamp that generates high-intensity white light such as a mercury lamp or a halogen lamp is used. Further, as the video display element DS, for example, a liquid crystal display element that displays video (or images) input from an external input device (such as a personal computer or a storage device) is used.

The optical system PL for image projection apparatus includes a reference projection lens group G1 composed of a plurality of projection lenses arranged in order from the image display element DS side along the optical axis and formed rotationally symmetrically with respect to the center axis, and the center axis And a free-form surface lens group G2 composed of a plurality of free-form surface lenses formed in a non-rotationally symmetric manner, and a free-form surface mirror M having a reflection surface formed in a non-rotationally symmetric manner with respect to the central axis. Is done. In such an image projection apparatus optical system PL, light emitted from the image display element DS is transmitted through the reference projection lens group G1 and the free-form surface lens group G2, reflected by the free-form surface mirror M in an oblique direction, and projected. Projected onto the surface R. In the image projection apparatus optical system PL of the present embodiment, the free-form surface lens group G2 and the free-form surface mirror M are incorporated as described above, and the image display element DS is reflected by the free-form surface mirror M from the reference projection lens group G1. The trapezoidal distortion generated in the image projected on the projection plane R is corrected by translation (shifting) in a direction perpendicular to the optical axis before the optical axis.

  In this embodiment, the optical axis direction of the reference projection lens group G1 is the Z direction, the vertical direction in FIG. 1 perpendicular to the Z direction is the Y direction, and the longitudinal direction in FIG. 1 perpendicular to the Z direction and the Y direction is the vertical direction. Sometimes referred to as the X direction. That is, the image display element DS is configured to be able to translate (shift) in the X and Y directions using a position adjustment mechanism (screw mechanism) (not shown), and the image display element DS is moved by the position adjustment mechanism (screw mechanism) at the time of manufacture or the like. By adjusting the position by parallel translation (shift) in the XY directions, the trapezoidal distortion of the image projected on the projection plane R is corrected.

In the free-form surface lens group G2, the mirror-side free-form surface lens closest to the free-form surface mirror M (for example, the third free-form surface lens L23 in the embodiment) and the element side arranged next to the mirror-side free-form surface lens Of a free-form surface lens (for example, the second free-form surface lens L22 in the embodiment), a cross-section including at least one of the optical axes (for example, an optical axis from the reference projection lens group G1 before being reflected by the free-form surface mirror M, and The y-z cross section passing through the optical axis after being reflected by the free-form surface mirror M and the x-z cross section perpendicular to the y-z cross section) has a meniscus shape with the concave surface facing the image display element DS side. It is preferable. The yz cross section and the xz cross section in this embodiment are cross sections determined by a three-dimensional orthogonal coordinate system (xyz coordinate system) in which the z axis coincides with the optical axis.

  In the image projection apparatus optical system PL of the present embodiment, a trapezoidal distortion generated in an image projected obliquely by combining the use of a free-form surface and the shift of the image display element DS with respect to the reference projection lens group G1. Is corrected. When a rotationally asymmetric trapezoidal distortion is corrected using a free-form surface, the free-form surface itself has a rotationally asymmetric shape, and rotationally asymmetric aberration occurs on this surface. Therefore, the free-form lens group G2 must suppress the generation of rotationally asymmetric aberration as much as possible while correcting the trapezoidal distortion. The above conditions are for satisfying this.

  Since the image projection apparatus optical system PL of the present embodiment performs enlarged projection, the principal ray emitted from each point of the image display element DS becomes a divergent ray after passing (transmitting) the reference projection lens group G1. At this time, if the free-form surface lens has a meniscus shape with the concave surface facing the image display element DS as in the above condition, the light incident angle becomes small and the light can be bent without difficulty. In addition, the meniscus shape makes it possible to cancel the rotationally asymmetric aberration that occurred on the first surface (front surface of the lens) immediately on the next surface (the rear surface of the lens). Thus, it becomes possible to correct trapezoidal distortion. If the above conditions are not satisfied, a large amount of rotationally asymmetrical aberrations occur when correcting trapezoidal distortion on a free-form surface, and all aberrations are good at short distances, especially when downsizing the optical system. It becomes very difficult when it has to be corrected.

  For example, as shown in FIG. 33, the central axis of the free-form surface lens group G2 is inclined with respect to the optical axis from the reference projection lens group G1 before being reflected by the free-form surface mirror M, and the free-form surface with respect to the optical axis When the inclination angle of the central axis of the lens group G2 is θ, the distance from the optical axis to the center of the image display element DS is h, and the focal length of the reference projection lens group G1 is f, the following conditional expression (1 It is preferable that the conditions represented by

  0.7 ≦ | h / (f × sin θ) | ≦ 1.5 (1)

  Here, the central axis of the free-form surface lens group G2 refers to a local coordinate system (hereinafter referred to as a local coordinate system) for representing each function in each free-form surface constituting the group. Define the origin of the coordinate system as a straight line. At this time, if the origin of each local coordinate system is not on a straight line, the height from the optical axis of the coordinate origin on the forefront surface (surface closest to the image display element DS) of the free-form surface lens group G2 (perpendicular to the optical axis). An inclination line using the distance from the optical axis of the coordinate origin on the last surface (most image side surface) of the free-form surface lens group G2 and the distance on the optical axis between these two points, The obtained inclination straight line is set as the central axis of the free-form surface lens group G2.

  Since the display surface of the image display element DS (hereinafter simply referred to as the element surface) is shifted with respect to the optical axis, even the chief ray emitted from the center of the image display element DS is relative to the normal of each free-form surface. Incident at an angle. As a result, the light ray emitted from the end from the optical axis most in the element plane is incident at a small angle with respect to the normal of the free-form surface, but the light ray emitted from the end farthest from the optical axis in the element plane. Is incident at a very large angle with respect to the normal of the free-form surface. In this state, an asymmetrical aberration occurs between the light beams emitted from both ends of the image display element DS (that is, the aberration is not rotationally symmetric with respect to the center of the image plane I), and the free-form surface lens group This is not preferable because it imposes an extra burden on G2. In order to solve this, by tilting the central axis of the free-form surface lens group G2 with respect to the optical axis, the incident angle (relative to the normal line) of the light rays emitted from both ends of the image display element DS to the free-form surface is reduced. It is only necessary to relax the asymmetry and improve the symmetry of the generated aberration. At this time, the direction in which the free-form surface lens group G2 is tilted is most preferably in the same plane as the direction in which the image display element DS is shifted.

  Therefore, if the inclination angle θ satisfies the conditional expression (1), the symmetry of aberrations at both ends of the element can be kept at a satisfactory level, and aberration correction can be performed efficiently. If the tilt angle θ does not satisfy the conditional expression (1), the symmetry of the aberrations at both ends of the element deteriorates to a level that cannot be ignored, placing a wasteful burden on the free-form surface lens group G2, and as a result Aberration correction becomes difficult.

  If the following conditional expression (1-1) is satisfied instead of the conditional expression (1), the principal ray emitted from the center of the image display element DS is closer to the central axis of the free-form surface lens group G2. As a result, the symmetry of the incident angle of the light beam emitted from both ends of the image display element DS to the free-form surface is improved, and the trapezoidal distortion correction and the aberration correction can be further improved.

  0.9 ≦ | h / (f × sin θ) | ≦ 1.2 (1-1)

  The projection lens closest to the image display element DS in the reference projection lens group G1 is a meniscus lens having a convex surface facing the image side, and the projection lens closest to the image side in the reference projection lens group G1 is convex toward the image display element DS. The meniscus lens is preferably oriented. In the present embodiment, since the image display element DS is shifted with respect to the optical axis, and the optical system PL for the image projection apparatus is an object side telecentric, it exits from a position close to the optical axis of the image display element DS. Compared with light, the light emitted from a position away from the optical axis is larger on each surface of the reference projection lens group G1 and tends to be bent rapidly. Therefore, in the image display element DS, a large asymmetry occurs between the aberrations generated by the light beam emitted from the point closest to the optical axis and the light beam emitted from the point farthest from the optical axis, and the aberration is obtained at all angles of view. It is difficult to correct well in a balanced manner. In addition, these asymmetrical aberrations are basically not canceled out by the asymmetrical aberration generated when the free-form surface lens group G2 corrects the trapezoidal distortion, and the burden on the free-form surface lens group G2 is increased as much as possible. It is better to suppress it.

The above conditions are for solving the problems described above. Reference projection lens group G1
The meniscus lens (projection lens) closest to the image display element DS is arranged with the convex surface facing the image side so that the incident angle becomes small with respect to the divergent light beam emitted from each point on the image display element DS. When the principal rays emitted from each point of the image display element DS are substantially parallel and enter the reference projection lens group G1, and then enter the most image side projection lens in the reference projection lens group G1, the reference projection lens group It becomes a convergent light beam by the positive refractive power component of G1. Therefore, the projection lens arranged closest to the image side is a meniscus lens, and the convex surface is arranged facing the image display element DS side, whereby the incident angle of each principal ray can be reduced. By satisfying this condition, the aberration generated at each angle of view can be reduced, and as a result, the influence of the asymmetrical aberration generated in the reference projection lens group G1 on the imaging can be reduced. For this reason, the burden on the free-form surface lens group G2 is reduced, and it is possible to correct the trapezoidal distortion and the various aberrations with good balance in the entire optical system.

  The angle formed by the principal ray from the center of the image display element DS after being reflected by the free-form curved mirror M and the optical axis from the reference projection lens group G1 before being reflected by the free-form curved mirror M is α, and the light When the distance from the axis to the center of the image display element DS is h and the focal length of the reference projection lens group G1 is f, it is preferable that the condition expressed by the following conditional expression (2) is satisfied.

0.14 ≦ | {sin ⁻¹ (h / f)} / α | ≦ 0.20 (2)

  In this embodiment, the amount of trapezoidal distortion is reduced by shifting the image display element DS with respect to the optical axis. Normally, when oblique projection is performed, if the display surface of the image display element DS which is the object surface is shifted while keeping the tilt angle of the reflection mirror with respect to the optical axis (before being reflected by the mirror) constant, trapezoidal distortion It is possible to translate the image plane with almost no change in the generation amount. In the present embodiment, this is utilized to the maximum, and the image plane I is arranged at a desired position while shifting the video display element DS to keep the amount of trapezoidal distortion as low as possible.

  Conditional expression (2) is for determining the optimum value of the shift amount of the video display element DS and the tilt angle of the free-form curved mirror M (reflection mirror) (in the formula, from the center of the video display element DS). The inclination angle of the emitted principal ray with respect to the optical axis is for convenience, and this angle uniquely determines the inclination angle of the free-form curved mirror M). When the condition is less than the lower limit value of the conditional expression (2), since the tilt angle of the free-form curved mirror M is too large with respect to the shift amount of the image display element DS, the amount of trapezoidal distortion increases, and the image is relatively This is not preferable because the effect of shifting the display element DS becomes thin. On the other hand, when the condition exceeds the upper limit value of the conditional expression (2), it is advantageous in correcting the trapezoidal distortion, but the effective diameter of the entire optical system becomes too large because the shift amount of the image display element DS increases. Therefore, it is not preferable because it is difficult to reduce the size of the optical system. In addition, after the light beam emitted from the end of the image display element DS closest to the optical axis is reflected by the free-form surface mirror M, there is a high possibility that it collides with the free-form surface lens adjacent to the mirror M. There are some problems that should be avoided.

  If the following conditional expression (2-1) is satisfied instead of the above conditional expression (2), the shift amount of the video display element DS and the inclination angle of the free-form curved mirror M are further optimized. This is advantageous in terms of aberration correction.

0.16 ≦ | {sin ⁻¹ (h / f)} / α | ≦ 0.19 (2-1)

  Further, it is preferable that the condition expressed by the following conditional expression (3) is satisfied, where f is the focal length of the reference projection lens group G1 and TL is the total length of the optical system PL for the image projection apparatus.

  15 ≦ | TL / f | ≦ 20 (3)

  Note that the total length TL of the optical system PL for the video projection apparatus is a distance on the optical axis from the display surface (object surface) of the video display element DS to the image plane I.

  Conditional expression (3) is for optimizing the balance between the size of the optical system and the power of the reference projection lens group G1. When the condition is less than the lower limit value of the conditional expression (3), the focal length of the reference projection lens group G1 is increased, so that the property of the reference projection lens group G1 becomes a telephoto type, and the maximum field angle of the principal ray is reduced. Therefore, although it is advantageous for making the entire optical system compact in the xy section, the entire back focus is extended due to insufficient power of the reference projection lens group G1. In order to reduce this, the free-form surface lens group G2 must have a large positive power, and the asymmetrical aberration generated due to this is corrected by the free-form surface lens group G2 itself (reference projection lens group). In G1, asymmetrical aberration cannot be corrected by the angle of view), and the burden increases. For this reason, it is difficult to simultaneously perform trapezoidal distortion correction and aberration correction, which is not preferable. On the other hand, when the condition exceeds the upper limit value of the conditional expression (3), the focal length of the reference projection lens group G1 is shortened so that the property of the reference projection lens group G1 becomes a wide angle type, and the maximum angle of view of the principal ray is large. Therefore, the xy cross-sectional area of the optical system increases, which leads to an increase in the size of the apparatus, which is not preferable. In addition, since the back focus becomes too short, the free-form surface lens group G2 must have a large negative power in order to extend it, and the trapezoidal distortion correction and the aberration correction are performed simultaneously as in the above case. Should be avoided because it becomes difficult.

  If the following conditional expression (3-1) is satisfied instead of the above conditional expression (3), the balance between the size of the optical system and the power of the reference projection lens group G1 is made more optimal. Therefore, it is possible to more compactly and correct aberrations more efficiently.

  16 ≦ | TL / f | ≦ 18 (3-1)

  In the above-described free-form surface lens having the meniscus shape in at least one of the y-z cross section and the x-z cross-section among the free-form surface lens closest to the mirror and the adjacent free-form surface lens, the image At the intersection of the principal ray that passes through the center of the image display element on the display surface of the display element DS and emerges from a straight line parallel to the local coordinate system x-axis or y-axis of the element, and the lens surface of the lens on the image display element DS side When the normal vector (of the lens surface) is Nr1, and the normal vector (of the lens surface) at the intersection of the principal ray and the lens surface on the free-form mirror M side is Nr2, the inner product of Nr1 and Nr2 Preferably satisfies the condition represented by the following conditional expression (4). Note that the z-axis of the local coordinate system of the video display element DS is parallel to the optical axis, and the center of the video display element is an intersection of diagonal lines of the square video display element DS.

  0.9 ≦ Nr1 ・ Nr2 <1 (4)

  At this time, if a function that gives a free-form surface is represented by z = f (x, y) and the values of curvature c incorporated therein are all 0 (zero), an arbitrary point on the surface is obtained. The normal vector N at P (a, b) is given by the following equation (5).

  In the above equation (5), φ is used to normalize the vector and is given by the following equation (6).

  In the present embodiment, the free curved surface is expressed by matching the origin of the function z = f (x, y) that gives the free curved surface on all surfaces with the origin of the local coordinate system on the surface.

  As described above, in the image projection apparatus optical system PL of the present embodiment, an image projected obliquely by combining the use of a free-form surface and shifting the image display element DS with respect to the reference projection lens group G1. Corrects the trapezoidal distortion that occurs in. Then, at least one of the mirror-side free-form surface lens and the element-side free-form surface lens is formed in a meniscus shape having a concave surface directed toward the image display element DS as described above, thereby correcting the trapezoidal distortion and rotationally asymmetric. Occurrence of aberration is suppressed. In addition to this, if the conditional expression (4) is satisfied, the difference between the light beam angle before passing through the lens and the light beam angle after passing through the lens must be small (assuming that the value of the conditional expression (4) is When it is “1”, the free-form surface is equivalent to a parallel plane plate for the principal ray, and it moves parallel but does not bend. It is possible to efficiently bend the light beam while suppressing the occurrence of the If this conditional expression (4) is not satisfied, a large amount of rotationally asymmetric aberration is generated when correcting trapezoidal distortion on a free-form surface, and all aberrations are observed at short distances, particularly when the optical system is downsized. It is very difficult to correct this well.

  If the conditional expression (4-2) is satisfied for the mirror-side free-form surface lens and the conditional expression (4-1) is satisfied for the element-side free-form surface lens instead of the conditional expression (4), the efficiency is further improved. In addition, trapezoidal distortion can be corrected while suppressing the occurrence of aberrations, and further downsizing of the optical system can be realized.

0.920 <Nr1 · Nr2 <0.999 (4-1)
0.985 <Nr1, Nr2 <1.000 (4-2)

  As described above, according to the present embodiment, the optical system PL for a video projection apparatus that can satisfactorily correct the trapezoidal distortion of a projected image, and the video projection apparatus PRJ including the same, with a compact configuration. Can be obtained.

  Embodiments of the present application will be described below with reference to the accompanying drawings. In each embodiment, an aspheric surface that is rotationally symmetric with respect to the optical axis (center axis) and a free-form surface that is not rotationally symmetric with respect to the central axis are used. Therefore, before describing each embodiment, these defining formulas will be described.

  First, an aspheric surface rotationally symmetric with respect to the optical axis (center axis) is defined by the following equation (7). In the following equation (7), Z is the sag amount of the surface parallel to the optical axis, c is the curvature at the surface vertex (on the optical axis), k is the conic constant, and h is the optical axis. Is a distance perpendicular to this, and A to J are coefficients for each power series term of h.

  Next, a free-form surface that is not rotationally symmetric with respect to the central axis is defined by the following equation (8). In the following equation (8), Z is the sag amount of the surface parallel to the central axis, c is the curvature at the surface vertex (origin), k is the conic constant, and h is the central axis. It is the distance from the origin in a plane perpendicular to this at the origin, and Cj is a coefficient of the xy polynomial. Further, in the following equation (8), a three-dimensional coordinate system (for example, an xyz coordinate system) having an origin on the central axis in each plane and matching the central axis and one of the coordinate axes (for example, the z axis) is used. Each of them is expanded on the coordinate system.

  Here, the relationship represented by the following Expression (9) and Expression (10) is established between j, m, and n in Expression (8).

(First embodiment)
1st Example of this application is described using FIGS. 1-6 and Tables 1-6. 1 is a side sectional view (y-z sectional view) of an optical system for an image projection apparatus according to a first embodiment, and FIG. 2 is a plan sectional view (x of an optical system for an image projection apparatus according to the first embodiment). -Z sectional view). The optical system PL for image projection apparatus according to the first embodiment is composed of a plurality of projection lenses L11 to L15 arranged in order from the image display element DS side along the optical axis and formed rotationally symmetrical with respect to the central axis. Reference projection lens group G1, a free-form surface lens group G2 made up of a plurality of free-form surface lenses L21 to L23 formed non-rotationally symmetric with respect to the center axis, and a reflection surface formed non-rotationally symmetric with respect to the center axis And a free-form surface mirror M. Two parallel flat plates are arranged between the display surface (element surface) of the video display element DS and the reference projection lens group G1, and the parallel flat plate is arranged such that the video display element DS side is the video display element. A DS cover glass CV is a prism P (PBS: polarization beam splitter) that reflects S-polarized light and transmits P-polarized light on the image side. A stop S is disposed between the reference projection lens group G1 and the free-form surface lens group G2.

  The reference projection lens group G1 is arranged in order from the image display element DS side along the optical axis, and includes a first projection lens L11 that is a meniscus lens having a convex surface toward the image side, and a biconvex second projection lens L12. , A biconvex third projection lens L13, a biconcave fourth projection lens L14, and a fifth projection lens L15 which is a meniscus lens having a convex surface facing the element side. The element side lens surface of the first projection lens L11, the element side lens surface of the third projection lens L13, the image side lens surface of the fourth projection lens L14, and the image side lens surface of the fifth projection lens L15. The lens surface is aspheric. Further, the third projection lens L13 and the fourth projection lens L14 are bonded lenses.

  The free-form surface lens group G2 includes a first free-form surface lens L21, a second free-form surface lens L22, and a third free-form surface lens L23 arranged in order from the image display element DS side, and the second free-form surface lens L22. In addition, the yz section and the xz section in the third free-form surface lens L23 have a meniscus shape with a concave surface facing the element side. The central axis of the free-form surface lens group G2 is the point at which the stop S (and the optical axis intersect) with respect to the optical axis from the reference projection lens group G1 before being reflected by the free-form surface mirror M (hereinafter simply referred to as the optical axis). ) In the yz plane with a tilt of −10 degrees (tilt angle θ). As for the free-form curved mirror M, the z-axis of the local coordinate system (xyz coordinate system) in the free-form curved mirror M is tilted by +25 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis. . In each of the following embodiments, when the z axis of each local coordinate system is parallel to the optical axis, it is defined as 0 degree, and the counterclockwise direction is defined as positive.

  In the optical system PL for image projection apparatus according to the first embodiment, the object side (element side) numerical aperture is 0.1786, and the shift amount h at the center of the image display element DS is +2.9976 mm in the Y direction. The size of the image display element DS is 7.68 mm × 5.76 mm, the projection size is 284.48 mm × 213.36 mm, and the enlargement magnification is about 37 times. The focal length f of the entire reference projection lens group G1 is 14.903 mm.

  Table 1 below shows numerical data of the optical system PL for image projection apparatus according to the first example. In the table (numerical data of the optical system) shown in each of the following examples, “* a” described therein represents that the surface is a rotationally symmetric aspheric surface, and “* f” represents This indicates that the surface is a non-rotationally symmetric free-form surface.

(Table 1)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 11.00000 1.80400 / 46.6
3 plane 5.70000
4 * a -16.30000 2.91783 1.74300 / 49.3
5 -15.50000 0.10000
6 68.10035 5.72790 1.56907 / 71.3
7 -20.03844 0.50000
8 * a 10.61721 5.51718 1.59240 / 68.3
9 -36.94050 2.30000 1.68893 / 31.1
10 * a 7.68118 4.40000
11 7.37790 2.00000 1.85280 / 39.0
12 * a 9.37830 2.97928
13 (aperture) plane 2.50000
14 * f xy polynomial surface 4.50000 1.53113 / 55.7
15 * f xy polynomial surface 9.00000
16 * f xy polynomial surface 5.00000 1.53113 / 55.7
17 * f xy polynomial surface 7.00000
18 * f xy polynomial surface 5.00000 1.53113 / 55.7
19 * f xy polynomial surface 20.00134
20 * f xy polynomial surface -164.00020 Reflection Image plane Plane

In Table 1, the surface spacing from the 13th surface to the 18th surface is the distance on the central axis of the free-form surface lens group G2. Since the central axis of the free-form surface lens group G2 is inclined by 10 degrees (reference numeral omitted) with respect to the optical axis, the distance on the optical axis from the thirteenth surface to the eighteenth surface is 33 × cos10 = 32.49866.

  In Table 1, the fourth surface to the twelfth surface are lens surfaces of the rotationally symmetric reference projection lens group G1, and among them, the fourth surface, the eighth surface, the tenth surface, and the twelfth surface rotate. It is a symmetric aspherical surface. Table 2 below shows the aspheric coefficients of the fourth surface, the eighth surface, the tenth surface, and the twelfth surface, respectively.

(Table 2)
Term 4th surface coefficient 8th surface coefficient c -0.0613497 0.0941867
k 0 0
A (4th order) 9.9088811E-05 -3.1038464E-04
B (6th) -2.8955599E-06 -5.1478378E-07
C (8th) 2.4889943E-08 2.6492821E-08
D (10th order) -1.2338807E-10 -2.2239744E-10

Term 10th surface coefficient 12th surface coefficient c 0.1301883 0.1066291
k 0 0
A (4th) -1.2454654E-03 6.8479877E-04
B (6th) 7.7249972E-06 8.9013004E-06
C (8th) 1.2820448E-08 -3.7952079E-07
D (10th) -2.0976044E-09 1.7454868E-08

  In Table 1, the 14th to 20th surfaces are non-rotationally symmetric free-form surfaces. In the present embodiment, the twentieth surface is the reflecting surface of the free-form curved mirror M. Tables 3 to 5 below show the term coefficients of these free-form surfaces.

(Table 3)
Term 14th surface coefficient 15th surface coefficient 16th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 1.9017402E-01 4.6190137E-01 7.5000000E-01
C4 (x ^ 2) -9.0463444E-03 -1.8248624E-02 -5.0268949E-02
C6 (y ^ 2) 1.9901180E-02 1.3545914E-02 -1.0580380E-01
C8 (x ^ 2 * y) -1.5876899E-03 -6.2633387E-04 3.2190974E-03
C10 (y ^ 3) -2.8638290E-03 -2.6556035E-03 3.6027098E-03
C11 (x ^ 4) 2.2373047E-05 -1.3198696E-04 -2.8811759E-04
C13 (x ^ 2 * y ^ 2) 9.7873842E-05 -1.9643685E-04 1.3746441E-04
C15 (y ^ 4) 8.6829974E-05 -9.9585679E-05 -8.6281332E-05
C17 (x ^ 4 * y) 2.8102666E-05 3.9614649E-05 -3.5972749E-05
C19 (x ^ 2 * y ^ 3) 2.3073814E-05 5.2232811E-05 -1.0428197E-04
C21 (y ^ 5) 1.5826670E-05 3.7379938E-05 -1.5272786E-05
C22 (x ^ 6) 8.1635735E-06 3.6697812E-06 2.9032630E-06
C24 (x ^ 4 * y ^ 2) 1.4924226E-05 3.6893346E-06 -2.7668264E-06
C26 (x ^ 2 * y ^ 4) 9.0047886E-06 -1.8709069E-06 -1.2232493E-05
C28 (y ^ 6) 8.4877049E-07 -3.4209027E-06 -2.6120613E-06
C30 (x ^ 6 * y) 7.9605046E-07 4.7509752E-07 -7.4551526E-07
C32 (x ^ 4 * y ^ 3) 1.4252740E-06 5.9365012E-07 -1.5686349E-06
C34 (x ^ 2 * y ^ 5) 1.0061147E-06 4.5397687E-07 1.6987288E-07
C36 (y ^ 7) 1.9029851E-07 4.0552333E-08 -2.9128550E-07
C37 (x ^ 8) -2.0145807E-07 -3.8057374E-08 6.1493894E-09
C39 (x ^ 6 * y ^ 2) -8.4240038E-07 -4.6641587E-08 2.1254851E-07
C41 (x ^ 4 * y ^ 4) -1.2064874E-06 -1.1327879E-07 3.8963217E-07
C43 (x ^ 2 * y ^ 6) -7.0474317E-07 -1.1026217E-07 1.3211609E-07
C45 (y ^ 8) 9.0383420E-08 1.6397257E-07 3.6381641E-08

(Table 4)
Term 17th surface coefficient 18th surface coefficient 19th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 3.6794235E-01 0 0
C4 (x ^ 2) -4.8955595E-02 -1.2236224E-02 -5.8941663E-03
C6 (y ^ 2) -6.0000772E-02 1.1373750E-02 1.1952780E-03
C8 (x ^ 2 * y) -2.1780198E-03 -3.4058713E-03 -3.0310322E-04
C10 (y ^ 3) 1.4111447E-04 5.8199513E-04 5.6705178E-04
C11 (x ^ 4) -6.9484918E-05 -1.1637318E-05 -5.4380362E-05
C13 (x ^ 2 * y ^ 2) -3.5607551E-05 -3.7461801E-04 -1.5688477E-04
C15 (y ^ 4) -8.0269089E-05 -1.7452312E-04 -9.7384098E-05
C17 (x ^ 4 * y) -2.6293767E-05 -3.9616502E-06 -1.0951191E-05
C19 (x ^ 2 * y ^ 3) -5.7329188E-05 -1.8115510E-05 -1.2666053E-05
C21 (y ^ 5) -1.0531173E-05 2.1234432E-07 9.5244138E-07
C22 (x ^ 6) 7.4839706E-07 -3.8450369E-07 -6.4320374E-08
C24 (x ^ 4 * y ^ 2) -1.6765308E-06 -1.0060228E-06 -3.1130393E-07
C26 (x ^ 2 * y ^ 4) -3.1228268E-06 -1.2647042E-06 -6.8072767E-07
C28 (y ^ 6) -5.8782823E-07 -1.1309675E-07 -6.0161949E-08
C30 (x ^ 6 * y) -1.1005613E-07 -3.4148587E-08 4.2187489E-08
C32 (x ^ 4 * y ^ 3) -1.6027269E-07 -1.4228554E-07 6.0081161E-08
C34 (x ^ 2 * y ^ 5) -1.4889681E-08 -7.7241928E-08 -1.3708831E-09
C36 (y ^ 7) -3.1095056E-08 3.2432906E-08 3.1784441E-09
C37 (x ^ 8) 0 -6.6662373E-10 0
C39 (x ^ 6 * y ^ 2) 0 -8.7870095E-09 0
C41 (x ^ 4 * y ^ 4) 0 -1.5762050E-08 0
C43 (x ^ 2 * y ^ 6) 0 -4.8371822E-09 0
C45 (y ^ 8) 0 -1.0119274E-09 0

(Table 5)
Term 20th surface coefficient c 0
C1 (k) 0
C3 (y) 0
C4 (x ^ 2) 1.2419868E-02
C6 (y ^ 2) 2.5155559E-03
C8 (x ^ 2 * y) 4.4039503E-04
C10 (y ^ 3) 9.6899474E-05
C11 (x ^ 4) -4.9823517E-06
C13 (x ^ 2 * y ^ 2) 7.9731841E-06
C15 (y ^ 4) 9.0524527E-07
C17 (x ^ 4 * y) -3.1378864E-07
C19 (x ^ 2 * y ^ 3) 4.9042232E-08
C21 (y ^ 5) -1.1443662E-08
C22 (x ^ 6) -4.0167980E-10
C24 (x ^ 4 * y ^ 2) -1.0080975E-08
C26 (x ^ 2 * y ^ 4) -3.6181076E-11
C28 (y ^ 6) -2.3211822E-10
C30 (x ^ 6 * y) -2.9290586E-10
C32 (x ^ 4 * y ^ 3) -1.4357516E-10
C34 (x ^ 2 * y ^ 5) 1.7613577E-11
C36 (y ^ 7) 1.1803116E-13
C37 (x ^ 8) -4.0949986E-12
C39 (x ^ 6 * y ^ 2) -1.2701846E-11
C41 (x ^ 4 * y ^ 4) 9.5303660E-13
C43 (x ^ 2 * y ^ 6) -4.6943679E-14
C45 (y ^ 8) -6.0962092E-14
C47 (x ^ 8 * y) -1.2432017E-13
C49 (x ^ 6 * y ^ 3) -1.2371629E-13
C51 (x ^ 4 * y ^ 5) 3.0336552E-14
C53 (x ^ 2 * y ^ 7) -7.0954219E-15
C55 (y ^ 9) -1.2438464E-15

  The corresponding values for conditional expressions (1) to (3) are shown below.

Conditional expression (1) | h / (f × sin θ) | =
| 2.9976 / {14.9030 × sin (-10 °)} | = 1.158
Conditional expression (2) | {sin ⁻¹ (h / f)} / α | =
｜ {sin ^-1 (2.9976 / 14.9030)} / 63.9164 | = 0.182
Conditional expression (3) | TL / f | =
| 261.3424 / 14.9030 | = 17.536

Table 6 below shows corresponding values for conditional expression (4). Regarding the xz cross section, since the free-form surface is axisymmetric with respect to the z axis, the description of the negative region of the x coordinate is omitted.

(Table 6)
(Second free-form surface lens L22: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.958558693
0 0.3576 0.961421039
0 0.5976 0.964213497
0 0.8376 0.966814910
0 1.0776 0.969158965
0 1.3176 0.971222172
0 1.5576 0.973010367
0 1.7976 0.974546818
0 2.0376 0.975863167
0 2.2776 0.976993161
0 2.5176 0.977968777
0 2.7576 0.978818126
0 2.9976 0.979564635
0 3.2376 0.980227068
0 3.4776 0.980820024
0 3.7176 0.981354664
0 3.9576 0.981839477
0 4.1976 0.982280968
0 4.4376 0.982684228
0 4.6776 0.983053364
0 4.9176 0.983391802
0 5.1576 0.983702502
0 5.3976 0.983988071
0 5.6376 0.984250855
0 5.8776 0.984492976

(Second free-form surface lens L22: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.979564635
0.32 2.9976 0.979388334
0.64 2.9976 0.978862073
0.96 2.9976 0.977993680
1.28 2.9976 0.976795841
1.6 2.9976 0.975285506
1.92 2.9976 0.973483003
2.24 2.9976 0.971410810
2.56 2.9976 0.969092042
2.88 2.9976 0.966548720
3.2 2.9976 0.963799996
3.52 2.9976 0.960860516
3.84 2.9976 0.957739079

(Third free-form curved lens L23: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.997990912
0 0.3576 0.997838638
0 0.5976 0.997775463
0 0.8376 0.997816603
0 1.0776 0.997963427
0 1.3176 0.998203808
0 1.5576 0.998513970
0 1.7976 0.998861976
0 2.0376 0.999211927
0 2.2776 0.999528301
0 2.5176 0.999779953
0 2.7576 0.999942468
0 2.9976 0.999999984
0 3.2376 0.999945222
0 3.4776 0.999778550
0 3.7176 0.999506439
0 3.9576 0.999139492
0 4.1976 0.998690570
0 4.4376 0.998173421
0 4.6776 0.997601695
0 4.9176 0.996988921
0 5.1576 0.996348961
0 5.3976 0.995698333
0 5.6376 0.995056849
0 5.8776 0.994453938

(Third free-form curved lens L23: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.999999984
0.32 2.9976 0.999984182
0.64 2.9976 0.999935566
0.96 2.9976 0.999850421
1.28 2.9976 0.999722274
1.6 2.9976 0.999541528
1.92 2.9976 0.999295048
2.24 2.9976 0.998965786
2.56 2.9976 0.998532581
2.88 2.9976 0.997970215
3.2 2.9976 0.997249881
3.52 2.9976 0.996340125
3.84 2.9976 0.995208311

  Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (4) are satisfied.

  3 to 6 are lateral aberration diagrams of the optical system PL for the image projection apparatus according to the first example. In each graph showing aberrations, C represents C-line (λ = 656.3 nm), e represents e-line (λ = 546.1 nm), and g represents g-line (λ = 435.8 nm) aberration. The description of each aberration diagram is the same in other examples, and the description is omitted. From the respective aberration diagrams, it can be seen that in the first example, the lateral aberration is corrected well at each point (object point) and has excellent optical performance.

(Second embodiment)
A second embodiment of the present application will be described with reference to FIGS. 7 to 12 and Tables 7 to 12. FIG. FIG. 7 is a side sectional view (y-z sectional view) of the optical system for the image projection apparatus according to the second embodiment, and FIG. 8 is a plan sectional view (x of the optical system for the image projection apparatus according to the second embodiment). -Z sectional view). The optical system for the image projection apparatus of the second embodiment has the same configuration as the optical system for the image projection apparatus of the first embodiment, and the same reference numerals as those in the first embodiment are assigned to the respective parts. The detailed explanation is omitted.

  In the optical system PL for image projection apparatus according to the second example, the object side (element side) numerical aperture is 0.1786, the shift amount h at the center of the image display element DS is +2.9976 mm in the Y direction, The size of the video display element DS is 7.68 mm × 5.76 mm, the projection size is 284.48 mm × 213.36 mm, and the enlargement magnification is about 37 times. The focal length f of the entire reference projection lens group G1 is 14.9444 mm.

  Further, the central axis of the free-form surface lens group G2 is inclined by −16 degrees (inclination angle θ) in the yz plane with the stop S (the point where the optical axis intersects) as the center with respect to the optical axis. As for the free-form surface mirror M, the z-axis of the local coordinate system (xyz coordinate system) in the free-form surface mirror M is inclined by +25 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis. .

  Table 7 below shows numerical data of the optical system PL for image projection apparatus according to the second example.

(Table 7)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 11.00000 1.80400 / 46.6
3 plane 5.70000
4 * a -16.30000 2.76248 1.74300 / 49.3
5 -15.50000 0.10000
6 110.76719 5.25607 1.56907 / 71.3
7 -18.08244 0.50000
8 * a 10.68699 5.33400 1.59240 / 68.3
9 -37.91040 2.30000 1.68893 / 31.1
10 * a 7.75150 4.40000
11 7.23030 2.00000 1.85280 / 39.0
12 * a 9.16280 3.23699
13 (aperture) plane 2.50000
14 * f xy polynomial surface 4.50000 1.53113 / 55.7
15 * f xy polynomial surface 9.00000
16 * f xy polynomial surface 5.00000 1.53113 / 55.7
17 * f xy polynomial surface 7.00000
18 * f xy polynomial surface 5.00000 1.53113 / 55.7
19 * f xy polynomial surface 20.77836
20 * f xy polynomial surface -164.93661 Reflection Image plane Plane

In Table 7, the surface interval from the 13th surface to the 18th surface is the distance on the central axis of the free-form surface lens group G2. Since the central axis of the free-form surface lens group G2 is inclined by 16 degrees (reference numeral omitted) with respect to the optical axis, the distance on the optical axis from the thirteenth surface to the eighteenth surface is 33 × cos16 = 31.72164.

  In Table 7, the fourth surface to the twelfth surface are lens surfaces of the rotationally symmetric reference projection lens group G1, and among them, the fourth surface, the eighth surface, the tenth surface, and the twelfth surface rotate. It is a symmetric aspherical surface. Table 8 below shows the aspherical coefficients of the fourth surface, the eighth surface, the tenth surface, and the twelfth surface, respectively.

(Table 8)
Term 4th surface coefficient 8th surface coefficient c -0.0613497 0.0935717
k 0 0
A (4th) 9.3933465E-05 -3.1372044E-04
B (6th) -3.0170024E-06 -4.8084750E-07
C (8th) 2.7443594E-08 2.7734677E-08
D (10th order) -1.5585598E-10 -2.1093749E-10

Term 10th surface coefficient 12th surface coefficient c 0.1290073 0.1091369
k 0 0
A (4th order) -1.2133091E-03 6.7195610E-04
B (6th) 7.5421804E-06 7.8658158E-06
C (8th) 1.7677369E-08 -3.2126987E-07
D (10th) -1.8874145E-09 1.4776291E-08

  In Table 7, the 14th to 20th surfaces are non-rotationally symmetric free-form surfaces. In the present embodiment, the twentieth surface is the reflecting surface of the free-form curved mirror M. Tables 9 to 11 below show each term coefficient of these free-form surfaces.

(Table 9)
Term 14th surface coefficient 15th surface coefficient 16th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 1.9580512E-01 3.6110108E-01 7.5000000E-01
C4 (x ^ 2) -1.2438872E-02 -1.8500655E-02 -4.8086037E-02
C6 (y ^ 2) 1.9293518E-02 1.3319012E-02 -1.0822370E-01
C8 (x ^ 2 * y) -1.9755341E-03 -9.0623395E-04 3.1350939E-03
C10 (y ^ 3) -3.1199298E-03 -3.1522150E-03 3.7349131E-03
C11 (x ^ 4) 3.9942175E-06 -1.1931680E-04 -2.5671932E-04
C13 (x ^ 2 * y ^ 2) -2.5006396E-05 -2.9473484E-04 2.9048311E-04
C15 (y ^ 4) -5.8736593E-05 -3.1242030E-04 -8.8880492E-05
C17 (x ^ 4 * y) 1.2301093E-05 2.6113297E-05 -3.3172052E-05
C19 (x ^ 2 * y ^ 3) -8.9880237E-06 2.8632718E-05 -6.9786892E-05
C21 (y ^ 5) 5.3192773E-06 3.2143917E-05 -9.0064384E-06
C22 (x ^ 6) 7.1161820E-06 2.7681937E-06 1.7756512E-06
C24 (x ^ 4 * y ^ 2) 1.3171391E-05 2.0728985E-06 2.6490209E-06
C26 (x ^ 2 * y ^ 4) 6.7196696E-06 -5.0287983E-06 -9.6688425E-06
C28 (y ^ 6) -8.5420370E-07 -3.5465019E-06 -1.6387400E-06
C30 (x ^ 6 * y) 1.8932948E-06 1.0238000E-06 -3.1152824E-07
C32 (x ^ 4 * y ^ 3) 4.8997837E-06 2.3608102E-06 -1.2494475E-06
C34 (x ^ 2 * y ^ 5) 5.4060592E-06 3.4487694E-06 -2.0455352E-07
C36 (y ^ 7) 6.6091238E-07 1.3366134E-07 -3.1403956E-07
C37 (x ^ 8) -2.6751392E-07 -5.1519592E-08 4.7092733E-09
C39 (x ^ 6 * y ^ 2) -1.2634642E-06 -2.7527982E-07 9.3651834E-08
C41 (x ^ 4 * y ^ 4) -2.2717212E-06 -6.2851956E-07 1.8589842E-07
C43 (x ^ 2 * y ^ 6) -1.2924015E-06 -4.8679982E-07 7.4889826E-08
C45 (y ^ 8) 6.0587039E-08 8.1699148E-08 -2.3334636E-08

(Table 10)
Term 17th surface coefficient 18th surface coefficient 19th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 5.0850667E-01 0 0
C4 (x ^ 2) -4.6912833E-02 -4.8381629E-03 -2.0666297E-03
C6 (y ^ 2) -5.5736842E-02 1.3716731E-02 -1.5706974E-03
C8 (x ^ 2 * y) -1.7693755E-03 -2.1000760E-03 5.6042051E-04
C10 (y ^ 3) 7.6106293E-04 8.9392339E-04 6.8643941E-04
C11 (x ^ 4) -8.2328512E-05 -9.9870510E-06 -3.3820075E-05
C13 (x ^ 2 * y ^ 2) 3.8036183E-05 -3.3188059E-04 -1.0177859E-04
C15 (y ^ 4) -4.4101205E-05 -1.7856989E-04 -8.7420222E-05
C17 (x ^ 4 * y) -1.6373033E-05 1.4712986E-06 -7.6831037E-06
C19 (x ^ 2 * y ^ 3) -4.3672036E-05 -7.4714593E-06 -6.9289403E-06
C21 (y ^ 5) -8.6405068E-06 1.0075778E-06 1.0870990E-06
C22 (x ^ 6) 4.7736240E-07 -2.5706163E-07 -1.1669556E-07
C24 (x ^ 4 * y ^ 2) 1.3092725E-06 1.3634289E-07 -4.4245496E-07
C26 (x ^ 2 * y ^ 4) -1.3113113E-06 -6.4642124E-08 -4.3388361E-07
C28 (y ^ 6) -8.7396056E-07 -1.8349710E-07 -1.1078306E-07
C30 (x ^ 6 * y) -1.2341987E-07 -2.4778701E-09 3.4003785E-08
C32 (x ^ 4 * y ^ 3) -2.5839902E-07 -1.2873568E-08 6.2448821E-08
C34 (x ^ 2 * y ^ 5) -6.4236420E-08 -5.6427438E-08 -4.6376596E-09
C36 (y ^ 7) -4.5019918E-09 2.1479736E-08 -1.2859120E-09
C37 (x ^ 8) 0 -8.2831769E-10 0
C39 (x ^ 6 * y ^ 2) 0 -7.0562072E-09 0
C41 (x ^ 4 * y ^ 4) 0 -1.3391919E-08 0
C43 (x ^ 2 * y ^ 6) 0 -1.0632525E-08 0
C45 (y ^ 8) 0 -1.5803851E-09 0

(Table 11)
Term 20th surface coefficient c 0
C1 (k) 0
C3 (y) 0
C4 (x ^ 2) 1.2723682E-02
C6 (y ^ 2) 2.6881471E-03
C8 (x ^ 2 * y) 4.4338292E-04
C10 (y ^ 3) 1.0339531E-04
C11 (x ^ 4) -5.7495028E-06
C13 (x ^ 2 * y ^ 2) 7.6713113E-06
C15 (y ^ 4) 8.8481415E-07
C17 (x ^ 4 * y) -3.5525128E-07
C19 (x ^ 2 * y ^ 3) 5.7025914E-08
C21 (y ^ 5) -1.3628931E-08
C22 (x ^ 6) 3.4426229E-10
C24 (x ^ 4 * y ^ 2) -1.0102287E-08
C26 (x ^ 2 * y ^ 4) 3.4030696E-10
C28 (y ^ 6) -2.0201988E-10
C30 (x ^ 6 * y) -1.7866777E-10
C32 (x ^ 4 * y ^ 3) -1.3254942E-10
C34 (x ^ 2 * y ^ 5) 1.0848522E-11
C36 (y ^ 7) 1.6954808E-12
C37 (x ^ 8) -8.7214282E-13
C39 (x ^ 6 * y ^ 2) -9.9501323E-12
C41 (x ^ 4 * y ^ 4) 1.9526861E-13
C43 (x ^ 2 * y ^ 6) 1.7942253E-14
C45 (y ^ 8) -5.4122699E-14
C47 (x ^ 8 * y) 3.1805774E-14
C49 (x ^ 6 * y ^ 3) -1.6391044E-13
C51 (x ^ 4 * y ^ 5) 2.0436415E-14
C53 (x ^ 2 * y ^ 7) -9.7459895E-16
C55 (y ^ 9) -1.5218592E-15

  The corresponding values for conditional expressions (1) to (3) are shown below.

Conditional expression (1) | h / (f × sin θ) | =
| 2.9976 / {14.9444 × sin (-16 °)} | = 0.728
Conditional expression (2) | {sin ⁻¹ (h / f)} / α | =
｜ {sin ^-1 (2.9976 / 14.9444)} / 63.7723 | = 0.181
Conditional expression (3) | TL / f | =
｜ 261.7262 / 14.9444 ｜ ＝ 17.513

Table 12 below shows corresponding values for the conditional expression (4). Regarding the xz cross section, since the free-form surface is axisymmetric with respect to the z axis, the description of the negative region of the x coordinate is omitted.

(Table 12)
(Second free-form surface lens L22: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.995237664
0 0.3576 0.996337114
0 0.5976 0.997235084
0 0.8376 0.997912051
0 1.0776 0.998387968
0 1.3176 0.998699160
0 1.5576 0.998882378
0 1.7976 0.998967057
0 2.0376 0.998973522
0 2.2776 0.998914444
0 2.5176 0.998797451
0 2.7576 0.998627694
0 2.9976 0.998409736
0 3.2376 0.998148644
0 3.4776 0.997850392
0 3.7176 0.997521775
0 3.9576 0.997170078
0 4.1976 0.996802683
0 4.4376 0.996426721
0 4.6776 0.996048814
0 4.9176 0.995674931
0 5.1576 0.995310316
0 5.3976 0.994959473
0 5.6376 0.994626200
0 5.8776 0.994313626

(Second free-form surface lens L22: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.998409736
0.32 2.9976 0.998260445
0.64 2.9976 0.997815928
0.96 2.9976 0.997086117
1.28 2.9976 0.996087094
1.6 2.9976 0.994840344
1.92 2.9976 0.993371637
2.24 2.9976 0.991709518
2.56 2.9976 0.989883447
2.88 2.9976 0.987921698
3.2 2.9976 0.985849225
3.52 2.9976 0.983685719
3.84 2.9976 0.981444126

(Third free-form curved lens L23: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.992358399
0 0.3576 0.991405008
0 0.5976 0.990687801
0 0.8376 0.990254176
0 1.0776 0.990128742
0 1.3176 0.990314250
0 1.5576 0.990793492
0 1.7976 0.991531597
0 2.0376 0.992478820
0 2.2776 0.993573980
0 2.5176 0.994748597
0 2.7576 0.995931563
0 2.9976 0.997053973
0 3.2376 0.998053670
0 3.4776 0.998879062
0 3.7176 0.999491835
0 3.9576 0.999868370
0 4.1976 0.999999815
0 4.4376 0.999890971
0 4.6776 0.999558285
0 4.9176 0.999027328
0 5.1576 0.998330178
0 5.3976 0.997503124
0 5.6376 0.996585022
0 5.8776 0.995616566

(Third free-form curved lens L23: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.997053973
0.32 2.9976 0.997072053
0.64 2.9976 0.997125715
0.96 2.9976 0.997213013
1.28 2.9976 0.997329999
1.6 2.9976 0.997469745
1.92 2.9976 0.997621145
2.24 2.9976 0.997767665
2.56 2.9976 0.997886211
2.88 2.9976 0.997946357
3.2 2.9976 0.997910179
3.52 2.9976 0.997732869
3.84 2.9976 0.997364335

  Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (4) are satisfied.

  9 to 12 are lateral aberration diagrams of the optical system PL for image projection apparatus according to the second example. From the aberration diagrams, it can be seen that in the second example, the lateral aberration is corrected well at each point (object point) and the optical performance is excellent.

(Third embodiment)
A third embodiment of the present application will be described with reference to FIGS. 13 to 18 and Tables 13 to 18. FIG. FIG. 13 is a side sectional view (y-z sectional view) of the optical system for the image projection apparatus according to the third embodiment, and FIG. 14 is a plan sectional view (x of the optical system for the image projection apparatus according to the third embodiment). -Z sectional view). The optical system for the image projection apparatus of the third embodiment has the same configuration as the optical system for the image projection apparatus of the first embodiment, and the same reference numerals as those in the first embodiment are assigned to the respective parts. The detailed explanation is omitted.

  In the optical system PL for image projection apparatus according to the third example, the object side (element side) numerical aperture is 0.1786, the shift amount h at the center of the image display element DS is +2.9976 mm in the Y direction, The size of the video display element DS is 7.68 mm × 5.76 mm, the projection size is 284.48 mm × 213.36 mm, and the enlargement magnification is about 37 times. The focal length f of the entire reference projection lens group G1 is 17.0000 mm.

  Further, the central axis of the free-form surface lens group G2 is inclined by −7 degrees (inclination angle θ) in the yz plane with the stop S (the point where the optical axis intersects) as the center with respect to the optical axis. As for the free-form surface mirror M, the z-axis of the local coordinate system (xyz coordinate system) in the free-form surface mirror M is inclined by +25 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis. .

  Table 13 below shows numerical data of the optical system PL for the image projection apparatus according to the third example.

(Table 13)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 11.00000 1.80400 / 46.6
3 plane 5.70000
4 * a -16.30000 2.00000 1.74300 / 49.3
5 -15.50000 0.10000
6 259.57028 9.16763 1.56907 / 71.3
7 -18.79180 0.50000
8 * a 10.73108 5.35327 1.59240 / 68.3
9 -43.78993 2.30000 1.68893 / 31.1
10 * a 7.97050 4.40000
11 9.66527 2.00000 1.85280 / 39.0
12 * a 14.76397 4.80030
13 (aperture) plane
14 * f xy polynomial surface 4.50000 1.53113 / 55.7
15 * f xy polynomial surface 9.00000
16 * f xy polynomial surface 5.00000 1.53113 / 55.7
17 * f xy polynomial surface 7.00000
18 * f xy polynomial surface 5.00000 1.53113 / 55.7
19 * f xy polynomial surface 19.74598
20 * f xy polynomial surface -164.99999 Reflection Image plane Plane

  In Table 13, the surface spacing from the 13th surface to the 18th surface is the distance on the central axis of the free-form surface lens group G2. Since the center axis of the free-form surface lens group G2 is inclined by 7 degrees (reference number omitted) with respect to the optical axis, the distance on the optical axis from the thirteenth surface to the eighteenth surface is 33 × cos7 = 32.75402.

  In Table 13, the fourth surface to the twelfth surface are lens surfaces of the rotationally symmetric reference projection lens group G1, and among these, the fourth surface, the eighth surface, the tenth surface, and the twelfth surface are rotated. It is a symmetric aspherical surface. Table 14 below shows the aspheric coefficients of the fourth surface, the eighth surface, the tenth surface, and the twelfth surface, respectively.

(Table 14)
Term 4th surface coefficient 8th surface coefficient c -0.0613497 0.0931873
k 0 0
A (4th) 9.8303034E-05 -3.1854287E-04
B (6th) -2.6439913E-06 -6.5557465E-07
C (8th order) 2.3211008E-08 3.0118204E-08
D (10th order) -1.2863754E-10 -1.9046065E-10

Term 10th surface coefficient 12th surface coefficient c 0.1254626 0.0677325
k 0 0
A (4th) -1.1658784E-03 4.7103565E-04
B (6th) 8.4071416E-06 2.4416210E-06
C (8th) -1.5309401E-09 -2.0352803E-07
D (10th order) -1.0367962E-09 3.3287730E-09

  In Table 13, the 14th to 20th surfaces are non-rotationally symmetric free-form surfaces. In the present embodiment, the twentieth surface is the reflecting surface of the free-form curved mirror M. Tables 15 to 17 below show the term coefficients of these free-form surfaces.

(Table 15)
Term 14th surface coefficient 15th surface coefficient 16th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 2.2040640E-01 5.5048823E-01 7.5000000E-01
C4 (x ^ 2) 1.4092673E-03 -1.1322644E-02 -5.3161207E-02
C6 (y ^ 2) 2.2440040E-02 1.4200633E-02 -1.1297661E-01
C8 (x ^ 2 * y) -1.1012939E-03 -3.4226464E-04 2.7545397E-03
C10 (y ^ 3) -1.7101610E-03 -1.2823663E-03 3.3774765E-03
C11 (x ^ 4) 1.8931706E-04 2.3467713E-05 -3.1105623E-04
C13 (x ^ 2 * y ^ 2) 3.8603390E-04 1.4477096E-04 -1.2288847E-04
C15 (y ^ 4) 2.3267863E-04 1.2842722E-04 -6.3840492E-05
C17 (x ^ 4 * y) 3.3884267E-05 4.7398665E-05 -4.6126262E-05
C19 (x ^ 2 * y ^ 3) 3.4284840E-05 5.8690943E-05 -1.5622924E-04
C21 (y ^ 5) 2.3963308E-05 4.2129645E-05 -3.2435078E-05
C22 (x ^ 6) 2.2286710E-06 2.6003361E-06 2.5361125E-06
C24 (x ^ 4 * y ^ 2) 6.3546120E-06 6.2477217E-06 -5.4325227E-06
C26 (x ^ 2 * y ^ 4) 5.5627421E-06 4.0258271E-06 -1.0003427E-05
C28 (y ^ 6) -6.3122620E-07 -1.2523914E-06 -2.5292275E-06
C30 (x ^ 6 * y) 4.2559203E-07 6.3269332E-07 -2.8809426E-07
C32 (x ^ 4 * y ^ 3) 1.2403478E-06 1.2696384E-06 -4.8667234E-07
C34 (x ^ 2 * y ^ 5) 9.4819403E-07 5.0022589E-07 5.1288137E-07
C36 (y ^ 7) 3.2479232E-07 4.4381802E-07 -3.5298739E-07
C37 (x ^ 8) -6.7480900E-08 -1.5853476E-08 9.9838450E-09
C39 (x ^ 6 * y ^ 2) -5.1870414E-07 -8.9328419E-08 2.4072554E-07
C41 (x ^ 4 * y ^ 4) -1.1992359E-06 -5.1310016E-07 4.9179665E-07
C43 (x ^ 2 * y ^ 6) -9.0378581E-07 -6.0636841E-07 2.2248514E-07
C45 (y ^ 8) -9.0036139E-08 -4.5672854E-08 6.8352160E-08

(Table 16)
Term 17th surface coefficient 18th surface coefficient 19th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 2.5643078E-01 0 0
C4 (x ^ 2) -5.4308097E-02 -2.8113188E-02 -1.2067103E-02
C6 (y ^ 2) -6.2774080E-02 1.3159909E-02 5.2787505E-03
C8 (x ^ 2 * y) -3.0205506E-03 -4.3377969E-03 -5.6700691E-04
C10 (y ^ 3) -7.7372680E-05 9.9688256E-04 7.2620897E-04
C11 (x ^ 4) -5.3553884E-05 -2.9680780E-06 -7.2371373E-05
C13 (x ^ 2 * y ^ 2) -1.3866645E-04 -4.4069446E-04 -2.2942944E-04
C15 (y ^ 4) -9.1371709E-05 -1.7546092E-04 -1.1056755E-04
C17 (x ^ 4 * y) -3.3129864E-05 -3.0654527E-06 -1.0759068E-05
C19 (x ^ 2 * y ^ 3) -6.4136679E-05 -1.8129855E-05 -1.6667456E-05
C21 (y ^ 5) -1.3800234E-05 1.3209626E-07 1.5899750E-06
C22 (x ^ 6) 6.6661035E-07 -8.2413297E-07 -1.0386711E-07
C24 (x ^ 4 * y ^ 2) -2.4903772E-06 -1.0899324E-06 -1.8692485E-07
C26 (x ^ 2 * y ^ 4) -2.7310101E-06 -7.7747118E-07 -6.5245305E-07
C28 (y ^ 6) -9.4509034E-07 -1.6805523E-07 5.6559539E-08
C30 (x ^ 6 * y) -6.3362895E-09 -4.9174351E-08 6.1866641E-08
C32 (x ^ 4 * y ^ 3) -1.4647683E-07 -1.4746587E-07 5.8527036E-08
C34 (x ^ 2 * y ^ 5) -8.0935068E-08 -2.7550591E-08 4.5357624E-09
C36 (y ^ 7) -7.9777541E-08 5.1526516E-08 5.9110087E-09
C37 (x ^ 8) 0 -1.6970826E-09 0
C39 (x ^ 6 * y ^ 2) 0 -1.4373678E-08 0
C41 (x ^ 4 * y ^ 4) 0 -1.6081114E-08 0
C43 (x ^ 2 * y ^ 6) 0 -4.2674846E-09 0
C45 (y ^ 8) 0 -5.7488958E-10 0

(Table 17)
Term 20th surface coefficient c 0
C1 (k) 0
C3 (y) 0
C4 (x ^ 2) 1.2806832E-02
C6 (y ^ 2) 2.6925851E-03
C8 (x ^ 2 * y) 4.8559349E-04
C10 (y ^ 3) 1.0539235E-04
C11 (x ^ 4) -5.4314810E-06
C13 (x ^ 2 * y ^ 2) 1.0093535E-05
C15 (y ^ 4) 1.0772751E-06
C17 (x ^ 4 * y) -3.6376953E-07
C19 (x ^ 2 * y ^ 3) 7.5045544E-08
C21 (y ^ 5) -1.4077557E-08
C22 (x ^ 6) 1.8447159E-09
C24 (x ^ 4 * y ^ 2) -1.1398853E-08
C26 (x ^ 2 * y ^ 4) -5.3697556E-10
C28 (y ^ 6) -2.8923316E-10
C30 (x ^ 6 * y) -1.5828439E-10
C32 (x ^ 4 * y ^ 3) -1.6378545E-10
C34 (x ^ 2 * y ^ 5) 1.5358314E-11
C36 (y ^ 7) 2.7243933E-12
C37 (x ^ 8) -1.1103242E-11
C39 (x ^ 6 * y ^ 2) -1.3575238E-11
C41 (x ^ 4 * y ^ 4) 1.1941981E-12
C43 (x ^ 2 * y ^ 6) 1.8944086E-14
C45 (y ^ 8) -7.5061887E-14
C47 (x ^ 8 * y) -6.3615937E-13
C49 (x ^ 6 * y ^ 3) -7.2692831E-14
C51 (x ^ 4 * y ^ 5) 2.7916816E-14
C53 (x ^ 2 * y ^ 7) -9.2489160E-15
C55 (y ^ 9) -2.8579612E-15

  The corresponding values for conditional expressions (1) to (3) are shown below.

Conditional expression (1) | h / (f × sin θ) | =
| 2.9976 / {17.0000 × sin (-7 °)} | = 1.447
Conditional expression (2) | {sin ⁻¹ (h / f)} / α | =
｜ {sin ^-1 (2.9976 / 17.0000)} / 64.0816 | = 0.158
Conditional expression (3) | TL / f | =
| 266.5212 / 17.0000 | = 15.678

Table 18 below shows corresponding values for conditional expression (4). Regarding the xz cross section, since the free-form surface is axisymmetric with respect to the z axis, the description of the negative region of the x coordinate is omitted.

(Table 18)
(Second free-form surface lens L22: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.936391588
0 0.3576 0.937654407
0 0.5976 0.939075070
0 0.8376 0.940591150
0 1.0776 0.942163048
0 1.3176 0.943769504
0 1.5576 0.945401643
0 1.7976 0.947057118
0 2.0376 0.948735281
0 2.2776 0.950433859
0 2.5176 0.952147191
0 2.7576 0.953865866
0 2.9976 0.955577367
0 3.2376 0.957267336
0 3.4776 0.958921010
0 3.7176 0.960524519
0 3.9576 0.962065864
0 4.1976 0.963535500
0 4.4376 0.964926538
0 4.6776 0.966234658
0 4.9176 0.967457831
0 5.1576 0.968595915
0 5.3976 0.969650238
0 5.6376 0.970623183
0 5.8776 0.971517811

(Second free-form surface lens L22: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.955577367
0.32 2.9976 0.955355886
0.64 2.9976 0.954695268
0.96 2.9976 0.953606780
1.28 2.9976 0.952108588
1.6 2.9976 0.950224810
1.92 2.9976 0.947984276
2.24 2.9976 0.945418974
2.56 2.9976 0.942562304
2.88 2.9976 0.939447239
3.2 2.9976 0.936104507
3.52 2.9976 0.932560938
3.84 2.9976 0.928838113

(Third free-form curved lens L23: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.998092051
0 0.3576 0.998154305
0 0.5976 0.998294043
0 0.8376 0.998498015
0 1.0776 0.998746599
0 1.3176 0.999016660
0 1.5576 0.999284520
0 1.7976 0.999528616
0 2.0376 0.999731517
0 2.2776 0.999881125
0 2.5176 0.999971014
0 2.7576 0.999999996
0 2.9976 0.999971125
0 3.2376 0.999890421
0 3.4776 0.999765527
0 3.7176 0.999604552
0 3.9576 0.999415246
0 4.1976 0.999204515
0 4.4376 0.998978316
0 4.6776 0.998741848
0 4.9176 0.998499988
0 5.1576 0.998257923
0 5.3976 0.998022000
0 5.6376 0.997800814
0 5.8776 0.997606531

(Third free-form curved lens L23: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.999971125
0.32 2.9976 0.999910295
0.64 2.9976 0.999730585
0.96 2.9976 0.999440038
1.28 2.9976 0.999051087
1.6 2.9976 0.998579161
1.92 2.9976 0.998040898
2.24 2.9976 0.997452097
2.56 2.9976 0.996825563
2.88 2.9976 0.996169034
3.2 2.9976 0.995483357
3.52 2.9976 0.994761072
3.84 2.9976 0.993985541

  Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (4) are satisfied.

  15 to 18 are lateral aberration diagrams of the optical system PL for the image projection apparatus according to the third example. From the aberration diagrams, it can be seen that in the third example, the lateral aberration is corrected satisfactorily at each point (object point) and has excellent optical performance.

(Fourth embodiment)
A fourth embodiment of the present application will be described with reference to FIGS. 19 to 24 and Tables 19 to 24. FIG. FIG. 19 is a side sectional view (yz sectional view) of the optical system for an image projection apparatus according to the fourth embodiment, and FIG. 20 is a plan sectional view (x of the optical system for an image projection apparatus according to the fourth embodiment). -Z sectional view). The optical system for the image projection apparatus of the fourth embodiment has the same configuration as the optical system for the image projection apparatus of the first embodiment, and the same reference numerals as those in the first embodiment are attached to the respective parts for details. The detailed explanation is omitted.

  In the optical system PL for image projection apparatus according to the fourth example, the object side (element side) numerical aperture is 0.1786, the shift amount h at the center of the image display element DS is +2.9976 mm in the Y direction, The size of the video display element DS is 7.68 mm × 5.76 mm, the projection size is 284.48 mm × 213.36 mm, and the enlargement magnification is about 37 times. The focal length f of the entire reference projection lens group G1 is 18.0013 mm.

  Further, the central axis of the free-form surface lens group G2 is inclined by −8 degrees (inclination angle θ) in the yz plane with the stop S (the point where the optical axis intersects) as the center with respect to the optical axis. Regarding the free-form surface mirror M, the z-axis of the local coordinate system (xyz coordinate system) of the free-form surface mirror M is inclined by +29 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis. .

  Table 19 below shows numerical data of the optical system PL for the image projection apparatus according to the fourth example.

(Table 19)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 11.00000 1.80400 / 46.6
3 plane 5.70000
4 * a -16.30000 3.19412 1.74300 / 49.3
5 -15.50000 0.10000
6 180.22745 9.09824 1.56907 / 71.3
7 -23.41457 0.50000
8 * a 11.03256 6.27236 1.59240 / 68.3
9 -57.70554 2.30000 1.68893 / 31.1
10 * a 8.41355 4.40000
11 17.70162 2.00000 1.85280 / 39.0
12 * a 49.32665 4.75238
13 (aperture) plane 2.50000
14 * f xy polynomial surface 4.50000 1.53113 / 55.7
15 * f xy polynomial surface 9.00000
16 * f xy polynomial surface 5.00000 1.53113 / 55.7
17 * f xy polynomial surface 7.00000
18 * f xy polynomial surface 5.00000 1.53113 / 55.7
19 * f xy polynomial surface 19.82115
20 * f xy polynomial surface -244.88093 Reflection Image plane Plane

  In Table 19, the surface spacing from the 13th surface to the 18th surface is the distance on the central axis of the free-form surface lens group G2. Since the central axis of the free-form surface lens group G2 is inclined by 8 degrees (reference numeral omitted) with respect to the optical axis, the distance on the optical axis from the thirteenth surface to the eighteenth surface is 33 × cos8 = 32.67885.

  In Table 19, the fourth surface to the twelfth surface are lens surfaces of the rotationally symmetric reference projection lens group G1, and among them, the fourth surface, the eighth surface, the tenth surface, and the twelfth surface rotate. It is a symmetric aspherical surface. Table 20 below shows the aspherical coefficients of the fourth, eighth, tenth and twelfth surfaces, respectively.

(Table 20)
Term 4th surface coefficient 8th surface coefficient c -0.0613497 0.0906408
k 0 0
A (4th) 1.4135382E-04 -3.0017937E-04
B (6th) -2.9321862E-06 -7.0914612E-07
C (8th order) 2.3410566E-08 2.9054854E-08
D (10th order) -1.1169176E-10 -1.8023721E-10

Term 10th surface coefficient 12th surface coefficient c 0.1188559 0.0202730
k 0 0
A (4th) -1.1170852E-03 3.4302952E-04
B (6th) 8.5331844E-06 2.2010909E-06
C (8th) -1.2747387E-08 -1.8994630E-07
D (10th) -7.5833050E-10 3.3391376E-09

  In Table 19, the 14th to 20th surfaces are non-rotationally symmetric free-form surfaces. In the present embodiment, the twentieth surface is the reflecting surface of the free-form curved mirror M. Tables 21 to 23 below show the term coefficients of these free-form surfaces.

(Table 21)
Term 14th surface coefficient 15th surface coefficient 16th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 1.8624979E-01 4.6434103E-01 7.5000000E-01
C4 (x ^ 2) -1.1024024E-02 -2.1445033E-02 -5.4178517E-02
C6 (y ^ 2) 2.4433088E-02 1.6404487E-02 -1.1733503E-01
C8 (x ^ 2 * y) -2.7345496E-03 -2.1321446E-03 2.2461839E-03
C10 (y ^ 3) -3.2027256E-03 -3.2543042E-03 3.8795578E-03
C11 (x ^ 4) 1.6860859E-04 2.6024584E-06 -1.6552252E-04
C13 (x ^ 2 * y ^ 2) 2.3138601E-04 -1.4742572E-04 -1.8290840E-04
C15 (y ^ 4) 1.4256407E-04 -9.6638324E-05 -1.3328312E-04
C17 (x ^ 4 * y) 3.2985670E-05 4.2463592E-05 -9.0113748E-06
C19 (x ^ 2 * y ^ 3) 2.6030332E-05 3.4723173E-05 -1.4095239E-04
C21 (y ^ 5) 1.3866620E-05 2.6659731E-05 -2.4870752E-05
C22 (x ^ 6) 3.9755555E-07 5.4717406E-07 2.8815362E-06
C24 (x ^ 4 * y ^ 2) 3.7268089E-06 2.2850176E-06 1.5025443E-06
C26 (x ^ 2 * y ^ 4) 4.2841988E-07 -3.5481315E-06 -7.2968226E-06
C28 (y ^ 6) -5.6224427E-07 -2.2222772E-06 -2.3275773E-06
C30 (x ^ 6 * y) 5.5004544E-07 3.4598088E-07 -7.4822471E-07
C32 (x ^ 4 * y ^ 3) 1.4850174E-06 1.3236604E-06 -1.7595488E-06
C34 (x ^ 2 * y ^ 5) 7.1143019E-07 6.1425145E-07 9.3141027E-07
C36 (y ^ 7) 1.9147672E-07 2.4394252E-07 2.1152270E-07
C37 (x ^ 8) -5.9112964E-09 3.3968034E-08 1.3696403E-08
C39 (x ^ 6 * y ^ 2) -4.7078888E-07 -1.0140388E-07 1.6985221E-07
C41 (x ^ 4 * y ^ 4) -7.3525407E-07 -2.3158528E-07 4.2837824E-07
C43 (x ^ 2 * y ^ 6) -3.6008419E-07 -1.5660100E-07 -5.6388993E-08
C45 (y ^ 8) 1.2857277E-08 2.8653987E-08 -7.0606063E-08

(Table 22)
Term 17th surface coefficient 18th surface coefficient 19th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 3.3167316E-01 0 0
C4 (x ^ 2) -5.0862229E-02 -1.1255351E-02 -6.4431487E-03
C6 (y ^ 2) -5.6407987E-02 9.6398834E-03 -2.6039280E-03
C8 (x ^ 2 * y) -2.7872352E-03 -3.0778037E-03 -4.6360861E-04
C10 (y ^ 3) 1.2440008E-04 9.1822883E-04 5.8292233E-04
C11 (x ^ 4) -1.0049499E-05 -2.2101511E-05 -5.8124382E-05
C13 (x ^ 2 * y ^ 2) -1.5656323E-04 -3.5529827E-04 -1.6103847E-04
C15 (y ^ 4) -4.5345698E-05 -1.6951281E-04 -1.0306543E-04
C17 (x ^ 4 * y) -1.1080632E-05 -1.3392883E-06 -8.3784638E-06
C19 (x ^ 2 * y ^ 3) -6.5091786E-05 -1.8977198E-05 -1.1899882E-05
C21 (y ^ 5) -5.3513351E-06 4.2046129E-06 2.9415003E-06
C22 (x ^ 6) 7.5199897E-07 -2.1224670E-07 4.4587101E-08
C24 (x ^ 4 * y ^ 2) -2.0134336E-07 -1.5804485E-07 -2.0663801E-08
C26 (x ^ 2 * y ^ 4) -1.5678188E-06 -7.6340839E-07 -5.8643979E-07
C28 (y ^ 6) -9.3685246E-07 -2.3978139E-07 -1.5133013E-08
C30 (x ^ 6 * y) -1.1104190E-07 2.3268573E-08 6.7300031E-08
C32 (x ^ 4 * y ^ 3) -1.7223080E-07 -3.4073899E-08 5.3166433E-08
C34 (x ^ 2 * y ^ 5) 2.1905492E-07 -7.7919911E-09 -1.0086907E-08
C36 (y ^ 7) -3.2628260E-08 4.4345086E-08 5.0826389E-09
C37 (x ^ 8) 0 -7.1452091E-10 0
C39 (x ^ 6 * y ^ 2) 0 -6.3254785E-09 0
C41 (x ^ 4 * y ^ 4) 0 -8.4198638E-09 0
C43 (x ^ 2 * y ^ 6) 0 1.4375907E-09 0
C45 (y ^ 8) 0 -1.3008481E-09 0

(Table 23)
Term 20th surface coefficient c 0
C1 (k) 0
C3 (y) 0
C4 (x ^ 2) 1.0623879E-02
C6 (y ^ 2) 2.7498835E-04
C8 (x ^ 2 * y) 3.8773475E-04
C10 (y ^ 3) 6.1352732E-05
C11 (x ^ 4) -4.9661904E-06
C13 (x ^ 2 * y ^ 2) 8.1026962E-06
C15 (y ^ 4) 1.0549727E-06
C17 (x ^ 4 * y) -3.9992646E-07
C19 (x ^ 2 * y ^ 3) 6.6656723E-08
C21 (y ^ 5) -5.9430169E-09
C22 (x ^ 6) 1.0510045E-09
C24 (x ^ 4 * y ^ 2) -1.4793497E-08
C26 (x ^ 2 * y ^ 4) -3.1177694E-10
C28 (y ^ 6) -3.5852047E-10
C30 (x ^ 6 * y) -9.0092954E-11
C32 (x ^ 4 * y ^ 3) -2.2331876E-10
C34 (x ^ 2 * y ^ 5) 1.3362352E-11
C36 (y ^ 7) 5.2243906E-13
C37 (x ^ 8) -1.4681526E-11
C39 (x ^ 6 * y ^ 2) -4.9170434E-12
C41 (x ^ 4 * y ^ 4) 9.4393834E-13
C43 (x ^ 2 * y ^ 6) 1.2824092E-13
C45 (y ^ 8) -1.7826471E-14
C47 (x ^ 8 * y) -8.9534601E-13
C49 (x ^ 6 * y ^ 3) 1.1803808E-13
C51 (x ^ 4 * y ^ 5) 2.5034309E-14
C53 (x ^ 2 * y ^ 7) -5.6400971E-15
C55 (y ^ 9) -1.6204323E-15

  The corresponding values for conditional expressions (1) to (3) are shown below.

Conditional expression (1) | h / (f × sin θ) | =
| 2.9976 / {18.0013 × sin (-8 °)} | = 1.197
Conditional expression (2) | {sin ⁻¹ (h / f)} / α | =
｜ {sin ^-1 (2.9976 / 18.0013)} / 66.5111 | = 0.144
Conditional expression (3) | TL / f | =
| 348.3980 / 18.0013 | = 19.354

Table 24 below shows corresponding values for the conditional expression (4). Regarding the xz cross section, since the free-form surface is axisymmetric with respect to the z axis, the description of the negative region of the x coordinate is omitted.

(Table 24)
(Second free-form surface lens L22: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.981509671
0 0.3576 0.980937403
0 0.5976 0.980350694
0 0.8376 0.979748356
0 1.0776 0.979134545
0 1.3176 0.978517091
0 1.5576 0.977905846
0 1.7976 0.977311219
0 2.0376 0.976743018
0 2.2776 0.976209666
0 2.5176 0.975717788
0 2.7576 0.975272135
0 2.9976 0.974875768
0 3.2376 0.974530360
0 3.4776 0.974236570
0 3.7176 0.973994358
0 3.9576 0.973803232
0 4.1976 0.973662388
0 4.4376 0.973570782
0 4.6776 0.973527124
0 4.9176 0.973529867
0 5.1576 0.973577169
0 5.3976 0.973666896
0 5.6376 0.973796617
0 5.8776 0.973963645

(Second free-form surface lens L22: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.974875768
0.32 2.9976 0.974746711
0.64 2.9976 0.974361476
0.96 2.9976 0.973725777
1.28 2.9976 0.972848861
1.6 2.9976 0.971743082
1.92 2.9976 0.970423319
2.24 2.9976 0.968906248
2.56 2.9976 0.967209493
2.88 2.9976 0.965350695
3.2 2.9976 0.963346571
3.52 2.9976 0.961211998
3.84 2.9976 0.958959219

(Third free-form curved lens L23: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.990714267
0 0.3576 0.991942155
0 0.5976 0.993155023
0 0.8376 0.994330091
0 1.0776 0.995443793
0 1.3176 0.996473086
0 1.5576 0.997396737
0 1.7976 0.998196483
0 2.0376 0.998857986
0 2.2776 0.999371490
0 2.5176 0.999732144
0 2.7576 0.999939962
0 2.9976 0.999999477
0 3.2376 0.999919119
0 3.4776 0.999710445
0 3.7176 0.999387316
0 3.9576 0.998965126
0 4.1976 0.998460207
0 4.4376 0.997889457
0 4.6776 0.997270274
0 4.9176 0.996620802
0 5.1576 0.995960526
0 5.3976 0.995311203
0 5.6376 0.994698138
0 5.8776 0.994151604

(Third free-form curved lens L23: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.999999477
0.32 2.9976 0.999993317
0.64 2.9976 0.999974282
0.96 2.9976 0.999940681
1.28 2.9976 0.999889610
1.6 2.9976 0.999816823
1.92 2.9976 0.999716595
2.24 2.9976 0.999581564
2.56 2.9976 0.999402616
2.88 2.9976 0.999168823
3.2 2.9976 0.998867477
3.52 2.9976 0.998484247
3.84 2.9976 0.998003453

  Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (4) are satisfied.

  21 to 24 are lateral aberration diagrams of the optical system PL for the image projection apparatus according to the fourth example. From the aberration diagrams, it can be seen that in the fourth example, the lateral aberration is satisfactorily corrected at each point (object point) and has excellent optical performance.

(5th Example)
A fifth embodiment of the present application will be described with reference to FIGS. 25 to 30 and Tables 25 to 30. FIG. FIG. 25 is a side sectional view (y-z sectional view) of the optical system for the image projection apparatus according to the fifth embodiment, and FIG. 26 is a plan sectional view (x of the optical system for the image projection apparatus according to the fifth embodiment). -Z sectional view). Note that the optical system for the image projection apparatus of the fifth embodiment has the same configuration as the optical system for the image projection apparatus of the first embodiment, and the same reference numerals as those in the first embodiment are assigned to the respective parts. The detailed explanation is omitted.

  In the optical system PL for image projection apparatus according to the fifth example, the object side (element side) numerical aperture is 0.1786, the shift amount h at the center of the image display element DS is +2.9976 mm in the Y direction, The size of the video display element DS is 7.68 mm × 5.76 mm, the projection size is 284.48 mm × 213.36 mm, and the enlargement magnification is about 37 times. The focal length f of the entire reference projection lens group G1 is 14.7000 mm.

  Further, the central axis of the free-form surface lens group G2 is inclined by −11 degrees (inclination angle θ) in the yz plane with the stop S (the point where the optical axis intersects) as the center with respect to the optical axis. As for the free-form surface mirror M, the z-axis of the local coordinate system (xyz coordinate system) in the free-form surface mirror M is tilted by +21 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis. .

  Table 25 below shows numerical data of the optical system PL for image projection apparatus according to the fifth example.

(Table 25)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 11.00000 1.80400 / 46.6
3 plane 5.70000
4 * a -16.30000 4.00754 1.74300 / 49.3
5 -15.50000 0.10000
6 105.12365 5.19304 1.56907 / 71.3
7 -19.90881 0.50000
8 * a 10.83191 5.70425 1.59240 / 68.3
9 -28.20215 2.30000 1.68893 / 31.1
10 * a 7.85271 4.40000
11 6.24533 2.00000 1.85280 / 39.0
12 * a 7.11741 3.15660
13 (aperture) plane 2.50000
14 * f xy polynomial surface 4.50000 1.53113 / 55.7
15 * f xy polynomial surface 9.00000
16 * f xy polynomial surface 5.00000 1.53113 / 55.7
17 * f xy polynomial surface 7.00000
18 * f xy polynomial surface 5.00000 1.53113 / 55.7
19 * f xy polynomial surface 20.10630
20 * f xy polynomial surface -160.51244 Reflection Image plane Plane

In Table 25, the surface interval from the 13th surface to the 18th surface is the distance on the central axis of the free-form surface lens group G2. Since the central axis of the free-form surface lens group G2 is inclined by 11 degrees (reference numeral omitted) with respect to the optical axis, the distance on the optical axis from the thirteenth surface to the eighteenth surface is 33 × cos11 = 32.39370.

  In Table 25, the fourth surface to the twelfth surface are lens surfaces of the rotationally symmetric reference projection lens group G1, and among them, the fourth surface, the eighth surface, the tenth surface, and the twelfth surface rotate. It is a symmetric aspherical surface. Table 26 below shows the aspheric coefficients of the fourth, eighth, tenth, and twelfth surfaces, respectively.

(Table 26)
Term 4th surface coefficient 8th surface coefficient c -0.0613497 0.0923198
k 0 0
A (4th order) 1.1285100E-04 -2.9105180E-04
B (6th) -3.0858143E-06 -7.3640615E-07
C (8th) 2.6739137E-08 2.5555202E-08
D (10th order) -1.2907718E-10 -1.8787527E-10

Term 10th surface coefficient 12th surface coefficient c 0.1273446 0.1405006
k 0 0
A (4th) -1.2449229E-03 8.9651528E-04
B (6th) 7.4929188E-06 2.0258580E-05
C (8th) 1.6338571E-08 -6.3100424E-07
D (10th) -1.7895014E-09 5.3871857E-08

  In Table 25, the 14th to 20th surfaces are non-rotationally symmetric free-form surfaces. In the present embodiment, the twentieth surface is the reflecting surface of the free-form curved mirror M. Tables 27 to 29 below show the term coefficients of these free-form surfaces.

(Table 27)
Term 14th surface coefficient 15th surface coefficient 16th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 1.0966179E-01 3.7504985E-01 7.5000000E-01
C4 (x ^ 2) -1.7141062E-02 -2.4668511E-02 -4.5643681E-02
C6 (y ^ 2) 1.7502880E-02 9.7742914E-03 -1.0739646E-01
C8 (x ^ 2 * y) -1.1604515E-03 -1.2815957E-04 2.4898442E-03
C10 (y ^ 3) -3.0557684E-03 -2.8709938E-03 3.0690997E-03
C11 (x ^ 4) 6.4003489E-05 -1.1427213E-04 -2.4873330E-04
C13 (x ^ 2 * y ^ 2) 1.7552755E-04 -1.8304434E-04 2.2500215E-04
C15 (y ^ 4) 1.5607923E-04 -9.2505642E-05 -9.9249595E-05
C17 (x ^ 4 * y) 3.1702113E-05 3.8476913E-05 -4.3508304E-05
C19 (x ^ 2 * y ^ 3) 1.2585720E-05 4.4842551E-05 -1.0297671E-04
C21 (y ^ 5) -1.5476363E-06 2.1297119E-05 -2.7136344E-05
C22 (x ^ 6) 1.2459029E-05 3.9371426E-06 3.0838115E-06
C24 (x ^ 4 * y ^ 2) 3.3511372E-05 9.0957407E-06 -3.5898752E-07
C26 (x ^ 2 * y ^ 4) 3.2477610E-05 9.8154495E-06 -7.7628170E-06
C28 (y ^ 6) 9.2117713E-06 2.7106113E-06 -3.3281140E-06
C30 (x ^ 6 * y) 8.5898774E-07 4.3541358E-07 -7.1203984E-07
C32 (x ^ 4 * y ^ 3) 2.2148371E-06 6.7866313E-07 -1.0175281E-06
C34 (x ^ 2 * y ^ 5) 1.9741645E-06 7.1268546E-07 -4.7396510E-07
C36 (y ^ 7) 5.0446158E-07 -2.9389879E-07 -3.8422133E-07
C37 (x ^ 8) -1.3877969E-07 2.3948975E-08 9.0991120E-09
C39 (x ^ 6 * y ^ 2) -1.0173985E-06 1.0086336E-07 1.7840180E-07
C41 (x ^ 4 * y ^ 4) -2.4312511E-06 -3.8942153E-07 3.0348654E-07
C43 (x ^ 2 * y ^ 6) -1.7595565E-06 -4.3707280E-07 1.9945794E-07
C45 (y ^ 8) -4.7256086E-08 1.3284734E-07 4.8634887E-08

(Table 28)
Term 17th surface coefficient 18th surface coefficient 19th surface coefficient c 0 0 0
C1 (k) 0 0 0
C3 (y) 3.7533966E-01 0 0
C4 (x ^ 2) -4.7703024E-02 -1.2440704E-02 -4.5700142E-03
C6 (y ^ 2) -6.3861131E-02 1.3120378E-02 3.3693285E-03
C8 (x ^ 2 * y) -2.1790974E-03 -2.7904567E-03 2.8592936E-04
C10 (y ^ 3) -4.8959686E-05 7.1676026E-04 8.2297418E-04
C11 (x ^ 4) -5.6218474E-05 2.9204157E-06 -5.1570559E-05
C13 (x ^ 2 * y ^ 2) -4.1824941E-06 -3.9243813E-04 -1.8943141E-04
C15 (y ^ 4) -1.2987500E-04 -1.9817071E-04 -1.0442241E-04
C17 (x ^ 4 * y) -2.3548255E-05 1.4038037E-06 -9.8364228E-06
C19 (x ^ 2 * y ^ 3) -4.2554587E-05 -1.1486751E-05 -1.5656531E-05
C21 (y ^ 5) -1.0489516E-05 2.1973996E-06 1.0288827E-06
C22 (x ^ 6) 8.7003975E-07 -2.8532031E-07 -4.5774516E-09
C24 (x ^ 4 * y ^ 2) -1.1754575E-06 -5.9531020E-07 -3.6363195E-07
C26 (x ^ 2 * y ^ 4) -1.6514636E-06 -2.8363526E-07 -6.0977479E-07
C28 (y ^ 6) -5.6885201E-07 4.0187914E-08 -6.5488911E-08
C30 (x ^ 6 * y) -1.4513914E-07 -5.4026724E-08 3.2591459E-08
C32 (x ^ 4 * y ^ 3) -1.6904333E-07 -1.2187787E-07 8.7205562E-08
C34 (x ^ 2 * y ^ 5) -1.9579896E-07 -7.2578748E-08 5.6190605E-09
C36 (y ^ 7) -5.7041513E-08 4.0822265E-08 4.2282473E-09
C37 (x ^ 8) 0 -5.2629522E-10 0
C39 (x ^ 6 * y ^ 2) 0 -1.1450586E-08 0
C41 (x ^ 4 * y ^ 4) 0 -2.3510642E-08 0
C43 (x ^ 2 * y ^ 6) 0 -8.5151144E-09 0
C45 (y ^ 8) 0 -2.1982753E-09 0

(Table 29)
Term 20th surface coefficient c 0
C1 (k) 0
C3 (y) 0
C4 (x ^ 2) 1.2535724E-02
C6 (y ^ 2) 4.0754809E-03
C8 (x ^ 2 * y) 4.2072496E-04
C10 (y ^ 3) 1.1618271E-04
C11 (x ^ 4) -5.5846671E-06
C13 (x ^ 2 * y ^ 2) 6.6536246E-06
C15 (y ^ 4) 8.1721322E-07
C17 (x ^ 4 * y) -3.3297935E-07
C19 (x ^ 2 * y ^ 3) 3.1563652E-08
C21 (y ^ 5) -1.2761657E-08
C22 (x ^ 6) -8.3506781E-10
C24 (x ^ 4 * y ^ 2) -9.9833763E-09
C26 (x ^ 2 * y ^ 4) 1.8319267E-10
C28 (y ^ 6) -1.9493518E-10
C30 (x ^ 6 * y) -3.2130471E-10
C32 (x ^ 4 * y ^ 3) -1.4774256E-10
C34 (x ^ 2 * y ^ 5) 2.0601390E-11
C36 (y ^ 7) 8.0970687E-14
C37 (x ^ 8) -2.7350270E-12
C39 (x ^ 6 * y ^ 2) -1.4367506E-11
C41 (x ^ 4 * y ^ 4) 5.0038842E-13
C43 (x ^ 2 * y ^ 6) -1.8888101E-13
C45 (y ^ 8) -6.7428035E-14
C47 (x ^ 8 * y) -6.9255343E-14
C49 (x ^ 6 * y ^ 3) -1.5679024E-13
C51 (x ^ 4 * y ^ 5) 2.3317504E-14
C53 (x ^ 2 * y ^ 7) -8.7565034E-15
C55 (y ^ 9) -1.2692483E-15

  The corresponding values for conditional expressions (1) to (3) are shown below.

Conditional expression (1) | h / (f × sin θ) | =
｜ 2.9976 ／ {14.7000 × sin (-11 °)} ｜ ＝ 1.069
Conditional expression (2) | {sin ⁻¹ (h / f)} / α | =
｜ {sin ^-1 (2.9976 / 14.7000)} / 59.2602 | = 0.199
Conditional expression (3) | TL / f | =
| 258.7739 / 14.7000 | = 17.604

Table 30 below shows the corresponding values for conditional expression (4). Regarding the xz cross section, since the free-form surface is axisymmetric with respect to the z axis, the description of the negative region of the x coordinate is omitted.

(Table 30)
(Second free-form surface lens L22: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.954802484
0 0.3576 0.956397837
0 0.5976 0.958657852
0 0.8376 0.961317102
0 1.0776 0.964133726
0 1.3176 0.966918469
0 1.5576 0.969542998
0 1.7976 0.971934116
0 2.0376 0.974061480
0 2.2776 0.975924338
0 2.5176 0.977540119
0 2.7576 0.978935806
0 2.9976 0.980141974
0 3.2376 0.981188980
0 3.4776 0.982104732
0 3.7176 0.982913555
0 3.9576 0.983635805
0 4.1976 0.984287930
0 4.4376 0.984882835
0 4.6776 0.985430385
0 4.9176 0.985937959
0 5.1576 0.986410996
0 5.3976 0.986853477
0 5.6376 0.987268326
0 5.8776 0.987657727

(Second free-form surface lens L22: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.980141974
0.32 2.9976 0.979940618
0.64 2.9976 0.979340624
0.96 2.9976 0.978354065
1.28 2.9976 0.977000490
1.6 2.9976 0.975306012
1.92 2.9976 0.973301876
2.24 2.9976 0.971022516
2.56 2.9976 0.968503092
2.88 2.9976 0.965776679
3.2 2.9976 0.962871339
3.52 2.9976 0.959807414
3.84 2.9976 0.956595315

(Third free-form curved lens L23: element yz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 0.1176 0.999166389
0 0.3576 0.999034687
0 0.5976 0.998899216
0 0.8376 0.998784532
0 1.0776 0.998714017
0 1.3176 0.998705886
0 1.5576 0.998769640
0 1.7976 0.998903879
0 2.0376 0.999095948
0 2.2776 0.999323487
0 2.5176 0.999557528
0 2.7576 0.999766562
0 2.9976 0.999920774
0 3.2376 0.999995697
0 3.4776 0.999974716
0 3.7176 0.999850094
0 3.9576 0.999622604
0 4.1976 0.999300075
0 4.4376 0.998895327
0 4.6776 0.998424079
0 4.9176 0.997903235
0 5.1576 0.997349945
0 5.3976 0.996781620
0 5.6376 0.996217148
0 5.8776 0.995679481

(Third free-form curved lens L23: element xz cross section)
Object position (x coordinate) Object position (y coordinate) Normal inner product (Nr1 / Nr2)
0 2.9976 0.999920774
0.32 2.9976 0.999889386
0.64 2.9976 0.999796173
0.96 2.9976 0.999643665
1.28 2.9976 0.999435107
1.6 2.9976 0.999173073
1.92 2.9976 0.998857747
2.24 2.9976 0.998485032
2.56 2.9976 0.998044733
2.88 2.9976 0.997519114
3.2 2.9976 0.996882114
3.52 2.9976 0.996099533
3.84 2.9976 0.995130408

  Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (4) are satisfied.

  FIGS. 27 to 30 are lateral aberration diagrams of the optical system PL for image projection apparatus according to the fifth example. From the aberration diagrams, it can be seen that in the fifth example, the lateral aberration is corrected satisfactorily at each point (object point) and has excellent optical performance.

As described above, according to each of the embodiments, it is possible to realize the optical system PL for the image projection apparatus and the image projection apparatus PRJ including the image projection apparatus optical system PL that can satisfactorily correct the trapezoidal distortion of the projected image while having a compact configuration. it can.

  In the above-described embodiment, the projection plane R (image plane I) is set on the same plane as the installation plane Q of the video projection device PRJ (housing BD). However, the present invention is not limited to this. You may make it set on the surface parallel to the installation surface Q.

PRJ image projection device DS image display element PL optical system for image projection device G1 reference projection lens group L11 first projection lens L12 second projection lens L13 third projection lens L14 fourth projection lens L15 fifth projection lens G2 free-form surface lens group L21 First free-form surface lens L22 Second free-form surface lens (element-side free-form surface lens)
L23 Third free-form surface lens (mirror-side free-form surface lens)
M Free-form curved mirror Q Installation surface

Claims (5)

An image projection apparatus comprising an image display element and an optical system for an image projection apparatus ,
It is used in a state where it is installed on a predetermined installation surface, and the image displayed on the image display element is enlarged and projected from an oblique direction on the same surface as the installation surface or a surface substantially parallel to the installation surface,
The optical system for the image projection device is:
A projection lens group consisting of projection lenses formed in a rotationally symmetric manner with respect to the central axis, arranged in order from the image display element side along the optical axis, and a plurality of freedoms formed in a rotationally symmetric manner with respect to the central axis A free-form surface lens group composed of a curved lens, and a free-form surface mirror having a reflecting surface formed non-rotationally symmetric with respect to the central axis,
It is possible to correct a trapezoidal distortion generated in an image projected on the projection surface by translating the image display element in a direction perpendicular to the optical axis from the projection lens group before being reflected by the free-form curved mirror. Has been
In the free-form surface lens group, a cross section including the optical axis in at least one of a mirror-side free-form surface lens closest to the free-form surface mirror and an element-side free-form surface lens arranged next to the mirror-side free-form surface lens Has a meniscus shape with a concave surface facing the image display element side,
The angle formed between the principal ray from the center of the image display element after being reflected by the free-form curved mirror and the optical axis is α, the distance from the optical axis to the center of the image display element is h, and the projection When the focal length of the lens group is f, the following expression 0.14 ≦ | {sin ⁻¹ (h / f)} / α | ≦ 0.20
Image projection equipment that satisfies the condition. An image projection apparatus comprising an image display element and an optical system for an image projection apparatus ,
It is used in a state where it is installed on a predetermined installation surface, and the image displayed on the image display element is enlarged and projected from an oblique direction on the same surface as the installation surface or a surface substantially parallel to the installation surface,
The optical system for the image projection device is:
A projection lens group consisting of projection lenses formed in a rotationally symmetric manner with respect to the central axis, arranged in order from the image display element side along the optical axis, and a plurality of freedoms formed in a rotationally symmetric manner with respect to the central axis A free-form surface lens group composed of a curved lens, and a free-form surface mirror having a reflecting surface formed non-rotationally symmetric with respect to the central axis,
It is possible to correct a trapezoidal distortion generated in an image projected on the projection surface by translating the image display element in a direction perpendicular to the optical axis from the projection lens group before being reflected by the free-form curved mirror. Has been
In the free-form surface lens group, a cross section including the optical axis in at least one of a mirror-side free-form surface lens closest to the free-form surface mirror and an element-side free-form surface lens arranged next to the mirror-side free-form surface lens Has a meniscus shape with a concave surface facing the image display element side,
When the focal length of the projection lens group is f and the total length of the optical system for the image projection apparatus is TL, the following expression 15 ≦ | TL / f | ≦ 20
Image projection equipment that satisfies the condition. Image projection equipment according to claim 1 or claim 2, characterized in that the center axis of the free-form surface lens is inclined with respect to the optical axis. When the inclination angle of the central axis of the free-form surface lens group with respect to the optical axis is θ, the distance from the optical axis to the center of the image display element is h, and the focal length of the projection lens group is f, Formula 0.7 ≦ | h / (f × sin θ) | ≦ 1.5
Image projection equipment according to claim 3, characterized by satisfying the condition. In the free-form surface lens group, at least one of the cross-sectional shapes of the mirror-side free-form surface lens closest to the free-form surface mirror and the element-side free-form surface lens arranged next to the mirror-side free-form surface lens is the projection In the first cross section passing through the optical axis from the lens group before being reflected by the free-form curved mirror and the optical axis after being reflected by the free-form curved mirror, or a second cross section perpendicular to the first cross section, It has a meniscus shape with a concave surface facing the image display element side,
The coordinate axis in the optical axis direction from the projection lens group before being reflected by the free-form curved mirror is the z axis, the coordinate axis perpendicular to the z axis along the first cross section is the y axis, and the z axis and the The coordinate axis perpendicular to the y axis is the x axis,
In the free-form surface lens having the meniscus shape among the mirror-side free-form surface lens and the element-side free-form surface lens, a straight line passing through the center of the element on the display surface of the video display element and parallel to the y-axis or the x-axis The normal vector of the lens surface at the intersection of the principal ray emitted from above and the lens surface on the image display element side is Nr1, and the lens surface at the intersection of the principal ray and the lens surface on the free-form surface mirror side When the normal vector is Nr2, the inner product of the Nr1 and the Nr2 is expressed by the following formula: 0.9 ≦ Nr1 · Nr2 <1
Image projection equipment according to any one of claims 1 to 4, characterized by satisfying the condition.

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