JP5834622B2 - Optical system for image projection device and image projection device - Google Patents

Description

The present invention relates to an optical system for a video projection device and a video projection device.

An image projection device (so-called projector) that projects an image of an image display element in an enlarged manner,
Several schemes have been devised and put into practical use. 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. Further, in the case of the oblique projection method as described above, since the installation position is likely to be limited, improvement in ease of use such as mounting a simple image plane adjustment mechanism (for example, a focusing mechanism) is also required.

The present invention has been made in view of such problems, and has an optical system for a video projection apparatus that has a focusing function and can satisfactorily correct trapezoidal distortion of a projected image, while having a compact configuration. An object of the present invention is to provide an image projection apparatus including the same.

In order to achieve such an object, according to an aspect of the present invention, an optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction, A rotationally symmetric lens group composed of a plurality of rotationally symmetric lenses formed in rotational symmetry with respect to the optical axis , arranged in order from the image display element side along the optical axis , and non-rotationally symmetric with respect to the optical axis . A free-form surface lens group formed of a plurality of free-form surface lenses, and a free-form surface mirror having a reflection surface formed non-rotationally symmetric with respect to the optical axis , and at least two of the free-form surface lens groups When moved in parallel along the free-form surface lens, respectively the optical axis, translated along the image plane is the optical axis, the free-form surface lens group includes a mirror nearest side free curved lens in the free-form surface mirror Each of the three free-form surface lenses, with respect to a light beam emitted from an arbitrary object point in the image display element, in order from the image display element side, positive refractive power, negative refractive power, and A normal vector with respect to the lens surface at a position where the principal ray emitted from the arbitrary object point is incident on the lens surface on the image display element side in the mirror-side free-form surface lens is Nr1. When the normal vector for the lens surface at the position where the principal ray exits from the lens surface on the free-form surface mirror side of the mirror-side free-form surface lens is Nr2, the inner product of Nr1 and Nr2 is
0.85 ≦ Nr1 ・ Nr2 <1.00
An optical system for an image projection apparatus is provided that satisfies the above condition .
According to another aspect of the present invention, there is provided an optical system for a video projection apparatus that enlarges an image displayed on the video display element and projects the image on a predetermined projection surface from an oblique direction, the optical system being configured along an optical axis. A rotationally symmetric lens group composed of a plurality of rotationally symmetric lenses formed in rotational symmetry with respect to the optical axis and a plurality of free lenses formed in a non-rotational symmetry with respect to the optical axis, arranged in order from the image display element side. 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 optical axis, and each of at least two free-form surface lenses in the free-form surface lens group When translated along the optical axis, the image plane translates along the optical axis, and the free-form surface lens group includes three free-form surface lenses including a mirror-side free-form surface lens closest to the free-form surface mirror. Each of the three free-form surface lenses is along the optical axis having a meniscus shape with a concave surface facing the image display element side with respect to a light bundle emitted from an arbitrary object point in the image display element. The reflecting surface of the free-form surface mirror has a shape with a convex surface facing the image display element side, and the principal ray emitted from the arbitrary object point is the image on the mirror-side free-form surface lens. A normal vector for the lens surface at a position incident on the lens surface on the display element side is Nr1, and the principal ray is emitted from the lens surface on the free curved mirror side of the mirror side free curved lens. When the normal vector for the surface is Nr2, the inner product of Nr1 and Nr2 is
0.85 ≦ Nr1 ・ Nr2 <1.00
An optical system for an image projection apparatus is provided that satisfies the above condition.

Further, according to an aspect of the present invention, the image is projected from an oblique direction on a surface that is used on a predetermined installation surface and is substantially the same as the installation surface or substantially parallel to the installation surface. There is provided an image projection apparatus, wherein the optical system constituting the image projection apparatus is the optical system for an image projection apparatus according to the present invention.

According to the present invention, the trapezoidal distortion of a projected image can be satisfactorily corrected while having a focusing function while having a compact configuration.

It is a yz cross-section optical path figure in the reference | standard position of the optical system for image projection apparatuses which concerns on 1st Example. FIG. 3 is an xz cross-sectional optical path diagram at a reference position of the optical system for the image projection apparatus according to the first example. FIG. 6 is a first lateral aberration diagram at the reference position of the optical system for the video projector according to the first example. FIG. 6 is a second lateral aberration diagram at the reference position of the optical system for the video projector according to Example 1. It is a distortion aberration figure in the standard position of the optical system for image projection devices concerning the 1st example. It is a yz cross-section optical path figure in the intermediate position of the optical system for image projection apparatuses which concerns on 1st Example. It is a xz section optical path figure in the middle position of the optical system for picture projection devices concerning the 1st example. FIG. 6 is a first lateral aberration diagram at an intermediate position of the optical system for the image projection device according to Example 1. It is a 2nd lateral aberration figure in the middle position of the optical system for image projection devices concerning the 1st example. It is a distortion aberration figure in the intermediate position of the optical system for video projection devices concerning the 1st example. It is a yz cross-section optical path figure in the maximum expansion position of the optical system for image projection apparatuses which concerns on 1st Example. It is an xz section optical path figure in the maximum expansion position of the optical system for image projection devices concerning the 1st example. FIG. 6 is a first lateral aberration diagram at the maximum magnification position of the optical system for a video projector according to the first example. It is a 2nd lateral aberration figure in the maximum expansion position of the optical system for image projectors concerning the 1st example. It is a distortion aberration figure in the maximum expansion position of the optical system for image projection apparatuses which concerns on 1st Example. It is a yz cross-section optical path figure in the reference position of the optical system for image projection apparatuses which concerns on 2nd Example. It is a xz section optical path figure in the standard position of the optical system for image projection devices concerning the 2nd example. It is a 1st lateral aberration figure in the standard position of the optical system for image projection devices concerning the 2nd example. It is a 2nd lateral aberration figure in the standard position of the optical system for image projection devices concerning the 2nd example. It is a distortion aberration figure in the standard position of the optical system for image projection devices concerning the 2nd example. It is a yz cross-section optical path figure in the intermediate position of the optical system for image projection apparatuses which concerns on 2nd Example. It is a xz section optical path figure in the middle position of the optical system for image projection devices concerning the 2nd example. It is a 1st lateral aberration figure in the intermediate position of the optical system for image projection apparatuses concerning the 2nd example. It is a 2nd lateral aberration figure in the middle position of the optical system for image projection devices concerning the 2nd example. It is a distortion aberration figure in the intermediate position of the optical system for image projection apparatuses which concerns on 2nd Example. It is a yz cross-section optical path figure in the maximum expansion position of the optical system for image projection apparatuses which concerns on 2nd Example. It is an xz section optical path figure in the maximum expansion position of the optical system for image projection devices concerning the 2nd example. It is a 1st lateral aberration figure in the maximum expansion position of the optical system for image projection apparatuses concerning 2nd Example. It is a 2nd lateral aberration figure in the maximum expansion position of the optical system for image projection apparatuses concerning 2nd Example. It is a distortion aberration figure in the maximum expansion position of the optical system for video projectors concerning the 2nd example. It is a yz cross-section optical path figure in the reference position of the optical system for image projection apparatuses which concerns on 3rd Example. It is an xz section optical path figure in the standard position of the optical system for image projection devices concerning the 3rd example. It is a 1st lateral aberration figure in the standard position of the optical system for image projection apparatuses concerning the 3rd example. It is a 2nd lateral aberration figure in the standard position of the optical system for image projection devices concerning the 3rd example. It is a distortion aberration figure in the reference position of the optical system for image projection apparatuses concerning the 3rd example. It is a yz cross-section optical path figure in the intermediate position of the optical system for image projection apparatuses which concerns on 3rd Example. It is a xz section optical path figure in the middle position of the optical system for image projection devices concerning the 3rd example. It is a 1st lateral aberration figure in the middle position of the optical system for image projection apparatuses concerning the 3rd example. It is a 2nd lateral aberration figure in the middle position of the optical system for image projection devices concerning the 3rd example. It is a distortion aberration figure in the intermediate position of the optical system for video projectors concerning the 3rd example. It is a yz cross-section optical path figure in the maximum expansion position of the optical system for video projectors concerning 3rd Example. It is an xz section optical path figure in the maximum expansion position of the optical system for image projection devices concerning the 3rd example. It is a 1st lateral aberration figure in the maximum expansion position of the optical system for image projection apparatuses concerning 3rd Example. It is the 2nd lateral aberration figure in the maximum expansion position of the optical system for image projection devices concerning the 3rd example. It is a distortion aberration figure in the maximum expansion position of the optical system for image projection apparatuses which concerns on 3rd Example. It is a perspective view of a video projection device. It is a schematic diagram which shows the inside of a video projector. It is explanatory drawing which shows an example of a local coordinate system.

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 this embodiment, information such as the position, shape, and ray position of each lens surface is not represented by a single representative coordinate system, but the right-handed system xy is used as a coordinate system unique to each lens surface.
Z orthogonal coordinates (hereinafter referred to as a local coordinate system: see, for example, FIG. 48) are arranged, and the information is shared between adjacent (front and back) 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, in the cross section (plane) passing through the optical axis before and after reflection by the free-form surface mirror M, the coordinate axis in the central axis direction with the direction from the image display element DS toward the free-form surface mirror M being positive is the z-axis. The coordinate axis perpendicular to the z axis is the y axis, and the coordinate axis perpendicular to the z axis and the y axis is the x axis. However, the z axis does not necessarily have to be parallel to the central axis. As 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 lens group G1 coming out of the object plane (the 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 rotationally symmetric 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, it is assumed that 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, an image projection apparatus PRJ of this embodiment is shown in FIGS. In addition,
46 is a perspective view of the image projection device PRJ, and FIG. 47 is a schematic diagram showing the inside of the image projection device PRJ. 46 and 47, the image projection apparatus PRJ includes a cylindrical box-shaped housing BD having a window W on the front surface, an image display element DS accommodated in each of the housings BD, and an image projection. And an apparatus optical system PL. Such a video projection device PRJ
For example, it 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 image display element via a polarizing prism. After being incident on the DS, the image (light) obtained by being reflected by the image display element DS,
For details, the image projection device PRJ (via the image projection device optical system PL and the window W, which will be described later, is provided.
The projection screen R is configured to be enlarged and projected from an oblique direction on a projection surface R set on the same (or parallel) surface as the installation surface Q of the housing BD).

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 rotationally symmetric lens group G1 composed of a plurality of rotationally symmetric lenses formed in a rotationally symmetric manner with respect to the central axis, arranged in order from the video display element DS side along the optical axis, A free-form surface lens group G2 composed of a plurality of free-form surface lenses formed non-rotationally symmetric with respect to the axis, and a free-form surface mirror M having a reflection surface formed non-rotationally symmetric with respect to the central axis Composed. In such an image projection apparatus optical system PL, the light emitted from the image display element DS is transmitted through the rotationally symmetric 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, when at least two free-form surface lenses in the free-form surface lens group G2 are translated along the optical axis, the image plane translates along the optical axis. It is like that. Note that at least two free-form surface lenses in the free-form surface lens group G2 are configured to be able to translate independently along the optical axis using a focusing mechanism (not shown).

By combining the oblique projection format and the free-form surface, the trapezoidal distortion caused by the oblique projection can be corrected by the free-form surface, so that the entire optical system can be configured very compactly. Also, by moving at least two free-form surface lenses in the free-form surface lens group G2 along the optical axis, it is possible to obtain good focusing performance without enlarging the size of the optical system. If the above conditions are not satisfied, it becomes very difficult to propose an optical system having a small size and good focusing performance, which is not preferable.

In addition, when at least two free-form surface lenses in the free-form surface lens group G2 are translated along the optical axis, the image plane translates along the optical axis and the size of the image plane changes. May be. Thereby, it is possible not only to have a focusing function but also to adjust the size of the image plane.

The free-form surface lens group G2 includes three free-form surface lenses that are arranged in positive, negative, and positive power in order from the image display element DS side with respect to a light beam emitted from an arbitrary object point in the image display element DS. Consists of Each of these three free-form surface lenses has a cross section along the optical axis having a meniscus shape with a concave surface facing the image display element DS with respect to a light bundle emitted from an arbitrary object point in the image display element DS (for example, X-z cross section including the optical axis). Note that the xz cross section and the yz 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 such a free-form surface lens, on the lens surfaces on both sides of the mirror-side free-form surface lens closest to the free-form surface mirror M, a principal ray having a certain angle of view (emitted from an arbitrary object point) is an image on the mirror-side free-form surface lens. The normal vector for the lens surface at the position incident on the lens surface on the display element DS side is Nr1, and the lens at the position where this principal ray is emitted from the lens surface on the free-form mirror M side of the mirror-side free-form surface lens. When the normal vector to the surface is Nr2, it is preferable that the inner product of Nr1 and Nr2 satisfies the following conditional expression (1).

  0.85 ≦ Nr1 · Nr2 <1.00 (1)

In the optical system of the present embodiment, focusing is performed by individually moving a part of the free-form surface lens group along the optical axis. At this time, as a first condition, if the power arrangement of each free-form surface lens is a positive, negative, positive power arrangement in order from the image display element DS side,
For example, the magnification of the image can be changed by moving the middle negative lens, and the image can be formed at a desired position by moving the positive lens on the mirror side.

As a second condition, the cross-sectional shape of all free-form surface lenses in an arbitrary direction is a meniscus shape with the concave surface facing the image display element DS, and the shape of the free-form surface mirror M in the cross-section is an image. If a convex mirror having a convex surface facing the display element DS is used, for example, a free-form surface lens group G
By changing the magnification by changing the distance between 2 and the free-form surface mirror M, and further moving the individual free-form surface lenses, it is possible to form an image at a desired position. Furthermore, a lens shape combining the first condition and the second condition described above (for example, a cross section of a free-form surface lens is a cross-sectional shape that satisfies the first condition, and another cross section is a second condition. It is more preferable that focusing can be performed more efficiently.

Further, when focusing is performed by the free-form surface lens group G2, these free-form surface lenses must have some power, and the problem of chromatic aberration cannot be ignored.
However, if the lens configuration has a positive, negative, and positive power arrangement as in the first condition, a certain degree of chromatic aberration correction can be achieved by appropriately distributing the power. In addition, as in the second condition, the mirror surface (reflective surface) of the free-form surface mirror M that does not generate chromatic aberration with a load of magnification.
Therefore, the occurrence of chromatic aberration can be minimized by making the shape of the free-form surface lens into a meniscus shape that does not have much power with respect to light rays of each angle of view.

By satisfying conditional expression (1) above in addition to the above conditions, it becomes possible to correct trapezoidal distortion and light aberration in a very good state while having a focusing function.
When correcting a rotationally asymmetric trapezoidal distortion on a free-form surface, the free-form surface itself has a rotationally asymmetric shape, and rotationally asymmetric aberration occurs on this surface. For this reason, the free-form surface lens group G2 must suppress the generation of rotationally asymmetric aberrations as much as possible while correcting trapezoidal distortion. The above conditions are for satisfying this.

Since the optical system of the present embodiment is an enlarged projection, the principal ray emitted from each point of the image display element DS becomes a divergent ray after passing (transmitting) through the rotationally symmetric lens group G1 and the aperture stop S immediately after it. . At this time, if the mirror-side free-form surface lens satisfies the conditional expression (1), the difference between the light beam angle before passing through the lens and the light beam angle after passing through the lens must be reduced (assuming that the conditional expression (
When the value of 1) is “1”, the free-form surface is equivalent to a parallel plane plate for the principal ray, and it moves in parallel but does not bend. Thus, it is possible to efficiently bend the light beam while suppressing the occurrence of aberrations (including rotationally asymmetric components). Further, when the conditional expression (1) is satisfied, the lens shape is inevitably a meniscus shape, so that the non-rotationally symmetric aberration generated on the first surface (lens front surface) is reduced to the next surface (
The lens can be canceled immediately at the rear surface of the lens, and the trapezoidal distortion can be corrected efficiently while suppressing the occurrence of non-rotationally symmetric aberration. If the conditional expression (1) is not satisfied, non-rotationally symmetric aberration occurs when correcting the trapezoidal distortion on the free-form surface. In particular, the optical system is downsized while having the focusing function. Sometimes, it is very difficult to correct aberrations when all aberrations must be corrected well at short distances and at many positions.

If the following conditional expression (1-1) is satisfied instead of the above conditional expression (1), the trapezoidal distortion and the light aberration can be corrected more efficiently, and compatibility with the focusing function is further facilitated. It becomes.

  0.90 ≦ Nr1 · Nr2 <1.00 (1-1)

The free-form surface lens that performs focusing in the free-form surface lens group G2 is a mirror-side free-form surface lens closest to the free-form surface mirror M and an element-side free-form surface lens arranged next to the mirror-side free-form surface lens. Is desirable. As described above, by simplifying the portion to be focused as much as possible, it is possible to contribute to downsizing, cost reduction, and manufacturing tolerance reduction of the apparatus.

Further, the length of the range in which the mirror-side free-form surface lens can be translated (that is, the absolute value of the maximum movement amount of the mirror-side free-form surface lens with respect to the lens position at the reference position) is X, and the element-side free-form surface lens is parallel. When the length of the movable range (that is, the absolute value of the maximum movement amount of the element-side free-form surface lens with respect to the lens position at the reference position) is Y, the condition represented by the following conditional expression (2) is satisfied. It is desirable to be satisfied. The reference position is the arrangement of the optical system when the image plane is the smallest.

  7 ≦ X / Y ≦ 10 (2)

Conditional expression (2) shows the relationship between the amount of movement X of the mirror-side free-form surface lens that mainly performs focusing and the amount of movement Y of the element-side free-form surface lens that mainly changes the magnification when performing focusing. It is a thing. When the condition is less than the lower limit of conditional expression (2), the amount of movement of the lens that performs focusing is insufficient, so that it is possible to sufficiently correct the focus shift and aberration caused by the movement of the lens that changes the magnification. It is not preferable. On the other hand, when the condition exceeds the upper limit value of the conditional expression (2), the moving amount of the lens for focusing is too large with respect to the moving amount of the lens for changing the magnification. Correction of focus shift and aberration caused by movement becomes excessive. Further, both lenses may be too close to each other depending on the focusing position, which is not preferable because it causes a problem in manufacturing.

If the following conditional expression (2-1) is satisfied instead of the above conditional expression (2), the movement ratio of the two lenses is optimized, and focusing can be performed more efficiently. .
It is also desirable because it can avoid manufacturing problems such as the possibility of contact between both lenses.

  7.4 ≦ X / Y ≦ 9.4 (2-1)

Further, when the size of the image plane changes when focusing is performed, the focal length of the rotationally symmetric lens group G1 is set to f, and the area ratio of the maximum area to the minimum area of the image plane when the size of the image plane changes is When M, it is desirable to satisfy the condition represented by the following conditional expression (3). In addition,
When the image area at the reference position is 1, the maximum magnification of the image area by focusing is M.

  15 ≦ M × f ≦ 35 (3)

Conditional expression (3) shows the relationship between the power of the rotationally symmetric lens group G1 and the maximum magnification by focusing. In the case of a condition that falls below the lower limit value of conditional expression (3), it is necessary to shorten the focal length (increase the lens power) in order to sufficiently obtain the amount of change in the image plane magnification due to focusing, and the size of the optical system is reduced. Is advantageous. However, it is difficult to correct the aberration (astigmatism and the like) generated in the rotationally symmetric lens group G1 associated therewith, which leads to insufficient trapezoidal distortion correction and poor resolution performance as a whole. On the other hand, the condition exceeding the upper limit value of the conditional expression (3) is not preferable because the balance between the power of the rotationally symmetric lens group G1 and the enlargement magnification due to focusing is lost, and it is particularly difficult to downsize the optical system.

If the following conditional expression (3-1) is satisfied instead of the above conditional expression (3), the balance between the power of the rotationally symmetric lens group G1 and the enlargement magnification by focusing can be kept optimal. It becomes easy to achieve both good focusing performance and downsizing.

  20 ≦ M × f ≦ 30 (3-1)

The length of the free-form surface lens group G2 on the optical axis is L, the thickness of the mirror-side free-form surface lens on the optical axis is FLe, and the thickness of the element-side free-form surface lens on the optical axis is FLm. In this case, it is desirable to satisfy the condition represented by the following conditional expression (4). The length L on the optical axis of the free-form surface lens group G2 is the distance on the optical axis from the lens surface closest to the image display element DS to the lens surface closest to the free-form surface mirror M in the free-form surface lens group G2. It is.

  {L- (FLe + FLm)} / L ≦ 0.6 (4)

Conditional expression (4) is for minimizing the deterioration in image forming performance during focusing by suppressing the amount of aberration generated by the two free-form surface lenses that move during focusing. When the optical system satisfies the conditional expression (4), the thickness of the free-form surface lens that moves during focusing is sufficiently secured, so that the light beam can be bent gently. Therefore, the generation amount of various aberrations including chromatic aberration is suppressed, and the control thereof is facilitated. Therefore, these lenses can be provided with sufficient performance as a focusing lens. When the condition exceeds the upper limit value of conditional expression (4), the thickness of the free-form surface lens that moves during focusing is not sufficiently secured, and it is necessary to bend the light beam suddenly at each lens surface. For this reason, a large amount of aberration occurs and it is difficult to control the aberration, which is not preferable as a focusing lens. This is particularly a problem when the optical system is downsized.

If the following conditional expression (4-1) is satisfied instead of the above conditional expression (4), the thickness of the free-form surface lens that moves during focusing becomes an optimum value, and these lenses serve as focusing lenses. This is desirable because it provides better performance.

  0.45 ≦ {L− (FLe + FLm)} / L ≦ 0.55 (4-1)

Further, when the focal length of the rotationally symmetric lens group G1 is f and the total length of the image projection apparatus optical system PL is TL, the condition expressed by the following conditional expression (5) is satisfied at any focusing position. It is desirable. 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 video display element surface to the image plane (imaging plane).

  19 ≦ TL / f ≦ 28 (5)

Conditional expression (5) is for making an appropriate balance between the size of the optical system and the power of the rotationally symmetric lens group G1. When the condition is less than the lower limit value of the conditional expression (5), the focal length of the rotationally symmetric lens group G1 becomes longer, so that the property of the rotationally symmetric lens group G1 becomes a telephoto type, and the maximum field angle of the principal ray becomes smaller. This is advantageous for making the entire optical system compact in the xy section, but the back focus is extended at each focusing position due to insufficient power of the rotationally symmetric 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 (the rotationally symmetric 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 (5), the focal length of the rotationally symmetric lens group G1 is shortened so that the property of the rotationally symmetric lens group G1 becomes a wide-angle type, and the maximum angle of view of the principal ray increases. . For this reason, the xy cross-sectional area of the optical system increases, leading to an increase in the size of the apparatus, which is not preferable. In addition to this, the back focus becomes too short at each focusing position, so the free-form surface lens group must have a large negative power to extend it, and as in the case above, trapezoidal distortion correction and aberration correction Should be avoided as it becomes difficult to do at the same time.

If the following conditional expression (5-1) is satisfied instead of the conditional expression (5), the balance between the size of the optical system and the power of the rotationally symmetric lens group G1 is made closer to an appropriate balance. Therefore, it becomes easy to achieve both the miniaturization of the optical system and the imaging performance of the optical system.

  20 ≦ TL / f ≦ 27.5 (5-1)

As described above, according to the present embodiment, the optical system PL for an image projection apparatus that has a focusing function and can satisfactorily correct trapezoidal distortion of a projected image, and a compact configuration thereof, and this Can be obtained.

In the above conditional expression (1), if the 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), A normal vector N at an arbitrary point P (a, b) on the curved surface is given by the following equation (6).

Also, φ in the above equation (6) is for normalizing the vector and is given by the following equation (7).

Embodiments of the present application will be described below with reference to the accompanying drawings. In each embodiment, the optical axis (center axis)
And a free-form surface that is rotationally symmetric with respect to the central axis.
Therefore, before describing each embodiment, these defining formulas will be described.

First, an aspherical surface that is rotationally symmetric with respect to the optical axis (center axis) is defined by the following equation (8). In the following equation (8), 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 (9). In the following equation (9), Z is the sag amount of the surface parallel to the central axis, and c is the surface vertex (origin).
K is the conic constant, h is the distance from the origin in the plane perpendicular to this at the origin on the central axis, and Cj is the coefficient of the xy polynomial. Further, in the following equation (9), 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 equations (10) and (11) is established between j, m, and n in equation (9).

(First embodiment)
1st Example of this application is described using FIGS. 1-15 and Table 1-Table 7. FIG. FIG. 1 is a yz sectional optical path diagram at the reference position of the optical system for image projection apparatus according to the first embodiment, and FIG. 2 is an xz sectional optical path diagram at the reference position of the optical system for image projection apparatus. In addition,
In each of the following embodiments, the arrangement of the optical system when the size of the image plane is the smallest is referred to as the reference position, and the arrangement of the optical system when the size of the image plane is the largest is referred to as the maximum magnification position. The arrangement of the optical system in the middle of the maximum magnification position is referred to as an intermediate position. FIG. 6 is a yz sectional optical path diagram at an intermediate position of the optical system for an image projection apparatus, and FIG. 7 is an xz sectional optical path diagram at an intermediate position of the optical system for an image projection apparatus. FIG. 11 is a yz sectional optical path diagram at the maximum magnification position of the optical system for the image projection apparatus, and FIG. 12 is an xz sectional optical path diagram at the maximum magnification position of the optical system for the image projection apparatus.

The optical system PL for image projection apparatus according to the first example is arranged in order from the image display element DS side along the optical axis, and a plurality of rotationally symmetric lenses L11 to L14 formed in rotational symmetry with respect to the central axis.
A rotationally symmetric lens group G1, and a free-form surface lens group G2 composed of a plurality of free-form surface lenses L21 to L23 formed in a non-rotationally symmetric manner with respect to the center axis, and formed in a non-rotationally symmetric manner with respect to the center axis. And a free-form surface mirror M having a reflecting surface. Two parallel flat plates are arranged between the display surface (element surface) of the video display element DS and the rotationally symmetric lens group G1, and this parallel flat plate has a video display element on the video display element DS side. DS cover glass CV
The image side is a prism P (PBS: polarization beam splitter) that reflects S-polarized light and transmits P-polarized light. A stop S is disposed between the rotationally symmetric lens group G1 and the free-form surface lens group G2.

The rotationally symmetric lens group G1 is arranged in order from the image display element DS side along the optical axis, a biconvex first rotationally symmetric lens L11, a second rotationally symmetric lens L12 having a convex surface facing the element side, and an image. The lens includes a third rotationally symmetric lens L13 having a concave surface on the side, and a fourth rotationally symmetric lens L14 that is a meniscus lens having a convex surface on the image side. The element-side lens surface of the second rotationally symmetric lens L12, the image-side lens surface of the third rotationally symmetric lens L13, and the image-side lens surface of the fourth rotationally symmetric lens L14 are aspherical surfaces. Further, the second rotationally symmetric lens L12 and the third rotationally symmetric lens L13 are bonded lenses.

The free-form surface lens group G2 is a first free-form surface lens L arranged in order from the image display element DS side.
21, a second free-form surface lens L22, and a third free-form surface lens L23.
The yz section and xz in the second free-form surface lens L22 and the third free-form surface lens L23
The cross section has a meniscus shape with a concave surface facing the element side.

Regarding 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 +34 degrees in the yz plane with the coordinate origin as the center with respect to the optical axis.
Similarly, the z axis (normal line) of the image plane I is −5 with respect to the optical axis reflected by the free-form surface mirror M.
Since the optical system is inclined by 8 degrees, the optical system is inclined by 10 degrees with respect to the image plane I as a whole. 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 0.2174, and the size of the image display element DS is 7.52 mm × 5.64 mm. The projection size is A4 size (297 mm × 210 mm) to A3 size (420 mm × 297 mm), the enlargement magnification is about 37 times to about 52 times, and the image area ratio M is M = (A3 size area / A4
Size area) = 2. The focal length f of the entire rotationally symmetric lens group G1 is 1
4.509 mm.

Table 1 below shows numerical data of the optical system PL for image projection apparatus according to the first example. In addition,
In the tables (numerical data of optical systems) shown in the following examples, “* a” described therein is used.
"Represents that the surface is a rotationally symmetric aspheric surface, and" * f "represents that the surface is a non-rotationally symmetric free-form surface. Further, the surface intervals D1 to D4 in Table 1 are the surface intervals that change during focusing.

(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 12.00000 1.51680 / 64.2
3 Plane 2.78289
4 10.26354 5.23663 1.48563 / 85.2
5 -35.89695 0.95928
6 * a 8.82752 4.25466 1.77200 / 50.0
7 -1298.50570 2.00001 1.72250 / 29.2
8 * a 4.65625 2.72881
9 -8.97081 2.61795 1.59170 / 60.7
10 * a -5.35597 0.20000
11 (Aperture) Plane 2.02048
12 * f xy polynomial surface 2.50000 1.53113 / 55.7
13 * f xy polynomial surface (D1)
14 * f xy polynomial surface 5.99389 1.53113 / 55.7
15 * f xy polynomial surface (D2)
16 * f xy polynomial surface 6.50000 1.53113 / 55.7
17 * f xy polynomial surface (D3)
18 * f xy polynomial surface (D4) Reflection Image plane Plane

In Table 1, the fourth surface to the tenth surface are lens surfaces of the rotationally symmetric rotationally symmetric lens group G1, and among them, the sixth surface, the eighth surface, and the tenth surface are rotationally symmetric aspheric surfaces. . In Table 2 below,
The aspherical coefficients of the sixth surface, the eighth surface, and the tenth surface are respectively shown.

(Table 2)
Term 6th surface coefficient 8th surface coefficient
r (curvature radius) 8.8275240 4.6562474
k -0.6794540 0
A (4th) -1.6580140E-04 4.3157337E-05
B (6th) -3.0761392E-06 -8.6364580E-06
C (8th) -2.1198967E-07 -2.6557814E-06
D (10th) 4.5478226E-09 2.3527679E-07
E (12th order) -9.5013552E-11 0

Term 10th surface coefficient
r (radius of curvature) -5.3559736
k 0
A (4th) 8.6067885E-04
B (6th) -2.2156964E-05
C (8th) 1.8705602E-07
D (10th) -1.2930366E-08
E (12th) -1.5886018E-09

In Table 1, the 12th to 18th surfaces are non-rotationally symmetric free-form surfaces. In this embodiment, the eighteenth 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 12th surface coefficient 13th surface coefficient 14th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 0.0000000E + 00 0.0000000E + 00 -1.1878133E-02
C4 (x ² ) -4.8753129E-02 -7.2284799E-02 -3.5983529E-02
C6 (y ² ) -1.5323795E-02 -5.8699828E-02 -2.1855722E-02
C8 (x ² y) 1.9519724E-03 1.3932029E-03 -6.5060134E-03
C10 (y ³ ) 2.2597778E-03 1.2125649E-03 -8.4754865E-03
C11 (x ⁴ ) 1.1500387E-03 2.2216942E-04 4.2882514E-05
C13 (x ² y ² ) 2.2451110E-03 5.6664028E-04 1.5173686E-04
C15 (y ⁴ ) 1.2747926E-03 4.7315215E-04 -3.2018351E-04
C17 (x ⁴ y) 2.0655009E-05 -5.3111911E-06 -3.6186400E-05
C19 (x ² y ³ ) 9.4122315E-05 1.4650238E-04 3.1670389E-04
C21 (y ⁵ ) 5.2184171E-05 9.9698153E-05 2.4879271E-04
C22 (x ⁶ ) -5.1965636E-05 -1.3881796E-05 8.1207661E-06
C24 (x ⁴ y ² ) -1.4972992E-04 -5.2654793E-05 -1.5352041E-05
C26 (x ² y ⁴ ) -1.4325986E-04 -5.2636673E-05 -1.9595555E-05
C28 (y ⁶ ) -4.6021350E-05 -2.2076244E-05 -1.2619721E-05
C30 (x ⁶ y) 2.7978958E-06 2.0410529E-06 9.6052038E-07
C32 (x ⁴ y ³ ) 6.2109480E-06 4.4767377E-06 -3.0913650E-06
C34 (x ² y ⁵ ) 8.5178641E-06 3.5384629E-06 -1.3226712E-05
C36 (y ⁷ ) 2.6942811E-06 4.2871783E-07 -8.7554738E-06
C37 (x ⁸ ) 1.2360133E-06 5.5563947E-07 2.2953209E-07
C39 (x ⁶ y ² ) 5.0140563E-06 2.1988374E-06 5.5619869E-07
C41 (x ⁴ y ⁴ ) 7.1581722E-06 2.7028827E-06 3.6574280E-07
C43 (x ² y ⁶ ) 5.8020347E-06 2.8427366E-06 -1.5965125E-07
C45 (y ⁸ ) 1.0368509E-06 4.5550188E-07 -8.2971928E-07
C47 (x ⁸ y) -1.2743765E-07 -4.9957062E-08 9.8043753E-10
C49 (x ⁶ y ³ ) 1.2572352E-07 2.4687834E-08 -3.5038922E-08
C51 (x ⁴ y ⁵ ) 6.3445722E-07 4.2636935E-07 1.8691555E-07
C53 (x ² y ⁷ ) 3.2752800E-07 4.0760185E-07 6.0548650E-07
C55 (y ⁹ ) 6.6879906E-08 6.6935075E-08 1.8532687E-07
C56 (x ¹⁰ ) -5.1330500E-09 -4.7074519E-09 -7.3337126E-09
C58 (x ⁸ y ² ) -1.7023850E-07 -1.0311878E-07 -2.7797573E-08
C60 (x ⁶ y ⁴ ) -4.2317903E-07 -2.3031545E-07 -4.4827024E-08
C62 (x ⁴ y ⁶ ) -4.8504868E-07 -2.1339742E-07 6.7198700E-09
C64 (x ² y ⁸ ) -2.8016277E-07 -1.1109973E-07 8.5254261E-08
C66 (y ¹⁰ ) -4.2546887E-08 -1.6275011E-08 4.0461349E-08

(Table 4)
Term 15th surface coefficient 16th surface coefficient 17th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 1.3841104E-01 1.7604824E-01 2.9956361E-02
C4 (x ² ) -9.4152682E-03 -2.2201665E-02 -2.2646548E-02
C6 (y ² ) 6.0772699E-02 -2.8650816E-02 -3.4948327E-02
C8 (x ² y) -8.3653728E-03 -6.3257036E-04 -5.1117325E-04
C10 (y ³ ) -1.2476190E-02 3.5102441E-04 -1.0112292E-04
C11 (x ⁴ ) -8.7357536E-05 -1.0610384E-04 -3.3800888E-05
C13 (x ² y ² ) 2.4756423E-04 -3.4562884E-04 -1.8823876E-04
C15 (y ⁴ ) -1.2955250E-07 -3.6840282E-04 -2.0398511E-04
C17 (x ⁴ y) 6.7388562E-06 1.1598170E-05 8.7307215E-06
C19 (x ² y ³ ) 2.7358081E-04 6.6588726E-06 5.6750988E-06
C21 (y ⁵ ) 3.1283799E-04 -1.6628244E-05 -5.6404389E-06
C22 (x ⁶ ) 4.6128899E-06 -3.0150163E-07 -2.8179218E-07
C24 (x ⁴ y ² ) -5.3077923E-06 1.3779940E-06 7.3148655E-07
C26 (x ² y ⁴ ) -4.0446447E-05 6.7039471E-06 1.7840331E-06
C28 (y ⁶ ) -3.7005306E-05 3.1818828E-06 5.0161332E-07
C30 (x ⁶ y) -7.7569868E-07 4.5883534E-08 -1.1681552E-08
C32 (x ⁴ y ³ ) -1.6141580E-06 -4.1334998E-08 -1.3672298E-08
C34 (x ² y ⁵ ) -6.7458114E-06 5.8865611E-07 5.8515653E-08
C36 (y ⁷ ) -4.5485562E-06 1.5937924E-07 1.3081597E-08
C37 (x ⁸ ) -2.9162307E-09 1.2671378E-08 2.8800579E-09
C39 (x ⁶ y ² ) -9.5142253E-08 -4.7386079E-08 -1.0455710E-08
C41 (x ⁴ y ⁴ ) 4.4825183E-07 2.9556988E-08 5.3327450E-09
C43 (x ² y ⁶ ) 1.3201514E-06 -7.9806604E-08 -1.3308572E-08
C45 (y ⁸ ) 9.1629603E-07 -2.2799249E-08 -4.5262777E-09
C47 (x ⁸ y) 1.4012508E-08 -1.3269142E-09 -1.2160493E-10
C49 (x ⁶ y ³ ) 3.3552688E-08 2.2198651E-10 1.1636528E-10
C51 (x ⁴ y ⁵ ) 3.9883675E-08 2.6570502E-09 2.1286789E-09
C53 (x ² y ⁷ ) 9.3311671E-08 -6.3675373E-09 1.1409162E-09
C55 (y ⁹ ) 2.5577149E-08 9.1627034E-10 2.2983182E-10
C56 (x ¹⁰ ) -5.4484795E-10 -1.4465686E-10 -1.5438612E-11
C58 (x ⁸ y ² ) -1.3405979E-09 3.4824620E-10 2.4534853E-11
C60 (x ⁶ y ⁴ ) -4.6377423E-09 1.2386226E-10 1.5057373E-11
C62 (x ⁴ y ⁶ ) -8.5483241E-09 -6.9555901E-11 7.3774865E-11
C64 (x ² y ⁸ ) -1.6763430E-08 1.0083004E-09 1.7214332E-10
C66 (y ¹⁰ ) -7.2446753E-09 -4.6093983E-11 1.3276968E-11

(Table 5)
Term 18th surface coefficient c (curvature) 0
C1 (k) 0
C3 (y) 0.0000000E + 00
C4 (x ² ) 1.0712469E-02
C6 (y ² ) 3.3187726E-05
C8 (x ² y) 5.1197132E-04
C10 (y ³ ) 9.0670917E-05
C11 (x ⁴ ) -5.2484767E-06
C13 (x ² y ² ) 2.0439416E-05
C15 (y ⁴ ) 5.0161336E-06
C17 (x ⁴ y) -5.7531968E-07
C19 (x ² y ³ ) 7.0753457E-07
C21 (y ⁵ ) 2.2056979E-07
C22 (x ⁶ ) 1.0549107E-08
C24 (x ⁴ y ² ) -4.2888123E-08
C26 (x ² y ⁴ ) 1.3316517E-08
C28 (y ⁶ ) 5.1714369E-09
C30 (x ⁶ y) 1.0070162E-09
C32 (x ⁴ y ³ ) -2.3017330E-09
C34 (x ² y ⁵ ) -3.8275997E-10
C36 (y ⁷ ) -3.3181345E-11
C37 (x ⁸ ) -1.7492155E-11
C39 (x ⁶ y ² ) 9.1998574E-11
C41 (x ⁴ y ⁴ ) -1.0920736E-10
C43 (x ² y ⁶ ) -2.9272082E-11
C45 (y ⁸ ) -7.5519009E-12
C47 (x ⁸ y) -5.4570412E-13
C49 (x ⁶ y ³ ) 4.1683053E-12
C51 (x ⁴ y ⁵ ) -3.8127362E-12
C53 (x ² y ⁷ ) -4.7449678E-13
C55 (y ⁹ ) -2.4858820E-13
C56 (x ¹⁰ ) 9.0568802E-15
C58 (x ⁸ y ² ) -1.5496994E-14
C60 (x ⁶ y ⁴ ) 7.4715548E-14
C62 (x ⁴ y ⁶ ) -6.0451838E-14
C64 (x ² y ⁸ ) 8.2423031E-16
C66 (y ¹⁰ ) -2.8104474E-15

Table 6 below shows changes in the surface distances D1 to D4 due to focusing. The surface distance D4 corresponds to the back focus (Bf) of the optical system.

(Table 6)
Reference position Intermediate position Maximum position D1 2.99949 2.85926 2.75950
D2 8.50683 7.39500 6.57001
D3 28.50000 29.75117 30.67505
D4 199.60000 249.60000 299.60000

Table 7 below shows corresponding values for conditional expression (1). Table 7 shows that total 35
It is a calculation result at a point. 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 7)
Object point x coordinate Object point y coordinate Nr1, Nr2
0.00 0.00 0.98752
0.00 0.94 0.99594
0.94 0.94 0.99581
0.94 0.00 0.98740
0.94 -0.94 0.97405
0.00 -0.94 0.97402
0.00 1.88 0.99989
0.94 1.88 0.99989
1.88 1.88 0.99917
1.88 0.94 0.99547
1.88 0.00 0.98718
1.88 -0.94 0.97433
1.88 -1.88 0.95711
0.94 -1.88 0.95538
0.00 -1.88 0.95484
0.00 2.82 0.99778
0.94 2.82 0.99753
1.88 2.82 0.99677
2.82 2.82 0.99548
2.82 1.88 0.99824
2.82 0.94 0.99501
2.82 0.00 0.98712
2.82 -0.94 0.97521
2.82 -1.88 0.96011
2.82 -2.82 0.94653
1.82 -2.82 0.94161
0.94 -2.82 0.93853
0.00 -2.82 0.93748
3.76 2.82 0.99358
3.76 1.88 0.99685
3.76 0.94 0.99445
3.76 0.00 0.98739
3.76 -0.94 0.97680
3.76 -1.88 0.96422
3.76 -2.82 0.95301

  The corresponding values for conditional expressions (2) to (5) are shown below.

Conditional expression (2) X / Y = 2.15505 / 0.23999 ≒ 9.06
Conditional expression (3) M × f = 2 × 14.5086 ≒ 29.02
Conditional expression (4) {L- (FLe + FLm)} / L = (26.5002-12.4939) /26.5002≈0.53
Conditional expression (5)
Reference position: TL / f = 291.10091 / 14.5086 ≒ 20.06
Intermediate position: TL / f = 341.10091 / 14.5086 ≒ 23.51
Maximum expansion position: TL / f = 391.10091 / 14.5086 ≒ 26.96

Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (5) are satisfied.

3 to 4 are lateral aberration diagrams at the reference position of the optical system for the image projection apparatus according to the first example, and FIGS. 8 to 9 are lateral aberration diagrams at the intermediate position of the optical system for the image projection apparatus. 13 to 14 are lateral aberration diagrams at the maximum magnification position of the optical system for the image projection apparatus.
5 is a distortion diagram at the reference position of the optical system for the image projection apparatus according to the first embodiment, and FIG. 10 is a distortion diagram at an intermediate position of the optical system for the image projection apparatus.
FIG. 15 is a distortion diagram at the maximum magnification position of the optical system for the image projection apparatus. In the lateral aberration diagram, C is C line (λ = 656.3 nm), e is e line (λ = 546.1 nm), g is g
The aberrations at the line (λ = 435.8 nm) are shown. The explanation of the lateral aberration diagram is the same in the other examples, and the explanation is omitted. From the aberration diagrams, it can be seen that in the first example, the lateral aberration and distortion at each point (object point) are corrected well, and the optical performance is excellent.

(Second embodiment)
A second embodiment of the present application will be described with reference to FIGS. 16 to 30 and Tables 8 to 14. FIG. FIG. 16 is a yz sectional optical path diagram at the reference position of the optical system for image projection apparatus according to the second embodiment, and FIG. 17 is an xz sectional optical path diagram at the reference position of the optical system for image projection apparatus. FIG. 21 is a yz sectional optical path diagram at an intermediate position of the optical system for an image projection apparatus, and FIG. 22 is an xz sectional optical path diagram at an intermediate position of the optical system for an image projection apparatus. FIG. 26 is a yz sectional optical path diagram at the maximum magnification position of the optical system for the image projection apparatus, and FIG. 27 is an xz sectional optical path diagram at the maximum magnification position of the image projection apparatus optical system. In addition,
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 case of the first embodiment are assigned to the respective parts. Is omitted.

In the optical system PL for image projection apparatus according to the second example, the object side (element side) numerical aperture is 0.21.
74, the size of the video display element DS is 7.52 mm × 5.64 mm, the projection size is A4 size (297 mm × 210 mm) to A4 × 1.4 times, and the enlargement magnification is about 37.
The image area ratio M is M = 1.4. The rotationally symmetric lens group G
The focal length f of one whole is 14.547 mm.

  Table 8 below shows numerical data of the optical system PL for the image projection apparatus according to the second example.

(Table 8)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 12.00000 1.51680 / 64.2
3 Plane 2.41398
4 10.99531 5.12192 1.48563 / 85.2
5 -30.05457 1.22080
6 * a 8.67468 4.21782 1.77200 / 50.0
7 558.15901 2.00000 1.72250 / 29.2
8 * a 4.54141 2.76157
9 -10.05410 2.63471 1.59170 / 60.7
10 * a -5.60858 0.20000
11 (aperture) plane 2.02722
12 * f xy polynomial surface 2.50000 1.53113 / 55.7
13 * f xy polynomial surface (D1)
14 * f xy polynomial surface 6.00000 1.53113 / 55.7
15 * f xy polynomial surface (D2)
16 * f xy polynomial surface 6.50000 1.53113 / 55.7
17 * f xy polynomial surface (D3)
18 * f xy polynomial surface (D4) Reflection Image plane Plane

In Table 8, the fourth surface to the tenth surface are the lens surfaces of the rotationally symmetric rotationally symmetric lens group G1, and among them, the sixth surface, the eighth surface, and the tenth surface are rotationally symmetric aspherical surfaces. . In Table 9 below,
The aspherical coefficients of the sixth surface, the eighth surface, and the tenth surface are respectively shown.

(Table 9)
Term 6th surface coefficient 8th surface coefficient
r (radius of curvature) 8.6746823 4.5414080
k -0.6008124 0
A (4th) -1.4828948E-04 1.2959109E-04
B (6th) -2.6497453E-06 -1.1102148E-05
C (8th) -2.1757627E-07 -1.9497066E-06
D (10th order) 5.2425200E-09 1.7227296E-07
E (12th order) -1.1061821E-10 0

Term 10th surface coefficient
r (radius of curvature) -5.6085776
k 0
A (4th) 6.7842606E-04
B (6th) -2.0988949E-05
C (8th) -1.3110211E-08
D (10th order) -1.7297194E-08
E (12th) -1.7248861E-09

In Table 8, the 12th to 18th surfaces are non-rotationally symmetric free-form surfaces. In this embodiment, the eighteenth surface is the reflecting surface of the free-form curved mirror M. In Tables 10 to 12 below,
Each term coefficient of these free-form surfaces is shown.

(Table 10)
Term 12th surface coefficient 13th surface coefficient 14th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 0.0000000E + 00 0.0000000E + 00 -9.2357736E-03
C4 (x ² ) -5.1113659E-02 -7.0504603E-02 -2.5946152E-02
C6 (y ² ) -1.9953139E-02 -5.5610615E-02 -5.4355341E-03
C8 (x ² y) 2.2966659E-03 1.5013555E-03 -6.8618402E-03
C10 (y ³ ) 2.0744394E-03 8.9896322E-04 -8.6545133E-03
C11 (x ⁴ ) 1.1896044E-03 3.0139028E-04 1.9808596E-05
C13 (x ² y ² ) 2.3163335E-03 6.3484682E-04 -1.3015077E-04
C15 (y ⁴ ) 1.2557804E-03 3.9222389E-04 -5.5444344E-04
C17 (x ⁴ y) 1.5571116E-05 3.0824203E-07 -1.9865355E-05
C19 (x ² y ³ ) 1.1692070E-04 1.9653691E-04 3.3816503E-04
C21 (y ⁵ ) 7.6889912E-05 1.4479429E-04 2.6134041E-04
C22 (x ⁶ ) -3.4055720E-05 -7.2244090E-06 6.6488030E-06
C24 (x ⁴ y ² ) -9.5404492E-05 -2.5656130E-05 -8.1518374E-06
C26 (x ² y ⁴ ) -8.9388093E-05 -1.7709593E-05 6.6331064E-06
C28 (y ⁶ ) -3.3843957E-05 -1.0524020E-05 2.8108419E-06
C30 (x ⁶ y) 2.7178442E-06 2.3939439E-06 6.2524550E-07
C32 (x ⁴ y ³ ) 8.9221766E-06 7.0927988E-06 -2.1953991E-06
C34 (x ² y ⁵ ) 1.0671022E-05 4.7150241E-06 -9.9471960E-06
C36 (y ⁷ ) 2.6584955E-06 1.9266023E-07 -6.5544832E-06
C37 (x ⁸ ) 8.5577616E-07 5.1106459E-07 9.7704241E-08
C39 (x ⁶ y ² ) 3.0073129E-06 1.7098666E-06 1.3287027E-07
C41 (x ⁴ y ⁴ ) 3.1477638E-06 1.5809061E-06 -4.9445153E-07
C43 (x ² y ⁶ ) 3.9571971E-06 2.3090866E-06 -1.3631042E-06
C45 (y ⁸ ) 1.1483685E-06 6.8743269E-07 -9.0546779E-07
C47 (x ⁸ y) -1.2229136E-07 -6.7200197E-08 -6.7299894E-09
C49 (x ⁶ y ³ ) -4.4600914E-08 -1.0565916E-07 -9.4568518E-08
C51 (x ⁴ y ⁵ ) 3.6194097E-07 3.2466371E-07 7.2101927E-08
C53 (x ² y ⁷ ) 2.7715642E-07 5.0171962E-07 4.1291818E-07
C55 (y ⁹ ) 9.7065198E-08 1.3179638E-07 1.5100958E-07
C56 (x ¹⁰ ) -9.1624614E-09 -8.3203934E-09 -3.9564890E-09
C58 (x ⁸ y ² ) -1.4643487E-07 -1.0079784E-07 -1.8544132E-08
C60 (x ⁶ y ⁴ ) -2.3272439E-07 -1.6082283E-07 -2.8609936E-08
C62 (x ⁴ y ⁶ ) -2.9047970E-07 -1.2920168E-07 2.9081871E-08
C64 (x ² y ⁸ ) -2.3603245E-07 -6.9584718E-08 9.3593250E-08
C66 (y ¹⁰ ) -5.3603414E-08 -1.8582724E-08 2.8480596E-08

(Table 11)
Term 15th surface coefficient 16th surface coefficient 17th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 1.6415646E-01 2.2102161E-01 4.5486999E-02
C4 (x ² ) -6.1235883E-03 -2.1075100E-02 -2.1182760E-02
C6 (y ² ) 6.4305689E-02 -3.4175543E-02 -3.6803105E-02
C8 (x ² y) -8.8287325E-03 -5.2391039E-04 -5.3653001E-04
C10 (y ³ ) -1.3135331E-02 5.3444278E-04 -1.5958015E-04
C11 (x ⁴ ) -8.2334143E-05 -9.9618997E-05 -3.5368539E-05
C13 (x ² y ² ) 2.0999696E-04 -3.1637536E-04 -1.7629467E-04
C15 (y ⁴ ) 2.2787132E-06 -4.0490002E-04 -2.1773046E-04
C17 (x ⁴ y) 1.2664868E-05 1.0570257E-05 8.0599375E-06
C19 (x ² y ³ ) 2.9590300E-04 9.9428258E-06 7.6001846E-06
C21 (y ⁵ ) 3.2571465E-04 -1.1679266E-05 -4.3185828E-06
C22 (x ⁶ ) 4.0176250E-06 -3.8356867E-07 -2.5390033E-07
C24 (x ⁴ y ² ) -7.1758035E-06 1.8621180E-07 6.0707440E-07
C26 (x ² y ⁴ ) -4.1691178E-05 5.0561167E-06 1.7035210E-06
C28 (y ⁶ ) -3.7808288E-05 3.7599906E-06 6.2353164E-07
C30 (x ⁶ y) -7.9532133E-07 1.3348038E-07 2.4872136E-09
C32 (x ⁴ y ³ ) -1.1377716E-06 2.3744185E-07 2.7004318E-08
C34 (x ² y ⁵ ) -6.1208196E-06 5.2276312E-07 3.0273316E-08
C36 (y ⁷ ) -4.0517021E-06 -1.7746845E-07 -6.9644320E-09
C37 (x ⁸ ) -3.9447431E-09 8.3567044E-09 1.5434574E-09
C39 (x ⁶ y ² ) -9.3633775E-08 -5.1605801E-08 -1.1813073E-08
C41 (x ⁴ y ⁴ ) 4.6723520E-07 8.1112703E-08 8.0444833E-09
C43 (x ² y ⁶ ) 1.2523632E-06 -3.0626144E-08 -1.6658596E-08
C45 (y ⁸ ) 8.3752541E-07 -1.5488626E-08 -7.5046614E-09
C47 (x ⁸ y) 1.1853379E-08 -2.6972061E-09 -2.4905499E-10
C49 (x ⁶ y ³ ) 2.2060761E-08 -1.1173618E-09 1.5914662E-11
C51 (x ⁴ y ⁵ ) 2.7666665E-10 -4.3043689E-09 2.1794070E-09
C53 (x ² y ⁷ ) 4.5460619E-08 -7.3225646E-09 1.3225503E-09
C55 (y ⁹ ) 1.5920667E-08 2.2726059E-09 3.4156342E-12
C56 (x ¹⁰ ) -3.9631701E-10 -5.4189456E-11 -2.3960824E-12
C58 (x ⁸ y ² ) -8.7779042E-10 5.5285802E-10 4.2668576E-11
C60 (x ⁶ y ⁴ ) -3.3853107E-09 -3.8440982E-11 2.6136137E-11
C62 (x ⁴ y ⁶ ) -4.0718059E-09 2.0794724E-10 1.5297180E-10
C64 (x ² y ⁸ ) -9.8564134E-09 8.3854352E-10 2.4689494E-10
C66 (y ¹⁰ ) -5.6764319E-09 -8.2065308E-11 2.8817235E-11

(Table 12)
Term 18th surface coefficient c (curvature) 0
C1 (k) 0
C3 (y) 0.0000000E + 00
C4 (x ² ) 1.0679176E-02
C6 (y ² ) -5.0547536E-05
C8 (x ² y) 5.2795696E-04
C10 (y ³ ) 9.3452749E-05
C11 (x ⁴ ) -4.8705006E-06
C13 (x ² y ² ) 2.1539501E-05
C15 (y ⁴ ) 5.3470192E-06
C17 (x ⁴ y) -5.6592698E-07
C19 (x ² y ³ ) 7.1284942E-07
C21 (y ⁵ ) 2.2557111E-07
C22 (x ⁶ ) 9.5759026E-09
C24 (x ⁴ y ² ) -4.7266486E-08
C26 (x ² y ⁴ ) 1.1199479E-08
C28 (y ⁶ ) 4.9126122E-09
C30 (x ⁶ y) 9.1434430E-10
C32 (x ⁴ y ³ ) -2.6242517E-09
C34 (x ² y ⁵ ) -4.4437238E-10
C36 (y ⁷ ) -4.7928797E-11
C37 (x ⁸ ) -1.2925262E-11
C39 (x ⁶ y ² ) 9.2366163E-11
C41 (x ⁴ y ⁴ ) -1.1716910E-10
C43 (x ² y ⁶ ) -2.8578363E-11
C45 (y ⁸ ) -7.9425002E-12
C47 (x ⁸ y) -3.8216010E-13
C49 (x ⁶ y ³ ) 4.3020004E-12
C51 (x ⁴ y ⁵ ) -3.7634386E-12
C53 (x ² y ⁷ ) -4.6915215E-13
C55 (y ⁹ ) -2.4810915E-13
C56 (x ¹⁰ ) -1.6650928E-15
C58 (x ⁸ y ² ) -5.4341127E-15
C60 (x ⁶ y ⁴ ) 7.4058369E-14
C62 (x ⁴ y ⁶ ) -5.6208467E-14
C64 (x ² y ⁸ ) -2.4979218E-16
C66 (y ¹⁰ ) -2.6696366E-15

Table 13 below shows changes in the surface distances D1 to D4 due to focusing. The surface distance D4 corresponds to the back focus (Bf) of the optical system.

(Table 13)
Reference position Intermediate position Maximum position D1 3.46796 3.36136 3.29444
D2 8.23458 7.58884 7.10884
D3 28.50000 29.25178 29.79823
D4 199.60000 224.60000 244.00000

Table 14 below shows corresponding values for conditional expression (1). Table 14 shows the calculation results for a total of 35 points on the entire object surface. 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 14)
Object point x coordinate Object point y coordinate Nr1, Nr2
0.00 0.00 0.98364
0.00 0.94 0.99296
0.94 0.94 0.99286
0.94 0.00 0.98354
0.94 -0.94 0.96941
0.00 -0.94 0.96936
0.00 1.88 0.99876
0.94 1.88 0.99864
1.88 1.88 0.99831
1.88 0.94 0.99264
1.88 0.00 0.98331
1.88 -0.94 0.96973
1.88 -1.88 0.95203
0.94 -1.88 0.95026
0.00 -1.88 0.94969
0.00 2.82 0.99966
0.94 2.82 0.99949
1.88 2.82 0.99893
2.82 2.82 0.99793
2.82 1.88 0.99769
2.82 0.94 0.99235
2.82 0.00 0.98325
2.82 -0.94 0.97063
2.82 -1.88 0.95515
2.82 -2.82 0.94199
1.82 -2.82 0.93722
0.94 -2.82 0.93432
0.00 -2.82 0.93334
3.76 2.82 0.99634
3.76 1.88 0.99666
3.76 0.94 0.99202
3.76 0.00 0.98354
3.76 -0.94 0.97228
3.76 -1.88 0.95948
3.76 -2.82 0.94857

  The corresponding values for conditional expressions (2) to (5) are shown below.

Conditional expression (2) X / Y = 1.29823 / 0.17353 ≒ 7.48
Conditional expression (3) M × f = 1.4 × 14.5468 ≒ 20.37
Conditional expression (4) {L- (FLe + FLm)} / L = (26.7025-12.5000) /26.7025≒0.53
Conditional expression (5)
Reference position: TL / f = 291.10057 / 14.5468 ≒ 20.01
Intermediate position: TL / f = 316.10057 / 14.5468 ≒ 21.73
Maximum expansion position: TL / f = 335.50057 / 14.5468 ≒ 23.06

Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (5) are satisfied.

18 to 19 are lateral aberration diagrams at the reference position of the optical system for the image projection apparatus according to the second example, and FIGS. 23 to 24 are lateral aberration diagrams at the intermediate position of the optical system for the image projection apparatus. 28 to 29 are lateral aberration diagrams at the maximum magnification position of the optical system for the image projection apparatus. 20 is a distortion diagram at the reference position of the optical system for the image projection apparatus according to the second embodiment, FIG. 25 is a distortion diagram at an intermediate position of the optical system for the image projection apparatus, and FIG. It is a distortion aberration figure in the maximum expansion position of the optical system for projection apparatuses. From the respective aberration diagrams, it can be seen that in the second example, the lateral aberration and distortion at each point (object point) are corrected well, and the optical performance is excellent.

(Third embodiment)
A third embodiment of the present application will be described with reference to FIGS. 31 to 45 and Tables 15 to 21. FIG.
FIG. 31 is a yz sectional optical path diagram at the reference position of the optical system for image projection apparatus according to the third embodiment, and FIG. 32 is an xz sectional optical path diagram at the reference position of the optical system for image projection apparatus. FIG. 36 is a y-z cross-sectional optical path diagram at an intermediate position of the image projection apparatus optical system, and FIG. 37 is an x-z cross-section optical path diagram at an intermediate position of the image projection apparatus optical system. FIG. 41 is a y-z cross-sectional optical path diagram at the maximum magnification position of the optical system for the image projection apparatus.
FIG. 42 is an xz cross-sectional optical path diagram at the maximum magnification position of the optical system for the image projection apparatus. 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 0.21.
74, the size of the image display element DS is 7.52 mm × 5.64 mm, the projection size is A4 size (297 mm × 210 mm) to A4 × 1.7 times, and the enlargement magnification is about 37
Times to about 48 times, and the image area ratio M is M = 1.7. The rotationally symmetric lens group G
The focal length f of the whole 1 is 14.249 mm.

  Table 15 below shows numerical data of the optical system PL for image projection apparatus according to the third example.

(Table 15)
Surface number Curvature radius Surface spacing Refractive index / νd
Element plane Plane 1.00000
1 plane 0.70000 1.51680 / 64.2
2 Plane 12.00000 1.51680 / 64.2
3 Plane 2.75267
4 10.66974 5.22425 1.48563 / 85.2
5 -32.35107 0.92664
6 * a 8.48251 4.14061 1.77200 / 50.0
7 1034.60239 2.00000 1.72250 / 29.2
8 * a 4.56228 2.76063
9 -9.18306 2.57476 1.59170 / 60.7
10 * a -5.43098 0.20000
11 (aperture) plane 2.01049
12 * f xy polynomial surface 3.00000 1.53113 / 55.7
13 * f xy polynomial surface (D1)
14 * f xy polynomial surface 6.10686 1.53113 / 55.7
15 * f xy polynomial surface (D2)
16 * f xy polynomial surface 7.28657 1.53113 / 55.7
17 * f xy polynomial surface (D3)
18 * f xy polynomial surface (D4) Reflection Image plane Plane

In Table 15, the fourth surface to the tenth surface are lens surfaces of the rotationally symmetric rotationally symmetric lens group G1, and among them, the sixth surface, the eighth surface, and the tenth surface are rotationally symmetric aspheric surfaces. . Table 16 below
Shows the aspherical coefficients of the sixth surface, the eighth surface, and the tenth surface, respectively.

(Table 16)
Term 6th surface coefficient 8th surface coefficient
r (radius of curvature) 8.4825102 4.5622806
k -0.5800101 0
A (4th) -1.4275972E-04 1.0894794E-04
B (6th) -2.4964144E-06 -9.4707615E-06
C (8th) -2.1003651E-07 -2.1002589E-06
D (10th) 4.9092727E-09 1.8437220E-07
E (12th order) -1.0536137E-10 0

Term 10th surface coefficient
r (radius of curvature) -5.4309758
k 0
A (4th) 8.5771456E-04
B (6th) -2.3080187E-05
C (8th) 1.6498133E-07
D (10th) -2.7388097E-08
E (12th) -1.0064713E-09

In Table 15, the 12th to 18th surfaces are non-rotationally symmetric free-form surfaces. In this embodiment, the eighteenth surface is the reflecting surface of the free-form curved mirror M. Tables 17 to 19 below show the term coefficients of these free-form surfaces.

(Table 17)
Term 12th surface coefficient 13th surface coefficient 14th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 0.0000000E + 00 0.0000000E + 00 -4.1523143E-02
C4 (x ² ) -4.9695904E-02 -7.2370923E-02 -3.3428254E-02
C6 (y ² ) -1.4820859E-02 -5.6846856E-02 -1.9178502E-02
C8 (x ² y) 2.1065182E-03 1.5437012E-03 -6.1997772E-03
C10 (y ³ ) 2.3096591E-03 1.1549874E-03 -8.6525821E-03
C11 (x ⁴ ) 1.1882164E-03 2.4820486E-04 8.6290923E-05
C13 (x ² y ² ) 2.3322939E-03 5.1110436E-04 -4.4298048E-05
C15 (y ⁴ ) 1.2639874E-03 3.1029959E-04 -5.7359837E-04
C17 (x ⁴ y) 1.3870729E-05 -1.8146579E-05 -5.0089272E-05
C19 (x ² y ³ ) 7.1401209E-05 1.2505544E-04 2.8736815E-04
C21 (y ⁵ ) 5.0541477E-05 1.1193359E-04 2.6626295E-04
C22 (x ⁶ ) -4.9395565E-05 -1.1723734E-05 6.9575061E-06
C24 (x ⁴ y ² ) -1.4176396E-04 -4.4297148E-05 -1.6372457E-05
C26 (x ² y ⁴ ) -1.3287266E-04 -3.3325267E-05 -3.2341747E-06
C28 (y ⁶ ) -4.4910994E-05 -1.4237892E-05 -1.6531776E-06
C30 (x ⁶ y) 2.5331457E-06 2.4351045E-06 1.8912372E-06
C32 (x ⁴ y ³ ) 5.9198911E-06 4.8926323E-06 -1.1869155E-06
C34 (x ² y ⁵ ) 8.9036006E-06 3.8390190E-06 -1.0119813E-05
C36 (y ⁷ ) 2.7115185E-06 -6.8364672E-08 -8.1056020E-06
C37 (x ⁸ ) 1.3065296E-06 5.6398830E-07 1.6864007E-07
C39 (x ⁶ y ² ) 4.7584862E-06 1.9561843E-06 5.9261211E-07
C41 (x ⁴ y ⁴ ) 6.0275099E-06 1.8067217E-06 5.1818751E-08
C43 (x ² y ⁶ ) 5.4519492E-06 2.0830061E-06 -7.6800065E-07
C45 (y ⁸ ) 1.2600446E-06 4.5139936E-07 -1.0237634E-06
C47 (x ⁸ y) -9.7324527E-08 -4.7966864E-08 -2.0304747E-08
C49 (x ⁶ y ³ ) 9.0762650E-08 -5.9867854E-08 -1.0502197E-07
C51 (x ⁴ y ⁵ ) 4.1032849E-07 2.1664193E-07 6.4002719E-08
C53 (x ² y ⁷ ) 1.8422278E-07 3.3790107E-07 5.4622285E-07
C55 (y ⁹ ) 5.1430120E-08 7.7731850E-08 1.9115617E-07
C56 (x ¹⁰ ) -1.7312122E-08 -1.0071233E-08 -6.1645192E-09
C58 (x ⁸ y ² ) -1.8305352E-07 -9.7284499E-08 -2.9696234E-08
C60 (x ⁶ y ⁴ ) -3.2513537E-07 -1.6099041E-07 -4.8393446E-08
C62 (x ⁴ y ⁶ ) -3.7429905E-07 -1.2765889E-07 1.4283328E-08
C64 (x ² y ⁸ ) -2.6143979E-07 -6.0469348E-08 1.0414332E-07
C66 (y ¹⁰ ) -4.8148129E-08 -1.2138504E-08 4.0835070E-08

(Table 18)
Term 15th surface coefficient 16th surface coefficient 17th surface coefficient c (curvature) 0 0 0
C1 (k) 0 0 0
C3 (y) 1.3661614E-01 2.1101062E-01 3.0932936E-02
C4 (x ² ) -6.2254231E-03 -2.0077891E-02 -2.0862817E-02
C6 (y ² ) 6.5479594E-02 -2.8897199E-02 -3.4825421E-02
C8 (x ² y) -8.4440389E-03 -5.3593145E-04 -4.5412349E-04
C10 (y ³ ) -1.3024528E-02 6.3831197E-04 -2.7991535E-05
C11 (x ⁴ ) -7.7430279E-05 -1.1114784E-04 -3.6720191E-05
C13 (x ² y ² ) 1.5200792E-04 -3.0960985E-04 -1.5840170E-04
C15 (y ⁴ ) -1.0301055E-04 -3.9144686E-04 -1.9420219E-04
C17 (x ⁴ y) 3.1109828E-06 8.8257556E-06 7.0410636E-06
C19 (x ² y ³ ) 2.8218191E-04 1.0959497E-05 6.5249848E-06
C21 (y ⁵ ) 3.5003846E-04 -1.4910972E-05 -5.2686065E-06
C22 (x ⁶ ) 4.6028947E-06 -2.2751319E-07 -2.1485846E-07
C24 (x ⁴ y ² ) -5.0839387E-06 1.6844856E-07 4.7520540E-07
C26 (x ² y ⁴ ) -3.7758291E-05 5.2803778E-06 1.3742850E-06
C28 (y ⁶ ) -3.7091626E-05 3.8474273E-06 5.2579407E-07
C30 (x ⁶ y) -5.5328142E-07 1.3264689E-07 -2.9501617E-09
C32 (x ⁴ y ³ ) -1.0358579E-06 1.5351398E-07 1.9371420E-08
C34 (x ² y ⁵ ) -6.5675949E-06 5.6292167E-07 4.5071792E-08
C36 (y ⁷ ) -5.0856627E-06 1.1253811E-07 2.6869354E-08
C37 (x ⁸ ) -7.4736243E-09 9.5198825E-09 1.5249172E-09
C39 (x ⁶ y ² ) -1.4862989E-07 -4.6570790E-08 -9.1856518E-09
C41 (x ⁴ y ⁴ ) 4.0948745E-07 8.4053851E-08 8.7788956E-09
C43 (x ² y ⁶ ) 1.2354547E-06 -6.0194023E-08 -1.0627187E-08
C45 (y ⁸ ) 9.3814167E-07 -2.8544071E-08 -6.0404839E-09
C47 (x ⁸ y) 1.1290276E-08 -2.3565839E-09 -1.1137258E-10
C49 (x ⁶ y ³ ) 2.4705630E-08 5.9955445E-10 1.5692667E-10
C51 (x ⁴ y ⁵ ) 2.1668391E-09 -5.3767229E-09 1.7651208E-09
C53 (x ² y ⁷ ) 7.6777885E-08 -5.9169370E-09 1.1446173E-09
C55 (y ⁹ ) 2.4217797E-08 -2.4194993E-11 -1.0433703E-11
C56 (x ¹⁰ ) -5.1035147E-10 -7.8568971E-11 -3.2668760E-12
C58 (x ⁸ y ² ) -4.3332272E-10 5.0378017E-10 3.1549902E-11
C60 (x ⁶ y ⁴ ) -3.5051635E-09 -3.1288345E-10 6.9367831E-12
C62 (x ⁴ y ⁶ ) -3.3071469E-09 1.9607866E-10 7.3464755E-11
C64 (x ² y ⁸ ) -1.4409152E-08 8.4089578E-10 1.5626206E-10
C66 (y ¹⁰ ) -6.9444227E-09 7.7732921E-11 2.6275706E-11

(Table 19)
Term 18th surface coefficient c (curvature) 0
C1 (k) 0
C3 (y) 0.0000000E + 00
C4 (x ² ) 1.0633387E-02
C6 (y ² ) -2.6252661E-05
C8 (x ² y) 5.1540406E-04
C10 (y ³ ) 8.9798891E-05
C11 (x ⁴ ) -4.7422886E-06
C13 (x ² y ² ) 2.0411220E-05
C15 (y ⁴ ) 5.0043320E-06
C17 (x ⁴ y) -5.6768646E-07
C19 (x ² y ³ ) 6.8536430E-07
C21 (y ⁵ ) 2.1921238E-07
C22 (x ⁶ ) 7.9973832E-09
C24 (x ⁴ y ² ) -4.4183307E-08
C26 (x ² y ⁴ ) 1.2318775E-08
C28 (y ⁶ ) 5.1914661E-09
C30 (x ⁶ y) 9.5326758E-10
C32 (x ⁴ y ³ ) -2.4246884E-09
C34 (x ² y ⁵ ) -3.8238914E-10
C36 (y ⁷ ) -2.9586201E-11
C37 (x ⁸ ) -8.8084630E-12
C39 (x ⁶ y ² ) 8.9390156E-11
C41 (x ⁴ y ⁴ ) -1.1138032E-10
C43 (x ² y ⁶ ) -2.8770097E-11
C45 (y ⁸ ) -7.5172893E-12
C47 (x ⁸ y) -4.4869053E-13
C49 (x ⁶ y ³ ) 4.1449487E-12
C51 (x ⁴ y ⁵ ) -3.7431360E-12
C53 (x ² y ⁷ ) -4.8969649E-13
C55 (y ⁹ ) -2.5394523E-13
C56 (x ¹⁰ ) -3.9329363E-15
C58 (x ⁸ y ² ) -5.9092158E-15
C60 (x ⁶ y ⁴ ) 7.0428459E-14
C62 (x ⁴ y ⁶ ) -5.7295348E-14
C64 (x ² y ⁸ ) 1.5121098E-16
C66 (y ¹⁰ ) -2.9818795E-15

Table 20 below shows changes in the surface distances D1 to D4 due to focusing. The surface distance D4 corresponds to the back focus (Bf) of the optical system.

(Table 20)
Standard position Intermediate position Maximum position D1 2.91016 2.76597 2.70973
D2 7.40713 6.40354 5.98327
D3 28.50000 29.64702 30.12286
D4 199.60000 248.00000 273.00000

Table 21 below shows corresponding values for conditional expression (1). Table 21 shows the calculation results for a total of 35 points over the entire object surface. 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 21)
Object point x coordinate Object point y coordinate Nr1, Nr2
0.00 0.00 0.98109
0.00 0.94 0.99262
0.94 0.94 0.99248
0.94 0.00 0.98097
0.94 -0.94 0.96365
0.00 -0.94 0.96357
0.00 1.88 0.99918
0.94 1.88 0.99900
1.88 1.88 0.99844
1.88 0.94 0.99214
1.88 0.00 0.98073
1.88 -0.94 0.96407
1.88 -1.88 0.94237
0.94 -1.88 0.94019
0.00 -1.88 0.93951
0.00 2.82 0.99883
0.94 2.82 0.99855
1.88 2.82 0.99771
2.82 2.82 0.99621
2.82 1.88 0.99746
2.82 0.94 0.99164
2.82 0.00 0.98064
2.82 -0.94 0.96519
2.82 -1.88 0.94614
2.82 -2.82 0.92913
1.88 -2.82 0.92207
0.94 -2.82 0.91920
0.00 -2.82 0.91793
3.76 2.82 0.99384
3.76 1.88 0.99586
3.76 0.94 0.99100
3.76 0.00 0.98091
3.76 -0.94 0.96717
3.76 -1.88 0.95136
3.76 -2.82 0.93744

  The corresponding values for conditional expressions (2) to (5) are shown below.

Conditional expression (2) X / Y = 1.622286 / 0.17353 ≒ 8.10
Conditional expression (3) M × f = 1.7 × 14.2485 ≒ 24.22
Conditional expression (4) {L- (FLe + FLm)} / L = (26.7107-13.3934) /26.7107≈0.50
Conditional expression (5)
Reference position: TL / f = 291.10077 / 14.2485 ≒ 20.43
Intermediate position: TL / f = 339.50077 / 14.2485 ≒ 23.83
Maximum expansion position: TL / f = 364.50077 / 14.2485 ≒ 25.58

Thus, in this embodiment, it can be seen that all the conditional expressions (1) to (5) are satisfied.

33 to 34 are lateral aberration diagrams at the reference position of the optical system for the image projection apparatus according to the third example, and FIGS. 38 to 39 are lateral aberration diagrams at the intermediate position of the optical system for the image projection apparatus. 43 to 44 are lateral aberration diagrams at the maximum magnification position of the optical system for the image projection apparatus. FIG. 35 is a distortion diagram at the reference position of the optical system for the video projector according to the third embodiment, FIG. 40 is a distortion diagram at the intermediate position of the optical system for the video projector, and FIG. It is a distortion aberration figure in the maximum expansion position of the optical system for projection apparatuses. From the aberration diagrams, it can be seen that in the third example, the lateral aberration and distortion at each point (object point) are corrected well, and the optical performance is excellent.

As described above, according to each embodiment, the optical system PL for an image projection apparatus that has a focusing function and can correct the trapezoidal distortion of a projected image satisfactorily while having a compact configuration, and an image projection provided with the optical system PL The device PRJ can be realized.

In the above-described embodiment, the projection surface R (image surface I) is the image projection device PRJ (housing BD).
) Is set on the same plane as the installation plane Q, but is not limited to this, and can be set on a plane parallel to the installation plane Q by a focusing function.

PRJ image projection device DS image display element PL optical system for image projection device G1 rotationally symmetric lens group L11 first rotationally symmetric lens L12 second rotationally symmetric lens L13 third rotationally symmetric lens L14 fourth rotationally symmetric 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 surface mirror I Image surface Q Installation surface R Projection surface

Claims (9)

An optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction,
A rotationally symmetric lens group composed of a plurality of rotationally symmetric lenses formed in rotational symmetry with respect to the optical axis , arranged in order from the image display element side along the optical axis , and non-rotationally symmetric with respect to the optical axis . A free-form surface lens group including a plurality of free-form surface lenses formed, and a free-form surface mirror having a reflection surface formed non-rotationally symmetric with respect to the optical axis ,
Wherein when the translating respectively along the optical axis at least two free-form surface lens in the free-form surface lens group moves in parallel along the image plane is the optical axis,
The free-form surface lens group includes three free-form surface lenses including a mirror-side free-form surface lens closest to the free-form surface mirror,
The three free-form surface lenses have a positive refracting power, a negative refracting power, and a positive refracting power in order from the image display element side with respect to a light beam emitted from an arbitrary object point in the image display element. ,
A normal vector with respect to the lens surface at a position where the principal ray emitted from the arbitrary object point is incident on the lens surface on the image display element side of the mirror-side free-form surface is Nr1, and the principal ray is on the mirror side. When a normal vector with respect to the lens surface at the position of exiting from the lens surface on the free-form surface mirror side in the free-form surface lens is Nr2, the inner product of Nr1 and Nr2 is
0.85 ≦ Nr1 ・ Nr2 <1.00
An optical system for an image projection apparatus, characterized by satisfying the following conditions . An optical system for an image projection apparatus that enlarges an image displayed on an image display element and projects the image on a predetermined projection surface from an oblique direction,
A rotationally symmetric lens group composed of a plurality of rotationally symmetric lenses formed in rotational symmetry with respect to the optical axis, arranged in order from the image display element side along the optical axis, and non-rotationally symmetric with respect to the optical axis. A free-form surface lens group including a plurality of free-form surface lenses formed, and a free-form surface mirror having a reflection surface formed non-rotationally symmetric with respect to the optical axis,
When at least two free-form surface lenses in the free-form surface lens group are translated along the optical axis, the image plane translates along the optical axis,
The free-form surface lens group includes three free-form surface lenses including a mirror-side free-form surface lens closest to the free-form surface mirror,
Each of the three free-form surface lenses has a cross section along the optical axis having a meniscus shape with a concave surface facing the image display element side with respect to a light bundle emitted from an arbitrary object point in the image display element. And
The reflection surface of the free-form curved mirror has a shape with a convex surface facing the image display element side,
A normal vector with respect to the lens surface at a position where the principal ray emitted from the arbitrary object point is incident on the lens surface on the image display element side of the mirror-side free-form surface is Nr1, and the principal ray is on the mirror side. When a normal vector with respect to the lens surface at the position of exiting from the lens surface on the free-form surface mirror side in the free-form surface lens is Nr2, the inner product of Nr1 and Nr2 is
0.85 ≦ Nr1 ・ Nr2 <1.00
An optical system for an image projection apparatus, characterized by satisfying the following conditions. When the at least two free-form surface lenses are translated along the optical axis, the image plane translates along the optical axis, and the size of the image plane changes. Item 3. The optical system for an image projection apparatus according to Item 1 or 2. The at least two free-form surface lenses in the free-form surface lens group are the mirror-side free-form surface lens and an element-side free-form surface lens arranged next to the mirror-side free-form surface lens. 4. The optical system for a video projection device according to any one of 3 above. When the length of the movable range of the mirror-side free curved lens is X and the length of the movable range of the element-side free curved lens is Y, the following formula
7 ≦ X / Y ≦ 10
The optical system for an image projection apparatus according to claim 4, wherein the following condition is satisfied. When the at least two free-form surface lenses are translated along the optical axis, the image plane translates along the optical axis, and the size of the image plane changes.
When the focal length of the rotationally symmetric lens group is f and the area ratio of the maximum area to the minimum area of the image plane when the size of the image plane changes is M,
15 [mm] ≦ M × f ≦ 35 [mm]
The optical system for a video projection apparatus according to claim 1, wherein the following condition is satisfied. The at least two free-form surface lenses in the free-form surface lens group are the mirror-side free-form surface lens and the element-side free-form surface lens arranged next to the mirror-side free-form surface lens,
The length on the optical axis of the free-form surface lens group is L, the thickness on the optical axis of the mirror-side free-form surface lens is FLe, and the thickness on the optical axis of the element-side free-form surface lens is FLm. When
{L- (FLe + FLm)} / L ≦ 0.6
The optical system for an image projection apparatus according to claim 1, wherein the following condition is satisfied. When the focal length of the rotationally symmetric lens group is f and the total length of the optical system for the image projection apparatus is TL, the following formula
19 ≦ TL / f ≦ 28
The optical system for a video projection apparatus according to claim 1, wherein the following condition is satisfied. An image projection device that is used in a state where it is installed on a predetermined installation surface and projects an image from an oblique direction on the same surface as the installation surface or a surface substantially parallel to the installation surface, the image projection device 9. An image projection apparatus, wherein the optical system constituting the image projection apparatus is an optical system for an image projection apparatus according to any one of claims 1 to 8.

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