HEAD-UP DISPLAY DEVICE

Abstract

A head-up display device is improved in performance by a reduction in size and the satisfactory correction of optical aberration. A head-up display device includes an image display surface that displays an image, a reflective optical surface that is disposed at a position facing an predetermined observation position of an observer, and a projection optical system that projects the image displayed on the image display surface to the reflective optical surface disposed at the predetermined observation position and allows the observer to visually recognize the enlarged image as a virtual image. In a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror and a second mirror in this order from the image display surface and Conditional Expression (1) is satisfied.

Claims

1. A head-up display device comprising: a projection optical system that projects an image displayed on an image display surface to a reflective optical surface disposed at a position facing an predetermined observation position of an observer and allows the observer to visually recognize the enlarged image as a virtual image, wherein in a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror and a second mirror in this order from the image display surface and Conditional Expression (1) is satisfied,
0.05<.sub.3/|.sub.12|<0.3(1) where, .sub.3: power of the reflective optical surface near the optical axis, and .sub.12: power of a combined optical system of the first and second mirrors.

2. The head-up display device according to claim 1, wherein Conditional Expression (2) is satisfied,
2<.sub.12*L.sub.3<10(2) where, L.sub.3: a gap between the second mirror and the reflective optical surface on the optical axis.

3. The head-up display device according to claim 1, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.

4. The head-up display device according to claim 2, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.

5. The head-up display device according to claim 1, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.

6. The head-up display device according to claim 2, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.

7. The head-up display device according to claim 3, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.

8. The head-up display device according to claim 4, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.

9. The head-up display device according to claim 1, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

10. The head-up display device according to claim 2, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

11. The head-up display device according to claim 3, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

12. The head-up display device according to claim 4, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

13. The head-up display device according to claim 5, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

14. The head-up display device according to claim 6, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

15. The head-up display device according to claim 7, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

16. The head-up display device according to claim 8, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.

17. The head-up display device according to claim 9, further comprising: a diffuser that is provided on the image display surface present at a formation position of the intermediate image.

18. The head-up display device according to claim 10, further comprising: a diffuser that is provided on the image display surface present at a formation position of the intermediate image.

19. The head-up display device according to claim 1, wherein Conditional Expression (1-1) is satisfied.
0.1<.sub.3/|.sub.12|<0.2(1-1)

20. The head-up display device according to claim 1, wherein Conditional Expression (2-1) is satisfied,
3<.sub.12*L.sub.3<5(2-1) where, L.sub.3: a gap between the second mirror and the reflective optical surface on the optical axis.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] FIG. 1 is a schematic diagram of a driver's seat of a bus on which a head-up display device according to an embodiment of the invention is mounted.

[0024] FIG. 2 is a diagram showing the schematic structure of a head-up display device of Example 1 of the invention seen in an x-axis direction.

[0025] FIG. 3 is a diagram showing the schematic structure of the head-up display device of Example 1 of the invention seen in a y-axis direction.

[0026] FIG. 4 is a diagram showing the schematic structure of the head-up display device of Example 1 of the invention seen in a z-axis direction.

[0027] FIG. 5 is a diagram showing the schematic structure of a head-up display device of Example 2 of the invention seen in the x-axis direction.

[0028] FIG. 6 is a diagram showing the schematic structure of the head-up display device of Example 2 of the invention seen in the y-axis direction.

[0029] FIG. 7 is a diagram showing the schematic structure of the head-up display device of Example 2 of the invention seen in the z-axis direction.

[0030] FIG. 8 is a diagram showing the schematic structure of a head-up display device of Example 3 of the invention seen in the x-axis direction.

[0031] FIG. 9 is a diagram showing the schematic structure of the head-up display device of Example 3 of the invention seen in the y-axis direction.

[0032] FIG. 10 is a diagram showing the schematic structure of the head-up display device of Example 3 of the invention seen in the z-axis direction.

[0033] FIG. 11 is a diagram showing the schematic structure of a head-up display device of Example 4 of the invention seen in the x-axis direction.

[0034] FIG. 12 is a diagram showing the schematic structure of the head-up display device of Example 4 of the invention seen in the y-axis direction.

[0035] FIG. 13 is a diagram showing the schematic structure of the head-up display device of Example 4 of the invention seen in the z-axis direction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0036] An embodiment of the invention will be described in detail below with reference to drawings. FIG. 1 is a schematic diagram of a driver's seat of a bus on which a head-up display device according to an embodiment of the invention is mounted, FIG. 2 is a diagram showing the schematic structure of a head-up display device of Example 1 seen in an X-axis direction, FIG. 3 is a diagram showing the schematic structure of the head-up display device of Example 1 seen in a Y-axis direction, and FIG. 4 is a diagram showing the schematic structure of the head-up display device of Example 1 seen in a Z-axis direction. For convenience sake, this embodiment will be described with reference to the drawings of the head-up display device of Example 1, but the same description as the description of this embodiment can be made even in head-up display devices of Examples 2 to 4.

[0037] Further, a head-up display device will be described as a head-up display device, which is mounted on a bus, in the embodiment to be described below. However, the invention is not limited to a head-up display device mounted on a bus, and the head-up display device can be mounted on large vehicles, such as a truck, a ship, and a heavy machine or the like.

[0038] As shown in FIG. 1, a head-up display device 10 of this embodiment is disposed in an internal space of a bus 11, that is, on the ceiling of the bus 11, on the rear side or lateral side of a driver's seat, or the like; reflects an image representing information, such as travel speed, emitted from the inside of the head-up display device 10 by a combiner (reflective optical surface) 13 standing on the upper surface of a dashboard 12; and enlarges and displays the image as a virtual image 16 on the front side of a observer (driver) P beyond a front window 14.

[0039] An image is reflected by the combiner 13 in this embodiment, but the front window 14 may be made as a reflective optical surface and an image may be directly reflected by the front window 14.

[0040] As shown in FIGS. 2 to 4, the head-up display device 10 includes a projection optical system 20 including an image display surface 17 that displays an image, a first mirror 18, and a second mirror 19. In this embodiment, an optical path, which extends from the center of the image display surface 17 and reaches a center 15a of an eye box 15, is referred to as an optical axis. That is, an optical path A that extends from the center of the image display surface 17, is reflected by the combiner 13, and reaches the center 15a of the eye box 15, and an optical path B that passes through the combiner 13 and reaches the virtual image 16 as shown in FIG. 1 are referred to as the optical axis. In this embodiment, the eye box 15 means a range in which an observer P appropriately can observe the virtual image 16 in a state in which the head-up display device 10 is fixed, and the center 15a of the eye box 15 means the center of the range in which the observer P can observe the virtual image 16.

[0041] The head-up display device 10 is adapted so that display light emitted from the image display surface 17 is reflected by the first and second mirrors 18 and 19 in this order, and reaches the combiner 13. The projection optical system 20, which includes the image display surface 17, the first mirror 18, and the second mirror 19, is provided inside a device housing, and allows the display light of the image to pass through an opening formed on the device housing. The device housing is not shown in FIGS. 2 to 4.

[0042] The image, which is displayed on the image display surface 17, may be an image that is formed as an intermediate image on the basis of image information by an optical system (not shown) positioned on the front side of the projection optical system 20, that is, on the opposite side to the first and second mirrors 18 and 19 with the image display surface 17 sandwich therebetween on the optical axis. In this case, a diffuser may be provided on the image display surface 17 that is present at a formation position of the intermediate image, and the range of the eye box 15 can be enlarged according to this aspect.

[0043] Further, the power of the combiner 13 near the optical axis and the power of a combined optical system of the first and second mirrors 18 and 19 are adapted so as to satisfy Conditional Expression (1),

0.05<.sub.3/|.sub.12|<0.3(1)

[0044] where, .sub.3: power of the reflective optical surface near the optical axis, and

[0045] .sub.12: the power of the combined optical system of the first and second mirrors.

[0046] Here, Conditional Expression (1) will be described in detail. In this embodiment, the shapes of the reflective surfaces of the first and second mirrors 18 and 19 are expressed by Expression (3),

[00001]$\begin{array}{cc}z=\frac{C_{\_.Math.k}*\left(x^2+y^2\right)}{1+\sqrt{1-C_{\_.Math.k}^2*\left(x^2+y^2\right)}}+\underset{i,j}{.Math.}.Math.D_{\mathrm{ij}.Math.\_.Math.k}*x^i*y^j& \left(3\right)\end{array}$

[0047] where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins,

[0048] C_.sub.k: the reciprocal of the radius of curvature, and

[0049] D.sub.ij.sub._.sub.k: free-form surface coefficient.

[0050] k denotes the number of the mirror and k is in the range of 1 to 3 in this embodiment. Further, each of i and j denotes a positive integer and i and j are in the range of 1 to 8 in this embodiment. Furthermore, *, that is, the asterisk of Expression (3) means multiplication.

[0051] The surface shape in an x-z cross-section is expressed by Expression (4) in a case in which y is 0 in Expression (3).

[00002]$\begin{array}{cc}z=\frac{C_{\_.Math.k}*x^2}{1+\sqrt{1-C_{\_.Math.k}^2*x^2}}+D_{20.Math.\_.Math.k}*x^2+D_{30.Math.\_.Math.k}*x^3+\mathrm{.Math.}& \left(4\right)\end{array}$

[0052] In a case in which z of Expression (4) is f(x), Expression (5) and Expression (6) are obtained.

[00003]$\begin{array}{cc}{f}^{}\left(x\right)=\frac{C_{\_.Math.k}*x}{\sqrt{1-C_{\_.Math.k}^2*x^2}}+2*D_{20.Math.\_.Math.k}*x+3*D_{30.Math.\_.Math.k}*x^2+\mathrm{.Math.}& \left(5\right)\\ f^{}\left(x\right)=\frac{C_{\_.Math.k}}{\sqrt{{\left(1-C_{\_.Math.k}^2*x^2\right)}^3}}+2*D_{20.Math.\_.Math.k}+6*D_{30.Math.\_.Math.k}*x+\mathrm{.Math.}& \left(6\right)\end{array}$

[0053] Expression (7) is obtained from the Maclaurin series expansion of f(x).

[00004]$\begin{array}{cc}f\left(x\right)=f\left(0\right)+\frac{f^{}\left(0\right)}{1!}*x+\frac{f^{}\left(0\right)}{2!}*x^2+\frac{f^{}\left(0\right)}{3!}*x^3+\mathrm{.Math.}& \left(7\right)\end{array}$

[0054] However, since x is very small near the optical axis, Expression (8) is obtained in a case in which Expression (7) is approximated with the ignorance of third- or higher-order terms.

[00005]$\begin{array}{cc}f\left(x\right)=f\left(0\right)+\frac{f^{}\left(0\right)}{1!}*x+\frac{f^{}\left(0\right)}{2!}*x^2=\frac{C_{\_.Math.k}+2*D_{20.Math.\_.Math.k}}{2}*x^2& \left(8\right)\end{array}$

[0055] Expression (8) represents that the surface shape in the x-z cross-section corresponds to a paraboloid of which the curvature is C_.sub.k+2*D.sub.20.sub._.sub.k. Since the power of the reflective optical surface is expressed by =2*(curvature), power .sub.x in the x-z cross-section is expressed by Expression (9).

.sub.x=2*(C_.sub.k+2*D.sub.20.sub.k)(9)

[0056] Likewise, power .sub.y, in a y-z cross-section is expressed by Expression (10).

.sub.y=2*(C_.sub.k+2*D.sub.02.sub._.sub.k)(10)

[0057] An average of .sub.x and .sub.y is defined as the power .sub.k of each mirror by Expression (11).

.sub.k=2*(C_.sub.k+D.sub.20.sub._.sub.k+D.sub.02.sub._.sub.k)(11)

[0058] The powers .sub.1 and .sub.2 of the first and second mirrors 18 and 19 near the optical axis are expressed from Expression (11) by Expressions (12) and (13), respectively.

.sub.1=2*(C_.sub.1+D.sub.20.sub._.sub.1+D.sub.02.sub._.sub.1)(12)

.sub.2=2*(C_.sub.2+D.sub.20.sub._.sub.2+D.sub.02.sub._.sub.2)(13)

[0059] Further, in a case in which a gap between the first and second mirrors 18 and 19 on the optical axis is denoted by L.sub.2, the power .sub.12 of the combined optical system of the first and second mirrors 18 and 19 is expressed by Expression (14).

.sub.12=.sub.1+.sub.2L.sub.2*.sub.1*.sub.2(14)

[0060] Further, the power .sub.3 of the reflective optical surface near the optical axis is expressed from Expression (11) by Expression (15).

.sub.3=2*(C_.sub.3+D.sub.20.sub._.sub.3+D.sub.02.sub._.sub.3)(15)

[0061] The value of Conditional Expression (1) is calculated using .sub.1, .sub.2, .sub.3, and .sub.12 that are defined as described above.

[0062] Conditional Expression (1) determines a preferable numerical range of a ratio of the power .sub.3 of the combiner 13 to the absolute value of the power .sub.12 of the combined optical system of the first and second mirrors 18 and 19. Since the projection optical system 20 is increased in size in a case in which the value of Conditional Expression (1) is made too large or too small, it is possible to reduce the size of the projection optical system 20 and to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers .sub.1 and .sub.2 of the first and second mirrors 18 and 19, the power .sub.3 of the combiner 13, and the gap L.sub.2 between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not smaller than the lower limit of Conditional Expression (1). Further, it is possible to reduce the size of the projection optical system 20 and to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers .sub.i and .sub.2 of the first and second mirrors 18 and 19, the power .sub.3 of the combiner 13, and the gap L.sub.2 between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not larger than the upper limit of Conditional Expression (1). The projection optical system 20 can have more satisfactory characteristics in a case in which Conditional Expression (1-1) is satisfied.

0.1<.sub.3/|.sub.12|<0.2(1-1)

[0063] Conditional Expression (2) determines a preferable numerical range of a value of the product of the power .sub.12 of the combined optical system of the first and second mirrors 18 and 19 and a gap L.sub.3 between the second mirror 19 and the combiner 13 on the optical axis. It is possible to reduce the size of the projection optical system 20 and to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers .sub.1 and .sub.2 of the first and second mirrors 18 and 19, the gap L.sub.3 between the second mirror 19 and the combiner 13 on the optical axis, and the gap L.sub.2 between the first and second mirrors 18 and 19 on the optical axis so that the value is not equal to or not smaller than the lower limit of Conditional Expression (2). It is possible to reduce the size of the projection optical system 20 and to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers .sub.1 and .sub.2 of the first and second mirrors 18 and 19, the gap L.sub.3 between the second mirror 19 and the combiner 13 on the optical axis, and the gap L.sub.2 between the first and second mirrors 18 and 19 on the optical axis so that the value is not equal to or not larger than the upper limit of Conditional Expression (2). The projection optical system 20 can have more satisfactory characteristics in a case in which Conditional Expression (2-1) is satisfied.

3<.sub.12*L.sub.3<5(2-1)

[0064] It is preferable that the angle of luminous flux toward the combiner 13 from the projection optical system 20 is made variable by the movement of at least one mirror selected from the first and second mirrors 18 and 19 in the head-up display device 10 of this embodiment. According to this structure, an observer (driver) P can correct the deviation of the angle of luminous flux that is caused by a manufacturing error of the projection optical system 20. The observer (driver) P can correct the deviation of the angle of luminous flux while seeing the virtual image 16 by moving the mirror after the projection optical system 20 is installed.

[0065] Further, it is preferable that the angle of luminous flux toward the combiner 13 from the projection optical system 20 is made variable by the movement of the mirror, which is disposed at a position closest to the center 15a of the eye box 15, of the first and second mirrors 18 and 19 in the head-up display device 10 of this embodiment. According to this structure, the deviation of the angle of luminous flux can be corrected after the projection optical system 20 is installed. Furthermore, since the observer (driver) P can operate the mirror physically closest to a seating position (predetermined observation position), the ease of an operation can be improved.

[0066] In this embodiment, for the change of the angle of luminous flux, the mirror may be moved, the inclination of the mirror may be changed, the mirror may be rotated about the optical axis, and the mirror may be moved by a combination thereof.

[0067] The head-up display device 10 includes the projection optical system 20 that projects an image displayed on the image display surface 17 to the combiner 13 disposed at a position facing an predetermined observation position of an observer P and allows the observer P to visually recognize the enlarged image as the virtual image 16. In a case in which an optical path, which extends from the center of the image display surface 17 and reaches the center 15a of the eye box 15, is referred to as the optical axis, the projection optical system 20 includes the first mirror 18 and the second mirror 19 in this order from the image display surface 17, and Conditional Expression (1) is satisfied. Accordingly, it is possible to obtain the head-up display device that can be improved in performance by a reduction in size and the satisfactory correction of optical aberration.

0.05<.sub.3/|.sub.12|<0.3(1)

[0068] Next, Examples of numerical values of the head-up display device of the invention will be described. First, a head-up display device of Example 1 will be described.

[0069] Table 1 shows the arrangement coordinate data of the respective elements of the head-up display device. Here, combinations of an absolute coordinate system, which uses the center of the image display surface 17 shown in FIGS. 2 to 4 as an origin, and local coordinate systems, which are set on the surfaces of the respective elements, such as the first mirror 18, the second mirror 19, and the combiner 13, will be described.

[0070] The local coordinate systems will be set as described below. The origins, an x-axis component vector, a y-axis component vector, and a z-axis component vector of each local coordinate system, are expressed as (x,y,z), (Vx.sub.x,Vx.sub.y,Vx.sub.z), (Vy.sub.x,Vy.sub.y,Vy.sub.z), and (Vz.sub.x,Vz.sub.y,Vz.sub.z) on the absolute coordinate system, respectively. A plane (y-z plane) orthogonal to an x axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to an x axis of the local coordinate system. A plane (x-z plane) orthogonal to a y axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to a y axis of the local coordinate system. A plane (x-y plane) orthogonal to a z axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to a z axis of the local coordinate system.

[0071] Further, each of the first mirror 18, the second mirror 19, and the combiner 13 is a mirror having power, and Table 2 shows data about the shapes of the reflective surfaces of the respective mirrors. The shape of the reflective surface of each mirror is expressed by Expression (3). The first mirror 18 corresponds to a case in which k is 1 in Expression (3), the second mirror 19 corresponds to a case in which k is 2 in Expression (3), and the combiner 13 corresponds to a case in which k is 3 in Expression (3). However, since the respective values of the respective mirrors are written in Table 3, a value of k is not written in Table 3.

[00006]$\begin{array}{cc}z=\frac{C_{\_.Math.k}*\left(x^2+y^2\right)}{1+\sqrt{1-C_{\_.Math.k}^2*\left(x^2+y^2\right)}}+\underset{i,j}{.Math.}.Math.D_{\mathrm{ij}.Math.\_.Math.k}*x^i*y^j& \left(3\right)\end{array}$

[0072] where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins (mm),

[0073] C_.sub.k: the reciprocal of the radius of curvature (1/mm), and

[0074] D.sub.ij.sub._.sub.k: free-form surface coefficient.

TABLE-US-00001 TABLE 1 EXAMPLE 1 COORDINATES OF x AXIS y AXIS z AXIS ORIGINS OF OF LOCAL OF LOCAL OF LOCAL RESPECTIVE COORDINATE COORDINATE COORDINATE SURFACES SYSTEM SYSTEM SYSTEM x y z Vxx Vxy Vxz Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.00 0.00 0.00 0.0865 0.6282 0.7732 0.2100 0.7702 0.6023 0.9739 0.1103 0.1986 DISPLAY SURFACE FIRST 27.50 15.00 70.00 0.9565 0.2461 0.1566 0.2415 0.9692 0.0484 0.1637 0.0085 0.9865 MIRROR SECOND 150.00 50.00 75.00 0.9277 0.1716 0.3317 0.1384 0.9829 0.1216 0.3469 0.0669 0.9355 MIRROR REFLECTIVE 154.36 519.33 1400.00 0.9801 0.0000 0.1987 0.0711 0.9338 0.3506 0.1856 0.3577 0.9152 OPTICAL SURFACE CENTER 135.00 200.00 725.00 0.9191 0.0000 0.3940 0.1571 0.9171 0.3665 0.3613 0.3988 0.8429 OF EYE BOX VIRTUAL 4151.84 4930.84 10725.00 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE-US-00002 TABLE 2 EXAMPLE 1 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 2.4495550021E03 3.3680163223E04 1.8123694370E04 D.sub.20 1.8214469422E03 3.5904233070E04 5.2854702320E06 D.sub.11 8.7017909731E04 1.7273094903E05 6.4918006193E06 D.sub.02 8.6097699172E04 3.6834805320E04 9.9609596958E06 D.sub.30 9.3043865749E07 4.4424134636E07 6.5339952161E09 D.sub.21 7.8994334886E07 1.8653076038E07 5.5257325934E09 D.sub.12 1.6144454006E06 2.8029580440E07 1.3634753277E08 D.sub.03 2.9782366769E07 9.3100890002E08 3.5294924921E09 D.sub.40 1.8907576445E09 7.2815870486E10 1.1578397395E10 D.sub.31 3.7352161411E09 1.9262977141E10 1.6289570344E10 D.sub.22 3.1679222650E09 8.7647225118E10 2.3582174462E10 D.sub.13 7.7090991815E09 5.6546691526E10 3.8212093384E12 D.sub.04 1.2031562445E08 3.5022537126E10 8.1604074480E12 D.sub.50 2.6626204983E11 1.2314877705E12 3.1570899899E14 D.sub.41 1.3436940238E11 2.2029721328E13 3.2104130044E13 D.sub.32 3.0073395111E11 8.0172282186E12 1.1140697905E12 D.sub.23 6.6142362664E12 6.6990160357E13 1.0929481028E13 D.sub.14 2.4572837147E11 1.8005538048E12 5.2838003867E14 D.sub.05 1.3480661526E11 1.5424425175E12 2.6460336862E14 D.sub.60 5.9766398825E14 3.0227922357E15 5.5162569483E16 D.sub.51 1.1648141724E13 7.2809490062E15 1.4402144301E15 D.sub.42 8.4284055338E14 8.8841456994E15 1.0317331698E15 D.sub.33 1.8904975791E13 1.8710543009E17 3.4251045478E15 D.sub.24 1.8793253436E13 3.2172586325E14 1.5159822593E15 D.sub.15 2.1911068889E13 1.0583913642E14 6.3795035317E16 D.sub.06 9.7897514608E14 1.7117911410E15 2.4276625514E16 D.sub.70 2.0215537157E16 5.7932053262E18 1.9696711496E18 D.sub.61 8.2810591963E16 1.2985382913E18 5.8196611233E18 D.sub.52 1.3609388864E15 4.3864577956E17 3.7446545207E18 D.sub.43 9.5178392208E16 7.0538019089E18 6.2561234185E18 D.sub.34 1.6453270693E15 5.2301328619E17 1.4637356601E17 D.sub.25 9.0719130599E16 6.0817356242E17 4.6861369370E18 D.sub.16 2.8813138304E15 3.8583887686E18 3.2285521038E18 D.sub.07 3.2019645698E15 2.7113261717E17 1.1161501335E18 D.sub.80 2.6595530493E20 8.2511126128E20 2.5786076063E21 D.sub.71 2.0883613761E18 4.0091388511E20 1.8540185155E20 D.sub.62 1.5340784568E18 2.1111612220E20 4.2956742584E20 D.sub.53 2.2453138558E18 1.7638298210E20 2.1991590362E20 D.sub.44 4.2304808201E20 1.8410048844E19 1.0525446825E20 D.sub.35 5.0551581407E18 2.2687009958E20 3.4781129454E20 D.sub.26 3.1224362129E18 4.1654319635E19 1.9235251585E20 D.sub.17 6.2366737433E18 8.1154606908E20 2.5356481643E21 D.sub.08 3.5031841902E18 3.9769371812E21 1.3242931871E21

[0075] Since symbol and meaning of each data mentioned in the description of Example 1 and a method of describing each data are the same as those in the following examples as long as not particularly stated, the repeated description thereof will be omitted below.

[0076] Next, a head-up display device of Example 2 will be described. FIGS. 5 to 7 are diagrams showing the schematic structure of the head-up display device of Example 2. Further, Table 3 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 2, and Table 4 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE-US-00003 TABLE 3 EXAMPLE 2 COORDINATES OF x AXIS OF LOCAL y AXIS OF LOCAL z AXIS OF LOCAL ORIGINS OF COORDINATE COORDINATE COORDINATE RESPECTIVE SURFACES SYSTEM SYSTEM SYSTEM x y z Vxx Vxy Vxz Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.00 0.00 0.00 0.0865 0.6282 0.7732 0.2100 0.7702 0.6023 0.9739 0.1103 0.1986 DISPLAY SURFACE FIRST 120.00 57.50 80.00 0.0125 0.0808 0.9966 0.1720 0.9817 0.0818 0.9850 0.1725 0.0016 MIRROR SECOND 45.00 65.00 125.00 0.8385 0.1160 0.5325 0.1757 0.9824 0.0627 0.5158 0.1462 0.8441 MIRROR REFLECTIVE 98.00 593.53 1350.00 0.9696 0.0000 0.2449 0.0981 0.9162 0.3886 0.2243 0.4008 0.8883 OPTICAL SURFACE CENTER 245.00 215.00 675.00 0.8915 0.0000 0.4530 0.2026 0.8945 0.3987 0.4052 0.4472 0.7974 OF EYE BOX VIRTUAL 4836.48 -5822.79 10675.00 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE-US-00004 TABLE 4 EXAMPLE 2 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 1.1827231295E03 3.1274062966E04 1.8454964279E04 D.sub.20 7.0886802901E05 1.6183462824E05 4.5306193754E06 D.sub.11 1.6410962016E04 2.8782413726E05 3.2525280701E06 D.sub.02 9.1721035618E05 1.4359033573E04 1.2760124112E05 D.sub.30 6.2141752331E07 4.3483108768E07 2.1392498016E09 D.sub.21 5.8242499829E07 2.9069057993E07 8.1907401535E09 D.sub.12 2.2027915492E07 1.9350341388E07 1.3659858465E08 D.sub.03 1.9735036813E07 2.1394365333E07 4.3508318498E09 D.sub.40 4.0614867564E09 4.2211960385E09 8.8427824478E11 D.sub.31 3.8672597928E10 3.3546006574E09 3.5752039721E11 D.sub.22 3.7267027632E09 4.0093542278E09 8.7783364029E11 D.sub.13 5.6801450488E09 1.9332697263E09 2.9790870464E11 D.sub.04 8.6927415028E09 3.9083044552E09 4.5018104202E11 D.sub.50 1.0005774655E11 3.9072827201E11 8.0606945507E15 D.sub.41 3.3021582823E12 5.7538800881E11 2.0408829305E13 D.sub.32 1.2721971833E10 2.9233337170E11 4.1384185265E13 D.sub.23 3.1304301153E11 1.9628797803E11 3.2421063286E13 D.sub.14 3.4135054440E11 4.4206709771E11 3.6641389252E13 D.sub.05 3.0699948407E11 6.5987281313E12 7.7246802382E14 D.sub.60 2.1603135159E13 2.2747273168E13 2.5869071851E15 D.sub.51 3.2858709808E13 3.9472379572E13 8.2971682305E16 D.sub.42 5.0426635900E13 5.6071021169E14 1.5994744084E15 D.sub.33 3.7640188150E13 3.6341579150E15 1.2221823119E15 D.sub.24 5.3070233752E13 1.0765695901E13 9.7854096911E16 D.sub.15 1.0556867050E13 1.7247524694E13 8.6471215730E16 D.sub.06 9.6062217823E14 6.3980703850E14 1.3405642123E15 D.sub.70 4.4892105664E15 1.3243972036E15 1.2125205598E18 D.sub.61 3.4400813692E17 9.8632903236E16 3.2992294067E18 D.sub.52 3.4697471985E15 1.7035576187E16 7.0496719531E18 D.sub.43 7.8794355945E16 1.0064123569E15 6.2886219333E18 D.sub.34 8.2192822974E16 2.1645667833E15 4.3385068365E18 D.sub.25 1.5778706113E15 6.1527631830E16 4.3658348773E18 D.sub.16 7.8141939809E16 1.1397356111E15 3.4161337049E18 D.sub.07 7.2137449570E16 1.1505609381E16 9.9579935545E19 D.sub.80 3.2686579076E19 2.9682628135E18 3.5366078987E20 D.sub.71 7.6115952145E18 4.2381256827E18 7.1008429915E21 D.sub.62 5.1913476667E17 4.1720738288E18 1.8097386130E20 D.sub.53 1.0966861132E17 9.6524918533E18 8.8544346554E21 D.sub.44 5.5576325046E18 5.8677137577E18 9.7863227228E22 D.sub.35 1.7977260612E18 3.1075255683E18 1.7731389072E22 D.sub.26 1.4119536389E18 1.2378772848E17 7.4361022206E21 D.sub.17 4.8763325855E18 7.4914577875E18 9.1633139304E21 D.sub.08 8.4056745559E18 3.6996159848E18 1.2577574956E20

[0077] Next, a head-up display device of Example 3 will be described. FIGS. 8 to 10 are diagrams showing the schematic structure of the head-up display device of Example 3. Further, Table 5 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 3, and Table 6 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE-US-00005 TABLE 5 EXAMPLE 3 COORDINATES OF x AXIS OF LOCAL y AXIS OF LOCAL z AXIS OF LOCAL ORIGINS OF COORDINATE COORDINATE COORDINATE RESPECTIVE SURFACES SYSTEM SYSTEM SYSTEM x y z Vxx Vxy Vxz Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.00 0.00 0.00 0.9551 0.0411 0.2935 0.0674 0.9945 0.0800 0.2886 0.0962 0.9526 DISPLAY SURFACE FIRST 27.50 20.00 70.00 0.9784 0.0300 0.2044 0.0184 0.9981 0.0583 0.2058 0.0533 0.9772 MIRROR SECOND 170.00 55.00 75.00 0.9174 0.0800 0.3898 0.0696 0.9967 0.0408 0.3918 0.0103 0.9200 MIRROR REFLECTIVE 130.09 338.32 1400.00 0.9848 0.0000 0.1736 0.0286 0.9863 0.1622 0.1712 0.1647 0.9714 OPTICAL SURFACE CENTER 135.00 240.00 725.00 0.9308 0.0000 0.3655 0.0491 0.9909 0.1250 0.3622 0.1343 0.9224 OF EYE BOX VIRTUAL 3792.26 1696.53 10725.00 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE-US-00006 TABLE 6 EXAMPLE 3 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 2.4726302179E04 6.3166593843E05 2.3249341810E04 D.sub.20 1.0734426648E03 3.8353281411E04 2.7185989959E05 D.sub.11 6.6908589888E05 9.0823278602E05 4.9965869145E06 D.sub.02 2.8549088036E05 4.2529484610E04 1.2868375236E05 D.sub.30 1.2209595685E06 5.9593634185E07 8.7169180708E09 D.sub.21 1.0964527626E06 2.6887388240E07 5.3149077477E09 D.sub.12 1.1615776978E06 3.9898524258E07 2.1868698394E08 D.sub.03 2.8887176547E07 5.4608114986E08 6.3253009452E09 D.sub.40 3.3633310599E09 3.6045403941E10 1.2412620919E10 D.sub.31 3.9107118518E09 9.0862714741E10 2.7811640303E11 D.sub.22 3.8567034154E09 1.0774854253E09 2.3702737029E10 D.sub.13 6.8805106055E10 2.0158211611E10 1.4015983399E12 D.sub.04 8.2269940505E09 4.1969153761E10 5.0536563392E12 D.sub.50 1.7935635677E11 7.6213542694E14 1.5431966397E13 D.sub.41 5.1238143013E11 3.1548787770E12 2.8641605747E13 D.sub.32 8.6496061997E11 1.5570532154E11 1.3578335133E12 D.sub.23 1.3877003664E11 6.7230730515E12 2.1301625386E13 D.sub.14 2.4322402201E11 4.9422281046E12 3.3227814084E13 D.sub.05 3.0567447375E12 2.0822889243E12 1.5566991741E13 D.sub.60 1.1285454970E14 1.9339719028E15 2.3315508617E17 D.sub.51 1.6296635098E14 3.9737292174E15 1.1472507208E15 D.sub.42 1.3938270077E14 4.3387794133E15 9.2996523405E16 D.sub.33 1.2049511660E14 8.6977982146E16 1.1691924780E17 D.sub.24 1.6736902017E14 7.3383997583E15 7.3944331621E16 D.sub.15 4.3866674952E14 1.8475922993E15 4.1877406020E17 D.sub.06 1.2405321497E13 2.9656057252E15 6.8996064778E17 D.sub.70 1.3097737800E16 2.4939241874E18 5.0495546769E19 D.sub.61 1.0944079104E16 6.1270309256E19 2.8453049093E18 D.sub.52 6.2205073038E16 4.2843332468E17 8.5572120312E18 D.sub.43 4.9559163982E17 8.6115502482E18 5.8947508519E19 D.sub.34 5.1921254361E16 1.2974776843E17 1.0991693278E18 D.sub.25 2.2621302025E16 4.7313505197E18 1.9330040621E18 D.sub.16 4.2443529757E16 4.7864315214E17 1.3197476762E18 D.sub.07 4.0510679147E16 1.2816426632E17 8.6025103825E19 D.sub.80 5.8794116604E19 3.6118072794E20 4.3779933882E21 D.sub.71 6.4243904695E19 2.5467120870E19 7.5089047359E21 D.sub.62 4.0612115247E19 6.9285517971E20 1.5477178063E20 D.sub.53 2.3132827354E19 1.9504209971E19 2.3846680718E21 D.sub.44 7.5837437488E19 9.5328241023E20 1.8332518131E20 D.sub.35 8.5680766963E20 1.1005359611E19 5.7303209067E21 D.sub.26 1.2999306815E18 2.9561090410E19 4.0062505040E21 D.sub.17 1.5385890162E18 8.8669241107E20 5.9892226783E21 D.sub.08 9.9373605147E19 8.5101837861E20 3.5454485272E21

[0078] Next, a head-up display device of Example 4 will be described. FIGS. 11 to 13 are diagrams showing the schematic structure of the head-up display device of Example 4. Further, Table 7 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 4, and Table 8 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE-US-00007 TABLE 7 EXAMPLE 4 COORDINATES OF x AXIS OF LOCAL y AXIS OF LOCAL z AXIS OF LOCAL ORIGINS OF COORDINATE COORDINATE COORDINATE RESPECTIVE SURFACES SYSTEM SYSTEM SYSTEM x y z Vxx Vxy Vxz Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.00 0.00 0.00 0.0040 0.8593 0.5114 0.0498 0.5110 0.8582 0.9988 0.0220 0.0448 DISPLAY SURFACE FIRST 130.00 48.50 80.00 0.0013 0.0338 0.9994 0.0709 0.9969 0.0336 0.9975 0.0708 0.0037 MIRROR SECOND 55.00 65.00 125.00 0.8705 0.0713 0.4869 0.0576 0.9974 0.0430 0.4887 0.0094 0.8724 MIRROR REFLECTIVE 44.00 318.47 1350.00 0.9815 0.0000 0.1915 0.0302 0.9875 0.1550 0.1891 0.1579 0.9692 OPTICAL SURFACE CENTER 235.00 215.00 675.00 0.9242 0.0000 0.3820 0.0536 0.9901 0.1296 0.3782 0.1403 0.9150 OF EYE BOX VIRTUAL 3898.33 1747.96 10675.00 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE-US-00008 TABLE 8 EXAMPLE 4 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 1.3874920062E03 2.5746897981E04 2.2241097057E04 D.sub.20 7.1059333981E05 4.3007817428E05 8.7068975470E06 D.sub.11 4.8427096875E05 3.3127572851E05 2.6098745563E06 D.sub.02 3.7651004171E04 3.8216989743E05 2.1378507715E06 D.sub.30 1.8127045394E07 2.1452404828E07 3.8641547811E10 D.sub.21 7.3930417748E07 2.9697671853E07 9.9629355691E09 D.sub.12 3.5012810969E07 2.0477405977E07 3.0684246904E09 D.sub.03 1.7158062573E07 4.5280308597E08 4.1073949216E09 D.sub.40 5.1979601752E10 2.4357158969E10 3.3744935747E11 D.sub.31 4.8353709749E09 3.5987168288E09 2.1877424153E11 D.sub.22 1.5688173195E10 2.4332725190E10 1.6582956136E11 D.sub.13 7.5710957239E10 8.5902602671E10 5.3265481025E12 D.sub.04 2.9726693078E09 1.0167508904E09 2.1555182024E13 D.sub.50 2.3497957992E11 1.3381200026E12 1.2606133923E13 D.sub.41 1.9171463826E11 9.0524510612E13 2.1307818233E16 D.sub.32 1.8373321321E11 1.5341216727E11 9.0557650251E14 D.sub.23 3.8445244952E12 1.8099134151E12 8.6892487399E14 D.sub.14 5.5855812862E12 1.9187659031E12 3.7052683829E15 D.sub.05 1.1372290021E12 1.6353412454E12 2.0513505411E14 D.sub.60 1.3106806336E14 2.8360010887E14 3.0921469316E16 D.sub.51 2.2503692543E14 6.0222808147E14 2.3518498242E17 D.sub.42 1.6205183417E13 3.7200372757E14 5.6860410972E16 D.sub.33 1.0326941468E13 1.6817655869E14 1.6792768221E16 D.sub.24 4.4374045952E14 6.9455274528E14 1.2415384300E15 D.sub.15 2.2066805410E14 6.9185428147E15 8.4674656579E17 D.sub.06 1.2409372696E15 9.9836216490E15 3.1868829069E17 D.sub.70 5.2587256957E16 2.0664775322E16 4.1493011047E19 D.sub.61 2.5598013028E16 2.5176835032E16 3.6191841930E20 D.sub.52 7.3376243905E16 8.3391332990E16 2.4393653996E19 D.sub.43 3.0043948876E17 1.4149821009E16 2.4467902692E19 D.sub.34 2.7136475244E16 5.9245408730E17 9.3096145236E19 D.sub.25 1.9148840354E16 5.1950832456E17 3.5226424325E19 D.sub.16 7.1345486116E18 1.4591288480E16 1.3791435127E19 D.sub.07 1.6493391255E17 8.8506592323E18 1.5046023726E19 D.sub.80 1.3401703164E18 9.5464094033E19 3.1219193456E21 D.sub.71 9.5473564707E19 9.6820156735E19 6.5810102908E21 D.sub.62 1.7529665508E18 2.9970851966E19 5.9836631262E21 D.sub.53 1.3372707249E18 1.1310200938E18 2.3742523264E21 D.sub.44 3.5429685942E19 6.0701693777E19 1.0911967212E20 D.sub.35 9.8562716990E20 2.1163149112E18 7.2027082226E21 D.sub.26 3.8960191660E19 8.9873707916E19 6.5038104134E22 D.sub.17 2.9075338016E19 7.1530136853E19 1.2116249478E22 D.sub.08 8.3048886705E20 3.0137320048E19 9.0623022861E23

[0079] Values corresponding to Conditional Expressions (1) and (2) of the head-up display devices of Examples 1 to 4 are shown in Table 9.

TABLE-US-00009 TABLE 9 VALUES OF CONDITIONAL EXPRESSIONS EXPRESSION NUMBER EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 EXAMPLE 4 C.sub..sub.1 2.4496E03 1.1827E03 2.4726E04 1.3875E03 C.sub..sub.2 3.3680E04 3.1274E04 6.3167E05 2.5747E04 C.sub..sub.3 1.8124E04 1.8455E04 2.3249E04 2.2241E04 D.sub.20.sub..sub.1 1.8214E03 7.0887E05 1.0734E03 7.1059E05 D.sub.20.sub..sub.2 3.5904E04 1.6183E05 3.8353E04 4.3008E05 D.sub.20.sub..sub.3 5.2855E06 4.5306E06 2.7186E05 8.7069E06 D.sub.02.sub..sub.1 8.6098E04 9.1721E05 2.8549E05 3.7651E04 D.sub.02.sub..sub.2 3.6835E04 1.4359E04 4.2529E04 3.8217E05 D.sub.02.sub..sub.3 9.9610E06 1.2760E05 1.2868E05 2.1379E06 L.sub.1 76.68931 155.26188 77.82191 160.16320 L.sub.2 193.01878 87.78525 206.29166 89.00702 L.sub.3 1547.87486 1567.72868 1502.49312 1496.66139 .sub.1 4.6574E04 2.3238E03 1.5953E03 1.8798E03 .sub.2 2.1284E03 9.4503E04 1.7440E03 5.0536E04 .sub.3 3.7182E04 4.0368E04 3.8488E04 4.3168E04 .sub.12 2.4028E03 3.0760E03 2.7653E03 2.3006E03 (1) .sub.3/|.sub.12| 0.1547472 0.1312345 0.1391802 0.1876360 (2) .sub.12*L.sub.3 3.7192157 4.8223757 4.1548774 3.4432875 It is understood from the above-mentioned data that all the head-up display devices of Examples 1 to 4 are head-up display devices capable of being improved in performance by a reduction in size and the satisfactory correction of optical aberration since satisfying Conditional Expressions (1) and (2).

[0080] Here, values corresponding to Conditional Expressions (1) and (2) of the head-up display device disclosed in JP2013-61554A are shown in Table 10 as Comparative Examples.

TABLE-US-00010 TABLE 10 RELATED ART EXPRESSION COMPARATIVE COMPARATIVE COMPARATIVE NUMBER EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 C.sub..sub.1 6.4103E03 4.8248E03 4.8249E03 C.sub..sub.2 3.7037E03 0.0000E+00 1.0000E+02 C.sub..sub.3 0.0000E+00 1.5480E03 3.0000E+02 D.sub.20.sub..sub.1 D.sub.20.sub..sub.2 D.sub.20.sub..sub.3 D.sub.02.sub..sub.1 D.sub.02.sub..sub.2 D.sub.02.sub..sub.3 L.sub.1 65.00000 31.00000 42.00000 L.sub.2 80.00000 92.00000 71.00000 L.sub.3 120.00000 110.00000 90.00000 .sub.1 1.2821E02 9.6496E03 9.6497E03 .sub.2 7.4074E03 0.0000E+00 2.0000E+02 .sub.3 0.0000E+00 3.0960E03 6.0000E+02 .sub.12 2.1842E03 9.6496E03 6.2964E+01 (1) .sub.3/|.sub.12| 0.0000000 0.3208411 9.5292001 (2) .sub.12*L.sub.3 0.2621083 1.0614516 5666.7925424 Since all head-up display devices of Comparative Examples 1 to 3 do not satisfy Conditional Expressions (1) and (2) from the above-mentioned data, the same effects as the effects of the invention cannot be obtained.

[0081] The invention has been described using the embodiment and Examples. However, the invention is not limited to the embodiment and Examples and may have various modifications. Both the first and second mirrors have positive power in Examples 1 to 4. However, Conditional Expression (1) can be satisfied even though any one of the first and second mirrors may have negative power in the invention. Further, for example, the positions and sizes of the respective elements of the head-up display device may have other values without being limited to values that are mentioned in Examples of numerical values.

EXPLANATION OF REFERENCES

[0082] 10: head-up display device [0083] 11: bus [0084] 12: dashboard [0085] 13: combiner (reflective optical surface) [0086] 14: front window [0087] 15: eye box [0088] 15a: center of eye box [0089] 16: virtual image [0090] 17: image display surface [0091] 18: first mirror [0092] 19: second mirror [0093] 20: projection optical system [0094] P: observer (driver)