Patent Publication Number: US-10317676-B2

Title: Head-up display device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. § 119 to Japanese Patent Application No. 2016-169021, filed on Aug. 31, 2016. Each of the above application(s) is hereby expressly incorporated by reference, in its entirety, into the present application. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a head-up display device for a moving body, such as an automobile or the like, and more particularly, to a head-up display device for a large vehicle. 
     2. Description of the Related Art 
     In the past, a head-up display device has been known as a device that displays information, such as the indication of a direction, calling for attention, and a travel speed, to a driver of an automobile or the like. The head-up display device is to project the virtual image of an image, which is to be displayed, to the reflective optical surface of a front window, a combiner, or the like so that a driver can recognize information required for the driving of an automobile or the like without taking his eyes off from the field of view. JP2013-61554A is proposed as such a head-up display device. JP2013-61554A discloses a head-up display device in which an image forming unit mounted on a vehicle, such as a passenger car, is disposed in front of a driver so that the driver can visually recognize an enlarged virtual image of a two-dimensional image formed on an image display surface by a first mirror, a second mirror, and a reflective optical surface. 
     SUMMARY OF THE INVENTION 
     It is desired that the movement of the line of sight of a driver at the time of confirming information displayed by the head-up display device is reduced for safety or the prevention of driver&#39;s eyestrain in the head-up display device. In order to reduce the movement of the line of sight of a driver, it is preferable that the focal position of the virtual image is distant from the driver as much as possible. The length of an optical path between the image display surface and the reflective optical surface in the head-up display device needs to be long to make this structure. 
     In recent years, head-up display devices to be mounted on not only a passenger car but also large vehicles, such as a bus, a truck, a ship, and a heavy machine, have been desired to be developed. A space in which the head-up display device can be disposed in the large vehicle is different from that in a passenger car, and the head-up display device can also be disposed on the rear side or lateral side of a driver&#39;s seat, on the ceiling, or the like. According to the arrangement, since the length of an optical path between the reflective optical surface, which is disposed in front of an observer, and the image display surface in the head-up display device can be increased, it is easy to make the focal position of the virtual image be distant from the driver. 
     However, the head-up display device needs to be reduced in size to increase the degree of freedom of arrangement of the head-up display device as described above. 
     Further, since an improvement in performance is further required for the head-up display device, it is desired that optical aberration is satisfactorily corrected for an improvement in performance. 
     The invention has been made in consideration of the above-mentioned circumstances, and an object of the invention is to provide a head-up display device that can be improved in performance by a reduction in size and the satisfactory correction of optical aberration. 
     A head-up display device of the invention comprises 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. 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&lt;φ 3 /|φ 12 |&lt;0.3  (1)
 
     where, φ 3 : power of the reflective optical surface near the optical axis, and 
     φ 12 : power of a combined optical system of the first and second mirrors. 
     The “eye box” of the invention means a range in which an observer appropriately can observe the virtual image in a state in which the head-up display device is fixed. 
     Further, the “image display surface” of the invention includes not only the image display surface of an image display element itself but also an image display surface of a diffusion member in a case in which an image displayed on the image display element is temporarily projected to the diffusion member, such as a diffuser or the like, to enlarge the eye box. 
     It is preferable that the head-up display device of the invention satisfies any one of Conditional Expressions (1-1) to (2-1). As a preferable aspect, the head-up display device of the invention may satisfy any one of Conditional Expressions (1-1) to (2-1) or may satisfy an arbitrary combination thereof,
 
0.1&lt;φ 3 /|φ 12 |&lt;0.2  (1-1)
 
2&lt;φ 12   *L   3 &lt;10  (2)
 
3&lt;φ 12   *L   3 &lt;5  (2-1)
 
     where, L 3 : a gap between the second mirror and the reflective optical surface on the optical axis. 
     In the head-up display device of the invention, it is preferable that 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. 
     Furthermore, in the head-up display device of the invention, it is more preferable that 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. 
     In the invention, “movement of the mirror” means a change in the movement of the mirror, such as the movement of the mirror itself, a change in the inclination of the mirror, and the rotation of the mirror about the optical axis. 
     Moreover, in the head-up display device of the invention, the image may be an image that is formed as an intermediate image on the basis of image information by an optical system. 
     In this case, the head-up display device may further comprise a diffuser that is provided on the image display surface present at a formation position of the intermediate image. 
     In the invention, the “projection optical system” means an optical system between the image display surface and the second mirror, and the “optical system” means an optical system that is positioned on the opposite side to the first and second mirrors with the image display surface sandwich therebetween. 
     The head-up display device of the invention comprises 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. 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. 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&lt;φ 3 /|φ 12 |&lt;0.3  (1)
 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a driver&#39;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 of the invention seen in an x-axis direction. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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. 
         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 
     An embodiment of the invention will be described in detail below with reference to drawings.  FIG. 1  is a schematic diagram of a driver&#39;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&#39; 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. 
     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. 
     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&#39;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 . 
     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 . 
     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  15   a  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  15   a  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  15   a  of the eye box  15  means the center of the range in which the observer P can observe the virtual image  16 . 
     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 . 
     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. 
     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&lt;φ 3 /|φ 12 |&lt;0.3  (1)
 
     where, φ 3 : power of the reflective optical surface near the optical axis, and 
     φ 12 : the power of the combined optical system of the first and second mirrors. 
     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), 
     
       
         
           
             
               
                 
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     where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins, 
     C_   k   : the reciprocal of the radius of curvature, and 
     D ij   _   k : free-form surface coefficient. 
     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. 
     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). 
     
       
         
           
             
               
                 
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     In a case in which z of Expression (4) is f(x), Expression (5) and Expression (6) are obtained. 
     
       
         
           
             
               
                 
                   
                     
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     Expression (7) is obtained from the Maclaurin series expansion of f(x). 
     
       
         
           
             
               
                 
                   
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     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. 
     
       
         
           
             
               
                 
                   
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                           + 
                           
                             2 
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                               D 
                               
                                 20 
                                 ⁢ 
                                 
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                         x 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Expression (8) represents that the surface shape in the x-z cross-section corresponds to a paraboloid of which the curvature is C_   k   +2*D 20   _   k . Since the power φ of the reflective optical surface is expressed by “φ=−2*(curvature)”, power φ x  in the x-z cross-section is expressed by Expression (9).
 
φ x =−2*( C _   k   +2* D   20     —k   )  (9)
 
     Likewise, power φ y , in a y-z cross-section is expressed by Expression (10).
 
φ y =−2*( C _   k   +2* D   02   _   k )  (10)
 
     An average of φ x  and φ y  is defined as the power φ k  of each mirror by Expression (11).
 
φ k =−2*( C _   k     +D   20   _   k   +D   02   _   k )  (11)
 
     The powers φ 1  and φ 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.
 
φ 1 =−2*( C _   1     +D   20   _   1   +D   02   _   1 )  (12)
 
φ 2 =−2*( C _   2     +D   20   _   2   +D   02   _   2 )  (13)
 
     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 2 , the power φ 12  of the combined optical system of the first and second mirrors  18  and  19  is expressed by Expression (14).
 
φ 12 =φ 1 +φ 2   −L   2 *φ 1 *φ 2   (14)
 
     Further, the power φ 3  of the reflective optical surface near the optical axis is expressed from Expression (11) by Expression (15).
 
φ 3 =−2*( C _   3     +D   20   _   3   +D   02   _   3 )  (15)
 
     The value of Conditional Expression (1) is calculated using φ 1 , φ 2 , φ 3 , and φ 12  that are defined as described above. 
     Conditional Expression (1) determines a preferable numerical range of a ratio of the power φ 3  of the combiner  13  to the absolute value of the power φ 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 φ 1  and φ 2  of the first and second mirrors  18  and  19 , the power φ 3  of the combiner  13 , and the gap L 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 φ 1  and φ 2  of the first and second mirrors  18  and  19 , the power φ 3  of the combiner  13 , and the gap L 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&lt;φ 3 /|φ 12 |&lt;0.2  (1-1)
 
     Conditional Expression (2) determines a preferable numerical range of a value of the product of the power φ 12  of the combined optical system of the first and second mirrors  18  and  19  and a gap L 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 φ 1  and φ 2  of the first and second mirrors  18  and  19 , the gap L 3  between the second mirror  19  and the combiner  13  on the optical axis, and the gap L 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 φ 1  and φ 2  of the first and second mirrors  18  and  19 , the gap L 3  between the second mirror  19  and the combiner  13  on the optical axis, and the gap L 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&lt;φ 12   *L   3 &lt;5  (2-1)
 
     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. 
     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  15   a  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. 
     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. 
     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  15   a  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&lt;φ 3 /|φ 12 |&lt;0.3  (1)
 
     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. 
     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. 
     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 x ,Vx y ,Vx z ), (Vy x ,Vy y ,Vy z ), and (Vz x ,Vz y ,Vz 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. 
     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. 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         
                           C 
                           
                             _ 
                             ⁢ 
                             k 
                           
                         
                         * 
                         
                           ( 
                           
                             
                               x 
                               2 
                             
                             + 
                             
                               y 
                               2 
                             
                           
                           ) 
                         
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 C 
                                 
                                   _ 
                                   ⁢ 
                                   k 
                                 
                                 2 
                               
                               * 
                               
                                 ( 
                                 
                                   
                                     x 
                                     2 
                                   
                                   + 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           i 
                           , 
                           j 
                         
                       
                       ⁢ 
                       
                         
                           D 
                           
                             ij 
                             ⁢ 
                             _ 
                             ⁢ 
                             k 
                           
                         
                         * 
                         
                           x 
                           i 
                         
                         * 
                         
                           y 
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins (mm), 
     C_   k   : the reciprocal of the radius of curvature (1/mm), and 
     D ij   _   k : free-form surface coefficient. 
     
       
         
           
               
             
               
                 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 2 
               
             
            
               
                   
               
               
                 EXAMPLE 1 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 REFLECTIVE 
               
               
                   
                 FIRST 
                 SECOND 
                 OPTICAL 
               
               
                   
                 MIRROR 
                 MIRROR 
                 SURFACE 
               
               
                   
               
               
                 C 
                 2.4495550021E−03 
                 −3.3680163223E−04 
                 −1.8123694370E−04  
               
               
                 D 20   
                 −1.8214469422E−03  
                 −3.5904233070E−04 
                 5.2854702320E−06 
               
               
                 D 11   
                 −8.7017909731E−04  
                  1.7273094903E−05 
                 −6.4918006193E−06  
               
               
                 D 02   
                 −8.6097699172E−04  
                 −3.6834805320E−04 
                 −9.9609596958E−06  
               
               
                 D 30   
                 9.3043865749E−07 
                 −4.4424134636E−07 
                 −6.5339952161E−09  
               
               
                 D 21   
                 −7.8994334886E−07  
                 −1.8653076038E−07 
                 −5.5257325934E−09  
               
               
                 D 12   
                 1.6144454006E−06 
                  2.8029580440E−07 
                 −1.3634753277E−08  
               
               
                 D 03   
                 −2.9782366769E−07  
                 −9.3100890002E−08 
                 −3.5294924921E−09  
               
               
                 D 40   
                 −1.8907576445E−09  
                 −7.2815870486E−10 
                 1.1578397395E−10 
               
               
                 D 31   
                 3.7352161411E−09 
                  1.9262977141E−10 
                 1.6289570344E−10 
               
               
                 D 22   
                 3.1679222650E−09 
                 −8.7647225118E−10 
                 2.3582174462E−10 
               
               
                 D 13   
                 7.7090991815E−09 
                  5.6546691526E−10 
                 3.8212093384E−12 
               
               
                 D 04   
                 −1.2031562445E−08  
                  3.5022537126E−10 
                 −8.1604074480E−12  
               
               
                 D 50   
                 2.6626204983E−11 
                  1.2314877705E−12 
                 3.1570899899E−14 
               
               
                 D 41   
                 −1.3436940238E−11  
                  2.2029721328E−13 
                 3.2104130044E−13 
               
               
                 D 32   
                 −3.0073395111E−11  
                 −8.0172282186E−12 
                 1.1140697905E−12 
               
               
                 D 23   
                 6.6142362664E−12 
                 −6.6990160357E−13 
                 1.0929481028E−13 
               
               
                 D 14   
                 2.4572837147E−11 
                 −1.8005538048E−12 
                 5.2838003867E−14 
               
               
                 D 05   
                 1.3480661526E−11 
                 −1.5424425175E−12 
                 2.6460336862E−14 
               
               
                 D 60   
                 5.9766398825E−14 
                 −3.0227922357E−15 
                 5.5162569483E−16 
               
               
                 D 51   
                 −1.1648141724E−13  
                 −7.2809490062E−15 
                 −1.4402144301E−15  
               
               
                 D 42   
                 8.4284055338E−14 
                 −8.8841456994E−15 
                 −1.0317331698E−15  
               
               
                 D 33   
                 1.8904975791E−13 
                 −1.8710543009E−17 
                 3.4251045478E−15 
               
               
                 D 24   
                 1.8793253436E−13 
                 −3.2172586325E−14 
                 1.5159822593E−15 
               
               
                 D 15   
                 2.1911068889E−13 
                  1.0583913642E−14 
                 −6.3795035317E−16  
               
               
                 D 06   
                 9.7897514608E−14 
                 −1.7117911410E−15 
                 −2.4276625514E−16  
               
               
                 D 70   
                 2.0215537157E−16 
                  5.7932053262E−18 
                 1.9696711496E−18 
               
               
                 D 61   
                 −8.2810591963E−16  
                 −1.2985382913E−18 
                 5.8196611233E−18 
               
               
                 D 52   
                 −1.3609388864E−15  
                  4.3864577956E−17 
                 −3.7446545207E−18  
               
               
                 D 43   
                 −9.5178392208E−16  
                  7.0538019089E−18 
                 6.2561234185E−18 
               
               
                 D 34   
                 −1.6453270693E−15  
                  5.2301328619E−17 
                 1.4637356601E−17 
               
               
                 D 25   
                 9.0719130599E−16 
                 −6.0817356242E−17 
                 4.6861369370E−18 
               
               
                 D 16   
                 2.8813138304E−15 
                  3.8583887686E−18 
                 3.2285521038E−18 
               
               
                 D 07   
                 3.2019645698E−15 
                 −2.7113261717E−17 
                 −1.1161501335E−18  
               
               
                 D 80   
                 −2.6595530493E−20  
                 −8.2511126128E−20 
                 −2.5786076063E−21  
               
               
                 D 71   
                 −2.0883613761E−18  
                  4.0091388511E−20 
                 −1.8540185155E−20  
               
               
                 D 62   
                 −1.5340784568E−18  
                 −2.1111612220E−20 
                 −4.2956742584E−20  
               
               
                 D 53   
                 −2.2453138558E−18  
                 −1.7638298210E−20 
                 −2.1991590362E−20  
               
               
                 D 44   
                 4.2304808201E−20 
                 −1.8410048844E−19 
                 −1.0525446825E−20  
               
               
                 D 35   
                 5.0551581407E−18 
                 −2.2687009958E−20 
                 3.4781129454E−20 
               
               
                 D 26   
                 3.1224362129E−18 
                 −4.1654319635E−19 
                 1.9235251585E−20 
               
               
                 D 17   
                 6.2366737433E−18 
                  8.1154606908E−20 
                 2.5356481643E−21 
               
               
                 D 08   
                 3.5031841902E−18 
                 −3.9769371812E−21 
                 −1.3242931871E−21  
               
               
                   
               
            
           
         
       
     
     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. 
     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 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 4 
               
             
            
               
                   
               
               
                 EXAMPLE 2 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 REFLECTIVE 
               
               
                   
                   
                   
                 OPTICAL 
               
               
                   
                 FIRST MIRROR 
                 SECOND MIRROR 
                 SURFACE 
               
               
                   
               
               
                 C 
                 −1.1827231295E−03  
                 −3.1274062966E−04 
                 −1.8454964279E−04 
               
               
                 D 20   
                 −7.0886802901E−05  
                 −1.6183462824E−05 
                 −4.5306193754E−06 
               
               
                 D 11   
                 −1.6410962016E−04  
                  2.8782413726E−05 
                  3.2525280701E−06 
               
               
                 D 02   
                 9.1721035618E−05 
                 −1.4359033573E−04 
                 −1.2760124112E−05 
               
               
                 D 30   
                 −6.2141752331E−07  
                 −4.3483108768E−07 
                 −2.1392498016E−09 
               
               
                 D 21   
                 −5.8242499829E−07  
                  2.9069057993E−07 
                 −8.1907401535E−09 
               
               
                 D 12   
                 2.2027915492E−07 
                  1.9350341388E−07 
                 −1.3659858465E−08 
               
               
                 D 03   
                 1.9735036813E−07 
                 −2.1394365333E−07 
                 −4.3508318498E−09 
               
               
                 D 40   
                 −4.0614867564E−09  
                  4.2211960385E−09 
                  8.8427824478E−11 
               
               
                 D 31   
                 3.8672597928E−10 
                 −3.3546006574E−09 
                  3.5752039721E−11 
               
               
                 D 22   
                 3.7267027632E−09 
                 −4.0093542278E−09 
                  8.7783364029E−11 
               
               
                 D 13   
                 −5.6801450488E−09  
                  1.9332697263E−09 
                  2.9790870464E−11 
               
               
                 D 04   
                 −8.6927415028E−09  
                  3.9083044552E−09 
                  4.5018104202E−11 
               
               
                 D 50   
                 −1.0005774655E−11  
                 −3.9072827201E−11 
                  8.0606945507E−15 
               
               
                 D 41   
                 −3.3021582823E−12  
                  5.7538800881E−11 
                  2.0408829305E−13 
               
               
                 D 32   
                 1.2721971833E−10 
                  2.9233337170E−11 
                  4.1384185265E−13 
               
               
                 D 23   
                 −3.1304301153E−11  
                 −1.9628797803E−11 
                  3.2421063286E−13 
               
               
                 D 14   
                 −3.4135054440E−11  
                 −4.4206709771E−11 
                  3.6641389252E−13 
               
               
                 D 05   
                 −3.0699948407E−11  
                  6.5987281313E−12 
                  7.7246802382E−14 
               
               
                 D 60   
                 2.1603135159E−13 
                  2.2747273168E−13 
                 −2.5869071851E−15 
               
               
                 D 51   
                 −3.2858709808E−13  
                 −3.9472379572E−13 
                 −8.2971682305E−16 
               
               
                 D 42   
                 −5.0426635900E−13  
                 −5.6071021169E−14 
                 −1.5994744084E−15 
               
               
                 D 33   
                 3.7640188150E−13 
                  3.6341579150E−15 
                 −1.2221823119E−15 
               
               
                 D 24   
                 5.3070233752E−13 
                  1.0765695901E−13 
                 −9.7854096911E−16 
               
               
                 D 15   
                 1.0556867050E−13 
                  1.7247524694E−13 
                 −8.6471215730E−16 
               
               
                 D 06   
                 −9.6062217823E−14  
                  6.3980703850E−14 
                 −1.3405642123E−15 
               
               
                 D 70   
                 −4.4892105664E−15  
                 −1.3243972036E−15 
                  1.2125205598E−18 
               
               
                 D 61   
                 3.4400813692E−17 
                  9.8632903236E−16 
                 −3.2992294067E−18 
               
               
                 D 52   
                 −3.4697471985E−15  
                 −1.7035576187E−16 
                 −7.0496719531E−18 
               
               
                 D 43   
                 7.8794355945E−16 
                 −1.0064123569E−15 
                 −6.2886219333E−18 
               
               
                 D 34   
                 −8.2192822974E−16  
                  2.1645667833E−15 
                 −4.3385068365E−18 
               
               
                 D 25   
                 1.5778706113E−15 
                  6.1527631830E−16 
                 −4.3658348773E−18 
               
               
                 D 16   
                 7.8141939809E−16 
                  1.1397356111E−15 
                 −3.4161337049E−18 
               
               
                 D 07   
                 7.2137449570E−16 
                 −1.1505609381E−16 
                 −9.9579935545E−19 
               
               
                 D 80   
                 −3.2686579076E−19  
                  2.9682628135E−18 
                  3.5366078987E−20 
               
               
                 D 71   
                 7.6115952145E−18 
                 −4.2381256827E−18 
                  7.1008429915E−21 
               
               
                 D 62   
                 5.1913476667E−17 
                 −4.1720738288E−18 
                  1.8097386130E−20 
               
               
                 D 53   
                 1.0966861132E−17 
                  9.6524918533E−18 
                  8.8544346554E−21 
               
               
                 D 44   
                 5.5576325046E−18 
                 −5.8677137577E−18 
                 −9.7863227228E−22 
               
               
                 D 35   
                 −1.7977260612E−18  
                 −3.1075255683E−18 
                 −1.7731389072E−22 
               
               
                 D 26   
                 1.4119536389E−18 
                 −1.2378772848E−17 
                  7.4361022206E−21 
               
               
                 D 17   
                 4.8763325855E−18 
                 −7.4914577875E−18 
                  9.1633139304E−21 
               
               
                 D 08   
                 8.4056745559E−18 
                 −3.6996159848E−18 
                  1.2577574956E−20 
               
               
                   
               
            
           
         
       
     
     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 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 6 
               
             
            
               
                   
               
               
                 EXAMPLE 3 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 REFLECTIVE 
               
               
                   
                   
                   
                 OPTICAL 
               
               
                   
                 FIRST MIRROR 
                 SECOND MIRROR 
                 SURFACE 
               
               
                   
               
               
                 C 
                  2.4726302179E−04 
                 −6.3166593843E−05 
                 −2.3249341810E−04 
               
               
                 D 20   
                 −1.0734426648E−03 
                 −3.8353281411E−04 
                  2.7185989959E−05 
               
               
                 D 11   
                 −6.6908589888E−05 
                 −9.0823278602E−05 
                 −4.9965869145E−06 
               
               
                 D 02   
                  2.8549088036E−05 
                 −4.2529484610E−04 
                  1.2868375236E−05 
               
               
                 D 30   
                  1.2209595685E−06 
                 −5.9593634185E−07 
                 −8.7169180708E−09 
               
               
                 D 21   
                  1.0964527626E−06 
                  2.6887388240E−07 
                 −5.3149077477E−09 
               
               
                 D 12   
                  1.1615776978E−06 
                  3.9898524258E−07 
                 −2.1868698394E−08 
               
               
                 D 03   
                 −2.8887176547E−07 
                  5.4608114986E−08 
                  6.3253009452E−09 
               
               
                 D 40   
                 −3.3633310599E−09 
                 −3.6045403941E−10 
                  1.2412620919E−10 
               
               
                 D 31   
                 −3.9107118518E−09 
                  9.0862714741E−10 
                  2.7811640303E−11 
               
               
                 D 22   
                  3.8567034154E−09 
                 −1.0774854253E−09 
                  2.3702737029E−10 
               
               
                 D 13   
                  6.8805106055E−10 
                 −2.0158211611E−10 
                 −1.4015983399E−12 
               
               
                 D 04   
                 −8.2269940505E−09 
                  4.1969153761E−10 
                 −5.0536563392E−12 
               
               
                 D 50   
                  1.7935635677E−11 
                  7.6213542694E−14 
                 −1.5431966397E−13 
               
               
                 D 41   
                  5.1238143013E−11 
                 −3.1548787770E−12 
                 −2.8641605747E−13 
               
               
                 D 32   
                 −8.6496061997E−11 
                 −1.5570532154E−11 
                  1.3578335133E−12 
               
               
                 D 23   
                  1.3877003664E−11 
                 −6.7230730515E−12 
                  2.1301625386E−13 
               
               
                 D 14   
                  2.4322402201E−11 
                 −4.9422281046E−12 
                  3.3227814084E−13 
               
               
                 D 05   
                  3.0567447375E−12 
                  2.0822889243E−12 
                 −1.5566991741E−13 
               
               
                 D 60   
                  1.1285454970E−14 
                  1.9339719028E−15 
                  2.3315508617E−17 
               
               
                 D 51   
                 −1.6296635098E−14 
                  3.9737292174E−15 
                  1.1472507208E−15 
               
               
                 D 42   
                  1.3938270077E−14 
                  4.3387794133E−15 
                 −9.2996523405E−16 
               
               
                 D 33   
                  1.2049511660E−14 
                  8.6977982146E−16 
                  1.1691924780E−17 
               
               
                 D 24   
                 −1.6736902017E−14 
                 −7.3383997583E−15 
                  7.3944331621E−16 
               
               
                 D 15   
                  4.3866674952E−14 
                 −1.8475922993E−15 
                 −4.1877406020E−17 
               
               
                 D 06   
                 −1.2405321497E−13 
                  2.9656057252E−15 
                 −6.8996064778E−17 
               
               
                 D 70   
                  1.3097737800E−16 
                  2.4939241874E−18 
                  5.0495546769E−19 
               
               
                 D 61   
                 −1.0944079104E−16 
                 −6.1270309256E−19 
                  2.8453049093E−18 
               
               
                 D 52   
                 −6.2205073038E−16 
                  4.2843332468E−17 
                 −8.5572120312E−18 
               
               
                 D 43   
                 −4.9559163982E−17 
                  8.6115502482E−18 
                 −5.8947508519E−19 
               
               
                 D 34   
                 −5.1921254361E−16 
                 −1.2974776843E−17 
                  1.0991693278E−18 
               
               
                 D 25   
                 −2.2621302025E−16 
                 −4.7313505197E−18 
                  1.9330040621E−18 
               
               
                 D 16   
                  4.2443529757E−16 
                 −4.7864315214E−17 
                  1.3197476762E−18 
               
               
                 D 07   
                 −4.0510679147E−16 
                  1.2816426632E−17 
                 −8.6025103825E−19 
               
               
                 D 80   
                  5.8794116604E−19 
                 −3.6118072794E−20 
                 −4.3779933882E−21 
               
               
                 D 71   
                 −6.4243904695E−19 
                  2.5467120870E−19 
                 −7.5089047359E−21 
               
               
                 D 62   
                 −4.0612115247E−19 
                  6.9285517971E−20 
                 −1.5477178063E−20 
               
               
                 D 53   
                 −2.3132827354E−19 
                  1.9504209971E−19 
                 −2.3846680718E−21 
               
               
                 D 44   
                 −7.5837437488E−19 
                 −9.5328241023E−20 
                 −1.8332518131E−20 
               
               
                 D 35   
                  8.5680766963E−20 
                  1.1005359611E−19 
                  5.7303209067E−21 
               
               
                 D 26   
                 −1.2999306815E−18 
                 −2.9561090410E−19 
                  4.0062505040E−21 
               
               
                 D 17   
                  1.5385890162E−18 
                 −8.8669241107E−20 
                 −5.9892226783E−21 
               
               
                 D 08   
                 −9.9373605147E−19 
                  8.5101837861E−20 
                 −3.5454485272E−21 
               
               
                   
               
            
           
         
       
     
     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 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 8 
               
             
            
               
                   
               
               
                 EXAMPLE 4 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 REFLECTIVE 
               
               
                   
                   
                   
                 OPTICAL 
               
               
                   
                 FIRST MIRROR 
                 SECOND MIRROR 
                 SURFACE 
               
               
                   
               
               
                 C 
                 −1.3874920062E−03  
                 −2.5746897981E−04 
                 −2.2241097057E−04 
               
               
                 D 20   
                 7.1059333981E−05 
                  4.3007817428E−05 
                  8.7068975470E−06 
               
               
                 D 11   
                 −4.8427096875E−05  
                  3.3127572851E−05 
                  2.6098745563E−06 
               
               
                 D 02   
                 3.7651004171E−04 
                 −3.8216989743E−05 
                 −2.1378507715E−06 
               
               
                 D 30   
                 1.8127045394E−07 
                  2.1452404828E−07 
                 −3.8641547811E−10 
               
               
                 D 21   
                 7.3930417748E−07 
                 −2.9697671853E−07 
                  9.9629355691E−09 
               
               
                 D 12   
                 −3.5012810969E−07  
                 −2.0477405977E−07 
                 −3.0684246904E−09 
               
               
                 D 03   
                 −1.7158062573E−07  
                 −4.5280308597E−08 
                  4.1073949216E−09 
               
               
                 D 40   
                 −5.1979601752E−10  
                 −2.4357158969E−10 
                  3.3744935747E−11 
               
               
                 D 31   
                 4.8353709749E−09 
                  3.5987168288E−09 
                  2.1877424153E−11 
               
               
                 D 22   
                 −1.5688173195E−10  
                 −2.4332725190E−10 
                  1.6582956136E−11 
               
               
                 D 13   
                 7.5710957239E−10 
                 −8.5902602671E−10 
                 −5.3265481025E−12 
               
               
                 D 04   
                 −2.9726693078E−09  
                  1.0167508904E−09 
                  2.1555182024E−13 
               
               
                 D 50   
                 2.3497957992E−11 
                 −1.3381200026E−12 
                  1.2606133923E−13 
               
               
                 D 41   
                 −1.9171463826E−11  
                  9.0524510612E−13 
                 −2.1307818233E−16 
               
               
                 D 32   
                 1.8373321321E−11 
                 −1.5341216727E−11 
                  9.0557650251E−14 
               
               
                 D 23   
                 −3.8445244952E−12  
                 −1.8099134151E−12 
                 −8.6892487399E−14 
               
               
                 D 14   
                 5.5855812862E−12 
                 −1.9187659031E−12 
                  3.7052683829E−15 
               
               
                 D 05   
                 1.1372290021E−12 
                  1.6353412454E−12 
                 −2.0513505411E−14 
               
               
                 D 60   
                 −1.3106806336E−14  
                  2.8360010887E−14 
                 −3.0921469316E−16 
               
               
                 D 51   
                 2.2503692543E−14 
                 −6.0222808147E−14 
                  2.3518498242E−17 
               
               
                 D 42   
                 −1.6205183417E−13  
                  3.7200372757E−14 
                  5.6860410972E−16 
               
               
                 D 33   
                 −1.0326941468E−13  
                 −1.6817655869E−14 
                  1.6792768221E−16 
               
               
                 D 24   
                 4.4374045952E−14 
                  6.9455274528E−14 
                 −1.2415384300E−15 
               
               
                 D 15   
                 2.2066805410E−14 
                 −6.9185428147E−15 
                 −8.4674656579E−17 
               
               
                 D 06   
                 −1.2409372696E−15  
                  9.9836216490E−15 
                 −3.1868829069E−17 
               
               
                 D 70   
                 −5.2587256957E−16  
                 −2.0664775322E−16 
                 −4.1493011047E−19 
               
               
                 D 61   
                 2.5598013028E−16 
                 −2.5176835032E−16 
                 −3.6191841930E−20 
               
               
                 D 52   
                 −7.3376243905E−16  
                  8.3391332990E−16 
                  2.4393653996E−19 
               
               
                 D 43   
                 3.0043948876E−17 
                  1.4149821009E−16 
                 −2.4467902692E−19 
               
               
                 D 34   
                 2.7136475244E−16 
                 −5.9245408730E−17 
                 −9.3096145236E−19 
               
               
                 D 25   
                 1.9148840354E−16 
                 −5.1950832456E−17 
                 −3.5226424325E−19 
               
               
                 D 16   
                 −7.1345486116E−18  
                  1.4591288480E−16 
                 −1.3791435127E−19 
               
               
                 D 07   
                 1.6493391255E−17 
                 −8.8506592323E−18 
                 −1.5046023726E−19 
               
               
                 D 80   
                 −1.3401703164E−18  
                 −9.5464094033E−19 
                  3.1219193456E−21 
               
               
                 D 71   
                 9.5473564707E−19 
                 −9.6820156735E−19 
                 −6.5810102908E−21 
               
               
                 D 62   
                 1.7529665508E−18 
                  2.9970851966E−19 
                  5.9836631262E−21 
               
               
                 D 53   
                 −1.3372707249E−18  
                  1.1310200938E−18 
                 −2.3742523264E−21 
               
               
                 D 44   
                 −3.5429685942E−19  
                 −6.0701693777E−19 
                 −1.0911967212E−20 
               
               
                 D 35   
                 −9.8562716990E−20  
                 −2.1163149112E−18 
                 −7.2027082226E−21 
               
               
                 D 26   
                 3.8960191660E−19 
                 −8.9873707916E−19 
                 −6.5038104134E−22 
               
               
                 D 17   
                 2.9075338016E−19 
                  7.1530136853E−19 
                  1.2116249478E−22 
               
               
                 D 08   
                 8.3048886705E−20 
                  3.0137320048E−19 
                 −9.0623022861E−23 
               
               
                   
               
            
           
         
       
     
     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 9 
               
             
            
               
                   
               
               
                 VALUES OF CONDITIONAL EXPRESSIONS 
               
            
           
           
               
               
               
               
               
            
               
                 EXPRES- 
                   
                   
                   
                   
               
               
                 SION 
                   
                   
                   
                   
               
               
                 NUMBER 
                 EXAMPLE 1 
                 EXAMPLE 2 
                 EXAMPLE 3 
                 EXAMPLE 4 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 C_1 
                 2.4496E−03 
                 −1.1827E−03 
                 2.4726E−04 
                 −1.3875E−03 
               
               
                   
                 C_2 
                 −3.3680E−04 
                 −3.1274E−04 
                 −6.3167E−05 
                 −2.5747E−04 
               
               
                   
                 C_3 
                 −1.8124E−04 
                 −1.8455E−04 
                 −2.3249E−04 
                 −2.2241E−04 
               
               
                   
                 D 20 _1 
                 −1.8214E−03 
                 −7.0887E−05 
                 −1.0734E−03 
                 7.1059E−05 
               
               
                   
                 D 20 _2 
                 −3.5904E−04 
                 −1.6183E−05 
                 −3.8353E−04 
                 4.3008E−05 
               
               
                   
                 D 20 _3 
                 5.2855E−06 
                 −4.5306E−06 
                 2.7186E−05 
                 8.7069E−06 
               
               
                   
                 D 02 _1 
                 −8.6098E−04 
                 9.1721E−05 
                 2.8549E−05 
                 3.7651E−04 
               
               
                   
                 D 02 _2 
                 −3.6835E−04 
                 −1.4359E−04 
                 −4.2529E−04 
                 −3.8217E−05 
               
               
                   
                 D 02 _3 
                 −9.9610E−06 
                 −1.2760E−05 
                 1.2868E−05 
                 −2.1379E−06 
               
               
                   
                 L 1   
                 76.68931 
                 155.26188 
                 77.82191 
                 160.16320 
               
               
                   
                 L 2   
                 193.01878 
                 87.78525 
                 206.29166 
                 89.00702 
               
               
                   
                 L 3   
                 1547.87486 
                 1567.72868 
                 1502.49312 
                 1496.66139 
               
               
                   
                 φ 1   
                 4.6574E−04 
                 2.3238E−03 
                 1.5953E−03 
                 1.8798E−03 
               
               
                   
                 φ 2   
                 2.1284E−03 
                 9.4503E−04 
                 1.7440E−03 
                 5.0536E−04 
               
               
                   
                 φ 3   
                 3.7182E−04 
                 4.0368E−04 
                 3.8488E−04 
                 4.3168E−04 
               
               
                   
                 φ 12   
                 2.4028E−03 
                 3.0760E−03 
                 2.7653E−03 
                 2.3006E−03 
               
               
                 (1) 
                 φ 3 /|φ 12 | 
                 0.1547472 
                 0.1312345 
                 0.1391802 
                 0.1876360 
               
               
                 (2) 
                 φ 12 *L 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 sataisfactory correction of optical aberration since satisfyling Conditional Expressions (1) and (2). 
     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 10 
               
             
            
               
                   
               
               
                 RELATED ART 
               
            
           
           
               
               
               
               
               
            
               
                 EX- 
                   
                 COMPAR-  
                 COMPAR-  
                 COMPAR-  
               
               
                 PRESSION 
                   
                 ATIVE  
                 ATIVE  
                 ATIVE  
               
               
                 NUMBER 
                   
                 EXAMPLE 1 
                 EXAMPLE 2 
                 EXAMPLE 3 
               
               
                   
               
               
                   
                 C_1 
                 6.4103E−03 
                 4.8248E−03 
                 −4.8249E−03 
               
               
                   
                 C_2 
                 −3.7037E−03 
                 0.0000E+00 
                 1.0000E+02 
               
               
                   
                 C_3 
                 0.0000E+00 
                 −1.5480E−03 
                 −3.0000E+02 
               
               
                   
                 D 20 _1 
                   
                   
                   
               
               
                   
                 D 20 _2 
                   
                   
                   
               
               
                   
                 D 20 _3 
                   
                   
                   
               
               
                   
                 D 02 _1 
                   
                   
                   
               
               
                   
                 D 02 _2 
                   
                   
                   
               
               
                   
                 D 02 _3 
                   
                   
                   
               
               
                   
                 L 1   
                 65.00000 
                 31.00000 
                 42.00000 
               
               
                   
                 L 2   
                 80.00000 
                 92.00000 
                 71.00000 
               
               
                   
                 L 3   
                 120.00000 
                 110.00000 
                 90.00000 
               
               
                   
                 φ 1   
                 −1.2821E−02 
                 −9.6496E−03 
                 9.6497E−03 
               
               
                   
                 φ 2   
                 7.4074E−03 
                 0.0000E+00 
                 −2.0000E+02 
               
               
                   
                 φ 3   
                 0.0000E+00 
                 3.0960E−03 
                 6.0000E+02 
               
               
                   
                 φ 12   
                 2.1842E−03 
                 −9.6496E−03 
                 −6.2964E+01 
               
               
                 (1) 
                 φ 3 /|φ 12 | 
                 0.0000000 
                 0.3208411 
                 9.5292001 
               
               
                 (2) 
                 φ 12 *L 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 cannnot be obtained. 
     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 
     
         
         
           
               10 : head-up display device 
               11 : bus 
               12 : dashboard 
               13 : combiner (reflective optical surface) 
               14 : front window 
               15 : eye box 
               15   a : center of eye box 
               16 : virtual image 
               17 : image display surface 
               18 : first mirror 
               19 : second mirror 
               20 : projection optical system 
             P: observer (driver)