Patent Publication Number: US-2018045958-A1

Title: Head-up display and moving body equipped with head-up display

Description:
This application is a continuation-in-part of the PCT International Application No. PCT/JP2016/003245 filed on Jul. 8, 2016, which claims the benefit of foreign priority of Japanese patent application 2015-155735 filed on Aug. 6, 2015, the contents all of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a head-up display that projects an image on a transparent-type reflective member to present a virtual image. 
     2. Description of the Related Art 
     Unexamined Japanese Patent Publication No. 2012-093506 discloses a head-up display device that projects an image to be displayed on a windshield. The head-up display device includes a liquid crystal display, a standard light source, a concave mirror, and a concave cylindrical lens. The liquid crystal display forms a basic image to be a base of an image to be displayed. The standard light source radiates light from a rear surface side toward the liquid crystal display. The concave mirror reflects a light image of the basic image to project an image to be displayed on a windshield. The concave cylindrical lens has a concave curved surface that extends along a y-axis direction, that is curved into a concave shape in an x-axis direction, and that is facing the concave mirror. The concave cylindrical lens is positioned between the liquid crystal display and the concave mirror. Further, rotation of the concave cylindrical lens about an x axis can cause a z axis to incline with respect to optical axis OA from the standard light source toward the concave mirror. 
     SUMMARY 
     The present disclosure provides a head-up display that presents a virtual image having high contrast. 
     The head-up display of the present disclosure projects an image on a transparent reflective member to allow an observer to visually recognize a virtual image. The head-up display includes a display device and a projection optical system. The projection optical system includes a refractive optical system and a concave mirror. The display device displays the image. The projection optical system projects the image displayed on the display device to a visual point of an observer. The refractive optical system includes at least one optical element. The concave mirror has a concave reflection surface. The refractive optical system is positioned on an optical path between the display device and the concave mirror. In the refractive optical system, an incident surface of a lens element having negative power into which light of the image displayed on the display device is incident is concave. 
     The head-up display of the present disclosure is effective for presenting a virtual image having high contrast. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is schematic diagram for describing a vehicle mounted with a head-up display according to a first exemplary embodiment. 
         FIG. 2  is a schematic diagram illustrating a configuration of the head-up display according to the first exemplary embodiment. 
         FIG. 3  is a schematic diagram illustrating the configuration of the head-up display according to the first exemplary embodiment. 
         FIG. 4  is a schematic diagram illustrating the configuration of the head-up display according to the first exemplary embodiment. 
         FIG. 5  is a schematic diagram illustrating a configuration of a head-up display according to a second exemplary embodiment. 
         FIG. 6  is a schematic diagram illustrating a configuration of a head-up display according to a third exemplary embodiment. 
         FIG. 7  is a diagram illustrating data of a projection optical system according to Example 1. 
         FIG. 8  is a diagram illustrating data of the projection optical system according to Example 1. 
         FIG. 9  is a diagram illustrating data of the projection optical system according to Example 1. 
         FIG. 10  is a diagram illustrating data of the projection optical system according to Example 1. 
         FIG. 11  is a diagram illustrating data of the projection optical system according to Example 1. 
         FIG. 12  is a diagram illustrating data of the projection optical system according to Example 1. 
         FIG. 13  is a diagram illustrating data of a projection optical system according to Example 2. 
         FIG. 14  is a diagram illustrating data of the projection optical system according to Example 2. 
         FIG. 15  is a diagram illustrating data of the projection optical system according to Example 2. 
         FIG. 16  is diagram illustrating data of the projection optical system according to Example 2. 
         FIG. 17  is a diagram illustrating data of a projection optical system according to Example 3. 
         FIG. 18  is a diagram illustrating data of the projection optical system according to Example 3. 
         FIG. 19  is a diagram illustrating data of the projection optical system according to Example 3. 
         FIG. 20  is a diagram illustrating data of the projection optical system according to Example 3. 
         FIG. 21  is a diagram illustrating data of a projection optical system according to Example 4. 
         FIG. 22  is a diagram illustrating data of the projection optical system according to Example 4. 
         FIG. 23  is a diagram illustrating data of the projection optical system according to Example 4. 
         FIG. 24  is a diagram illustrating data of the projection optical system according to Example 4. 
         FIG. 25  is a diagram illustrating optical data of the head-up displays according to Examples 1 to 4. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, exemplary embodiments will be described in detail with reference to the drawings as appropriate. However, a detailed description more than necessary may be omitted. For example, a detailed description of a well-known matter or a repetitive description of a substantially identical configuration may be omitted. Such omissions are aimed to prevent the following description from being redundant than necessary, and to help those skilled in the art easily understand the following description. 
     Note that the attached drawings and the following description are provided for those skilled in the art to fully understand the present disclosure, and are not intended to limit the subject matter as described in the claims. 
     First Exemplary Embodiment 
     A first exemplary embodiment will be described below with reference to  FIGS. 1 to 4 . 
     [1-1. Configuration] 
     [1-1-1. Overall Configuration of Head-Up Display] 
     Specific exemplary embodiments and examples of head-up display  100  of the present disclosure will be described below with reference to the drawings. 
       FIG. 1  is a diagram illustrating a cross section of vehicle  200  mounted with head-up display  100  of the present disclosure. Vehicle  200  includes main body  201 , drive unit  202  that moves main body  201 , head-up display  100  mounted on the main body, and windshield  220  fixed to main body  201 . Drive unit  202  includes drive source  203  such as an engine and a motor, and driving wheel  204  that is driven by drive source  203 . Head-up display  100  is disposed inside dashboard  210  below windshield  220  of vehicle  200 . Observer D recognizes, as virtual image I, an image projected on windshield  220  by head-up display  100 . In addition to vehicle  200 , head-up display  100  may be mounted on a mobile body having a wind protection such as a two-wheeled vehicle. 
       FIG. 2  is a schematic diagram illustrating a configuration of head-up display  100  according to the present exemplary embodiment.  FIG. 3  is a schematic diagram for describing head-up display  100  according to the present exemplary embodiment. 
     As illustrated in  FIGS. 2 and 3 , head-up display  100  includes display device  110  and projection optical system  120 . Head-up display  100  reflects image to be displayed  111  displayed by display device  110  via windshield  220 , and guides image to be displayed  111  to viewpoint region  300  of observer D to allow observer D to visually recognize virtual image I. Camera  170  detects a viewpoint position of observer D. 
     In the present disclosure, front side refers to a direction in which the windshield  220  of vehicle  200  is present from a viewpoint of observer D, and rear side refers to a direction opposite to forward. Further, downward refers to a direction of the ground where vehicle  200  travels, and upward refers to a direction opposite to downward. Outer side refers to a left side from a viewpoint of observer D when vehicle  200  is a left-hand drive vehicle, and inner side refers to a right side from a viewpoint of observer D. Further, viewpoint region  300  is a region where observer D can visually recognize complete virtual image I. 
     Further, in display device  110 , an optical path from a center of image to be displayed  111  to a center of virtual image I is referred to as reference beam Lc. Reference beam Lc visually recognized by observer D actually reaches observer D from display device  110  via an optical system. Accordingly, a beam from display device  110  to observer D that corresponds to reference beam Lc emitted from the center of virtual image I is also referred to as reference beam Lc. Further, an optical path corresponding to these beams is also referred to as reference beam Lc. The same holds true for reference inner side beam Li and reference outer side beam Lo which are described in the following. On display device  110 , a display position corresponding to a vehicle outer side end of virtual image I is reference outer side image end Do, and a display position corresponding to a vehicle inner side end of virtual image I is reference inner side image end Di. An optical path from reference outer side image end Do to the vehicle outer side end of virtual image I is referred to as reference outer side beam Lo, and an optical path from reference inner side image end Di to the vehicle inner side end of virtual image I is referred to as reference inner side beam Li. Note that, it is assumed that the viewpoint of observer D is at the center of viewpoint region  300 . 
     Display device  110  displays image to be displayed  111  based on control made by a controller such as a CPU (not illustrated). Examples of display device  110  to be used may include a liquid crystal display with a backlight, an organic light emitting diode (electroluminescence), and a plasma display. Further, as display device  110 , image to be displayed  111  may be generated by using a screen that enables diffused reflection and a projector or a scanning laser. Image to be displayed  111  can display various pieces of information, such as road traffic navigation display, a distance to a vehicle ahead, the remaining battery charge of a vehicle, and a current vehicle speed. Further, display device  110  electronically distorts image to be displayed  111  in advance in accordance with distortion that occurs at projection optical system  120  and windshield  220 , and a position of observer D that is obtained by camera  170 . Thus, observer D can visually recognize excellent virtual image I. Further, display device  110  displaces the display of display pixels of a plurality of wavelengths for each display position in accordance with chromatic aberration that occurs at the projection optical system  120 . Thus, observer D can visually recognize excellent virtual image I. 
     Projection optical system  120  includes first lens  121  having negative power, first mirror  122  having a concave reflection surface, second lens  123  having positive power. Projection optical system  120  projects image to be displayed  111  displayed by display device  110  on windshield  220 . Specifically, image light of image to be displayed  111  displayed by display device  110  is incident to first mirror  122  via first lens  121 . The image light reflected by first mirror  122  is projected on windshield  220  via second lens  123 . 
     [1-1-2. Configuration of Projection Optical System] 
     A configuration of projection optical system  120  will be described below with reference to  FIGS. 2 and 3 . 
     First lens  121  is positioned on a front side of vehicle  200  with respect to display device  110 , and is inclined with respect to a direction perpendicular to a display surface of display device  110 . First lens  121  has a negative meniscus shape having a concave surface on a display device  110  side (incident surface) and a convex surface on a first mirror  122  side (emitting surface). The incident surface and the emitting surface of first lens  121  have power only in a right/left direction of the vehicle but do not have power in an upper/lower direction. As a result, even when external light such as sun light is reflected by first lens  121 , the external light is not incident to viewpoint region  300 . 
     First mirror  122  is positioned on a front side of vehicle  200  with respect to first lens  121 , and a reflection surface of first mirror  122  is eccentrically disposed so as to reflect the beam emitted from first lens  121  toward second lens  123 . The reflection surface of first mirror  122  is concave. Thus, image to be displayed  111  displayed by display device  110  can be enlarged and visually recognized as virtual image I by observer D. Further, first mirror  122  has a free-form surface. This is to correct distortion of the virtual image due to reflection, so that excellent virtual image I can be observed over the entire region of viewpoint region  300 . 
     Second lens  123  has positive power as a whole, and an emitting surface of second lens  123  has a Fresnel shape with ridges extending linearly in the front-rear direction of vehicle  200 . Further, second lens  123  is positioned to be higher than first mirror  122 , and refracts a beam reflected by first mirror  122  toward windshield  220 . Second lens  123  having positive power as a whole enables image to be displayed  111  displayed by display device  110  to be enlarged and visually recognized as virtual image I by observer D. Further, first mirror  122  can be reduced in size. Further, the emitting surface of second lens  123  is a free-form surface. Thus, asymmetric screen distortion that occurs at windshield  220  can be satisfactorily corrected. Further, the Fresnel shape of the emitting surface of second lens  123  enables a lens thickness of second lens  123  to be reduced, and head-up display  100  to be reduced in size. 
     First lens  121  is disposed to be higher than a lower end of the reflection surface of first mirror  122 . This enables head-up display  100  to have a reduced thickness in the upper/lower direction of vehicle  200 . 
     Further, as illustrated in  FIG. 4 , length L of reference beam Lc between image to be displayed  111  displayed on display device  110  and first lens  121  is shorter than length M of reference beam Lc between first mirror  122  and first lens  121 . This suppresses the fluctuation of the amount of chromatic aberration that occurs at first lens  121  in viewpoint region  300 . 
     [1-3. Effects and Others] 
     Head-up display  100  according to the first exemplary embodiment includes display device  110  that displays image to be displayed  111 , and projection optical system  120  that projects image to be displayed  111  displayed on display device  110 . Projection optical system  120  includes first lens  121 , first mirror  122 , and second lens  123  in this order from display device  110  on the optical path. 
     Head-up display  100  according to the first exemplary embodiment projects image to be displayed  111  displayed on display device  110  on windshield  220  to present virtual image I to observer D. Accordingly, image to be displayed  111  displayed on display device  110  can be visually recognized by observer D without obstructing a front view of observer D. 
     Further, use of head-up display  100  of the present disclosure can achieve a small head-up display in which image distortion is satisfactorily corrected on the entire region of viewpoint region  300 . That is, observer D can visually recognize excellent virtual image I at any position in viewpoint region  300 . 
     Since the incident surface of first lens  121  is concave toward display device  110 , expansion of a beam emitted from display device  110  and incident to first lens  121  can be suppressed, which enables presenting virtual image I having excellent contrast characteristics. 
     Further, since first lens  121  has a negative meniscus shape having a convex emitting surface, an incident angle of a beam emitted from display device  110  to the lens surface of first lens  121  can be made small, which can reduce an influence of distortion due to eccentricity. 
     In projection optical system  120 , first lens  121  having negative power as a whole is disposed immediately after display device  110 . In other words, since the surface of first lens  121 , into which light of image to be displayed  111  displayed on display device  110  is first incident, is concave, the positive power of first mirror  122  can be increased, which can reduce the size of head-up display  100 . 
     Second Exemplary Embodiment 
     Head-up display  100  according to a second exemplary embodiment is different from head-up display  100  according to the first exemplary embodiment in that second lens  123  is not provided. Points different from the first exemplary embodiment will be mainly described below with reference to  FIG. 5 , and descriptions of similar parts of the configuration will be omitted. 
     [2-1. Configuration] 
     [2-1-1. Overall Configuration of Head-Up Display] 
       FIG. 5  is a schematic diagram for describing an optical path for describing head-up display  100  according to the second exemplary embodiment. As illustrated in  FIG. 5 , head-up display  100  includes display device  110  and projection optical system  120 . Projection optical system  120  includes first lens  121  having negative power, and first mirror  122  having a concave reflection surface. 
     Projection optical system  120  projects image to be displayed  111  displayed by display device  110  on windshield  220 . Specifically, image light of image to be displayed  111  displayed by display device  110  is incident to first mirror  122  via first lens  121 . The image light reflected by first mirror  122  is projected on windshield  220 . 
     First lens  121  is positioned on the front side of vehicle  200  with respect to display device  110 , and is inclined with respect to a direction perpendicular to the display surface of display device  110 . Further, first lens  121  has a negative meniscus shape having a concave surface on the display device  110  side and a convex emitting surface. Further, the incident surface and the emitting surface of first lens  121  have power only in the right/left direction of the vehicle but do not have power in the upper/lower direction. As a result, even when external light such as sun light is reflected by first lens  121 , the external light is not incident to viewpoint region  300 . 
     First mirror  122  is positioned on the front side of vehicle  200  with respect to first lens  121 , and a reflection surface of first mirror  122  is eccentrically disposed so as to reflect a beam emitted from first lens  121  toward windshield  220 . The reflection surface of first mirror  122  is concave. Thus, image to be displayed  111  displayed by display device  110  can be enlarged and visually recognized as virtual image I by observer D. Further, first mirror  122  has a free-form surface. This is to correct distortion of the virtual image due to reflection, so that excellent virtual image I can be observed over the entire region of viewpoint region  300 . 
     In projection optical system  120 , first lens  121  having negative power as a whole is disposed immediately after display device  110 . A surface of first lens  121 , to which light of image to be displayed  111  displayed on display device  110  is first incident, is a concave surface. Since first lens  121  has the negative power as a whole, the positive power of first mirror  122  can be increased, which can reduce the size of head-up display  100 . 
     In the second exemplary embodiment, one first mirror  122  is disposed immediately after first lens  121 , but a plurality of mirrors may be disposed. 
     First lens  121  is disposed to be higher than a lower end of the reflection surface of first mirror  122 . This enables head-up display  100  to have a reduced thickness in the upper/lower direction of vehicle  200 . Further, a length of reference beam Lc between display device  110  and first lens  121  is shorter than a length of reference beam Lc between first mirror  122  and first lens  121 . This suppresses the fluctuation of the amount of chromatic aberration that occurs at first lens  121  in viewpoint region  300 . 
     [2-2. Effects and Others] 
     Head-up display  100  according to the second exemplary embodiment includes display device  110  that displays image to be displayed  111 , and projection optical system  120  that projects image to be displayed  111  displayed on display device  110 . Projection optical system  120  has first lens  121  and first mirror  122  in this order from display device  110  on the optical path. This configuration can realize a small head-up display in which image distortion is satisfactorily corrected on the entire region of viewpoint region  300 . That is, observer D can visually recognize excellent virtual image I at any position in viewpoint region  300 . 
     Since the incident surface of first lens  121  is concave toward display device  110 , expansion of a beam that is emitted from display device  110  and is incident to first lens  121  can be suppressed, which enables presenting virtual image I that is excellent in contrast characteristics. 
     Further, since first lens  121  has a negative meniscus shape having a convex emitting surface, an incident angle of a beam that is emitted from display device  110  to the lens surface of first lens  121  can be made small, which can reduce an influence of distortion due to eccentricity. 
     In projection optical system  120 , first lens  121  having negative power as a whole is disposed immediately after display device  110 . A surface of first lens  121 , to which light of image to be displayed  111  displayed on display device  110  is first incident, is a concave surface. Since first lens  121  has the negative power as a whole, the positive power of first mirror  122  can be increased, which can reduce the size of head-up display  100 . Further, since the incident surface of first lens  121  is concave, an angle formed between light incident from display device  110  and the incident surface can be enlarged. This suppresses degradation of optical characteristics caused when the incident angle is too small. 
     Third Exemplary Embodiment 
     A third exemplary embodiment will be described below with reference to  FIG. 6 . Head-up display  100  according to the third exemplary embodiment is different from head-up display  100  according to the first exemplary embodiment in that head-up display  100  has two mirrors in projection optical system  120  but does not have second lens  123 . Points different from the first exemplary embodiment will be mainly described below with reference to  FIG. 6 , and descriptions of similar parts of the configuration will be omitted. 
     [3-1. Configuration] 
     [3-1-1. Overall Configuration of Head-Up Display] 
       FIG. 6  is a schematic diagram illustrating an optical path for describing head-up display  100  according to the third exemplary embodiment. As illustrated in  FIG. 6 , head-up display  100  includes display device  110  and projection optical system  120 . 
     Projection optical system  120  includes first lens  121  having negative power, first mirror  122  having a convex reflection surface, and second mirror  124  having a concave reflection surface. Projection optical system  120  projects image to be displayed  111  displayed by display device  110  on windshield  220 . Specifically, image light of image to be displayed  111  displayed by display device  110  is incident to first mirror  122  via first lens  121 . The image light reflected by first mirror  122  is incident to second mirror  124 . The image light reflected by second mirror  124  is projected on windshield  220 . 
     [3-1-2. Configuration of Projection Optical System] 
     First lens  121  is positioned to be higher than display device  110 , and has negative power as a whole. Further, first lens  121  has a negative meniscus shape having a concave incident surface facing display device  110  and a convex emitting surface. Disposition of first lens  121  in front of display device  110  can reduce an angle of a beam emitted from display device  110 , which enables displaying virtual image I having excellent contrast characteristics. Further, first lens  121  has at least one free-form surface. Thus, asymmetric screen distortion that occurs at first mirror  122 , second mirror  124 , and windshield  220  can be corrected in an excellent manner. Further, the incident surface and the emitting surface of first lens  121  have power only in the right/left direction of the vehicle but do not have power in the upper/lower direction. As a result, even when external light such as sun light is reflected by first lens  121 , the external light is not incident to viewpoint region  300 . 
     First mirror  122  has a convex reflection surface formed by a free-form surface. First mirror  122  is positioned to be higher than first lens  121 , and the reflection surface of first mirror  122  is eccentrically disposed so as to reflect a beam emitted from first lens  121  toward second mirror  124 . 
     Second mirror  124  has a concave reflection surface formed by a free-form surface. Second mirror  124  is positioned on the front side of vehicle  200  of first lens  121 , and a reflection surface of second mirror  124  is eccentrically disposed so as to reflect the beam emitted from first mirror  122  toward windshield  220 . 
     The lower end of first mirror  122  is disposed to be positioned higher than the lower end of the reflection surface of second mirror  124 . This enables head-up display  100  to have a reduced thickness in the upper/lower direction of the vehicle. Further, the length of reference beam Lc between display device  110  and first lens  121  is shorter than a length of reference beam Lc between first mirror  122  and second mirror  124 . This suppresses the fluctuation of the amount of chromatic aberration that occurs at first lens  121  in viewpoint region  300 . 
     [3-3. Effects and Others] 
     Head-up display  100  according to the third exemplary embodiment includes display device  110  that displays image to be displayed  111 , and projection optical system  120  that projects image to be displayed  111  displayed on display device  110 . Projection optical system  120  includes first lens  121 , first mirror  122 , and second mirror  124  in this order from display device  110  on the optical path. This configuration can realize a small head-up display in which image distortion on the entire region of viewpoint region  300  is satisfactorily corrected. That is, observer D can visually recognize excellent virtual image I at any position in viewpoint region  300 . 
     Since the incident surface of first lens  121  is concave toward display device  110 , expansion of a beam output from display device  110  and incident to first lens  121  can be suppressed, which enables presenting virtual image I having excellent contrast characteristics. 
     Further, first lens  121  has a negative meniscus shape having a convex emitting surface. This reduces the incident angle of a beam emitted from display device  110  to the lens surface of first lens  121 , which can reduce the influence of distortion due to eccentricity. 
     In projection optical system  120 , first lens  121  having negative power as a whole is disposed immediately after display device  110 . In other words, since the surface of first lens  121 , into which the light of image to be displayed  111  displayed on display device  110  is first incident, is concave, positive power of second mirror  124  can be increased, which can reduce the size of head-up display  100 . 
     In the following, a description will be given of conditions which are desirably satisfied by head-up display  100  according to the first to third exemplary embodiments. Note that, a plurality of preferable conditions are stipulated for head-up display  100  according to the exemplary embodiments, and a configuration that satisfies all the conditions is most desirable. Nevertheless, it is also possible to obtain optical systems that exhibit respective effects by satisfying individual conditions. 
     The power of first lens  121  of the present disclosure is stronger in the right/left direction of the vehicle than in the upper/lower direction of the vehicle. Thus, observer D can visually recognize virtual image I having excellent contrast characteristics over the entire region of viewpoint region  300  which is set to be laterally longer. 
     Head-up display  100  of the present disclosure desirably satisfies the following Condition (1). 
       0.5&lt; H/L&lt; 10.0  (1)
 
     where 
     H represents a length from reference outer side image end Do to reference inner side image end Di, and 
     L represents an optical path length of a reference beam from the display device to the incident surface of first lens  121 . 
     Condition (1) is a condition for, as illustrated in  FIG. 4 , defining a ratio between a maximum lateral screen size of display device  110  (a length from reference outer side image end Do to reference inner side image end Di), and an optical path length of reference beam Lc from display device  110  to the incident surface of first lens  121 . When Condition (1) is satisfied, quality of virtual image I can be enhanced and at the same time the size of head-up display  100  can be reduced. When the ratio exceeds an upper limit of Condition (1), the optical path length of reference beam Lc from display device  110  to the surface of first lens  121  on the display device  110  side becomes small, which necessitates a curvature of the surface of first lens  121  on the display device  110  side to be weakened, and thus sufficient negative power cannot be secured, and observer D becomes difficult to visually recognize virtual image I having high contrast. Further, when the emitting surface of first lens  121  is made concave to provide negative power in order to enhance the contrast, an emitting angle of a beam from the emitting surface of first lens  121  becomes large, and correcting screen distortion satisfactorily becomes difficult. When the ratio is less than a lower limit in Condition (1), an interval between display device  110  and first lens  121  becomes large, and proving small-sized head-up display  100  becomes difficult. 
     Satisfaction of the following Condition (1)′ further enhances the above effect. 
       1.0&lt; H/L&lt; 6.0  (1)′
 
     Satisfaction of the following Condition (1)″ further enhances the above effect. 
       1.3&lt; H/L&lt; 4.0  (1)″
 
     Further, head-up display  100  of the present disclosure desirably satisfies the following Condition (2). 
       1.0&lt; M/L&lt; 13.0  (2)
 
     where 
     M represents an optical path length of the reference beam from the emitting surface of first lens  121  to first mirror  122 . 
     Conditional expression (2) is a conditional expression for defining a ratio between the optical path length of reference beam Lc from display device  110  to the incident surface of first lens  121 , and the optical path length of reference beam Lc from the emitting surface of first lens  121  to first mirror  122 . When Condition (2) is satisfied, the size of head-up display  100  can be reduced. When the ratio is less than a lower limit of Condition (2), an interval between first lens  121  and first mirror  122  becomes small, and avoiding interference between a beam reflected by first mirror  122  and first lens  121  becomes difficult. Further, when the ratio exceeds an upper limit of Condition (2), the interval between first lens  121  and first mirror  122  becomes large, and providing small-sized head-up display  100  becomes difficult. 
     Satisfaction of the following Condition (2)′ further enhances the above effect. 
       1.3&lt; M/L&lt; 7.0  (2)′
 
     Further, satisfaction of the following Condition (2)″ further enhances the above effect. 
       1.45&lt; H/L&lt; 6.0  (2)″
 
     NUMERICAL EXAMPLES 
     Numerical examples corresponding to the first to third exemplary embodiments will be described below with reference to  FIGS. 7 to 25 . 
     Specific example of the display device according to the present technique will be described below. In the following examples, a unit of length in tables is (mm), and a unit of angle is (degrees). Further, a free-form surface is defined by the following mathematic expression 1. 
     
       
         
           
             
               
                 
                   
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                   ] 
                 
               
             
           
         
       
     
     where z is a sag at position (x, y) from axes defining a surface, r is a radius of curvature at an origin on the axes defining a surface, c is a curvature at the origin on the axes defining a surface, k is a Korenich constant which corresponds to C 1  of the polynomial coefficient, C j  (j&gt;1) is a coefficient of monomial x m y n , and m and n are each an integer equal to or greater than 0. 
     Further, in Examples, a coordinate origin being a reference is a center of an image (display surface) displayed on display device  110 . In the tables, the horizontal direction in a display surface is X axis, the vertical direction in the display surface is Y axis, and the direction perpendicular to the display surface is Z axis. 
     Further, a toroidal surface is formed by a locus when an outline on an xz plane defined by the following mathematic expression 2 is rotated about an axis shifted to a position on the x axis separated from the origin by a radius of curvature ry. 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         c 
                         x 
                       
                        
                       
                         x 
                         2 
                       
                     
                     
                       1 
                       + 
                       
                         
                           1 
                           - 
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 k 
                               
                               ) 
                             
                              
                             
                               c 
                               x 
                               2 
                             
                              
                             
                               x 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Mathematic 
                      
                     
                         
                     
                      
                     Expression 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Further, in eccentricity data, ADE refers to an amount of rotation of a mirror or a lens from a Z axis direction to a Y axis direction about the X axis; BDE refers to an amount of rotation from an X axis direction to the Z axis direction about the Y axis; and CDE refers to an amount of rotation from the X axis direction to the Y axis direction about the Z axis. 
     Numerical Example 1 
       FIGS. 7 to 12  show data of the projection optical system according to Example 1 (the first exemplary embodiment).  FIG. 7  shows eccentricity data at surfaces of the optical elements of projection optical system  120 .  FIGS. 8 and 9  show radius of curvature.  FIGS. 10 and 11  show polynomial coefficients representing a shape of a free-form surface.  FIG. 12  shows aspheric coefficients of the emitting surface of second lens  123 . 
     Numerical Example 2 
       FIGS. 13 to 16  show data of the projection optical system according to Example 2 (the second exemplary embodiment). Projection optical system  120  according to Example 2 is configured by negative-power first lens  121  having a spherical incident surface having a concave shape and a convex emitting surface, and first mirror  122  having a concave reflection surface. 
       FIG. 13  shows data of the optical elements of projection optical system  120 .  FIG. 14  shows radius of curvature.  FIGS. 15 and 16  show polynomial coefficients representing a shape of a free-form surface. 
     Numerical Example 3 
       FIGS. 17 to 20  show data of the projection optical system according to Example 3 (the second exemplary embodiment). The projection optical system according to Example 3 is configured by negative-power first lens  121  and first mirror  122  having a concave reflection surface. An incident surface of first lens  121  has negative power only in a right/left direction of image to be displayed  111 , and an emitting surface of first lens  121  has positive power only in the right/left direction of the image to be displayed. 
       FIG. 17  shows data of the optical elements of projection optical system  120 .  FIGS. 18 and 19  show radius of curvature.  FIG. 20  shows polynomial coefficients representing a shape of a free-form surface. 
     Numerical Example 4 
       FIGS. 21 to 24  show data of the projection optical system according to Example 4 (the third exemplary embodiment).  FIG. 21  shows data of the optical elements of projection optical system  120 .  FIG. 22  shows radius of curvature.  FIGS. 23 and 24  show polynomial coefficients representing a shape of a free-form surface. 
       FIG. 25  shows a virtual image size and a distance between observer D and virtual image I in Examples 1 to 4. 
     Table 1 show corresponding values of Conditional Expressions (1) and (2) according to the first to third exemplary embodiments. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Example 1 
                 Example 2 
                 Example 3 
                 Example 4 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Conditional Expression 
                 3.59 
                 2.49 
                 1.84 
                 1.76 
               
               
                 (l) 
               
               
                 Conditional Expression 
                 5.29 
                 4.18 
                 3.06 
                 1.49 
               
               
                 (2) 
               
               
                   
               
            
           
         
       
     
     Other Exemplary Embodiments 
     As described above, the first to third exemplary embodiments have been described as illustration of the technique disclosed in this application. However, the technique of the present disclosure is not limited to the first to third exemplary embodiments, and is applicable to exemplary embodiments where modifications, replacements, additions, omissions, and the like are appropriately made. In addition, the components described in the first to third exemplary embodiments can be combined to obtain a new exemplary embodiment. 
     In the first to third exemplary embodiments, while first lens  121  has been described as a negative meniscus lens, first lens may have flat and concave surfaces, or both the surfaces may be concave. 
     In the first to third exemplary embodiments, as one example of the refractive optical system, an example where one lens element is disposed on the immediately emitting side of display device  110  has been described, but a plurality of lens elements may be disposed. When a plurality of lens elements are disposed, a surface on the display device side of a lens element, into which light emitted from the display device is first incident, is desirably concave. 
     In the third exemplary embodiment, the two mirrors are disposed in projection optical system  120 , but three or more mirrors may be disposed or one mirror may be disposed. 
     As first mirror  122  in head-up display  100  according to the first exemplary embodiment, and first mirror  122  and second mirror  124  in head-up display  100  according to the second exemplary embodiment, rotationally asymmetric mirrors have been used. However, mirrors each may have a so-called saddle-shaped surface in which a symbol of a curvature differs between the X direction and the Y direction. 
     The surface of first lens  121  according to the first to third exemplary embodiments is not limited to a free-form surface, and may be spherical, aspheric, toroidal, or anamorphic. Alternatively, these lenses may be eccentrically disposed with respect to reference beam Lc. 
     The surface of first lens  121  on the display device  110  side according to the first to third exemplary embodiments does not have to be entirely concave, and may be partially concave. 
     The reflection surface of first mirror  122  according to the first exemplary embodiment is not limited to a free-form surface, and may be spherical, aspheric, toroidal, or anamorphic. Alternatively, these mirrors may be eccentrically disposed with respect to reference beam Lc. 
     The emitting surface of second lens  123  according to the first exemplary embodiment is not limited to a free-form surface, and may be spherical, aspheric, toroidal, or anamorphic. Further, second lens  123  is not limited to a linear Fresnel lens, and may be a Fresnel lens in which grooves are circularly disposed, or may be a bulk lens without any grooves. 
     In the first exemplary embodiment, one first mirror  122  is disposed on the emitting surface side of first lens  121 , but a plurality of mirrors may be disposed. Still further, in the first exemplary embodiment, while one second lens  123  is disposed, a plurality of lens elements may be disposed, or lens elements may not be disposed. 
     The reflection surface of first mirror  122  in the third exemplary embodiment is convex, but may be flat or concave. 
     The surfaces of first mirror  122  and second mirror  124  according to the third exemplary embodiment are not limited to a free-form surface, and may be spherical, aspheric, toroidal, or anamorphic. Further, such a mirror may be eccentrically disposed with respect to reference beam Lc. 
     In the third exemplary embodiment, first mirror  122  is disposed on a rear side of the vehicle with respect to second mirror  124 , but the present disclosure is not limited thereto. First mirror  122  may be disposed on a front side of the vehicle with respect to second mirror  124 , or first mirror  122  and second mirror  124  may be disposed in the right/left direction of the vehicle (the direction perpendicular to  FIG. 6 ). 
     Still further, in the third exemplary embodiment, while display device  110  is disposed to be lower than first mirror  122 , the present disclosure is not limited thereto. For example, display device  110  may be disposed to be higher than first mirror  122 , or may be disposed on the rear side of the vehicle with respect to first mirror  122 , or display device  110  and first mirror  122  may be disposed in the right/left direction of the vehicle (the direction perpendicular to  FIG. 6 ). 
     Note that, the exemplary embodiments described above are illustrations of the technique of the present disclosure. Therefore, various changes, replacements, additions, or omissions may be made to the exemplary embodiments within the scope of claims or their equivalents. 
     The present disclosure is applicable to a head-up display that uses a refractive optical system such as a lens. Specifically, the present disclosure is applicable to a head-up display for a vehicle.