Patent Publication Number: US-2023161156-A1

Title: Head-up display and moving body with head-up display mounted thereon

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation of U.S. patent application Ser. No. 16/892,397, filed on Jun. 4, 2020, which is a Continuation of International Patent Application No. PCT/JP2018/039307, filed on Oct. 23, 2018, which claims the benefit of foreign priority of Japanese Patent Application No. 2017-236946 filed on Dec. 11, 2017, the contents all of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a head-up display and a moving body with the head-up display mounted thereon. 
     BACKGROUND ART 
     PTL 1 discloses a head-up display configured to project a displayed image on a windshield. The head-up display has a display surface, and includes a display device configured to display an image on the display surface, a concave mirror, and a lens disposed between the concave mirror and the display surface and configured to condense light. The head-up display further includes a first optical system configured to form an image from beams emitted from the display surface and passing the lens and the concave mirror to form an intermediate image obtained by enlarging the image. The head-up display still further includes a second optical system configured to project the intermediate image on the windshield. The intermediate image formed by the first optical system is larger than the image displayed on the display surface by the display device. This configuration achieves reduction in size of the first optical system and the second optical system. 
     CITATION LIST 
     Patent Literature 
     PTL 1: Unexamined Japanese Patent Publication No. 2017-120388 
     SUMMARY 
     The present disclosure provides a head-up display that can be reduced in size and effectively inhibits stray light caused by outside light. 
     The present disclosure provides a head-up display configured to project an image on a transparent reflection member to cause an observer to visually recognize a virtual image, the head-up display including: a display device configured to display the image; and a projection optical system configured to project the image displayed by the display device as the virtual image for the observer. The projection optical system is configured to form the image as an intermediate image, and includes a first lens configured to condense light, and a first optical element configured to diffuse light. The first lens and the first optical element are disposed in this order along an optical path from the display device. The first lens is inclined with respect to a reference beam which is defined as a beam reaching a center of a viewpoint region of the observer and corresponding to a center of the virtual image. 
     The head-up display according to the present disclosure is configured to provide a less distorted virtual image, can be reduced in size, and effectively inhibit stray light caused by outside light. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is an explanatory schematic view of a vehicle equipped with a head-up display according to a first exemplary embodiment. 
         FIG.  2    is a schematic view depicting a configuration of the head-up display according to the first exemplary embodiment. 
         FIG.  3    is an explanatory schematic view depicting telephoto arrangement according to the first exemplary embodiment. 
         FIG.  4    is a schematic view depicting a configuration of a relay optical system according to the first exemplary embodiment. 
         FIG.  5    is a schematic view depicting a configuration of a head-up display according to a second exemplary embodiment. 
         FIG.  6    is a schematic view depicting a configuration of a head-up display according to a third exemplary embodiment. 
         FIG.  7    is a view depicting behavior of a head-up display according to a fourth exemplary embodiment. 
         FIG.  8    is a schematic view depicting a configuration of a head-up display according to a fifth exemplary embodiment. 
         FIG.  9    is a view depicting behavior of a head-up display according to a sixth exemplary embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Exemplary embodiments will hereinafter be described with appropriate reference to the drawings. The description may not include details beyond necessity. For example, already well-known matters may not be described in detail, and substantially identical configurations may not be described repeatedly. These prevent unnecessary redundancy in the following description and lead to easier comprehension by the person skilled in the art. 
     The inventor(s) provide the accompanying drawings and the following description for full comprehension of the present disclosure by the person skilled in the art, without any intention to limit the subject matter recited in the claims. 
     (First Exemplary Embodiment) 
     The first exemplary embodiment will be described below with reference to  FIG.  1    to  FIG.  4   . 
     [1-1. Configuration] 
     [1-1-1. Entire Configuration of Head-Up Display] 
     Head-up display  100  according to a specific exemplary embodiment and a practical example of the present disclosure will be described hereinafter with reference to the drawings. 
       FIG.  1    is a sectional view of vehicle  200  equipped with head-up display  100  according to the present disclosure. As depicted in  FIG.  1   , head-up display  100  is disposed in dashboard  210  below windshield  220  of vehicle  200 . Observer D recognizes an image projected from head-up display  100  as virtual image I. 
       FIG.  2    is a schematic view depicting a configuration of head-up display  100  according to the present exemplary embodiment.  FIG.  3    is an explanatory schematic view depicting the configuration of head-up display  100  according to the present exemplary embodiment. 
     As depicted in  FIG.  2   , head-up display  100  includes display device  110  and projection optical system  140 . Head-up display  100  projects an image displayed by display device  110  on windshield  220 . Projected light is reflected by windshield  220  and is guided into viewpoint region  300  of observer D. Head-up display  100  accordingly causes observer D to visually recognize virtual image I. A viewpoint corresponds to a principal point of an eye of observer D considered as a lens. Viewpoint region  300  corresponds to a region including the viewpoint of observer D, and enables observer D to visually recognize entire virtual image I. 
     The present disclosure refers to a forward direction indicating a direction from observer D to windshield  220  of vehicle  200 . A backward direction indicates a direction opposite to the forward direction. A downward direction indicates a direction toward a ground surface on which vehicle  200  travels. An upward direction indicates a direction opposite to the downward direction. An inward direction indicates a direction from observer D on a driver&#39;s seat to a passenger seat. An outward direction indicates a direction opposite to the inward direction. Viewpoint region  300  corresponds to a region enabling observer D to visually recognize entire virtual image I. 
     As depicted in  FIG.  2   , it is assumed that beams emitted from display device  110  include beam L reaching viewpoint region  300 . The beams emitted from display device  110  also include reference beam Lc passing a center of virtual image I and reaching a center of viewpoint region  300 . When viewed from observer D, reference beam Lc corresponds to an optical path from the center of virtual image I to the viewpoint of observer D. Reference beam Lc visually recognized by observer D actually is emitted from display device  110  and reaches observer D via the optical system. A beam corresponding to reference beam Lc emitted from the center of virtual image I and running from display device  110  to observer D is also called reference beam Lc. Optical paths corresponding to these beams are also called reference beam Lc. It is assumed that the viewpoint of observer D is positioned at the center of viewpoint region  300 . 
     Display device  110  displays an image on a diffusing surface or the like under control of a controller such as a CPU (not depicted). Examples of display device  110  include a liquid crystal display equipped with a backlight unit, an organic light-emitting diode, and a plasma display. Display device  110  may alternatively be constituted by a screen configured to diffuse or reflect light, and a projector or a scanning laser to generate an image. Display device  110  is configured to display various information such as a road travel guide, distance to a vehicle travelling ahead, vehicle battery residual quantity, and current vehicle speed. Display device  110  may optionally be configured to electronically distort an image preliminarily in accordance with distortion generated by projection optical system  130  or windshield  220  and a position of observer D acquired by a camera (not depicted). This configuration enables preferred visual recognition of virtual image I by observer D. Display device  110  may optionally be configured to preliminarily display pixels having a plurality of wavelengths displaced per display position in accordance with chromatic aberration generated by projection optical system  130 . This configuration enables preferred visual recognition of virtual image I by observer D. 
     Projection optical system  140  includes relay optical system  120  and projection optical system  130 . Relay optical system  120  includes second lens  121 , first mirror  122  serving as a second optical element, first lens  123 , and second mirror  124  serving as a first optical element. Relay optical system  120  forms an image from beams emitted from display device  110  to form intermediate image M obtained by enlarging the image thus displayed. Intermediate image M is formed by enlarging the image displayed on the screen of display device  110 . Intermediate image M can thus have a large size even if the image displayed on the screen of display device  110  has a small size. This achieves reduction in size of the screen of display device  110 . Intermediate image M having such a large size leads to magnification decrease in projection optical system  130 . This enables decrease in positive power of third mirror  125  included in projection optical system  130  for inhibition of distortion on the screen. 
     Intermediate image M does not need to be formed at a position preferred for the intermediate image. Intermediate image M may have spherical aberration, comatic aberration, field curvature, and astigmatism. 
     Projection optical system  130  includes third mirror  125 . Projection optical system  130  reflects, at third mirror  125 , intermediate image M formed by relay optical system  120 . Projection optical system  130  accordingly projects intermediate image M on windshield  220 . Intermediate image M is an aerial image formed in a space, and is not formed on a projection surface causing diffusion and reflection. Third mirror  125  is disposed on an optical path from intermediate image M to windshield  220 . 
     [1-1-2. Arrangement Configuration of Projection Optical System, Relay Optical System, and Display Device] 
     As depicted in  FIG.  2   , second lens  121  is positioned ahead of display device  110  in vehicle  200 . As depicted in  FIG.  2   , second lens  121  is inclined counterclockwise from reference beam Lc in an XZ planar view of  FIG.  2   . This configuration prevents stray light caused by outside light entering a case and being reflected by a display surface of display device  110  or first mirror  122 . 
     Second lens  121  is a free-form surface lens having difference between curvature in an X axis direction and curvature in a Y axis direction. Second lens  121  has a surface (incidence surface) adjacent to display device  110 , and the surface is shaped to be planar toward display device  110  in the X axis direction and the Y axis direction. Second lens  121  has another surface (emission surface) adjacent to first mirror  122 , and the surface is shaped to be convex toward first mirror  122  in the X axis direction and the Y axis direction. 
     First mirror  122  is positioned ahead of second lens  121  in vehicle  200 . First mirror  122  condenses beams emitted from second lens  121  and reflects the beams toward first lens  123 . First mirror  122  has a reflecting surface eccentric to reflect an image displayed by display device  110  toward second mirror  124 . The reflecting surface of first mirror  122  is concave. Specifically, first mirror  122  expands light incident from second lens  121  to be projected on first lens  123 . First mirror  122  is shaped to have a free-form surface. This shape enables strain correction of a virtual image caused by reflection. 
     As depicted in  FIG.  2   , first lens  123  is positioned behind first mirror  122  in vehicle  200 . As depicted in  FIG.  2   , first lens  123  is inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  2   . First lens  123  is inclined with respect to reference beam Lc at an exemplary angle from 15 degrees to 30 degrees. This configuration prevents stray light caused by outside light entering the case and being reflected by first mirror  122  or second mirror  124 . 
     First lens  123  is a free-form surface lens having difference between curvature in the X axis direction and curvature in the Y axis direction. First lens  123  has a surface (incidence surface) adjacent to first mirror  122 , and the incidence surface is shaped to be convex toward first mirror  122  in the X axis direction and the Y axis direction. First lens  123  has another surface (emission surface) adjacent to second mirror  124 , and the emission surface is shaped to be planar toward display device  110  in the X axis direction and the Y axis direction. 
     Second mirror  124  is positioned behind first lens  123  in vehicle  200 . Second mirror  124  diffuses beams emitted from first lens  123 , and forms intermediate image M obtained by enlarging a display image at an optical path between second mirror  124  and third mirror  125 . Second mirror  124  has a reflecting surface eccentric to enlarge the display image projected from first lens  123  and form intermediate image M at the optical path between second mirror  124  and third mirror  125 . The reflecting surface of second mirror  124  is convex. Second mirror  124  is shaped to have a free-form surface. This shape enables strain correction of a virtual image caused by reflection. 
     Projection optical system  130  includes third mirror  125  serving as a third optical element. Third mirror  125  is positioned ahead of second mirror  124  in vehicle  200 . Third mirror  125  condenses beams diffused by second mirror  124 , and projects intermediate image M on windshield  220 . Third mirror  125  has a reflecting surface eccentric to project intermediate image M on windshield  220 . The reflecting surface of third mirror  125  is concave. Third mirror  125  is shaped to have a free-form surface. This shape enables strain correction of a virtual image caused by reflection. 
     In projection optical system  140  according to the present exemplary embodiment, first mirror  122 , first lens  123  configured to condense light, and second mirror  124  serving as the first optical element configured to diffuse light and form intermediate image M are disposed in this order along an optical path from display device  110 . First lens  123  and second mirror  124  configured to form intermediate image M are disposed in the order along the optical path, so that intermediate image M can be formed adjacent to an emission end of first lens  123 . This leads to reduction in size of first lens  123  itself and reduction in size of head-up display  100 . 
     In relay optical system  120  according to the present exemplary embodiment, first lens  123  having positive power and second mirror  124  having negative power are disposed after display device  110  and before intermediate image M. Relay optical system  120  has so-called telephoto arrangement. In such telephoto arrangement, first lens  123  increases negative power of second mirror  124  and second mirror  124  increases positive power of first lens  123 . That is, first lens  123  and second mirror  124  improve power each other. This leads to reduction in entire length of relay optical system  120  and reduction in size of head-up display  100 . 
       FIG.  3    is an explanatory view indicating effect of telephoto arrangement.  FIG.  3    depicts relay optical system  120  and projection optical system  130  disposed linearly for easier comprehension. As apparent from  FIG.  3   , in comparison to part (A) of  FIG.  3    according to a comparative example without provision of first lens  123 , part (B) of  FIG.  3    depicts relay optical system  120  having short entire length in the present exemplary embodiment with telephoto arrangement of first lens  123  and second mirror  124 . 
     Beams forming intermediate image M are limited around second mirror  124  having negative power and configured to form intermediate image M. First lens  123  having positive power is disposed adjacent to second mirror  124  having negative power to achieve telephoto arrangement, which enables reduction in size of first lens  123  itself. 
     As depicted in  FIG.  4   , the incidence surface and the emission surface of second lens  121  according to the present exemplary embodiment are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  4   . Furthermore, the incidence surface and the emission surface of first lens  123  are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  4   . Reflected light of outside light at first lens  123  is reflected to pass above first mirror  122 , whereas reflected light of outside light at second lens  121  is reflected to pass below first mirror  122 . Outside light is thus prevented from being incident on viewpoint region  300 . Second lens  121  and first lens  123  are each desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on second lens  121  or first lens  123  is reflected by the incidence surface or the emission surface of second lens  121  or first lens  123 . Second lens  121  and first lens  123  being inclined with respect to reference beam Lc indicates that second lens  121  and first lens  123  each have an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respect to a plane perpendicular to reference beam Lc. 
     Second lens  121  according to the present exemplary embodiment has a wedge shape with gradual decrease in lens thickness toward a lower end with respect to reference beam Lc. First lens  123  has a wedge shape with gradual decrease in lens thickness toward an upper end with respect to reference beam Lc. When second lens  121  is inclined with respect to reference beam Lc as described above and the emission surface of second lens  121  is assumed to be convex symmetrically with respect to reference beam Lc, beams passing a portion above reference beam Lc, of second lens  121  and beams passing another portion below reference beam Lc, of second lens  121  are different in terms of optical path length. When first lens  123  is similarly inclined with respect to reference beam Lc and the incidence surface of first lens  123  is assumed to be convex symmetrically with respect to reference beam Lc, beams passing a portion above reference beam Lc, of first lens  123  and beams passing another portion below reference beam Lc, of first lens  123  are different in terms of optical path length. 
     In view of this, second lens  121  according to the present exemplary embodiment has the wedge shape with gradual decrease in lens thickness toward the lower end with respect to reference beam Lc. First lens  123  has the wedge shape with gradual decrease in lens thickness toward the upper end with respect to reference beam Lc. This configuration causes beams emitted from display device  110  and transmitted through the portion above reference beam Lc, of second lens  121  (i.e. a thick portion of second lens  121 ) to be reflected by first mirror  122 . The reflected beams pass the portion above reference beam Lc, of first lens  123  (i.e. a thin portion of first lens  123 ). Beams emitted from display device  110  and transmitted through the portion below reference beam Lc, of second lens  121  (i.e. a thin portion of second lens  121 ) are reflected by first mirror  122 . The reflected beams pass the portion below reference beam Lc, of first lens  123  (i.e. a thick portion of first lens  123 ). Beams passing second lens  121  and first lens  123  are adjusted in terms of optical path length in this manner to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     The emission surface of second lens  121  according to the present exemplary embodiment is directed downward in comparison to the incidence surface. That is, second lens  121  has a wedge shape in the Y axis direction. Second lens  121  has the wedge sectional shape in the Y axis direction, so that light passing above second lens  121  is longer in optical path length than light passing below second lens  121 . The optical path length until image light emitted from display device  110  reaches first mirror  122  can be changed in accordance with the position in the Y axis direction. This enables preferred correction of eccentric field curvature generated at first mirror  122 . 
     [1-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the first exemplary embodiment is configured to project an image on windshield  220  (exemplifying a transparent reflection member) and cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. First lens  123  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by first lens  123  or the like. Projection optical system  140  includes first lens  123  configured to condense light, and second mirror  124  exemplifying the first optical element configured to diffuse light, which are disposed in the order along the optical path from display device  110 . In head-up display  100  according to the first exemplary embodiment, first lens  123  having positive power is disposed ahead of second mirror  124  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This accordingly leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . 
     Second mirror  124  exemplifies the first optical element according to the first exemplary embodiment. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D. 
     In head-up display  100  according to the first exemplary embodiment, first lens  123  has at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Head-up display  100  according to the first exemplary embodiment includes first lens  123  having the wedge shape. Even when first lens  123  is inclined with respect to reference beam Lc, beams passing first lens  123  can thus be adjusted in terms of optical path length. 
     Head-up display  100  according to the first exemplary embodiment includes first mirror  122  exemplifying the second optical element, and second lens  121 . First mirror  122  is disposed between display device  110  and first lens  123 . Second lens  121  is disposed between display device  110  and first mirror  122 . Second lens  121  has the wedge shape and includes at least one free-form surface. In head-up display  100  according to the first exemplary embodiment, first lens  123  and second lens  121  are disposed such that beams passing a thin portion of a first one of these lenses pass a thick portion of a second one of the lenses and beams passing a thick portion of the first one pass a thin portion of the second one. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can be uniformized in terms of optical path length. 
     In head-up display  100  according to the first exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     Vehicle  200  exemplifying a moving body according to the first exemplary embodiment includes head-up display  100  and windshield  220  serving as a transparent reflection member. This configuration enables observer D as a driver of vehicle  200  to visually recognize an image projected on windshield  220  as virtual image I. 
     (Second Exemplary Embodiment) 
     The second exemplary embodiment will be described next with reference to  FIG.  5   . 
     [2-1. Configuration] 
       FIG.  5    is an explanatory schematic view depicting optical paths of head-up display  100  according to the second exemplary embodiment. As depicted in  FIG.  5   , head-up display  100  according to the present exemplary embodiment includes third lens  126  having first lens unit  126   a,  and second lens unit  126   b  integrally provided with first lens unit  126   a,  and first lens unit  126   a  and second lens unit  126   b  correspond to the first lens and the second lens according to the first exemplary embodiment. 
     Third lens  126  is positioned ahead of display device  110  and second mirror  124  in vehicle  200 , as depicted in  FIG.  5   . As depicted in  FIG.  5   , third lens  126  has a surface facing first mirror  122  and shaped to be convex toward first mirror  122  in the X axis direction and the Y axis direction. As depicted in  FIG.  5   , third lens  126  has a surface facing display device  110  and second mirror  124  and having a planar shape with a plane directed toward display device  110  and second mirror  124 . Third lens  126  is a free-form surface lens with the convex shape having difference between curvature in the X axis direction and curvature in the Y axis direction. 
     On the optical path from display device  110  to first mirror  122 , second lens unit  126   b  has a planar surface serving as an incidence surface and a convex surface serving as an emission surface. The incidence surface and the emission surface of second lens unit  126   b  are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  5   . This configuration prevents stray light caused by outside light entering the case and being reflected by the display surface of display device  110  and first mirror  122 . 
     On the optical path from first mirror  122  to second mirror  124 , first lens unit  126   a  has a planar surface serving as an emission surface and a convex surface serving as an incidence surface. First lens unit  126   a  is inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  5   . This configuration prevents stray light caused by outside light entering the case and being reflected by the display surface of display device  110  and first mirror  122 . 
     In relay optical system  120  according to the present exemplary embodiment, first lens unit  126   a  having positive power and second mirror  124  having negative power are disposed after display device  110  and before intermediate image M. Relay optical system  120  has so-called telephoto arrangement. In such telephoto arrangement, first lens unit  126   a  increases negative power of second mirror  124  and second mirror  124  increases positive power of first lens unit  126   a.  That is, first lens unit  126   a  and second mirror  124  improve power each other. This leads to reduction in entire length of relay optical system  120  and reduction in size of head-up display  100 . 
     As described above, the present exemplary embodiment provides first lens unit  126   a  disposed between first mirror  122  serving as the second optical element and third mirror  125  configured to project intermediate image M. Particularly, third lens  126  having positive power is disposed ahead of second mirror  124  having negative power and serving as the first optical element configured to form intermediate image M in the order along the optical path from display device  110 . This leads to reduction in entire length of relay optical system  120  and reduction in size of first lens unit  126   a  itself for reduction in size of head-up display  100 . 
     Third lens  126  according to the present exemplary embodiment includes first lens unit  126   a  and second lens unit  126   b  integrally provided with first lens unit  126   a,  and first lens unit  126   a  and second lens unit  126   b  correspond to second lens  121  and first lens  123  according to the first exemplary embodiment. First lens unit  126   a  and second lens unit  126   b  each have a wedge shape with gradual decrease in lens thickness toward the end relatively to the center of third lens  126 . In the above case where third lens  126  is inclined with respect to reference beam Lc, beams passing a portion above reference beam Lc, of second lens unit  126   b  and beams passing another portion below reference beam Lc, of second lens unit  126   b  are different in terms of optical path length on the optical path from display device  110  to first mirror  122 . Similarly, beams passing a portion above reference beam Lc, of second lens unit  126   b  and beams passing another portion below reference beam Lc, of second lens unit  126   b  are different in terms of optical path length on the optical path from first mirror  122  to second mirror  124 . 
     In view of this, the present exemplary embodiment provides second lens unit  126   b  having the wedge shape with gradual decrease in lens thickness toward the lower end with respect to reference beam Lc, and first lens unit  126   a  having the wedge shape with gradual decrease in lens thickness toward the upper end with respect to reference beam Lc. This configuration causes beams emitted from display device  110  and transmitted through the portion above reference beam Lc, of second lens unit  126   b  (i.e. a thick portion of second lens unit  126   b ) to be reflected by first mirror  122 . The reflected beams pass the portion above reference beam Lc, of first lens unit  126   a  (i.e. a thin portion of first lens unit  126   a ). 
     Beams emitted from display device  110  and transmitted through the portion below reference beam Lc, of second lens unit  126   b  (i.e. a thin portion of second lens unit  126   b ) are reflected by first mirror  122 . The reflected beams pass the portion below reference beam Lc, of first lens unit  126   a  (i.e. a thick portion of first lens unit  126   a ). 
     In the present exemplary embodiment, beams passing second lens unit  126   b  and first lens unit  126   a  in third lens  126  are adjusted in terms of optical path length in this manner to uniformize optical path length of beams regardless of a passed portion of third lens  126 . 
     Third lens  126  is desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface of third lens  126 . Third lens  126  being inclined with respect to reference beam Lc indicates that third lens  126  has an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respective to a plane perpendicular to reference beam Lc. 
     On the optical path from display device  110  to first mirror  122 , the emission surface of second lens unit  126   b  is directed downward in comparison to the incidence surface. Second lens unit  126   b  has a wedge shape in the Y axis direction. Second lens unit  126   b  has the wedge sectional shape in the Y axis direction, so that light passing above second lens unit  126   b  is longer in optical path length than light passing below second lens unit  126   b  on the optical path from display device  110  to the first mirror  122 . The optical path length until image light emitted from display device  110  reaches first mirror  122  can be changed in accordance with the position in the Y axis direction. This enables preferred correction of eccentric field curvature generated at first mirror  122 . 
     As described above, the present exemplary embodiment provides third lens  126  including first lens unit  126   a  and second lens unit  126   b  integrally provided with first lens unit  126   a,  and first lens unit  126   a  and second lens unit  126   b  correspond to second lens  121  and first lens  123  according to the first exemplary embodiment. This configuration achieves reduction in a number of components and reduction in production cost for head-up display  100 . 
     [2-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the second exemplary embodiment is configured to cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. Third lens  126  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by third lens  126  or the like. Projection optical system  140  includes third lens  126  configured to condense light, and second mirror  124  exemplifying the first optical element configured to diffuse light, which are disposed in the order along the optical path from display device  110 . Third lens  126  includes first lens unit  126   a  and second lens unit  126   b  integrally provided with first lens unit  126   a,  and first lens unit  126   a  and second lens unit  126   b  correspond to first lens  123  and second lens  121  according to the first exemplary embodiment. In head-up display  100  according to the second exemplary embodiment, third lens  126  and second mirror  124  are disposed in the order along the optical path from display device  110 . Accordingly, intermediate image M can be formed adjacent to an emission end of first lens unit  126   a,  and first lens unit  126   a  itself can be reduced in size. This leads to reduction in size of head-up display  100 . Third lens  126  integrally includes second lens  121  and first lens  123  according to the first exemplary embodiment. This configuration achieves reduction in the number of components and reduction in production cost for head-up display  100 . 
     Projection optical system  140  according to the second exemplary embodiment includes third lens  126  and second mirror  124  configured to diffuse light, which are disposed in the order along the optical path from display device  110 . First lens unit  126   a  having positive power is thus disposed ahead of second mirror  124  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This leads to reduction in entire length of relay optical system  120  and reduction in size of first lens unit  126   a  for reduction in size of head-up display  100 . 
     In the present exemplary embodiment, beams emitted from display device  110  pass third lens  126  twice on the optical path from display device  110  to first mirror  122  and on the optical path from first mirror  122  to second mirror  124 . Also in this case, projection optical system  140  similarly includes first mirror  122  configured to condense light, third lens  126  configured to condense light, second mirror  124  configured to diffuse light, and third mirror  125  configured to project intermediate image M, which are disposed in the order along the optical path from display device  110 . Similarly, beams emitted from display device  110  proceed via first mirror  122 , third lens  126 , second mirror  124 , and third mirror  125  in the mentioned order, and causes observer D to visually recognize virtual image I. 
     In head-up display  100  according to the second exemplary embodiment, third lens  126  has at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Third lens  126  in head-up display  100  according to the second exemplary embodiment includes first lens unit  126   a  and second lens unit  126   b  each having the wedge shape. Even when third lens  126  is inclined with respect to reference beam Lc, beams passing third lens  126  can thus be adjusted in terms of optical path length. 
     In head-up display  100  according to the second exemplary embodiment, third lens  126 , which integrally includes first lens unit  126   a  and second lens unit  126   b  corresponding to first lens  123  and second lens  121  according to the first exemplary embodiment, has the wedge shape. Accordingly, beams passing a thin portion of second lens unit  126   b  on the optical path from display device  110  to first mirror  122  pass a thick portion of first lens unit  126   a  on the optical path from first mirror  122  to second mirror  124 . Similarly, beams passing a thick portion of second lens unit  126   b  on the optical path from display device  110  to first mirror  122  pass a thin portion of first lens unit  126   a  on the optical path from first mirror  122  to second mirror  124 . Even when third lens  126  is inclined with respect to reference beam Lc, beams passing third lens  126  can thus be uniformized in terms of optical path length. 
     In head-up display  100  according to the second exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     (Third Exemplary Embodiment) 
     The third exemplary embodiment will be described next with reference to  FIG.  6   . 
     [3-1. Configuration] 
       FIG.  6    is an explanatory schematic view depicting optical paths of head-up display  100  according to the third exemplary embodiment. As depicted in  FIG.  6   , head-up display  100  according to the present exemplary embodiment includes fourth lens  127  alternatively exemplifying the second optical element. 
     Display device  110  and second lens  121  according to the present exemplary embodiment are configured similarly to display device  110  and second lens  121  according to each of the exemplary embodiments described above. The present exemplary embodiment is different from the above exemplary embodiments in terms of disposed positions. As depicted in  FIG.  6   , display device  110  and second lens  121  according to the present exemplary embodiment are positioned ahead of fourth lens  127  serving as the second optical element in vehicle  200 . 
     As depicted in  FIG.  6   , fourth lens  127  has an incidence surface facing second lens  121  and an emission surface facing first lens  123 , both of which are shaped to be convex toward second lens  121  and first lens  123  in the X axis direction and the Y axis direction. Fourth lens  127  is a free-form surface lens with the convex shape having difference between curvature in the X axis direction and curvature in the Y axis direction. 
     Second lens  121 , fourth lens  127 , and first lens  123  according to the present exemplary embodiment are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  6   . This configuration prevents stray light caused by outside light entering the case and being reflected by second lens  121 , fourth lens  127 , or first lens  123 . 
     As described above, the present exemplary embodiment adopts fourth lens  127  serving as the second optical element. First lens  123  is disposed between fourth lens  127  and third mirror  125  configured to project intermediate image M. Particularly, first lens  123  having positive power is disposed ahead of second mirror  124  having negative power and serving as the first optical element configured to form intermediate image M in the order along the optical path from display device  110 . This leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . 
     The present exemplary embodiment is different from the first exemplary embodiment in terms of positional relation between first lens  123  and second lens  121 , and positions of thick portions and thin portions with respect to reference beam Lc are opposite to each other. Similarly to the first exemplary embodiment, beams passing second lens  121  and first lens  123  are thus adjusted in terms of optical path length to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     [3-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the third exemplary embodiment is configured to cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. First lens  123  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by first lens  123 , second lens  121 , or fourth lens  127 . Projection optical system  140  includes fourth lens  127  exemplifying the second optical element, first lens  123  configured to condense light, and second mirror  124  exemplifying the first optical element configured to diffuse light, which are disposed in the order along the optical path from display device  110 . In head-up display  100  according to the third exemplary embodiment, first lens  123  having positive power is disposed ahead of second mirror  124  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This accordingly leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . 
     In head-up display  100  according to the third exemplary embodiment, first lens  123 , second lens  121 , and fourth lens  127  each have at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Head-up display  100  according to the third exemplary embodiment includes first lens  123  and second lens  121  each having the wedge shape. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can thus be adjusted in terms of optical path length. 
     In head-up display  100  according to the third exemplary embodiment, positions, with respect to reference beam Lc, of thick portions and thin portions of first lens  123  and second lens  121  are opposite to each other. Similarly to the first exemplary embodiment, beams passing second lens  121  and first lens  123  are thus adjusted in terms of optical path length to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     In head-up display  100  according to the third exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     (Fourth Exemplary Embodiment) 
     The fourth exemplary embodiment will be described next with reference to  FIG.  7   . 
     [4-1. Configuration] 
       FIG.  7    is an explanatory schematic view depicting optical paths of head-up display  100  according to the fourth exemplary embodiment. As depicted in  FIG.  7   , head-up display  100  according to the present exemplary embodiment includes fifth lens  128  disposed ahead of first lens  123  on the optical path from first mirror  122  to second mirror  124 . 
     Fifth lens  128  is a free-form surface lens having difference between curvature in the X axis direction and curvature in the Y axis direction. Fifth lens  128  has a planar incidence surface adjacent to first mirror  122  and an emission surface adjacent to first lens  123  and concave toward first lens  123  in the X axis direction. The emission surface of fifth lens  128  has curvature in the Y axis direction less than curvature in the X axis direction. That is, fifth lens  128  has a shape in the Y axis direction, provided with a concave surface having the curvature less than the curvature in the X axis direction, a convex surface, or a planar surface. 
     As depicted in  FIG.  7   , the incidence surface and the emission surface of fifth lens  128  according to the present exemplary embodiment are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  7   . This configuration causes reflected light to pass above fifth lens  128 . The reflected light is thus prevented from being incident on viewpoint region  300 . Fifth lens  128  is desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  and second mirror  124  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on fifth lens  128  is reflected by the incidence surface or the emission surface of fifth lens  128 . Fifth lens  128  being inclined with respect to reference beam Lc indicates that fifth lens  128  has an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respective to a plane perpendicular to reference beam Lc. 
     Fifth lens  128  is a lens element having negative refractive power. Fifth lens  128  thus configured is disposed ahead of first lens  123  on the optical path from first mirror  122  to second mirror  124 , to inhibit chromatic aberration generated at first lens  123 . 
     In projection optical system  140  according to the present exemplary embodiment, fifth lens  128 , first mirror  122  serving as the second optical element configured to condense light, and second mirror  124  serving as the first optical element configured to form intermediate image M are disposed in the order along the optical path from display device  110 . First lens  123  is disposed ahead of second mirror  124  configured to form intermediate image M in the order along the optical path from display device  110 , so that intermediate image M can be formed adjacent to the emission end of first lens  123 . First lens  123  itself can thus be reduced in size. This leads to reduction in size of head-up display  100 . Furthermore, the negative refractive power of fifth lens  128  inhibits chromatic aberration generated at first lens  123 . 
     In relay optical system  120  according to the present exemplary embodiment, first lens  123  having positive power and second mirror  124  having negative power are disposed after display device  110  and before intermediate image M. Relay optical system  120  has so-called telephoto arrangement. In such telephoto arrangement, first lens  123  increases negative power of second mirror  124  and second mirror  124  increases positive power of first lens  123 . That is, first lens  123  and second mirror  124  improve power each other. This leads to reduction in entire length of relay optical system  120  and reduction in size of head-up display  100 . 
     As depicted in  FIG.  7   , the incidence surface and the emission surface of second lens  121  according to the present exemplary embodiment are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  7   . Furthermore, the incidence surface and the emission surface of first lens  123  are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  7   . Reflected light of outside light at first lens  123  is reflected to pass below second mirror  124 , and reflected light of outside light at second lens  121  is reflected to pass below first mirror  122 . The reflected light is thus prevented from being incident on viewpoint region  300 . Second lens  121  and first lens  123  are each desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  or second mirror  124  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on second lens  121  or first lens  123  is reflected by the incidence surface or the emission surface of second lens  121  or first lens  123 . Second lens  121  and first lens  123  being inclined with respect to reference beam Lc indicates that second lens  121  and first lens  123  each have an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respect to a plane perpendicular to reference beam Lc. 
     Similarly to the first exemplary embodiment, positions of thick portions and thin portions of first lens  123  and second lens  121  with respect to reference beam Lc are opposite to each other. Similarly to the first exemplary embodiment, beams passing second lens  121  and first lens  123  are thus adjusted in terms of optical path length to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     [4-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the fourth exemplary embodiment is configured to cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. First lens  123  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by fifth lens  128  or the like. Projection optical system  140  includes first lens  123  configured to condense light, and second mirror  124  exemplifying the first optical element configured to diffuse light, which are disposed in the order along the optical path from display device  110 . In head-up display  100  according to the fourth exemplary embodiment, first lens  123  having positive power is disposed ahead of second mirror  124  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This accordingly leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . Furthermore, fifth lens  128  is disposed ahead of first lens  123  in the order along the optical path from display device  110 . The negative refractive power of fifth lens  128  can thus inhibit chromatic aberration generated at first lens  123 . 
     Head-up display  100  according to the fourth exemplary embodiment includes first mirror  122  exemplifying the second optical element, and second mirror  124  exemplifying the first optical element. This enables formation of intermediate image M by sufficiently enlarging an image displayed by small display device  110 , and projection by further enlarging intermediate image M for observer D. 
     In head-up display  100  according to the fourth exemplary embodiment, second lens  121 , first lens  123 , and fifth lens  128  each have at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Head-up display  100  according to the fourth exemplary embodiment includes first lens  123  and second lens  121  each having the wedge shape. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can thus be adjusted in terms of optical path length. 
     Head-up display  100  according to the fourth exemplary embodiment includes second lens  121  disposed between display device  110  and first mirror  122 . Second lens  121  has the wedge shape and includes at least one free-form surface. In head-up display  100  according to the fourth exemplary embodiment, first lens  123  and second lens  121  are disposed such that beams passing a thin portion of a first one of these lenses pass a thick portion of a second one of the lenses and beams passing a thick portion of the first one pass a thin portion of the second one. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can be uniformized in terms of optical path length. 
     In head-up display  100  according to the fourth exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     (Fifth Exemplary Embodiment) 
     The fifth exemplary embodiment will be described next with reference to  FIG.  8   . 
     [5-1. Configuration] 
       FIG.  8    is an explanatory schematic view depicting optical paths of head-up display  100  according to the fifth exemplary embodiment. As depicted in  FIG.  8   , head-up display  100  according to the present exemplary embodiment includes sixth lens  129  disposed behind intermediate image M in the order along the optical path from second mirror  124  to third mirror  125 . 
     Sixth lens  129  is a free-form surface lens having difference between curvature in the X axis direction and curvature in the Y axis direction. Sixth lens  129  has a planar emission surface adjacent to third mirror  125  and an incidence surface adjacent to intermediate image M and concave toward first lens  123  in the X axis direction. The incidence surface of second mirror  124  has curvature in the Y axis direction less than curvature in the X axis direction. That is, sixth lens  129  has a shape in the Y axis direction, provided with a concave surface having the curvature less than the curvature in the X axis direction, a convex surface, or a planar surface. 
     As depicted in  FIG.  8   , the incidence surface and the emission surface of sixth lens  129  according to the present exemplary embodiment are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  8   . This configuration causes reflected light to pass below sixth lens  129 . The reflected light is thus prevented from being incident on viewpoint region  300 . Sixth lens  129  is desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on third mirror  125  and second mirror  124  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on second mirror  124  and third mirror  125  when outside light emitted from second mirror  124  and incident on sixth lens  129  is reflected by the incidence surface or the emission surface of sixth lens  129 . Sixth lens  129  being inclined with respect to reference beam Lc indicates that sixth lens  129  has an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respective to a plane perpendicular to reference beam Lc. 
     Sixth lens  129  is a lens element having negative refractive power. Sixth lens  129  thus configured is disposed behind the optical elements of relay optical system  120  on the optical path from display device  110  to third mirror  125 . This configuration reduces an aberration correction load of the optical elements to achieve higher resolution. 
     In projection optical system  140  according to the present exemplary embodiment, first mirror  122  serving as the second optical element configured to condense light and second mirror  124  serving as the first optical element configured to form intermediate image M are disposed in the order along the optical path from display device  110 . First lens  123  is disposed ahead of second mirror  124  configured to form intermediate image M in the order along the optical path from display device  110 , so that intermediate image M can be formed adjacent to the emission end of first lens  123 . First lens  123  itself can thus be reduced in size. This leads to reduction in size of head-up display  100 . Sixth lens  129  is disposed behind intermediate image M. This configuration reduces the aberration correction load of the optical elements in relay optical system  120  to achieve higher resolution. 
     In relay optical system  120  according to the present exemplary embodiment, first lens  123  having positive power and second mirror  124  having negative power are disposed after display device  110  and before intermediate image M. Relay optical system  120  has so-called telephoto arrangement. In such telephoto arrangement, first lens  123  increases negative power of second mirror  124  and second mirror  124  increases positive power of first lens  123 . That is, first lens  123  and second mirror  124  improve power each other. This leads to reduction in entire length of relay optical system  120  and reduction in size of head-up display  100 . 
     As depicted in  FIG.  8   , the incidence surface and the emission surface of second lens  121  according to the present exemplary embodiment are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  8   . Furthermore, the incidence surface and the emission surface of first lens  123  are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  8   . Reflected light of outside light at first lens  123  is reflected to pass below second mirror  124 , and reflected light of outside light at second lens  121  is reflected to pass below first mirror  122 . The reflected light is thus prevented from being incident on viewpoint region  300 . Second lens  121  and first lens  123  are each desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  or second mirror  124  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on second lens  121  or first lens  123  is reflected by the incidence surface or the emission surface of second lens  121  or first lens  123 . Second lens  121  and first lens  123  being inclined with respect to reference beam Lc indicates that second lens  121  and first lens  123  each have an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respect to a plane perpendicular to reference beam Lc. 
     Similarly to the first exemplary embodiment, positions of thick portions and thin portions of first lens  123  and second lens  121  with respect to reference beam Lc are opposite to each other. Similarly to the first exemplary embodiment, beams passing second lens  121  and first lens  123  are thus adjusted in terms of optical path length to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     [5-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the fifth exemplary embodiment is configured to cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. First lens  123  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by sixth lens  129  or the like. Projection optical system  140  includes first lens  123  configured to condense light, and second mirror  124  exemplifying the first optical element configured to diffuse light, which are disposed in the order along the optical path from display device  110 . In head-up display  100  according to the fifth exemplary embodiment, first lens  123  having positive power is disposed ahead of second mirror  124  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This accordingly leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . Furthermore, sixth lens  129  is disposed behind relay optical system  120  in the order along the optical path from display device  110 . This configuration reduces the aberration correction load of the optical elements in relay optical system  120  to achieve higher resolution. 
     Head-up display  100  according to the fifth exemplary embodiment includes first mirror  122  exemplifying the second optical element, and second mirror  124  exemplifying the first optical element. This enables formation of intermediate image M by sufficiently enlarging an image displayed by small display device  110 , and projection by further enlarging intermediate image M for observer D. 
     In head-up display  100  according to the fifth exemplary embodiment, second lens  121 , first lens  123 , and sixth lens  129  each have at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Head-up display  100  according to the fifth exemplary embodiment includes first lens  123  and second lens  121  each having the wedge shape. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can thus be adjusted in terms of optical path length. 
     Head-up display  100  according to the fifth exemplary embodiment includes second lens  121  disposed between display device  110  and first mirror  122 . Second lens  121  has the wedge shape and includes at least one free-form surface. In head-up display  100  according to the fourth exemplary embodiment, first lens  123  and second lens  121  are disposed such that beams passing a thin portion of a first one of these lenses pass a thick portion of a second one of the lenses and beams passing a thick portion of the first one pass a thin portion of the second one. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can be uniformized in terms of optical path length. 
     In head-up display  100  according to the fifth exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     (Sixth Exemplary Embodiment) 
     The sixth exemplary embodiment will be described next with reference to  FIG.  9   . 
     [6-1. Configuration] 
       FIG.  9    is an explanatory schematic view depicting optical paths of head-up display  100  according to the sixth exemplary embodiment. As depicted in  FIG.  9   , head-up display  100  according to the present exemplary embodiment includes seventh lens  150  alternatively exemplifying the first optical element. 
     First mirror  122  according to the present exemplary embodiment is configured similarly to first mirror  122  according to each of the first and second exemplary embodiments. The present exemplary embodiment is different from the above exemplary embodiments in terms of disposed positions. As depicted in  FIG.  9   , first mirror  122  according to the present exemplary embodiment is disposed in head-up display  100  at a rearmost position of vehicle  200 . Display device  110  and second lens  121  according to the present exemplary embodiment are configured similarly to display device  110  and second lens  121  according to each of the above exemplary embodiments. The present exemplary embodiment is different from the above exemplary embodiments in terms of disposed positions. As depicted in  FIG.  9   , display device  110  and second lens  121  according to the present exemplary embodiment are positioned ahead of first mirror  122  in vehicle  200 . 
     First lens  123  according to the present exemplary embodiment is configured similarly to first lens  123  according to each of the first and third exemplary embodiments. The present exemplary embodiment is, however, different in terms of the disposed position. First lens  123  according to the present exemplary embodiment is positioned behind seventh lens  150  serving as the first optical element in vehicle  200 . 
     Seventh lens  150  is a free-form surface lens having difference between curvature in the X axis direction and curvature in the Y axis direction. Seventh lens  150  has a planar incidence surface adjacent to first lens  123  and an emission surface adjacent to third mirror  125  and concave toward third mirror  125  in the X axis direction. The emission surface of seventh lens  150  has curvature in the Y axis direction less than curvature in the X axis direction. That is, seventh lens  150  has a shape in the Y axis direction, provided with a concave surface having the curvature less than the curvature in the X axis direction, a convex surface, or a planar surface. 
     As depicted in  FIG.  9   , the incidence surface and the emission surface of seventh lens  150  according to the present exemplary embodiment are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  9   . This configuration causes reflected light to pass below seventh lens  150 . The reflected light is thus prevented from being incident on viewpoint region  300 . Seventh lens  150  is desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  and third mirror  125  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on seventh lens  150  is reflected by the incidence surface or the emission surface of seventh lens  150 . Seventh lens  150  being inclined with respect to reference beam Lc indicates that seventh lens  150  has an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respective to a plane perpendicular to reference beam Lc. 
     Furthermore, the emission surface of seventh lens  150  has a wedge shape in the XZ planar view of  FIG.  9   . Seventh lens  150  has the wedge sectional shape in the Y axis direction, so that light passing above seventh lens  150  is longer in optical path length than light passing below seventh lens  150 . The optical path length until image light emitted from display device  110  forms intermediate image M can be changed in accordance with the position in the Y axis direction. This enables preferred correction of eccentric field curvature generated at first mirror  122 . 
     In projection optical system  140  according to the present exemplary embodiment, first mirror  122  serving as the second optical element configured to condense light and seventh lens  150  serving as the first optical element configured to form intermediate image M are disposed in the order along the optical path from display device  110 . First mirror  122  and seventh lens  150  interpose first lens  123  configured to condense light. First lens  123  is disposed between first mirror  122  configured to form intermediate image M and seventh lens  150  configured to form intermediate image M, so that intermediate image M can be formed adjacent to the emission end of first lens  123 . First lens  123  itself can thus be reduced in size. This leads to reduction in size of head-up display  100 . 
     In relay optical system  120  according to the present exemplary embodiment, first lens  123  having positive power and seventh lens  150  having negative power are disposed after display device  110  and before intermediate image M. Relay optical system  120  has so-called telephoto arrangement. In such telephoto arrangement, first lens  123  increases negative power of seventh lens  150  and seventh lens  150  increases positive power of first lens  123 . That is, first lens  123  and seventh lens  150  improve power each other. This leads to reduction in entire length of relay optical system  120  and reduction in size of head-up display  100 . 
     As depicted in  FIG.  9   , the incidence surface and the emission surface of second lens  121  according to the present exemplary embodiment are inclined clockwise from reference beam Lc in the XZ planar view of  FIG.  9   . Furthermore, the incidence surface and the emission surface of first lens  123  are inclined counterclockwise from reference beam Lc in the XZ planar view of  FIG.  9   . Reflected light of outside light at first lens  123  is reflected to pass above first mirror  122 , whereas reflected light of outside light at second lens  121  is reflected to pass below first mirror  122 . The reflected light is thus prevented from being incident on viewpoint region  300 . Second lens  121  and first lens  123  are each desirably inclined with respect to reference beam Lc at an angle preventing reflected light from being incident on first mirror  122  when outside light incident along reference beam Lc is reflected by the incidence surface or the emission surface. Such inclination more desirably has an angle preventing reflected light from being incident on first mirror  122  when outside light emitted from first mirror  122  and incident on second lens  121  or first lens  123  is reflected by the incidence surface or the emission surface of second lens  121  or first lens  123 . Second lens  121  and first lens  123  being inclined with respect to reference beam Lc indicates that second lens  121  and first lens  123  each have an optical refracting surface including a portion that is overlapped with reference beam Lc and is not horizontal with respect to a plane perpendicular to reference beam Lc. 
     Similarly to the first exemplary embodiment, positions of thick portions and thin portions of first lens  123  and second lens  121  with respect to reference beam Lc are opposite to each other. Similarly to the first exemplary embodiment, beams passing second lens  121  and first lens  123  are thus adjusted in terms of optical path length to uniformize optical path length of beams regardless of passed portions of second lens  121  and first lens  123 . 
     [6-2. Effects and the Like] 
     Head-up display  100  exemplifying the head-up display according to the sixth exemplary embodiment is configured to cause observer D to visually recognize virtual image I. Head-up display  100  includes display device  110  exemplifying a display device, and projection optical system  140 . Display device  110  displays an image. Projection optical system  140  is configured to form the image displayed by display device  110  as intermediate image M. First lens  123  included in projection optical system  140  is inclined with respect to reference beam Lc. Even in a case where outside light enters projection optical system  140 , this configuration inhibits stray light caused by outside light reflected by seventh lens  150  or the like. Projection optical system  140  includes first lens  123  configured to condense light, and seventh lens  150  exemplifying the first optical element, which are disposed in the order along the optical path from display device  110 . In head-up display  100  according to the sixth exemplary embodiment, first lens  123  having positive power is disposed ahead of seventh lens  150  having negative power and configured to form intermediate image M in the order along the optical path from display device  110  to achieve telephoto arrangement. This accordingly leads to reduction in entire length of relay optical system  120  and reduction in size of first lens  123  itself for reduction in size of head-up display  100 . 
     The sixth exemplary embodiment adopts first mirror  122  exemplifying the second optical element, and third mirror  125  serving as projection optical system  130 . This enables formation of intermediate image M by sufficiently enlarging an image displayed by small display device  110 , and projection by further enlarging intermediate image M for observer D. 
     Head-up display  100  according to the sixth exemplary embodiment includes seventh lens  150  having negative power, exemplifying the first optical element, and disposed adjacent to intermediate image M. Seventh lens  150  thus serves as a so-called field lens. This enables reduction in size of first lens  123 , first mirror  122 , and second lens  121 . 
     In head-up display  100  according to the sixth exemplary embodiment, first lens  123 , second lens  121 , and seventh lens  150  each have at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like head-up display  100 . 
     Head-up display  100  according to the sixth exemplary embodiment includes first lens  123 , second lens  121 , and seventh lens  150  each having the wedge shape. Even when first lens  123 , second lens  121 , and seventh lens  150  are inclined with respect to reference beam Lc, beams passing first lens  123 , second lens  121 , and seventh lens  150  can be adjusted in terms of optical path length. 
     Head-up display  100  according to the sixth exemplary embodiment includes second lens  121  disposed between display device  110  and first mirror  122  exemplifying the second optical element. Second lens  121  has the wedge shape and includes at least one free-form surface. In head-up display  100  according to the sixth exemplary embodiment, first lens  123  and second lens  121  are disposed such that beams passing a thin portion of a first one of these lenses pass a thick portion of a second one of the lenses and beams passing a thick portion of the first one pass a thin portion of the second one. Even when first lens  123  and second lens  121  are inclined with respect to reference beam Lc, beams passing first lens  123  and second lens  121  can be uniformized in terms of optical path length. 
     In head-up display  100  according to the sixth exemplary embodiment, intermediate image M is an aerial image formed in a space on the optical path from display device  110  to virtual image I. This enables formation of intermediate image M by enlarging an image displayed by small display device  110  and projection by further enlarging intermediate image M for observer D, without adding any member configured to form intermediate image M. 
     (Other Exemplary Embodiments) 
     The first to sixth exemplary embodiments have been described above as exemplification of the technique disclosed in the present application. The technique disclosed in the present disclosure should not be limitedly applicable to these exemplary embodiments, but is also applicable to any exemplary embodiment achieved by modification, replacement, addition, removal, or the like. Furthermore, constituent elements described in the first to sixth exemplary embodiments can be combined to achieve any new exemplary embodiment. 
     The first to sixth exemplary embodiments each provide second lens  121  exemplifying a dioptric system disposed between display device  110  and first mirror  122 . The dioptric system is not limited to second lens  121  constituted y a single lens element. The dioptric system may include a plurality of lens elements disposed between display device  110  and first mirror  122 . In the case where the plurality of lens elements is provided, the lens element initially receiving light emitted from the display device desirably has positive power. 
     The first to sixth exemplary embodiments each provide single third mirror  125  serving as projection optical system  140 . Two or more mirrors may alternatively be disposed. Such a mirror to be added may be disposed ahead of third mirror  125  in the vehicle, or may be disposed laterally inside or outside the vehicle, specifically, vertically on the sheet of any one of  FIG.  1   ,  FIG.  2   , and  FIG.  4    to  FIG.  9   . 
     The first to sixth exemplary embodiments each adopt relay optical system  120  including a lens element. However, head-up display  100  should not be limited to such a configuration. For example, third mirror  125  and windshield  220  may interpose any additional lens element. 
     First mirror  122 , second mirror  124 , and third mirror  125  in head-up display  100  according to any one of the first to sixth exemplary embodiments are assumed as rotationally asymmetric mirrors. However, these mirrors should not be limited to such rotationally asymmetric mirrors. These mirrors may alternatively be shaped to have a so-called saddle surface having difference in sign between curvature in the X axis direction and curvature the Y axis direction. 
     The lens elements adopted in any one of the first to sixth exemplary embodiments should not be limited to have the free-form surface. The surface of each of the lens elements may alternatively have a troidal shape, an anamorphic shape, or a cylindrical shape. Furthermore, the lens in any one of these shapes may be disposed eccentric with respect to reference beam Lc. 
     The emission surface of fifth lens  128  according to the fourth exemplary embodiment, the incidence surface of sixth lens  129  according to the fifth exemplary embodiment, and the emission surface according to the sixth exemplary embodiment do not need to be entirely concave in the X direction, but may locally have a convex surface. 
     The planar surface of each of the lens elements according to the first to sixth exemplary embodiments may be convex, concave, or locally curved. 
     The reflecting surface of each of first mirror  122 , second mirror  124 , and third mirror  125  according to any one of the first to fifth exemplary embodiments should not be limited to the free-form surface. The reflecting surface of each of these mirrors may alternatively have a spherical shape, an aspherical surface, a troidal shape, or an anamorphic shape. The mirror in any one of these shapes may be disposed eccentric with respect to reference beam Lc. 
     Head-up display  100  according to any one of the first to sixth exemplary embodiments is disposed below dashboard  210 , but may alternatively be disposed above dashboard  210 . 
     The exemplary embodiments have been described above as exemplification of the technique disclosed in the present disclosure. There have been provided the accompanying drawings and the detailed description. Accordingly, the constituent elements mentioned in the accompanying drawings and the detailed description may include constituent elements essentially needed for achievement of an object as well as constituent elements inessentially needed for achievement of the object. Such inessential constituent elements should not be regarded as being essential just because these constituent elements are mentioned in the accompanying drawings and the detailed description. 
     The above exemplary embodiments are provided to exemplify the technique disclosed in the present disclosure, and can thus be subjected to modification, replacement, addition, removal, or the like in various manners within the scope of claims or an equivalent scope. 
     (Summary of Exemplary Embodiments) 
     (1) The present disclosure provides a head-up display configured to project an image on a transparent reflection member to cause an observer to visually recognize a virtual image, and including: a display device configured to display the image; and a projection optical system configured to project the image displayed by the display device as the virtual image for the observer. The projection optical system is configured to form the image as an intermediate image, and includes a first lens configured to condense light, and a first optical element configured to diffuse light. The first lens and the first optical element are disposed in an order along an optical path from the display device. When a beam reaching a center of a viewpoint region of the observer and corresponding to a center of the virtual image is set as a reference beam, the first lens is inclined with respect to the reference beam. 
     In this manner, the projection optical system includes the first lens configured to condense light and the first optical element configured to diffuse light disposed in the order along the optical path from the display device, and the first lens is inclined with respect to the reference beam. Even in a case where outside light enters the projection optical system, this configuration inhibits stray light caused by outside light reflected by the first lens or the like. In the projection optical system, the first lens having positive power is disposed ahead of the first optical element having negative power and configured to form the intermediate image in the order along the optical path from the display device to achieve telephoto arrangement. This accordingly leads to reduction in entire length of the relay optical system and reduction in size of the first lens itself for reduction in size of the head-up display. 
     (2) In the head-up display according to (1), the first optical element is a mirror. This enables formation of the intermediate image by sufficiently enlarging the image displayed by the small display device, and projection by further enlarging the intermediate image for the observer. 
     (3) In the head-up display according to (1) or (2), the first lens has at least one free-form surface. This achieves inhibition of outside light reflection and preferred optical properties in an image optical system like a head-up display. 
     (4) In the head-up display according to any one of (1) to (3), the first lens has a wedge shape. Even when the first lens is inclined with respect to a reference beam, a beam passing the first lens can thus be adjusted in terms of optical path length. 
     (5) In the head-up display according to (4), the projection optical system includes a second optical element configured to condense light, and a second lens configured to condense light. The second lens, the second optical element, and the first lens are disposed in the order along the optical path from the display device. The second lens has a wedge shape. The second lens has at least one free-form surface. The first lens and the second lens are disposed such that a beam passing a thin portion of the first lens passes a thick portion of the second lens and a beam passing a thick portion of the first lens passes a thin portion of the second lens. Even when the first lens and the second lens are inclined with respect to the reference beam, a beam passing the first lens and the second lens can be uniformized in terms of optical path length. 
     (6) In the head-up display according to (5), the first lens and the second lens are formed integrally with each other. This configuration achieves reduction in a number of components and reduction in production cost for the head-up display. 
     (7) In the head-up display according to (5), the projection optical system includes a lens having negative refractive power, disposed ahead of the first lens on the optical path from the second optical element to the first optical element, and inclined with respect to the reference beam. This configuration reduces an aberration correction load of the optical elements to achieve higher resolution. 
     (8) In the head-up display according to (5), the projection optical system includes a lens having negative refractive power, disposed behind the intermediate image on the optical path from the first optical element to the virtual image, and inclined with respect to the reference beam. This configuration reduces an aberration correction load of the optical elements to achieve higher resolution. 
     (9) In the head-up display according to any one of (1) to (8), the intermediate image is an aerial image formed in a space on the optical path. This enables formation of the intermediate image by enlarging the image displayed by the small display device and projection by further enlarging the intermediate image for the observer, without adding any member configured to form the intermediate image. 
     INDUSTRIAL APPLICABILITY 
     The present disclosure is applicable to a head-up display including a dioptric system such as a lens. The present disclosure is specifically applicable to a head-up display mounted on a vehicle or the like. 
     REFERENCE MARKS IN THE DRAWINGS 
       100  head-up display 
       110  display device 
       120  relay optical system 
       121  second lens 
       122  first mirror 
       123  first lens 
       124  second mirror 
       125  third mirror 
       126  third lens 
       127  fourth lens 
       128  fifth lens 
       129  sixth lens 
       130  projection optical system 
       140  projection optical system 
       150  seventh lens 
       200  vehicle 
       210  dashboard 
       220  windshield 
       300  viewpoint region 
     D observer 
     I virtual image 
     M intermediate image 
     L beam 
     Lc reference beam