Aerial image display device

Abstract

An aerial image display device according to the present disclosure comprises: a display unit; and an optical system that forms an image of image light emitted from the display unit as an aerial image of a real image. In the aerial image display device, when an area obtained by integrating a first modulation transfer function of the aerial image formed by the optical system on a spatial frequency axis is denoted by S1, the optical system is an ideal optical system having a diffraction-limited resolution, and an area obtained by integrating a second modulation transfer function of an ideal aerial image formed by the ideal optical system is denoted by S2, the ratio S1 / S2 of the area S1 to the area S2 is 0.58 or more.

Description

Aerial image display device

[0001] The present disclosure relates to an aerial image display device.

[0002] 2. Description of the Related Art Conventionally, an aerial image display device is known, for example, as described in Patent Document 1.

[0003] JP 2011-253128 A

[0004] The aerial image display device disclosed herein is an aerial image display device comprising a display unit and an optical system that forms an aerial image of a real image from image light emitted from the display unit, wherein when the area obtained by integrating a first modulation transfer function of the aerial image formed by the optical system on the spatial frequency axis is S1, the optical system is an ideal optical system having diffraction-limited resolution, and the area obtained by integrating a second modulation transfer function of the ideal aerial image formed by the ideal optical system on the spatial frequency axis is S2, the ratio S1 / S2 of the area S1 to the area S2 is 0.58 or greater.

[0005] 9A and 9B are side views illustrating a defocus operation of the imaging device.

[0023] FIG. 9B is a cross-sectional view showing the configuration of an aerial image display device according to one embodiment of the present disclosure.

[0024] FIG. 9C is a cross-sectional view showing the configuration of an aerial image display device according to another embodiment of the present disclosure.

[0025] FIG. 10B is a graph showing an example of a modulation transfer function.

[0026] FIG. 11C is a diagram illustrating an example of an aerial image viewed by a user of the aerial image display device of FIG. 1.

[0027] FIG. 12B is a diagram illustrating the definition of the curvature of a first concave mirror.

[0028] FIG. 13A is a perspective view showing a measurement system for calculating the modulation transfer function of an aerial image formed by the aerial image display device.

[0029] FIG. 14A is a diagram showing an example of a test pattern for calculating the modulation transfer function.

[0030] FIG. 15B is a partial enlarged view showing the captured image of the test pattern captured by an imaging device.

[0031] FIG. 16A is a graph showing a luminance distribution waveform calculated from the captured image of FIG. 15B.

[0032] FIG. 17B is a diagram showing another example of a test pattern for calculating the modulation transfer function.

[0033] FIG. 18A is a side view illustrating a defocus operation of the imaging device.

[0034] FIG. 19B is a partial enlarged view showing an example of a test pattern for calculating the modulation transfer function.

[0035] 19 is a diagram showing an example of an image of a test pattern captured by an imaging device. FIG. 19 is a graph showing the in-focus position of each imaging portion. FIG. 19 is a diagram explaining optical axis deviation corresponding to the graph of FIG. 17. FIG. 19 is a graph showing the in-focus position of each imaging portion. FIG. 20 is a diagram explaining optical axis deviation corresponding to the graph of FIG. 20. FIG. 21 is a diagram explaining rotational operations of the imaging device. FIG. 21 is a graph showing the relationship between the MTF area S1 of an aerial image formed by the optical system and the sharpness (width ratio W / Q: (half width) / (quarter width)) of the luminance distribution waveform of the aerial image when the F-number of the imaging device is 3. FIG. 21 is a graph showing the relationship between the MTF area S1 of an aerial image formed by the optical system and the sharpness (width ratio W / Q: (half width) / (quarter width)) of the luminance distribution waveform of the aerial image when the F-number of the imaging device is 8.

[0006] Conventional aerial image display devices are configured to form a real aerial image from image light emitted from a display panel using optical components such as a polarizing filter, a beam splitter, etc. Conventional aerial image display devices often suffer from reduced resolution and brightness of the aerial image.

[0007] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. The drawings referred to below are schematic. The dimensional ratios and the like in the drawings do not necessarily correspond to the actual ones. In this specification, for convenience, a Cartesian coordinate system XYZ is defined in some drawings. The X-axis direction is also referred to as the first direction or height direction. The Y-axis direction is also referred to as the second direction or width direction (horizontal direction, lateral direction). The Z-axis direction is also referred to as the third direction or depth direction.

[0008] 1 to 23 are diagrams or graphs illustrating an aerial image display device according to an embodiment of the present disclosure. In Figures 7 to 9, 11, 12, and 14 to 16, the second band-shaped image (black image) is shown at a brightness higher than the actual brightness for ease of illustration.

[0009] As shown in FIG. 1 , an aerial image display device 2 according to an embodiment of the present disclosure includes a display unit 3 and an optical system 5 .

[0010] The display unit 3 includes a display panel 4. The display panel 4 has a display surface 4a and displays an image formed as an aerial image R on the display surface 4a. That is, the display panel 4 emits image light Lp that is formed as an aerial image R from the display surface 4a. The display panel 4 may be a transmissive display panel or a self-luminous display panel. When the display panel 4 is a transmissive display panel, the display unit 3 may include an illuminator such as a backlight. When the display panel 4 is a self-luminous display panel, the display unit 3 does not need to include an illuminator.

[0011] The transmissive display panel may include a liquid crystal panel. The transmissive display panel may have a known liquid crystal panel configuration. Examples of known liquid crystal panels include various liquid crystal panels such as an IPS (In-Plane Switching) type, an FFS (Fringe Field Switching) type, a VA (Vertical Alignment) type, and an ECB (Electrically Controlled Birefringence) type. In addition to liquid crystal panels, the transmissive display panel also includes a MEMS (Micro Electro Mechanical Systems) shutter type display panel. The self-luminous display panel may include a plurality of self-luminous elements. Examples of the self-luminous elements include various self-luminous elements such as an LED (Light Emitting Diode), an organic EL (Electro Luminescence), and an inorganic EL.

[0012] The optical system 5 focuses the image light Lp emitted from the display unit 3 as a real aerial image R. The optical system 5 may be composed of a reflective member such as a concave mirror or a convex mirror. As shown in FIG. 1 , the optical system 5 may be composed of a first concave mirror 5 a, a convex mirror 5 b, and a second concave mirror 5 c.

[0013] The first concave mirror 5a is configured to reflect the image light Lp emitted from the display unit 3 in a direction different from the direction toward the display unit 3. The first concave mirror 5a may be a free-form concave mirror. The first concave mirror 5a is not limited to a free-form concave mirror, and may be a spherical concave mirror or an aspherical concave mirror.

[0014] The convex mirror 5b is configured to reflect the image light Lp reflected by the first concave mirror 5a in a direction different from the direction toward the first concave mirror 5a. The convex mirror 5b may be a free-form convex mirror. The convex mirror 5b is not limited to a free-form convex mirror, but may also be a spherical convex mirror or an aspherical convex mirror.

[0015] The second concave mirror 5c is configured to reflect the image light Lp reflected by the convex mirror 5b in a direction different from the direction toward the convex mirror 5b, thereby forming an aerial image R. The second concave mirror 5c may be a free-form concave mirror. The second concave mirror 5c is not limited to a free-form concave mirror, but may also be a spherical concave mirror or an aspherical concave mirror.

[0016] As shown in FIG. 1 , the aerial image display device 2 may be configured such that a first concave mirror 5a and a second concave mirror 5c face each other at an angle, the display panel 4 is located between the first concave mirror 5a and the second concave mirror 5c, and the inclination of the display surface 4a of the display panel 4 relative to the reflective surface (also referred to as the first reflective surface) 5ar of the first concave mirror 5a is smaller than the inclination of the display surface 4a of the display panel 4 relative to the reflective surface (also referred to as the second reflective surface) 5cr of the second concave mirror 5c. Because the first concave mirror 5a and the second concave mirror 5c face each other at an angle and the display panel 4 is located between the first concave mirror 5a and the second concave mirror 5c, the aerial image display device 2 is compact. In particular, the vertical dimension of the aerial image display device 2 (the X-axis direction in FIG. 1 ) is reduced. Because the inclination of the display surface 4a of the display panel 4 with respect to the first reflecting surface 5ar of the first concave mirror 5a is smaller than the inclination of the display surface 4a of the display panel 4 with respect to the second reflecting surface 5cr of the second concave mirror 5c, the display surface 4a of the display panel 4 and the first reflecting surface 5ar of the first concave mirror 5a become nearly parallel. As a result, the angle of incidence of the rays of image light Lp emitted from the display surface 4a with respect to the first reflecting surface 5ar becomes smaller, thereby reducing distortion of the aerial image R and increasing the brightness of the aerial image R. The inclination of the display surface 4a of the display panel 4 with respect to the first reflecting surface 5ar of the first concave mirror 5a may be defined as the inclination angle between the display surface 4a (or a virtual plane 4ai in space including the display surface 4a) and a tangent plane (or a virtual plane 5ai in space including the tangent plane) that is tangent to the vertex 5ap of the curvature of the first reflecting surface 5ar. Similarly, the inclination of the display surface 4a of the display panel 4 with respect to the second reflecting surface 5cr of the second concave mirror 5c may be defined as the inclination angle between the display surface 4a (or a virtual surface 4ai in space including the display surface 4a) and the tangent plane (or a virtual surface 5ci in space including the tangent plane) that is tangent to the vertex 5cp of the curvature of the second reflecting surface 5cr.

[0017] In the above configuration, the convex mirror 5b may be located between the first concave mirror 5a and the second concave mirror 5c. In this case, the optical system 5 of the aerial image display device 2 is made smaller. In particular, the vertical dimension of the optical system 5 is made smaller. Furthermore, the convex mirror 5b may be closer to the first concave mirror 5a and the second concave mirror 5c than to the display panel 4. In this case, the optical system 5 of the aerial image display device 2 is made even smaller. In particular, the horizontal dimension of the optical system 5 (the Z-axis direction in FIG. 1 ) is made smaller.

[0018] The aerial image display device 2 is not limited to the configuration shown in Fig. 1. The optical system 5 may be configured with a first concave mirror 5d and a second concave mirror 5e, as shown in Fig. 2.

[0019] The first concave mirror 5d is configured to reflect the image light Lp emitted from the display unit 3 in a direction different from the direction toward the display unit 3. The first concave mirror 5d may be a free-form concave mirror. The first concave mirror 5d is not limited to a free-form concave mirror, and may be a spherical concave mirror or an aspherical concave mirror.

[0020] The second concave mirror 5e is configured to reflect the image light Lp reflected by the first concave mirror 5d in a direction different from the direction toward the first concave mirror 5d, thereby forming an aerial image R. The second concave mirror 5e may be a free-form concave mirror. The second concave mirror 5e is not limited to a free-form concave mirror, but may also be a spherical concave mirror or an aspherical concave mirror.

[0021] As shown in FIG. 2 , the aerial image display device 2 may be configured such that the curvature of the first concave mirror 5d is greater than the curvature of the second concave mirror 5e, the first concave mirror 5d and the second concave mirror 5e face each other at an angle, and the display panel 4 is located between the first concave mirror 5d and the second concave mirror 5e. Because the curvature of the first concave mirror 5d is greater than the curvature of the second concave mirror 5e, the display panel 4 can be positioned closer to the first concave mirror 5d. As a result, the aerial image display device 2 can be made more compact. In particular, the horizontal dimension of the aerial image display device 2 can be reduced. Because the display panel 4 is located between the first concave mirror 5d and the second concave mirror 5e, the aerial image display device 2 can be made even more compact. In particular, the vertical dimension of the aerial image display device 2 can be reduced.

[0022] The free-form surfaces that define the reflecting surfaces of free-form concave mirrors and free-form convex mirrors may be XY polynomial surfaces (also called SPS XYP surfaces) defined by the following formulas (1) and (2). The XY polynomial surfaces are expanded into polynomials of up to the tenth degree that are added to the reference conic surface. Therefore, in formulas (1) and (2), the sum of m and n is 10 or less. In formula (1), z is the sag of the surface parallel to the z axis (optical axis), c is the vertex curvature, and r is the radial distance (i.e., r ２ = x ２ +y ２ ), k is the conic constant, and Cj is the monomial x ｍ y ｎ is the coefficient of

[0023] 1 and 2 , the aerial image display device 2 may include a housing 6. Components 2a of the aerial image display device 2, such as the display unit 3 and optical system 5, may be located inside the housing 6. The components 2a may include a circuit board, wiring, cables, heat dissipation components such as a heat sink, holding members for holding the optical system 5, and adjustment members for adjusting the position of the optical system 5. The housing 6 may be made of, for example, a resin material, a metal material, a ceramic material, or the like.

[0024] At least a portion of the housing 6 that faces the user of the aerial image display device 2 is configured as an image light emitting unit 6a. Image light Lp, which is formed as the aerial image R, is emitted from inside the housing 6 to outside the housing 6 via the image light emitting unit 6a. The image light emitting unit 6a may be configured to include, for example, a light-shielding film or light-shielding glass. In this case, when using the aerial image display device 2, it becomes difficult for the user 20 to view the components 2a located inside the housing 6, thereby improving the visibility of the aerial image R.

[0025] The resolution of the aerial image R can be expressed by a modulation transfer function (MTF). The modulation transfer function is a performance index for evaluating the resolution of the optical system 5 and can be used as a resolution index for comparing the resolution of the aerial image R. The modulation transfer function is a function of the spatial frequency ν (1 / mm) and is maximized when ν = 0. The modulation transfer function may be normalized so that its maximum value is 1. In this case, the closer the value of the modulation transfer function is to 1, the higher the resolution of the optical system 5 (i.e., the resolution of the aerial image R). Note that while the value of the modulation transfer function itself may be used as the performance index of the optical system 5, the resolution of the optical system 5 (i.e., the resolution of the aerial image R) can be evaluated with high accuracy by using the area obtained by integrating the modulation transfer function on the spatial frequency axis as the performance index of the optical system 5.

[0026] In the optical system 5, the resolution inevitably deteriorates due to the diffraction of light. Furthermore, the resolution also deteriorates due to manufacturing tolerances and positioning errors of the reflecting members that make up the optical system 5. Therefore, the aerial image R formed by the optical system 5 is an aerial image with reduced resolution due to the above factors. An ideal optical system has the same configuration as the optical system 5 but has a diffraction-limited resolution. In other words, an ideal optical system is an optical system in which the degradation of resolution is limited only to the degradation that inevitably occurs due to the diffraction of light. An ideal aerial image formed by an ideal optical system is an aerial image in which the degradation of resolution is theoretically minimized. Regarding the diffraction limit, for example, even when light from a point light source is geometrically focused at a single focal point by an aberration-free optical system in a vacuum, it actually expands to a certain size due to the wave properties of light. This size is approximately 1.22λ / D (radians) = 2.5 × 10, where λ is the wavelength of light and D is the diameter of an optical element (e.g., a lens). ５ It has an angular spread of λ / D (seconds), which is called the diffraction limit.

[0027] FIG. 3 is a graph showing an example of a modulation transfer function. In the graph of FIG. 3, the modulation transfer function K1 of the aerial image R formed by the optical system 5 (hereinafter also referred to as the first modulation transfer function) is shown by a dashed line, and the modulation transfer function K2 of an ideal aerial image formed by an ideal optical system (hereinafter also referred to as the second modulation transfer function) is shown by a solid line. As shown in FIG. 3, the first modulation transfer function K1 is smaller than the second modulation transfer function K2. Therefore, the area S1 obtained by integrating the first modulation transfer function K1 on the spatial frequency axis (hereinafter also referred to as the MTF area) is smaller than the area S2 obtained by integrating the second modulation transfer function K2 on the spatial frequency axis, and the area ratio S1 / S2 is smaller than 1. The closer the area ratio S1 / S2 is to 1, the higher the resolution of the aerial image R actually formed by the aerial image display device 2.

[0028] The aerial image display device 2 is configured such that, when S1 is the area obtained by integrating a first modulation transfer function K1 of an aerial image R formed by the optical system 5 over a spatial frequency axis, and the optical system 5 is an ideal optical system having diffraction-limited resolution and S2 is the area obtained by integrating a second modulation transfer function K2 of an ideal aerial image formed by the ideal optical system over the spatial frequency axis, the ratio S1 / S2 of the area S1 to the area S2 is 0.85 or greater. Therefore, the aerial image display device 2 can suppress degradation of resolution.

[0029] The modulation transfer function can be calculated using a measurement system 1 described below. The measurement system 1 includes an imaging device 7 capable of capturing an aerial image R. The modulation transfer function can be calculated based on the captured data of the aerial image R output from the imaging device 7.

[0030] The first modulation transfer function K1 and the second modulation transfer function K2 may be normalized so that their maximum values ​​are 1. In this case, when the aerial image R is captured by the imaging device 7 with an aperture value set to 8, the area S1 obtained by integrating the first modulation transfer function K1 on the spatial frequency axis may be 6 or greater. This improves the resolution when the eye 20e of the user 20 views the aerial image R. Furthermore, when the aerial image R is captured by the imaging device 7 with an aperture value set to 3, the area S1 obtained by integrating the first modulation transfer function K1 on the spatial frequency axis may be 12.7 or greater. This allows the user 20 to view the aerial image R with reduced resolution degradation and reduced optical axis deviation. Note that the optical axis deviation refers to the deviation between the actual optical axis direction Da of the aerial image R formed by the aerial image display device 2 and the designed optical axis direction Dad of the aerial image R formed by the aerial image display device 2 (see FIGS. 1 and 2 ).

[0031] 23 is a graph showing the relationship between the MTF area S1 of the aerial image R formed by the optical system 5 and the width ratio W / Q, which represents the sharpness of the luminance distribution waveform of the aerial image R, when the F-number (aperture value) of the imaging device 7 is 8. The luminance distribution waveform is also referred to as the line spread function (LSF) shown in FIG. 10 . W is the half-value width of the LSF shown in FIG. 10 , and Q is the quarter-value width (hereinafter also referred to as half-value width or quarter-value width) of the LSF shown in FIG. 10 . That is, the width ratio W / Q is (half-value width) / (quarter-value width), and is the ratio of the half-value width W to the quarter-value width Q of the line spread function, as shown in FIG. 10 . In the graph of Figure 23, the values ​​on the upper horizontal axis indicate the value of the MTF area S1, and the values ​​on the lower horizontal axis indicate the value of the area ratio S1 / S2, with the value of the area S2 being 7.25. When the F-number of the imaging device 7 is 8, the contrast of the aerial image R tends to be low due to the small area of ​​the light receiving section (lens aperture) of the imaging device 7. That is, the sharpness of the luminance distribution waveform tends to be low, and the value of the MTF area S1 of the aerial image R tends to be small overall. Furthermore, the smaller the value of the MTF area S1 of the aerial image R, i.e., the lower the contrast of the aerial image R, the lower the sharpness of the luminance distribution waveform tends to be. Furthermore, as shown in Figure 23, the sharpness of the luminance distribution waveform increases sharply when the MTF area S1 of the aerial image R is approximately 4.2 or greater. Therefore, when S1 is approximately 4.2 or greater, S1 / S2 (S2 = 7.25) is approximately 0.58 or greater.

[0032] FIG. 22 is a graph showing the relationship between the MTF area S1 of the aerial image R formed by the optical system 5 and the width ratio W / Q, which represents the sharpness of the luminance distribution waveform of the aerial image R, when the F-number of the imaging device 7 is 3. In the graph of FIG. 22, the numerical values ​​on the upper horizontal axis indicate the value of the MTF area S1, and the numerical values ​​on the lower horizontal axis indicate the value of the area ratio S1 / S2, with the value of the area S2 being 14.9. When the F-number of the imaging device 7 is 3, the contrast of the aerial image R tends to be high due to the large area of ​​the light receiving section (lens aperture) of the imaging device 7. That is, the sharpness of the luminance distribution waveform tends to be high, and the value of the MTF area S1 of the aerial image R tends to be large overall. Furthermore, the larger the value of the MTF area S1 of the aerial image R, i.e., the higher the contrast of the aerial image R, the higher the sharpness of the luminance distribution waveform tends to be. 22, the sharpness of the luminance distribution waveform improves sharply when the MTF area S1 of the aerial image R is 12.7 or greater. Therefore, S1 may be 12.7 or greater, in which case S1 / S2 (S2=14.9) becomes 0.85 or greater.

[0033] 23, the sharpness of the luminance distribution waveform drops sharply when the MTF area S1 of the aerial image R is less than 6. In other words, when the MTF area S1 of the aerial image R is 6 or greater, the sharpness of the luminance distribution waveform is in its highest region of 0.68 or greater, and the sharpness of the luminance distribution waveform asymptotically approaches the sharpness of an ideal aerial image, approximately 0.7. That is, when S1 is 6 or greater, the sharpness of the luminance distribution waveform is an almost constant value approximating the sharpness of an ideal aerial image, approximately 0.7. Therefore, S1 may be 6 or greater, in which case S1 / S2 (S2 = 7.25) is 0.83 or greater.

[0034] In the case where the F-number of the imaging device 7 shown in FIG. 22 is 3 and in the case where the F-number of the imaging device 7 shown in FIG. 23 is 8, S1 / S2 may be 0.85 or more.

[0035] The aerial image display device 2 can reduce distortion of the aerial image R formed by the optical system 5 to 5% or less. FIG. 4 shows simulation results showing the aerial image R viewed by the user 20 of the aerial image display device 2 of FIG. 1. In FIG. 4, to facilitate visual understanding of the distortion of the aerial image R, the aerial image R is depicted as an aerial image with a grid pattern, and coordinate axes indicating the direction and amount of distortion are shown. In FIG. 4, the solid line indicates the aerial image R viewed by the user 20, and the dashed line indicates a virtual aerial image IR without distortion. Distortion of the aerial image R can include distortion in the planar direction (direction parallel to the paper surface) and distortion in the depth direction (direction perpendicular to the paper surface), but FIG. 4 only shows distortion in the planar direction. Note that, unlike FIGS. 1 and 2, in FIG. 4, the X-axis direction is the horizontal direction and the Y-axis direction is the height direction.

[0036] As shown in Figure 4, distortion of the aerial image R is likely to occur at the outer periphery of the aerial image R, with distortion particularly likely to be significant at the four corners of the aerial image R (lower right corner LR, upper right corner UR, lower left corner LL, and upper left corner UL). Table 1 shows the distortion from the aerial image IR at the corners LR, UR, LL, and UL. As shown in Table 1, the aerial image display device 2 can suppress distortion at the corners LR, UR, LL, and UL to within ±5%.

[0037]

[0038] The + (plus) direction of the X direction corresponds to the right direction in FIG. 4 , and the − (minus) direction of the X direction corresponds to the left direction in FIG. 4 . The + (plus) direction of the Y direction corresponds to the upward direction in FIG. 4 , and the − (minus) direction of the Y direction corresponds to the downward direction in FIG. 4 . However, in Table 1, for the distortion of the aerial image R, distortion toward the outside of the aerial image IR in both the X and Y directions is taken as a positive value, and distortion toward the inside of the aerial image IR is taken as a negative value. For example, at the lower right corner LR, the outward direction in the X direction (rightward: expanding direction) is taken as the + (plus) direction, the inward direction in the X direction (leftward: contracting direction) is taken as the − (minus) direction, the outward direction in the Y direction (downward: expanding direction) is taken as the + (plus) direction, and the inward direction in the Y direction (upward: contracting direction) is taken as the − (minus) direction. The same applies to the upper right corner UR, the lower left corner LL, and the upper left corner UL. The same applies to the following tables showing distortion of the aerial image R.

[0039] The distortion at the corners LR, UR, LL, and UL is calculated as follows. The distortion in the X direction at the corners LR, UR, LL, and UL is defined as the length of deviation in the X direction relative to the length LX of the top edge of the rectangular aerial image IR (the bottom edge is the same length as the top edge). Because the length of the bottom edge of the aerial image IR is the same as the length LX of the top edge, the length LX of the top edge is used as the reference. For example, the distortion in the X direction at the corner UR is defined as the length ΔXUR of deviation in the X direction from the upper right corner CUR of the aerial image IR relative to the length LX of the top edge. In other words, the distortion in the X direction at the corner UR is defined as (ΔXUR / LX) × 100 (%). Because the corner UR is distorted inward of the aerial image IR in the X direction, the value is negative (-). The distortion in the X direction at the corners LR, LL, and UL is defined similarly. When the aerial image IR has a shape other than a rectangle, the reference length in the X direction may be an average length or a maximum length.

[0040] The distortion in the Y direction of the corners LR, UR, LL, and UL is defined as the deviation length in the Y direction relative to the length LY of the right side (the left side is the same length as the right side) of the rectangular aerial image IR. Because the length of the left side of the aerial image IR is the same as the length LY of the right side, the length LY of the right side is used as the reference. For example, the distortion in the Y direction of the corner UR is defined as the deviation length ΔYUR in the Y direction from the upper right corner CUR of the aerial image IR relative to the length LY of the right side. That is, the distortion in the Y direction of the corner UR is defined as (ΔYUR / LY) × 100 (%). Because the corner UR is distorted inward of the aerial image IR in the Y direction, it has a negative (negative) value. The distortion in the Y direction of the corners LR, LL, and UL is defined similarly. If the aerial image IR has a shape other than rectangular, the reference length in the Y direction may be the average length or the maximum length.

[0041] In the optical system 5 of the aerial image display device 2 shown in FIG. 1, the curvature Sa of the first concave mirror 5a may be approximately 0.35 to 0.45, the curvature Sb of the convex mirror 5b may be approximately 0.15 to 0.25, and the curvature Sc of the second concave mirror 5c may be approximately 0.25 to 0.35. In this case, the area ratio S1 / S2 can be 0.85 or greater while suppressing distortion of the aerial image R to 5% or less. In the optical system 5 of the aerial image display device 2 shown in FIG. 2, the curvature Sd of the first concave mirror 5d may be approximately 0.2 to 0.3, and the curvature Se of the second concave mirror 5e may be approximately 0.05 to 0.15. In this case, the area ratio S1 / S2 can be 0.85 or greater while suppressing distortion of the aerial image R to 5% or less. The curvatures Sa, Sb, Sc, Sd, and Se can vary depending on the size, shape, and angle of view (spread of light) of the display panel 4, and are therefore not limited to the above ranges.

[0042] As shown in FIG. 5, the curvature Sa of the first concave mirror 5a is determined by defining a line segment LS that passes through the center of the reflecting surface 5aa of the first concave mirror 5a and connects both ends of the reflecting surface 5aa as 2×H, and defining a maximum length (also referred to as a maximum depth) between a point on the reflecting surface 5aa and the line segment LS in the direction along the optical axis OA as D. ＭＡＸ When this is done, D ＭＡＸ / H. ＭＡＸWhen / H changes depending on how the cross section is taken, D when the position of the cross section is changed ＭＡＸ The maximum value of / H may be set as the curvature Sa. The curvatures Sb, Sc, Sd, and Se are also defined in the same way as the curvature Sa.

[0043] The aerial image display device 2 can achieve a brightness of 800 cd / m2 or more for the aerial image R formed by the optical system 5. The aerial image display device 2 has an optical system 5 that is composed only of reflective members and does not include optical members that transmit a portion of the incident light, such as a polarizing filter or beam splitter, thereby achieving a high utilization rate of the image light Lp. This allows the aerial image display device 2 to form a high-brightness aerial image R while suppressing increases in power consumption. The brightness of the aerial image R may be measured using a commercially available luminance meter. The brightness of the aerial image R may be measured using a luminance meter located at the position of the imaging device 7 (see FIG. 6 ).

[0044] Next, a description will be given of calculation of the modulation transfer function of the aerial image R. The modulation transfer function of the aerial image R can be calculated using a measurement system 1. As shown in FIG. 6 , the measurement system 1 includes an imaging device 7, a control unit 8, and an acquisition unit 14.

[0045] The imaging device 7 is assumed to be the eye 20e of the user 20 (see Figures 1 and 2) and captures the aerial image R formed by the aerial image display device 2. The imaging device 7 is located away from the aerial image display device 2 in a design optical axis direction Dad of the aerial image display device 2. The imaging device 7 captures the aerial image R formed by the aerial image display device 2 in the design optical axis direction Dad of the aerial image display device 2. The design optical axis direction Dad refers to the design optical axis direction of the aerial image R formed by the aerial image display device 2. The design optical axis direction Dad may be, for example, a direction perpendicular to the width direction of the housing 6 or a direction perpendicular to the emission surface of the image light emission unit 6a. The aerial image display device 2 is disposed so that the design optical axis direction Dad coincides with the depth direction. Note that the imaging direction 7d of the imaging device 7 is not limited to the design optical axis direction. The control unit 8 may control the first rotation device 12 to rotate the imaging device 7 around a predetermined rotation axis. That is, the control unit 8 may control the imaging device 7 to capture the aerial image R in a direction different from the design optical axis direction (depth direction).

[0046] The imaging device 7 includes an imaging element. The imaging element may be, for example, a CCD (Charge Coupled Device) imaging element or a CMOS (Complementary Metal Oxide Semiconductor) imaging element. The imaging device 7 may be a camera (for example, a CCD camera) including multiple imaging elements and optical elements such as an objective lens. The imaging device 7 may be capable of changing the aperture value (F-number). The imaging device 7 may be capable of changing the aperture value within a range of 2 to 22.

[0047] The control unit 8 may function as a control unit of the measurement system 1. The control unit 8 may be connected to each component of the measurement system 1 and control each component. The control unit 8 may also function as a control unit of the aerial image display device 2 when calculating the modulation transfer function of the aerial image R. The control unit 8 may, for example, control the aerial image R formed by the aerial image display device 2. The control unit 8 may include one or more processors. The processor may include at least one of a general-purpose processor configured to load a specific program and execute a specific function, and a dedicated processor specialized for specific processing. The dedicated processor may include an application-specific integrated circuit (ASIC). The processor may include a programmable logic device (PLD). The PLD may include a field-programmable gate array (FPGA). The control unit 8 may include at least one of a system-on-a-chip (SoC) and a system-in-a-package (SiP) configured to cooperate with one or more processors.

[0048] The acquisition unit 14 may store image data of the captured image generated by the imaging device 7. When the imaging device 7 generates a captured image, the control unit 8 may acquire the image data of the captured image via the acquisition unit 14. When the imaging device 7 generates a captured image, the imaging device 7 may automatically output the image data of the captured image to the acquisition unit 14. The acquisition unit 14 may be a temporary storage device such as a buffer memory. The method of transmitting and receiving signals between the control unit 8 and the imaging device 7, the method of transmitting and receiving signals between the acquisition unit 14 and the imaging device 7, and the method of transmitting and receiving signals between the acquisition unit 14 and the control unit 8 may use at least one of a wired communication method, a wireless communication method, an infrared communication method, etc.

[0049] When calculating the modulation transfer function of the aerial image R, the control unit 8 controls the aerial image display device 2 to form a test pattern (hereinafter simply referred to as an aerial image) 9 in the air as shown in FIGS. 6 and 7 . FIG. 7 shows a test pattern 9 without blurring (resolution degradation). The test pattern 9 may be a repeated pattern of first band-shaped images 9a and second band-shaped images 9b. The first band-shaped images 9a and second band-shaped images 9b may be elongated images in the vertical direction (X-axis direction). The test pattern 9 may include at least three first band-shaped images 9a. While FIG. 7 shows an example in which the first band-shaped images 9a are white images and the second band-shaped images 9b are black images, this is not limiting. The first band-shaped images 9a and second band-shaped images 9b may differ in at least one of brightness and color.

[0050] When the first band-shaped image 9a and the second band-shaped image 9b are images that are elongated in the vertical direction (X-axis direction), the height direction of the imaging device 7 (for example, a direction perpendicular to the top surface of the imaging device 7) may be tilted by approximately 3 to 5 degrees around a rotation axis that is parallel to the depth direction (Z-axis direction). In this case, the number of samples taken when calculating the modulation transfer function of the test pattern 9 can be increased, making it possible to calculate the modulation transfer function of the test pattern 9 with high accuracy.

[0051] FIG. 8 shows an example of an overall image of test pattern 9 formed by the aerial image display device 2. The control unit 8 controls the imaging device 7 to capture an image of at least one imaging portion of the test pattern 9. The at least one imaging portion may be, for example, at least one of the multiple imaging portions F1 to F7 shown in FIG. 8. The at least one imaging portion may be multiple imaging portions F3 to F5, or multiple imaging portions F1 to F7. The following describes a case where the imaging device 7 captures images of imaging portions F1 to F7 of the test pattern 9. Note that "to" means "through," and the same applies hereinafter.

[0052] In the test pattern 9, the imaging portion F4 may be located near the center of the imaging plane Rp (in the X-axis direction and the Y-axis direction) of the aerial image R. The imaging portions F3 to F5 may be aligned in a predetermined direction within the imaging plane Rp of the aerial image 9. The predetermined direction may be, but is not limited to, the Y-axis direction (width direction). The predetermined direction may be the X-axis direction (up-down direction, height direction) or a direction tilted from the X-axis direction and the Y-axis direction (diagonal direction). The imaging portions F1, F2, F6, and F7 may be located at the four corners of the test pattern 9, as shown in FIG. 8 . The following description will be given assuming that the imaging portions F3 to F5 are aligned in the Y-axis direction (width direction) within the imaging plane of the aerial image 9, unless otherwise specified.

[0053] The imaging device 7 captures multiple imaging portions F1 to F7 of the test pattern 9 and outputs image data of multiple captured images P1 to P7. The multiple captured images P1 to P7 are images of multiple imaging portions F1 to F7, respectively. The test pattern 9 may be configured such that each of the multiple captured images P1 to P7 includes at least one image of a first band-shaped image 9a (white image portion in FIG. 7). The test pattern 9 may be configured such that each of the multiple captured images P1 to P7 includes one image of a first band-shaped image 9a, as shown in FIG. 9. In this case, processing of the image data of each captured image P1 to P7 is simplified, and the modulation transfer function can be calculated with high accuracy. While FIG. 9 shows the captured image P3, the same applies to the captured images P1, P2, P4 to P7.

[0054] The distance between the imaging device 7 and the test pattern 9 in the depth direction (Z-axis direction) may be set to a predetermined imaging distance (also referred to as an initial setting distance). The initial setting distance may be, for example, 300 mm to 700 mm, or may be 500 mm. The distance between the imaging device 7 and the aerial image 9 may be the distance between the imaging device 7 and the vicinity of the center of the aerial image 9 (e.g., imaging portion F4). The focal length of the imaging device 7 is fixed to a predetermined focal length. The predetermined focal length may coincide with the initial setting distance. Hereinafter, unless otherwise specified, it is assumed that the distance between the imaging device 7 and the aerial image 9 is set to the initial setting distance. Note that the distance between the imaging device 7 and the aerial image 9 in the depth direction does not need to be fixed to the initial setting distance. As will be described in detail later, the control unit 8 may control the moving device 11 to change the distance between the imaging device 7 and the aerial image 9 from the initial setting distance. That is, the control unit 8 may perform a defocus operation to make the distance between the imaging device 7 and the aerial image 9 different from the focal length of the imaging device 7.

[0055] When controlling the imaging device 7 to capture the test pattern 9, the control unit 8 may control the imaging device 7 to set the aperture value to a value greater than 3 or to a value less than or equal to 3. Setting the aperture value of the imaging device 7 to a relatively large value (e.g., 8) allows for evaluation of the resolution at which the eye 20e of the user 20 views the test pattern 9. Setting the aperture value of the imaging device 7 to a relatively small value (e.g., 3) allows for a shallower (shorter) depth of field (also referred to as focal depth of field) of the imaging device 7. That is, the range in which the subject is in focus in the depth direction can be reduced (narrower). As a result, the position of the subject (i.e., the multiple imaging portions F3, F4, and F5) in the depth direction can be accurately measured, allowing for accurate calculation of the modulation transfer function. Furthermore, it allows for accurate measurement of the optical axis deviation between the actual optical axis direction Da of the aerial image R formed by the aerial image display device 2 and the designed optical axis direction Dad of the aerial image R formed by the aerial image display device 2.

[0056] The control unit 8 acquires image data of multiple captured images P1 to P7 from the imaging device 7 via the acquisition unit 14. The control unit 8 scans the luminance values ​​of each pixel arranged in the width direction (left-right direction in FIG. 9 ) for the multiple captured images P1 to P7, performs binning processing, and calculates luminance distribution waveforms LSF1 to LSF7 as shown in FIG. 10 . The luminance distribution waveforms LSF1 to LSF7 are luminance distribution waveforms calculated from the image data of the captured images P1 to P7. The luminance distribution waveforms LSF1 to LSF7 are pulse-like waveforms that represent changes in luminance with position in the Y-axis direction. The horizontal axis in FIG. 10 represents changes in position in the Y-axis direction. In FIG. 10 , the highest value (peak value) of the luminance distribution waveform is displayed at the 30th pixel among multiple pixels (e.g., 60 pixels) in the Y-axis direction. The luminance distribution waveform is also referred to as a line spread function (LSF).

[0057] When the captured images P1 to P7 include an image of one first band-shaped image 9a as shown in Fig. 9, the line spread functions LSF1 to LSF7 have a substantially Gaussian shape as shown in Fig. 10. Hereinafter, the measurement method of the optical axis direction based on the characteristic values ​​of the LSF will also be referred to as the LSF method.

[0058] The control unit 8 calculates modulation transfer functions MTF1 to MTF7 such as the first modulation transfer function K1 shown in Fig. 3 by Fourier transforming each of the line spread functions LSF1 to LSF7 as shown in the following equation (3). Note that the Fourier transform is an operation for converting, for example, a function expressed by a pulse waveform into a curve expressed by continuous values ​​in the frequency domain (a sine waveform curve, a cosine waveform curve, or a continuous curve expressed by a composite curve of these). In equation (3), LSF(x) collectively represents the line spread functions LSF1 to LSF7 as a function of position x in the captured images P1 to P7. MTF(ν) collectively represents the modulation transfer functions MTF1 to MTF7 as a function of spatial frequency ν. C is a constant for normalizing MTF(0) to "1".

[0059] MTF(ν) can be considered an index representing the resolution based on the contrast of the captured images P1 to P7. For example, the larger the value of the modulation transfer function MTF4 in the region where the spatial frequency ν is high (approximately 6 / mm to 16 / mm), the closer the distance between the imaging portion F4 and the imaging device 7 to the focal length of the imaging device 7 can be determined. The same applies to the modulation transfer functions MTF1 to MTF3 and MTF5 to MTF7. The upper and lower limits of the integral interval in equation (3) may be replaced with finite values, which reduces the processing load on the control unit 8. When calculating the modulation transfer function MTF(ν) using equation (3), a method such as discrete Fourier transform or fast Fourier transform may be used.

[0060] The control unit 8 measures areas A1 to A7 obtained by integrating the modulation transfer functions MTF1 to MTF7 on the spatial frequency axis, respectively, as expressed in the following equation (4). The integration interval in equation (4) may be replaced with a finite interval (for example, a range of 0 / mm to 18 / mm), in which case the processing load on the control unit 8 can be reduced.

[0061] The control unit 8 may set the average value of the areas A1 to A7 as the area S1 of the first modulation transfer function K1. In this case, it is possible to evaluate the level of average resolution across the entire aerial image R. The control unit 8 may set the weighted average of the areas A1 to A7 as the area S1 of the first modulation transfer function K1. In this case, by increasing the weighting of the areas A3, A4, and A5, it is possible to evaluate the level of resolution near the center of the aerial image R. Alternatively, by increasing the weighting of the areas A1, A2, A6, and A7, it is possible to evaluate the level of resolution at the corners of the aerial image R. The control unit 8 may set the smallest value A of the areas A1 to A7 as the area S1 of the first modulation transfer function K1. ＭＩＮ may be set as the area S1 of the first modulation transfer function K1. In this case, the level of resolution over the entire aerial image R can be evaluated.

[0062] The modulation transfer functions MTF1 to MTF7 do not have to be calculated by Fourier transforming the line spread functions LSF1 to LSF7, but may be calculated directly from the image data of the captured images P1 to P7 by the chart method, respectively.

[0063] When calculating the modulation transfer functions MTF1 to MTF7 using the chart method, the control unit 8 controls the aerial image display device 2 to form a test pattern (hereinafter simply referred to as an aerial image) 9' as shown in FIG. 11. Note that FIG. 11 shows an ideal aerial image 9' free of blur (resolution degradation) and optical axis misalignment. The aerial image 9' is configured such that each of the imaging portions F1 to F7 includes multiple square wave charts 9c, 9d, 9e, and 9f with different spatial frequencies (the pitch of the white image portions). Therefore, each of the captured images P1 to P7 includes images of multiple square wave charts 9c to 9f with different spatial frequencies ν, as shown in FIG. 12. The control unit 8 controls the imaging device 7 to capture the aerial image 9', generate captured images P1 to P7 capturing the imaging portions F1 to F7, and output image data for the captured images P1 to P7. The imaging device 7 does not need to be inclined with respect to the upper surface 10a of the device stand 10 when capturing the aerial image 9'. The control unit 8 calculates the maximum and minimum luminance values ​​aν and bν of the partial images captured from each of the square wave charts 9c to 9f for each captured image P1 to P7, as well as the contrast ratio cν = (aν - bν) / (aν + bν). Furthermore, the control unit 8 normalizes the contrast ratio cν of each spatial frequency ν by the contrast ratio cν of the lowest spatial frequency ν to calculate a square wave response function (SWRF). The control unit 8 converts the square wave response function to a sine wave response function and calculates modulation transfer functions MTF1 to MTF7. The Coltman's equation may be used when converting the square wave response function to a sine wave response function. The Coltman's equation may use up to four terms or up to 12 terms.

[0064] The above describes a method for calculating the first modulation transfer function of the aerial image 9 actually formed by the aerial image display device 2. The second modulation transfer function K2 of an ideal aerial image formed by an ideal optical system may be calculated by simulation. Alternatively, a simulated image simulating the ideal aerial image may be placed on the imaging plane Rp, and the second modulation transfer function may be calculated based on image data obtained by capturing the simulated image with the imaging device 7. The simulated image may be a repeated pattern of first band-shaped images 9a and second band-shaped images 9b, similar to the test pattern 9 shown in Figures 7 and 8.

[0065] In the aerial image display device 2, a misalignment (hereinafter also referred to as optical axis misalignment) may occur between the optical axis direction Da of the aerial image R formed by the aerial image display device 2 and the design optical axis direction Dad due to, for example, manufacturing tolerances or positioning errors of the reflective members that make up the optical system 5. When optical axis misalignment occurs, deviations in display quality such as brightness and resolution occur within the imaging plane Rp of the aerial image R, and it may be impossible to accurately calculate the modulation transfer functions MTF1 to MTF7. The measurement system 1 may be configured to measure the optical axis misalignment of the aerial image display device 2. The measurement system 1 may be configured to calibrate the optical axis misalignment of the aerial image display device 2.

[0066] The measurement system 1 for measuring the optical axis deviation of the aerial image display device 2 will be described below.

[0067] As shown in FIG. 6 , the measurement system 1 may include a moving device 11 that moves the imaging device 7 along the depth direction (Z direction). The moving device 11 is configured to move the imaging device 7 in increments of a predetermined distance ΔZ. The predetermined distance ΔZ may be, for example, approximately 1 mm to 5 mm, or approximately 1 mm to 2 mm. The moving device 11 may include, for example, a rail 11r, a holding member (also referred to as a support member) 11h, and a moving table (also referred to as a slider) 11t on the upper surface of which the holding member 11h is installed. The rail 11r is located on the upper surface 10a of the device table 10 and extends along the depth direction. The holding member 11h supports and holds the imaging device 7. With the holding member 11h holding the imaging device 7, the moving table 11t can move along the depth direction on the rail 11r. The movement of the moving table 11t along the depth direction may be controlled by the control unit 8.

[0068] As shown in FIG. 6 , the measurement system 1 may include a first rotation device 12 that rotates the imaging device 7 around a first rotation axis RA1. The first rotation axis RA1 may be parallel to a direction (e.g., the X-axis direction) perpendicular to a predetermined direction (e.g., the Y-axis direction) in which the imaging portions F3, F4, and F5 are aligned within the imaging plane Rp. The first rotation axis RA1 may be a rotation axis that passes through the imaging device 7. The first rotation device 12 is configured to rotate the imaging device 7 in units of a predetermined angle ΔΘ. The predetermined angle ΔΘ may be, for example, approximately 0.1° to 2.0°, or approximately 0.5° to 1°. The first rotation device 12 may be provided in the moving device 11. For example, the first rotation device 12 may be installed between the moving stage 11t and the holding member 11h. The first rotation device 12 may rotate the holding member 11h of the moving device 11 and the imaging device 7 held by the holding member about the first rotation axis RA1. The first rotation device 12 may rotate only the imaging device 7 about the first rotation axis RA1 without rotating the holding member 11h of the moving device 11. The rotation of the imaging device 7 about the first rotation axis RA1 is controlled by the control unit 8. The first rotation device 12 may be a stepping motor device, a linear motor device, an ultrasonic motor device, or a manual rotation device including a rotation adjustment device such as a manually rotated knob or screw.

[0069] 1 and 2, the aerial image display device 2 may include a second rotation device 13 located within the housing 6 and rotating the entire component 2a around a second rotation axis RA2. The second rotation axis RA2 may be parallel to a direction (e.g., the X-axis direction) perpendicular to a predetermined direction in which the imaging portions F3, F4, and F5 are aligned within the imaging plane Rp. The second rotation device 13 may rotate only the entire component 2a around the second rotation axis RA2 without rotating the housing 6. The rotation of the aerial image display device 2 or the entire component 2a around the second rotation axis RA2 is controlled by the control unit 8.

[0070] [Measurement of Optical Axis Direction of Aerial Image] Next, the operation of the measurement system 1 for measuring the actual optical axis direction Da of the test pattern 9 imaged by the aerial image display device 2 will be described.

[0071] First, the operation of the measurement system 1 for measuring whether the actual optical axis direction Da of the aerial image 9 coincides with the imaging direction 7d of the imaging device 7 and whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad will be described. The imaging direction 7d of the imaging device 7 may be the optical axis direction (also referred to as the central axis direction) of the objective lens of the camera, or may be a direction perpendicular to the imaging surface of a CCD imaging element or the like. The imaging direction 7d of the imaging device 7 may be assumed to be the line of sight of the eye 20e of the user 20 facing the aerial image display device 2.

[0072] When measuring whether the actual optical axis direction Da of the aerial image 9 coincides with the imaging direction 7d of the imaging device 7, it is first assumed that the aerial image display device 2 is facing the imaging device 7. If the actual optical axis direction Da of the aerial image 9 does not coincide with the imaging direction 7d of the imaging device 7 (if the actual optical axis direction Da is misaligned with the imaging direction 7d), the amount of misalignment between the optical axis direction Da and the imaging direction 7d can be measured by a method (defocusing method) of translating the imaging device 7 back and forth in the depth direction, as described below, to measure the optical axis direction Da. Furthermore, by rotating the imaging device 7 around the first rotation axis RA1 to align the imaging direction 7d with the optical axis direction Da, the optical axis direction Da can be measured and the aerial image display device 2 can also be accurately faced toward the imaging device 7.

[0073] The actual positional deviation between the optical axis direction Da and the imaging direction 7d may exist only in the height direction (X-axis direction), only in the width direction (Y-axis direction), or in both the height direction (X-axis direction) and the width direction (Y-axis direction). In each case, the positional deviation can be measured and adjustments can be made to eliminate the positional deviation.

[0074] To measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad (see FIGS. 1 and 2 ) of the aerial image display device 2, the aerial image display device 2 is accurately positioned at a predetermined position directly facing the imaging device 7. For example, the aerial image display device 2 may be positioned so that the image light emitting unit 6a of the aerial image display device 2 is perpendicular to the imaging direction 7d of the imaging device 7. In this case, it is assumed that the imaging direction 7d is a predetermined imaging direction 7da (the imaging direction 7da that coincides with the design optical axis direction Dad). In other words, if there is no optical axis misalignment between the actual optical axis direction Da and the design optical axis direction Dad, the amount of misalignment between the optical axis direction Da and the imaging direction 7da is not measured. However, if there is optical axis misalignment between the actual optical axis direction Da and the design optical axis direction Dad, the amount of misalignment between the optical axis direction Da and the imaging direction 7da is measured by a method (defocusing method) of translating the imaging device 7 back and forth in the depth direction, which will be described later. Furthermore, the optical axis direction Da and the design optical axis direction Dad may be aligned by adjusting the arrangement of the components 2a of the aerial image display device 2, replacing the components 2a, etc., to eliminate the optical axis misalignment between the optical axis direction Da and the design optical axis direction Dad.

[0075] The optical axis misalignment between the actual optical axis direction Da and the design optical axis direction Dad may exist only in the height direction (X-axis direction), only in the width direction (Y-axis direction), or in both the height direction (X-axis direction) and the width direction (Y-axis direction). In each case, the positional misalignment can be measured and adjustments can be made to eliminate the positional misalignment.

[0076] Below, as a specific example, we will explain the operation of the measurement system 1, which measures the agreement or disagreement between the actual optical axis direction Da of the aerial image 9 and the design optical axis direction Dad in a plane perpendicular to the height direction (X-axis direction) based on the image data of the captured images P3 to P5, but this is not limited to this.

[0077] <Measurement of Optical Axis Direction Based on Characteristic Value of Line Spread Function of Luminance Distribution Waveform> As described above, the control unit 8 acquires image data of a plurality of captured images P3 to P5 from the imaging device 7. The control unit 8 calculates luminance distribution waveforms LSF3 to LSF5 as shown in FIG. 10 based on the image data of the plurality of captured images P3 to P5.

[0078] The control unit 8 calculates characteristic values ​​V3, V4, and V5 of the line spread functions LSF3 to LSF5, respectively. In this specification, characteristic values ​​V1 to V7 refer to the characteristic values ​​of the line spread functions LSF1 to LSF7, respectively. The characteristic value may be the peak value H of the line spread function, the half-width W of the line spread function, or the ratio of the half-width W to the quarter-width Q of the line spread function (hereinafter also referred to as the width ratio W / Q) (see FIG. 10). The peak value H is the maximum value of the line spread function. For example, the larger the peak value H of the line spread function LSF4 (the closer it is to 1 in the case of FIG. 10), the closer it can be determined that the distance between the imaging portion F4 and the imaging device 7 is to the focal length of the imaging device 7. Furthermore, the larger the peak value H of the line spread function LSF4, the higher the resolution (contrast value) of the aerial image R can be determined. The same applies to the peak values ​​H of the line spread functions LSF3 and LSF5.

[0079] The half-value width W is the width of a line spread function having a brightness of approximately 50% of the peak value H, and is expressed in units of the number of pixels. For example, it can be determined that the smaller the half-value width W of the line spread function LSF4, the closer the distance between the imaging portion F4 and the imaging device 7 is to the focal length of the imaging device 7. The same is true for the half-value width W of the line spread functions LSF3 and LSF5. Furthermore, it can be determined that the smaller the half-value width W of the line spread function LSF4, the higher the resolution (contrast value) of the aerial image R is.

[0080] The quarter-value width Q is the width of the line spread function having a brightness of approximately 25% of the peak value H, and is expressed in units of the number of pixels. For example, the larger the width ratio W / Q (the closer to 1), the closer it can be determined that the distance between the imaging portion F4 and the imaging device 7 is to the focal length of the imaging device 7. The same is true for the width ratios W / Q of the line spread functions LSF3 and LSF5. Furthermore, the larger the width ratio W / Q, the higher the resolution (contrast value) of the aerial image R can be determined to be.

[0081] The characteristic value may be a combination value obtained from the peak value H and the half-width W. The combination value may be a value obtained by dividing the peak value H by the half-width W, or may be another value. When the characteristic value is a combination value obtained by dividing the peak value H by the half-width W, it can be determined that the greater the combination value of the line spread function LSF4, the closer the distance between the imaging portion F4 and the imaging device 7 is to the focal length of the imaging device 7. Furthermore, it can be determined that the greater the combination value of the line spread function LSF4, the higher the resolution (contrast value) of the aerial image R. The same applies to the combination values ​​of the line spread functions LSF3 and LSF5.

[0082] The control unit 8 may calculate multiple differences between the multiple characteristic values ​​V3 to V5 (i.e., V3-V4, V3-V5, and V4-V5), and may determine that the actual optical axis direction Da of the aerial image 9 coincides with the depth direction (i.e., the design optical axis direction Dad) if all of the absolute values ​​of the multiple differences are equal to or less than the threshold value T1. The control unit 8 may determine that the optical axis direction Da of the aerial image 9 does not coincide with the depth direction if at least one of the absolute values ​​of the multiple differences exceeds the threshold value T1. The threshold value T1 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0083] For example, when the characteristic values ​​V3 to V5 are a peak value H or a width ratio W / Q, the control unit 8 may determine that the optical axis direction of the aerial image 9 coincides with the depth direction when the absolute value of the difference between the multiple characteristic values ​​V3 to V5 is less than or equal to a threshold value T1.

[0084] When the plurality of characteristic values ​​V3 to V5 are a peak value H or a width ratio W / Q, and all of the plurality of characteristic values ​​V3 to V5 are equal to or greater than threshold value T2, control unit 8 may determine that the optical axis direction Da of the aerial image 9 coincides with the depth direction. When the plurality of characteristic values ​​V3 to V5 are a peak value H or a width ratio W / Q, and at least one of characteristic values ​​V3 to V5 is less than threshold value T2, control unit 8 may determine that the optical axis direction Da of the aerial image 9 does not coincide with the depth direction. Threshold value T2 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0085] When the characteristic values ​​V3 to V5 have a half-width W, the control unit 8 may determine that the optical axis direction Da of the aerial image R coincides with the depth direction when all of the characteristic values ​​V3 to V5 are equal to or smaller than the threshold value T3. When the characteristic values ​​V3 to V5 have a half-width W, the control unit 8 may determine that the optical axis direction Da of the aerial image 9 does not coincide with the depth direction when at least one of the characteristic values ​​V3 to V5 exceeds the threshold value T3. The threshold value T3 may be set as appropriate based on the required specifications of the aerial image display device 2, etc.

[0086] The measurement system 1 can systematically measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad, based on the characteristic values ​​V3 to V5 of the line spread functions LSF3 to LSF5. Therefore, the measurement system 1 makes it possible to calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2. That is, in order to coincide the actual optical axis direction Da with the design optical axis direction Dad, measures such as adjusting the arrangement of at least some of the components 2a of the aerial image display device 2 or replacing at least some of the components 2a can be adopted.

[0087] <Measurement of Optical Axis Direction Based on Area of ​​Modulation Transfer Function> The measurement system 1 can determine whether the actual optical axis direction Da of the aerial image 9 coincides with the imaging direction 7d and whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad, based on the area of ​​the modulation transfer function (see FIG. 3). Below, we will describe the operation of the measurement system 1 that determines whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad, based on the area of ​​the modulation transfer function. In addition, the method of measuring the optical axis direction based on the area of ​​the modulation transfer function (hereinafter also referred to as the MTF area) is also referred to as the MTF area method.

[0088] The control unit 8 calculates modulation transfer functions MTF3 to MTF5 by Fourier transforming each of the line spread functions LSF3 to LSF5 calculated from the captured images P3 to P5, as expressed in equation (3). Furthermore, the control unit 8 integrates each of the modulation transfer functions MTF3 to MTF5 on the spatial frequency axis, as expressed in equation (4), to measure the MTF areas A3 to A5. It should be noted that the modulation transfer functions MTF3 to MTF5 do not have to be calculated by Fourier transforming the line spread functions LSF3 to LSF5. The modulation transfer functions MTF3 to MTF5 may be calculated directly from the image data of the captured images P3 to P5 using the chart method.

[0089] The control unit 8 may calculate multiple differences between the multiple MTF areas A3 to A5 (i.e., A3-A4, A3-A5, and A4-A5), and may determine that the actual optical axis direction Da of the aerial image 9 coincides with the depth direction (design optical axis direction Dad) if all of the absolute values ​​of the multiple differences are equal to or less than a threshold value T4. The control unit 8 may determine that the optical axis direction of the aerial image 9 does not coincide with the depth direction if at least one of the absolute values ​​of the multiple differences exceeds the threshold value T4. The threshold value T4 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0090] The control unit 8 may determine that the actual optical axis direction Da of the aerial image 9 coincides with the depth direction when all of the MTF areas A3 to A5 are equal to or greater than the threshold value T5. The control unit 8 may determine that the actual optical axis direction Da of the aerial image 9 does not coincide with the depth direction when at least one of the MTF areas A3 to A5 is less than the threshold value T5. The threshold value T5 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0091] The measurement system 1 can systematically measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad, based on the MTF areas A3 to A5. Because the area of ​​the modulation transfer function MTF is not easily affected by external light, etc., by using the MTF areas A3 to A5, it is possible to accurately measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad. Therefore, the measurement system 1 makes it possible to accurately calibrate the actual optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0092] Next, the operation of the measurement system 1 that measures the optical axis deviation of the aerial image 9 (deviation between the actual optical axis direction Da and the design optical axis direction Dad) and calibrates the optical axis deviation of the aerial image display device 2 will be described. When the control unit 8 determines that the actual optical axis direction Da of the aerial image 9 does not coincide with the design optical axis direction (depth direction) Dad, the control unit 8 may measure the optical axis deviation of the actual optical axis direction Da of the aerial image 9 from the design optical axis direction Dad. The control unit 8 may measure the optical axis deviation of the actual optical axis direction Da of the aerial image 9 from the design optical axis direction Dad without determining whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad.

[0093] [Measurement of Optical Axis Shift Due to Defocus Operation] First, the operation of the measurement system 1, which measures optical axis shift by moving the imaging device 7 along the imaging direction 7d, will be described. The control unit 8 controls the moving device 11 to move the imaging device 7 along the imaging direction (Z-axis direction) 7d as shown in FIG. 13, so that the imaging device 7 is positioned at multiple positions with different coordinates (Z coordinates) in the imaging direction 7d. The Z coordinates of the multiple positions are collectively represented by Zj, and Zj is expressed as Zj = Z0 + j × ΔZ. Z0 is the initial coordinate of the imaging device 7 in the imaging direction 7d, and is the Z coordinate of the imaging device 7 when the distance between the imaging device 7 and the aerial image 9 is the initial setting distance. ΔZ may be, for example, approximately 0.1 mm to 5 mm, or approximately 0.2 mm to 2 mm. j is an integer in the range of -m1≦j≦m2 (m1 and m2 are natural numbers). m1 and m2 may be natural numbers from 1 to 20, for example, but are not limited to natural numbers from 1 to 20.

[0094] The control unit 8 controls the imaging device 7 to capture an aerial image 9 in an imaging direction 7d from each position represented by a Z coordinate Zj (-m1≦j≦m2). FIG. 14 shows an example of an aerial image 9 captured by the imaging device 7 located at a position with a Z coordinate Z0. FIG. 15 shows an example of an aerial image 9 captured by the imaging device 7 located at a position with a Z coordinate Zja (ja is a positive integer). FIG. 16 shows an example of an aerial image 9 captured by the imaging device 7 located at a position with a Z coordinate Zjb (jb is a negative integer). Because the focal length of the imaging device 7 is fixed at an initial setting distance, it can be seen that the blur of the imaging portions F3, F4, and F5 changes as the imaging device 7 moves. The imaging device 7 outputs image data for (m1+m2+1) captured images P3 to P5 for each of the imaging portions F3 to F5 to the control unit 8. The control unit 8 acquires image data of (m1+m2+1) captured images P3 to P5 for each of the imaging regions F3 to F5 from the imaging device 7. The control unit 8 may acquire the image data from the imaging device 7 via the acquisition unit 14.

[0095] <Measurement of Optical Axis Shift Based on Characteristic Value of Line Spread Function of Brightness Distribution Waveform> First, a case where the optical axis shift of the aerial image 9 is measured based on the characteristic value of the line spread function will be described. For each of the imaging portions F3 to F5, the control unit 8 calculates (m1+m2+1) line spread functions LSF3, LSF4, and LSF5 based on the image data of (m1+m2+1) captured images P3 to P5, and calculates (m1+m2+1) characteristic values ​​V3 to V5. Hereinafter, it is assumed that the characteristic values ​​V3 to V5 are the peak value H of the line spread functions LSF3 to LSF5, or a combined value obtained by dividing the peak value H by the half-width W. For each of the imaging portions F3 to F5, the control unit 8 calculates the maximum value V among the (m1+m2+1) characteristic values ​​V3 to V5. ＭＡＸ and the characteristic values ​​V3 to V5 are the maximum value V ＭＡＸ The Z coordinate (hereinafter also referred to as the in-focus position) of the imaging device 7 when

[0096] 17 is a graph showing the in-focus positions FP3 to FP5 of the imaging portions F3 to F5. In this specification, the in-focus positions FP1 to FP7 are the positions where the characteristic values ​​V1 to V7 reach the maximum value V ＭＡＸThis refers to the in-focus position when the optical axis deviation is 0 mm. FIG. 17 also shows the in-focus positions FP1, FP2, FP6, and FP7 of the imaging portions F1, F2, F6, and F7. The in-focus positions FP1, FP2, FP6, and FP7 can be calculated in the same way as the in-focus positions FP3 to FP5. In FIG. 17, the in-focus positions FP3 to FP5 of the imaging portions F3 to F5 are shown with the in-focus position FP4 of the imaging portion F4 as the reference position (0 mm). FIG. 17 shows the in-focus positions FP3 to FP5 of the imaging portions F3 to F5 when optical axis deviation occurs.

[0097] In Figure 17, the sign of the in-focus position FP3 (+1.0 mm) of the imaging portion F3 is different from the sign of the in-focus position FP5 (-0.8 mm) of the imaging portion F5. This means that an optical axis misalignment has occurred, as shown in Figure 18. That is, the in-focus position FP3 is located 1.0 mm closer to the imaging device 7 relative to the focal length of the imaging device 7, and the in-focus position FP5 is located 0.8 mm farther from the imaging device 7 relative to the focal length of the imaging device 7. When the in-focus positions FP3 and FP5 have opposite signs, the control unit 8 determines that the optical axis of the aerial image 9 is misaligned from the depth direction by an angle θ that satisfies the following equation (5). In equation (5), |FP3| is the absolute value of the in-focus position FP3, |FP5| is the absolute value of the in-focus position FP5 (see FIG. 17), and L is the designed length of the aerial image 9 in the width direction (Y-axis direction).

[0098] If the controller 8 determines that the optical axis direction Da of the aerial image 9 deviates from the design optical axis direction (depth direction) Dad by an angle θ, the controller 8 controls the second rotation device 13 (see FIGS. 1 and 2 ), which rotates the entire component 2a of the aerial image display device 2, to rotate the aerial image display device 2 by an angle θ around the second rotation axis RA2. This allows the optical axis deviation of the aerial image R formed by the aerial image display device 2 to be calibrated. As a result, the user can view an aerial image R with reduced optical axis deviation and high display quality. The controller 8 controls the second rotation device 13 to rotate the aerial image display device 2 clockwise or counterclockwise by the angle θ when viewed from above the device stand 10. The controller 8 may determine the direction to rotate the aerial image display device 2 based on the signs of the focus positions FP3 and FP5 so that the optical axis direction Da of the aerial image 9 is parallel to (i.e., coincides with) the design optical axis direction Dad. The second rotation device 13 may be a manual rotation device equipped with a stepping motor device, a linear motor device, an ultrasonic motor device, or a rotation adjustment device such as a manually rotated knob or screw.

[0099] FIG. 19 shows the focus positions FP3 to FP5 of the imaging portions F3 to F5 when no optical axis misalignment occurs. FIG. 19 also shows the focus positions FP1, FP2, FP6, and FP7 of the imaging portions F1, F2, F6, and F7. The focus positions FP1, FP2, FP6, and FP7 can be calculated in the same manner as the focus positions FP3 to FP5. In FIG. 19, the focus position FP3 (-0.6 mm) of the imaging portion F3 and the focus position FP5 (-0.6 mm) of the imaging portion F5 have the same sign, which indicates that no optical axis misalignment occurs (or the optical axis misalignment is reduced), as shown in FIG. If the sign of the focusing position FP3 and the sign of the focusing position FP5 are the same sign, the control unit 8 determines that the actual optical axis direction Da of the aerial image 9 does not deviate from the designed optical axis direction (depth direction) Dad, and there is no need to rotate the component 2a of the aerial image display device 2.

[0100] The above-described operation of the measurement system 1 is an operation when the peak value H or a combined value obtained by dividing the peak value H by the half-width W is used as the characteristic values ​​V3 to V5 of the line spread functions LSF3 to LSF5. When the half-width W is used as the characteristic values ​​V3 to V5 of the line spread functions LSF3 to LSF5, the control unit 8 determines the minimum value V of the (m1+m2+1) characteristic values ​​V3 to V5 for each of the imaging regions F3 to F5. ＭＩＮ Calculate the characteristic values ​​V3 to V5 to find the minimum value V ＭＩＮ The Z coordinate of the image pickup device 7 when V is equal to V is set to one of the focus positions FP3 to FP5. ＭＩＮ may be the same as the threshold T1.

[0101] The measurement system 1 can systematically measure the optical axis deviation between the actual optical axis direction Da of the aerial image 9 and the design optical axis direction Dad based on the characteristic values ​​V3 to V5 of the line spread functions LSF3 to LSF5 by performing a defocusing operation on the imaging device 7. Therefore, the measurement system 1 makes it possible to calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0102] <Measurement of Optical Axis Shift Based on Area of ​​Modulation Transfer Function MTF> Next, a case will be described where the optical axis shift (shift between the optical axis direction Da and the design optical axis direction Dad) of the aerial image 9 is measured based on the area of ​​the modulation transfer function MTF. The control unit 8 calculates (m1+m2+1) modulation transfer functions MTF3 to MTF5 for each of the imaging portions F3 to F5 based on the image data of (m1+m2+1) captured images P3 to P5, and measures (m1+m2+1) MTF areas A3 to A5. The control unit 8 calculates the maximum value A of the (m1+m2+1) MTF areas A3 to A5 for each of the imaging portions F3 to F5. ＭＡＸ and the MTF areas A3 to A5 are the maximum value A ＭＡＸ The Z coordinates (focus positions FP3 to FP5) of the image pickup device 7 are calculated.

[0103] The control unit 8 determines whether the MTF areas A3 to A5 are the maximum value A ＭＡＸBased on the focusing positions FP3 to FP5 at which the optical axis shift (tilt angle θ) of the aerial image 9 is measured, and the optical axis shift of the aerial image R formed by the aerial image display device 2 can be calibrated. The operation of the measurement system 1 that measures the optical axis shift of the aerial image 9 based on the MTF areas A3 to A5 and calibrates the optical axis shift of the aerial image is similar to the operation of the measurement system 1 that measures the optical axis shift of the aerial image 9 based on the characteristic values ​​V3 to V5 and calibrates the optical axis shift of the aerial image, and therefore a detailed description thereof will be omitted.

[0104] The control unit 8 may calculate (m1+m2+1) line spread functions LSF3 to LSF5 for each of the imaging regions F3 to F5 based on the image data of the (m1+m2+1) captured images P3 to P5, and may calculate (m1+m2+1) modulation transfer functions MTF3 to MTF5 by performing a Fourier transform on the (m1+m2+1) line spread functions LSF3 to LSF5. Alternatively, the control unit 8 may calculate (m1+m2+1) modulation transfer functions MTF3 to MTF5 for each of the imaging regions F3 to F5 using the chart method based on the image data of the (m1+m2+1) captured images P3 to P5.

[0105] By performing a defocusing operation on the imaging device 7, the measurement system 1 can systematically measure the optical axis deviation between the optical axis direction of the aerial image 9 and the design optical axis direction based on changes in the MTF areas A3 to A5 that accompany movement of the imaging device 7. As shown in FIG. 13 , the defocusing operation is an operation that changes the degree of focus (degree of in-focusness, degree of blurring of the captured image) of each imaging portion of the aerial image 9 by moving the imaging device 7 back and forth in the imaging direction 7d. Because the area of ​​the modulation transfer function MTF is not easily affected by external light, etc., using the MTF areas A3 to A5 makes it possible to accurately measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad. Therefore, the measurement system 1 makes it possible to accurately calibrate the actual optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0106] [Measurement of Optical Axis Misalignment by Rotation Operation] Next, the operation of the measurement system 1 for measuring optical axis misalignment (misalignment between the optical axis direction Da and the design optical axis direction Dad) by rotating the imaging device 7 around the first rotation axis RA1 will be described. The control unit 8 controls the first rotation device 12 to rotate the imaging device 7 around the first rotation axis RA1 as shown in FIG. 21 to capture the aerial image 9 in multiple imaging directions 7d, each having a different angle with the depth direction (Z-axis direction). The multiple imaging directions 7d are directions that form an angle collectively represented by Θk with the depth direction (design optical axis direction Dad). Θk is also referred to as the imaging angle. Θk is expressed as Θk = k × ΔΘ. ΔΘ may be, for example, approximately 0.1° to 2°, or approximately 0.5° to 1°. k is an integer in the range of -n1≦k≦n2 (n1 and n2 are natural numbers). Each of n1 and n2 may be, for example, a natural number between 1 and 20, but is not limited to a natural number between 1 and 20. Fig. 21 shows a case where the rotation angle of the imaging device 7 is Θka (ka is a positive integer) and a case where the rotation angle of the imaging device 7 is Θkb (kb is a negative integer).

[0107] The control unit 8 controls the imaging device 7 to capture an aerial image 9 in each direction where the imaging angle is represented by Θk (-n1≦k≦n2). The imaging device 7 outputs image data of (n1+n2+1) captured images P3 to P5 for each of the imaging portions F3 to F5 to the control unit 8. The control unit 8 acquires image data of (n1+n2+1) captured images P3 to P5 from the imaging device 7 for each of the imaging portions F3 to F5. The control unit 8 may acquire the image data from the imaging device 7 via the acquisition unit 14.

[0108] <Measurement of Optical Axis Shift Based on Characteristic Values ​​of Line Spread Functions> First, a case where the optical axis shift of the aerial image 9 is measured based on the characteristic values ​​of the line spread functions will be described. For each of the imaging portions F3 to F5, the control unit 8 calculates (n1+n2+1) line spread functions LSF3 to LSF5 based on the image data of (n1+n2+1) captured images P3 to P5, and calculates (n1+n2+1) characteristic values ​​V3 to V5. The characteristic values ​​V3 to V5 may be the peak value H or the half-width W of the line spread functions LSF3 to LSF5. The characteristic values ​​V3 to V5 may also be a combined value obtained by dividing the peak value H by the half-width W.

[0109] The control unit 8 calculates multiple differences (i.e., V3-V4, V3-V5, and V4-V5) between the multiple characteristic values ​​V3 to V5 for each imaging angle Θk, and may determine that the actual optical axis direction Da of the aerial image 9 is inclined by the inclination angle Θ1 with respect to the depth direction (design optical axis direction Dad) when the absolute values ​​of the multiple differences are equal to or smaller than a threshold value T6 at a certain imaging angle Θ1. The threshold value T6 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0110] When the characteristic values ​​V3 to V5 are at peak value H or width ratio W / Q, and all of the characteristic values ​​V3 to V5 are equal to or greater than threshold value T7 at a certain imaging angle Θ2, the control unit 8 may determine that the actual optical axis direction Da of the aerial image is inclined by inclination angle Θ2 with respect to the design optical axis direction Dad. The threshold value T7 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0111] When the characteristic values ​​V3 to V5 have a half-width W, and all of the characteristic values ​​V3 to V5 are equal to or smaller than a threshold value T8 at a certain imaging angle Θ3, the control unit 8 may determine that the actual optical axis direction Da of the aerial image is inclined by the inclination angle Θ3 with respect to the design optical axis direction Dad. The threshold value T8 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0112] When the controller 8 determines that the actual optical axis direction Da of the aerial image 9 deviates from the design optical axis direction (depth direction) Dad by the tilt angles Θ1, Θ2, and Θ3, the controller 8 controls the second rotation device 13 to rotate the aerial image display device 2 around the second rotation axis RA2 by a rotation angle equal to the tilt angles Θ1, Θ2, and Θ3. This allows the optical axis deviation of the aerial image R formed by the aerial image display device 2 to be calibrated. As a result, the user can view an aerial image R with reduced optical axis deviation and high display quality. The controller 8 controls the second rotation device 13 to rotate the aerial image display device 2 clockwise or counterclockwise by a rotation angle equal to the tilt angles Θ1, Θ2, and Θ3 when viewed from above the device stand 10. The controller 8 may determine the direction in which to rotate the aerial image display device 2 so as to eliminate the optical axis deviation of the aerial image 9.

[0113] By rotating the imaging device 7, the measurement system 1 can systematically measure the optical axis deviation between the actual optical axis direction Da and the design optical axis direction Dad of the aerial image 9 based on changes in the characteristic values ​​V3 to V5 that accompany the rotation of the imaging device 7. Therefore, the measurement system 1 makes it possible to calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0114] <Measurement of Optical Axis Shift Based on Area of ​​Modulation Transfer Function MTF> Next, a case will be described where the optical axis shift of the aerial image 9 is measured based on the area of ​​the modulation transfer function MTF. The control unit 8 calculates (n1+n2+1) modulation transfer functions MTF for each of the imaging portions F3 to F5 based on the image data of (n1+n2+1) captured images P3 to P5, and measures (n1+n2+1) MTF areas A3 to A5.

[0115] The control unit 8 may calculate multiple differences (i.e., A3-A4, A3-A5, and A4-A5) between the multiple MTF areas A3 to A5 for each imaging angle Θk, and if the absolute values ​​of the multiple differences at a certain imaging angle Θ4 are equal to or smaller than a threshold value T9, it may determine that the actual optical axis direction Da of the aerial image 9 is inclined by the inclination angle Θ4 with respect to the depth direction (design optical axis direction Dad). The threshold value T9 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0116] When all of the MTF areas A3 to A5 are equal to or greater than the threshold value T10 at a certain imaging angle Θ5, the control unit 8 may determine that the actual optical axis direction Da of the aerial image is inclined by the inclination angle Θ5 with respect to the design optical axis direction Dad. The threshold value T10 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0117] The control unit 8 may calculate (n1+n2+1) line spread functions LSF3 to LSF5 for each of the imaging regions F3 to F5 based on the image data of the (n1+n2+1) captured images P3 to P5, and may calculate (n1+n2+1) modulation transfer functions MTF3 to MTF5 by performing a Fourier transform on the (n1+n2+1) line spread functions LSF3 to LSF5. Alternatively, the control unit 8 may calculate (n1+n2+1) modulation transfer functions MTF3 to MTF5 for each of the imaging regions F3 to F5 using the chart method based on the image data of the (n1+n2+1) captured images P3 to P5.

[0118] By rotating the imaging device 7, the measurement system 1 can systematically measure the optical axis misalignment between the actual optical axis direction Da of the aerial image 9 and the design optical axis direction Dad based on the MTF areas A3 to A5. Because the area of ​​the modulation transfer function MTF is not easily affected by external light, etc., by using the MTF areas A3 to A5, it is possible to accurately measure whether the actual optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad. Therefore, the measurement system 1 makes it possible to accurately calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0119] The above describes the operation of the measurement system 1, which measures the optical axis shift about the height direction (X-axis direction) perpendicular to the width direction (Y-axis direction) based on multiple captured images P3 to P5 obtained by capturing multiple imaging sites F3 to F5 aligned in the width direction (Y-axis direction) within the imaging plane Rp of the aerial image 9, and calibrates the optical axis shift. However, the operation is not limited to this. The measurement system 1 can also measure the optical axis shift about the width direction (Y-axis direction) perpendicular to the height direction (X-axis direction) based on multiple captured images (e.g., multiple captured images P1, P3, P6 or multiple captured images P2, P5, P7) obtained by capturing multiple imaging sites (e.g., multiple imaging sites F1, F3, F6 or multiple imaging sites F2, F5, F7) aligned in the height direction (X-axis direction) within the imaging plane Rp of the aerial image 9, and calibrate the optical axis shift. Alternatively, the measurement system 1 can measure the optical axis shift in the height direction (X-axis direction) and the width direction (Y-axis direction) based on multiple captured images of multiple imaging locations F1 to F7 within the imaging plane Rp of the aerial image 9, and calibrate these optical axis shifts. The line spread functions LSF1, LSF2, LSF6, and LSF7 can be calculated in the same manner as the line spread functions LSF3 to LSF5. The characteristic values ​​V1, V2, V6, and V7 can be calculated in the same manner as the characteristic values ​​V3, V4, and V5. The modulation transfer functions MTF1, MTF2, MTF6, and MTF7 can be calculated in the same manner as the modulation transfer functions MTF3, MTF4, and MTF5. The MTF areas A1, A2, A6, and A7 can be measured in the same manner as the MTF areas A3 to A5.

[0120] The optical axis deviation is measured using the measurement system 1, and if an optical axis deviation exists, the optical axis deviation is calibrated, thereby enabling the modulation transfer functions MTF1 to MTF7 to be calculated with high accuracy. As a result, degradation of the resolution of the aerial image display device 2 can be suppressed.

[0121] The present disclosure can be implemented with the following configurations (1) to (15).

[0122] (1) An aerial image display device comprising a display unit and an optical system that forms an aerial image of a real image from image light emitted from the display unit, wherein when the area obtained by integrating a first modulation transfer function of the aerial image formed by the optical system on the spatial frequency axis is S1, the optical system is an ideal optical system having a diffraction-limited resolution, and the area obtained by integrating a second modulation transfer function of the ideal aerial image formed by the ideal optical system on the spatial frequency axis is S2, the ratio S1 / S2 of the area S1 to the area S2 is 0.58 or greater.

[0123] (2) The aerial image display device according to the above configuration (1), wherein the S1 / S2 is 0.85 or more.

[0124] (3) An aerial image display device as described in the above configuration (2), wherein when the aerial image is captured by an imaging device with an aperture value set to 8 and the first modulation transfer function and the second modulation transfer function are normalized so that their maximum values ​​are 1, the area S1 is 6 or greater.

[0125] (4) An aerial image display device as described in the above configuration (2), wherein when the aerial image is captured by an imaging device with an aperture value set to 3 and the first modulation transfer function and the second modulation transfer function are normalized so that their maximum values ​​are 1, the area S1 is 12.7 or more.

[0126] (5) The aerial image display device according to any one of the above configurations (1) to (4), wherein the distortion of the aerial image is 5% or less.

[0127] (6) An aerial image display device as described in the above configuration (5), wherein the distortion of the aerial image is defined by the distortion of the corner, when the corner of the aerial image located at the end of the ideal rectangular aerial image is used as a reference and the deviation length from the edge expressed as a percentage is defined as the distortion of the corner.

[0128] (7) The aerial image display device according to the above configuration (6), wherein the distortion of the aerial image is a distortion of the four corners.

[0129] (8) The aerial image display device according to the above configuration (6) or (7), wherein the distortion of the aerial image is greatest at the four corners.

[0130] (9) The brightness of the aerial image is 800 cd / m ２ The aerial image display device according to any one of the above configurations (1) to (8).

[0131] (10) An aerial image display device according to any one of the above configurations (1) to (9), wherein the optical system comprises: a first concave mirror that reflects image light emitted from the display unit in a direction different from the direction toward the display unit; a convex mirror that reflects the image light reflected by the first concave mirror in a direction different from the direction toward the first concave mirror; and a second concave mirror that reflects the image light reflected by the convex mirror in a direction different from the direction toward the convex mirror, and forms a real aerial image.

[0132] (11) The aerial image display device according to the above configuration (10), wherein the first concave mirror and the second concave mirror are free-form concave mirrors, and the convex mirror is a free-form convex mirror.

[0133] (12) An aerial image display device as described in the above configuration (10) or (11), wherein the first concave mirror and the second concave mirror face each other at an inclination, the display unit is located between the first concave mirror and the second concave mirror, and the inclination of the display surface of the display unit relative to the reflective surface of the first concave mirror is smaller than the inclination of the display surface of the display unit relative to the reflective surface of the second concave mirror.

[0134] (13) An aerial image display device described in any of the above configurations (1) to (9), wherein the optical system comprises: a first concave mirror that reflects image light emitted from the display unit in a direction different from the direction toward the display unit; and a second concave mirror that reflects the image light reflected by the first concave mirror in a direction different from the direction toward the first concave mirror, and forms a real aerial image.

[0135] (14) The aerial image display device according to the above configuration (13), wherein the first concave mirror and the second concave mirror are free-form concave mirrors.

[0136] (15) An aerial image display device as described in the above configuration (13) or (14), wherein the curvature of the first concave mirror is greater than the curvature of the second concave mirror, the first concave mirror and the second concave mirror face each other at an angle, and the display unit is located between the first concave mirror and the second concave mirror.

[0137] The aerial image display device of the present disclosure can suppress a decrease in the resolution of the aerial image. Furthermore, the aerial image display device of the present disclosure can reduce distortion of the aerial image and suppress a decrease in the brightness of the aerial image.

[0138] Although the embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the above-described embodiments, and various modifications and improvements are possible within the scope of the gist of the present disclosure. Furthermore, configurations formed by combining two or more of the above-described various embodiments are also included in the present disclosure.

[0139] REFERENCE SIGNS LIST 1 Measurement system 2 Aerial image display device 2a Constituent member 3 Display unit 4 Display panel 4a Display surface 4ai Virtual surface 5 Optical system 5a First concave mirror 5aa Reflecting surface 5ai Virtual surface 5ap Vertex 5ar Reflecting surface (first reflecting surface) 5b Convex mirror 5c Second concave mirror 5ci Virtual surface 5cp Vertex 5cr Reflecting surface (second reflecting surface) 5d First concave mirror 5e Second concave mirror 6 Housing 6a Image light emitting unit 7 Imaging device 7d Imaging direction 7da Imaging direction 8 Control unit 9, 9' Test pattern (aerial image) 9a First strip-shaped image 9b Second strip-shaped image 9c Rectangular wave chart 10 Device stand 10a Top surface 11 Moving device 11h Holding member 11r Rail 11t Moving table 12 First rotation device 13 Second rotation device 14 Acquisition unit 20 User 20e Eye Da Optical axis direction of aerial image Dad Design optical axis direction Lp Image light F1 to F7 Imaging portion P1 to P7 Captured image R Aerial image Rp Imaging plane

Claims

1. An aerial image display device comprising a display unit and an optical system that forms a real aerial image from the image light emitted from the display unit, wherein when the area S1 obtained by integrating a first modulation transfer function of the aerial image formed by the optical system on the spatial frequency axis is defined as S1, the optical system is an ideal optical system having a diffraction-limited resolution, and the area S2 obtained by integrating a second modulation transfer function of the ideal aerial image formed by the ideal optical system on the spatial frequency axis is defined as S2, the ratio S1 / S2 of area S1 to area S2 is 0.58 or greater.

2. The aerial image display device according to claim 1, wherein said S1 / S2 is 0.85 or more.

3. An aerial image display device as described in claim 2, wherein when the aerial image is captured by an imaging device with an aperture value set to 8, and the first modulation transfer function and the second modulation transfer function are normalized so that their maximum values ​​are 1, the area S1 is 6 or greater.

4. An aerial image display device as described in claim 2, wherein when the aerial image is captured by an imaging device with an aperture value set to 3, and the first modulation transfer function and the second modulation transfer function are normalized so that their maximum values ​​are 1, the area S1 is 12.7 or more.

5. An aerial image display device according to any one of claims 1 to 4, wherein the distortion of the aerial image is 5% or less.

6. An aerial image display device as described in claim 5, wherein the distortion of the aerial image is defined by the distortion of a corner, the corner being defined as the deviation length from an ideal rectangular aerial image side, of a corner of the aerial image located at the end of the ideal rectangular aerial image, expressed as a percentage.

7. The aerial image display device according to claim 6, wherein the distortion of the aerial image is a distortion of the four corners.

8. An aerial image display device according to claim 6 or 7, wherein the distortion of the aerial image is greatest at the four corners.

9. The brightness of the aerial image is 800 cd / m ２ The aerial image display device according to any one of claims 1 to 8, wherein:

10. An aerial image display device as described in any one of claims 1 to 9, wherein the optical system comprises: a first concave mirror that reflects the image light emitted from the display unit in a direction different from the direction toward the display unit; a convex mirror that reflects the image light reflected by the first concave mirror in a direction different from the direction toward the first concave mirror; and a second concave mirror that reflects the image light reflected by the convex mirror in a direction different from the direction toward the convex mirror, forming a real aerial image.

11. An aerial image display device as described in claim 10, wherein the first concave mirror and the second concave mirror are free-form concave mirrors, and the convex mirror is a free-form convex mirror.

12. An aerial image display device as described in claim 10 or 11, wherein the first concave mirror and the second concave mirror face each other in an inclined state, the display unit is located between the first concave mirror and the second concave mirror, and the inclination of the display surface of the display unit relative to the reflective surface of the first concave mirror is smaller than the inclination of the display surface of the display unit relative to the reflective surface of the second concave mirror.

13. An aerial image display device as described in any one of claims 1 to 9, wherein the optical system comprises: a first concave mirror that reflects the image light emitted from the display unit in a direction different from the direction toward the display unit; and a second concave mirror that reflects the image light reflected by the first concave mirror in a direction different from the direction toward the first concave mirror, forming a real aerial image.

14. The aerial image display device according to claim 13, wherein the first concave mirror and the second concave mirror are free-form concave mirrors.

15. An aerial image display device as described in claim 13 or 14, wherein the curvature of the first concave mirror is greater than the curvature of the second concave mirror, the first concave mirror and the second concave mirror face each other at an angle to each other, and the display unit is positioned between the first concave mirror and the second concave mirror.