Resolution measuring device

Abstract

A resolution measuring device according to the present disclosure measures the resolution of a midair image in a midair image display device that includes a display unit and that forms an image of image light of a display image emitted from the display unit as a midair image of a real image, the resolution measuring device comprising a comparing unit. The comparing unit compares an area obtained by integrating, on the spatial frequency axis, a first modulation transfer function of a first captured image obtained by capturing the midair image, and an area obtained by integrating, on the spatial frequency axis, a second modulation transfer function of a second captured image obtained by imaging the display image.

Description

Resolution measuring device

[0001] The present disclosure relates to a resolution measurement device.

[0002] 2. Description of the Related Art Conventionally, for example, an aerial image display device described in Patent Document 1 and a modulation transfer function (MTF) measuring device described in Patent Document 2 are known.

[0003] JP 2011-253128 A JP 2002-357507 A

[0004] The resolution measuring device disclosed herein is a resolution measuring device that measures the resolution of an aerial image in an aerial image display device that includes a display unit and forms an aerial image of a real image using image light of a display image emitted from the display unit, and is equipped with a comparison unit that is configured to compare an area S1 obtained by integrating a first modulation transfer function of a first captured image that captures the aerial image on a spatial frequency axis with an area S2 obtained by integrating a second modulation transfer function of a second captured image that captures the display image on the spatial frequency axis.

[0005] 9 is a graph showing a luminance distribution waveform measured from the captured image of FIG. 9.

[0023] FIG. 9 is a cross-sectional view showing an example of an aerial image display device used in the resolution measurement device of the present disclosure.

[0024] FIG. 10 is a cross-sectional view showing another example of an aerial image display device used in the resolution measurement device of the present disclosure.

[0025] FIG. 11 is a graph showing an example of a modulation transfer function.

[0026] FIG. 12 is a diagram showing an example of an aerial image visually recognized by a user of the aerial image display device of FIG. 1.

[0027] FIG. 13 is a diagram explaining the definition of the curvature of a first concave mirror.

[0028] FIG. 14 is a perspective view showing the configuration of a resolution measurement device according to an embodiment of the present disclosure.

[0029] FIG. 15 is a diagram showing an example of a test pattern for calculating a modulation transfer function (MTF).

[0030] FIG. 16 is a diagram showing a captured image of the test pattern captured by an imaging device.

[0031] FIG. 17 is a partially enlarged view showing the captured image of the test pattern captured by the imaging device.

[0032] FIG. 18 is a graph showing a luminance distribution waveform measured from the captured image of FIG.

[0033] FIG. 19 is a diagram explaining the tilt angle of the first concave mirror in the aerial image display device of FIG. 2.

[0034] FIG. 19 is a diagram showing another example of a test pattern for calculating a modulation transfer function.

[0035] FIG. 10 is a partially enlarged view showing the captured image of the test pattern captured by the imaging device.

[0036] FIG. 11 is a side view explaining a defocus operation for the imaging device. 21. A partially enlarged view showing an example of a captured image of a test pattern captured by an imaging device. A partially enlarged view showing an example of a captured image of a test pattern captured by an imaging device. A diagram showing an example of a captured image of a test pattern captured by an imaging device. A graph showing the focus position of each imaging portion. A diagram explaining optical axis deviation corresponding to the graph of FIG. 19. A graph showing the focus position of each imaging portion. A diagram explaining optical axis deviation corresponding to the graph of FIG. 21. A diagram explaining rotational operation of the imaging device. A graph showing the MTFs of multiple imaging portions F1 to F7 and display image D listed in Table 3, and the MTFs of Conventional Examples 1 and 2. A diagram showing character information displayed by the aerial image of Conventional Example 1. A diagram showing character information displayed by the aerial image of the aerial image display device of FIG. 1. A graph excerpting a portion of the graph of FIG. 24. A graph showing the change in the ratio S1 / S2 depending on the angle of deviation from the reference angle of the free-form concave mirror of the aerial image display device shown in FIG. 2.

[0006] Patent Document 1 describes an aerial image display device that forms a real aerial image from image light emitted from a display panel using optical components such as a beam splitter, a half mirror, etc. Patent Document 2 describes an aerial image observation method as a method for evaluating the optical performance of lenses used in optical devices such as cameras, and an MTF measurement device based on the aerial image observation method.

[0007] Conventional MTF measurement devices are not sufficient to measure with high precision the resolution of an aerial image formed by an aerial image display device, and are not capable of measuring the direction of the optical axis of the aerial image.

[0008] 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, the vertical direction, or the height direction. The Y-axis direction is also referred to as the second direction, the horizontal direction, or the width direction. The Z-axis direction is also referred to as the third direction or the depth direction.

[0009] 1 to 28 are diagrams or graphs for explaining the aerial image display device and the resolution measurement device used in the resolution measurement device of the present disclosure. In Figures 7 to 10, 13, 14, and 16 to 18, the second band-shaped image (black image) is shown at a brightness higher than the actual brightness.

[0010] 1 , an aerial image display device 2 used in a resolution measurement device 1 according to an embodiment of the present disclosure includes a display unit 3. The aerial image display device 2 displays an image (hereinafter also referred to as a display image) D on the display unit 3, and forms image light Lp of the display image D emitted from the display unit 3 as a real aerial image R. The aerial image display device 2 may include an optical system 5 that forms the image light Lp of the display image D as an aerial image R on a virtual imaging plane Rp.

[0011] 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. In other words, the display unit 3 emits image light Lp, which is formed as an aerial image R, from the display surface 4a of the display panel 4. 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.

[0012] 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.

[0013] The optical system 5 focuses the image light Lp emitted from the display unit 3 as an aerial image R. The optical system 5 may be composed of reflective members (reflecting mirrors) 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 5a, a convex mirror 5b, and a second concave mirror 5c. The optical system 5 may include a free-form reflecting mirror.

[0014] 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 (also referred to as a first 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.

[0015] 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.

[0016] 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 (also referred to as a second free-form concave mirror). The second concave mirror 5c is not limited to a free-form concave mirror, and may be a spherical concave mirror or an aspherical concave mirror.

[0017] The optical system 5 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, which illustrates a two-mirror system. The optical system 5 includes the first concave mirror 5d that faces the display unit 3 at an angle, and the second concave mirror 5e that faces the first concave mirror 5d at an angle and forms the aerial image R.

[0018] 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 (also referred to as a first 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.

[0019] 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 (also referred to as a second free-form concave mirror). The second concave mirror 5e is not limited to a free-form concave mirror, and may be a spherical concave mirror or an aspherical concave mirror.

[0020] 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

[0021] The aerial image display device 2 may be configured such that the maximum diameter of the reflecting surface of the second free-form concave mirror 5c (5e) is longer than the maximum diameter of the reflecting surface of the first free-form concave mirror 5a (5d), and the curvature of the first free-form concave mirror 5a (5d) is greater than the curvature of the second free-form concave mirror 5c (5e). By configuring the maximum diameter of the reflecting surface of the second free-form concave mirror 5c (5e) to be longer than the maximum diameter of the reflecting surface of the first free-form concave mirror 5a (5d), the aerial image R can be enlarged and distortion of the aerial image R can be reduced. Furthermore, by configuring the curvature of the first free-form concave mirror 5a (5d) to be greater than the curvature of the second free-form concave mirror 5c (5e), ​​distortion of the aerial image R can be suppressed while the area ratio S1 / S2 (see below), which is an index of resolution of the aerial image R, can be set to 0.4 or greater.

[0022] The aerial image display device 2 may be configured so that no other optical elements are included in the optical path from the display unit 3 to the second free-form concave mirror 5e via the first free-form concave mirror 5d. In this case, it is possible to prevent a decrease in the brightness of the aerial image R and to prevent an increase in distortion of the aerial image R. As a result, a high-brightness and high-resolution aerial image R can be formed.

[0023] In the configuration of Figure 1 depicting a three-mirror system, where Ra is the maximum diameter of the reflecting surface of the first free-form concave mirror 5a, Rb is the maximum diameter of the reflecting surface of the free-form convex mirror 5b, and Rc is the maximum diameter of the reflecting surface of the second free-form concave mirror 5c, Rc > Ra > Rb may be satisfied. Also, where Sa is the curvature of the first free-form concave mirror 5a, Sb is the curvature of the free-form convex mirror 5b, and Sc is the curvature of the second free-form concave mirror 5c, Sa > Sc > Sb may be satisfied. By maximizing Rc, the aerial image R can be enlarged and distortion of the aerial image R can be reduced. By minimizing Rb, the size of the free-form convex mirror 5b that diffuses light is minimized, thereby suppressing an increase in distortion of the aerial image R and suppressing a decrease in the brightness of the aerial image R. By satisfying Sa > Sc, the curvature of the second free-form concave mirror 5c can be made relatively smaller than that of the first free-form concave mirror 5a, thereby suppressing an increase in distortion of the aerial image R. Furthermore, the display unit 3 can be positioned closer to the first free-form concave mirror 5a, which has high light-gathering properties. Furthermore, by minimizing Sb, the curvature of the free-form convex mirror 5b, which diffuses light, is minimized, thereby further suppressing an increase in distortion of the aerial image R. Therefore, the area ratio S1 / S2, which is an index of resolution of the aerial image R, can be set to 0.4 or more while suppressing distortion of the aerial image R.

[0024] The aerial image display device 2 may be configured so that no other optical elements are included in the optical path from the display unit 3 to the second free-form concave mirror 5c via the first free-form concave mirror 5a and the free-form convex mirror 5b. In this case, it is possible to prevent a decrease in the brightness of the aerial image R and to prevent an increase in distortion of the aerial image R. As a result, a high-brightness and high-resolution aerial image R can be formed.

[0025] 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.

[0026] 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.

[0027] The internal space of the housing 6 may also be depressurized. In this case, the air in the space through which the image light Lp propagates is thin, which reduces attenuation of the image light Lp and prevents a decrease in the brightness of the aerial image R. The air pressure in the internal space of the housing 6 may be 0.1 times or more and less than 1 time atmospheric pressure, but is not limited to this range.

[0028] The humidity of the internal space of the housing 6 may also be low. In this case, the moisture (water vapor) contained in the air in the space through which the image light Lp propagates is low, which reduces attenuation of the image light Lp and prevents a decrease in the brightness of the aerial image R. The humidity of the internal space of the housing 6 may be, at room temperature (approximately 25°C), a relative humidity of approximately 5% to 50%, or may be a relative humidity of approximately 10% to 30%, but is not limited to these ranges.

[0029] Furthermore, a dust attracting member such as a dust attracting film or an electrostatic attracting film may be provided on the inner wall of the housing 6. The dust attracting member may be attached to the inner wall of the housing 6 with an adhesive member such as an adhesive or an adhesive sheet. In this case, since there is little dust in the air in the space through which the image light Lp propagates, attenuation of the image light Lp is reduced, and a decrease in the luminance of the aerial image R can be suppressed.

[0030] Next, the resolution of the aerial image R formed by the aerial image display device 2 will be described. The aerial image R formed via the optical system 5 has a lower resolution than the display image D displayed on the display surface 4 a of the display panel 4. The degradation in resolution of the aerial image R includes unavoidable degradation due to diffraction of light as well as degradation due to manufacturing tolerances and positioning errors of the reflective members that make up the optical system 5. The resolution of the aerial image R and the resolution of the display image D can be quantitatively evaluated, for example, by comparing the modulation transfer function of the aerial image R with the modulation transfer function of the display image D. In other words, the degree of degradation in the resolution of the aerial image R relative to the resolution of the display image D can be quantitatively evaluated by comparing the modulation transfer function of the display image D with the modulation transfer function of the aerial image R.

[0031] The modulation transfer function (MTF) is a performance index for evaluating the resolution of the display panel 4 and the optical system 5. The modulation transfer function can be used as a resolution index for comparing the resolution of the display image D and 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 of the display image D is to 1, the higher the resolution of the display image D. Similarly, the closer the value of the modulation transfer function of the aerial image R is to 1, the higher the resolution of the aerial image R is. While the value of the modulation transfer function itself may be used as the resolution index of the display image D and the aerial image R, the resolution of the display image D and 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 resolution index of the display image D and the aerial image R. The modulation transfer function of the aerial image R can be calculated, for example, based on a captured image of the aerial image R captured by an imaging device. The modulation transfer function of the display image D can be calculated based on, for example, a captured image of the display image D captured by an imaging device.

[0032] 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 (hereinafter also referred to as the first modulation transfer function) is shown by a dashed line, and the modulation transfer function K2 of the display image D (hereinafter also referred to as the second modulation transfer function) is shown by a solid line. As shown in FIG. 3, at any spatial frequency ν, the value of the first modulation transfer function K1 may be equal to or less than the value of the second modulation transfer function K2. The area S1 obtained by integrating the first modulation transfer function K1 on the spatial frequency axis may be equal to or less than the area S2 obtained by integrating the second modulation transfer function K2 on the spatial frequency axis. Therefore, the ratio S1 / S2 of the area S1 to the area S2 may be equal to or less than 1. The closer the ratio S1 / S2 is to 1, the less degradation in resolution caused by the optical system 5 is, and the higher the resolution of the aerial image R can be. Hereinafter, the ratio S1 / S2 of the area S1 to the area S2 may be referred to as the ratio S1 / S2, the area ratio S1 / S2, or the MTF area ratio S1 / S2.

[0033] The resolution measurement device 1 may include a determination unit that determines the ratio S1 / S2 of the area S1 to the area S2. The determination unit may be located inside the comparison unit 15 (shown in FIG. 6) or downstream of the comparison unit 15. The determination unit 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 a specific process. 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 measurement unit 8 may include at least one of a system-on-a-chip (SoC) and a system-in-a-package (SiP) in which one or more processors are configured to cooperate with each other.

[0034] In the aerial image display device 2, the optical system 5 is composed only of reflective members, and degradation of the resolution of the aerial image R due to refraction, deflection, etc. of the image light Lp can be reduced, so that the ratio S1 / S2 of the area S1 to the area S2 can be set to 0.4 or more. As a result, the aerial image display device 2 can reduce degradation of the resolution of the aerial image R and suppress deterioration of the display quality of the aerial image R.

[0035] If the ratio S1 / S2 is less than 0.4, the resolution of the aerial image R deteriorates. For example, if the aerial image R includes text information, the reduced resolution of the text information causes the text information to become blurred, making it difficult for the user 20 to read. The graph in Figure 24 shows the MTF of the aerial image of Conventional Example 1 (manufactured by Asukanet Co., Ltd., product name "ASKA3D") and the MTF of the aerial image of Conventional Example 2 (a configuration in which a beam splitter and a retroreflector are disposed between two reflecting mirrors). Table 1 lists the data for the MTF, MTF area (S1, S2), and MTF area ratio (S1 / S2) of Conventional Examples 1 and 2. Figure 25 shows the text information displayed by the aerial image of Conventional Example 1. In Conventional Example 1, the ratio S1 / S2 is 0.26, and the resolution of the text information deteriorates, causing the text information to become blurred, making it difficult for the user 20 to read. The MTF area ratios S1 / S2 shown in Table 1 are values ​​rounded off to two decimal places.

[0036]

[0037] Figure 26 shows text information displayed by the aerial image R of the aerial image display device 2 shown in Figure 1. The text information is displayed clearly with high resolution, making it easy for the user 20 to read. The aerial image R in Figure 26 has a ratio S1 / S2 of 0.4 or greater, and as will be described later, the ratio S1 / S2 is 0.9 or greater at spatial frequencies of 0 to 12 (1 / mm) and 0.8 or greater at spatial frequencies of 7 to 10 (1 / mm).

[0038] Conventional example 1 uses an optical element that reflects image light from a display device and forms an aerial image, and includes a plurality of glass plates (also referred to as glass plate group a) having an Al (aluminum) reflective film on their surfaces and a plurality of glass plates (also referred to as glass plate group b) having an Al reflective film on their surfaces. The glass plate group a is erected so that its main surfaces are parallel to each other, and the glass plate group b is stacked on the glass plate group a and erected so that its main surfaces are parallel to each other. The directions of the main surfaces of the glass plate group a and the main surfaces of the glass plate group b are perpendicular to each other. In plan view, the glass plate group a and the glass plate group b form a plurality of rectangular openings. The size of the openings determines the resolution. In other words, larger openings tend to degrade the resolution. It is physically difficult to make the openings smaller, which is thought to lead to a deterioration in the resolution of the aerial image.

[0039] Conventional example 2 has a configuration in which a beam splitter and a retroreflector are placed between two reflecting mirrors. The beam splitter reduces the brightness of the aerial image, and the retroreflector tends to degrade the resolution of the aerial image. As a result, the contrast of the aerial image is significantly reduced, making the resolution of the aerial image more likely to deteriorate. The retroreflector is made up of multiple fine hemispherical retroreflective elements arranged in a matrix, and the resolution is determined by the size of the retroreflective elements. It is physically difficult to make the retroreflective elements fine, and the retroreflective elements reflect a portion of the incident light, so it is thought that the resolution of the aerial image is more likely to deteriorate.

[0040] By setting the ratio S1 / S2 to 0.4 or greater, degradation of the resolution of the text information displayed by the aerial image R is effectively suppressed. As a result, the text information can be clearly displayed by the aerial image R, making it easier for the user 20 to read. The text information may be advertisements, explanatory notes, presentation materials, papers, etc. The text information may also include a large number of characters with a font size of approximately 8 to 12 points (also referred to as normal characters) used in general documents, for example, normal characters accounting for 50% or more of the total text. The text information may also include large characters with a font size exceeding 12 points, modified characters, pictograms, and other characters used for advertising and warning purposes.

[0041] The aerial image display device 2 can reduce distortion of the aerial image R to 5% or less. FIG. 4 shows simulation results of 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, ideal aerial image (also referred to as an ideal 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 width direction and the Y-axis direction is the height direction.

[0042] 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 2 shows the distortion from the aerial image IR at the corners LR, UR, LL, and UL. As shown in Table 2, the aerial image display device 2 can suppress distortion at the corners LR, UR, LL, and UL to within ±5%.

[0043]

[0044] The + (plus) direction in the X-axis direction corresponds to the right direction in FIG. 4 , and the − (minus) direction in the X-axis direction corresponds to the left direction in FIG. 4 . The + (plus) direction in the Y-axis direction corresponds to the upward direction in FIG. 4 , and the − (minus) direction in the Y-axis direction corresponds to the downward direction in FIG. 4 . However, in Table 2, for the distortion of the aerial image R, distortion toward the outside of the aerial image IR in both the X-axis and Y-axis 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-axis direction (rightward: expanding direction) is taken as the + (plus) direction, the inward direction in the X-axis direction (leftward: contracting direction) is taken as the − (minus) direction, the outward direction in the Y-axis direction (downward: expanding direction) is taken as the + (plus) direction, and the inward direction in the Y-axis 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 the distortion of the aerial image R.

[0045] The distortion at the corners LR, UR, LL, and UL is calculated as follows. Using the edge of the ideal aerial image IR as a reference, the distortion is defined as the length of deviation of the corner of the aerial image R located at the end of that edge, expressed as a percentage. The distortion in the X-axis direction of the corners LR, UR, LL, and UL is defined as the deviation length in the X-axis direction relative to the length LX of the top edge (the bottom edge is the same length as the top edge) of the rectangular aerial image IR. 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-axis direction of the corner UR is defined as the deviation length ΔXUR in the X-axis 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-axis direction of the corner UR is defined as (ΔXUR / LX) × 100 (%). Because the corner UR is distorted inward of the aerial image IR in the X-axis direction, the value is negative (-). The distortion of the corners LR, LL, and UL in the X-axis direction is also defined in a similar manner. If the aerial image IR has a shape other than a rectangle, the reference length in the X-axis direction may be an average length or a maximum length.

[0046] The distortion of the corners LR, UR, LL, and UL in the Y-axis direction is defined as the deviation length in the Y-axis 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 of the corner UR in the Y-axis direction is defined as the deviation length ΔYUR in the Y-axis 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 of the corner UR in the Y-axis direction is defined as (ΔYUR / LY) × 100 (%). Because the corner UR is distorted inward of the aerial image IR in the Y-axis direction, the value is negative (-). The distortion of the corners LR, LL, and UL in the Y-axis direction is defined similarly. If the aerial image IR has a shape other than rectangular, the reference length in the Y-axis direction may be the average length or the maximum length.

[0047] 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.

[0048] 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.

[0049] According to the aerial image display device 2, degradation in the resolution of the aerial image R can be reduced, and distortion of the aerial image R can also be reduced, so that degradation in the display quality of the aerial image R can be further suppressed.

[0050] The aerial image display device 2 sets the brightness of the aerial image R formed by the optical system 5 to 800 cd / m ２ (cd: candela) or more. In the aerial image display device 2, the optical system 5 is composed only of reflective members and does not include transmissive reflective members such as beam splitters or half mirrors, so utilization of the image light Lp is high. Therefore, the aerial image display device 2 can 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, for example, by a luminance meter placed at the position of the imaging device 7 (see FIG. 6).

[0051] The brightness of the image displayed on the display unit 3 is 1000 cd / m ２ In the aerial image display device 2, the optical system 5 is configured to be composed of only reflective members and does not include transmissive reflective members such as beam splitters or half mirrors, so the utilization rate of the image light Lp is high. For this reason, the luminance of the image displayed on the display unit 3 can be set to 1000 cd / m or less. ２ Even if the brightness of the aerial image display device 2 is less than 800 cd / m, it is possible to form a high-brightness aerial image R while suppressing an increase in power consumption of the aerial image display device 2. ２ More than 1000cd / m ２ It may be 900 cd / m or less, ２ More than 1000cd / m ２ The range may be, but is not limited to, these ranges.

[0052] According to the aerial image display device 2, degradation in the resolution of the aerial image R can be reduced, and degradation in the luminance of the aerial image R can also be reduced, so degradation in the display quality of the aerial image R can be further suppressed.

[0053] Next, a comparison between the area S1 and the area S2 will be described. The comparison between the area S1 and the area S2 can be performed using the resolution measurement device 1. As shown in FIG. 6, the resolution measurement device 1 includes a comparison unit 15. The comparison unit 15 is configured to compare the area S1 and the area S2. For example, the comparison unit 15 may be configured to include a comparator such as a comparator. The comparison unit 15 may be configured to determine the size relationship between the area S1 and the area S2, or to measure the ratio S1 / S2 of the area S1 to the area S2.

[0054] The resolution measurement device 1 may include a measurement unit 8. The measurement unit 8 is configured to calculate a first modulation transfer function K1 of the aerial image R based on image data of a captured image of the aerial image R (hereinafter also referred to as a first captured image), and measure an area S1 obtained by integrating the first modulation transfer function K1 on the spatial frequency axis. The measurement unit 8 is also configured to calculate a second modulation transfer function K2 of the display image D based on image data of a captured image of the display image D (hereinafter also referred to as a second captured image), and measure an area S2 obtained by integrating the second modulation transfer function K2 on the spatial frequency axis. The measurement unit 8 may include a comparison unit 15. In other words, the comparison unit 15 may constitute a part of the measurement unit 8.

[0055] The resolution measurement device 1 may include an imaging device 7. The imaging device 7 is assumed to be the eye 20e of the user 20 (see FIGS. 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 (see FIGS. 1 and 2 ) 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 Dad. The measurement unit 8 may control the first rotation device 12 to rotate the imaging device 7 around a predetermined rotation axis. That is, the measurement 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).

[0056] 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 (also referred to as the F-number). The imaging device 7 may be capable of changing the aperture value within a range of 2 to 22.

[0057] The resolution measurement device 1 does not need to include the imaging device 7. If the resolution measurement device 1 does not include the imaging device 7, the resolution measurement device 1 may have an input terminal for inputting a signal from an external imaging device. The external imaging device may be directly connected to the input terminal. The external imaging device may be indirectly connected to the input terminal via a shared network. The resolution measurement device 1 may acquire a captured image of the aerial image R formed by the aerial image display device 2 from the external imaging device.

[0058] The measurement unit 8 may function as a control unit of the resolution measurement device 1. The measurement unit 8 may be connected to each component of the resolution measurement device 1 and control each component. Components controlled by the measurement unit 8 may include the imaging device 7 and the comparison unit 15. If the resolution measurement device 1 does not include the imaging device 7, the measurement unit 8 may control an external imaging device. The measurement 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. For example, the measurement unit 8 may control the display image D displayed on the display unit 3, i.e., the aerial image R formed by the aerial image display device 2. The measurement 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 measurement unit 8 may include at least one of a System-on-a-Chip (SoC) and a System-in-a-Package (SiP) in which one or more processors are configured to work together.

[0059] The resolution measurement device 1 may include an acquisition unit 14. The acquisition unit 14 may store image data of the captured image generated by the imaging device 7. When the imaging device 7 generates the captured image, the measurement unit 8 may acquire the image data of the captured image via the acquisition unit 14. When the imaging device 7 generates the 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 measurement 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 measurement unit 8 may use at least one of a wired communication method, a wireless communication method, an infrared communication method, etc.

[0060] Next, measurement of the modulation transfer function K1 and area S1 of the aerial image R will be described. When measuring the modulation transfer function K1 of the aerial image R, the measurement 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 FIGS. 6 and 7 on the imaging plane Rp as the aerial image R. FIG. 7 shows an aerial image 9 that is free of blur (i.e., resolution degradation). FIG. 7 can also be said to be a display pattern that the measurement unit 8 displays on the display surface 4a of the display panel 4 in order to form the aerial image 9 on the imaging plane Rp. It is assumed that the optical axis direction Da (see FIGS. 1 and 2) of the aerial image 9 coincides with the design optical axis direction Dad.

[0061] The aerial image 9 may have a rectangular outer shape when viewed along the imaging direction 7d of the imaging device 7. The aerial image 9 may be a repeating 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 aerial image 9 may include at least three first band-shaped images 9a. While FIG. 7 illustrates 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 the second band-shaped images 9b may differ in at least one of brightness and color.

[0062] 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 K1 of the aerial image 9 can be increased, making it possible to calculate the modulation transfer function K1 of the aerial image 9 with high accuracy.

[0063] FIG. 8 shows an example of the overall image of the aerial image 9 captured by the imaging device 7. FIG. 9 shows an example of the overall image of the aerial image 9 when viewed along the imaging direction 7d of the imaging device 7. The measurement unit 8 may control the imaging device 7 to capture at least one imaging portion in the aerial image 9. The at least one imaging portion may be 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 imaging portions F1 to F7 in the aerial image 9. Note that "to" means "through," and the same applies hereinafter.

[0064] The imaging portion F4 may be located near the center of the aerial image 9 when viewed along the imaging direction 7d of the imaging device 7. The center of the aerial image 9 may be the intersection of two diagonals of the aerial image 9. The imaging portions F3 to F5 may be aligned in a predetermined direction within the imaging plane Rp. 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 (height direction) or a direction tilted (diagonal) from the X-axis direction and the Y-axis direction. Hereinafter, unless otherwise specified, the imaging portions F3 to F5 are assumed to be aligned in the Y-axis direction (width direction) within the imaging plane Rp. The imaging portions F1, F2, F6, and F7 may be located at the four corners of the aerial image 9, respectively.

[0065] The imaging device 7 captures multiple imaging portions F1-F7 of the aerial image 9 and outputs image data of the multiple captured images P1-P7. The multiple captured images P1-P7 are captured images of the multiple imaging portions F1-F7, respectively. The aerial image 9 may be configured such that each of the multiple captured images P1-P7 includes at least one image of a first strip-shaped image 9a (white image portion in FIG. 9). The aerial image 9 may be configured such that each of the multiple captured images P1-P7 includes one image of a first strip-shaped image 9a, as shown in FIG. 10. In this case, processing of the image data of each captured image P1-P7 is simplified, and the modulation transfer function of the aerial image 9 can be calculated with high accuracy. Each captured image P1-P7 may have approximately 50-100 pixels in the vertical direction and approximately 50-100 pixels in the horizontal direction.

[0066] The captured images P1, P2, P6, and P7 may be captured images of four corners of an 80% region 9g of the aerial image 9, as shown in Fig. 10. Note that the 80% region 9g refers to a partial region of the aerial image 9, as shown in Fig. 10, in which the number of pixels in the first direction (X-axis direction) is approximately 80% of the number of pixels HP in the first direction of the aerial image 9, the number of pixels in the second direction (Y-axis direction) is approximately 80% of the number of pixels WP in the second direction of the aerial image 9, and the center of the region coincides with that of the aerial image 9.

[0067] The distance between the imaging device 7 and the aerial image 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, the distance between the imaging device 7 and the aerial image 9 is assumed to be 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 measurement 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. In other words, the measurement unit 8 may perform a defocus operation to make the distance between the imaging device 7 and the aerial image 9 and the focal length of the imaging device 7 different.

[0068] When the imaging device 7 captures the aerial image 9, the measurement unit 8 may control the imaging device 7 to set the aperture value (also referred to as the F-number) to a value of 3 or less. Setting the aperture value of the imaging device 7 to a relatively small value (3 or less) can reduce (i.e., shorten) the depth of field (also referred to as the focal depth of field) of the imaging device 7. In other words, setting the aperture value of the imaging device 7 to a relatively small value can reduce (i.e., narrow) the range in which the subject is in focus in the depth direction. As a result, the position of the subject (i.e., the multiple imaging portions F1 to F7) in the depth direction can be accurately measured, and the modulation transfer function of the aerial image R can be accurately calculated. Furthermore, as will be described in detail later, it is possible to accurately measure the optical axis deviation between the actual optical axis direction Da of the aerial image 9 formed by the aerial image display device 2 and the design optical axis direction Dad of the aerial image R formed by the aerial image display device 2.

[0069] The measurement unit 8 acquires image data of multiple captured images P1 to P7 from the imaging device 7 via the acquisition unit 14. The measurement unit 8 scans the luminance values ​​of each pixel arranged in the width direction (the left-right direction in FIG. 9 ) for each of the multiple captured images P1 to P7, performs binning processing, and calculates (measures) luminance distribution waveforms LSF1 to LSF7 as shown in FIG. 11 . LSF in FIG. 11 collectively represents the luminance distribution waveforms LSF1 to LSF7. The luminance distribution waveforms LSF1 to LSF7 each refer to a luminance distribution waveform 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. 11 represents changes in position in the Y-axis direction. In FIG. 11 , the highest value (peak value) of the luminance distribution waveform is displayed at the position of the 30th pixel among multiple pixels (e.g., 60 pixels) in the Y-axis direction. The luminance distribution waveform is also called a line spread function (LSF). 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. 11.

[0070] The measurement 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 that converts, for example, a function expressed by a pulse waveform into a curve expressed by continuous values ​​in the frequency domain (a continuous curve expressed as a sine waveform curve, a cosine waveform curve, or 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.

[0071] 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 can reduce the processing load on the measurement 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.

[0072] The measurement 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 12 / mm), in which case the processing load on the measurement unit 8 can be reduced.

[0073] The measurement unit 8 may use the average value of the areas A1 to A7 as the area S1 of the modulation transfer function K1. In this case, it is possible to evaluate the level of average resolution across the entire aerial image 9. The measurement unit 8 may use the weighted average value of the areas A1 to A7 as the area S1 of the 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 9. 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 9. The measurement unit 8 may use the smallest value A1 of the areas A1 to A7 as the area S1 of the modulation transfer function K1. ＭＩＮ may be used as the area S1 of the modulation transfer function K1. In this case, the level of resolution over the entire aerial image 9 can be evaluated.

[0074] Next, the measurement of the modulation transfer function K2 and the area S2 of the display image D will be described. The modulation transfer function K2 of the display image D can be measured based on image data of a captured image of the display image D (hereinafter also referred to as a second captured image). The second captured image is a captured image obtained by capturing an image of the display surface 4a displaying a display pattern for forming the aerial image 9. The display surface 4a may be captured by an imaging device 7 with an aperture value set to 3 or less. The distance between the imaging device 7 and the display surface 4a may be set to an initial setting distance (i.e., the distance between the imaging device 7 and the aerial image 9). The area S2 can be calculated and measured by integrating the modulation transfer function K2 of the display image D on the spatial frequency axis.

[0075] The measurement unit 8 may calculate the modulation transfer function K2 of the display image D in the same manner as calculating the modulation transfer function K1. In other words, the measurement unit 8 may calculate the at least one modulation transfer function K2 by measuring at least one line spread function based on image data of at least one captured image obtained by capturing at least one imaging region of the display image D and performing a Fourier transform on the at least one line spread function. The measurement unit 8 may measure the area S2 of the modulation transfer function K2 in the same manner as measuring the area S1 of the modulation transfer function K1. In other words, the measurement unit 8 may measure the area of ​​the at least one modulation transfer function K2 by integrating the at least one modulation transfer function K2 on the spatial frequency axis. The measurement unit 8 may determine the area S2 as the average value, weighted average value, or minimum value of the areas of the at least one modulation transfer function K2 in the same manner as measuring the area S1 of the modulation transfer function K1.

[0076] The modulation transfer function K2 of the display image D may be calculated based on image data of a simulated image captured by the imaging device 7, the simulated image simulating the display surface 4a displaying a display pattern for forming the aerial image 9. The simulated image may be disposed within the imaging plane Rp of the aerial image R. The modulation transfer function K2 of the display image D may be calculated by simulation.

[0077] When calculating the modulation transfer function K1 of the aerial image 9, the measurement unit 8 does not need to calculate the modulation transfer functions MTF1 to MTF7 by Fourier transforming each of the line spread functions LSF1 to LSF7. The measurement unit 8 may use the chart method to directly calculate the modulation transfer functions MTF1 to MTF7 from the image data of each of the captured images P1 to P7.

[0078] When calculating the modulation transfer functions MTF1 to MTF7 using the chart method, the measurement 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. 13 as the aerial image R. Note that FIG. 13 illustrates 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. 14. The measurement unit 8 controls the imaging device 7 to capture the aerial image 9', generate captured images P1 to P7 by 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 measurement unit 8 calculates the maximum and minimum luminance values ​​aν and bν of the partial images captured of each square wave chart 9c-9f for each captured image P1-P7, as well as the contrast ratio cν = (aν - bν) / (aν + bν). Furthermore, the measurement 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 measurement unit 8 converts the square wave response function to a sine wave response function and calculates modulation transfer functions MTF1-MTF7. The well-known 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.

[0079] The same applies to the modulation transfer function K2 of the display image D. The measurement unit 8 does not need to calculate the modulation transfer function K2 by performing a Fourier transform on at least one line spread function. The measurement unit 8 may directly calculate the modulation transfer function K2 from image data of an image obtained by capturing an image of the display surface 4a displaying a display pattern for forming the aerial image 9′ using the chart method.

[0080] The comparison unit 15 is configured to acquire the areas S1 and S2 from the measurement unit 8 and compare the areas S1 and S2. The comparison of the areas S1 and S2 may be performed by calculating and measuring the ratio S1 / S2 of the area S1 to the area S2. The comparison unit 15 may be configured to output the result obtained by comparing the areas S1 and S2 (e.g., the ratio S1 / S2) to an external device such as a personal computer.

[0081]

[0082] Next, specific examples of modulation transfer functions K1 and K2 will be described. Table 3 shows the MTF values ​​(hereinafter also referred to as MTF values) of each of the imaging portions F1 to F7 for the aerial image 9 (see FIG. 8) formed by the aerial image display device 2 of FIG. 1, with spatial frequencies ν ranging from 0 to 12 (1 / mm). FIG. 24 is a graph including the MTF values ​​from Table 3. The MTF value of the imaging portion F1 refers to the MTF value calculated based on the image data of the captured image P1 obtained by capturing the imaging portion F1. The same applies to the MTF values ​​of the imaging portions F2 to F7. Table 3 also shows the MTF values ​​calculated based on the image data of the captured image obtained by capturing the display image D. Furthermore, Table 3 shows the MTF area obtained by integrating the MTF of each of the imaging regions F1 to F7 on the spatial frequency axis, the MTF area obtained by integrating the MTF of the displayed image D on the spatial frequency axis, and the ratio (MTF area ratio) S1 / S2 of the MTF area of ​​each of the imaging regions F1 to F7 to the MTF area of ​​the displayed image D. The MTF area ratios S1 / S2 shown in Table 3 are values ​​rounded to two decimal places. Furthermore, Table 3 shows the standard deviation of the MTF values ​​of the imaging regions F1 to F7 when the spatial frequency ν is changed in the range of 0 to 12 (1 / mm).

[0083] 24 , according to the aerial image display device 2, the MTF area ratio S1 / S2 is 0.9 or more at all of the imaging portions F1 to F7, and therefore it is possible to suppress a decrease in the resolution of the aerial image R and to suppress variations in the resolution within the imaging plane Rp of the aerial image R. Therefore, the aerial image display device 2 can suppress a decrease in the display quality of the aerial image R.

[0084] As shown in Table 3, the aerial image display device 2 has a small maximum value (i.e., 0.022666) of the standard deviation of the MTF values ​​of the imaging portions F1 to F7, and therefore can further suppress variations in resolution within the imaging plane Rp of the aerial image R. Therefore, the aerial image display device 2 can further suppress deterioration in the display quality of the aerial image R.

[0085] As shown in Table 3 and Figure 24, at spatial frequencies 0 to 12, which is a practical spatial frequency range, S1 / S2 is 0.9 or higher for all imaging portions F1 to F7, and the degree of degradation of the resolution (MTF) of the aerial image R relative to the resolution (MTF) of the displayed image D is small. This is thought to be due to the fact that no optical elements other than reflecting mirrors are used in the optical system 5, that free-form mirrors such as a free-form concave mirror and a free-form convex mirror are used in the optical system 5, and that the angle of deviation from the reference angle (design tilt angle) of the free-form mirror is small, i.e., the placement error is small.

[0086] Fig. 27 is a graph excerpted from the graph of Fig. 24. Table 4 is a table of MTF numerical data, MTF area, and ratio S1 / S2 of the graph of Fig. 27. As shown in Fig. 27 and Table 4, in the spatial frequency range of 7 to 10, which is a more practical range of spatial frequencies and where there is a large deviation (degree of degradation) from the resolution (MTF) of the displayed image D, the ratio S1 / S2 may be 0.8 or more.

[0087]

[0088]

[0089] Table 5 shows the MTF values ​​of the aerial image 9 formed by the aerial image display device 2 of Figure 2 when the tilt angle Φ of the first concave mirror 5d is changed, with the spatial frequency ν ranging from 0 to 12 (1 / mm) for each tilt angle Φ. Figure 28 is a graph showing the change in the ratio S1 / S2 depending on the angle of deviation from the reference angle (Φd) in Table 5. As shown in Figure 12, the tilt angle Φ is the angle formed by the imaginary plane IP including the display surface 4a and the tangent plane TP of the first concave mirror 5d. The tangent plane TP is the plane that contacts the reflective surface of the first concave mirror 5d at the vertex of the reflective surface of the first concave mirror 5d (i.e., the origin of the free-form surface). Note that Figure 12 does not show the housing 6 and the second rotation device 13. Table 5 and Figure 28 show simulation results for the ratio S1 / S2 when the tilt angle Φ is changed within the range of Φd - 5.5° ≤ Φ ≤ Φd + 1.5°. Φd is the design tilt angle Φ of the first concave mirror 5d and is also referred to as the reference angle (design tilt angle). The MTF values ​​shown in Table 5 are the MTF values ​​of each imaging portion F1 to F7 of the aerial image 9 formed by the aerial image display device 2, but they may also be the average value (average value of multiple measurements) of the MTF values ​​of each imaging portion F1 to F7. Furthermore, Table 5 shows, for each tilt angle Φ, the MTF area obtained by integrating the MTF of the aerial image 9 on the spatial frequency axis, and the ratio (MTF area ratio) S1 / S2 of the MTF area of ​​the aerial image 9 to the MTF area of ​​the display image D. As described above, the MTF area of ​​the display image D is the MTF area measured based on the image data of the captured image of the display image D. The MTF area ratios S1 / S2 shown in Table 5 are values ​​rounded off to two decimal places.

[0090] As shown in Table 5 and FIG. 28 , the aerial image display device 2 maximizes the MTF area ratio S1 / S2 when the tilt angle Φ is the reference angle Φd. As the deviation of the tilt angle Φ from the reference angle Φd increases, the MTF area ratio S1 / S2 decreases. When the tilt angle Φ is Φd-2.5°≦Φ≦Φd+1.5°, the aerial image display device 2 achieves an MTF area ratio S1 / S2 of 0.9 or greater, thereby suppressing degradation of the resolution of the aerial image R. Furthermore, when the deviation angle is greater than approximately -2.5° in absolute value, S1 / S2 rapidly decreases. In other words, when the deviation angle is greater than approximately -2.5° in absolute value, the degradation of resolution rapidly increases. Therefore, the aerial image display device 2 can suppress degradation of the resolution of the aerial image R even when the tilt angle Φ of the first concave mirror 5d deviates from the reference angle Φd, as long as it is within the range of Φd-2.5°≦Φ≦Φd+1.5°.

[0091] In this embodiment, the reference angle Φd may be, for example, 29.64°, 30.41°, 22.79°, or 24.25°, but is not limited to these values.

[0092] Furthermore, when the angle between the virtual imaging plane Rp of the aerial image R and the tangent plane of the second concave mirror 5e is defined as the reference angle Φe, the angle may be, but is not limited to, 37.92°, 46.82°, 37.94°, or 36.67°. The tangent plane of the second concave mirror 5e is a plane that is tangent to the reflecting surface at the vertex of the second concave mirror 5e (also referred to as the origin of the free-form surface). The angle of deviation of the second concave mirror 5e from the reference angle Φe may be approximately -1.0° to +2.0°. In this case, degradation of the resolution of the aerial image R can be suppressed.

[0093] In this embodiment, for example, the following combination values ​​of Φd and Φe can be used, but are not limited to these combination values: Combination value 1: Φd = 29.64°, Φe = 37.92° Combination value 2: Φd = 30.41°, Φe = 46.82° Combination value 3: Φd = 22.79°, Φe = 37.94° Combination value 4: Φd = 24.25°, Φe = 36.67°

[0094] In the above, it was assumed that the optical axis direction Da of the aerial image 9 coincides with the design optical axis direction Dad. However, for example, due to manufacturing tolerances or positioning errors of the reflecting members constituting the optical system 5, a deviation may occur between the optical axis direction Da of the aerial image 9 and the design optical axis direction Dad (hereinafter referred to as optical axis deviation of the aerial image display device 2, or simply as optical axis deviation). When an optical axis deviation occurs, a deviation occurs in the display quality, such as brightness and resolution, within the imaging plane Rp of the aerial image 9, and it may be impossible to accurately calculate the modulation transfer functions MTF1 to MTF7 of the aerial image 9. The resolution measurement device 1 may be configured to measure the optical axis deviation of the aerial image display device 2. The resolution measurement device 1 may also be configured to measure the optical axis deviation of the aerial image display device 2 and calibrate the optical axis deviation.

[0095] The resolution measuring device 1 configured to measure the optical axis deviation of the aerial image display device 2 will be described below.

[0096] As shown in FIGS. 6 and 15 , the resolution measurement device 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 measurement unit 8.

[0097] As shown in FIG. 6 , the resolution measurement device 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 may be controlled by the measurement 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.

[0098] The resolution measurement device 1 may include a second rotation device 13 (see FIGS. 1 and 2 ) that rotates the aerial image display device 2 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 be located within the housing 6 of the aerial image display device 2. The second rotation device 13 may rotate the entire component 2a (the display unit 3 and the optical system 5) within the housing 6 around the second rotation axis RA2. In other words, 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 may be controlled by the measurement unit 8.

[0099] <<Measurement of the Optical Axis Direction of the Aerial Image>> Next, the operation of the resolution measurement device 1 for measuring the actual optical axis direction Da of the aerial image 9 formed by the aerial image display device 2 will be described.

[0100] First, the operation of the resolution measurement device 1 will be described, which measures 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. 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.

[0101] 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.

[0102] 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.

[0103] 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 surface of the image light emitting unit 6 a of the aerial image display device 2 facing the imaging device 7 is perpendicular to the imaging direction 7 d of the imaging device 7. In this case, it is assumed that the imaging direction 7 d is a predetermined imaging direction 7 da (the imaging direction 7 da that coincides with the design optical axis direction Dad). That is, 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 7 da 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 7 da is measured by a method of translating the imaging device 7 back and forth in the depth direction (defocusing method), 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.

[0104] 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.

[0105] Below, as a specific example, we will explain the operation of the resolution measurement device 1, which measures the agreement or disagreement between the actual optical axis direction Da and the design optical axis direction Dad of the aerial image 9 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.

[0106] <Measurement of the optical axis direction based on the characteristic value of the line spread function of the luminance distribution waveform> First, a method for measuring the optical axis direction Da of the aerial image 9 based on the characteristic value of the line spread function of the luminance distribution waveform will be described. The method for measuring the optical axis direction Da based on the characteristic value of the line spread function is also called the LSF method. Below, an operation of the resolution measurement device 1 for determining whether the optical axis direction Da matches the design optical axis direction Dad based on the characteristic value of the line spread function will be described.

[0107] In the LSF method, the measurement unit 8 acquires image data of multiple captured images P3 to P5 from the imaging device 7 and calculates luminance distribution waveforms LSF3 to LSF5 as shown in FIG. 11 based on the image data of the multiple captured images P3 to P5. The measurement 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 W / Q of the half width W to the quarter width Q. 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 can be determined that the distance between the imaging region F4 and the imaging device 7 is to the focal length of the imaging device 7. The same applies to the peak values ​​H of the line spread functions LSF3 and LSF5. 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 pixels. For example, 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 applies to the half-value width W of the line spread functions LSF3 and LSF5. The half-value width Q is the width of a line spread function having a brightness of approximately 25% of the peak value H and is expressed in units of pixels. The half-value width Q is also referred to as the quarter width or quarter width. The characteristic value may be a combined value obtained by combining at least two of the peak value H, the half-value width W, and the half-value width Q. The combined value may be a value obtained by dividing the peak value H by the half-value 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 larger 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. The same applies to the combination values ​​of the line spread functions LSF3 and LSF5.

[0108] The half-width of the line spread function LSF is an index representing the degree of spread of a pulse-like (mountain-shaped) function. The half-width includes the full width at half maximum (FWHM) and the half width at half maximum (HWHM), which is half the full width at half maximum. Generally, when simply referring to the half-width, the half-width refers to the full width at half maximum. In this specification, unless otherwise specified, the half-width refers to the full width at half maximum. In the luminance distribution waveform shown in FIG. 11 , the half-width (full width at half maximum) is a numerical value indicating the spread of the distribution that monotonically decreases around the peak value H, and is the distance between the positions indicated by half the value of the peak value H on both sides of the peak value H.

[0109] The measurement 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 measurement 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.

[0110] For example, when the characteristic values ​​V3 to V5 are the peak value H of the line spread function (a value in the range of 0 to 1.0 as shown in FIG. 11 ), the measurement unit 8 may determine that the optical axis direction Da of the aerial image 9 coincides with the depth direction when all of the absolute values ​​of the differences between the multiple characteristic values ​​V3 to V5 are equal to or less than a threshold value T2 (e.g., 0.2). When the threshold value T2 is 0.2, the threshold value T2 corresponds to 20% of the maximum peak value 1.0. The threshold value T2 may be, but is not limited to, 0.15 (15%), 0.1 (10%), 0.05 (5%), 0.03 (3%), or the like.

[0111] When the characteristic values ​​V3 to V5 are at their peak value H, the measurement unit 8 may determine that the optical axis direction Da of the aerial image 9 coincides with the depth direction when all of the plurality of characteristic values ​​V3 to V5 are equal to or greater than the threshold value T3. When the characteristic values ​​V3 to V5 are at their peak value H, the measurement 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 is less than 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.

[0112] For example, when the characteristic values ​​V3 to V5 are the peak value H of the line spread function (a value in the range of 0 to 1.0 as shown in FIG. 11 ), and all of the characteristic values ​​V3 to V5 are equal to or greater than a threshold value T4 (e.g., 0.7), it may be determined that the optical axis direction Da of the aerial image 9 coincides with the depth direction. When the threshold value T4 is 0.7, this corresponds to 70% of the maximum peak value of 1.0. The threshold value T4 may be 0.8 (80%) or 0.9 (90%), but is not limited to these values.

[0113] When the characteristic values ​​V3 to V5 have a half-width W, the measurement unit 8 may determine that the optical axis direction Da of the aerial image 9 coincides with the depth direction when all of the characteristic values ​​V3 to V5 are equal to or smaller than the threshold value T5. When the characteristic values ​​V3 to V5 have a half-width W, the measurement 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 T5. The threshold value T5 may be set as appropriate based on the required specifications of the aerial image display device 2, etc.

[0114] For example, when the characteristic values ​​V3 to V5 are each a half-width W, and all of the characteristic values ​​V3 to V5 are equal to or less than a threshold value T6 (for example, the number of pixels is 5), it may be determined that the optical axis direction Da of the aerial image 9 coincides with the depth direction. The number of pixels as the threshold value T6 may be, for example, an integer between 1 and 5, but is not limited to these values.

[0115] The resolution measurement device 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 resolution measurement device 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.

[0116] <Measurement of Optical Axis Direction Based on Area of ​​Modulation Transfer Function> Next, a method for measuring the optical axis direction Da of the aerial image 9 based on the area of ​​the modulation transfer function will be described. The method for measuring the optical axis direction Da based on the area of ​​the modulation transfer function is also called the MTF area method. The resolution measurement device 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 areas A3 to A5 of the modulation transfer functions MTF3 to MTF5. Below, the operation of the resolution measurement device 1 for determining whether the optical axis direction Da coincides with the design optical axis direction Dad based on the area of ​​the MTF will be described.

[0117] The measurement 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 by equation (3).

[0118] The modulation transfer functions MTF3 to MTF5 do not have to be calculated by Fourier transforming the line spread functions LSF3 to LSF5, but may be calculated directly from the image data of the captured images P3 to P5 by the chart method.

[0119] The measurement 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 images 9, 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 the threshold value T7. The measurement unit 8 may determine that the optical axis direction of the aerial images 9, 9' does not coincide with the depth direction if at least one of the absolute values ​​of the multiple differences exceeds the threshold value T7. The threshold value T7 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0120] The measurement unit 8 may determine that the actual optical axis direction Da of the aerial images 9, 9' coincides with the depth direction when all of the MTF areas A3 to A5 are equal to or greater than the threshold T8. The measurement unit 8 may determine that the actual optical axis direction Da of the aerial images 9, 9' does not coincide with the depth direction when at least one of the MTF areas A3 to A5 is less than the threshold T8. The threshold T8 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0121] The resolution measurement device 1 can systematically measure whether the actual optical axis direction Da of the aerial images 9, 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 images 9, 9' coincides with the design optical axis direction Dad. Therefore, the resolution measurement device 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.

[0122] <<Measurement and Calibration of Optical Axis Misalignment of Aerial Image Display>> Next, a description will be given of the operation of the resolution measurement device 1 that measures the optical axis misalignment of the aerial image display device 2 (i.e., the misalignment between the optical axis direction Da and the design optical axis direction Dad) and calibrates the optical axis misalignment of the aerial image display device 2. When the measurement 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 measurement unit 8 may measure the optical axis misalignment of the actual optical axis direction Da of the aerial image 9 from the design optical axis direction Dad. The measurement unit 8 may measure the optical axis misalignment 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.

[0123] [Measurement of Optical Axis Shift Due to Defocus Operation] First, the operation of the resolution measurement device 1, which measures optical axis shift by moving the imaging device 7 along the imaging direction 7d, will be described. The measurement 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. 15, 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.

[0124] The measurement 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. 16 shows an example of an aerial image 9 captured by the imaging device 7 located at a position with a Z coordinate Z0. FIG. 17 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. 18 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 measurement unit 8. The measurement 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 measurement unit 8 may acquire the image data from the imaging device 7 via the acquisition unit 14.

[0125] <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 display device 2 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 measurement 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 measurement unit 8 calculates the maximum value V ＭＡＸ The characteristic values ​​V3 to V5 are measured and the maximum value V ＭＡＸ The Z coordinate (hereinafter also referred to as the in-focus position) of the imaging device 7 when

[0126] 19 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 focal length FP1 is equal to or less than the focal length FP2. FIG. 19 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 manner as the in-focus positions FP3 to FP5. In FIG. 19, 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. 19 shows the in-focus positions FP3 to FP5 of the imaging portions F3 to F5 when optical axis misalignment occurs.

[0127] In Figure 19, the sign of the focal position FP3 (+1.0 mm) of the imaging portion F3 is different from the sign of the focal position FP5 (-0.8 mm) of the imaging portion F5. This means that an optical axis misalignment has occurred, as shown in Figure 20. That is, the focal 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 focal 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 focal positions FP3 and FP5 have opposite signs, the measurement 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. 19), and L is the designed length of the aerial image 9 in the width direction (Y-axis direction).

[0128] If the measurement unit 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 measurement unit 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 about the second rotation axis RA2. This allows the optical axis deviation of the aerial image display device 2 to be calibrated, thereby enabling the user to view a high-quality aerial image R with reduced optical axis deviation. The measurement unit 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. Based on the signs of the focus positions FP3 and FP5, the measurement unit 8 may determine the direction in which to rotate the aerial image display device 2 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.

[0129] FIG. 21 shows the focus positions FP3 to FP5 of the imaging portions F3 to F5 when no optical axis misalignment occurs. FIG. 21 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. 21, 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 measurement 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.

[0130] The above operation of the resolution measurement device 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 measurement unit 8 determines the minimum value V among the (m1+m2+1) characteristic values ​​V3 to V5 for each of the imaging portions 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.

[0131] The resolution measurement device 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 resolution measurement device 1 makes it possible to calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0132] <Measurement of Optical Axis Shift Based on Area of ​​Modulation Transfer Function MTF> Next, a case will be described where the optical axis shift (i.e., the shift between the optical axis direction Da and the design optical axis direction Dad) of the aerial image 9 (or aerial image 9') is measured based on the area of ​​the modulation transfer function MTF. The measurement 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 S3 to S5. The measurement unit 8 calculates the maximum value S of the (m1+m2+1) MTF areas S3 to S5 for each of the imaging portions F3 to F5. ＭＡＸ and the MTF areas S3 to S5 are the maximum value S ＭＡＸ The Z coordinates (focus positions FP3 to FP5) of the imaging device 7 are measured.

[0133] The measurement unit 8 measures the MTF areas A3 to A5 to determine the maximum value S 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 resolution measurement device 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 9 is similar to the operation of the resolution measurement device 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 9, and therefore a detailed description thereof will be omitted.

[0134] The measurement 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 measurement 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.

[0135] By performing a defocusing operation on the imaging device 7, the resolution measurement device 1 can systematically measure the optical axis misalignment between the optical axis direction Da of the aerial images 9, 9' and the design optical axis direction Dad based on changes in the MTF areas A3 to A5 associated with the movement of the imaging device 7. As shown in FIG. 15 , the defocusing operation involves moving the imaging device 7 back and forth in the imaging direction 7d to change the degree of focus (degree of in-focusness, degree of blurring of the captured image) of each imaging portion of the aerial images 9, 9'. Because the area of ​​the modulation transfer function MTF is not easily affected by external light, etc., the MTF areas S3 to S5 can be used to accurately measure whether the actual optical axis direction Da of the aerial images 9, 9' coincides with the design optical axis direction Dad. Therefore, the resolution measurement device 1 enables accurate calibration of the actual optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0136] [Measurement of Optical Axis Misalignment by Rotation Operation] Next, the operation of the resolution measurement device 1, which measures optical axis misalignment (the deviation 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 measurement unit 8 controls the first rotation device 12 to rotate the imaging device 7 around the first rotation axis RA1, as shown in FIG. 23 , to capture the aerial image 9 in multiple imaging directions 7d, each of which has 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. 23 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).

[0137] The measurement 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 measurement unit 8. The measurement 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 measurement unit 8 may acquire the image data from the imaging device 7 via the acquisition unit 14.

[0138] <Measurement of Optical Axis Shift Based on Characteristic Values ​​of Line Spread Functions> First, a case will be described in which the optical axis shift of the aerial image 9 (i.e., the shift between the optical axis direction Da and the design optical axis direction Dad) is measured based on the characteristic values ​​of the line spread functions. The measurement unit 8 calculates (n1+n2+1) line spread functions LSF3 to LSF5 for each of the imaging portions F3 to F5 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 values ​​H or the half-widths 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.

[0139] The measurement 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 if the absolute values ​​of the multiple differences at a certain imaging angle Θ1 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 at the angle Θ1 with respect to the depth direction (i.e., the designed 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.

[0140] When the characteristic values ​​V3 to V5 are at peak value H, and all of the characteristic values ​​V3 to V5 are equal to or greater than threshold value T10 at a certain imaging angle Θ2, the measurement unit 8 may determine that the actual optical axis direction Da of the aerial image is tilted at angle Θ2 with respect to the depth direction. The threshold value T10 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0141] 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 T11 at a certain imaging angle Θ3, the measurement unit 8 may determine that the actual optical axis direction Da of the aerial image 9 is tilted at an angle Θ3 with respect to the depth direction. The threshold value T11 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0142] When the measurement unit 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 angles Θ1, Θ2, and Θ3, the measurement unit 8 controls the second rotation device 13 to rotate the aerial image display device 2 around the second rotation axis RA2 by rotation angles equal to the 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, it becomes possible for the user to view an aerial image R with reduced optical axis deviation and high display quality. The measurement unit 8 controls the second rotation device 13 to rotate the aerial image display device 2 clockwise or counterclockwise by rotation angles equal to the angles Θ1, Θ2, and Θ3 when viewed from above the device stand 10. The measurement unit 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.

[0143] By rotating the imaging device 7, the resolution measurement device 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 changes in the characteristic values ​​V3 to V5 that accompany the rotation of the imaging device 7. Therefore, the resolution measurement device 1 makes it possible to calibrate the optical axis direction Da of the aerial image R formed by the aerial image display device 2.

[0144] <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 measurement 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 S3 to S5.

[0145] The measurement unit 8 calculates 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 T12, it may determine that the actual optical axis direction Da of the aerial image 9 is inclined at the angle Θ4 with respect to the depth direction (i.e., the design optical axis direction Dad). The threshold value T12 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0146] When all of the MTF areas A3 to A5 are equal to or greater than the threshold value T13 at a certain imaging angle Θ5, the measurement unit 8 may determine that the actual optical axis direction Da of the aerial image 9 is tilted at the angle Θ5 with respect to the design optical axis direction Dad. The threshold value T13 may be set as appropriate based on the required specifications of the aerial image display device 2.

[0147] The measurement 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 measurement 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.

[0148] By rotating the imaging device 7, the resolution measurement device 1 can systematically measure the optical axis misalignment between the actual optical axis direction Da of the aerial images 9, 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., using the MTF areas A3 to A5 makes it possible to accurately measure whether the actual optical axis direction Da of the aerial images 9, 9' coincides with the design optical axis direction Dad. Therefore, the resolution measurement device 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.

[0149] The above describes the operation of the resolution measurement device 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-P5 captured of multiple imaging sites F3-F5 aligned in the width direction (Y-axis direction) within the imaging plane Rp of the aerial images 9 and 9′, and calibrates the optical axis shift. However, the operation is not limited to this. The resolution measurement device 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) captured of 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 images 9 and 9′, and calibrate the optical axis shift. Alternatively, the resolution measurement device 1 can measure the optical axis misalignment around 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 images 9 and 9', and calibrate these optical axis misalignments. 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.

[0150] The optical axis misalignment is measured using the resolution measurement device 1, and if an optical axis misalignment exists, the optical axis misalignment is calibrated, thereby enabling accurate measurement of the area S1 obtained by integrating the modulation transfer function K1 of the aerial images 9, 9' on the spatial frequency axis. As a result, degradation of the resolution of the aerial image R formed by the aerial image display device 2 can be suppressed.

[0151] According to the present disclosure, it is possible to provide a resolution measuring device that can measure the resolution of an aerial image with high accuracy and can measure the optical axis direction of the aerial image.

[0152] The present disclosure can be implemented in the following configurations (1) to (16).

[0153] (1) A resolution measuring device for measuring the resolution of an aerial image in an aerial image display device that includes a display unit and forms the image light of a display image emitted from the display unit as a real aerial image, the resolution measuring device comprising a comparison unit, wherein the comparison unit is configured to compare an area S1 obtained by integrating a first modulation transfer function of a first captured image that captures the aerial image on a spatial frequency axis with an area S2 obtained by integrating a second modulation transfer function of a second captured image that captures the display image on the spatial frequency axis.

[0154] (2) The resolution measuring device according to the above configuration (1), wherein the first modulation transfer function is obtained by Fourier transforming a first luminance distribution waveform of the first captured image, and the second modulation transfer function is obtained by Fourier transforming a second luminance distribution waveform of the second captured image.

[0155] (3) The resolution measuring device described in the above configuration (2), wherein the first luminance distribution waveform and the second luminance distribution waveform are respectively acquired based on the first captured image and the second captured image when a predetermined display pattern is displayed on the display unit, the display pattern being a repeating pattern of a first band-shaped image and a second band-shaped image, and the first band-shaped image and the second band-shaped image differ in at least one of luminance and color.

[0156] (4) A resolution measurement device according to any one of the above configurations (1) to (3), wherein the first captured image and the second captured image are images captured by an imaging device with an aperture value set to 3 or less.

[0157] (5) The resolution measuring device according to any one of the above configurations (1) to (4), further comprising a determining unit that determines the ratio S1 / S2 of the area S1 to the area S2.

[0158] (6) The resolution measuring device according to the above configuration (5), wherein the determining unit determines that the resolution of the aerial image is high when the ratio S1 / S2 is 0.4 or more.

[0159] (7) The resolution measurement device according to any one of the above configurations (1) to (6), wherein the aerial image includes text information.

[0160] (8) The aerial image display device is provided with an optical system that forms the image light of the display image emitted from the display unit into a real aerial image, and the optical system includes a free-form reflecting mirror, a resolution measuring device described in any of the above configurations (1) to (7).

[0161] (9) A resolution measuring device as described in the above configuration (8), wherein the free-form reflecting mirror includes a first free-form concave mirror that faces the display unit at an incline, and a second free-form concave mirror that faces the first free-form concave mirror at an incline and forms the aerial image.

[0162] (10) A resolution measuring device as described in the above configuration (9), wherein the maximum diameter of the reflecting surface of the second free-form concave mirror is longer than the maximum diameter of the reflecting surface of the first free-form concave mirror, and the degree of curvature of the first free-form concave mirror is greater than the degree of curvature of the second free-form concave mirror.

[0163] (11) A resolution measurement device according to the above configuration (9) or (10), in which no other optical elements are included in the optical path from the display unit to the second free-form concave mirror via the first free-form concave mirror.

[0164] (12) The resolution measuring device according to the above configuration (9), wherein a free-form convex mirror is present in the optical path between the first free-form concave mirror and the second free-form concave mirror.

[0165] (13) A resolution measuring device according to the above configuration (12), wherein, when the maximum diameter of the reflecting surface of the first free-form concave mirror is Ra, the maximum diameter of the reflecting surface of the free-form convex mirror is Rb, and the maximum diameter of the reflecting surface of the second free-form concave mirror is Rc, Rc>Ra>Rb holds; and when the curvature of the first free-form concave mirror is Sa, the curvature of the free-form convex mirror is Sb, and the curvature of the second free-form concave mirror is Sc, Sa>Sc>Sb holds.

[0166] (14) A resolution measurement device according to the above configuration (12) or (13), which does not include any other optical elements in the optical path from the display unit to the second free-form concave mirror via the first free-form concave mirror and the free-form convex mirror.

[0167] (15) The luminance of the aerial image is 800 cd / m ２The resolution measuring device according to any one of claims 1 to 14, wherein the resolution is equal to or greater than 10 ...

[0168] (16) The luminance of the display image is 1000 cd / m ２ (cd: candela) or less.

[0169] 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 present disclosure. Furthermore, the present disclosure also includes configurations that combine two or more of the above-described various embodiments.

[0170] DESCRIPTION OF SYMBOLS 1 Resolution measurement device 2 Aerial image display device 2a Constituent member 3 Display unit 4 Display panel 4a Display surface 5 Optical system 5a First concave mirror 5aa Reflecting surface 5b Convex mirror 5c Second concave mirror 5d First concave mirror 5e Second concave mirror 6 Housing 6a Image light emitting unit 7 Imaging device 7d, 7da Imaging direction 8 Measurement unit 9, 9' Test pattern (aerial image) 9a First strip-shaped image 9b Second strip-shaped image 9c Rectangular wave chart 9g 80% area 10 Device stand 10a Top surface 11 Moving device 11h Holding member 11r Rail 11t Moving table 12 First rotating device 13 Second rotating device 14 Acquisition unit 15 Comparison unit 20 User 20e Eye D Display image Da Optical axis direction Dad Optical axis direction (design optical axis direction) K1 Modulation transfer function (first modulation transfer function) K2 Modulation transfer function (second modulation transfer function) Lp Image light R Aerial image Rp Image plane

Claims

1. A resolution measuring device for measuring the resolution of an aerial image in an aerial image display device which includes a display unit and forms a real aerial image using the image light of a display image emitted from the display unit, the resolution measuring device comprising a comparison unit configured to compare an area S1 obtained by integrating a first modulation transfer function of a first captured image which captures the aerial image on a spatial frequency axis with an area S2 obtained by integrating a second modulation transfer function of a second captured image which captures the display image on a spatial frequency axis.

2. The resolution measuring device of claim 1, wherein the first modulation transfer function is obtained by Fourier transforming a first luminance distribution waveform of the first captured image, and the second modulation transfer function is obtained by Fourier transforming a second luminance distribution waveform of the second captured image.

3. The resolution measuring device of claim 2, wherein the first luminance distribution waveform and the second luminance distribution waveform are respectively acquired based on the first captured image and the second captured image when a predetermined display pattern is displayed on the display unit, the display pattern being a repeating pattern of a first band-shaped image and a second band-shaped image, and the first band-shaped image and the second band-shaped image differ in at least one of luminance and color.

4. A resolution measuring device according to any one of claims 1 to 3, wherein the first captured image and the second captured image are images captured by an imaging device with an aperture value set to 3 or less.

5. A resolution measuring device according to any one of claims 1 to 4, further comprising a determination unit for determining a ratio S1 / S2 of the area S1 to the area S2.

6. The resolution measuring device according to claim 5, wherein the determining unit determines that the resolution of the aerial image is high when the ratio S1 / S2 is 0.4 or greater.

7. A resolution measuring device according to any one of claims 1 to 6, wherein the aerial image includes character information.

8. The resolution measuring device according to any one of claims 1 to 7, wherein the aerial image display device is provided with an optical system that forms an aerial image of a real image from the image light of the display image emitted from the display unit, and the optical system includes a free-form reflecting mirror.

9. A resolution measuring device as described in claim 8, wherein the free-form curved reflecting mirror includes a first free-form curved concave mirror that faces the display unit at an incline, and a second free-form curved concave mirror that faces the first free-form curved concave mirror at an incline and forms the aerial image.

10. A resolution measuring device as described in claim 9, wherein the maximum diameter of the reflecting surface of the second free-form concave mirror is longer than the maximum diameter of the reflecting surface of the first free-form concave mirror, and the degree of curvature of the first free-form concave mirror is greater than the degree of curvature of the second free-form concave mirror.

11. A resolution measuring device according to claim 9 or 10, which does not include any other optical element in the optical path from said display unit through said first free-form concave mirror to said second free-form concave mirror.

12. The resolution measuring device according to claim 9, wherein a free-form convex mirror is provided in the optical path between said first free-form concave mirror and said second free-form concave mirror.

13. The resolution measuring device of claim 12, wherein, when the maximum diameter of the reflective surface of the first free-form concave mirror is Ra, the maximum diameter of the reflective surface of the free-form convex mirror is Rb, and the maximum diameter of the reflective surface of the second free-form concave mirror is Rc, Rc>Ra>Rb holds; and, when the degree of curvature of the first free-form concave mirror is Sa, the degree of curvature of the free-form convex mirror is Sb, and the degree of curvature of the second free-form concave mirror is Sc, Sa>Sc>Sb holds.

14. A resolution measuring device as described in claim 12 or 13, which does not include any other optical elements in the optical path from the display unit through the first free-form concave mirror and the free-form convex mirror to the second free-form concave mirror.

15. The brightness of the aerial image is 800 cd / m ２ The resolution measuring device according to any one of claims 1 to 14, wherein the resolution measuring device is 100% or more (cd: candela).

16. The luminance of the displayed image is 1000 cd / m ２ 16. The resolution measuring device according to claim 15, wherein the resolution is equal to or less than 1000 cd (candela).

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