JP6791330B2 - Lens array and head-up display - Google Patents

Description

The present invention relates to improving visibility in a display system using a lens array.

Conventionally, a technique for applying a transmissive screen using a microlens array to a head-up display, a laser projector, or the like has been proposed. When such a transmissive screen is used, there is an advantage that the influence of speckle noise can be suppressed as compared with the case where a diffuser plate is used. For example, Patent Document 1 discloses an image forming apparatus including a laser projector and a microlens array in which a plurality of microlenses are arranged. Further, in Patent Document 2, the pitch of each microlens is set so that the diffraction width of the light beam diffused by each microlens of the microlens array is equal to or less than the pupil diameter of the viewer, so that the light is diffused by the microlens. It is disclosed that the brightness unevenness caused by the peak of the diffracted light entering or not entering the pupil of the viewer is prevented.

JP-A-2010-145745 Japanese Unexamined Patent Publication No. 2013-06495

When a lens array is used as an intermediate image generating element in a head-up display or the like, there is a problem that brightness unevenness occurs when the pitch of the lens array is reduced, and resolution is lowered when the pitch is increased. Further, Patent Document 1 does not disclose any method for suppressing luminance unevenness. Further, in Patent Document 2, since the pitch of the lens array is widened, there is a problem that the resolution of the intermediate image generated by the lens array is lowered.

Examples of the problems to be solved by the present invention are as described above. A main object of the present invention is to provide a lens array and an image projection device capable of suitably suppressing luminance unevenness without lowering the resolution.

The invention according to claim is a lens array irradiated with laser light.
With a plurality of lenses arranged to form a first period structure,
Each of the plurality of lenses constitutes a plurality of basic blocks having a structure in which an optical path length difference is caused in the laser beam by combining a part of the plurality of lenses.
The optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array and the total or individual diffraction efficiency of the 1st-order diffracted light are substantially the same.

The invention according to claim is a lens array irradiated with laser light.
With a plurality of lenses arranged to form a first period structure,
Each of the plurality of lenses constitutes a plurality of basic blocks having a structure in which an optical path length difference is caused in the laser beam by combining a part of the plurality of lenses.
The optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array is substantially 0.

The schematic configuration of the head-up display is shown. The side view of the screen in the YZ plane is shown. The structure of the microlens array is shown. The diffracted light of the screen in the YZ plane is shown. The light intensity distribution of the diffracted light is shown. The relationship between the diffraction efficiency and the optical path length difference is shown. The light intensity distribution of the diffracted light when an optical path difference is provided in the diffracted light is shown. The intensity distribution of diffracted light at each wavelength of blue, green, and red is shown. The structure of the screen according to the first modification is shown. The relationship between the structure of the screen in the YZ plane and the diffracted light according to the first modification is shown. The light intensity distribution of the diffracted light according to the first modification is shown. The light intensity distribution of the diffracted light according to the first modification is shown. The light intensity distribution of the diffracted light according to the first modification is shown. The light intensity distribution of the diffracted light according to the first modification is shown. The structure of the screen according to the second modification is shown. The structure of the screen according to the modification 3 is shown. The structure of the screen according to the modification 4 is shown. The structure of the screen according to the modification 5 is shown. The structure of the screen according to the modified examples 7, 8 and 9 is shown.

In one preferred embodiment of the present invention, the lens array comprises a plurality of lenses having the same effective diameter and having a structure that causes a difference in optical path length with respect to transmitted light, and each of the plurality of lenses. Are arranged at intervals based on the effective diameter to form a two-dimensional basic periodic structure, and some of the plurality of lenses have a structure that causes a difference in optical path length. A basic block is formed by a combination, and the basic blocks are repeatedly arranged to form a two-dimensional second periodic structure having a longer period than the basic periodic structure, and the period indicated by the second periodic structure is , It is an integral multiple of the period indicated by the basic period structure.

The lens array has a plurality of lenses having the same effective diameter and having a structure that causes an optical path length difference with respect to transmitted light. Here, each of the plurality of lenses is arranged at intervals based on the effective diameter to form a two-dimensional basic periodic structure. Further, some of the plurality of lenses form a basic block by combining lenses having a structure that causes an optical path length difference. The basic block constitutes a two-dimensional second periodic structure having a longer period than the basic periodic structure. The period indicated by the second periodic structure is an integral multiple of the period indicated by the basic periodic structure.

Since the lens array has a second periodic structure having a period that is an integral multiple of the basic periodic structure based on the lens arrangement, diffracted light is preferably used so as to eliminate a gap in the light intensity distribution of the diffracted light at the viewpoint position. Spread to. Therefore, in this aspect, the lens array can suitably suppress the luminance unevenness while preventing the resolution deterioration due to changing the effective diameter of each lens.

In one aspect of the lens array, in the basic block, some of the lenses are combined in a grid pattern, and the lenses are staggered in different structures. According to this aspect, the lens array can generate the first-order diffracted light in the oblique direction of the 0th-order diffracted light, effectively fill the gap of the light intensity distribution of the diffracted light, and preferably suppress the luminance unevenness. it can.

In another aspect of the lens array, the period indicated by the second periodic structure is configured to be four times the period indicated by the basic periodic structure. According to this aspect, it is possible to prevent the primary diffracted light generated by the second periodic structure from overlapping at the same position, and it is possible to preferably suppress the luminance unevenness.

In another aspect of the lens array, the basic block is composed of at least three types of lenses in which some of the lenses are combined in a grid pattern and the optical path length difference is generated. Also in this aspect, it is possible to preferably form a second periodic structure having a period that is an integral multiple of the basic periodic structure based on the lens arrangement.

In another aspect of the lens array, the plurality of lenses have the same curvature among the plurality of lenses, and are arranged with a step to cause the difference in optical path length. According to this aspect, the lens of the lens array can preferably generate an optical path length difference of transmitted light.

In another aspect of the lens array, the optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array and the 1st-order diffracted light of the lens array are substantially the same. .. According to this aspect, the lens array can generate 0th-order and ± 1st-order diffracted light of the same intensity, and can suitably fill the gap of the light intensity distribution at the viewpoint position.

In another aspect of the lens array, the optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array is substantially 0. According to this aspect, the lens array can uniformly fill the light intensity distribution at the viewpoint position by the ± 1st order diffracted light.

In another aspect of the lens array, the optical path length difference is set to the shortest length or the second shortest length among the lengths satisfying the conditions for diffraction efficiency. The longer the optical path length difference, the greater the change in diffraction efficiency due to wavelength fluctuations. Therefore, according to this aspect, the lens array can preferably suppress that the ratio of the diffraction efficiency of the diffracted light of each order is significantly different for each wavelength even when the combined light of a plurality of wavelengths is incident. ..

In a preferred example of the lens array, it is preferable that the laser light source of the image projection device having at least one or more laser light sources irradiates the laser light source.

In another aspect of the lens array, the optical path length difference is set based on the longest wavelength of the laser light emitted by the laser light source. In general, the longer the wavelength, the wider the interval between diffracted lights. Therefore, according to this aspect, the lens array can suitably eliminate the gap of the light intensity distribution at the viewpoint position of the diffracted light for the light of all wavelengths.

In another aspect of the lens array, the optical path length difference is set based on the wavelength of the laser light emitted by the laser light source, which has the highest luminosity factor. Also in this aspect, the lens array can suitably suppress the luminance unevenness.

In another aspect of the lens array, the optical path length difference is set based on the wavelength between the longest wavelength and the most visible wavelength of the laser light emitted by the laser light source. Also in this aspect, the lens array can suitably suppress the luminance unevenness.

In a preferred example of the lens array, the plurality of lenses may all have substantially the same numerical aperture.

In another aspect of the lens array, the plurality of lenses cause the optical path length difference based on the difference in curvature. Also in this aspect, the lens array can preferably generate an optical path length difference with respect to the transmitted light.

In another aspect of the lens array, the plurality of lenses cause the optical path length difference based on the difference in the sign of curvature. Also in this aspect, the lens array can preferably generate an optical path length difference with respect to the transmitted light. Preferably, the lens array is mounted on a video projection device.

In another aspect of the lens array, the lens array is a reflective lens array having a reflective film on the lens array surface. Also in this aspect, the lens array can suitably suppress the luminance unevenness while preventing the resolution deterioration due to changing the effective diameter of each lens.

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

[Head-up display configuration]
FIG. 1A is a schematic configuration diagram of a head-up display which is one aspect of the “image projection device” in the present invention. The head-up display is a system for allowing a passenger of a vehicle equipped with a windshield 25 and a dashboard 29 to visually recognize a virtual image, and mainly includes a light source unit 1, a screen 2, and a concave mirror 3.

The light source unit 1 has laser elements of each color of red (R), green (G), and blue (B), and scans the combined light of the laser modulated based on the image signal on the screen 2 with a MEMS mirror. To do.

The screen 2 enlarges the exit pupil by widening the divergence angle of the light emitted from the light source unit 1. The screen 2 is a microlens array in which a plurality of microlenses are arranged. The light emitted from the screen 2 is incident on the concave mirror 3. As will be described later, the screen 2 is superposed with a phase structure having a period larger than the period of the microlens array, whereby diffracted light having a diffraction angle smaller than that generated by the microlens array is simultaneously generated. .. The screen 2 is an example of the "transparent substrate" in the present invention. Hereinafter, the horizontal direction of the intermediate image generated by the screen 2 is defined as the X-axis, the vertical direction is defined as the Y-axis, and the direction perpendicular to the incident surface of the screen 2 is defined as the Z-axis, and each positive direction is defined as shown in the figure.

The concave mirror 3 reflects the laser beam emitted from the screen 2 and causes it to reach the windshield 25. In this case, the concave mirror 3 reflects the laser beam to magnify the image indicated by the light. The laser beam reflected by the concave mirror 3 is further reflected by the windshield 25 and reaches the observer's eyes. As a result, the observer visually recognizes the virtual image.

The configuration of the head-up display shown in FIG. 1A is an example, and the configuration to which the present invention can be applied is not limited to this. For example, in the head-up display shown in FIG. 1B, the screen 2 is a reflective microlens array, and the reflective microlens array widens the diffusion angle of the light emitted from the light source unit 1. It may be configured to enlarge the ejection pupil with. In another example, in the head-up display, a combiner is provided between the windshield 25 and the eye point Pe, and the laser light reflected by the concave mirror 3 is reflected by the combiner to make the laser light of the light source unit 1 an eye point. The virtual image may be visually recognized by the driver by reaching Pe.

[screen]
(1) Schematic configuration of the screen FIG. 2 shows a side view of the screen 2 in the YZ plane. As shown in FIG. 2, the microlens array 20 in which microlenses 21 (21H, 21L) having different heights in the Z-axis direction are alternately arranged on the incident surface of the screen 2 on which the light from the light source 1 is incident. Is formed. Here, the high-stage microlens 21H has a higher apex position on the Z axis than the low-stage microlens 21L, and a step is formed between the high-stage microlens 21H and the low-stage microlens 21L. The effective diameter and numerical aperture of the microlens 21 are all the same regardless of whether the high-stage microlens 21H or the low-stage microlens 21L. Here, as shown in FIG. 2, the period of unevenness formed by the high-stage microlens 21H and the low-stage microlens 21L (also referred to as “unevenness period PC”) is the period of the microlens 21 (“lens period PL”). It is also called.), Which is an integral multiple of.

FIG. 3A is a diagram showing the height of the screen 2 on the incident surface. In FIG. 3, the rectangular region described as “high” corresponds to the high-stage microlens 21H, and the rectangular region described as “low” corresponds to the low-stage microlens 21L.

As shown in FIG. 3A, the high-stage microlens 21H and the low-stage microlens 21L are alternately arranged one by one in both the X-axis direction and the Y-axis direction, and are arranged on the X-axis and the Y-axis. On the other hand, it is asymmetric. The rectangular region (for example, the region in the frame 70) formed by the two staggered low-stage microlenses 21L and the two high-stage microlenses 21H is a unit structure having a periodic phase structure of the microlens array 20. (Also called a "basic block"). Each microlens 21 constitutes the "basic periodic structure" in the present invention, and the basic block constitutes the "second periodic structure" in the present invention.

FIG. 3B is an enlarged view of the basic block of the microlens array 20, and FIG. 3C is a diagram showing a step in the Z-axis direction between the low-stage microlens 21L and the high-stage microlens 21H. Is. As shown in FIG. 3B, the basic block has a structure divided into four in a rice field shape, and the diagonal regions have the same structure and the adjacent regions have different structures. In other words, the basic block is point-symmetrical with respect to the center position, and lenses having the same structure are staggered. Hereinafter, the width of the basic block in the X-axis direction is referred to as “Px”, and the width in the Y-axis direction is referred to as “Py”. In this case, assuming that "m" is the order in the X-axis direction and "n" is the order in the Y-axis direction, the diffraction angle "θx" in the X-axis direction of the light of the wavelength "λ" incident on the basic block is generally By optical calculation

と表され、基本ブロックに入射する光のＹ軸方向における回折角「θｙ」は、

The diffraction angle "θy" of the light incident on the basic block in the Y-axis direction is

と表される。また、図３（Ｂ）に示すように、低段マイクロレンズ２１Ｌと高段マイクロレンズ２１ＨとのＺ軸方向の段差を「Δ」とした場合、当該段差により生じる高段マイクロレンズ２１Ｈの透過光と低段マイクロレンズ２１Ｌの透過光との光路長差は、当該段差と同一距離の「Δ」となる。以後では、「Δ」を「段差Δ」又は「光路長差Δ」とも表記する。

It is expressed as. Further, as shown in FIG. 3B, when the step in the Z-axis direction between the low-stage microlens 21L and the high-stage microlens 21H is set to “Δ”, the transmitted light of the high-stage microlens 21H generated by the step is “Δ”. The difference in optical path length between the low-stage microlens 21L and the transmitted light of the low-stage microlens 21L is “Δ”, which is the same distance as the step. Hereinafter, “Δ” is also referred to as “step Δ” or “optical path length difference Δ”.

(2) Example of Light Intensity Distribution Next, an example of the light intensity distribution of the diffracted light of each microlens 21 of the screen 2 will be described with reference to FIGS. 4 and 5.

FIG. 4A shows diffracted light in the YZ plane when it is assumed that the microlens array 20 is not provided with a step Δ (that is, when only the lens array component is considered). Further, FIG. 5A shows the diffracted light in the virtual XY plane (also referred to as “reference plane Ptag”) separated from the screen 2 by the same distance as the eye point Pe in the case of FIG. 4A. Shows the light intensity distribution.

In this case, as shown in FIG. 5A, the major axis of each diffracted light on the reference surface Ptag (also referred to as “diffracted light size”) is the interval of each diffracted light on the reference surface Ptag (“diffracted light interval”). It is shorter than that, and there is a gap between each diffracted light. This gap causes uneven brightness. As shown in FIG. 5A, the diffracted light interval in the oblique direction is wider than the diffracted light interval in the X-axis direction and the Y-axis direction.

FIG. 4D shows diffracted light in the XZ plane on the assumption that the microlens array 20 is not provided with the step Δ. The relationship between the pitch PLx in the X direction of the microlens 21 and the diffraction angle θx of the primary diffracted light in the X direction of the beam is

と表される。
図４（Ｅ）は、マイクロレンズアレイ２０に段差Δが設けられていないと仮定した場合のＹＺ平面での回折光を示す。 マイクロレンズ２１のＹ方向のピッチＰＬｙとビームのＹ方向における1次回折光の回折角度θｙとの関係は、

It is expressed as.
FIG. 4E shows diffracted light in the YZ plane assuming that the microlens array 20 is not provided with a step Δ. The relationship between the pitch PLy of the microlens 21 in the Y direction and the diffraction angle θy of the first-order diffracted light in the Y direction of the beam is

と表される。
したがって、マイクロレンズから−Ｚ方向に距離「ｄ」だけ離れた仮想的なＸＹ平面での回折光のＸ方向における間隔「ｘ」は、

It is expressed as.
Therefore, the distance "x" in the X direction of the diffracted light in the virtual XY plane separated by the distance "d" in the −Z direction from the microlens is

と表され、同様に、マイクロレンズから−Ｚ方向に距離「ｄ」だけ離れた仮想的なＸＹ平面での回折光のＹ方向における間隔「ｙ」は、

Similarly, the distance "y" in the Y direction of the diffracted light in the virtual XY plane separated by the distance "d" in the −Z direction from the microlens is

と表される。

It is expressed as.

Further, when the full angle of the focusing angle of the light projected from the light source unit 1 and focused on the microlens array 20 is "2α", the beam size "w" at the viewpoint position is

と表される。
なお、前記集光角度の全角「２α」および視点位置でのビームサイズ「ｗ」は、幾何光学的に計算されるビームの輪郭から算出してもよいが、レーザビームの強度分布がガウシアン分布をしており、視点位置における光強度分布の半値全幅が幾何光学的に計算されるビームの輪郭より小さい場合、前記集光角度の全角「２α」はレーザビーム強度分布の半値全幅における集光角度の全角、ビームサイズ「ｗ」は視点位置におけるビーム強度分布の半値全幅として考えても良い。

It is expressed as.
The full width "2α" of the focusing angle and the beam size "w" at the viewpoint position may be calculated from the contour of the beam calculated geometrically and optically, but the intensity distribution of the laser beam has a Gaussian distribution. When the full width at half maximum of the light intensity distribution at the viewpoint position is smaller than the contour of the beam calculated geometrically and optically, the full width "2α" of the focusing angle is the focusing angle at the half width of the laser beam intensity distribution. The full width and beam size "w" may be considered as the full width at half maximum of the beam intensity distribution at the viewpoint position.

5 (D) shows the light intensity distribution of the diffracted light in the virtual XY plane at a position d away from the screen 2 in the cases of FIGS. 4 (D) and 4 (E). From FIG. 5D, it is the diffracted light that faces in the oblique direction that maximizes the interval of the diffracted light in the virtual XY plane, and the interval “u” of the diffracted light is

と表される。
このとき、前記斜め方向に相対する回折光の隙間「ｓ」は、斜め方向のビームサイズを「ｗ」としたときに、

It is expressed as.
At this time, the gap "s" of the diffracted light facing the diagonal direction is defined as "w" when the beam size in the diagonal direction is "w".

と表される。また、斜め方向におけるレーザビーム集光角度の全角を「２α」とし、式（９）に式（３）、式（４）、式（５）、式（６）、式（７）を代入すると、回折光の最大隙間ｓは

It is expressed as. Further, assuming that the total angle of the laser beam focusing angle in the oblique direction is "2α", the equations (3), (4), (5), (6), and (7) are substituted into the equation (9). , The maximum gap s of diffracted light is

と表される。この値が

It is expressed as. This value is

となる場合、すなわち

That is,

を満たすときに、仮想的なＸＹ平面において回折光の間に光が存在しない領域が存在し、輝度ムラが顕著となる。このように、マイクロレンズアレイ２０に段差Δが設けられていないと仮定した場合は、光源部１から投影される光の集光角αが小さい場合、または、マイクロレンズ２１のピッチが小さい場合の輝度ムラが顕著な状態になることがわかる。

When the condition is satisfied, there is a region where no light exists between the diffracted lights in the virtual XY plane, and the luminance unevenness becomes remarkable. As described above, when it is assumed that the microlens array 20 is not provided with the step Δ, the light focusing angle α projected from the light source unit 1 is small, or the pitch of the microlens 21 is small. It can be seen that the brightness unevenness becomes remarkable.

FIG. 4B shows the diffracted light in the YZ plane when only the step component of the microlens array 20 is considered. FIG. 5 (B) shows the light intensity distribution of the diffracted light on the reference plane Ptag in the case of FIG. 4 (B). In the examples of FIGS. 4 (B) and 5 (B), the step (that is, the optical path difference) Δ is set to “(N ± 0.283) λ” (“N” is an integer of 0 or more). There is.

In this case, as shown in FIG. 5B, the diffracted light having the order m and n of "0" (also referred to as "0th order diffracted light") and the diffracted light having the order m and n of "± 1" (also referred to as "0th order diffracted light"). (Also referred to as “first-order diffracted light”) is generated with the same intensity, and diffracted light in which at least one of the order m or n is an even number other than “0” (also referred to as “even-order diffracted light”) is not generated. Further, the higher the order, the lower the intensity of the diffracted light. These theoretical grounds will be described in detail in the section "(3) Analysis of Diffraction Efficiency". Further, as will be described later, the distribution of the diffraction efficiency of the 0th-order light and the 1st-order light can be adjusted by the optical path length difference Δ.

FIG. 4C shows diffracted light in the YZ plane of the microlens array 20 when the components of FIGS. 4A and 4B are combined. Further, FIG. 5 (C) shows the light intensity distribution of the diffracted light on the reference plane Ptag in the case of FIG. 4 (C). In FIG. 5C, the color of the 0th-order refracted light is drawn darker than that of the 1st-order diffracted light for easy identification.

As shown in FIG. 5 (C), in this case, the 0th-order diffracted light corresponding to the distribution of the diffracted light shown in FIG. 5 (A) is distributed on the reference plane Ptag, and the 0th-order diffracted light is distributed in four diagonal directions. The first-order diffracted light is arranged in each of the above. That is, in this case, the primary diffracted light is inserted into each of the diagonal gaps where the diffracted light interval is widest as compared with the examples of FIGS. 4 (A) and 5 (A) in which no step is provided. Therefore, in this example, the diffracted light interval can be efficiently filled with a small amount of diffracted light.

Further, since the uneven period PC is set to an integral multiple (here, 2 times) of the lens period PL, the diffracted light is regularly arranged on the reference plane Ptag, and the light intensity distribution at the viewpoint position is uniformly approached. Can be done. Further, in general, when a plurality of periodic structures are combined, if the repeating periods of the periodic structures are different, moire fringes occur due to the difference in the periods. Further, even when the same period or the period of a constant multiple is combined, moire fringes occur when the positional relationship is deviated. On the other hand, in the present embodiment, by imparting a concavo-convex period PC having a period of a constant multiple of the lens period PL, an inconsistency occurs between the individual period of the microlens 21 and the applied period of the constant multiple. do not do. Therefore, in this embodiment, moire fringes can be suitably suppressed.

(3) Analysis of Diffraction Efficiency Next, the diffraction efficiency of the diffracted light of the screen 2 will be described. The diffraction efficiency “I (m, n)” of the transmitted light having the wavelength λ passing through the phase structure having the basic block shown in FIG. 3 (B) is determined by using Px, Py, and Δ shown in FIG. It is represented by the formula (13).

ここで、「Ａ（ｘ、ｙ）」は強度分布、「φ（ｘ、ｙ）」は１周期分の位相分布（即ち光路長差分布）をそれぞれ示し、これらは以下の式（１４）、（１５）により表される。

Here, "A (x, y)" indicates the intensity distribution, and "φ (x, y)" indicates the phase distribution for one cycle (that is, the optical path length difference distribution), which are expressed in the following equations (14). It is represented by (15).

そして、式（１３）の回折効率Ｉ（ｍ、ｎ）に対し、式（１４）のＡ（ｘ、ｙ）及び式（１５）のφ（ｘ、ｙ）を代入すると、以下の式（１６）が得られる。

Then, when A (x, y) of the formula (14) and φ (x, y) of the formula (15) are substituted for the diffraction efficiency I (m, n) of the formula (13), the following formula (16) is substituted. ) Is obtained.

ここで、式（１６）において、破線の下線が引かれた項の値は、「ｍ＝０」かつ「ｎ＝０」のときのみ「１」となり、それ以外では「０」となる。また、一点鎖線の下線が引かれた項の値は、光路差Δに対してλの周期で値が０〜１の間で変動する。また、二点鎖線の下線が引かれた項の値は、「ｍ」、「ｎ」のいずれかが偶数の場合に「０」となり、「ｍ」、「ｎ」の絶対値が大きくなるほど絶対値が小さくなる。

Here, in the equation (16), the value of the item underlined by the broken line is "1" only when "m = 0" and "n = 0", and is "0" in other cases. Further, the value of the underlined term of the alternate long and short dash line fluctuates between 0 and 1 in the period of λ with respect to the optical path difference Δ. The value of the underlined term of the alternate long and short dash line is "0" when either "m" or "n" is an even number, and the larger the absolute value of "m" or "n", the more absolute it is. The value becomes smaller.

The diffraction efficiency of the 0th-order diffracted light is obtained by substituting "m = 0" and "n = 0" into the equation (16), and is expressed by the following equation (17).

同様に、１次回折光の回折効率は、式（１６）に「ｍ、ｎ＝±１」を代入することで得られ、いずれも以下の式（１８）により表される。

Similarly, the diffraction efficiency of the primary diffracted light is obtained by substituting "m, n = ± 1" into the equation (16), both of which are expressed by the following equation (18).

そして、式（１６）によれば、偶数次回折光の回折効率は「０」となり、回折光の次数が高くなるほど、回折光の回折効率が小さくなることが把握される。

Then, according to the equation (16), the diffraction efficiency of the even-order diffracted light becomes "0", and it is understood that the higher the order of the diffracted light, the lower the diffraction efficiency of the diffracted light.

FIG. 6 shows the relationship between the diffraction efficiency calculated based on the equation (16) and the normalized optical path length difference normalized by dividing the optical path length difference Δ by λ. Here, the graph "G0" shows the diffraction efficiency of the 0th-order diffracted light, the graph "G1" shows the individual diffraction efficiency of the 1st-order diffracted light, and the graph "G1A" shows the diffraction efficiency of the four first-order diffracted lights. The efficiency is shown, and the graph "G01A" shows the diffraction efficiency which is the sum of the diffraction efficiency of the 0th-order diffracted light and the diffraction efficiency of the four first-order diffracted light. As shown in FIG. 6, when the optical path length difference Δ is “(N ± 0.283) λ” (see condition [1]), the diffraction efficiency is the sum of the diffraction efficiencies of the 0th-order diffracted light and the 4th-order diffracted light. Are equal at "0.3965", the total diffraction efficiency of these is "0.793", and the remaining minute diffraction efficiency is distributed to higher-order diffracted light of odd-order and third-order or higher. In this case, as described with reference to FIGS. 4 (C) and 5 (C), the primary diffracted light is irradiated in each of the four diagonal directions of the 0th-order diffracted light, so that the gap between the diffracted lights is preferably filled. be able to.

When the optical path length difference Δ is “(N ± 0.377λ) (see condition [2]), the diffraction efficiency of the 0th-order diffracted light and the individual diffraction efficiency of the 1st-order diffracted light are“ 0.141 ”, respectively. The total diffraction efficiency of these is "0.705", and the remaining minute diffraction efficiency is distributed to higher-order diffracted light of odd-order and third-order or higher.

When the optical path length difference Δ is “(N ± 0.5) λ” (see condition [3]), the diffraction efficiency of the 0th-order diffracted light is “0”, and the diffraction of the four first-order diffracted light is diffracted. The efficiencies are "0.164", which is a total of "0.657", and the remaining minute diffraction efficiencies are distributed to higher-order diffraction light of odd-order and third-order or higher.

FIG. 7 shows the intensity distribution of the diffracted light on the reference plane Ptag when the optical path length difference Δ is “(N ± 0.5) λ”.

When the optical path length difference Δ is “(N ± 0.5) λ”, the intensity of the 0th-order diffracted light is “0”. Then, in the example of FIG. 7, the reference surface Ptag is filled with the primary diffracted light substantially evenly and without gaps, but when the unevenness cycle PC is set to twice the lens cycle PL, the unevenness cycle PC is used. Since the diffracted light interval is half of the diffracted light interval due to the lens period PL, the primary diffracted light generated by the uneven period PC for each of the diffracted light due to the lens period PL overlaps at the same position. As a result, the apparent number of diffracted lights is the same as when there is no step, and the diffracted light interval is also the same as when there is no step. Therefore, in this example, it is not possible to suppress the uneven brightness caused by the gap between the diffracted lights, which is not preferable. Therefore, when the concave-convex period PC is doubled with respect to the lens period PL as in this embodiment, the optical path length difference Δ is set to “N ± 0.283λ”, and the 0th-order light generated in the uneven period PC It is preferable to make the diffraction efficiency equal to the total diffraction efficiency of the four overlapping primary diffracted lights.

(4) Relationship between wavelength and periodic structure Since the light source unit 1 emits light having different wavelengths of R, G, and B, the low-stage microlens 21L and the high-stage microlens 21H are based on any of the RGB wavelengths. The problem is whether to design the step Δ with. This will be described.

In general, the diffraction angle of the diffracted light generated by the microlens array 20 becomes larger as the wavelength is longer, so that the diffracted light interval (see FIG. 5A) becomes wider as the wavelength is longer. The diffracted light size is determined by the numerical aperture of the light source unit 1 and does not depend on the wavelength. From the above, the longer the wavelength of light, the wider the diffracted light interval.

FIG. 8 (A) shows the intensity distribution of the diffracted light on the reference surface Ptag in the case of blue light (wavelength 435.8 nm), and FIG. 8 (B) shows the intensity distribution of the diffracted light in the case of green light (wavelength 438.1 nm). 8 (C) shows the intensity distribution on the reference plane Ptag in the case of red light (700 nm). As shown in FIGS. 8A to 8C, the diffracted light interval is the shortest in the case of blue light having the shortest wavelength, and the diffracted light interval is the longest in the case of red light having the longest wavelength.

In consideration of the above, in the first preferred example, the step Δ is set according to the wavelength at which the diffracted light interval is the longest (that is, the wavelength of red light). As a result, it is possible to prevent gaps in the intensity distribution of the diffracted light in any of the R, G, and B laser beams, and to suitably suppress the uneven brightness.

On the other hand, when the diffracted light interval does not differ greatly for each wavelength, as a second preferred example, it is preferable to set the step Δ according to the wavelength having the highest visual sensitivity (that is, the wavelength of green light). Further, as a third preferred example, the step Δ may be set according to the wavelength between the longest wavelength and the wavelength having the highest luminosity factor in consideration of both the diffracted light interval and the luminosity factor.

Here, a method of setting an integer N that defines a step (optical path length difference) Δ will be described. The step Δ becomes larger as the integer N is larger. Further, referring to the definition of the diffraction efficiency in the equation (16), it can be seen that the larger the step Δ, the larger the diffraction efficiency ratio between the 0th-order diffracted light and the 1st-order diffracted light for each RGB. That is, the larger the step Δ, the larger the change in diffraction efficiency due to wavelength fluctuation. In consideration of the above, it is preferable to set the integer N to "0" or "1" and make the step Δ as short as possible.

As described above, the microlens array 20 of the screen 2 according to the present embodiment has a structure formed on the incident surface of the screen 2 having the same effective diameter and causing an optical path length difference Δ with respect to transmitted light. It has a high-stage microlens 21H and a low-stage microlens 21L. Here, the high-stage microlens 21H and the low-stage microlens 21L are arranged at intervals based on the effective diameter to form a basic periodic structure of the lens period PL. Further, the high-stage microlens 21H and the low-stage microlens 21L form a basic block by combining lenses having a structure that causes an optical path length difference. The uneven period PC based on the basic block is an integral multiple of the lens period PL. With this configuration, the microlens array 20 can suitably suppress luminance unevenness while preventing a decrease in resolution due to changing the effective diameter of each lens.

[Modification example]
Next, a modification suitable for the above-described embodiment will be described. The modifications shown below may be applied in combination to the above-described examples.

(Modification example 1)
In the front view of the screen 2 shown in FIG. 3, the low-stage microlens 21L and the high-stage microlens 21H were alternately arranged one by one. Instead of this, a predetermined number of low-stage microlenses 21L and high-stage microlenses 21H may be alternately arranged.

FIG. 9A shows a side view of the screen 2A according to the modified example in the XY plane. Further, FIG. 9B shows a front view of the screen 2A in which the high-stage microlens 21H is represented as “high” and the low-stage microlens 21L is represented as “low”. Further, FIG. 9C shows a basic block of the microlens array 20 in the case of FIGS. 9A and 9B.

In the example of FIG. 9, the high-stage microlens 21H and the low-stage microlens 21L are alternately arranged in two vertical rows and two horizontal rows, respectively, and each of the clusters is staggered. .. The basic block shown in FIG. 9C is asymmetric with respect to the X-axis and the Y-axis and point-symmetric with respect to the center, as in the embodiment. Then, as shown in FIG. 9A, the unevenness period PC in this case is 4 times, which is an integral multiple of the lens period PL. Therefore, like the screen 2, the screen 2A can preferably generate diffracted light having a diffraction angle smaller than that of the diffracted light generated by the microlens array 20.

Next, the reason why the modified example 1 is more suitable will be described with reference to FIGS. 10 and 11.

FIG. 10A shows a configuration corresponding to the first embodiment, in which the diffracted light in the YZ plane is provided in the microlens array 20 with a step on the concave-convex period PC having a period twice that of the lens period PL. 11 (A) shows the light intensity distribution of the diffracted light on the reference plane Ptag. In this case, the primary diffracted light generated by the concave-convex period PC is generated just in the middle of the diffracted light generated by the lens period PL to fill the gap between the beams, thereby reducing the luminance unevenness. However, in this case, as shown in FIG. 11B, the primary diffracted light generated by the uneven period PC is overlapped at the same position with respect to the diffracted light generated by the lens period PL and adjacent to each other. For each of the diffracted light generated by the lens period PL, the concavo-convex period PC, for example, as the first diffracted light, (+1, + 1st order light), (-1, + 1st order light), (-1, -1st order) While a total of four diffracted lights such as light) and (-1, +1 order light) are generated, the apparent number of diffracted lights seems to be small, and more diffracted lights are spread over the reference. The effect of making the light intensity distribution of the surface Ptag uniform has been halved. In order to prevent the primary diffracted light generated by the uneven period PC from overlapping, the uneven period PC is set to 3 times or more the lens period PL, and the diffraction angle of the primary diffracted light is set with respect to the angular interval of the diffracted light generated by the lens period PL. It is preferably 1/3 or less.
In consideration of such a problem, in the first modification, a step is provided by a concave-convex cycle PC having a cycle of 4 times the lens cycle PL, and more diffracted light is spread on the reference plane Ptag.
FIG. 10B shows the diffracted light on the YZ plane when the microlens array 20 is provided with a step on the concave-convex cycle PC having a period four times the lens period PL, and FIG. 12A shows. The light intensity distribution of the diffracted light on the reference plane Ptag at that time is shown. In this case, as shown in FIG. 12B, the position of the primary diffracted light generated by the uneven period PC can be shifted with respect to the diffracted light generated by the lens period PL and adjacent to each other. That is, it is preferable because more diffracted light can be spread on the reference plane Ptag.
Here, the reason why it is preferable to provide the concave-convex cycle PC having a 4 times cycle with respect to the lens cycle PL will be described. In order to reduce the luminance unevenness, it is desirable that the diffracted light intensity of the primary diffracted light generated by the uneven period PC is the same, but for that purpose, it is preferable that the areas of the low-stage portion and the high-stage portion are the same. Further, if the concave-convex cycle PC is designed as an odd multiple of the lens cycle PL, the step is designed to be within the lens surface as shown in FIG. 10 (C). A lens containing a step is not preferable because the characteristics of the lens portion having no step are different from those of the lens portion having no step due to sagging of the step, manufacturing error, and the like, which causes uneven brightness. That is, the concave-convex period PC of the first modification needs to be an even multiple of the lens period PL, and also needs to be 3 times or more as described above. Therefore, it is 4 times in consideration of both conditions. By doing so, it is possible to prevent the step from entering the lens surface and to prevent the primary diffracted light generated by the uneven period PC from overlapping at the same position. Further, the same effect can be obtained by setting the unevenness period PC to 6 times or 8 times, but in that case, as shown in FIG. 13, the primary diffracted light generated by the uneven period PC is generated by the lens period PL. Since it is generated in the vicinity of the diffracted light, the diffracted interval becomes non-uniform when viewed as a whole diffracted light. That is, the period of the uneven period PC is preferably about 4 times the lens period PL.
Further, it is desirable to properly use the design conditions for the optical path length difference Δ generated at the step according to the lens period PL and the magnitude of the focusing angle α of the light projected from the light source unit 1.
When it is necessary to make the lens period PL finer or when it is necessary to make the focusing angle α of the light projected from the light source unit 1 relatively small, the optical path length difference Δ generated at the step is set to “N”. It is preferably ± 0.377λ ”(see FIG. 6, condition [2]). In this case, since the diffraction efficiency of the 0th-order diffracted light generated by the step period PC and the individual diffraction efficiency of the 1st-order diffracted light are equal at "0.141", the 0th-order diffracted light and the four 1st-order diffracted lights are used. It is preferable in that more diffracted light of uniform intensity can be spread.
Further, there are suitable examples when the lens period PL can be made relatively coarse and when the focusing angle α of the light projected from the light source unit 1 can be made relatively large. For the sake of explanation, when the intersection of the X-axis and the Y-axis is the origin O and the center of the 0th-order diffracted light generated by the concave-convex period PC is used as a reference, the (+1, +1) order light and the (-1, -1) order The direction in which light is generated is set as the R axis, and the direction in which (+1, +1) next light is generated is positive. Similarly, the direction in which the (-1, + 1) primary light and the (+1, -1) primary light are generated is set as the S axis, and the direction in which the (-1, + 1) primary light is generated is positive. FIG. 10 (D) shows the diffracted light on the RZ plane when the focusing angle α of the light source unit 1 is set relatively large so that the maximum gap of the diffracted light becomes zero, and FIG. 14 (A) shows. Shows the light intensity distribution at the viewpoint position Ptag at that time.
FIG. 14B shows four primary diffracted lights generated by the uneven period PC for one of the diffracted lights due to the lens period PL. In FIG. 14B, the focusing angle of the projector is determined so that the primary diffracted lights facing the R-axis and S-axis directions are in contact with each other so that no gap is generated between the four primary diffracted lights. By performing such a design, it is possible to eliminate a region where light does not exist at the viewpoint position Ptag.
Here, in FIG. 14B, the width of the beam group formed by the four primary diffracted lights in the R-axis and S-axis directions is exactly twice the size of the diffracted light generated by the lens period PL. Because it is

を満たす関係にあることがわかる。この際にはさらに、段差で発生する光路長差Δを「Ｎ±０．５λ」とし（図６、条件［３］参照）、図１４（Ａ）、図１４（Ｂ）で示すように、凹凸周期ＰＣによる０次回折光の回折効率をゼロとして０次回折光を消し去ることにより、１次回折光を均等間隔で、かつ光が存在しない領域が存在しないように整列させることができるので、より好適である。
以上の内容は、段差以外の手段で周期構造を適用した場合でも同様である。

（変形例２）
マイクロレンズ２１は、２段階にＺ軸方向の高さが設定されていた。これに代えて、マイクロレンズ２１は、３段階以上にＺ軸方向の高さが設定されていてもよい。

It can be seen that there is a relationship that satisfies. At this time, the optical path length difference Δ generated at the step is set to “N ± 0.5λ” (see FIG. 6, condition [3]), and as shown in FIGS. 14 (A) and 14 (B), By eliminating the 0th-order diffracted light by setting the diffraction efficiency of the 0th-order diffracted light by the concave-convex period PC to zero, the first-order diffracted light can be aligned at equal intervals and so that there is no region where no light exists, which is more preferable. Is.
The above contents are the same even when the periodic structure is applied by means other than the step.

(Modification 2)
The height of the microlens 21 in the Z-axis direction was set in two steps. Instead of this, the height of the microlens 21 in the Z-axis direction may be set in three or more steps.

FIG. 15A is an example of a basic block when the height of the microlens 21 in the Z-axis direction is set in three steps. In FIG. 15A, the “high” region indicates the microlens 21 having the highest height in the Z-axis direction, and the “low” region indicates the microlens 21 having the lowest height in the Z-axis direction. The "middle" region shows the microlens 21 whose height in the Z-axis direction is set to be the second highest (lowest). In the case of this basic block, the concavo-convex period PC is three times an integral multiple of the lens period PL. Therefore, even when the screen 2 has the basic block shown in FIG. 15A, it is possible to preferably generate diffracted light having a diffracted angle smaller than that generated by the microlens array 20.

FIG. 15B is an example of a basic block when the height of the microlens 21 in the Z-axis direction is set in five steps. In FIG. 15B, the height of each microlens 21 in the Z-axis direction is indicated by “1” to “5”. In the case of this basic block, the concave-convex period PC is 5 times, which is an integral multiple of the lens period PL. Therefore, even when the screen 2 has the basic block shown in FIG. 15B, it can preferably generate diffracted light having a diffraction angle smaller than that generated by the microlens array 20.

(Modification 3)
Instead of providing an uneven period PC having an integral multiple of the lens period PL due to a step of the microlens 21, an uneven period PC having an integral multiple of the lens period PL may be provided by making the radius of curvature of the microlens 21 different.

FIG. 16A shows a side view of the screen 2B according to the third modification in the XY plane. As shown in FIG. 16A, in this example, the microlens 21Ba having a large radius of curvature and the microlens 21Bb having the same effective diameter as the microlens 21Ba and having a small radius of curvature are alternately arranged. The array 20B is formed on the incident surface of the screen 2B. The microlens 21Bb has a higher apex position than the microlens 21Ba. In this case, the concave-convex period PC based on the microlens 21Bb and the microlens 21Ba is twice the lens period PL.

FIG. 16B is a front view of the screen 2B when the microlens 21Ba is represented as “large” and the microlens 21Bb is represented as “small”. Further, FIG. 16C shows a basic block of the microlens array 20B. As shown in FIGS. 16B and 16C, in this case, the microlens 21Ba and the microlens 21Bb are arranged asymmetrically with respect to each of the XY axes. Further, the basic block is divided into four in a rice field shape as in the embodiment, the diagonal regions of the basic block have the same structure, and the adjacent regions have different structures.

In this way, by using the microlenses 21Ba and 21Bb having different radii of curvature to form the concave-convex period PC having an integral multiple of the lens period PL, the diffraction angle is smaller than the diffraction light generated by the microlens array 20. Light can be suitably generated. Further, in the example of FIG. 16, since the microlens array 20B is not provided with a step, it is possible to suitably suppress the loss of light amount and the decrease in contrast due to the scattering of light at the step.

(Modification example 4)
Instead of providing a step on the microlens array 20, concave lenses and convex lenses having different curvature codes may be arranged side by side as the microlens 21.

FIG. 17A shows a side view of the screen 2C according to the third modification in the XY plane. As shown in FIG. 17A, in this example, the microlens array 20C in which the convex lens 21Ca and the concave lens 21Cb having the same effective diameter as the convex lens 21Ca are alternately arranged is formed on the incident surface of the screen 2C. There is. The apex position of the microlens 21Cb is lower than that of the microlens 21Ca in the Z-axis direction. In this case, the uneven period PC based on the microlens 21Cb and the microlens 21Ca is twice the lens period PL.

FIG. 17B is a front view of the screen 2C when the microlens 21Ca is described as “convex” and the microlens 21Bb is described as “concave”. Further, FIG. 17C shows a basic block of the microlens array 20C. As shown in FIGS. 17B and 17C, in this case, the microlens 21Ca and the microlens 21Cb are staggered, respectively. Further, the basic block is divided into four in a rice field shape as in the embodiment, the diagonal regions of the basic block have the same structure, and the adjacent regions have different structures.

In the example of FIG. 17, by arranging the convex lens 21Ca and the concave lens 21Cb in a staggered manner, an uneven period PC having an integral multiple of the lens period PL is formed. This also makes it possible to preferably generate diffracted light having a diffraction angle smaller than that of the diffracted light generated by the microlens array 20. Further, in the example of FIG. 17, since the microlens array 20C is not provided with a step, the light amount loss at the step can be suitably suppressed.

(Modification 5)
A plurality of different periodic structures may be added to the microlens array 20 so as to be an integral multiple of the lens period PL.

FIG. 18A shows a front view of the microlens array 20D to which a double periodic structure based on a step is added, and FIG. 18B shows a basic block of the microlens array 20D. As shown in FIG. 18, in the basic block of the microlens array 20D, a rectangular region (also referred to as an "intermediate block") composed of four microlenses 21 arranged in two vertical rows and two horizontal rows is further vertical and horizontal. It has a periodic structure composed of two rows. Here, each intermediate block is divided into two types based on the average height of each microlens 21 in the intermediate block. In FIG. 18, the center of the intermediate block having the higher average height is ". It is written as "high" and "low" in the center of the other intermediate block. The height of the four microlenses 21 in the intermediate block is divided into two stages in the Z-axis direction, and "high" is written in the center of the higher microlens 21 in the intermediate block to which the intermediate block belongs. In the center of the microlens 21 of the above, "low" is written. Then, the intermediate block has a structure divided into four in a paddy shape like the basic block of the embodiment, the diagonal regions have the same structure, and the adjacent regions have different structures. Similarly, when the basic block is regarded as a basic block consisting of four intermediate blocks, it has a structure divided into four in the shape of a paddy field, the diagonal areas have the same structure, and the adjacent areas have the same structure. It has a different structure.

In such a configuration, the incident light on the microlens array 20D is divided into 0th-order diffracted light and 1st-order diffracted light by the phase structure of the intermediate block, and each of these diffracted lights is further divided into 0th-order diffracted light and 1st-order diffracted light by the phase structure of the basic block. Divided into light. Therefore, in this case, even if the diffracted light interval is large when the intermediate block and the basic block are not added, the diffracted light is generated based on the intermediate block and the basic block, and the gap of the diffracted light intensity distribution on the reference plane Ptag is formed. It can be suitably filled.

The intermediate block and the basic block as described above may be formed only based on the stepped structure of the microlens 21, or may be formed based on the difference in radius of curvature or the like based on the modified example 3 or the modified example 4. Good.

(Modification 6)
The microlens array 20 may be formed on the surface opposite to the incident surface of the screen 2 instead of being formed on the incident surface of the screen 2, or may be formed on both surfaces of the screen 2.

(Modification 7)
The microlens array 20 may be a reflective lens array in which a reflective film is provided on the surface opposite to the lens array surface as shown in FIG. 19 (A).

(Modification 8)
In the configuration of the modified example 7, the light passes through the lens surface twice. In the case of a reflective lens array, light may be incident on the lens at an oblique angle, and the position of the lens surface through which light passes the first time and the position of the lens surface through which light passes after reflection may deviate. There is. In this case, moire fringes are generated as in the case of passing through two microlens arrays with misalignment, which is not preferable. Therefore, in the modified example 8, as shown in FIG. 19B, the microlens array 20 has a configuration in which a reflective film is provided on the lens array surface and an antireflection film is provided on the opposite surface. It has become. In this case, since the light is reflected by the lens surface itself, it undergoes periodic phase modulation by the lens array only once, as in the case of the transmissive lens array. This is preferable because it is possible to prevent the occurrence of moire fringes, which is a problem in the modified example 7. Further, it is difficult to remove the adhering dirt on the uneven lens surface, but in the configuration of the modified example 8, even if the dirt or the like adheres to the exposed lens surface, it affects the light. There is no. That is, it is preferable because it is possible to prevent deterioration of image quality due to dirt on the lens array surface.

(Modification 9)
In the modified example 9, as shown in FIG. 19C, the microlens array 20 is provided with a reflective film on the lens surface, and the lens surface is arranged on the light side. In this case, since the light does not pass through the inside of the lens surface, it is possible to prevent the loss of the amount of light due to the absorption of the material and the deterioration of the image quality due to the birefringence of the material and uneven transmittance, which is a suitable configuration. .. Further, since it is not necessary to apply an antireflection film to the opposite surface, the cost of parts can be reduced, which is preferable. Further, since the surface on the opposite side does not affect the performance of the lens array, the high surface accuracy required for the optical component is not required, and the difficulty of manufacturing the component can be alleviated, which is preferable. Further, since there is a degree of freedom in shape, it is possible to design according to the shape of surrounding parts, and the degree of freedom in designing the shape of parts is increased, which is preferable.

The microlens arrays 20 of the modifications 6 to 9 can be used as, for example, the screen 2 of the head-up display shown in FIG. 1 (B).

1 Light source 2 Screen 3 Concave mirror 20, 20A to 20D Microlens array 21 Microlens

Claims (11)

A lens array that is irradiated with laser light
With a plurality of lenses arranged to form a first period structure,
Each of the plurality of lenses constitutes a plurality of basic blocks having a structure in which an optical path length difference is caused in the laser beam by combining a part of the plurality of lenses.
The optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array and the total or individual diffraction efficiency of the 1st-order diffracted light are substantially the same. .. A lens array that is irradiated with laser light
With a plurality of lenses arranged to form a first period structure,
Each of the plurality of lenses constitutes a plurality of basic blocks having a structure in which an optical path length difference is caused in the laser beam by combining a part of the plurality of lenses.
The lens array is characterized in that the optical path length difference is set so that the diffraction efficiency of the 0th-order diffracted light of the lens array is set to be substantially 0. The optical path length difference is obtained when the wavelength of the laser beam is λ and an integer of 0 or more is N.
N ± 0.283λ or N ± 0.377λ
The lens array according to claim 1, wherein the lens array satisfies the above. The optical path length difference is obtained when the wavelength of the laser beam is λ and an integer of 0 or more is N.
N ± 0.5λ
The lens array according to claim 2, wherein the lens array satisfies the above. The lens array according to claim 3 or 4, wherein the integer N is 0 or 1. Any one of claims 1 to 5, wherein the plurality of lenses have the same curvature among the plurality of lenses, and the optical path length difference is caused by arranging the plurality of lenses with a step. The lens array described in the section. The lens array according to claim 6, wherein the effective diameter and the numerical aperture of each lens of the lens array are all equal. The lens according to any one of claims 1 to 7, wherein each of the plurality of basic blocks is arranged so as to form a second periodic structure that is four times the first periodic structure. array. In the lens array, a reflective film is formed on one surface, and an antireflection film is formed on the other surface.
The lens array according to claim 1 or 2, wherein the laser beam incident from the other surface is reflected by the reflective film formed on the one surface. The lens array according to any one of claims 1 to 9 is mounted on the lens array.
A light source unit that emits synthetic light obtained by modulating the laser light based on an image signal so as to scan the lens array.
A head-up display that allows an observer to visually recognize a virtual image of an intermediate image generated by the lens array. The light source unit has a plurality of laser light sources that emit laser light having different wavelengths.
The optical path length difference is the longest first wavelength of the laser light emitted by the laser light source, the second wavelength having the highest visual sensitivity among the laser light emitted by the laser light source, and the first wavelength and the second wavelength. The head-up display according to claim 10, wherein the head-up display is set based on any one of the third wavelengths, which is an intermediate wavelength of the above.

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