FLAT MICROLENS ARRAY AND PRODUCTION METHOD THEREOF

Abstract: A method of producing a microlens array by a diffusion method, which provides a microlens array having high convergence efficiency irrespective of a lens arrangement and a lens packaging ratio. A two-dimensional regular arrangement of a large number of distributed refractive index type microlenses is formed by diffusing materials which contribute to the increase of a refractive index of the substrate. The microlenses are densely arranged on the substrate surface, and diffusion fronts of individual microlenses are fused into those of the adjacent microlenses. The length of the area of fusion between two adjacent microlenses in the direction of the straight line connecting the centers of these two microlenses is not greater than 20 % of the pitch of the microlenses in said direction.

Description: Technical Field The present invention relates generally to a method of making a planar microlens array, and more particularly to a method of making a planar microlens array that is useful as a ) converging lens to converge light for illuminating a transmissive image display panel, such as a liquid crystal display panel having a plurality of pixels, onto pixel apertures to make the liquid crystal display panel brighter. Background Art This type of planar microlens array was disclosed by Hamanaka, et al. in Japanese Patent Publication No. 3-136004 or EP425251A (Refer to Fig. 1). The planar microlens array disclosed in the Publication is manufactured using the ion diffusion process. In the ion diffusion process, a glass substrate is used as a transparent substrate 1 on the surface of which a diffusion-inhibiting mask film comprising Ti, Al, Ni or Cr, etc. is formed using the sputtering and other thin-film forming processes, and then a desired array of circular mask apertures is formed on the diffusion-inhibiting mask film. After that, the transparent substrate is immersed for a predetermined period of time in a molten-salt bath containing ions contributing to increasing the refractive index of the substrate. As ions in the molten-salt bath are diffused through the mask apertures in the transparent substrate, a planar microlens array 82 having a plurality of microlenses of a refractive-index distribution type with decreasing refractive index from the vicinity of the center of each mask aperture toward the circumference thereof is formed. In a liquid crystal display panel having a delta (six-lobe) pixel array, this planar microlens array has microlenses of a hexagonal circumferential shape that are arranged two-dimensionally, regularly and densely on the surface of the transparent substrate, as shown in Fig. 1. In this case, the lens array is a six-lobe array. The circumferential shape of each microlens can be made into a desired hexagonal shape by providing a region 6 where the diffusion fronts 5 that are leading edges of the microlens ion diffused areas of the adjoining microlenses 4 are fused together, as shown in Fig. 2. In this case, lens filling rate, the ratio of the area occupied by microlenses to the total area of the transparent substrate on which lenses are formed, is almost 100%. Oikawa et al., on the other hand, disclosed a planar microlens array for use in liquid crystal display panels in Japanese Patent Publication No. 5-45642 or EP517500A (Refer to Fig. 3). A planar microlens array 82 is formed with the ion diffusion process using a diffusion-inhibiting mask film having formed oblong mask apertures. This planar microlens array 82 has microlenses 4 of an oblong circumferential shape, as shown in Fig. 4, by terminating ion diffusion in the state where diffusion fronts of the adjoining microlenses come in contact with each other. With this, the lens filling rate is short of 100% because of the existence of a lens unformed region where no lenses are formed, but a planar microlens array 82 having a relatively high lens filling rate is formed since the lens array is of a six-lobe type. These planar microlens arrays are suitable for condenser lenses to illuminate display images by converging light to illuminate a transmissive display panel, such as a liquid crystal display panel having a plurality of pixels, onto pixel apertures. A typical projection-type image display device having such a planar microlens array is shown in Fig. 5. In Fig. 5, the light emitted by a light source 86 is converged by a reflecting mirror 87 and a condenser lens 85 so as to direct toward a projection lens 89. The light flux passing through the condenser lens 85 is converged by a planar microlens array 82 onto a pixel aperture area (pixel aperture) 81b of a liquid crystal element formed between two substrates 81a of a liquid crystal panel 81, and projected onto a screen 88 by the projection lens 89. By using a planar microlens array as described above, the light flux that would otherwise been shielded by the pixel shielding area 81c of the liquid crystal display panel 81 can be converged onto the pixel aperture area 81b. As a result, the light flux reaching the screen 88 increases 2 to 2.5 times as much as that without the planar microlens array 82. The technologies disclosed in Japanese Patent Publication No.3-136004 and Japanese Patent Publication No.5-45642 are intended to improve overall converging efficiency in converging light onto the pixel apertures of the liquid crystal element. To further improve converging efficiency, it is generally necessary to further increase the lens filling rate of the planar microlens array. With the six-lobe lens array as disclosed in Japanese Patent Publication No.3-136004, the lens filling rate is almost 100%, with virtually no room left for further improvement. In terms of the improvement of overall converging efficiency, however, there still remains a problem. That is, regions where the diffusion fronts of the adjoining lenses are fused together contribute little to the conversion of light onto the pixel apertures that is illuminated because of their high astigmatism due to lowered rotational symmetry of the concentration distribution of diffused ions. In other words, an increase in the area where diffusion fronts are fused together could lead to a decrease, far from an improvement, in overall converging efficiency, even with 100% of the lens filling rate. Now, a model for forming two microlenses on a flat substrate with an ion diffusion process using circular mask apertures will be taken up as an example for simplicity. Figs. 6A through 6C are partially cross-sectional perspective views illustrating the state where two microlenses are formed on a transparent substrate 1. Ions are diffused through a circular mask aperture as a diffusion center 52, and diffusion fronts 5 that are leading edges of diffusion areas spread in concentrical semispheres. With the progress of ion diffusion, the two diffusion fronts eventually come into contact with each other (Fig. 6A). As ion diffusion further proceeds, the diffusion fronts are fused together, and the ion concentration gradient in the direction of a line connecting the adjoining diffusion centers decreases in the fused area. Thus, the diffusion speed in that direction decreases, and as a result, the diffusion fronts in the fused area form a continuum of curved surface, expanding in the direction orthogonally intersecting the aforementioned direction (in the direction of the boundary line with the adjoining lens) (Figs. 6B and 6C). Fig. 7 is a perspective view illustrating a solid body formed by the diffusion fronts viewed from the direction opposite to the surface on which lenses are formed. The area in which these diffusion fronts have been fused together is called an overlapped diffusion area 6. The length of the overlapped diffusion area 6 in the direction of a line connecting the lens centers is called the width W of the overlapped diffusion area 6. As the overlapped diffusion area 6 receives ions fed by both the diffusion centers 52 as the ion sources, the concentration distribution of diffused ions forms a gentle saddle shape in the direction of a line connecting the lens centers (in the X direction shown in Fig. 7). The overlapped diffusion area 6 has a lower refracting power than an equivalent independent microlens, causing a remarkable astigmatism, because of the smaller gradient of its ion concentration distribution in the X direction. Consequently, the light incident on this overlapped diffusion area 6 hardly converge on the neighborhood of the focal point of each lens on which the light is originally to converge, but on a narrow strip-like area connecting the centers of the adjoining lenses. The model of this state is shown in Fig. 8. In the figure, numeral 41 denotes a focal point of the microlens 4, 42 a converging area of the microlens, and 43 a converging plane, respectively. The light incident on the overlapped diffusion area 6 also converges on a strip connecting the focal points 41. Disclosure of the Invention It is an object of the present invention to provide a method of manufacturing planar microlens arrays having an excellent overall converging efficiency. According to the present invention, there is as defined in claim 1, provided a method of manufacturing a planar microlens array having a multitude of refractive-index distribution type microlenses of a polygonal circumferential shape arranged two-dimensionally and regularly on the surface of a planar transparent substrate, characterized in that the manufacturing method includes the steps of preparing a planar transparent substrate, forming on the surface of the substrate a diffusion-inhibiting mask film having a multitude of regularly arranged mask apertures of a shape connecting curves or broken lines passing inside straight lines that are parallel with and disposed at a predetermined interval inwardly away from sides of said polygonal circumferential shape, and forming microlenses over the almost entire surface of said substrate by diffusing in said substrate a material contributing to increasing the refractive index of said substrate through said mask apertures. Dependent claims define additional embodiments. Brief Description of the Drawings Fig. 1 is a perspective view of a prior-art planar microlens array. Fig. 2 is a plan view of the planar microlens array shown in Fig. 1. Fig. 3 is a perspective view of another prior-art planar microlens array. Fig. 4 is a plan view of the planar microlens array shown in Fig. 3. Fig. 5 is a cross-sectional view of optical paths in an image display device. Figs. 6A through 6C are partially cross-sectional perspective views illustrating a model of assistance in explaining the state where diffusion fronts are fused togther. Fig. 7 is a perspective view illustrating a solid body formed when the diffusion fronts have been fused together. Fig. 8 is a perspective view of a model of assistance in explaining the state of an ideal fusion from a rectangular mask aperture. Fig. 9A is a diagram illustrating a quadrilateral array of lenses. Fig. 9B is a diagram illustrating a six-lobe array of lenses. Fig. 10 is a model diagram of assistance in explaining the state of an ideal fusion from a rectangular mask aperture. Figs. 11A through 11C are diagrams illustrating the state where a diffusion front having rounded corners is formed from a rectangular mask aperture. Fig. 12A is a diagram illustrating a diffusion-inhibiting mask film having circular mask apertures Fig. 12B is a diagram illustrating a quadrilateral planar microlens array prepared using the diffusion-inhibiting mask film shown in Fig. 12A. Fig. 13 is a diagram illustrating converged light spots obtained through a planar microlens array comprising square lenses prepared using a diffusion-inhibiting mask film having circular apertures. Fig. 14 is a diagram illustrating the relationship between pixels (microlenses) and pixel apertures. Fig. 15A is a diagram illustrating a diffusion-inhibiting mask film having oblong mask apertures. Fig. 15B is a diagram illustrating a quadrilateral planar microlens array prepared using the diffusion-inhibiting mask film shown in Fig. 15A. Figs. 16A and 16B are diagrams illustrating still another embodiment of the planar microlens array according to the present invention. Figs. 17A and 17B are diagrams illustrating still another embodiment of the planar microlens array according to the present invention. Figs. 18A and 18B are diagrams illustrating still another embodiment of the planar microlens array according to the present invention. Best Mode for Carrying Out the Invention In a planar microlens array obtainable according to this invention, a multitude of lenses are densely, two-dimensionally and regularly arranged. Typical two-dimensional regular lens arrays include the four-lobe array and the six-lobe array. The four-lobe array is such that when one lens is noted from among lenses in the array, there are four lenses adjacent to that lens. The six-lobe array is such that when one lens is noted from among lenses in the array, there are six lenses adjacent to that lens. Fig. 9A shows a four-lobe array of lenses that are rectangular in the circumferential shape on the orthogonal X-Y coordinate system, and Fig. 9B shows a six-lobe array of lenses that are rectangular in the circumferential shape on the orthogonal X-Y coordinate system. In the figure, P X denotes an array pitch in the X-axis direction, P Y an array pitch in the Y-axis direction, respectively. Now, the aspect ratio of a lens having a rectangular circumferential shape will be described. When it is assumed that the length of short sides of the lens is a and the length of the long sides is b , then α (= b/a) is called the aspect ratio. When this aspect ratio α is large, a planar microlens array having a relatively large effective area and a good converging efficiency can be manufactured by using masks having oblong apertures, as disclosed in Japanese Patent Publication No.5-45642. Typical planar microlens arrays suitable for liquid-crystal display panels largely have lenses of aspect ratios of less than 2. The relationship between the aspect ratio and the filling rate of lenses manufactured using masks having oblong apertures, as disclosed in Japanese Patent Publication No.5-45642, in the four-lobe array of rectangular lenses is shown in Table 1. The relationship between the aspect ratio and filling rate of lens (in the four-lobe array of rectangular lenses) Aspect ratio α Lens filling rate Aspect ratio α Lens filling rate 1.0 0.785 1.6 0.866 1.1 0.805 1.7 0.874 1.2 0.821 1.8 0.881 1.3 0.835 1.9 0.887 1.4 0.847 2.0 0.893 1.5 0.857 The table indicates that as the lens aspect ratio increases from 1.0 to 2.0, the lens filling rate increases. Next, the shape of mask apertures will be discussed. The microlens array disclosed in Japanese Patent Publication No.3-136004 is of a six-lobe array where the circumferential shape of microlenses is hexagonal. The shape of mask apertures is circular. In the meantime, the shape of mask apertures when manufacturing with the diffusion process lenticular lenses of a virtually semi-circular cross-sectional shape is linear (refer to Fig.3 in Japanese Patent Publication No.61-201639, for example.) A detailed study of the state of diffusion at this time reveals that a diffusion front diffused through a given mask aperture proceeds linearly in parallel with the linear mask aperture. As the diffusion process further proceeds, that diffusion front comes in contact with another diffusion front through an adjacent mask aperture. Thus, lenticular lenses can be formed without gaps over the entire surface of the substrate. The present inventors et al. further advanced the idea of switching from the prior-art mask apertures of a circular or oblong shape to mask apertures of a rectangular shape in order to form lenses two--dimensionally without gaps over the entire surface of the substrate. Fig. 10 shows an ideal diffusion model from a mask aperture of a rectangular shape. Rounded corners of the diffusion front 5 in this figure are attributable to the fact that ions are spot-diffused starting from the four corners of the mask aperture 3. In the figure, numeral 51 denotes an iso-refractive-index curve. If the dimensions of mask apertures of a rectangular (square or rectangular) shape are relatively small, contribution of the rounded corner of a diffusion corner increases, with the result that the entire diffusion-front shape becomes dull. This will be described taking as an example a microlens of a 100µmx100µm in circumferential shape. Fig. 11A shows a diffusion front 5 (mask aperture 3: a 60µmx60µm square, distance d between the neighborhood of lens and mask aperture: 20µm, and diffusion length: 28µm). The front 5 of the diffusion region extending from the mask aperture 3 becomes a rectangular-shaped region, with rounded corners, that is obtained by adding an area equal to the diffusion length to the periphery of the mask aperture. With the dimensions of microlenses being the same, however, if the distance d is increased to obtain a relatively small rectangular mask aperture, the contribution of the spot diffusion effect at corners increases, and as a result, the shape of the diffusion front becomes dull, approaching a circle. Figs. 11B and 11C show the approximate shapes of diffusion fronts when mask apertures are a 50µmx50µm square and a 40µmx40µm square, respectively, and the diffusion length is set so that the diffusion regions becomes sufficiently dense with virtually no gaps. As is apparent from the figures, when the shape of a mask aperture is small, the overlapped diffusion regions become larger, making it difficult to obtain a good converging effect. This holds true not only for rectangular shapes but also for other polygonal shapes. In this way, with the relatively smaller shape of mask apertures, compared with the circumferential shape of microlenses, if the overlapped diffusion regions become larger due to the dulled corners of the diffusion fronts, that is, the contribution of the spot diffusion effect, it is necessary to modify the shape of mask apertures. In such a case, by modifying the shape of mask apertures into a shape of a polygon having inwardly concave sides by the amount of rounding of the diffusion fronts (hereinafter referred to as a star shape), the area of the overlapped diffusion regions can be reduced, thereby a larger converging effect can be obtained. Next, mask aperture setting conditions will be studied. To set the lens filling rate at almost 100% as one of mask aperture setting conditions, the ratio of the width W of the overlapped diffusion regions between two adjoining microlenses to the array pitch in the direction of a line connecting the centers of the two adjoining microlenses should preferably be less than 20%. In order to have the width W of the overlapped diffusion regions of almost zero, it is desirable to set the lens filling rate at more than 91%. By changing diffusion conditions from those where there are no overlapped diffusion regions (where there are lens unformed regions, with the diffusion fronts coming in contact with each other) to those where there are overlapped diffusion regions and the lens filling rate is 100% (where there are no lens unformed regions), a planar microlens array having both overlapped diffusion regions and microlens unformed regions can be formed. In this case, too, mask aperture forming and diffusion conditions should preferably be such that the ratio of the width W of the overlapped diffusion regions between two adjoining microlenses to the array pitch in the direction of a line connecting the centers of the two adjoining microlenses is less than 20%, and the lens filling rate is more than 91%. The diffusion process in the present invention is not limited to the ion diffusion process. The anneal process (Japanese Patent Publication No.60-256101, for example) for forming the refractive-index profile by thermal diffusion in which a thin film of a diffusion material is formed at positions corresponding to mask apertures, or the monomer diffusion copolymerization process (Japanese Patent Publication No.2-50102, for example) in which after a plastic substrate is obtained by semi-polymerizing a first monomer on a transparent substrate, and then a second monomer is diffused over the plastic substrate to complete polymerization may also be employed. In short, any methods of diffusing over a transparent substrate a material contributing to increasing the refractive index of the substrate to form a planar microlens array having a refractive-index gradient based on the concentration gradient of the material may be used. Furthermore, the mask aperture according to the present invention may be of a polygonal shape having straight chamfered portions about a few µm long or minute circular-arc portions on the apexes thereof, with no difference in its effects between them. (Preliminary tests) Prior to the description of embodiments of the present invention, the problem of the converging efficiency of lens will be discussed based on the results of preliminary tests conducted to compare the present invention with the prior art. Now, a planar microlens array as shown in Japanese Patent Publication No.3-136004, to which a four-lobe array of lenses having a rectangular circumferential shape is applied, will be taken as an example. Fig.12A is a plan view of a diffusion-inhibiting mask film, Fig. 12B is a plan view of a planar microlens array prepared using this diffusion-inhibiting mask film. As shown in Fig.12A, ions were diffused through circular mask apertures 3 arranged at pitches P X and P Y in X and Y directions, and overlapped diffusion regions 6 were provided between adjoining microlenses 4, as shown in Fig. 12B, so that the lens filling rate would become 100% and the circumferential shape of microlenses 4 would be of a rectangular shape. In this case, it was indicated that the width W of the overlapped diffusion region becomes very larger on the long sides of the rectangular microlens, compared with the six-lobe array of microlenses of a hexagonal circumferential shape because the diffusion fronts 5 become circles circumscribed with the rectangular microlenses 4. In the meantime, the effects of the presence of overlapped diffusion regions on the converging performance of microlenses were studied through experiments. Planar microlens arrays of several types were manufactured with the ion diffusion process using soda-lime glass as transparent substrates, on which T1 ions as ions contributing to increasing the refractive index of the substrate were diffused through circular 60µm-dia mask apertures arranged at pitches of P x =100µm in the X direction and P Y =100µm in the Y direction by controlling ion diffusion conditions so that diffusion fronts would become 100-141 (= √2x100)µm circles. As a result, it was revealed that the degree of fusion of diffusion fronts 5 between adjoining microlenses 4 increases where the width W of overlapped diffusion regions can be estimated to exceed 20% of the corresponding array pitch in the X or Y direction. It was also revealed that this substantially reduces the converging efficiency of microlenses. Fig. 13 shows a photograph of converged spots observed with an optical microscope by throwing almost parallel light on a planar microlens array in the state where the diameter of diffusion fronts was 141µm. In the figure, numeral 41 is a focal point of the microlens. In this instance, the width W of the overlapped diffusion regions 6 was estimated at 41µm, or 29% of the array pitches in the X and Y directions. The light incident on the overlapped diffusion regions 6 was not converged not only on the vicinity of the focal points of the microlens 4 but also on the crosslines connecting the focal points of the adjoining lenses. The aforementioned planar microlens array was used as the planar microlens array 82 of the image display device shown in Fig. 5, and a liquid-crystal display panel of 100µmx100µm square-shaped pixels 81d and 55µmx55µm square-shaped pixel-aperture regions 81b was used as the liquid-crystal display panel 81 in the figure (refer to Fig. 14.) In this case, it was revealed that the amount of light converging within the aperture regions 81b accounts for 52% of the incident light, and the amount of light reaching the screen 88 is reduced to less than 0.8 times as much as that in the six-lobe array of hexagonal lenses. Next, the problem of the lens filling rate will be discussed. In Japanese Patent Publication No.5-45642, the area ratio of microlens unformed regions is small, that is, the lens filling rate is sufficiently high for practical use, in the case of the six-lobe microlens array. With the square microlens array, however, it was indicated that when oblong microlenses are arranged densely, the ratio of microlens unformed regions is increased, that is, the lens filling rate is reduced. An example where the planar microlens array as disclosed in Japanese Patent Publication No.5-45642 is applied to a four-lobe array is shown in Figs. 15A and 15B. Fig. 15A is a plan view of a diffusion-inhibiting mask film, and Fig. 15B is a plan view of a planar micro-lens array manufactured using this diffusion-inhibiting mask film. An oblong microlens 4 inscribed in a rectangle can be formed by diffusing ions through the oblong mask aperture 3 and terminating ion diffusion in the state where diffusion fronts 5 come in contact with each other between the adjoining microlenses 4. It was revealed, however, that the lens filling rate is substantially reduced because the microlens unformed regions 7 become very large, and as a result, the converging efficiency of microlenses is also decreased by the amount of decrease in the lens filling rate. With a four-lobe array of the X-direction pitch of P x =100µm and the Y-direction pitch of P Y =150µm, for example, the lens filling rate is reduced to less than 80%. It was also revealed that when the above-mentioned microlenses are used in the image display device shown in Fig. 5, and a liquid-crystal display panel having approx. 100µmx100µm square-shaped pixels and 55µmx55µm square-shaped pixel aperture regions is used, the amount of light reaching the screen is reduced by the amount of decrease in the lens filling rate. (Preferred Embodiment 1) This embodiment is intended to modify the shape of rectangular apertures when the overlapped diffusion regions become large due to the rounding of the diffusion regions, that is, due to the contribution of the spot diffusion effects when the shape of the mask apertures is relatively smaller than the shape of the microlens, as described in reference to Figs. 11A through 11C. In this case, more pronounced light converging effects can be obtained by reducing the area of overlapped diffusion regions by changing the rectangular shape of mask apertures to a shape obtained by making the sides of the rectangle inwardly concave by the amount of rounding of the diffusion regions. More quantitatively speaking, the advance distance (diffusion length) of diffusion fronts in Figs. 11B and 11C in the direction of apexes (in the diagonal direction of the square) is different from that in the direction of sides (in the side direction of the square). It was experimentally demonstrated that the ratio between diffusion speed in the apex direction and that in the side direction are approximately 0.9:1. Thus, the shape of mask apertures is set so that the ratio between diffusion length in the apex direction and that in the side direction is maintained at 0.9:1. The mask aperture shown in Fig. 16A is an example where the dependence of diffusion length on the shape of a mask aperture is taken into consideration. The circumferential shape of the microlens shown in the figure is a square having apexes A, B, C and D. When it is assumed that a second square (apexes P, R, T and V) enclosed by straight lines that are parallel with, and separated by a distance d = 25µm from each side of the original square is provided within the original square, the mask aperture has such a shape (star shape) formed by connecting curves passing points Q, S, U and W lying inside the straight lines connecting the apexes of the second square. The recommendable shape of these curves is a parabolic, elliptic, hyperbolic or any other quadratic curve passing those points, or curves similar to it. The relative positions of points A, B, C and D, and points P, Q, R, S, T, U, V and W are determined in the following manner: Point P; A point on line segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO , or L AP = 0.5L AP , for example. Point R; A point on line segment BO at which distance L BR from point B is such that L BR = L AP . Point T; A point on line segment CO at which distance L CT from point C is such that L CT = L AP . Point V; A point on line segment DO at which distance L DV from point D is such that L DV = L AP . Point Q; A point obtained by shifting point E, the bisecting point of line segment PR, by L EQ in the direction of point O where 0 < L EQ ≤ 0.67L EO , or L EQ = 0.52L EO , for example. Point S; A point obtained by shifting point F, the bisecting point of line segment RT, by L FS in the direction of point O where 0 < L FS ≤ 0.67L FO , or L FS = 0.52L FO , for example. Point U; A point obtained by shifting point G, the bisecting point of line segment TV, by L GU in the direction of point O where L GU = L EQ . Point W; A point obtained by shifting point H, the bisecting point of line segment VP, by L HW in the direction of point O where L HW = L FS . When L AP is smaller than 0.25L AO , it is difficult to form a lens having good lens action. When L AP is larger than 0.67L AO , the mask aperture becomes smaller, the adverse effects of point diffusion could result. When L EQ and L FS are larger than 0.67L EO and 0.67L FO , respectively, the adverse effects of point diffusion could also result. When the circumferential shape of a microlens is a 100µmx100µm square, and d = 25µm, then L AP = 35µm, and the distance between points Q, S, U and W and the circumferential edges of the microlens is 38µm. It is indicated that the shape of mask aperture is set so that the ratio between diffusion length in the apex direction and that in the side direction is 0.9:1. When ion diffusion is performed through this mask aperture, and ion diffusion is discontinued at a point of time when the diffusion front has reached apexes A, B, C and D, the diffusion front 5 assumes a shape shown by dotted lines in the figure, with reduced rounded areas on the diffusion region. Even with this shape of mask apertures, the corners of the diffusion fronts are rounded at the apexes of the mask apertures. To cope with these unwantedly rounded diffusion fronts, the apex parts of mask apertures may be chamfered or rounded in advance. Since mask apertures are manufactured with photolithography, it is difficult to manufacture mask apertures of an extremely complex curved shape. Taking into account manufacturing accuracy and cost, therefore, points P, R, T and V in Fig. 16A may be connected by straight lines, instead of curves, as shown in Fig. 16B. (Preferred Embodiment 2) This embodiment is intended to modify the shape of mask apertures. Fig. 17A shows a modified mask aperture shape. When the circumferential shape of a hexagonal microlens is expressed by six apexes A, B, C, D, E and F, and a central point O, the mask aperture for the microlens has a shape (star shape) expressed by a curve connecting the following points P, Q, R, S, T, U, V, W, X, Y, Z, M and P in that order. Point P; A point on a segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO . Point R; A point on a segment BO at which distance L BR from point B is such that 0.25L BO ≤ L BR ≤ 0.67L BO . Point T; A point on a segment CO at which distance L CT from point C is such that 0.25L CO ≤ L CT ≤ 0.67L CO . Point V; A point on a segment DO at which distance L DV from point D is such that L DV = L AP . Point X; A point on a segment EO at which distance L EX from point E is such that L EX = L BR . Point Z; A point on a segment FO at which distance L FZ from point F is such that L FZ = L CT . Point Q; A point obtained by shifting point E, the bisecting point of segment PR, in the direction of point O by L EQ where 0 < L EQ ≤ 0.5L EO . Point S; A point obtained by shifting point F, the bisecting point of segment RT, in the direction of point O by L FS where 0 < L FS ≤ 0.5L FO . Point U; A point obtained by shifting point G, the bisecting point of segment TV, in the direction of point O by L GU where 0 < L GU ≤ 0.5L GO . Point W; A point obtained by shifting point H, the bisecting point of segment VX, in the direction of point O by L HW where L HW = L EQ . Point Y; A point obtained by shifting point I, the bisecting point of segment XZ, in the direction of point O by L IY where L IY = L FS . Point M; A point obtained by shifting point J, the bisecting point of segment ZP, in the direction of point O by L JM where L JM = L GU . When L AP , L BR and L CT are smaller than 0.25L AO , 0.25L BO and 0.25L CO , respectively, it is difficult to form a lens having good lens action. When L AP , L BR and L CT are larger than 0.67L AO , 0.67L BO and 0.67L CO , the mask aperture becomes smaller, the adverse effects of point diffusion could result. When L EQ , L FS and L GU are larger than 0.5L EO , 0.5L FO and 0.5L GO , respectively, the adverse effects of point diffusion could also result. By using mask apertures of such a shape, the rounding of the diffusion fronts 5 can be substantially reduced, as shown in the figure. Since mask apertures are manufactured with photolithography, it is difficult to manufacture mask apertures of an extremely complex curved shape. Taking into account manufacturing accuracy and cost, therefore, points P, R, T, V, X and Z in Fig. 17A may be connected by straight lines, instead of curves, as shown in Fig. 17B. Further modified embodiment of Figs. 16B and 17B will be described in the following. In the modified embodiments, the adjoining apexes of a second polygon are connected with three broken lines, rather than two broken lines in the above mentioned embodiment. Fig. 18A shows a mask aperture of a square shape, and Fig. 18B shows a mask aperture of a hexagonal shape. Points Q, S, U and W in Fig. 18A correspond to points Q, S, U and W in Fig. 16B, while points M, Q, S, U, W, Y and M in Fig. 22B correspond to points M, Q, S, U, W, Y and M in Fig. 21B. Industrial Applicability As described above, the present invention makes it possible to realize a planar microlens array with high converging efficiency regardless of the array types thereof. The method of manufacturing planar microlens arrays according to the present invention makes it possible to accomplish a planar microlens array with the lens filling rate of almost 100% and smaller overlapped diffusion regions, that is, with high lens effective area ratio. Furthermore, with an image display device combining a planar microlens array according to the present invention with a plurality of pixels, the amount of light reaching the screen can be increased because high converging efficiency can be realized regardless of pixel arrays of the display panel. Thus, an extremely bright image display device can be accomplished.

Claims: A method of manufacturing a planar microlens array having a plurality of refractive-index distribution type microlenses of a polygonal circumferential shape arranged two-dimensionally and regularly on the surface of a planar transparent substrate, said method including the steps of : preparing a planar transparent substrate, forming on the surface of said substrate a diffusion-inhibiting mask film (2) having a plurality of regularly arranged mask apertures (3) of a shape delimited by connecting curves or straight segments passing inside geometrical figure, delimited by straight lines that are parallel with and disposed at a predetermined interval inwardly away from sides of said polygonal circumferential shape, and wherein said curves or said straight segments connects the corners of said geometrical figures, in a manner such that each corner is connected to its two adjacent corners, forming microlenses over the almost entire surface of said substrate by diffusing in said substrate a material contributing to increasing the refractive index of said substrate through said mask apertures. A method of manufacturing a planar microlens array as set forth in Claim 1, wherein when said substance contributing to increasing the refractive index of said substrate is diffused with the ion diffusion process or the diffusion copolymerization process, diffusion time or copolymerization time is controlled so that said microlenses are densely arranged on the surface of said substrate, diffusion fronts (5) of said microlenses form regions where said diffusion fronts are fused with diffusion regions of adjoining microlenses, and the length, in the direction of a straight line connecting centers of adjoining two microlenses, of said regions where said two microlenses are fused together becoming less than 20% of an array pitch of said microlenses in said direction. A method of manufacturing a planar microlens array as set forth in Claim 1, wherein when said substance contributing to increasing the refractive index of said substrate is diffused with the ion diffusion process or the diffusion copolymerization process, diffusion time or copolymerization time is controlled so that said microlenses are densely arranged on the surface of said substrate, and diffusion fronts of said microlenses come in linear contact with, but are not fused with, diffusion fronts of adjoining microlenses. A method of manufacturing a planar microlens array as set forth in Claim 2 or 3, wherein the shape of said mask apertures is a square, hexagon or star shape. A method of manufacturing a planar microlens array as set forth in Claim 1, wherein the array of said mask apertures is a four-lobe array, said polygonal circumferential shape is a rectangle; when said rectangle is expressed by four apexes A, B, C and D, and an intersecting point O of diagonal lines AC and BD, each of said mask apertures has a shape expressed by straight lines connecting the following points P, Q, R, S, T, U, V, W and P in that order, Point P; a point on line segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO , Point R; a point on line segment BO at which distance L BR from point B is such that L BR = L AP , Point T; a point on line segment CO at which distance L CT from point C is such that L CT = L AP , Point V; a point on line segment DO at which distance L DV from point D is such that L DV = L AP , Point Q; a point obtained by shifting point E, the bisecting point of line segment PR, by L EQ in the direction of point 0 where 0 < L EQ ≤ 0.67L EO , Point S; a point obtained by shifting point F, the bisecting point of line segment RT, by L FS in the direction of point O where 0 < L FS ≤ 0.67L FO , Point U; a point obtained by shifting point G, the bisecting point of line segment TV, by L GU in the direction of point O where L GU = L EQ , and Point W; a point obtained by shifting point H, the bisecting point of line segment VP, by L HW in the direction of point O where L HW = L FS . A method of manufacturing a planar microlens array as set forth in Claim 5, wherein when the array of said mask-aperture is a four-lobe array, said rectangle is a square and L EQ = L FS . A method of manufacturing a planar microlens array as set forth in Claim 1, wherein the array of said mask apertures is a four-lobe array, said polygonal circumferential shape is a rectangle; when said rectangle is expressed by four apexes A, B, C and D, and an intersecting point O of diagonals AC and BD, each of said mask apertures has a shape enclosed by a curve connecting PQR, a curve connecting RST, a curve connecting TUV and a curve connecting VWP among the following points P, Q, R, S, T, U, V and W, Point P; a point-on line segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO , Point R; a point on line segment BO at which distance L BR from point B is such that L BR = L AP , Point T; a point on line segment CO at which distance L CT from point C is such that L CT = L AP , Point V; a point on line segment DO at which distance L DV from point D is such that L DV = L AP , Point Q; a point obtained by shifting point E, the bisecting point of line segment PR, by L EQ in the direction of point O where 0 < L EQ ≤ 0.67L EO , Point S; a point obtained by shifting point F, the bisecting point of line segment RT, by L FS in the direction of point 0 where 0 < L FS ≤ 0.67L FO , Point U; a point obtained by shifting point G, the bisecting point of line segment TV, by L GU in the direction of point O where L GU = L EQ , and Point W; a point obtained by shifting point H, the bisecting point of line segment VP, by L HW in the direction of point O where L HW = L FS . A method of manufacturing a planar microlens array as set forth in Claim 7, wherein said rectangle is a square and L EQ = L FS . A thod of manufacturing a planar microlens array as set forth in Claim 1, wherein the array of said mask apertures is a six-lobe array, said polygonal circumferential shape is a regular hexagonal; when said regular hexagonal is expressed by six apexes A, B, C, D, E and F, and a central point, each of said mask apertures has a shape expressed by straight lines connecting the following points P, Q, R, S, T, U, V, W, X, Y, Z, M and P in that order, Point P; a point on line segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO , Point R; a point on line segment BO at which distance L BR from point B is such that 0.25L BO ≤ L BR ≤ 0.67L BO , Point T; a point on line segment CO at which distance L CT from point C is such that 0.25L CO ≤ L CT ≤ 0.67L CO , Point V; a point on line segment DO at which distance L DV from point D is such that L DV = L AP , Point X; a point on line segment EO at which distance L EX from point E is such that L EX = L BR , Point Z; a point on line segment FO at which distance L FZ from point F is such that L FZ = L CT , Point Q; a point obtained by shifting point E, the bisecting point of line segment PR, by L EQ in the direction of point O where 0 < L EQ ≤ 0.5L EO , Point S; a point obtained by shifting point F, the bisecting point of line segment RT, by L FS in the direction of point O where 0 < L FS ≤ 0.5L FO , Point U; a point obtained by shifting point G, the bisecting point of line segment TV, by L GU in the direction of point O where 0 ≤ L GU ≤ 0.5L GO , Point W; a point obtained by shifting point H, the bisecting point of line segment VX, by L HW in the direction of point O where L HW = L EQ , Point Y; a point obtained by shifting point I, the bisecting point of line segment XZ, by L IY in the direction of point O where L IY = L FS , and Point M; a point obtained by shifting point J, the bisecting point of line segment ZP, by L JM in the direction of point O where L JM = L GU . A method of manufacturing a planar microlens array as set forth in Claim 1, wherein the array of said mask apertures is a six-lobe array, said polygonal circumferential shape is a regular hexagonal; when said regular hexagonal is expressed by six apexes A, B, C, D, E and F, and O, each of said mask apertures has a shape enclosed by a curve connecting PQR, a curve connecting RST, a curve connecting TUV, a curve connecting VWX, a curve connecting XYZ, and a curve connecting ZMP from among the following points of P, Q, R, S, T, U, V, W, X, Y, Z and M, Point P; a point on line segment AO at which distance L AP from point A is such that 0.25L AO ≤ L AP ≤ 0.67L AO , Point R; a point on line segment BO at which distance L BR from point B is such that 0.25L BO ≤ L BR ≤ 0.67L BO , Point T; a point on line segment CO at which distance L CT from point C is such that 0.25L CO ≤ L CT ≤ 0.67L CO , Point V; a point on line segment DO at which distance L DV from point D is such that L DV = L AP , Point X; a point on line segment EO at which distance L EX from point E is such that L EX = L BR , Point Z; a point on line segment FO at which distance L FZ from point F is such that L FZ = L CT , Point Q; a point obtained by shifting point E, the bisecting point of line segment PR, by L EQ in the direction of point O where 0 < L EQ ≤ 0.5L EO , Point S; a point obtained by shifting point F, the bisecting point of line segment RT, by L FS in the direction of point O where 0 < L FS ≤ 0.5L FO , Point U; a point obtained by shifting point G, the bisecting point of line segment TV, by L GU in the direction of point O where 0 ≤ L GU ≤ 0.5L GO , Point W; a point obtained by shifting point H, the bisecting point of line segment VX, by L HW in the direction of point O where L HW = L EQ , Point Y; a point obtained by shifting point I, the bisecting point of line segment XZ, by L IY in the direction of point O where L IY = L FS , and Point M; a point obtained by shifting point J, the bisecting point of line segment ZP, by L JM in the direction of point O where L JM = L GU . A method of manufacturing a planar microlens array as set forth in any one of claims 5 through 8, wherein the ratio of area occupied by said microlenses to the area of said substrate is more than 80% in the case where the circumferential shape of said mask apertures is a square, and more than 91% in the case where the aspect ratio of said microlenses is less than 2.

Inventors: HAMADA HIROSHI, HAMANAKA KENJIRO, NAKAMA KENICHI, TANIGUCHI SATOSHI, HAMADA, HIROSHI, HAMANAKA, KENJIRO, NAKAMA, KENICHI, TANIGUCHI, SATOSHI, HAMANAKA, Kenjiro Nippon Sheet Glass Co., Ltd., NAKAMA, Kenichi Nippon Sheet Glass Co., Ltd., TANIGUCHI, Satoshi Nippon Sheet Glass Co., Ltd.
Applicants: NIPPON SHEET GLASS CO LTD, SHARP KK, NIPPON SHEET GLASS CO., LTD., SHARP KABUSHIKI KAISHA
Application year: 1995
Main classification: G02B3
IPC codes: G02B3, G09F9