Patent Publication Number: US-6909121-B2

Title: Microlens array substrate, method of manufacturing the same, and display device

Description:
TECHNICAL FIELD 
   The present invention relates to a microlens array substrate, a method of manufacturing the same, and a display device. 
   BACKGROUND ART 
   A microlens array formed by a number of micro lenses arranged side by side has been applied to liquid crystal panels, for example. Each lens of the microlens array converges incident light upon each pixel to illuminate a display screen. 
   As a method of manufacturing a microlens array, methods using dry etching or wet etching have been known. However, these methods require a lithographic step each time when manufacturing an individual microlens array, thereby leading to increased costs. 
   Therefore, a method of manufacturing a microlens array by dripping a liquid resin onto a master mold having curved surfaces corresponding to lenses and removing the solidified resin has been developed as disclosed in Japanese Patent Application Laid-Open No. 3-198003. 
   A microlens array illuminates a display screen, but contrast between pixels is not improved by a conventional microlens array. A means for improving contrast is required in addition to a microlens array in order to provide a bright and vivid display on the screen. However, a conventional method of manufacturing a microlens array has given no attention to the improvement of contrast. 
   The present invention has been achieved to solve the above problem, and an objective of the present invention is to provide a microlens array substrate capable of improving contrast in addition to illuminating a screen, a method of manufacturing the same, and a display device. 
   SUMMARY 
   (1) A method of manufacturing a microlens array substrate according to the present invention comprises the steps of: 
   closely providing a substrate precursor between a first master mold having a plurality of curved surfaces and a second master mold having a plurality of projections to form a substrate having a plurality of lenses formed by the curved surfaces and recesses formed by the projections; 
   removing the first and second master molds from the substrate; and 
   filling the recesses with a shading material after the second master mold is removed. 
   According to the present invention, the substrate precursor is closely placed between the first and second master molds and the lenses are formed by transferring the shapes of the curved surfaces of the first master mold. A microlens array substrate having a plurality of lenses can be thus easily formed. Because each lens converges incident light, a display screen can be brightly illuminated. Moreover, because the first and second master molds can be used repeatedly as long as durability permits, the step of producing these master molds can be omitted in the steps of manufacturing the second and subsequent microlens array substrates, thereby reducing the number of steps and production costs. 
   The recesses are formed on the microlens array substrate by transferring the shapes of the projections of the second master mold, and the recesses are filled with the shading material. The shading material functions as a black matrix to improve contrast between pixels. 
   According to the present invention, a microlens array substrate capable of improving contrast in addition to illuminating brightly a display screen can be easily manufactured by transferring. 
   (2) In this manufacturing method, the substrate precursor may be closely placed between the first and second master molds such that each of the projections avoids being positioned right above the center of each of the curved surfaces. 
   Since each of the recesses on the microlens array substrate avoids being positioned right above the center of each of the lenses, a black matrix can be formed so as to avoid the center of the lenses. 
   (3) This manufacturing method may further comprise a step of forming a protective film by placing a protective film precursor on at least one of the shading material in the recesses and the lenses, and by solidifying the protective film precursor. 
   (4) The protective film precursor may be of a material which can be cured by applying energy. 
   (5) The energy may be at least one of light and heat. 
   (6) The protective film precursor may be a UV-curable resin. 
   (7) In this manufacturing method, the protective film precursor may be solidified after placing a reinforcing plate on the protective film precursor. 
   (8) The substrate precursor may be of a material which can be cured by applying energy. 
   By using such a material, the substrate precursor can be easily provided to minute parts of the first and second master molds, and so a microlens array substrate formed by precisely transferring the shapes of the curved surfaces and projections of the first and second master molds can be provided. 
   (9) The energy may be at least one of light and heat. 
   Therefore, a commonly used exposure apparatus, baking furnace, or hot plate can be used, thereby reducing facility costs and space. 
   (10) The substrate precursor may be a UV-curable resin. 
   As the UV-curable resin, an acrylic resin is preferable because of superior transparency and availability of various commercial resins and photosensitizers. 
   (11) In this manufacturing method, the recesses may be filled with the shading material by an ink jet method. 
   According to the ink jet method, the shading material can be provided at a high speed with no waste. 
   (12) In this manufacturing method, at least part of an inner surface of each of the recesses may be tapered such that an opening portion is wider than a bottom portion. 
   Since the tapered recesses can be reliably filled with the shading material, thus produced microlens array substrate is particularly suitable for a liquid crystal panel with high resolution. 
   (13) In this manufacturing method, only the opening portion of the inner surface may be tapered. 
   Such recesses permit only a small difference in thickness of the shading material, thereby ensuring uniform shading performance. The microlens array thus manufactured can provide a vivid image. 
   (14) A microlens array substrate according to the present invention comprises: a plurality of lenses formed on one surface of the microlens array substrate; a plurality of recesses formed on the other surface of the microlens array substrate such that each of the recesses avoids being positioned right above the center of each of the lenses; and a shading layer formed in the recesses. 
   According to the present invention, each lens converges incident light upon each pixel to brightly illuminate a display screen, and the shading layer formed in the recesses functions as a black matrix to improve contrast between pixels. 
   (15) The microlens array substrate may further comprise a protective film on at least one of the lenses and the shading layer. 
   (16) The microlens array substrate may further comprise a reinforcing plate on the protective film. 
   (17) In the microlens array substrate, at least part of an inner surface of each of the recesses may be tapered such that an opening portion is wider than a bottom portion. 
   Because the opening portion is wider than the bottom portion and the recesses can be reliably filled with the shading material, the microlens array substrate is particularly suitable for a liquid crystal panel with high resolution. 
   (18) In the microlens array substrate, only the opening portion of the inner surface may be tapered. 
   Such recesses permit only a small difference in thickness of the shading material, thereby ensuring uniform shading performance, and a vivid image can be provided. 
   (19) A microlens array substrate according to the present invention is manufactured by the above-described method. 
   (20) A display device according to the present invention comprises the above-described microlens array substrate and a light source which emits light toward the microlens array substrate, wherein the microlens array substrate is placed such that a surface on which the lenses are formed faces the light source. 
   (21) The relation between the light refractive index “na” of the material forming the microlens array substrate and the light refractive index “nb” outside the lenses may be “na&gt;nb”, when the lenses are convex lenses. 
   When light passes from a medium with a lower refractive index to a medium with a higher refractive index, the light is refracted to a direction approaching the normal line of the interface between the two media. When the relation between “na” and “nb” satisfies “na&gt;nb”, the incident light can be converged by using convex lenses. 
   (22) The relation between the light refractive index “na” of the material forming the microlens array substrate and the light refractive index “nb” outside the lenses may be “na&lt;nb”, when the lenses are concave lenses. 
   When light passes from a medium with a higher refractive index to a medium with a lower refractive index, the light is refracted to a direction away from the normal line of the interface between the two media. When the relation between “na” and “nb” satisfies “na&lt;nb”, the incident light can be converged by using concave lenses. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIGS. 1A-1C  illustrate a method of manufacturing a microlens array substrate according to a first embodiment of the present invention. 
       FIGS. 2A-2B  also illustrate the method of manufacturing a microlens array substrate according to the first embodiment. 
       FIGS. 3A-3C  also illustrate the method of manufacturing a microlens array substrate according to the first embodiment. 
       FIGS. 4A-4B  also illustrate the method of manufacturing a microlens array substrate according to the first embodiment. 
       FIGS. 5A-5C  illustrate a method of manufacturing a microlens array substrate according to a second embodiment of the present invention. 
       FIGS. 6A-6C  also illustrate the method of manufacturing a microlens array substrate according to the second embodiment. 
       FIG. 7  illustrates a method of manufacturing a microlens array substrate according to a third embodiment of the present invention. 
       FIGS. 8A-8D  also illustrate the method of manufacturing a microlens array substrate according to the third embodiment. 
       FIGS. 9A-9B  also illustrate the method of manufacturing a microlens array substrate according to the third embodiment. 
       FIG. 10  illustrates a modification of a mask used in the third embodiment. 
       FIG. 11  illustrates a microlens array substrate according to a fourth embodiment of the present invention. 
       FIGS. 12A-12E  illustrate a method of manufacturing a microlens array substrate according to the fourth embodiment. 
       FIGS. 13A-13C  also illustrate the method of manufacturing a microlens array substrate according to the fourth embodiment. 
       FIGS. 14A-14C  also illustrate the method of manufacturing a microlens array substrate according to the fourth embodiment. 
       FIG. 15  illustrates a liquid crystal projector in which the microlens array substrate manufactured in accordance with the present invention is incorporated. 
   

   BEST MODE FOR CARRYING OUT THE INVENTION 
   Preferred embodiments of the present invention will be described with reference to the drawings. 
   (First Embodiment) 
     FIGS. 1A-4B  illustrate a method of manufacturing a microlens array substrate according to a first embodiment of the present invention. 
   A first master mold  10  and a second master mold  20  shown in  FIG. 1A  are prepared. A plurality of curved surfaces  12  are formed on the first master mold  10 . Each of the curved surfaces  12  has a concave shape that is an inverted shape of a convex lens. On the second master mold  20 , a plurality of projections  22  are formed. These projections  22  form a black matrix as seen from a plan view (not shown). 
   The first and second master molds  10  and  20  are arranged such that the curved surfaces  12  face the projections  22  and each projection  22  avoids being positioned right above the center of each curved surface  12 . 
   A substrate precursor  30  (first light transmitting layer precursor) is then closely placed between the master mold  10  and the master mold  20 . The substrate precursor  30  is a material for a microlens array substrate  32  shown in FIG.  1 C. Although the master mold  10  is placed under the master mold  20  in  FIG. 1A , the master mold  20  may be placed under the master mold  10 . 
   As the substrate precursor  30 , various materials can be used without specific limitations insofar as the materials transmit light when formed into the microlens array substrate  32 . It is preferable that the materials can be cured by applying energy. Such a material can be handled as a low-viscous liquid when forming the microlens array substrate  32 . Therefore, the material can be easily filled into minute parts of the first and second master molds  10  and  20  at room temperature under normal pressure or under similar conditions. 
   As the energy, at least either light or heat is preferably used. Therefore, a general-purpose exposure apparatus, baking furnace, or hot plate can be used, thereby reducing facility costs and space. 
   As examples of such a material, UV-curable resins can be given. As the UV-curable resins, acrylic resins are suitable. The UV-curable acrylic resins which exhibit excellent transparency and are capable of being cured in a short period of time can be obtained by utilizing various commercially available resins or photosensitizers. 
   Specific examples of a main composition of the UV-curable acrylic resins include prepolymers, oligomers, monomers, and photopolymerization initiators. 
   Examples of prepolymers or oligomers include acrylates such as epoxy acrylates, urethane acrylates, polyester acrylates, polyether acrylates, and spiroacetal acrylates, methacrylates such as epoxy methacrylates, urethane methacrylates, polyester methacrylates, and polyether methacrylates, and the like. 
   Examples of monomers include monofunctional monomers such as 2-ethylhexyl acrylate, 2-ethylhexyl methacrylate, 2-hydroxyethyl acrylate, 2-hydroxyethyl methacrylate, N-vinyl-2-pyrrolidone, carbitol acrylate, tetrahydrofurfuryl acrylate, isobornyl acrylate, dicyclopentenyl acrylate, and 1,3-butanediol acrylate, bifunctional monomers such as 1,6-hexanediol diacrylate, 1,6-hexanediol dimethacrylate, neopentyl glycol diacrylate, neopentyl glycol dimethacrylate, ethylene glycol diacrylate, polyethylene glycol diacrylate, and pentaerythritol diacrylate, and polyfunctional monomers such as trimethylolpropane triacrylate, trimethylolpropane trimethacrylate, pentaerythritol triacrylate, and dipentaerythritol hexaacrylate. 
   Examples of photopolymerization initiators include radical-generating compounds such as acetophenones such as 2,2-dimethoxy-2-phenylacetophenone, butylphenones such as α-hydroxyisobutylphenone and p-isopropyl-α-hydroxyisobutylphenone, acetophenone halides such as p-tert-butyldichloroacetophenone, p-tert-butyltrichloroacetophenone and α, α-dichloro-4-phenoxyacetophenone, benzophenones such as benzophenone and N,N-tetraethyl-4,4-diaminobenzophenone, benzyls such as benzyl and benzyl dimethyl ketal, benzoins such as benzoin and benzoin alkyl ether, oximes such as 1-phenyl-1,2-propanedione-2-(o-ethoxycarbonyl)oxime, xanthones such as 2-methylthioxanthone, and 2-chlorothioxanthone, and Michler&#39;s ketone. 
   Compounds such as amines may be added to prevent oxygen from inhibiting curing, and a solvent may be added for making application easy, as required. 
   As examples of the solvent, one or a plurality of organic solvents selected from various organic solvents such as propylene glycol monomethyl ether acetate, propylene glycol monopropyl ether, methoxymethyl propionate, ethoxyethyl propionate, ethyl cellosolve, ethyl cellosolve acetate, ethyl lactate, ethyl pyruvinate, methyl amyl ketone, cyclohexanone, xylene, toluene, butyl acetate, or mixed solvents of these organic solvents can be used without specific limitations. 
   A predetermined amount of the substrate precursor  30  formed by the UV-curable acrylic resin and the like is provided onto the master mold  10  as shown in FIG.  1 A. 
   The substrate precursor  30  is spread to a predetermined area as shown in FIG.  1 B and the substrate precursor  30  is cured by exposing to UV light  40  from at least one of the master mold  10  side and the master mold  20  side, as shown in  FIG. 1C , to form the microlens array substrate  32  (first light transmitting layer) between the master molds  10  and  20 . Lenses  34  formed by transferring the shapes of the curved surfaces  12  are provided on one side of the microlens array substrate  32 , and a plurality of recesses  36  formed by transferring the shapes of the projections  22  are provided on the other side. The recesses  36  form a black matrix as seen from a plan view (not shown). Each recess  36  avoids being positioned right above the center of each lens  34 . 
   When spreading the substrate precursor  30  to a predetermined area, pressure may be applied to either the master mold  10  or the master mold  20 , or both, as required. Although the substrate precursor  30  is placed on the master mold  10  in this case, it may be placed on the master mold  20  or on both the master molds  10  and  20 . Alternatively, the substrate precursor  30  may be applied to one or both of the master mold  10  and the master mold  20  by using a spin coating method, dipping method, spray coating method, roll coating method, bar coating method, or the like. 
   The master mold  20  is then removed from the microlens array substrate  32  to open the recesses  36  formed by transferring the shapes of the projections  22 , as shown in FIG.  2 A. 
   The recesses  36  of the microlens array substrate  32  are filled with a shading material  42  to form a shading layer  38 , as shown in FIG.  2 B. The shading layer  38  functions as a black matrix. 
   As the shading material  42 , various materials can be used insofar as the materials do not transmit light and do exhibit durability. For example, materials in which a black dye or black pigment is dissolved in a solvent together with a binder resin are used as the shading material  42 . As the solvent, water or various organic solvents can be used without specific limitations. As the organic solvents, one of the following organic solvents or a mixed solution of a plurality of solvents selected from these solvents may be used. Examples of these organic solvents include propylene glycol monomethyl ether acetate, propylene glycol monopropyl ether, methoxymethyl propionate, ethoxyethyl propionate, ethyl cellosolve, ethyl cellosolve acetate, ethyl lactate, ethyl pyruvinate, methyl amyl ketone, cyclohexanone, xylene, toluene, butyl acetate, or mixed solvents of these organic solvents can be used. 
   There are no specific limitations to a method of filling the recesses  36  with the shading material  42 , but an ink jet method is preferable. By using the ink jet method, ink can be used at high speed as well as at low cost without any waste by applying a technique which has been put to practical use for ink jet printers. 
     FIG. 2B  illustrates the process of filling the recesses  36  with the shading material  42  by an ink jet head  44 . Specifically, the ink jet head  44  is placed so as to face the recesses  36  to jet the shading material  42  into each recess  36 . 
   As examples of the ink jet head  44 , ink jet heads which have been put to practical use for ink jet printers such as a piezo jet type of ink jet head which jets ink by applying pressure to ink by utilizing volumetric variation of a piezoelectric element or a type of ink jet head which jets ink by applying pressure produced by expanding the volume of ink or vaporizing ink by using an electrothermal energy conversion member as an energy-generating element. In these types, an injecting area and an injecting pattern can be optionally set. 
   In the present embodiment, the shading material  42  is jetted from the ink jet head  44 . Therefore, it is necessary to ensure the fluidity of the shading material  42  to enable jetting from the ink jet head  44 . 
   In order to fill the recesses  36  on the microlens array substrate  32  equally with the shading material  42 , the filling position is adjusted by some operation such as moving the ink jet head  44 . When the recesses are uniformly filled with the shading material, the filling process is completed. If a solvent component is included in the shading material  42 , the shading material  42  is then heated to remove the solvent component. Note that the shading material  42  shrinks when the solvent component is removed. It is therefore necessary to provide a sufficient amount of the shading material  42  to keep the thickness for ensuring a required shading property after the shrinkage. 
   A protective film precursor  46  (adhesive layer precursor) is then dropped onto the microlens array substrate  32  as shown in  FIG. 3A. A  material for the protective film precursor  46  can be selected from the above-described materials which can be used for the substrate precursor  30 . Then a reinforcing plate  48  is attached to the protective film precursor  46  to spread the protective film precursor  46 . The protective film precursor  46  may be spread on the microlens array substrate  32  or on the reinforcing plate  48  by a method such as a spin coating or roll coating prior to the attachment of the reinforcing plate  48 . 
   Although a glass substrate is usually used as the reinforcing plate  48 , there is no specific limitation on the material of the reinforcing plate insofar as it has characteristics such as light transmissibility and mechanical strength. For example, substrates or film substrates made of plastics such as polycarbonate, polyallylate, polyether sulfone, amorphous polyolefin, polyethylene terephthalate, and polymethyl methacrylate can be used as the reinforcing plate  48 . 
   The protective film precursor  46  is then cured by a process suitable for the composition of the protective film precursor  46  to form a protective film  50  (adhesive layer), as shown in FIG.  3 B. If a UV-curable acrylic resin is used, the protective film precursor  46  is cured by exposing to UV light under predetermined conditions. 
   The master mold  10  is then removed from the microlens array substrate  32  as shown in FIG.  3 C. The lenses  34  are formed on the microlens array substrate  32  by the curved surfaces  12  of the master mold  10 . The lenses  34  are convex lenses. 
   A protective film precursor  52  is closely placed between the lenses  34  of the microlens array substrate  32  and a reinforcing plate  54 , as shown in FIG.  4 A. This step is the same as the step shown in  FIG. 3A and a  material of the protective film precursor  52  (second light transmitting layer precursor) can be selected from the materials which can be used for the protective film precursor  46 . 
   The microlens array substrate  32  with the protective films  50  and  56  and the reinforcing plates  48  and  54  formed on both sides as shown in  FIG. 4B  is thus produced. The microlens array substrate  32  converges incident light from the side of the lenses  34 . 
   If the protective films  50  and  56  have characteristics required for the microlens array substrate such as mechanical strength, gas barrier characteristics, and chemical resistance, the reinforcing plates  48  and  54  are not needed. Moreover, if the microlens array substrate  32  itself exhibits sufficient strength and the shading layer  38  is not damaged, the protective films  50  and  56  can be omitted. 
   When the protective film  50  is formed, the following relation must be established between the light refractive index “na” of the microlens array substrate  32  and the light refractive index “nb” of the protective film precursor  52  forming the protective film  56  placed outside the lenses  34 :
 
na&gt;nb
 
Satisfying this condition makes it possible to pass the light from a medium having a lower refractive index to a medium having a higher refractive index. The light  58  is refracted and converged to a direction approaching the normal line of the interface between the two media to brightly illuminate the screen.
 
   According to the present embodiment, the substrate precursor  30  is closely placed between the first and second master molds  10  and  20 , and the lenses  34  are formed by transferring the shapes of the curved surfaces  12  of the first master mold  10 . The microlens array substrate  32  having a plurality of the lenses  34  can be thus easily manufactured. According to this manufacturing method, the materials are used with high efficiency and the number of steps can be reduced, thereby reducing production costs. Moreover, because the first and second master molds  10  and  20  can be repeatedly used as long as durability permits, the step of producing these master molds can be omitted in the steps of manufacturing the second and subsequent microlens array substrates, thereby reducing the number of steps and production costs. 
   The recesses  36  are formed on the microlens array substrate by transferring the shapes of the projections  22  of the second master mold  20 . The recesses  36  are filled with the shading material  42 . The shading layer  38  formed of the shading material  42  functions as a black matrix to improve the contrast between pixels. 
   According to the present embodiment, the microlens array substrate capable of improving the contrast and illuminating the screen can be easily manufactured by transferring. 
   (Second Embodiment) 
     FIGS. 5A-6C  illustrate a method of manufacturing a microlens array substrate according to a second embodiment of the present invention. 
   A substrate precursor  130  is closely placed between a first master mold  110  and the second master mold  20 , as shown in FIG.  5 A. Curved surfaces  112  are formed on the master mold  110 . Each curved surface  112  has a convex shape that is an inverse of the shape of a concave lens. The present embodiment differs from the first embodiment in the shape of the curved surfaces  112 . The master mold  20  is as same as in the first embodiment, and a material for the substrate precursor  130  can be selected from the materials used in the first embodiment. After the same step as in  FIG. 1C , a microlens array substrate  132  is formed. Recesses  136  are formed on the microlens array substrate  132  by transferring the shapes of the projections  22  and lenses  134  are formed by transferring the shapes of the curved surfaces  112 . The lenses  134  are concave lenses. 
   The second master mold  20  is then removed from the microlens array substrate  132  as shown in  FIG. 5B , and the recesses  136  are filled with a shading material to form a shading layer  138 , as shown in FIG.  5 C. These steps are the same as the steps shown in  FIGS. 2A and 2B . 
   A protective film  150  (adhesive layer) formed by the protective film precursor (adhesive layer precursor) is formed between the surface of the microlens array substrate  132  having the shading layer  138  and a reinforcing plate  148 , as shown in FIG.  6 A. The first master mold  110  is then removed from the microlens array substrate  132 , as shown in  FIG. 6B. A  protective film  156  (second light transmitting layer) and a reinforcing plate  154  are provided on the lenses  134  as in the step shown in FIG.  4 A. 
   The microlens array substrate  132  with the protective films  150  and  156  and the reinforcing plates  148  and  154  formed on both sides as shown in  FIG. 6C  is thus manufactured by the above steps. The microlens array substrate  132  converges incident light from the side of the lenses  134 . 
   This is based on the premise that the following relation must be established between the light refractive index “na′” of the microlens array substrate  132  and the light refractive index “nb′” of the protective film precursor forming the protective film  156  placed outside the lenses  134 :
 
na′&lt;nb′
 
Satisfying this condition makes it possible to pass the light from a medium having a higher refractive index to a medium having a lower refractive index. Light  158  is refracted and converged to a direction away from the normal line of the interface between the two media to illuminate the screen.
 
   Because the present embodiment differs from the first embodiment only in using the concave lenses instead of the convex lenses, the same effect as in the first embodiment can be achieved. 
   (Third Embodiment) 
     FIGS. 7-9B  illustrate a method of manufacturing a microlens array substrate according to a third embodiment of the present invention. In the present embodiment, a microlens array substrate  200  shown in  FIG. 7  is manufactured. The microlens array substrate  200  differs from the microlens array substrate  32  shown in  FIG. 2B  in the shape of recesses  202 . Specifically, each recess  202  has a tapered side. Because the opening of the recess  202  is wider than the bottom, it can be reliably filled with the shading material  42  (see  FIG. 2B ) even if the pixels are densely arranged. A master mold with projections each having a trapezoid cross section is used to form the recesses  202 . 
     FIGS. 8A-9B  illustrate a process of forming a master mold used for forming the recesses  202 . 
   A resist layer  214  is formed on a base  212 , as shown in FIG.  8 A. The base  212  is formed into a master mold by etching the surface thereof. Although there are no specific limitations to the materials for the base  212  insofar as the materials can be etched, silicon or quartz is preferable because projections can be formed by etching with high precision. 
   As a material for forming the resist layer  214 , for example, a commercially available positive resist which is normally used in the manufacture of a semiconductor device, and is obtained by compounding a diazonaphthoquinone derivative as a photosensitive agent with a cresol/novolak resin can be used. When the positive resist is exposed to radiation through a mask with a given pattern, the area exposed to radiation can be selectively removed by a developer. 
   As a method of forming the resist layer  214 , a spin coating method, dipping method, spray coating method, roll coating method, bar coating method, or the like can be used. 
   A mask  216  is then placed above the resist layer  214  and a predetermined area of the resist layer  214  is exposed to radiation  218  through the mask  216 , as shown in FIG.  8 B. The mask  216  has a pattern not to allow the areas required for the formation of projections  222  (see  FIG. 9B ) to be exposed to the radiation  218 . Radiation shielding area of the mask  216  has a frame-like shape corresponding to the shape of a black matrix. The black matrix has a shape according to the pixel arrangement such as a mosaic arrangement, delta arrangement, or stripe arrangement. 
   As the radiation, light having a wavelength from 200 nm to 500 nm is preferable. If light having this wavelength range is used, photolithographic technology established in the manufacture of a liquid crystal panel and the facilities used for this technology can be utilized, thereby reducing production costs. 
   After the resist layer  214  is exposed to the radiation  218 , the areas  217  exposed to the radiation  218  in the resist layer  214  are selectively removed by being developed under predetermined conditions, and part of the surface of the base  212  is exposed. The other part of the base is kept to be covered by the residual resist layer  214 , as shown in FIG.  8 C. 
   Each portion of the patterned resist layer  214  is softened by heating to be tapered at the side due to surface tension, as shown in FIG.  8 D. 
   The base  212  is then etched to a predetermined depth by an etchant  220  using the remaining resist layer  214  as a mask, as shown in FIG.  8 D. Specifically, dry etching such as anisotropy etching, for example, reactive ion etching (RIE) is performed. 
   Since each portion of the remaining resist layer  214  is tapered at the side, as the resist layer  214  is gradually reduced in size by etching, the base  212  is gradually exposed. The exposed area is continuously etched. Because the base  212  is continuously and gradually etched, projections each having a trapezoidal cross section are formed on the base  212  after etching, as shown in FIG.  9 A. 
   After removing the residual resist layer  214  on the projections  222  if necessary, a master mold  224  is obtained. 
   According to the present embodiment, each of the projections  222  on the master mold  224  has a trapezoidal cross section. By using the master mold  224  instead of the master mold  20  shown in  FIG. 1 , the recesses  202  in which the side thereof is tapered so that the opening is wider than the bottom can be formed. The recesses  202  can be reliably and easily filled with the shading material  42 . Therefore, the ink jet head can be controlled with ease and the manufacturing yield increases. 
   According to this embodiment, the master mold  224  is economical because it can be used repeatedly as long as durability permits. Moreover, the step of manufacturing the master mold  224  can be omitted in the manufacture of the second or subsequent microlens arrays, thereby reducing the number of steps as well as production costs. 
   In this embodiment, a positive resist is used for forming the recesses  222  on the substrate  212 . Alternatively, a negative resist may be used. When the negative resist is exposed to radiation through a mask with a given pattern, the areas exposed to the radiation are insolubilized, and the areas not exposed to the radiation can be selectively removed by a developer. In this case, a mask having a pattern which is the inverse of the pattern of the mask  216  is used. Alternatively, a resist may be directly exposed to laser beams or electron beams for patterning without using a mask. 
   If the side of the patterned resist layer  214  can be tapered as shown in  FIG. 8D  by adjusting the developing conditions, the step of heating the resist layer  214  may be omitted. 
     FIG. 10  illustrates a modification of the mask. A mask  240  shown in  FIG. 10  is a half-tone mask having a radiation transmitting area  242 , radiation shielding area  244 , and semi-radiation transmitting area  246  for the radiation  238 . The semi-radiation transmitting area  246  is formed so that the farther away from the radiation shielding area  244 , the greater amount of the radiation  238  passes therethrough. The transmittance is changed by changing the thickness of the shielding material which forms the semi-radiation transmitting area  246  in FIG.  10 . It is also possible to change the transmittance by changing shading of the semi-radiation transmitting area  246 . By using the mask  240 , the radiation  238  passes through the semi-radiation transmitting area  246  while being attenuated to expose the resist layer  234 . Specifically, the radiation  238  passes through the radiation transmitting area  246  such that the attenuation factor becomes greater from the radiation transmitting area  242  to the shielding area  244 . As a result, because degree of exposure to the radiation  238  decreases closer to the shielding area  244 , the area  237  is exposed to the radiation and the resist layer  234  having a tapered side remains, as shown in  FIG. 10. A  resist layer having a tapered side can be thus formed in this manner. 
   (Fourth Embodiment) 
     FIGS. 11-14C  illustrate a microlens array substrate according to a fourth embodiment of the present invention and a method of manufacturing thereof. In the present embodiment, a microlens array substrate  300  shown in  FIG. 11  is manufactured. The microlens array substrate  300  differs from the microlens array substrate  32  shown in  FIG. 2B  in the shape of recesses  302 . Specifically, only the opening edge of the side of the recesses  302  is tapered. Because the opening of the recess  302  in which the opening edge is tapered is wider than the bottom, the recess can be reliably filled with the shading material  42  (see FIG.  2 B), even if the pixels are densely arranged. A master mold having projections each having a tapered side at the base is used to form the recesses  202 . 
     FIGS. 12A-14C  illustrate a process of forming a master mold used for forming the recesses  302 . 
   A mask layer  314  is formed on a base  312  as shown in FIG.  12 A. There are no specific limitations to the materials for the base  312  insofar as the materials can be etched, but silicon or quartz is preferable because etching can be easily performed with high precision. 
   As the mask layer  314 , a material which can be firmly secured to the base  312  and difficult to be separated is preferable. For example, if the base  312  is formed of silicon, a silicon oxide film (SiO 2 ) formed by the thermal oxidation of the surface of the base  312  can be used as the mask layer  314 . The mask layer  314  is thus firmly secured to the base  312 . If the base  312  is formed of a metal, quartz, glass, or silicon, a film of any one of Al, Ni, Cr, W, Pt, Au, Ir, and Ti may be formed on the surface and used as the mask layer  314 . 
   A resist layer  316  is then formed on the mask layer  314  on the base  312 , as shown in FIG.  12 B. As a material of the resist layer  316  and the formation method thereof, the materials and the formation method which can be applied to the third embodiment can be used. 
   A mask  318  is placed above the resist layer  316  and a predetermined area of the resist layer  316  is exposed to radiation  320  through the mask  318 , as shown in FIG.  12 C. The mask  318  is patterned such that the radiation  320  passes through the area required for forming projections  334  of a master mold  332  (see  FIG. 14C ) which is finally manufactured. Radiation transmitting area of the mask  318  have a frame-like shape corresponding to the shape of a black matrix. The black matrix has a shape according to the pixel arrangement such as a mosaic arrangement, delta arrangement, or stripe arrangement. As the radiation, light having a wavelength from 200 nm to 500 nm is preferable. 
   After the resist layer  316  is exposed to the radiation  320 , the areas  317  exposed to the radiation  320  in the resist layer  316  are selectively removed by being developed under predetermined conditions to expose part of the surface of the mask layer  314 , and the other part of the mask layer  314  is kept to be covered by the residual resist layer  316 , as shown in FIG.  12 D. 
   Each portion of the patterned resist layer  316  is softened by heating to be tapered at the side due to surface tension, as shown in FIG.  12 E. 
   The mask layer  314  is then etched by an etchant  322  using the resist layer  316  with the tapered side as a mask, as shown in FIG.  12 E. Specifically, dry etching such as anisotropy etching, for example, reactive ion etching (RIE) is performed. 
   Since each portion of the remaining resist layer  316  is tapered at the side, as the resist layer  316  is gradually reduced in size by etching, the mask layer  314  is gradually exposed, and the exposed area is continuously etched. Because the mask layer  314  is thus continuously and gradually etched, the mask layer  314  is divided into portions each having a trapezoidal cross section, as shown in FIG.  13 A. Part of the base  312  under the mask layer  314  is also exposed. Specifically, exposed part of the base  312  surrounds each portion of the mask layer  314 . The exposed part has a frame-like shape corresponding to the shape of a black matrix. The black matrix has a shape according to the pixel arrangement such as a mosaic arrangement, delta arrangement, or stripe arrangement. It is preferable to terminate etching at the time when part of the surface of the base  312  is exposed. 
   After removing the remaining resist layer  316  on the mask layer  314 , if necessary, the exposed part of the base  312  is etched by an etchant  324 , as shown in FIG.  13 B. 
   In this case, the etching is high anisotropy etching in which etching proceeds perpendicularly to the surface of the base  312 , and is highly selective etching in which the base  312  is etched but the mask layer  314  is scarcely etched. 
   After etching, recesses  326  which are used for forming a master mold are formed in the base  312 , as shown in FIG.  13 C. The recesses  326  for forming a master mold have a frame-like shape corresponding to the shape of a black matrix. The black matrix has a shape according to the pixel arrangement such as a mosaic arrangement, delta arrangement, or stripe arrangement. 
   There are portions of the mask layer  314  each having a trapezoidal cross section on projections  325  surrounded by the recesses  326  for forming a master mold. The side of the projections  325  is vertical, and the side of each portion of the residual mask layer  314  is tapered. Therefore, the side of each recess  326  stand up vertically from the bottom and reversely-tapered at the opening edge so that its diameter gradually increased. 
   A metal film  328  is then formed to cover the surface of the base  312  on which the recesses  326  for forming a master mold are formed, as shown in  FIG. 14A , thereby making the surface electrically conductive. The metal film  328  may be formed of, for example, nickel (Ni) with a thickness from 500 to 1000 angstroms (10 −1  m). The metal film  328  can be formed by various methods such as sputtering, CVD, vapor deposition, or electroless plating. If the surface of the base  312  exhibits conductivity required for forming a metal layer using an electroforming method in the subsequent step, the electro-conduction treatment is not required. 
   Ni is further electrodeposited by an electroforming method using the metal film  328  as a negative electrode and chip-like or globular Ni as a positive electrode to form a thick metal layer  330 , as shown in FIG.  14 B. An example of an electroplating solution is shown as follows. 
   Nickel sulfamate: 550 g/l 
   Boric acid: 35 g/l 
   Nickel chloride: 5 g/l 
   Leveling agent: 20 mg/l 
   The metal film  328  and the metal layer  330  are removed from the base  312  as shown in  FIG. 14C , followed by washing as required, to obtain a master mold  332 . The metal film  328  may be removed from the master mold  332  by performing a removal treatment, as required. 
   On the master mold  332 , there are projections  334  corresponding to the recesses  326  for forming a master mold of the base  312 . Since the side of the recess  326  is reversely-tapered at the opening edge to increase the diameter gradually, the side of the projection  334  is tapered at the base and the diameter gradually becomes smaller in the direction toward the end. 
   According to the present embodiment, the projections  334  of the master mold  332  have the above-described shape. By using this master mold  332  instead of the master mold  20  in  FIG. 1 , the recesses  302  each having a side reversely-tapered to increase the diameter toward the opening edge can be formed. The recesses  302  can be filled with the shading material  42  reliably and easily. Therefore, the ink jet head can be controlled with ease and the manufacturing yield increases. 
   According to this embodiment, the master mold  332  is economical because it can be used repeatedly as long as durability permits. Moreover, the step of manufacturing the master mold  332  can be omitted in the manufacture of the second or subsequent microlens arrays, thereby reducing the number of steps as well as production costs. 
     FIG. 15  illustrates part of a liquid crystal projector to which the present invention is applied. This liquid crystal projector comprises a light valve  1  into which the microlens array substrate  132  manufactured by the method according to the second embodiment is incorporated and a lamp  2  as a light source. 
   The microlens array substrate  132  is placed so that the lenses  134  are concave as seen from the lamp  2 . A transparent common electrode  162  and an alignment film  164  are laminated on the reinforcing plate  148  on the side of the shading layer  138  as a black matrix. 
   A TFT substrate  174  is provided on the light valve  1  such that there is a gap between the TFT substrate  174  and the alignment film  164 . A transparent discrete electrode  170  and a thin film transistor  172  are provided on the TFT substrate  174  and an alignment film  168  is formed thereon. The TFT substrate  174  is placed such that the alignment film  168  faces the alignment film  164 . 
   A liquid crystal  166  is sealed between the alignment films  164  and  168  and is driven by applying voltage controlled by the thin film transistor  172 . 
   This liquid crystal projector can display a bright image because light  3  emitted from the lamp  2  is converged on each pixel by each lens  134 . Moreover, because the shading layer  138  functions as a black matrix, contrast between pixels can be improved.