Patent Publication Number: US-2011069385-A1

Title: Screen

Description:
BACKGROUND 
     1. Technical Field 
     The present invention relates to a screen which reflects projection light obliquely supplied from a projection device such as a projector for display of a projection image. 
     2. Related Art 
     An example of a known projection image reflecting screen which reflects light obliquely supplied from below to display an image such that the image can be viewed on the front surface side of the screen has a number of concaves or convexes on a screen substrate (for example, see JP-A-2009-15195). This screen has a reflection surface for reflecting projection light on a surface of each concave or convex in correspondence with the position of the projection supplied from a projection device such as a projector. In addition, the directions of the concaves or convexes provided on the screen substrate and disposed adjacent to one another in the vertical direction deviate from the horizontal direction of the screen substrate, which allows reflection of a large quantity of light obliquely supplied from below. 
     According to the screen disclosed in JP-A-2009-15195, however, a part of the projection light is blocked by projections formed by the adjoining concaves when the angle formed by the projection light from the projector and the screen normal line (angle of incidence) becomes a certain angle or larger. In this case, there is a possibility that loss of view in the image such as local light reduction is produced. 
     SUMMARY 
     It is an advantage of some aspects of the invention to provide a screen capable of reducing the possibility of blocking projection light and capable of decreasing loss of view. 
     A screen according to an aspect of the invention includes: a screen substrate; a first area disposed on the screen substrate and containing a first main line which has a plurality of first concaves for reflecting light and a first supplementary line which is disposed on the screen substrate at a position adjacent to the first main line and has the same number of second concaves as that of the first concaves formed adjacent to the second concaves, the first main line and the first supplementary line being alternately and repeatedly arranged; and a second area disposed on the screen substrate in a region where an angle of incidence of projection light with respect to the screen substrate becomes larger than in the first area and containing a second main line which has a plurality of third concaves for reflecting light and a second supplementary line which is disposed on the screen substrate at a position adjacent to the second main line and has a larger number of fourth concaves as that of the third concaves formed adjacent to the fourth concaves, the second main line and the second supplementary line being alternately and repeatedly arranged. 
     According to this screen, the first and second supplementary lines are provided as well as the first and second main lines. Thus, even when the angle of incidence of the projection light is large, a sufficient amount of the projection light can be supplied to the surfaces of the first and third concaves for reflection. Moreover, since the number of the fourth concaves on the second supplementary line is larger than the number of the third concaves on the second main line in the second area where the angle of incidence becomes relatively large, each height of projections formed by the third concave and the fourth concave adjacent to the third concave or the fourth concave and by a pair of the fourth concaves adjacent to each other becomes smaller than each height of the corresponding projections in the structure including the same number of the fourth concaves as that of the third concaves similarly to the first area. Thus, even when the angle of incidence of the projection light is larger in the second area than in the first area, the projection light is prevented from being blocked by the projections. Accordingly, loss of view can be reduced. 
     In a specific aspect of the invention, a reflection portion is formed at least on a part of each surface of the first concaves and the third concaves to reflect the projection light by the reflection portion to the front surface side. The portion other than the part having the reflection portion on each surface of the first concaves and the third concaves and each surface of the second concaves and the fourth concaves absorb or transmit the projection light. The portion other than the part having the reflection portion on each of the first concaves and the third concaves which reflects the projection light to the front surface side and each of the second concaves and the fourth concaves, i.e., the portions not intending to receive the projection light absorb the outside light or the like, for example, to improve the contrast of an image reflected by the screen. 
     In another aspect of the invention, at least a part of each of the first main line, the first supplementary line, the second main line, and the second supplementary line has a circular-arc shape. Since the first main line, the first supplementary line, the second main line, and the second supplementary line are circular-arc-shaped, the arrangements and shapes of the concaves contained in these lines can be matched with the entrance positions of the projection light. Thus, the projection light can be reflected in an adequate condition. It is preferable that the respective lines are alternately disposed on the screen substrate with no clearance left between one another. 
     In still another aspect of the invention, in the second area close to the boundary between the second area and the first area, the distance between at least a pair of the fourth concaves adjacent to the same third concave increases as the angle of incidence of the projection light with respect to the screen substrate becomes larger. Since the distance between the fourth concaves adjacent to each other in the second area close to the boundary between the second area and the first area gradually increases as the positions of the fourth concaves shift away from the first area, unevenness in switching in the boundary between the first area and the second area is not produced. It is assumed herein that the single third concave and at least a pair of the fourth concaves disposed for the corresponding third concave on the entrance side of the projection light are considered as a unit. The unevenness in switching herein refers to light unevenness observed as stepped or moiré pattern due to non-uniform change of apparent reflectance caused by different arrangements of the concaves in the two areas. 
     In yet another aspect of the invention, the number of the fourth concaves contained in the second supplementary line in the second area close to the boundary between the second area and the first area increases as the angle of incidence of the projection light with respect to the screen substrate becomes larger. Since the number of the fourth concaves in the second area close to the boundary between the second area and the first area gradually increases as the positions of the fourth concaves shift away from the first area, unevenness in switching in the boundary between the first area and the second area is not produced. 
     In still yet another aspect of the invention, the clearance between the first main line and the first supplementary line and the clearance between the second main line and the second supplementary line increase as the angle of incidence of the projection light with respect to the screen substrate becomes larger. In this case, the visibility angle can be secured even when the angle of incidence of the projection light with respect to the screen substrate is large. 
     In further another aspect of the invention, the screen further includes a third area disposed on the screen substrate in a region where the angle of incidence of the projection light with respect to the screen substrate becomes smaller than in the first area and containing a third main line which has a plurality of fifth concaves and reflects light by at least a part of each of the fifth concaves. In this case, the projection light can be efficiently reflected in the region where the angle of incidence of the projection light is small. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1A  is a front view of a screen according to a first embodiment, and  FIG. 1B  is a side view of the screen shown in  FIG. 1A . 
         FIG. 2A  illustrates an enlarged part of a first area of the screen, and  FIG. 2B  is a perspective view of the area shown in  FIG. 2A . 
         FIG. 3  schematically illustrates an arrangement pattern of concaves in the first area shown in  FIGS. 2A and 2B . 
         FIG. 4  is a cross-sectional view taken along a line A-A in  FIGS. 2A and 2B . 
         FIGS. 5A through 5D  illustrate changes of distances between concaves disposed in a direction perpendicular to arrangement lines. 
         FIG. 6A  illustrates an enlarged part of a second area of the screen, and  FIG. 6B  is a perspective view of the area shown in  FIG. 6A . 
         FIG. 7  schematically illustrates an arrangement pattern of concaves in the second area shown in  FIGS. 6A and 6B . 
         FIG. 8  is a cross-sectional view taken along a line B-B in  FIGS. 6A and 6B . 
         FIG. 9  schematically illustrates an arrangement pattern of concaves in a transition area. 
         FIG. 10  schematically illustrates an arrangement pattern of concaves in a third area. 
         FIG. 11  is a cross-sectional view of the third area shown in  FIG. 10  in the direction of projection light. 
         FIGS. 12A and 12B  are cross-sectional views showing the relationship between the concaves and the projection light. 
         FIG. 13  schematically illustrates an arrangement pattern of concaves in a transition area of the screen in a second embodiment. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     First Embodiment 
     A screen according to a first embodiment of the invention is hereinafter described with reference to the drawings. In the respective figures, a Z axis corresponds to the normal line direction of a screen  1 , a Y axis corresponds to the vertical direction crossing the Z axis at right angles and extending in parallel with the screen  1 , and an X axis corresponds to the horizontal direction crossing the Z axis at right angles and extending in parallel with the screen  1 . 
     As illustrated in  FIGS. 1A and 1B , the screen  1  is a reflection type screen which receives projection light PL from a projector  2  disposed below and in front of the screen  1  and supplies the projection light PL toward the front, i.e., the front surface side of the screen  1  (+Z axis direction) as reflection light RL. 
     The screen  1  includes a screen substrate  4  as a support body, and a surface portion  3  having a plurality of concaves  20  (see  FIGS. 2A ,  6 A, and other figures to be referred to later). 
     The screen substrate  4  is a sheet-shaped component made of materials containing light absorbing material. The light absorbing material is black polyvinyl chloride, black PET (polyethylene terephthalate) or the like, which allows the screen substrate  4  to absorb outside light OL and others. 
     The surface portion  3  is a layered portion having a base material constituted by the same light absorbing material as that of the screen substrate  4 . The surface portion  3  is provided throughout a surface  4   a  of the screen substrate  4  in the form of a skin, and is divided into sections of a first area AR 1 , a second area AR 2 , and a third area AR 3 . The first area AR 1 , the second area AR 2 , and the third area AR 3  are provided in correspondence with the ranges of angles of incidence θ 1 , θ 2 , and θ 3  (θ 3 &lt;θ 1 &lt;θ 2 ) of the projection light PL with respect to the screen substrate  4 , and are successively disposed such that the projection position of the projection light PL changes from the third area AR 3  to the first area AR 1  and further to the second area AR 2  as the angle of incidence increases from θ 3  to θ 1  and further to θ 2 . Since the first through third areas AR 1  through AR 3  are provided in correspondence with the angles of incidence θ 1 , θ 2 , and θ 3 , the boundaries between the respective areas AR 1 , AR 2 , and AR 3  have circular-arc shapes. It is assumed herein that the angles of incidence θ 1 , θ 2 , and θ 3  are angles formed by the normal line of a plane extending along the screen substrate  4  and the beam of the projection light PL. 
     Each of the first area AR 1 , the second area AR 2 , and the third area AR 3  has minute concave and convex structure on a surface (projection surface)  3   a  considering the angles of incidence θ 1 , θ 2 , and θ 3  of the projection light PL. That is, the plural concaves  20  provided in the respective areas have different shapes and different arrangements for each of the three areas AR 1 , AR 2 , and AR 3 . For example, the minute concave and convex structure as the arrangement condition of the concaves  20  gradually changes in accordance with the successively changeable angles of incidence θ 1  and θ 2  in the first and second areas AR 1  and AR 2  so as to secure view in each part of the screen  1  (secure a condition not containing loss of pixels as viewed from an observer). In addition, since the arrangement condition of the concaves  20  gradually changes in the first area AR 1 , unevenness in switching between the first area AR 1  and the third area AR 3  is not produced. A transition area ARx having modified minute concave and convex structure as the arrangement condition of the concaves  20  is provided in the second area AR 2  in the vicinity of the boundary between the second area AR 2  and the first area AR 1  so as to reduce unevenness in switching between the areas AR 2  and AR 1 . 
     Each of the concaves  20  provided in each of the first area AR 1 , the second area AR 2 , and the third area AR 3  basically has a spherical surface having substantially the same curvature (see  FIGS. 4 ,  8 ,  11 , and other figures to be referred to later), and is disposed adjacent to one another on substantially circular-arc-shaped curves (more specifically, arrangement lines R 1 , R 3 , and R 5 ) whose centers located at a reference point O of the screen  1 . The reference point O lies on a vertical line passing the center of the screen substrate  4  and extending in the Y axis direction, and corresponds to a cross point of an extension plane of the projection surface  3   a  of the screen  1  and an optical axis OA of a projection system of the projector  2 . 
       FIGS. 2A and 2B  illustrate an enlarged part of the first area AR 1  on the surface portion  3 .  FIG. 3  schematically illustrates an arrangement pattern of the concaves  20  shown in  FIGS. 2A and 2B .  FIG. 4  is a cross-sectional view taken along a line A-A in  FIG. 2A  in the direction of the projection light. In  FIGS. 2A and 2B , the projection light PL travels in the direction of the line A-A from the projector  2 . 
       FIG. 3  is a schematic illustration for explaining first main lines Lm 1  and first supplementary lines Ls 1  formed by the concaves  20 , and shows a condition in which first and second concaves  20   a  and  20   b  are arranged along the linear arrangement lines R 1  and R 2 . However, when viewed macroscopically, the first main lines Lm 1  and the first supplementary lines Ls 1  have a number of the first and second concaves  20   a  and  20   b  along the arrangement lines R 1  and R 2  extending in circular-arc shapes. In  FIG. 3 , the first and second concaves  20   a  and  20   b  have hemispherical shapes and are disposed with a clearance between one another for easy understanding of the explanation. In fact, however, the first and second concaves  20   a  and  20   b  are disposed such that the outer circumferences of the hemispherical shapes have overlaps with one another, the overlaps are removed to locate the concaves adjacent to one another. 
     As can be seen from  FIG. 3 , a center distance x 1  between each adjoining pair of the first concaves  20   a  on each of the first main lines Lm 1  is substantially uniform. Similarly, a center distance x 2  between each adjoining pair of the second concaves  20   b  on each of the first supplementary lines Ls 1  is substantially uniform. In fact, the first and second concaves  20   a  and  20   b  are disposed along the arrangement lines R 1  and R 2  with no clearance left between one another as illustrated in  FIG. 2A  and other figures. 
     The first area AR 1  has the first main lines Lm 1  and the first supplementary lines Ls 1  alternately and repeatedly disposed in a direction crossing the line arrangement directions. Each of the first main lines Lm 1  is paired with the first supplementary line Ls 1  positioned adjacent to the corresponding first main line Lm 1  on the surface portion  3  on the entrance side of the projection light PL (i.e., on the projector  2  side and approximately on the −Y axis direction side). As illustrated in  FIG. 3  and other figures, the number of the second concaves  20   b  forming each of the first supplementary lines Ls 1  in the first area AR 1  is the same as the number of the first concaves  20   a  forming the first main line Lm 1  paired with the corresponding first supplementary line Ls 1 . The first concave  20   a  and the second concave  20   b  adjacent to each other in a direction substantially perpendicular to the arrangement lines R 1  and R 2  on the paired first main line Lm 1  and first supplementary line Ls 1  constitute a unit UN containing the first and second concaves  20   a  and  20   b  with a ratio of approximately 1:1. For easy understanding of the explanation, the single first concave  20   a  on one of the first main lines Lm 1  and the single second concave  20   b  disposed adjacent to the corresponding first concave  20   a  on the entrance side of the projection light PL on the first supplementary line Ls 1  disposed adjacent to the corresponding first main line Lm 1  are determined as the unit UN which is regarded as a set in view of optical functions. The second concave  20   b  in the one unit UN has a function of securing an optical path through which the projection light PL enters the corresponding first concave  20   a  (see  FIG. 4 ). 
     The clearance between the paired lines Lm 1  and Ls 1  as the unit UN, and the interval between the first main lines Lm 1  and Lm 1  with the first supplementary line Ls 1  sandwiched therebetween, i.e., the pitch of the first main lines Lm 1  are now explained with reference to  FIGS. 5A and 5B . The clearance between the paired lines Lm 1  and Ls 1  and the pitch of the first main lines Lm 1 , strictly speaking, become larger as the angle of incidence θ 1  of the projection light PL with respect to the screen substrate  4  increases. 
       FIG. 5A  illustrates the first main line Lm 1  and the first supplementary line Ls 1  in a region where the angle of incidence θ 1  of the projection light PL is relatively small within the first area AR 1 .  FIG. 5B  illustrates the first main line Lm 1  and the first supplementary line Ls 1  in a region where the angle of incidence θ 1  of the projection light P 1  is relatively large within the first area AR 1 . A clearance h 2  between the paired first main line Lm 1  and first supplementary line Ls 1  in the region where the angle of incidence θ 1  of the projection light PL is relatively large becomes larger than a clearance h 1  between the paired first mainline Lm 1  and first supplementary line Ls 1  in the region where the angle of incidence θ 1  of the projection light PL is relatively small. Similarly, an interval (pitch) c 2  in the region where the angle of incidence θ 1  of the projection light PL is large becomes larger than an interval (pitch) c 1  in the region where the angle of incidence θ 1  is small. 
     In the area AR 1 , the clearance h 1  is set at zero in a region close to the boundary between the area AR 1  and the third area AR 3  (a region where the angle of incidence θ 1  is smaller), and the clearance between the paired lines Lm 1  and Ls 1  and the pitch of the first main lines Lm 1  gradually become larger as the position shifts away from the third area AR 3 . This structure prevents unevenness in switching between the first area AR 1  and the third area AR 3 . 
     The circular-arc curves along which the first main lines Lm 1  and the first supplementary lines Ls 1  are disposed (the arrangement lines R 1 , R 3 , and R 5 ) are not limited to “circular” shapes but may “elliptic” shapes, “freely curved” shapes, or combinations of these shapes. In addition, the arrangement lines R 1 , R 3 , and R 5  may be combinations of straight lines and curves constituting the “elliptic” shapes or the “freely curved” shapes. 
     Reflection films RS formed on the first concaves  20   a  are now explained with reference to  FIG. 4 . According to each structure of the first concaves  20   a , at least a part of the surface of the first concave  20   a  reflects the projection light PL toward the front, and the other part absorbs or transmits the outside light. More specifically, as can be seen from  FIG. 4 , the reflection film RS for reflecting the projection light PL is formed at a position for receiving the projection light PL from the projector  2  on a part of each surface Su 1  of the first concaves  20   a . On the other hand, the portion of the first concave  20   a  on which the reflection film RS is not formed absorbs entering light by the properties of the base material of the surface portion  3  and the screen substrate  4 . Thus, each of the first concaves  20   a  reflects the projection light PL supplied from below the screen  1  toward the observer side (toward the front of the screen  1 ) as the reflection light RL, and does not reflect the outside light OL supplied from above toward the observer side. 
     As can be seen from  FIG. 4 , the reflection film RS is not formed on each surface Su 2  of the second concaves  20   b . Thus, the second concaves  20   b  can absorb entering light by the properties of the base material of the surface portion  3  and the screen substrate  4 . 
     The second area AR 2  is now described. As illustrated in  FIG. 1B , the second area AR 2  is disposed in the area where the angle of incidence of the projection light PL with respect to the screen  1  becomes larger than in the first area AR 1 . 
       FIGS. 6A and 6B  illustrate an enlarged part of the second area AR 2  on the surface portion  3 .  FIG. 7  schematically illustrates an arrangement pattern of the concaves  20  shown in  FIGS. 6A and 6B .  FIG. 8  is a cross-sectional view taken along a line B-B in the direction of the projection light shown in  FIG. 6A . In  FIGS. 6A and 6B , the projection light PL travels in the direction of the line B-B from the projector  2 . 
       FIG. 7  is a schematic and enlarged illustration for explaining second main lines Lm 2  and second supplementary lines Ls 2  formed by the concaves  20 , and shows a condition in which third and fourth concaves  20   c  and  20   d  are arranged along the linear arrangement lines R 3  and R 4 . However, when viewed macroscopically, the second main lines Lm 2  and the second supplementary lines Ls 2  have a number of the third and fourth concaves  20   c  and  20   d  along the arrangement lines R 3  and R 4  extending in circular-arc shapes. In  FIG. 7 , the third and fourth concaves  20   c  and  20   d  have hemispherical shapes and are disposed with a clearance between one another for easy understanding of the explanation. In fact, however, the third and fourth concaves  20   c  and  20   d  are disposed such that the outer circumferences of the hemispherical shapes have overlaps with one another, the overlaps are removed to locate the concaves adjacent to one another. 
     As can be seen from  FIG. 7 , a center distance x 3  between each adjoining pair of the third concaves  20   c  on each of the second main lines Lm 2  is substantially uniform. Similarly, a center distance x 4  between each adjoining pair of the fourth concaves  20   d  on each of the second supplementary lines Ls 2  is substantially uniform. In fact, the third and fourth concaves  20   c  and  20   d  are disposed along the arrangement lines R 3  and R 4  with no clearance left between one another as illustrated in  FIG. 6A  and other figures. 
     The second area AR 2  has the second main lines Lm 2  and the second supplementary lines Ls 2  alternately and repeatedly disposed in a direction crossing the line arrangement directions. Each of the second main lines Lm 2  is paired with the second supplementary line Ls 2  positioned adjacent to the corresponding second main line Lm 2  on the surface portion  3  on the entrance side of the projection light PL (i.e., on the projector  2  side and approximately on the −Y axis direction side). As illustrated in  FIG. 7 , the number of the fourth concaves  20   d  forming each of the second supplementary lines Ls 2  in the second area AR is larger than the number of the third concaves  20   c  forming the second main line Lm 2  paired with the corresponding second supplementary line Ls 2 . In this embodiment, the third concave  20   c  and the fourth concave  20   d  adjacent to each other in a direction substantially perpendicular to the arrangement lines R 3  and R 4  on the paired second main line Lm 2  and second supplementary line Ls 2  constitute the unit UN containing the third and fourth concaves  20   c  and  20   d  with a ratio of approximately 1:2. For easy understanding of the explanation, the single third concave  20   c  on one of the second main lines Lm 2  and a pair of the fourth concaves  20   d  disposed adjacent to the corresponding third concave  20   c  on the entrance side of the projection light PL on the second supplementary line Ls 2  disposed adjacent to the corresponding second main line Lm 2  are determined as the unit UN which is regarded as a set in view of optical functions (see  FIG. 6A  and other figures). The pair of the fourth concaves  20   d  in the one unit UN have a function of securing an optical path through which the projection light PL enters the corresponding single third concave  20   c  (see  FIG. 8 ). 
     The clearance between the paired lines Lm 2  and Ls 2 , and the interval of the second main lines Lm 2  and Lm 2  with the second supplementary line Ls 2  sandwiched therebetween, i.e., the pitch of the second main lines Lm 2  are now explained with reference to  FIGS. 5C and 5D . The clearance between the paired lines Lm 2  and Ls 2  and the pitch of the second main lines Lm 2 , strictly speaking, become larger as the angle of incidence θ 2  of the projection light PL with respect to the screen substrate  4  increases. 
       FIG. 5C  illustrates the second main line Lm 2  and the second supplementary line Ls 2  in a region where the angle of incidence θ 2  of the projection light PL is relatively small within the second area AR 2 .  FIG. 5D  illustrates the second main line Lm 2  and the second supplementary line Ls 2  in a region where the angle of incidence θ 2  of the projection light PL is relatively large within the second area AR 2 . A clearance h 4  between the paired second main line Lm 2  and second supplementary line Ls 2  in the region where the angle of incidence θ 2  of the projection light PL is relatively large becomes larger than a clearance h 3  between the paired second main line Lm 2  and second supplementary line Ls 2  in the region where the angle of incidence θ 2  of the projection light PL is relatively small. Similarly, as for the pitch of the second main lines Lm 2 , an interval (pitch) c 4  in the region where the angle of incidence θ 2  of the projection light PL is relatively large becomes larger than an interval (pitch) c 3  in the region where the angle of incidence θ 2  of the projection light PL is relatively small. 
     The reflection films RS formed on the third concaves  20   c  are now explained with reference to  FIG. 8 . According to each structure of the third concaves  20   c , at least a part of the surface of the third concave  20   c  reflects the projection light PL toward the front, and the other part absorbs or transmits the outside light. More specifically, as can be seen from  FIG. 8 , the reflection film RS reflecting the projection light PL is formed at a position for receiving the projection light PL from the projector  2  on each surface Su 3  of the third concaves  20   c . On the other hand, the portion of the third concave  20   c  on which the reflection film RS is not formed absorbs entering light by the properties of the base material of the surface portion  3  and the screen substrate  4 . That is, each of the third concaves  20   c  reflects the projection light PL supplied from below the screen  1  toward the observer side as the reflection light RL, and does not reflect the outside light OL supplied from above toward the observer side. 
     As can be seen from  FIG. 8 , the reflection film RS is not formed on each surface Su 4  of the fourth concaves  20   d . Thus, the fourth concaves  20   d  can absorb entering light by the properties of the base material of the surface portion  3  and the screen substrate  4 . 
       FIG. 9  schematically illustrates an arrangement pattern of the concaves  20  in the transition area ARx provided in the second area AR 2  in the vicinity of the boundary between the second area AR 2  and the first area AR 1 . In the transition area ARx, the numbers of the third concaves  20   c  and the fourth concaves  20   d  constituting the one unit UN has a ratio of approximately 1:2, but the central distance between a pair of the fourth concaves  20   d  corresponding to the single third concave  20   c  is different. More specifically, as illustrated in  FIG. 9 , the central distance between the adjoining fourth concaves  20   d  within the one unit UN increases toward a relatively upper region (+Y axis direction), i.e., as the angle of incidence θ 2  of the projection light PL with respect to the screen substrate  4  becomes larger. In this case, central distances x 5 , x 6 , x 7  and x 8  between the respective adjoining pairs of the fourth concaves  20   d  shown in  FIG. 9  satisfy a relation x 5 &lt;x 6 &lt;x 7 &lt;x 8 . For example, in case of the second supplementary line Ls 2  closest to the first area AR 1 , the central distance x 5  between the adjoining fourth concaves  20   d  provided thereon within the same unit UN is substantially zero, producing an almost overlapping condition of the pair of the fourth concaves  20   d  in appearance. In case of the second supplementary line Ls 2  farthest from the first area AR 1 , however, the central distance x 8  of the adjoining fourth concaves  20   d  provided thereon within the same unit UN is approximately half of the central distance x 3  of the third concaves  20   c  in the adjoining two units UN. 
       FIG. 10  schematically illustrates an arrangement pattern of the concaves  20  in the third area AR 3 .  FIG. 11  is a cross-sectional view of the third area AR 3  in the direction of the projection light. The third area AR 3  has third main lines Lm 3 . Each of the third main lines Lm 3  has a number of fifth concaves  20   e  along the arrangement lines R 5  extending in circular-arc shapes in macroscopic view. A central distance x 9  between each adjoining pair of the fifth concaves  20   e  is substantially uniform. In fact, the fifth concaves  20   e  are disposed such that the outer circumferences of the hemispherical shapes have overlaps with one another, the overlaps are removed to locate the concaves adjacent to one another with no clearance left therebetween. As illustrated in  FIG. 11 , the reflection film RS reflecting the projection light PL is formed on each surface Su 5  of the fifth concaves  20   e  in a position for receiving the projection light PL from the projector  2 . On the other hand, the portion of the fifth concave  20   e  on which the reflection film RS is not formed absorbs entering light by the properties of the base material of the surface portion  3  and the screen substrate  4 . That is, the fifth concave  20   e  reflects the projection light PL supplied from below the screen  1  toward the observer side as the reflection light RL, and does not reflect the outside light OL supplied from above toward the observer side. 
     According to this structure, the first main lines Lm 1  in the first area AR 1  and the second main lines Lm 2  in the second area AR 2  are disposed such that the relation of the clearances h 1 &lt;h 2 &lt;h 3 &lt; 4  holds as illustrated in  FIGS. 5A through 5D . Thus, the density of the first main lines Lm 1  in the first area AR 1  is higher than the density of the second main lines Lm 2  in the second area AR 2 . 
     As can be seen from  FIGS. 3 ,  7 , and  10 , the distances x 1 , x 3 , and x 9  between the concaves  20   a ,  20   c , and  20   e  on the first main line Lm 1  in the first area AR 1 , the second main line Lm 2  in the second area AR 2 , and the third main line Lm 3  in the third area AR 3  are substantially uniform. In fact, however, the distances x 1 , x 3 , and x 9  of the concaves  20   a ,  20   c , and  20   e  are individually controlled such that an appropriate display condition of the entire screen  1  can be produced. 
     A manufacturing method of the screen  1  is now explained. Initially, in the screen  1 , manufacture of a base sheet forming the screen substrate  4  and the surface portion  3  is discussed. The base sheet is made of a material chiefly containing black polyvinyl chloride capable of absorbing light, for example. More specifically, the surface of a sheet made of polyvinyl chloride is heated and softened, and then concaves and convexes are formed by press working using a mold having concave and convex shapes corresponding to the shape of a number of the concaves  20 , for example. As a result, a number of minute concave and convex shapes corresponding to the concaves  20  ( 20   a ,  20   b ,  20   c ,  20   d , and  20   e ) are formed on the base sheet of the screen  1 . The sheet made of polyvinyl chloride may contain glass fibers or the like to increase the strength. 
     Next, a manufacture step of the reflection films RS formed on the first, third, and fifth concaves  20   a ,  20   c , and  20   e  on the base sheet of the screen  1  is explained. In this step, a film forming device which forms films by vacuum deposition is used for forming the reflection films RS, for example. The material used for forming the films is aluminum or the like. The base sheet of the screen  1  is fixed at a predetermined height along the inner wall surface of a cylindrical vacuum container included in the film forming device. The film forming device heats and evaporates the material of the films in the vacuum container, and deposits the reflection films RS on the first, third, and fifth concaves  20   a ,  20   c , and  20   e . The film forming device has an evaporation source in the vacuum container in the same direction as the supply direction of the projection light PL to the screen  1 . By this arrangement, the reflection films RS can be obliquely deposited in a direction inclined to the base sheet in correspondence with the projection light PL, and thus can be formed at appropriate positions on the first, third, and fifth concaves  20   a ,  20   c , and  20   e.    
     The base sheet forming the screen substrate  4  and the surface portion  3  may be a sheet-shaped base material chiefly containing transparent PET (polyethylene terephthalate) or the like having light transmissibility with light absorbing black ink applied to the back surface of the base material. 
     According to this method, the concaves  20  overlap with one another, and thus a projection is produced between each adjoining pair of the concaves  20 . More specifically, in the first area AR 1 , a projection  31  is formed at the corner between the first concaves  20   a  and the second concaves  20   b  in each adjoining pair of the units UN as illustrated in  FIGS. 2B and 4 . In the second area AR 2 , projections  32  are formed at the corner between the third concaves  20   c  and the fourth concaves  20   d  and the intermediate positions in each adjoining pair of the units UN as illustrated in  FIGS. 6B and 8 . As described above, the number of the fourth concaves  20   d  on the second supplementary line Ls 2  in the one unit UN in the second area AR 2  is larger than the number of the second concaves  20   b  on the first supplementary line Ls 1  in the one unit UN in the first area AR 1 . Thus, when the pitch of the arrangement lines R 1  of the first main lines Lm 1  is equal to the pitch of the arrangement lines R 3  of the second main lines Lm 2 , each height of the projections  32  formed between the adjoining pairs of the units UN in the Y axis direction in the second area AR 2  is relatively smaller than each height of the projections  31  formed between the adjoining pairs of the units UN in the Y axis direction in the first area AR 1 . 
     The relationship between the concaves  20  and the projection light PL is now described.  FIG. 12A  shows the relationship between the cross-sectional view of the concaves  20  in the first area AR 1  taken along the line A-A in  FIG. 2A  and projection lights PL 1  and PL 2 .  FIG. 12B  shows the relationship between the cross-sectional view of the concaves  20  in the second area AR 2  taken along the line B-B in  FIG. 6A  and the projection light PL 2 . The projections  31  and  32  particularly relating with the projection light PL in each of the first area AR 1  and the second area AR 2  are herein explained, though the heights of the projections at the boundaries between the concaves are not actually uniform even within the same area depending on the arrangement of the concaves  20 . As illustrated in  FIG. 12A , the projection light PL 1  reaches the reflection film RS on the first concave  20   a  without being blocked by the high projection  31  positioned on the first concave  20   a  on the entrance side of the projection light PL 1  in the first area AR 1  of the screen  1  shown in  FIGS. 1A and 1B . However, when a minute concave and convex structure similar to that of the first area AR 1  is provided in the second area AR 2  of the screen  1  shown in  FIGS. 1A and 1B , the projection light PL 2  is blocked by the high projection  31  as illustrated in  FIG. 12A . In this case, the projection light PL 2  does not reach the reflection film RS on the first concave  20   a . On the other hand, as illustrated in  FIG. 12B , the projection light PL 2  reaches the reflection film RS on the third concave  20   c  without being blocked by the low projection  32  positioned on the third concave  20   c  on the entrance side of the projection light PL 2  in the second area AR 2  of the screen  1  shown in  FIGS. 1A and 1B . 
     According to the screen  1  in this embodiment, the first and second supplementary lines Ls 1  and Ls 2  are provided as well as the first and second main lines Lm 1  and Lm 2 . Thus, even when the angle of incidence of the projection light PL with respect to the screen  1  is large, a sufficient amount of the projection light PL can be supplied to the reflection films RS formed on the first and third concaves  20   a  and  20   c . Moreover, since the number of the fourth concaves  20   d  on each of the second supplementary lines Ls 2  is larger than the number of the third concaves  20   c  on each of the second main lines Lm 2 , each height of the projections  32  in the second area AR 2  becomes smaller than each height of the projections  31  in the first area AR 1 . Thus, even when the angle of incidence of the projection light PL with respect to the screen  1  is larger in the second area AR 2  than in the first area AR 1 , the projection light PL is prevented from being blocked by the projections  32 . Accordingly, loss of view can be reduced. 
     According to this embodiment, the distance between the adjoining pair of the fourth concaves  20   d  adjacent to the third concaves  20   c  within the one unit UN in the transition area ARx gradually increases as the position of the unit UN shifts away from the first area AR 1 . Thus, the arrangement of the concaves  20  in the first area AR 1  can gradually change to the different arrangement of the concaves  20  in the second area AR 2 . Accordingly, unevenness in switching caused by the change from the first area AR 1  to the second area AR 2  is not produced in the display of the image reflected by the portion of the boundary between the first area AR 1  and the second area AR 2 . 
     Second Embodiment 
       FIG. 13  illustrates the screen  1  according to a second embodiment. The screen  1  in this embodiment has structure similar to that of the screen  1  in the first embodiment except for the arrangement pattern of the transition area ARx. Thus, the same explanation is not repeated herein. 
     In the transition area ARx, the number of the fourth concaves  20   d  corresponding to the third concave  20   c  within the one unit UN is not uniform. As illustrated in  FIG. 13 , the number of the adjoining fourth concaves  20   d  gradually increases as the angle of incidence of the projection light PL with respect to the screen substrate  4  becomes larger. More specifically, the increase in the number of the adjoining fourth concaves  20   d  on the second supplementary line Ls 2  closest to the first area AR 1  (the lowermost line in  FIG. 13 ) is zero, and thus the third concave  20   c  and the fourth concave  20   d  are provided with a ratio of 1:1 in appearance. The number of the fourth concaves  20   d  constituting the second supplementary line Ls 2  gradually increases as the position of the second supplementary line Ls 2  shifts away from the first area AR 1 . Thus, the number of the adjoining fourth concaves  20   d  on the second supplementary line Ls 2  (the uppermost line in  FIG. 13 ) is twice larger than the number of the third concaves  20   c  forming the second main line Lm 2 . In this case, the positions of the increased fourth concaves  20   d  in the arrangement direction are randomly determined. 
     According to the screen  1  in this embodiment, the number of the fourth concaves  20   d  on each of the second supplementary lines Ls 2  in the transition area ARx gradually increases as the positions of the fourth concaves  20   d  shift away from the first area AR 1 . Thus, unevenness in switching caused by the change from the first area AR 1  to the second area AR 2  in the boundary between the first area AR 1  and the second area AR 2  can be reduced. 
     It is not intended that the invention is limited to the respective embodiments described and depicted herein. For example, the arrangements and ranges of the first area AR 1 , the second area AR 2 , and the third area AR 3  are not limited to those shown in  FIGS. 1A and 1B  but may be any arrangements and ranges as long as the projection light PL received from the projector  2  can be efficiently reflected. For example, the projection light PL is not required to be supplied in the direction perpendicular to the respective lines Lm 1 , Lm 2 , Ls 1 , and Ls 2 . 
     While a pair of the fourth concaves  20   d  correspond to the single third concave  20   c  in the second area AR 2  in the embodiments, the number of the fourth concaves  20   d  may be three or larger, or numerals other than integers such as 2.5 and 3.5. In case of the structure including four or a larger number of the fourth concaves  20   d  corresponding to the single third concave  20   c , only the same advantages as those described above can be offered by the second supplementary lines Ls 2 , and the arrangement of the fourth concaves  20   d  and the like in the transition area ARx is difficult to be controlled. 
     While the reflection films RS are made of aluminum as the film forming material, the reflection films RS may be formed by silver or dielectric multilayer films other than aluminum, for example. When the reflection films RS are metal films, protection films can be further provided on the metal films. 
     According to the embodiments, the surface of the surface portion  3  may be activated before the reflection films RS are formed on the first, third, and fifth concaves  20   a ,  20   c , and  20   e . The surface of the surface portion  3  can be activated by reverse sputtering, plasma discharge, corona discharge, RF bombardment, atmospheric plasma, or other processing. When the surface of the surface portion  3  is activated by an appropriate manner, the adhesiveness and durability of the reflection films RS can be improved. 
     The third area AR 3  provided in the embodiments may be eliminated as long as the first and second areas AR 1  and AR 2  are disposed in such positions and ranges as to efficiently reflect the projection light PL received from the projector  2  in view of the whole screen  1 . 
     The entire disclosure of Japanese Patent Application No:2009-218619, filed Sep. 24, 2009 is expressly incorporated by reference herein.