Patent Publication Number: US-6211932-B1

Title: Fresnel lens and liquid crystal display device

Description:
This is a divisional of application Ser. No. 08/948,624, filed Oct. 10, 1997, which is a Divisional of application Ser. No. 08/508,632, filed Jul. 28, 1995 U.S. Pat. No. 5,751,387. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a fresnel lens having a shading layer and a display device such as a liquid crystal display device including magnifying fresnel lenses. 
     2. Description of the Related Art 
     Liquid crystal display devices can have relatively thin structures and have been used for many applications. Recently, projection type liquid crystal display devices having larger screens have been developed. A typical projection type liquid crystal display device includes a projection lens which projects a magnified image onto a screen. Also, optical elements other than a projection lens can be used for magnifying an image. 
     For example, Japanese Unexamined Patent Publication (Kokai) No. 5-188340 discloses a projection type liquid crystal display device including liquid crystal display panels, fresnel lenses for magnifying images produced by liquid crystal display panels, and a screen. In this case, the liquid crystal display device also includes arrays of convergently transmissive elements, and a screen. Each of the arrays of convergently transmissive elements is adapted to form an erect and real image having an identical size to an object, and each of the fresnel lenses serves to magnify the image from the array of convergently transmissive elements. 
     The convergently transmissive elements are made from plastic or glass in the form of transparent rods having the diameter of 1 mm to 2 mm, so that refractive index changes in each of the transparent rods in the radial direction thereof. By appropriately selecting the length and the distribution of refractive index thereof, it is possible to use each of the convergently transmissive elements so that it can form an erect and real image having an identical size to an object. A plurality of convergently transmissive elements are arranged in a close relationship to each other with the end surfaces of the elements arranged in a line or in a plane, to thereby form a row or an array of convergently transmissive elements. The array of convergently transmissive elements can be used as an imaging device for producing an erect and real image having an identical size to an object. The imaging device using the array of convergently transmissive elements has advantages, compared with a usual spherical lens, in that a focal distance is very short and an optical performance is uniform in the line or plane so that an adjustment of the distance between the lenses is not necessary. 
     However, when the array of convergently transmissive elements is used as the imaging device, it is not possible to change a magnification of the image although it is possible for individual convergently transmissive elements to be changed in magnification by changing the length of the elements. This is because magnified images produced by the individual convergently transmissive elements are inconsistently superposed, one on another, in the array and a normal image cannot be formed. Therefore, the array of convergently transmissive elements can be used only as a full size imaging device, and it is necessary to provide a magnifying means in addition to the array of convergently transmissive elements. 
     Japanese Examined Patent publications (Kokoku) No. 58-33526 and No. 61-12249 disclose an imaging device including an array of convergently transmissive elements and a convex lens or a concave lens as a magnifying means which is arranged on the inlet side or on the outlet side of the array of convergently transmissive elements. The convex lens or the concave lens can be of a single lens or a composite lens of a plurality of lens components to realize a desired magnification. However, when this imaging device is used with a magnifying device in a liquid crystal display device, a problem arises in that resolving power of the lens changes from the central portion to the peripheral region. 
     It has been found that a good image is obtained if the resolving power MTF is greater than 50 percent under the condition of 4 (1 p/mm) i.e., 4 pairs of white and black spots per millimeter. However, it is generally difficult to establish an image having resolving power MTF greater than 50 percent in the above described prior art. It is necessary that light passes through the peripheral region of the liquid crystal display panel at an angle of approximately 10 degrees relative to the normal line of the liquid crystal display panel in order to ensure resolving power MTF greater than 50 percent. The smaller the angle at the peripheral region is, the smaller the magnification of the device is. As a result, it is not possible to realize a liquid crystal display device having a thin structure if a convex lens or a concave lens is used with an array of convergently transmissive elements, although the array of convergently transmissive elements by itself can provide a liquid crystal display device having a thin structure. 
     Accordingly, a magnifying element is desired which can be used with an array of convergently transmissive elements and which can realize a liquid crystal display device having a thin structure. The use of a fresnel lens with an array of convergently transmissive elements is disclosed in the above described Japanese Unexamined Patent Publication (Kokai) No. 5-188340, but the manner in which the fresnel lens is used is not described in this prior art. The inventors have recently found that a good result is obtained if a fresnel lens is used as a magnifying element. 
     Further, in a liquid crystal display device, there is a problem that brightness of an image on a peripheral region of the screen is reduced relative to the brightness of the image on the central region of the screen. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to provide a fresnel lens constructed such that light is made incident to a configured surface thereof. 
     Another object of the present invention is to provide a display device having a thin structure by appropriately arranging a fresnel lens. 
     Another object of the present invention is to provide a display device in which the brightness of a screen is improved. 
     According to one aspect of the present invention, there is provided a fresnel lens comprising a body having a flat surface and a configured surface with periodic ridges, each of the ridges including a flat crest extending generally parallel to the flat surface and at least one inclined surface extending from the flat crest toward the flat surface, and a shading layer provided on the flat crest of each of the ridges. 
     Preferably, the flat crests have varying widths depending on the positions of the ridges. In this case, the at least one inclined surface comprises a main inclined surface arranged on one side of the flat crest and designed such that light is mainly incident to the body from the main inclined surface and a minor inclined surface arranged on the other side of the flat crest from the main inclined surface. 
     Preferably, the width of the flat crest is determined by the following relationship:              d   =     p          tan      r         tan        (     90   -   θ1     )       +     tan      r         ×     [     1   -       tan      θ2       tan      r         ]               (   1   )                         
     where d is the width of the flat crest, p is the pitch of the ridges, r is the angle of a major light ray made incident to the body from the main inclined surface relative to the axis, θ 1  is the angle the main inclined surface relative to the flat surface, and θ 2  is the angle of the minor inclined surface relative to the axis. 
     According to a further aspect of the present invention, there is provided a display device comprising at least one image modulator, an array of convergently transmissive elements receiving light from said at least one image modulator for forming an erect and real image, a fresnel lens including a body having a flat surface and a configured surface with neriodic ridges, the fresnel lens being arranged so that light is made incident from the array of convergently transmissive elements to the configured surface of the fresnel lens, and a screen receiving light from said at least one image modulator via the array of convergently transmissive elements and the fresnel lens. 
     Preferably, each of the ridges includes a flat crest extending generally parallel to the flat surface and at least one inclined surface extending from the flat crest toward the flat surface, and a shading layer is provided on the flat crest of each of the ridges. 
     Preferably, the flat crests have varying widths depending on the positions of the ridges. Preferably, the at least one inclined surface comprises a main inclined surface arranged on one side of the flat crest and designed such that light is mainly incident to the body from the main inclined surface and a minor inclined surface arranged on the other side of the flat crest from the main inclined surface. 
     Preferably, the at least one image modulator comprises a plurality of liquid crystal display panels, and the array of convergently transmissive elements and the fresnel lens are arranged for every liquid crystal display panel. Preferably, four sets of the liquid crystal display panels, the arrays of convergently transmissive elements and the fresnel lenses are arranged, with each set arranged in respective quarter portions in a rectangular region, the screen having a total display area four times greater than a display area necessary to receive an image from one set of the liquid crystal display panel, the array of convergently transmissive elements and the fresnel lens. 
     Preferably, a partition is arranged on or near the screen between two adjacent sets of the liquid crystal display panels, the arrays of convergently transmissive elements and the fresnel lenses for preventing light from straying from one set into the adjacent set. 
     Preferably, the screen has a predetermined display area, and said at least one image modulator has a main display area and a peripheral compensating area arranged such that the main display area forms an image on the predetermined display area via the array of convergently transmissive elements and the fresnel lens and the peripheral compensating area forms an image just outside the predetermined display area via the array of convergently transmissive elements and the fresnel lens. Preferably, the peripheral compensating area of said at least one image modulator is controlled to provide an image which is generally identical to a portion of an image delivered from the main display area of the at least one image modulator near the peripheral compensating area. 
     Preferably, between two adjacent liquid crystal display panels, said peripheral compensating area of one liquid crystal display panel is controlled to provide an image which is generally identical to a portion of an image delivered from the main display area of the adjacent liquid crystal display panel near the peripheral compensating area of said one liquid crystal display panel. 
     According to a further aspect of the present invention, there is Provided a display device comprising at least one image modulator, optical lens for magnifying an image output by said at least one image modulator, a screen for receiving an image from said at least one image modulator via said optical lens, the screen having a predetermined display area, and said at least one image modulator has a main display area and a peripheral compensating area arranged such that the main display area forms an image on the predetermined display area via said optical lens and the peripheral compensating area forms an image just outside the predetermined display area via said optical lens. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more apparent from the following description of the preferred embodiments, with reference to the accompanying drawings in which: 
     FIG. 1 is a cross-sectional view of a liquid crystal display device according to the embodiment of the present invention; 
     FIG. 2 is a plan view illustrating the arrangement of four liquid crystal display panels of FIG. 1; 
     FIGS. 3A to  3 C are views illustrating the feature of one of the convergently transmissive elements of FIG. 1; 
     FIG. 4 is a view illustrating the propagration of light in the convergently transmissive element; 
     FIG. 5 is a view illustrating formation of an erect and real image having an identical size to an object; 
     FIG. 6 is a diagrammatic perspective view of an array of convergently transmissive elements of FIG. 1; 
     FIG. 7 is a view illustrating the imaging surface and how the resolving power is reduced; 
     FIG. 8 is a cross-sectional view of the fresnel lens of FIG. 1; 
     FIG. 9 is a partial plan view of the fresnel lens of FIG. 8; 
     FIG. 10 is a cross-sectional view of a portion of the fresnel lens of FIGS. 8 and 9; 
     FIG. 11 is a cross-sectional view of a conventional fresnel lens; 
     FIG. 12 is similar to FIG. 10, but includes several dimensional characters for calculating the width of the shading layer on the flat crest of the ridge of the configured surface of the fresnel lens; 
     FIG. 13 is a plan view of the modified liquid crystal display panels; 
     FIG. 14 is a view illustrating the pictures produced by the main display area and the peripheral compensating area of the quid crystal display panel; 
     FIG. 15 is a view illustrating the image on the screen produced by two adjacent liquid crystal display panels; 
     FIG. 16 is a view illustrating the pictures produced by the main display area and the image of the peripheral compensating area of the liquid crystal display panel of FIG. 15; 
     FIG. 17 is a diagrammatic cross-sectional view of a liquid crystal display device similar to the arrangement of FIG. 13; 
     FIG. 18 is a cross-sectional view illustrating the course of light emerging from the main display area and the peripheral compensating area to the screen; 
     FIG. 19 is a plan view illustrating an element of an image on a screen; 
     FIG. 20 is a plan view of several elements of an image on a screen; and 
     FIG. 21 is a view illustrating how the brightness of the image at the peripheral region of the screen is reduced. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIGS. 1 and 2 show the liquid crystal display device  10  according to the present invention. The liquid crystal display device  10  includes four liquid crystal display panels  12  which are arranged in respective quarter portions in a rectangular region. Each liquid crystal display panel  12  includes an effective display region  12   a  and a non-display region  12   b  around the effective display region  12   a , the non-display region  12   b  being necessary for attaching a drive circuit or the like to the panel for driving the liquid crystal in the panel. Therefore, an image is not formed on the non-display region  12   b  and a discontinuous image is formed if four liquid crystal display panels  12  are directly seen. The embodiment realizes a continuous multi-display from discontinuous images from four liquid crystal display panels  12  by providing a magnifying element. 
     In FIG. 1, the liquid crystal display device  10  includes a backlight  14  on the rear side of the panels  12 , and arrays  16  of convergently transmissive elements on the front side of the respective panels  12 . The area of each of the arrays  16  of convergently transmissive elements is larger than the area of the effective display region  12   a , but smaller than the total area of the panel  12  including the non-display region  12   b . Each array  16  of convergently transmissive elements can form an erect and real image having an identical size to an object, i.e., an image produced by the liquid crystal display panel  12 . 
     The liquid crystal display device  10  includes fresnel lenses  18  on the output side of the arrays  16  of convergently transmissive elements, respectively. Each fresnel lens  18  includes a transparent body having a flat surface  18   a  and a configured surface  18   b , in a saw-shaped cross-section, with concentrically periodic ridges  19  as shown in FIGS. 8 and 9. In the present invention, the fresnel lens  18  is arranged such that light is mainly incident onto the configured surface  18   b  of the fresnel lens  18 . In the arrangement of FIG. 1, the configured surface  18   b  faces the array  16 . The flat surface  18   a  is thus arranged on the light emerging side. 
     The liquid crystal display device  10  also includes a screen  22  having a screen fresnel lens  20  on the front side of the fresnel lenses  18 . Light beams emerging from the fresnel lenses  18  divergently travel toward the screen  22  so that light beams emerging from the adjacent fresnel lenses  18  meet on the screen  22  without a discontinuity. Therefore, the non-display regions  12   b  of the liquid crystal display panels  12  cannot be seen by a person watching the screen  22 . The liquid crystal display panels  12  are one example of an image modulating means, and other types of image modulating means, which merge light, can be used. 
     The array  16  comprises a plurality of convergently transmissive elements  16   a  and the features of one of the convergently transmissive elements  16   a  is shown in FIGS. 3A to  3 C. The convergently transmissive element  16   a  is made from plastic or glass in the form of transparent rod having the diameter of 1 mm to 2 mm. The refractive index of the element  16   a  changes in the body thereof in the radial direction, as shown in FIG.  3 C. The distribution of the refractive index n(r) is represented by the following quadratic function 
     
       
           n ( r )= n   0 (1 −g   2   r   2 /2) 
       
     
     where r is the distance from the vertical axis, n 0  is refractive index on the vertical axis, and g is a distribution constant of the refractive index. 
     Light enters the convergently transmissive element  16   a  from its end surface and is bent toward a portion thereof at which the refractive index is higher while light passes through the convergently transmissive element  16   a , so that light travels along a periodically snaked course, as shown in FIG.  4 . The cycle P is expressed by P=2 π/g. If the length Z of the convergently transmissive element  16   a  is selected from the relationship of P/2&lt;Z&lt;3P/4, an erect and real image having an identical size to an object can be formed, as shown in FIG.  5 . The distance L is the distance between the object and the image. 
     FIG. 6 shows that the convergently transmissive elements  16   a  are arranged in a close relationship to each other with the end surfaces thereof arranged in a line or in a plane, to thereby form the array  16 . An erect and real image having an identical size to an object can be formed by the array  16 . The imaging device using the array  16  of convergently transmissive elements  16   a  offers advantages in that a focal distance is very short, and the optical performance is uniform in the line or plane. However, it is not possible for the array  16  of convergently transmissive elements  16   a  to change the magnification of the image relative to an object, although it is possible for individual convergently transmissive elements  16   a  to change the magnification if the length of the elements  16  is changed. This is because magnified images formed by the individual convergently transmissive elements  16   a  are inconsistently superposed one on another in the array  16  and a normal image is not formed in the array  16 . Therefore, the array  16  of convergently transmissive elements  16   a  can be used only as a full size imaging device, and the fresnel lenses  18  are used as a magnifying means. 
     In the embodiment, the area of the effective region  12   a  of the liquid crystal display panel  12  is 211.2 mm×158.4 mm, and the required magnification (a value of the sum of the area of the effective region  12   a  and the area of the ineffective region  12  divided by the area of the effective region  12   a ) is 1.09. Regarding the convergently transmissive elements  16   a , the refractive index n is 1.507, the distribution constant of refractive index g is 0.1847, the length Z is 18.89 mm, and the diameter is 1.18 mm. The magnifying fresnel lens  18  is made from an acryl having a refractive index of 1.494 and a radius of curvature in which the central curvature (cuy) is −0.00813668, the secondary constant is −0.775202×10 −8 , the tertiary constant is 0.318549×10 −13 , the quartic constant is −0.720974×10 −19 , and the quintic constant is −0.717576×10 −25 . The angle (AEP) of light emerging from the outermost peripheral position of the fresnel lens  18  relative to the normal line of the fresnel lens  18  is 28.3 degrees. The screen fresnel lens  20  serves to convert light beams emerging from the magnifying fresnel lens  18  with a variety of angles into parallel light beams, and is made from MS having a refractive index of 1.537. The resolving power MTF in this example is shown in the following table. 
     
       
         
           
               
               
               
            
               
                   
                   
               
               
                   
                 MTF (%) 
                   
               
            
           
           
               
               
               
            
               
                 AEP (°) 
                 2 (1 p/mm) 
                 4 (1 p/mm) 
               
               
                   
               
               
                 28.3 
                 89.7 
                 64.0 
               
               
                   
               
            
           
         
       
     
     In the further embodiment, the shape of the configured surface  18   b  of the fresnel lens  18  is changed so that the angle (AEP) of light emerging from the outermost peripheral position of the fresnel lens  18  is changed. The resolving power MTF is examined while changing the angle (AEP). In this example, the refractive index n of the convergently transmissive elements  16   a  is 1.505, the distribution constant of the refractive index g is 0.1847, the length Z is 18.895 mm, and the distance L is 20 mm. The thickness of the fresnel lens  18  is 2 mm and refractive index is 1.494. The fresnel lens  18  is arranged to contact the array  16  of convergently transmissive elements  16   a . In this arrangement, the curvature of the fresnel lens  18  is set in a parabolic shape so that a light beam (referred to as the main light beam) parallel to the optical axis of the fresnel lens  18  emerges from the outermost peripheral position of the fresnel lens  18  at an angle (AEP), and the focal point is at a position on a line passing through the center of the fresnel lens  18 . The resolving power MTF in this example is shown in the following table. It should be noted that the configured surface  18   b  is on the light incident side and the flat surface  18   a  is on the light emerging side. 
     
       
         
           
               
               
               
            
               
                   
                   
               
               
                   
                 MTF (%) 
                   
               
            
           
           
               
               
               
            
               
                 AEP (°) 
                 2 (1 p/mm) 
                 4 (1 p/mm) 
               
               
                   
               
               
                 10 
                 99.7 
                 98.9 
               
               
                 20 
                 98.1 
                 92.7 
               
               
                 30 
                 88.7 
                 61.1 
               
               
                 40 
                 88.9 
                 61.5 
               
               
                   
               
            
           
         
       
     
     As will be understood from this table, the obtained values for MTF are satisfactory even at an angle (AEP) of 40 degrees. Note that this result is obtained in an arrangement where the configured surface  18   b  is on the light incident side and the flat surface  18   a  is on the light emerging side. 
     It can be said that an image is formed substantially in a plane, however, the imaging surface is somewhat curved. Therefore, if the focal point is at a position on a line passing through the center of the fresnel lens  18 , a value for MTF at a peripheral position may be reduced. In the above table, the values for MTF at the angles (AEP) of 10 to 30 degrees are obtained when the focal point is at a position on a line passing through the center of the fresnel lens  18 , but the value for MTF at the angle (AEP) of 40 degrees is obtained when the focal point is adjusted so that a value for MTF at the center of the fresnel lens  18  is identical to a value for MTF at the outermost peripheral position of the fresnel lens  18 . 
     The following table shows the result of a test regarding resolving power MTF obtained when the flat surface  18   a  is on the light incident side and the configured surface  18   b  is on the light emerging side and the other conditions are similar to those of the above example. This result should be compared with resolving force MTF obtained when the configured surface  18   b  is on the light incident side and the flat surface  18   a  is on the light emerging side. 
     
       
         
           
               
               
               
            
               
                   
                   
               
               
                   
                 MTF (%) 
                   
               
            
           
           
               
               
               
            
               
                 AEP (°) 
                 2 (1 p/mm) 
                 4 (1 p/mm) 
               
               
                   
               
            
           
           
               
               
               
            
               
                 10 
                 95.8 
                 84.0 
               
               
                 12 
                 90.8 
                 65.0 
               
               
                 13 
                 86.9 
                 55.4 
               
               
                 14 
                 81.6 
                 41.5 
               
               
                 15 
                 76.1 
                 28.8 
               
               
                 20 
                 26.6 
                 5.5 
               
               
                   
               
            
           
         
       
     
     According to an estimation by observing the screen, it has been found that a produced image is good when a value for MTF is greater than 50 percent under the condition of 4 (1 p/mm). Therefore, in this comparative test, it can be said that an angle (AEP) equal to or lower than 13 degrees is satisfactory but the curvature of the fresnel lens is limited to this extent. 
     The inventors further tried to analyze the reason why the resolving power MTF is reduced when the flat surface  18   a  is on the light incident side and the configured surface  18   b  is on the light emerging side. 
     As shown in FIG. 7, it has been found that the focal length of the fresnel lens  18  becomes shorter as the position is displaced from the center of the fresnel lens  18  to the periphery thereof, and an imaging surface is distorted relative to the screen  22  as shown by the broken line F. In FIG. 7, the array  16  of the convergently transmissive elements  16   a  and the fresnel lens  18  are shown, but the fresnel lens  18  is arranged such that the configured surface  18   b  is on the light emerging side. 
     In the analysis of the distorted imaging surface, the angle (AIM) between light beams 30 and 31 which are inclined to the main light beam on either side of the main light beam at identical angles relative to the main light beam is noted. The angle (AIM) between light beams 30 and 31 becomes smaller when light is made incident to the fresnel lens  18 , and the angle (AIM) becomes greater when light emerges from the fresnel lens  18 , regardless of which surface is on the light incident side. This tendency is stronger as the angle between the incident or merging light and the incident or emerging surface becomes greater, that is, this tendency is stronger with respect to the configured surface  18   b . Therefore, the angle (AIM) between light beams  30  and  31  becomes greater in the arrangement where light emerges from the configured surface  18   b , and an image is formed far from the screen  22  as the angle (AIM) becomes greater, with the result that the resolving power MTF is reduced. The angle (AIM) does not become as great in the arrangement where light emerges from the flat surface  18   a , and in this case, it is possible to form an image on the screen  22 . 
     FIG. 10 shows the details of the fresnel lens  18  of FIG.  1 . As described above, the fresnel lens  18  has the flat surface  18   a  and the configured surface  18   b  with concentrically periodic ridges  19 . Each of the ridges  19  includes a flat crest  19   a  extending generally parallel to the flat surface  18   a  and an inclined surface  19   b  extending from the flat crest  19   a  toward the flat surface  18   a . A minor surface  19   c  which is perpendicular to the flat surface  18   a  in FIG. 10 is arranged on the opposite side of the flat crest  19   a  from the inclined surface  19   b . A shading layer  19   d  is provided on the flat crest  19   a  of each of the ridges  19 . The shading layer  19   d  can be easily formed by printing since the flat crest  19   a  is parallel to the flat surface  18   a.    
     FIG. 11 shows a conventional fresnel lens  18  having ridges  19 . It will be understood that the flat crest  19   a  of FIG. 10 is formed by cutting the apex of the ridge  19  of FIG.  10 . In the conventional fresnel lens  18  shown in FIG. 11, there is a problem of a straying beam inducing a ghost. That is, if light S is made incident to the inclined surface  19   b  at a position near the surface  19   c , light S is reflected by the minor surface  19   c  and changes its course in an uncontrolled direction to thereby induce a ghost. The shading layer  19   d  is provided to solve this problem. 
     As will be understood from FIG. 8, the shape or the slope of the ridges  19  changes depending on the positions of the ridges  19  and it is preferable that the flat crests  19   d  have varying widths depending on the positions of the ridges  19 . 
     As shown in FIG. 12, the surface  19   c  may be inclined relative to the flat surface  18   a  for the reason of fabrication of the fresnel lens  18 . As will be apparent, the main inclined surface  19   b  arranged on one side of the flat crest  19   a  is designed such that light is mainly incident to the body of the fresnel lens  18  from the main inclined surface  19   b , and the minor inclined surface  19   c  is arranged on the other side of the flat crest  19   a  from the main inclined surface  19   b.    
     Preferably, the width of the flat crest  19   a  is determined by the following relationship:              d   =     p          tan      r         tan        (     90   -   θ1     )       +     tan      r         ×     [     1   -       tan      θ2       tan      r         ]               (   1   )                         
     where d is the width of the flat crest  19   a , p is the pitch of the ridges  19 , r is the angle of a major light ray made incident to the body from the main inclined surface  19   a  relative to the axis, θ 1  is the angle the main inclined surface  19   b  relative to the flat surface  18   a , and θ 2  is the angle of the minor inclined surface  19   c  relative to the axis of the fresnel lens  18 . 
     FIGS. 13,  17  and  18  show the modified liquid crystal display device  10 , which includes four sets of the liquid crystal display panels  12 , the arrays  16  of convergently transmissive elements  16   a  and the fresnel lenses  18 , and a screen  22 . The four sets are arranged in respective quarter portions in a rectangular region. The screen  22  has a total display area four times greater than a predetermined display area  22   p  necessary to receive an image from one set of the liquid crystal display panel  12 , the array  16  of convergently transmissive elements and the fresnel lens  18 . That is, the screen  22  has a predetermined display area  22   p  for each of the liquid crystal display panel  12 . 
     A partition  26  is arranged on or near the screen  22  between two adjacent sets of the liquid crystal display panels  12 , the arrays  16  of convergently transmissive elements and the fresnel lenses  18  for preventing light from straying from one set into the adjacent set. 
     Each liquid crystal display panel  12  includes an effective display region  12   a  and a non-display region  12   b  around the effective display region  12   a , as described with reference to FIG.  2 . The effective display region  12   a  is further divided into a main display area  12   x  and a peripheral compensating area  12   y . The main display area  12   x  forms an image on the predetermined display area  22   p  via the array  16  of convergently transmissive elements and the fresnel lens  18 . The peripheral compensating area  12   y  forms an image just outside the predetermined display area  22   p  via the array  16  of convergently transmissive elements and the fresnel lens  18 . That is, the peripheral compensating area  12   y  does not contribute to the formation of the actual image on the screen  22 , but compensates for a loss in brightness in the peripheral region of the liquid crystal display panel  12 . As an example, the effective display region  12   a  includes 640×480 pixels, and the main display area  12   x  includes 620×465 pixels. 
     As shown in FIG. 14, the peripheral compensating area  12   y  of the liquid crystal display panel  12  is controlled to provide an image I 1  which is generally identical to a portion I 1  of an image delivered from the main display area  12   x  of the liquid crystal display panel  12  near the peripheral compensating area  12   y.    
     As alternatively shown in FIGS. 15 and 16, the peripheral compensating area  12   y  of the liquid crystal display panel  12  is controlled to provide an image I 2  which is generally identical to a portion I 2  of an image delivered from the main display area  12   x  of the adjacent liquid crystal display panel  12  near the peripheral compensating area  12   y  of said one liquid crystal display panel  12 . 
     FIG. 19 shows an element  50  of an image on a screen  22 . The element  50  should be a point at which several light beams are focussed, but in fact, light beams may scatter to a certain region  51  due to an aberration of the magnifying fresnel lens  18 . Therefore, the brightness of the element  50  may be reduced. FIG. 20 shows several elements  50 ,  50   a ,  50   b,    50   c , and  50   d , with their scattering regions  51 ,  51   a ,  51   b ,  51   c , and  50   d . The element  50  receives light from the other elements 50a,  50   b,    50   c , and  50   d  and the brightness of the element  50  may be compensated to some extent. FIG. 21 shows a peripheral portion of the screen  22  when the peripheral compensating area  12   y  is not provided. There are several elements  50 ,  50   a,    50   b,    50   c,  and  50   d , with their scattering regions  51 ,  51   a,    51   b,    51   c,  and  51   d  on the peripheral portion of the screen  22 , but the brightness of these elements may not be compensated since there are not surplus light components outside the predetermined display area  22   p.    
     As shown in FIG. 18, the peripheral compensating area  12   y  produces light outside the predetermined display area  22   p  and does not contribute to the formation of an actual image, but light emerged from the peripheral compensating area  12   y  may include scattered light components which compensate for the reduced brightness on the peripheral portion of the screen  22 .