Patent Publication Number: US-2009231740-A1

Title: Multi-curvature convex mirror having an enhanced field of vision

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims priority under 35 U.S.C. § 119(a)-(d) from Chinese Patent Application No. 200720107256.8 filed Mar. 14, 2007. 
     FIELD OF THE DISCLOSURE 
     The present disclosure relates to relates to mirrors and, more particularly, to a convex mirror having multiple reflecting surfaces, each having a respective curvature. 
     BACKGROUND 
     To enhance safety during operation thereof, many vehicles, for example, trucks, buses and automobiles, employ mirror systems that enable the drivers of the vehicles to see behind and/or to the side of the vehicle without turning their head in that direction. Such mirror systems typically include an interiorly-located mirror, commonly known as a “rear view” mirror, mounted in proximity to the upper interior side surface of the windshield and a pair of exteriorly-located mirrors, commonly known as “side view” mirrors, respectively mounted on a forward portion of the door assemblies for the driver and front seat passenger. 
     Most mirrors used to enable a driver to look behind or to one side of a vehicle may be classified as flat, convex or aspherical mirrors. A flat mirror has a generally planar reflective surface that tends to produce true and undistorted reflections of objects. However, because the field of vision produced by the planar reflective surface is relatively narrow, e.g., is typically bounded by planes generally orthogonal to the edges of the reflective surface, flat mirrors are characterized by a relatively large blind spot. In contrast, a convex mirror has a curved reflective surface and, when compared to a flat mirror, is generally characterized by a greater field of vision and a smaller blind spot. Indeed, as the curvature of the reflective surface is increased, the field of vision for the convex mirror increases while the size of the blind spot decreases. Thus, a mirror having a convexly curved reflecting surface will rectify many of the shortcomings of a mirror having a generally flat reflecting surface. Unfortunately, convex mirrors are not without their own shortcomings, most notably, distortions in the images of objects reflected thereby and difficulties when attempting to accurately judge the distance separating the mirror from the reflected objects. Furthermore, the severity of these shortcomings tends to worsen as the curvature of the reflective surface increases. 
     An aspherical mirror typically includes two or more convexly curved mirror surfaces, each of which is curved to a different extent. For example, one aspherical mirror known in the art includes primary and secondary mirror surfaces. The primary mirror surface encompasses approximately two-thirds of the aspherical mirror and is a convex mirror having a relatively small curvature of the reflective surface which causes the primary reflective surface to approximate that of a flat mirror. Accordingly, reflections appearing in the primary reflective surface are true and undistorted. The secondary mirror surface, on the other hand, covers approximately one-third of the aspherical mirror and is a convex mirror having a larger curvature of the reflective surface relative to the curvature of the primary reflective surface. Accordingly, the secondary mirror compensates for a portion of the relatively narrow field of view and the blind spot characterizing flat mirrors such as the primary reflective surface. The transition from the primary reflective surface to the secondary reflective surface is smooth, thereby minimizing any problems resulting from the difference between the undistorted image/smaller field of vision of the primary reflective surface and the relatively more distorted/greater field of vision of the secondary reflective surface. However, as most aspherical mirrors require a relatively large difference in the degree to which the secondary reflective surface is curved in order to remove any blind spots caused by the primary reflective surface, the transition between the primary and secondary reflective surface remains relatively sharp and, as a result, continues to affect proper judgment of the distance separating the mirror and an object reflected thereby. 
     It should be readily appreciated that a multi-curvature convex mirror which combines the advantages of larger field of view and a reduced or eliminated blind spot when compared to a flat mirror while simultaneously reducing the distortion and difficulty in estimating separation distances normally associated with convex mirrors would enjoy many advantages over both flat and convex mirrors currently in use. Such a multi-curvature convex mirror is described hereinbelow. 
     SUMMARY 
     In one embodiment, claimed herein is a multi-curvature convex mirror comprised of a primary reflective surface having a first curvature and a secondary reflective surface having a second curvature. The secondary reflective surface is in the form of a series of locations arranged in a line extending from a first edge of the primary reflective surface to a second edge of the primary In alternate aspects thereof, the multi-curvature convex mirror is configured to provide a vertically-oriented field of vision or a horizontally-oriented field of vision and in still further alternate aspects thereof, the multi-curvature convex mirror is employed as a side-view or a rear-view mirror for a vehicle. In a still further alternate aspect thereof, the primary and secondary surfaces are comprised of a series of locations, each defined by an x, y and z coordinate, determined in accordance with the equation 
     
       
         
           
             z 
             = 
             
               
                 x 
                 a 
               
               + 
               
                 y 
                 b 
               
             
           
         
       
     
     where 600≦a≦1,300 and 100≦|b−a|≦200. In further accordance with this aspect, if a is less than b, than the multi-curvature mirror has a vertically oriented field of view while, if a is greater than b, then the multi-curvature mirror has a horizontally oriented field of view. 
     In another embodiment, disclosed herein is a multi-curvature convex mirror comprised of a first reflective surface defined by a portion of the surface area of a greater sphere and a second reflective surface defined by a portion of the surface area of a lesser sphere. In various aspects thereof, the second reflective surface may be defined by the intersection of the surface area of the greater sphere and the surface area of the lesser sphere; have a curvature larger than the curvature of the greater sphere and/or have a radius r 1  (for example, 700 mm) less than a radius r 2  (for example, 780 mm) of the greater sphere and a center point c 1  separated from the center point c 2  of the greater sphere by a distance r 2 −r 1 . 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure, and for further details and advantages thereof, reference is now made to the drawings accompanying this disclosure, in which: 
         FIG. 1  is a first illustration which aids in an understanding of the principles underlying the teachings set forth herein; 
         FIG. 2  is a second illustration which aids in an understanding of the principles underlying the teachings set forth herein; 
         FIG. 3  is a perspective view of a multi-curvature convex mirror configured in accordance with the teachings set forth herein; 
         FIG. 4  is a first side view of the multi-curvature convex mirror of  FIG. 1 ; 
         FIG. 5  is a second side view of the multi-curvature convex mirror of  FIG. 1 ; 
         FIG. 6  is a top view of the multi-curvature convex mirror of  FIG. 1 ; 
         FIG. 7  is an enlarged perspective view of the multi-curvature convex mirror of  FIG. 3 ; 
         FIG. 8  illustrates the field of view for a vertically oriented embodiment of the multi-curvature convex mirror of  FIGS. 3-7 ; 
         FIG. 9  illustrates the field of view for left horizontally oriented and right horizontally oriented embodiments of the multi-curvature convex mirror of  FIGS. 3-7 . 
     
    
    
     DETAILED DESCRIPTION 
     The teachings set forth herein are susceptible to various modifications and alternative forms, specific embodiments of which are, by way of example, shown in the drawings and described in detail herein. It should be clearly understood, however, that the drawings and detailed description set forth herein are not intended to limit the disclosed teachings to the particular form disclosed. On the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of that which is defined by the claims appended hereto. 
     A. Theory 
     It is well known that a spherical surface is comprised of the set of all points in a three-dimensional space that are located a specified distance, commonly referred to as the radius r, from a single fixed point, commonly referred to as the center point c in that space. Further, as previously noted, the reflective surface of a convex mirror corresponds to a selected portion of a sphere. The multi-curvature convex mirror described and illustrated herein is based upon the concept that, rather than having the reflective surface of the mirror correspond to a selected portion of a single sphere, the reflective surface of the mirror should instead be configured such that a first portion of the reflective surface corresponds to a portion of the surface area of a first one of the pair of intersecting spheres and a second portion of the reflective surface corresponds to a portion of the surface of the second one of the pair of intersecting spheres. 
     The first sphere for which a portion of the surface thereof corresponds to a first portion of the reflective surface of the multi-curvature mirror has a center point c 1  and a radius r 1  and the second sphere for which a portion of the surface thereof corresponds to a second portion of the reflective surface of the multi-curvature mirror has a center point c 2  and a radius r 2 . As r 1 &lt;r 2 , the first sphere shall periodically be referred to as the “lesser” sphere while the second sphere shall periodically be referred to as the “greater” sphere. In the embodiment disclosed herein, the radius r 1  of the lesser sphere is approximately 700 mm and the radius r 2  of the greater sphere is approximately 780 mm. Of course, it should be clearly understood that the foregoing values are provided purely by way of example and that it is fully contemplated that, depending on the desired characteristics of the multi-curvature mirror to be produced thereby, one or both of the foregoing values may be varied. 
     As the radius r 1  of the lesser sphere is less than the radius r 2  of the greater sphere, it should be appreciated that, if the center points c 1  and c 2  shared the same coordinates (x,y,z), the lesser sphere would be entirely enclosed within the greater sphere. Here, however, the center point c 1  of the lesser sphere is located at coordinates (x 1 , y 1 ,z 1 ) while the center point c 2  of the greater sphere is located at coordinates (x 2 ,y 2 ,z 2 ), the coordinates (x 1 ,y 1 ,z 1 ) and (x 2 ,y 2 ,z 2 ) selected such that the center points c 1  and c 2  are located in a common plane and separated, in the common plane, by a distance d equal to r 2 −r 1 , which, in the disclosed example would result in a distance d equal to approximately 80 mm. By arranging the respective center points c 1  and c 2  in this manner, the lesser and greater spheres shall intersect along a line. 
     A highly simplified 2-dimensional example of this principle is illustrated in  FIG. 1 . Here, corresponding halves of a lesser circle  10  having a center point c 1  and a radius r 1  equal to 700 mm and a greater circle  20  having a center point c 2  and a radius r 2  equal to 780 mm. are shown. While the center point c 2  of the greater circle  20  is located at coordinates (x=0, y=0), the center point c 1  of the lesser circle  10  is offset +80 mm (r 2 −r 1 ) along the Y-axis and is located at coordinates (x=0, y=80 mm). As a result, while the lesser circle is generally located within the greater circle  20 , the lesser circle  10  intersects the greater circle  20  at a point P located along the Y-axis. 
     In  FIG. 2 , the foregoing example is extended to 3-dimensions. For ease of illustration, the lesser circle  10  is shown in  FIG. 2  as extending along the X-axis while the greater circle  20  is shown as extending along the Y-axis. To generate the shape of the reflective surface  30 , the greater circle  20  is rotated in the direction of the lesser circle  10 , i.e., direction D in  FIG. 2 . When viewed from along the X-axis, the shape of the reflective surface  30  is the lesser circle  10 , i.e., a curve defined by a 700 mm radius. When viewed from along the Y-axis, however, the shape of the reflective surface  30  is the greater circle  20 , i.e., a curve defined by a 780 mm radius. 
     Presuming that the lesser sphere has a radius r 1  and a center point (a 1 ,b 1 ,c 1 ), the greater sphere has a radius r 2  and a center point (a 2 ,b 2 ,c 2 ) and a location on the reflective surface  30  collectively formed by the lesser sphere and the greater sphere is (x,y,z), the following relationship exists for the lesser sphere: 
       ( x−a   1 ) 2 +( y−b   1 ) 2 +( z−c   1 ) 2   =r   1   2 . 
     Similarly, the following relationship exists for the greater sphere: 
       ( x−a   2 ) 2 +( y−b   2 ) 2 +( z−c   2 ) 2   =r   2   2 . 
     From these relationships, it may be concluded that the following relationship exists for the reflective surface  30 : 
         z =( r   2   2   −r   1   2   +a   1   2   −a   2   2   +b   1   2   −b   2   2   +c   1   2   −c   2   2 )/2( c   1   −c   2 )+ x /( a   2   −a   1 )( c   1   −c   2 )+ y /( b   1   −b   1 )( c   1   −c   2 ) 
     which may be simplified to: 
     
       
         
           
             z 
             = 
             
               
                 x 
                 a 
               
               + 
               
                 y 
                 b 
               
             
           
         
       
     
     where: 
     x is the coordinate, along the x-axis, of a location on the reflective surface  30 ; 
     y is the coordinate, along the y-axis, of a location on the reflective surface  30 ; 
     z is the coordinate, along the z-axis, of a location on the reflective surface  30 ; 
     a is a first constant; and 
     b is a second constant. 
     Locations on the reflective surface  30  are determined by setting x to a first series of integral values such as 0, 1, 2, 3, . . . , N (or, if desired, to a series of non-integral values), setting y to a second series of integral such as 0, 1, 2, 3, . . . , N (or, if desired, to a second series of non-integral values) and solving for z when a is set to have a range from 600 to 1,300 i.e., 600≦a≦1,300 and the absolute value of the difference between b and a shall be no less than 100 and no more than 200, i.e., 100≦|a−b|≦200. 
     B. Practice 
     Collectively referring now to  FIGS. 3-6 , a mirror  100 , for example, a side view mirror commonly employed by trucks, buses and automobiles, having a true and undistorted field of vision like that normally associated with a flat mirror but without the blind spot produced by such mirrors will now be described in greater detail. As may now be seen, the mirror  100  has a top side surface  102  which serves as a reflective surface for the mirror  100  and a bottom side surface  112  which serves as a base for the mirror  100 . As may be further seen, the reflective surface  102  has a generally rectangular shape that is defined by a first edge surface  104 , a second edge surface  106 , the second edge surface  106  being longer than and generally orthogonal to the first edge surface  104 , a third edge surface  108  generally orthogonal to the second edge surface  106 , the third edge surface  108  being approximately the same length as and generally parallel to the first edge surface  104  and a fourth edge surface  110  generally orthogonal to the third edge surface  108 , the fourth edge surface  110  being approximately the same length as and generally parallel to the second edge surface  106 . 
     As best seen in  FIGS. 4 and 5 , the general center of the mirror  100  bulges outwardly relative to the edge surfaces  104 ,  106 ,  108  and  110 . Thus, the mirror  100  is a member of the family of mirrors commonly referred to as convex mirrors. It should be clearly understood, however, that the specific shape and relative dimensions of the convex mirror  100  illustrated in  FIGS. 3-6  is purely exemplary and that it is fully contemplated that the mirror may be of a wide variety of shapes and sizes. The reflective surface  102  of the convex mirror  110  is a multi-curvature surface comprised of a first reflective sub-area having a first curvature and a second reflective sub-area having a second curvature. 
     Referring next to  FIG. 7 , the reflective surface  102  comprised of a first reflective sub-area  114  having a first curvature and a second reflective sub-area  116  having a second curvature may now be seen in greater detail. In the embodiment disclosed herein, the first reflective sub-area  114  has a first curvature which corresponds to a sphere having a radius of 780 mm while the second reflective sub-area  116  has a second curvature which corresponds to a sphere having a radius of 700 mm. As previously set forth, the locations on the multi-curvature reflective surface  102  may be determined by setting x to 0, 1, 2, 3, . . . , N, setting y to 0, 1, 2, 3, . . . , N (or, if desired, to a second series of non-integral values) and solving for z where 
     
       
         
           
             
               z 
               = 
               
                 
                   x 
                   a 
                 
                 + 
                 
                   y 
                   b 
                 
               
             
             , 
           
         
       
     
     600≦a≦1,300 and 100≦|a−b|≦200. 
     Importantly, depending on the process by which locations for the reflective surface  102  are determined, the multi-curvature convex mirror  100  may have a vertically oriented field of view such as the field of view  204  produced by the multi-curvature convex mirror  200  illustrated in  FIG. 8  or a horizontally oriented field of view such as the field of view  216 ,  218  produced by the multi-curvature convex mirror  220 ,  222 , respectively, illustrated in  FIG. 9 . In this regard, it should be noted that, if the reflective surface  102  of the multi-curvature convex mirror  100  is to have a vertically oriented field of view, the additional condition that A is less than B should be applied to the above equation when determining the locations corresponding to the reflective surface  102  of the multi-curvature convex mirror  100 . Conversely, if the reflective surface  102  of the multi-curvature convex mirror  100  is to have a horizontally oriented field of view, the additional condition that A is greater than B should be applied to the above equation when determining the locations corresponding to the reflective surface  102  of the multi-curvature convex mirror  100 . 
     The process of forming the multi-curvature convex mirror  100  is comprised of a series of steps. First, employing the aforementioned equation with sets of the x, y and z parameters, a computer-generated model of the multi-curvature convex mirror  100  is produced. A mold to be used in manufacturing the multi-curvature convex mirror  100  is then formed. When forming the mold, it is recommended that rectangular material of approximately twice the size of the dimensions of the desired multi-curvature convex mirror  100 , for example, mold square stock, be employed. In the embodiment disclosed herein, diatomite, a naturally occurring sedimentary rock, is used to construct the mold. Of course, it is fully contemplated that a wide variety of materials are suitable for use when constructing the mold. 
     The center of the rectangular material is then designated as the point of origin (0,0,0) from which the locations corresponding to the reflective surface  102  of the multi-curvature convex mirror  100  are identified. For a vertically oriented field of view, the locations are determined by proceeding downwardly from the point of origin. For a horizontally oriented field of view, the locations are determined by proceeding to the right of the square mold stock (if a right horizontally oriented multi-curvature convex mirror such as mirror  222  is desired) or by proceeding to the left of the square mold stock (if a left horizontally oriented multi-curvature convex mirror such as the mirror  220  is desired). 
     From the mold, a series of substrates, each having a surface that mirrors the surface of the computer-generated model of the multi-curvature convex mirror is produced. It is contemplated that float glass is a suitable material with which the substrates may be produced. Of course, any number of other materials are suitable for this purpose. Finally, it is contemplated that the multi-curvature convex mirrors are produced by coating the float glass with titanium, chromium, aluminum or other suitable reflective material. 
     The resultant multi-curvature convex mirror  100  is characterized by an enhanced field of view relative to conventional mirrors currently employed as rear or side view mirrors. For example,  FIG. 8  shows the vertically oriented field of view  202  when the side view mirror of vehicle  200  is a conventional mirror  200  and the enhanced vertically oriented field of view  204  when side view mirror of vehicle  200  is a multi-curvature convex mirror. Further by way of example,  FIG. 9  shows the left and right horizontally oriented field of views  212  and  214  when side view mirrors  220  and  222 , respectively, of vehicle  206  are conventional mirrors and the left and right horizontally oriented field of views  216  and  218  when side view mirrors  220  and  222 , respectively, of vehicle  206  are multi-curvature convex mirrors. As further seen in  FIG. 9 , the enhanced field of view  216 ,  218  resulting from use of the multi-curvature convex mirrors as the side view mirrors  220 ,  222  enable a driver to see vehicle  208 ,  210  (which are outside the field of view  212 ,  214 . 
     While a number of embodiments of a multi-curvature convex mirror have been shown and described herein, modifications thereof may be made by one skilled in the art without departing from the spirit and the teachings of the invention. The embodiments described herein are exemplary only, and are not intended to be limiting. Many variations, combinations, and modifications of the embodiments disclosed herein are possible and are within the scope of the teachings set forth herein. Accordingly, the scope of protection is not limited by the description set out above but is only defined by the claims appended hereto