Abstract:
An image forming system utilizing a light emitting diode (LED array) having LEDs arranged along a curved line. The LEDs are either edge emitting type LEDs or surface emitting type LEDs. The LEDs of the LED array emit light towards a center or optical axis of the lens. A plurality of lenses are connected together to form a lens array. Alternatively, two lens arrays can be utilized. If two lens arrays are utilized, each of the lenses in the lens array includes an aspherical surface. The curved LED array prevents the flaring of light and produces an even pattern of light emission on a light receiving surface such as a photoconductive drum.

Description:
This application is a continuation of application Ser. No. 09/124,833 filed on Jul. 30, 1998, now U.S. Pat. No. 5,962,874, which is a continuation of Ser. No. 08/744,311 filed Nov. 7, 1996, now U.S. Pat. No. 5,838,024. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is directed to a light emitting diode (LED) array for optical printers, digital copiers, facsimile machines, etc. More particularly, the present invention is directed to a light emitting diode array in which a plurality of light emitting elements are disposed along a curved line in order to reduce distortion. 
     2. Discussion of the Background 
     A light emitting diode array includes a plurality of light emitting elements which are disposed in at least one row. Such a light emitting diode array is used in an optical printer, a digital copier, or a facsimile machine. The light emitting diode array is more reliable for use under vibrations and noises than a laser beam printer. The light emitting diode array is also suitable for miniaturizing an optical image forming apparatus, as the light emitting diode array does not need a scanning mechanism such as a polygonal mirror as is required by the laser beam printer. 
     FIG. 8 illustrates a base  80  having mounted thereon a conventional light emitting diode array  70  with two lens arrays  90  and  100  for use in an optical image forming apparatus. The light emitting diode array  70  comprises a plurality of light emitting diodes  71  which are disposed in one row and on a straight line at the same predetermined distance from each other. The straight line on which the light emitting diodes  71  are disposed is perpendicular to an optical axis of lenses  91  and  101  in the lens arrays  90  and  100 . 
     A pattern of light emission from the light emitting diode array  70  is focused on a photosensitive body such as a photoconductive drum through the two lens arrays  90  and  100  so as to form an image on the photosensitive body. However, the above-mentioned optical image forming apparatus with light emitting diode array  70  and lens arrays  90  and  100  has a drawback in that light loss occurs at connecting portions  91   a ,  101   a  between each lens  91  and  101 , and in that flared light occurs on each lens  91  and  101 . As a result, a pattern of light emission onto the photosensitive body becomes uneven. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention provides for a novel light emitting diode array which can solve the aforementioned drawbacks, and, thus, an object of the present invention is to provide for a novel light emitting diode array in which a pattern of light emission onto the photosensitive body from the light emitting diode array and the lens array is uniform. 
     It is another object of the present invention to provide for a novel light emitting diode array in which the occurrence of light loss and flared light is prevented. 
     These and other objects are accomplished by a light emitting diode array for use in an optical image forming apparatus which has the LEDs arranged along a curved line. Light from the LEDs along the curved line is focused through a lens on a light receiving surface such as a photoconductive drum. This forms a latent image on the photoconductive drum which can be developed using conventional toner developing techniques into a toner image which is transferred onto a page in a conventional manner. The LEDs are edge emitting type LEDs or alternatively surface emitting type LEDs. The LEDs at the ends of the LED array are aimed toward and project light towards the center of the lens and also towards the optical axis of the lens. 
     The lens used by the present invention can include one lens array or two lens arrays in parallel. If two lens arrays are used, each of the lenses include an aspherical surface. The arrangement of the invention can be used in an image forming system such as a copier, printer, or facsimile machine. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the present invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
     FIGS. 1A and 1B are views showing the construction of an edge emitting type light emitting diode array in accordance with the present invention; 
     FIGS. 2A and 2B are views showing the construction of a surface emitting type light emitting diode array in accordance with the present invention; 
     FIG. 3 is a view showing the first embodiment of the light emitting diode array with a lens array for an optical image forming apparatus in accordance with the present invention; 
     FIG. 4 is a view showing an enlargement of the light emitting diode array with the lens array of FIG. 3; 
     FIGS. 5A,  5 B, and  5 C are diagrams of spherical aberration, astigmatism and distortional aberration, respectively, of the first embodiment of the light emitting diode array with the lens array for the optical image forming apparatus in accordance with the present invention; 
     FIG. 6 is a view showing the second embodiment of the light emitting diode array with two lens arrays for the optical image forming apparatus in accordance with the present invention; 
     FIGS. 7A,  7 B, and  7 C are diagrams of spherical aberration, astigmatism and distortional aberration, respectively, of the second embodiment of the light emitting diode array with two lens arrays for the optical image forming apparatus in accordance with the present invention; and 
     FIG. 8 is a view showing a conventional light emitting diode array with lens array for the optical image forming apparatus. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Preferred embodiments of a light emitting diode array and an optical image forming apparatus with the light emitting diode (LED) array in accordance with the present invention will now be explained with reference to the accompanying drawings, wherein like reference numerals are utilized to designate identical or corresponding elements throughout the several views. 
     FIGS. 1A and 1B are views showing the construction of an edge emitting type light emitting diode array in accordance with the present invention. Light emitting diodes  2  with light emitting elements  2 A are provided on a base  3 . The light emitting diode array has a plurality of light emitting diodes  2  which are disposed on a curved line with a same predetermined distance between each LED  2 . The Z direction is a light emitting direction, and the Y direction is a direction of a rotating axis of the photosensitive body. 
     FIGS. 2A and 2B are views showing the construction of a surface emitting type light emitting diode array in accordance with the present invention. A plurality of light emitting diodes  2 ′ are provided on a base  3 ′. The light emitting diode array has a plurality of light emitting diodes  2 ′ which are disposed on a curved line at a same predetermined distance from each other. 
     The edge emitting type LED array in FIG.  1  and the surface emitting type LED array in FIG. 2 are manufactured using a semiconductor forming process such as the LPE (Liquid Phase Epitaxial) method or the MOCVD (Metal Organized Chemical Vapor Deposit) method. The edge emitting type light emitting diode array is more easily manufactured than the surface emitting type LED array. 
     FIG. 3 is a view showing the first embodiment of the light emitting diode array having a lens array for the optical image forming apparatus in accordance with the present invention, and FIG. 4 is an enlarged view of FIG.  3 . It is to be noted that the elements illustrated in FIGS. 3 and 4 can correspond to similarly named elements in FIGS. 1A, lB,  2 A, and  2 B. As illustrated in FIGS. 3 and 4, the light emitting diode arrays  51  and  52  have a plurality of light emitting diodes  20  which are disposed on a curved line at a same predetermined distance from each other on a base  10 . The light emitting diode arrays  51  and  52  correspond to aspherical lenses  41  and  42  of a lens array  4 . The lens array  4  focuses the light from the LED array  51  to a photosensitive body  50 . The distance between the optical axes of lenses  41  and  42  are a predetermined distance P. In FIG. 3, the “R” values represent a radius of specific curvature and the “D” values represent a distance. Numeric values of the R and D values are provided below with respect to the first embodiment. 
     Luminous flux is emitted from the light emitting diode located at the end of the light emitting diode array  51  closest to the array  52  towards the optical axis of lens  41  at an angle  0  (and consequently towards the optical axis of the lens  41 ) onto the photosensitive body  50  so that amounts of the luminous flux from each of the diodes  20  of the array  51  to the lens  41  are equal. 
     As can be seen in FIGS. 1A,  2 A, and  3 , a direction of emission of light from the LEDs and a curved line connecting the LEDs are generally planar. For example, in FIG. 1A, the line connecting the LEDs is in the ZY plane and the light from the LEDs is also in the ZY plane. Additionally, in FIG. 2A, the curve connecting the LEDs is in the ZY plane and the direction of emission of the LEDs is also in the ZY plane. 
     The curved line of the light emitting diode array  51  and the aspherical surface of the lens  41  are explained herein. In the following description for the aspherical surface, an x-coordinate is set to be in conformity with the optical axis of the lens, and an h-coordinate is set to be perpendicular to the optical axis of the lens. 
     In the equation set forth below, r designates a radius of curvature of a surface on the optical axis, k designates a conical constant, and a, b, c and d designate aspherical coefficients of higher orders. In this case, as is well known, the aspherical surface is provided by a curved surface obtained by rotating a curve represented by the following formula around the optical axis of the lens. 
     
       
           z =( h   2/   r )/[1+{square root over ({1− k +L )( h/r +L ) 2 +L })}]+ a·h   4   b·h   6   +c·h   8   +d·h   10  +  (1)  
       
     
     A shape of the aspherical surface is specified by providing the radius of curvature on the optical axis of the lens, the conical constant and the aspherical coefficients of higher orders. 
     With respect to the aspherical coefficients, E and a number subsequent to this E designate a power. For example, E-9 shows 1/10 9  and this value 1/10 9  is multiplied by a numerical value which appears before the E. 
     In the following description for the curved line U on which the group of light emitting diodes for a respective lens is disposed, a y-coordinate is set to be in conformity with the arranging direction of the light emitting diode array. In the equation below, reference characters L, K, A, B, C and D designate coefficients. 
     
       
           U =( Y   2   /L )/[ 1+{square root over ({1+L −( 1+K +L )( Y/L +L ) 2 +L })}]+   A·Y   4   +B·Y   6   +C·Y   8   +D·Y   10  +  (2)  
       
     
     The shape of the curved line is defined by the coefficients of equation (2). As equation (2) has a similar format to equation (1) and equation (1) defines an aspherical curve, equation (2) also defines an aspherical curve. 
     In FIG. 3, the curved line of the LED array  51  includes several inherent features. The curved line contains three points at which the first derivative is zero, and two points of inflection. The definition of a point of inflection is a point at which there is a change in curvature of a curve from concave to convex or conversely. Further, the curved line of the LED array  51  contains a total of 5 maxima and minima. 
     First Embodiment 
     Below are parameters of a first exemplary embodiment of the invention, as illustrated in FIG.  3 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE I 
               
               
                   
                   
               
               
                   
                 Object 
                 Radius (mm) 
                 Index of Refraction 
               
               
                   
                   
               
             
             
               
                   
                 Diode Array 
                 1.469E-4 
                 1.0 
               
               
                   
                 1st Lens Surface 
                 4.034 
                 1.5721 
               
               
                   
                 2nd Lens Surface 
                 −83.729 
                 1.0 
               
               
                   
                 Photosensitive 
                 ∞ 
                 N/A 
               
               
                   
                 Body 
               
               
                   
                   
               
             
          
         
       
     
     D1=13.0 mm 
     D2=6.40 mm 
     D3=10.52 mm 
     D4=2.71 
     Parameters of the Aspherical Surface of the 1st Lens Surface: 
     r=4.034, k=0.2224, 
     a=−1.5650E−3, b=−1.2677E−4, 
     c=1.3081E−5, d=−1.5695E−6 
     Parameters of the Aspherical Surface of the 2nd Lens Surface: 
     r=−83.729, k=−583.6955, 
     a=3.5363E−3, b=3.8881E−4, 
     c=−2.364E−5, d=5.3886E−6 
     Parameters of the Curve Line: 
     L=1.469E−4, K=−444.7470, 
     A=−2.2664E−2, B=5.2473E−3, 
     C=−1.3095E−4, D=−3.7272E−5 
     Other parameters of the lenses are as follows: 
     Focal length: 6.91 mm 
     Brightness of lens (F No): 3.27 
     Valid diameter: 5.37 mm 
     Distance between each lens P: 5.47 mm 
     Lateral magnification: −1.10 
     When the image resolution is 600 dots per inch, the number of light emitting diodes in the array for each lens is lens 128 per 5.47 mm. 
     FIGS. 5A-5C are diagrams of spherical aberration, astigmatism and distortional aberration of the first embodiment of the light emitting diode array and the lens array for the optical image forming apparatus in accordance with the present invention. 
     In FIG. 5B, the broken (dashed) line represents the astigmatism along the meridional direction (the array arranging direction) and the solid line represents the astigmatism along the sagittal direction which is the direction perpendicular to the array arranging direction. In FIG. 5B, the dashed line is close to the vertical axis, thus indicating that this embodiment obtains a reduced meridional astigmatism. 
     FIG. 6 is a view showing the second embodiment of the light emitting diode array with two lens arrays for the optical image forming apparatus. As illustrated in FIG. 6, a light emitting diode  20 ′ is provided on the base  10 ′. The light emitting diode array has a plurality of light emitting diodes which are disposed on a curved line at a same predetermined distance from each other. The light emitting diode array corresponds to two aspherical lenses  41 A and  41 B of a lens array  4 ′. Luminous flux is emitted from the light emitting diode  20 ′ located at a lowermost edge of the light emitting array toward the center of the two lenses  41 A and  41 B (and consequently towards their optical axes) onto the photosensitive body  50 . 
     The curved line for the light emitting diode array and the aspherical surface of two lenses  41 A and  41 B are explained hereinafter. 
     Second Embodiment 
     Below are parameters of a second exemplary embodiment of the invention as illustrated in FIG.  6 . 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE II 
               
               
                   
                   
               
               
                   
                   
                   
                 Index of 
               
               
                   
                 Object 
                 Radius (mm) 
                 Refraction 
               
               
                   
                   
               
             
             
               
                   
                 Diode Array 
                 −1.958E-8 
                 1.0 
               
               
                   
                 1st Lens Surface 
                 −29.847 
                 1.5721 
               
               
                   
                 2nd Lens Surface 
                 ∞ 
                 1.0 
               
               
                   
                 3rd Lens Surface 
                 ∞ 
                 1.5721 
               
               
                   
                 4th Lens Surface 
                 −4.661 
                 1.0 
               
               
                   
                 Photosensitive 
                 ∞ 
                 N/A 
               
               
                   
                 Body 
               
               
                   
                   
               
             
          
         
       
     
     D1=11.00 mm 
     D2=2.50 mm 
     D3=2.00 mm 
     D4=2.5 mm 
     D5=20.00 mm 
     D6=2.71 mm 
     Spherical Surface of 1st Lens Surface: 
     r=−29.847, k=−504.7168, 
     a=−3.4307E−3, b=−1.8331E−4, 
     c=−5.6715E−5, d=1.1841E=5 
     Aspherical Surface of 4th Lens Surface: 
     r=−4.661, k=−1.2592, 
     a=6.3732E−4, b=−1.6292E−4, 
     c=−1.5340E−5, d=2.3309E−6 
     Curved Line: 
     L=−1.958E−8, K=−7.1770E+12 
     A=2.6166E−2, B=−1.2259E−2, 
     C=1.2925E−3, D=2.3840E−5 
     Focal length: 8.64 mm 
     Brightness of lens (F No): 3.67 
     Valid diameter: 5.40 mm 
     Distance between each lens P: 5.69 mm 
     Lateral magnification: −1.10 
     When the image resolution is 600 dots per inch, the number of light emitting diodes in the array is 134 per 5.69 mm. 
     FIGS. 7A-7C are diagrams of spherical aberration, astigmatism, and distortional aberration, respectively, of the second embodiment of the light emitting diode array with two lens arrays for the optical image forming apparatus in accordance with the present invention. In these Figures, the astigmatism in the meridional direction, corresponding to the broken line in FIG.  7 B and the distortional aberration illustrated in FIG. 7C are improved by arranging the LEDs on the curved line. 
     Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.