Abstract:
An optical scanning device for scanning a photoreceptor surface with a beam, said optical scanning device having: a light source for emitting the beam; an optical system for causing the beam emitted from the light source to converge; and a deflector that includes a polygon mirror with a plurality of reflecting surfaces and that deflects the beam that has passed through the optical system by rotations of the polygon mirror. Between the deflector and the photoreceptor surface, no optical system for causing the beam to converge or diverge is disposed. The optical system for causing the beam emitted from the light source to converge generates spherical aberration depending on which part of the optical system in a main-scanning direction the beam passes through. The beam enters into three or more adjacent reflecting surfaces of the polygon mirror at a time.

Description:
This application is based on Japanese Patent Application No. 2010-141558 filed on Jun. 22, 2010, the content of which is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Filed of the Invention 
     The present invention relates to an optical scanning device, and more particularly to an optical scanning device for irradiating a photosensitive drum with a light beam to form an electrostatic latent image on the photosensitive drum. 
     2. Description of Related Art 
     An example of well-known conventional optical scanning devices is a post-objective type optical scanning device (which will be hereinafter referred to merely as an optical scanning device) as disclosed by Japanese Patent Laid-Open Publication No. 5-241094. In the optical scanning device, a polygon mirror having cylindrical or spherical reflecting surfaces is employed, and thereby, the necessity of providing a scanning lens between the polygon mirror and the photosensitive drum is eliminated. 
     However, since the reflecting surfaces of the polygon mirror are not planar, the manufacturing cost of the optical scanning device is high. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide an optical scanning device that is less costly to manufacture. 
     According to an embodiment of the present invention, an optical scanning device for scanning a photoreceptor surface with a beam comprises: a light source for emitting the beam; an optical system for causing the beam emitted from the light source to converge; a deflector that includes a polygon mirror with a plurality of reflecting surfaces and that deflects the beam that has passed through the optical system by rotations of the polygon mirror; wherein no optical system for causing the beam to converge or diverge is disposed between the deflector and the photoreceptor surface; wherein the optical system generates spherical aberration depending on which part of the optical system in a main-scanning direction the beam passes through; and wherein the beam enters into three or more adjacent reflecting surfaces of the polygon mirror at a time. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       This and other objects and features of the present invention will be apparent from the following description with reference to the accompanying drawings, in which: 
         FIG. 1  is a structural view of an optical scanning device according to a first embodiment of the present invention; 
         FIG. 2  is a plan view of the optical scanning device from y direction; 
         FIG. 3  is a plan view of the optical scanning device from z direction; 
         FIG. 4  is a plan view of the optical scanning device from z direction; 
         FIG. 5  is an illustration of a deflector and a beam B; 
         FIG. 6  is an illustration of the deflector and the beam B; 
         FIG. 7  is an illustration of the deflector and the beam B; 
         FIG. 8  is a graph showing results of a first computer simulation performed on a first example of an optical scanning device; 
         FIG. 9  is a graph showing results of the first computer simulation performed on a first comparative example; 
         FIG. 10  is a graph showing results of a second computer simulation performed on the first comparative example; 
         FIG. 11  is a graph showing results of the second computer simulation performed on the first example of the optical scanning device; 
         FIG. 12  is a graph showing results of the second computer simulation performed on the first example of the optical scanning device; 
         FIG. 13  is a graph showing the intensity distribution on a photoreceptor surface when a test pattern was formed by the first example of the optical scanning device; 
         FIG. 14  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the first example of the optical scanning device; 
         FIG. 15  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the first example of the optical scanning device; 
         FIG. 16  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the first comparative example; 
         FIG. 17  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the first comparative example; 
         FIG. 18  is a graph showing results of a fourth computer simulation performed on the first example of the optical scanning device; 
         FIG. 19  is a graph showing results of the fourth computer simulation performed on the first comparative example; 
         FIG. 20  is a graph showing results of the first computer simulation performed on a second example of the optical scanning device; 
         FIG. 21  is a graph showing results of the first computer simulation performed on a second comparative example; 
         FIG. 22  is a graph showing results of the second computer simulation performed on the second comparative example; 
         FIG. 23  is a graph showing results of the second computer simulation performed on the second example of the optical scanning device; 
         FIG. 24  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the second example of the optical scanning device; 
         FIG. 25  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the second example of the optical scanning device; 
         FIG. 26  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the second comparative example; 
         FIG. 27  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the second comparative example; 
         FIG. 28  is a graph showing results of the fourth computer simulation performed on the second example of the optical scanning device; 
         FIG. 29  is a graph showing results of the fourth computer simulation performed on the second comparative example; 
         FIG. 30  is a graph showing results of the first computer simulation performed on a third example of the optical scanning device; 
         FIG. 31  is a graph showing results of the second computer simulation performed on a third example of the optical scanning device; 
         FIG. 32  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the third example of the optical scanning device; 
         FIG. 33  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the third example of the optical scanning device; 
         FIG. 34  is a graph showing results of the fourth computer simulation performed on the third example of the optical scanning device; 
         FIG. 35  is a structural view of an optical scanning device according to a third embodiment of the present invention; 
         FIG. 36  is a graph showing results of the first computer simulation performed on a fourth example of the optical scanning device; 
         FIG. 37  is a graph showing results of the second computer simulation performed on the fourth example of the optical scanning device; 
         FIG. 38  is a graph showing the relationship between vertical-line contrast and deflection angle θ in the fourth example of the optical scanning device; 
         FIG. 39  is a graph showing the relationship between horizontal-line contrast and deflection angle θ in the fourth example of the optical scanning device; and 
         FIG. 40  is a graph showing results of the fourth computer simulation performed on the fourth example of the optical scanning device. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Optical scanning devices according to some embodiments of the present invention will be described. 
     First Embodiment 
     Structure of the Optical Scanning Device 
     An optical scanning device according to a first embodiment of the present invention will be described with reference to the accompanying drawings.  FIG. 1  is a structural view of the optical scanning device  10  according to the first embodiment. In  FIG. 1 , a main-scanning direction on a photosensitive drum  20  is referred to as y direction, and a direction in which a rotary shaft of a polygon mirror extends is referred to as z direction. A direction that is orthogonal to the y direction and to the z direction is referred to as x direction.  FIG. 2  is a plan view of the optical scanning device  10  from the y direction. 
     The optical scanning device  10  is to scan a beam B on the photosensitive drum  20  in the y direction. As shown in  FIGS. 1 and 2 , the optical scanning device  10  comprises a light source  12 , a collimator lens  14 , a free-form-surface lens  16  and a deflector  18 . The light source  12 , which is, for example, a laser diode, emits a beam B 0 . 
     The collimator lens  14  and the free-form-surface lens  16  form an optical system  17  for causing the beam B 0  that is a divergent light to converge and to be focused onto the photosensitive drum  20 . The collimator lens  14  is an axisymmetric aspherical lens made of glass. The free-form-surface lens  16  is a non-axisymmetric lens made of resin. The free-form-surface lens  16  has a free-form surface on the side closer to the light source  12 . The free-form surface is of a rotationally asymmetric shape. More specifically, the free-form surface has two symmetric surfaces of which normal lines are orthogonal to each other. The normal line of one of the two surfaces is orthogonal to a rotation axis of a polygon mirror comprised in the deflector  18 . 
     The polygon mirror comprised in the deflector  18  has a plurality of reflecting surfaces. After passing through the collimator lens  14  and the free-form-surface lens  16 , the beam B is deflected with rotations of the polygon mirror. The beam B is a part of a beam B 0 , and this will be described later. 
     Between the deflector  18  and the photosensitive drum  20 , there are provided no optical elements, such as lenses and mirrors, for causing the beam B to converge. 
     The photosensitive drum  20  is driven to rotate at a specified velocity. The beam B is main-scanned by the rotations of the polygon mirror and sub-scanned by the rotations of the photosensitive drum  20 , and thereby, a two-dimensional electrostatic latent image is formed. 
     In the optical scanning device  10 , as described below, the optical path length of the beam B from the output surface of the free-form-surface lens  16  to the surface of the photosensitive drum  20  depends on the irradiation point of the photosensitive drum  20 .  FIGS. 3 and 4  are plan views of the optical scanning device  10  from z direction.  FIG. 3  shows the state where the negative edge in y direction of the photosensitive drum  20  is irradiated with the beam B.  FIG. 4  shows the state where the center in y direction of the photosensitive drum  20  is irradiated with the beam B. In the following, when viewed from z direction, the angle of the beam B to x axis is referred to as a deflection angle θ. The deflection angle θ has positive values in the counterclockwise direction. 
     As is apparent from  FIGS. 3 and 4 , the optical path length of the beam B from the output surface of the free-form-surface lens  16  to the surface of the photosensitive drum  20  in the case of  FIG. 3  is longer than the optical path length of the beam B from the output surface of the free-form-surface lens  16  to the surface of the photosensitive drum  20  in the case of  FIG. 4 . Thus, in the optical scanning device  10 , the optical path length of the beam B from the output surface of the free-form-surface lens  16  to the surface of the photosensitive drum  20  depends on what point of the photosensitive drum  20  is irradiated with the beam B. The optical scanning device  10 , therefore, has such a structure to permit the beam B to be focused onto the surface of the photosensitive drum  20  at all times even though the optical path length of the beam B from the output surface of the free-form-surface lens  16  to the surface of the photosensitive drum  20  varies. The structure is hereinafter described with reference to the accompanying drawings.  FIGS. 5 to 7  show the deflector  18  and the beam B.  FIG. 5  shows the state where the beam B is directed to the negative edge in y direction of the photosensitive drum  20 .  FIG. 7  shows the state where the beam B is directed to the positive edge in y direction of the photosensitive drum  20 .  FIG. 6  shows the state where the beam B is directed to the center in y direction of the photosensitive drum  20 . 
     In  FIGS. 5 to 7 , the beam that has passed through the free-form-surface lens  16  is denoted by B 0 . In the beam B 0 , a beam that enters into a specified reflecting surface m of the polygon mirror of the deflector  18  and that is reflected from the reflecting surface m is denoted by B. 
     As shown by  FIGS. 5 to 7 , the beam B 0  that has passed through the optical system  17  enters into adjacent three reflecting surfaces at all times during scanning of the photosensitive drum  20 . In this embodiment, during scanning of the photosensitive drum  20 , the beam B 0  enters into the specified reflecting surface m over the entire width in the main-scanning direction. The beam B reflected from the reflecting surface m is scanned on the photosensitive drum  20  in y direction. Beams reflected by reflecting surfaces other than the reflecting surface m are blocked by a light-blocking member. 
     Since the beam B 0  enters into a plurality of reflecting surfaces, a part of the beam B 0  that passed through any of various portions of the free-form-surface lens  16  can become the beam B. More specifically, when the beam B is directed to the negative edge in y direction of the photosensitive drum  20 , the beam B is the part of the beam B 0  that passed through the lower portion (seen in  FIG. 5 ) of the free-form-surface lens  16 . As shown by  FIG. 6 , when the beam B is directed to the center in y direction of the photosensitive drum  20 , the beam B is the part of the beam B 0  that passed through the middle portion of the free-form-surface lens  16 . As shown by  FIG. 7 , when the beam B is directed to the positive edge in y direction of the photosensitive drum  20 , the beam B is the part of the beam B 0  that passed through the upper portion of the free-form-surface lens  16 . 
     In the optical scanning device  10 , the optical system  17  composed of the collimator lens  14  and the free-form-surface lens  16  generates different spherical aberrations in the beam B in accordance with what portion of the optical system  17  the beam B passes through. In other words, the optical system  17  has such optical characteristics as to permit the length between the optical system  17  and the image point of the beam B to change in accordance with what portion of the optical system  17  the beam B passes through. More specifically, the optical system has such optical characteristics that the average wavefront curvature of the beam B when the beam B is directed to the negative and positive edges in y direction of the photosensitive drum  20  will be smaller than the average wavefront curvature of the beam B when the beam B is directed to the center in y direction of the photosensitive drum  20 . Thereby, when the beam B is directed to the both edges in y direction of the photosensitive drum  20 , the beam B is focused on a point relatively far from the optical system  17 , and when the beam B is directed to the center in y direction of the photosensitive drum  20 , the beam B is focused on a point relatively close to the optical system  17 . 
     As described above, in the optical scanning system  10 , since the beam B 0  enters into a plurality of reflecting surfaces of the polygon mirror, a part of the beam B 0  that passed through any of various portions of the free-form-surface lens  16  can become the beam B. Also, the optical system  17  including the free-form-surface lens  16  generates different spherical aberrations in the beam B in accordance with what portion of the optical system  17  the beam B passes through. The optical characteristics of the optical system  17  including the free-form-surface lens  16  are designed such that the beam B that is directed to the both edges in y direction of the photosensitive drum  20  can be focused on a point relatively far from the optical system  17  and that the beam B that is directed to the center in y direction of the photosensitive drum  20  can be focused on a point relatively close to the optical system  17 . Thus, it is possible to focus the beam B onto every point of the entire surface of the photosensitive drum  20 . 
     In the optical scanning device  10 , it is not necessary to use a polygon mirror with curved reflecting surfaces as used in the optical scanning device disclosed by Japanese Patent Laid-Open Publication No. 5-241094. Accordingly, the optical scanning device  10  is less costly to manufacture. 
     First Example 
     A first example of the optical scanning device  10 , which is an example according to the first embodiment, will be described below. In the first example of the optical scanning device  10 , the beam B 0  emitted from the light source  12  has a wavelength of 780 nm. The glass of the collimator lens  14  has a refractive index of 1.564, and the resin of the free-form-surface lens  16  has a refractive index of 1.525. The polygon mirror of the deflector  18  is in the shape of a dodecagon having an inscribed circle with a diameter of 10 mm. The deflection angle changes within the range from −25 degrees to 25 degrees. Table 1 shows the positional relationship among the collimator lens  14 , the free-form-surface lens  16 , the polygon mirror of the deflector  18  and the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                   
                   
                 Position of Origin of 
                 X-axis Vector in 
                 Y-axis Vector in 
               
               
                 Surface 
                 Name of 
                 Local Coordinate System 
                 Local Coordinate System 
                 Local Coordinate System 
               
             
          
           
               
                 Number 
                 Component 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
               
               
                   
               
             
          
           
               
                 1 
                 Collimator Lens 
                 119.09 
                 0.00 
                 10.42 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 2 
                   
                 116.10 
                 0.00 
                 10.16 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 3 
                 Free-form-surface 
                 99.24 
                 0.00 
                 8.68 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 4 
                 Lens 
                 94.26 
                 0.00 
                 8.25 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 5 
                 Polygon Mirror 
                 0.00 
                 0.00 
                 0.00 
                 −1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 6 
                 Photoreceptor 
                 245.00 
                 0.00 
                 −22.00 
                 1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 1.0000 
                 0.0000 
               
               
                   
                 Surface 
               
               
                   
               
             
          
         
       
     
     Surface No. 1 denotes the surface of the collimator lens  14  closer to the light source  12 . Surface No. 2 denotes the surface of the collimator lens  14  closer to the free-form-surface lens  16 . Surface No. 3 denotes the surface of the free-form-surface lens  16  closer to the collimator lens  14 . Surface No. 5 denotes the reflecting surface of the polygon mirror that reflects the beam B 0  at a deflection angle θ of 0 degrees. Surface No. 6 denotes the photoreceptor surface (the surface of the photosensitive drum  20 ). The surfaces 1 to 6 are expressed in respective peculiar coordinate systems, and table 1 shows the positions of the origins of the coordinate systems. 
     Surface No. 1 is a spherical surface and has a curvature of 4.33126×10 −3 . 
     Surface No. 2 is an axisymmetric aspherical surface and has a curvature of −6.68860×10 −2 . The shape of Surface No. 2 is expressed by the following expression (1), and the coefficients are shown by Table 2. 
     
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       
                         c 
                         ⁡ 
                         
                           ( 
                           
                             
                               y 
                               2 
                             
                             + 
                             
                               z 
                               2 
                             
                           
                           ) 
                         
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 c 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     y 
                                     2 
                                   
                                   + 
                                   
                                     z 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         12 
                       
                       ⁢ 
                       
                         
                           a 
                           i 
                         
                         ( 
                         
                           
                             
                               
                                 
                                   y 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   2 
                                 
                               
                               ) 
                             
                           
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Degree 
                 Coefficient 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 4 
                 2.50752 × 10 −5   
               
               
                   
                 6 
                 8.92745 × 10 −8   
               
               
                   
                 8 
                 −2.78758 × 10 −10    
               
               
                   
                 10 
                     2.15187 × 10 −11   
               
               
                   
                 12 
                 −2.55070 × 10 −13   
               
               
                   
                   
               
             
          
         
       
     
     Surface No. 3 is a free-form surface. The shape of Surface No. 3 is expressed by the following expression (2), and the coefficients are shown by Table 3. 
     
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       8 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         4 
                       
                       ⁢ 
                       
                         
                           a 
                           ij 
                         
                         ⁢ 
                         
                           y 
                           i 
                         
                         ⁢ 
                         
                           z 
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
             
             
               
                   
                   
               
               
                   
                 j 
                   
               
             
          
           
               
                 i 
                 0 
                 2 
                 4 
               
               
                   
               
               
                 0 
                 0.00000 × 10 −0   
                 2.54807 × 10 −3   
                 7.86216 × 10 −5   
               
               
                 2 
                 2.73998 × 10 −3   
                 1.28140 × 10 −4   
                 −9.35916 × 10 −5   
               
               
                 4 
                 −2.39846 × 10 −5   
                 −1.76113 × 10 −5   
                 1.52241 × 10 −5   
               
               
                 6 
                 3.10874 × 10 −6   
                 3.81174 × 10 −7   
                 −1.01763 × 10 −6   
               
               
                 8 
                 −1.63496 × 10 −7   
                 0.00000 × 10 −0   
                 0.00000 × 10 −0   
               
               
                   
               
             
          
         
       
     
     All coefficients except for the coefficients shown in Tables 1 to 3 are 0. 
     Surface No. 3 is a free-form surface expressed by an expression in which y and z are of degrees of even numbers. Therefore, surface No. 3 is a free-form surface that is symmetric about y axis and z axis. 
     Computer simulations were performed on the first example of the optical scanning device  10 . Also, an optical scanning device of the same structure as the first example of the optical scanning device  10  except for the point that the optical system  17  is replaced with an axisymmetric converging optical system that generates no aberrations on the axis was used as a first comparative example. In the first comparative example, the beam B after passing through the converging optical system is focused on a point 260 mm distant from the polygon mirror. 
     As a first computer simulation, changes in the beam peak intensity (beam profile intensity) on the photoreceptor surface (the surface of the photosensitive drum  20 ) with changes in the deflection angle θ were simulated, and this simulation was performed on the first example of the optical scanning device  10  and the first comparative example. Considering defocus possibly caused by changes in temperature, the simulation was conducted while the photoreceptor surface (the photosensitive drum  20 ) was moved in x direction in steps of 1 mm within the range from −3 mm to 3 mm.  FIG. 8  is a graph showing results of the first computer simulation performed on the first example of the optical scanning device  10 .  FIG. 9  is a graph showing results of the first computer simulation performed on the comparative example. The peak intensity is represented by values calculated by assuming the beam spot intensity with no aberrations as 1.  FIGS. 8 and 9  show changes in the peak intensity with changes in the deflection angle θ only within the range from 0 degrees to 25 degrees. This is because changes in the peak intensity with changes in the deflection angle θ within the range from −25 degrees to 0 degrees are the same as the changes in the peak intensity with changes in the deflection angle θ within the range from 0 degrees to 25 degrees. 
     In the first comparative example, as is apparent from the graph of  FIG. 9 , the peak intensity largely changes with changes in the deflection angle θ. This shows that in an optical scanning device using an axisymmetric converging optical system that generates no aberrations on the axis, there exists a deflection angle θ that makes the convergence of the beam B very bad. In the first example of the optical scanning device  10 , on the other hand, as shown by  FIG. 8 , the peak intensity does not change so largely even with changes in the deflection angle θ. This shows that by using the optical system  17  including the free-form-surface lens  16 , degradation in the convergence of the beam B with changes in the deflection angle θ can be suppressed. 
     Next, as a second computer simulation, changes in the defocus on the photoreceptor surface (the surface of the photosensitive drum  20 ) with changes in the deflection angle θ (field curvature) were simulated, and this simulation was performed on the first example of the optical scanning device  10  and the first comparative example. The defocus is represented by values showing the distances by which the photoreceptor surface (the photosensitive drum  20 ) was moved in x direction so that the beam B could be focused onto the photoreceptor surface. With respect to the first example of the optical scanning device  10 , the field curvature made by near-principal rays and the average field curvature made by the whole rays of the beam B were calculated. The principal ray means the center ray of the beam B after reflected by the polygon mirror to be used for image writing.  FIG. 10  shows results of the second computer simulation performed on the first comparative example.  FIGS. 11 and 12  show results of the second computer simulation performed on the first example of the optical scanning device  10 .  FIG. 11  shows the image surface of the near-principal rays, and  FIG. 12  shows the average image surface of the whole rays of the beam B.  FIGS. 11 and 12  each show the image surface of rays traveling on a surface in parallel to the main-scanning direction (which will be referred to as main-scanning-direction image surface) and the image surface of rays traveling on a surface in parallel to the sub-scanning direction (which will be referred to as sub-scanning-direction image surface). 
     In the first comparative example, as shown by  FIG. 10 , the curve showing the image surface falls steeply with increases in the deflection angle θ. This shows that in the first comparative example, as the irradiation point of the photosensitive drum  20  with the beam B comes closer to either edge in y direction, it is not possible to focus the beam B onto the surface of the photosensitive drum  20  without moving the photosensitive drum  20  in the negative direction along x axis. 
     In the first example of the optical scanning device  10 , as shown by  FIG. 11 , both of the curves showing the main-scanning-direction image surface and the sub-scanning-direction image surface of the near-principal rays fall steeply with increases in the deflection angle θ, which is similar to the case of the comparative example. When a notice is taken to a particular part of the beam B (the near-principal rays), in the first example of the optical scanning device  10  also, as the irradiation point of the photosensitive drum  20  with the beam B comes closer to either edge in y direction, the beam B cannot be focused onto the surface of the photosensitive drum  20  unless the photosensitive drum  20  is moved in the negative direction along x axis. 
     In the first example of the optical scanning device  10 , as shown by  FIG. 12 , however, both of the curves showing the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B do not fall so steeply even with increases in the deflection angle θ. In the first example of the optical scanning device  10 , the photosensitive drum  20  is scanned with not only the near-principal rays of the beam B but also the whole rays of the beam B. The portion of the optical system  17  where the beam B passes depends on the deflection angle θ. Further, since the free-form-surface lens  16  is used in the optical system  17 , the aberrations generated in the beam B depend on the portion of the optical system  17  where the beam B passes. As a result, as shown by  FIG. 12 , the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B do not show so steep field curvatures. This shows that in the first example of the optical scanning device  10 , it is possible to focus the beam B onto every point of the entire surface of the photosensitive drum  20  without moving the photosensitive drum  20  in x direction. 
     As is apparent from the graphs of  FIGS. 8 ,  12 ,  9  and  10 , the defocus and the peak intensity are not linked to each other in the first example of the optical scanning device  10 , while the defocus and the peak intensity are linked to each other in the first comparative example. This is because that in the first example of the optical scanning device  10 , the aberrations depend on the deflection angle θ. It is inferred that as a result of a combination of the tendency that the peak intensity becomes greater with decreases in the defocus (as shown by  FIG. 12 ) and the tendency that the peak intensity becomes lower with increases in the aberrations, the peak intensity characteristic shown by  FIG. 8  was obtained. 
     Next, as a third computer simulation, changes in the vertical-line contrast and changes in the horizontal-line contrast with changes in the deflection angle θ were simulated, and the third simulation was performed on the first example of the optical scanning device  10  and the first comparative example. Specifically, in each of the first example of the optical scanning device  10  and the comparative example, a vertical-line test pattern including vertical lines with two-dot widths at intervals of two-dot widths and a horizontal-line test pattern including horizontal lines with two-dot widths at intervals of two-dot widths were formed at every of various deflection angles θ, and the contrasts of the vertical-line test pattern and the horizontal-line test pattern were calculated. 
       FIG. 13  shows results of the third computer simulation performed on the first example of the optical scanning device  10 , and the graph of  FIG. 13  shows the intensity distribution on the photoreceptor surface (the surface of the photosensitive drum  20 ) when the test patterns were formed at a deflection angle θ of 25 degrees. The vertical axis of the graph shows the light intensity, and the horizontal axis of the graph shows the position on the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     In  FIG. 13 , the light intensity is represented by values obtained by assuming the light intensity of a solid image as 1. The graph of  FIG. 13  is a sinusoidal wave centering on 0.5. In the third computer simulation, the difference between the maximum value and the minimum value is calculated as a contrast. The vertical-line contrast and the horizontal-line contrast at the deflection angle θ of 25 degrees were 0.42 and 0.47, respectively. 
     Although not shown, similar graphs to the graph of  FIG. 13  were drawn to show the intensity distributions on the photoreceptor at other deflection angles θ. Then, in a manner similar to the manner of calculating the vertical-line contrast and the horizontal-line contrast at the deflection angle θ of 25 degrees, the vertical-line contrasts and the horizontal-line contrasts at the other deflection angles θ were calculated. Also, with respect to the comparative example, the same calculations were conducted. Further, considering defocus caused by changes in temperature, the simulation was conducted while the photoreceptor surface (the photosensitive drum  20 ) was moved in x direction in steps of 1 mm within the range from −3 mm to 3 mm. 
       FIG. 14  is a graph showing the relationship between the vertical-line contrast and the deflection angle θ in the first example of the optical scanning device  10 .  FIG. 15  is a graph showing the relationship between the horizontal-line contrast and the deflection angle θ in the first example of the optical scanning device  10 .  FIG. 16  is a graph showing the relationship between the vertical-line contrast and the deflection angle θ in the first comparative example.  FIG. 17  is a graph showing the relationship between the horizontal-line contrast and the deflection angle θ in the first comparative example. 
     As is apparent from  FIGS. 14 to 17 , the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ in the first example of the optical scanning device  10  than those in the first comparative example. Moreover, the vertical-line contrast and the horizontal-line contrast are less changeable with changes in position of the photoreceptor surface (the photosensitive drum  20 ) in the first example of the optical scanning device  10  than those in the first comparative example. Thus, the first example of the optical scanning device  10  has not only the advantage as shown by  FIG. 8  that the peak intensity is less changeable with changes in the deflection angle θ but also the advantage as shown by  FIGS. 14 and 15  that the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ. In the first example of the optical scanning device  10 , since the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ, it is possible to write vertical lines and horizontal lines of high picture quality. 
     Next, as a fourth computer simulation, changes in the average wavefront curvature of the beam B with changes in the deflection angle θ were simulated, and the fourth simulation was performed on the first example of the optical scanning device  10  and the first comparative example. Specifically, in each of the first example of the optical scanning device  10  and the first comparative example, the average wavefront curvature of the beam B incident to the reflecting surface m of the polygon mirror of the deflector  18  for every of various deflection angles θ was calculated.  FIG. 18  is a graph showing results of the fourth computer simulation performed on the first example of the optical scanning device  10 .  FIG. 19  is a graph showing results of the fourth computer simulation performed on the first comparative example. In  FIGS. 18 and 19 , the vertical axes show the curvature, and the horizontal axes show the deflection angle θ. 
     As shown by  FIG. 19 , in the first comparative example, the average wavefront curvature of the beam B is constant. The average wavefront curvature of the beam B is a reciprocal of the distance between the optical system and the image point of the beam B. Therefore,  FIG. 19  shows that in the first comparative example, it is impossible to focus the beam B onto every point of the entire photoreceptor surface (the entire surface of the photosensitive drum  20 ). 
     In the first example of the optical scanning device  10 , on the other hand, as shown by  FIG. 18 , both of the average wavefront curvature in the main-scanning direction and the average wavefront curvature in the sub-scanning direction of the beam B become smaller with increases in the deflection angle θ. This means that the beam B is focused on a farther point from the optical system  17  as the deflection angle θ becomes greater. Meanwhile, the distance between the optical system  17  and the photoreceptor surface (the surface of the photosensitive drum  20 ) becomes greater as the deflection angle θ becomes greater. Therefore, in the first example of the optical scanning device  10 , it is possible to focus the beam B onto every point of the entire photoreceptor surface (the surface of the photosensitive drum  20 ). Thus, the first example of the optical scanning device  10  can achieve better image writing performance than the first comparative example. 
     Second Example 
     Next, a second example of the optical scanning device  10 , which is an example according to the first embodiment, will be described below. In the second example of the optical scanning device  10 , the beam B 0  emitted from the light source  12  has a wavelength of 780 nm. The glass of the collimator lens  14  has a refractive index of 1.564, and the resin of the free-form-surface lens  16  has a refractive index of 1.525. The polygon mirror of the deflector  18  is in the shape of an icosagon having an inscribed circle with a diameter of 30 mm. The deflection angle changes within the range from −15 degrees to 15 degrees. Table 4 shows the positional relationship among the collimator lens  14 , the free-form-surface lens  16 , the polygon mirror of the deflector  18  and the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                   
                   
                 Position of Origin of 
                 X-axis Vector in 
                 Y-axis Vector in 
               
               
                 Surface 
                 Name of 
                 Local Coordinate System 
                 Local Coordinate System 
                 Local Coordinate System 
               
             
          
           
               
                 Number 
                 Component 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
               
               
                   
               
             
          
           
               
                 1 
                 Collimator Lens 
                 119.09 
                 0.00 
                 10.42 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 2 
                   
                 116.10 
                 0.00 
                 10.16 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 3 
                 Free-form-surface 
                 99.24 
                 0.00 
                 8.68 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 4 
                 Lens 
                 94.26 
                 0.00 
                 8.25 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 5 
                 Polygon Mirror 
                 0.00 
                 0.00 
                 0.00 
                 −1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 6 
                 Photoreceptor 
                 417.00 
                 0.00 
                 −37.00 
                 1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 1.0000 
                 0.0000 
               
               
                   
                 Surface 
               
               
                   
               
             
          
         
       
     
     Surface No. 1 denotes the surface of the collimator lens  14  closer to the light source  12 . Surface No. 2 denotes the surface of the collimator lens  14  closer to the free-form-surface lens  16 . Surface No. 3 denotes the surface of the free-form-surface lens  16  closer to the collimator lens  14 . Surface No. 5 denotes the reflecting surface of the polygon mirror that reflects the beam B 0  at a deflection angle θ of 0 degrees. Surface No. 6 denotes the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     Surface No. 1 is a spherical surface and has a curvature of 4.33126×10 −3 . 
     Surface No. 2 is an axisymmetric aspherical surface and has a curvature of −6.68860×10 −2 . The shape of Surface No. 2 is expressed by the expression (1) above, and the coefficients are shown by Table 2 above. 
     Surface No. 3 is a free-form surface. The shape of Surface No. 3 is expressed by the expression (2) above, and the coefficients are shown by Table 5. 
     
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
             
             
               
                   
                   
               
               
                   
                 j 
                   
               
             
          
           
               
                 I 
                 0 
                 2 
                 4 
               
               
                   
               
               
                 0 
                 0.00000 × 10 −0   
                 1.79089 × 10 −3   
                 5.39396 × 10 −6   
               
               
                 2 
                 1.83964 × 10 −3   
                 1.22090 × 10 −5   
                 −2.82543 × 10 −6   
               
               
                 4 
                 −3.40406 × 10 −6   
                 −7.47319 × 10 −7   
                 1.90333 × 10 −7   
               
               
                 6 
                 1.90297 × 10 −7   
                 8.25100 × 10 −9   
                 −4.76290 × 10 −9   
               
               
                 8 
                 −3.91001 × 10 −9   
                 0.00000 × 10 −0   
                 0.00000 × 10 −0   
               
               
                   
               
             
          
         
       
     
     All coefficients except for the coefficients shown in Tables 2, 4 and 5 are 0. 
     Computer simulations were performed on the second example of the optical scanning device  10 . Also, an optical scanning device of the same structure as the second example of the optical scanning device  10  except for the point that the optical system  17  is replaced with an axisymmetric converging optical system that generates no aberrations on the axis was used as a second comparative example. In the second comparative example, after passing through the converging optical system, the beam B is focused on a point 424 mm distant from the polygon mirror. 
     The above-described first computer simulation was performed on the second example of the optical scanning device  10  and the second comparative example. The description of the first computer simulation is not given here.  FIG. 20  is a graph showing results of the first computer simulation performed on the second example of the optical scanning device  10 .  FIG. 21  is a graph showing results of the first computer simulation performed on the second comparative example.  FIGS. 20 and 21  show changes in the peak intensity with changes in the deflection angle θ only within the range from 0 degrees to 15 degrees. This is because changes in the peak intensity with changes in the deflection angle θ within the range from −15 degrees to 0 degrees are the same as the changes in the peak intensity with changes in the deflection angle θ within the range from 0 degrees to 15 degrees. 
     In the second comparative example, as is apparent from the graph of  FIG. 21 , the peak intensity largely changes with changes in the deflection angle θ. This shows that in an optical scanning device using an axisymmetric converging optical system that generates no aberrations on the axis, there exists a deflection angle θ that makes the convergence of the beam B very bad. In the second example of the optical scanning device  10 , on the other hand, as shown by  FIG. 20 , the peak intensity does not change so largely even with changes in the deflection angle θ. This shows that by using the optical system  17  including the free-form-surface lens  16 , degradation in the convergence of the beam B with changes in the deflection angle θ can be suppressed. 
     Next, the above-described second computer simulation was performed on the second example of the optical scanning device  10  and the second comparative example. The description of the second computer simulation is not given here.  FIG. 22  is a graph showing results of the second computer simulation performed on the second comparative example.  FIG. 23  is a graph showing results of the second computer simulation performed on the second example of the optical scanning device  10 .  FIG. 23  shows the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B. 
     In the second comparative example, as shown by  FIG. 22 , the curve showing the image surface falls steeply with increases in the deflection angle θ. This shows that in the second comparative example, as the irradiation point of the photosensitive drum  20  with the beam B comes closer to either edge in y direction, it is not possible to focus the beam B onto the surface of the photosensitive drum  20  without moving the photosensitive drum  20  in the negative direction along x axis. 
     In the second example of the optical scanning device  10 , however, as shown by  FIG. 23 , both of the curves showing the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B do not fall so steeply even with increases in the deflection angle θ. In the second example of the optical scanning device  10 , the portion of the optical system  17  where the beam B passes depends on the deflection angle θ. Further, since the free-form-surface lens  16  is used in the optical system  17 , the aberrations generated in the beam B depend on the portion of the optical system  17  where the beam B passes. As a result, as shown by  FIG. 23 , the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B do not show so steep field curvatures. This shows that in the second example of the optical scanning device  10 , it is possible to focus the beam B onto every point of the entire surface of the photosensitive drum  20  without moving the photosensitive drum  20  in x direction. 
     Next, the above-described third computer simulation was performed. The description of the third computer simulation is not given here.  FIG. 24  is a graph showing the relationship between the vertical-line contrast and the deflection angle θ in the second example of the optical scanning device  10 .  FIG. 25  is a graph showing the relationship between the horizontal-line contrast and the deflection angle θ in the second example of the optical scanning device  10 .  FIG. 26  is a graph showing the relationship between the vertical-line contrast and the deflection angle θ in the second comparative example.  FIG. 25  is a graph showing the relationship between the horizontal-line contrast and the deflection angle θ in the second comparative example. 
     As is apparent from  FIGS. 24 to 27 , the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ in the second example of the optical scanning device  10  than those in the second comparative example. Moreover, the vertical-line contrast and the horizontal-line contrast are less changeable with changes in position of the photoreceptor surface (the photosensitive drum  20 ) in the second example of the optical scanning device  10  than those in the second comparative example. Thus, the second example of the optical scanning device  10  has not only the advantage as shown by  FIG. 20  that the peak intensity is less changeable with changes in the deflection angle θ but also the advantage as shown by  FIGS. 24 and 25  that the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ. In the second example of the optical scanning device  10 , since the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ, it is possible to write vertical lines and horizontal lines of high picture quality. 
     Further, it is apparent from the comparison of the graphs of  FIGS. 24 and 25  with the graphs of  FIGS. 14 and 15  that the vertical-line contrast and the horizontal-line contrast are less changeable with changes in the deflection angle θ in the second example of the optical scanning device  10  than those in the first example of the optical scanning device  10 . This is because the deflection angle θ changes within the range from −25 degrees to 25 degrees in the first example of the optical scanning device  10 , while the deflection angle θ changes within the range from −15 degrees to 15 degrees in the second example of the optical scanning device  10 . 
     Next, the above-described fourth computer simulation was performed. The description of the fourth computer simulation is not given here.  FIG. 28  is a graph showing results of the fourth computer simulation performed on the second example of the optical scanning device  10 .  FIG. 29  is a graph showing results of the fourth computer simulation performed on the second comparative example. In  FIGS. 28 and 29 , the vertical axes show the curvature, and the horizontal axes show the deflection angle θ. 
     As shown by  FIG. 29 , in the second comparative example, the average wavefront curvature of the beam B is constant. The average wavefront curvature of the beam B is a reciprocal of the distance between the optical system and the image point of the beam B. Therefore,  FIG. 29  shows that in the second comparative example, it is impossible to focus the beam B onto every point of the entire photoreceptor surface (the entire surface of the photosensitive drum  20 ). 
     In the second example of the optical scanning device  10 , on the other hand, as shown by  FIG. 28 , both of the average wavefront curvature in the main-scanning direction and the average wavefront curvature in the sub-scanning direction of the beam B become smaller with increases in the deflection angle θ. This means that the beam B is focused on a farther point from the optical system  17  as the deflection angle θ becomes greater. Meanwhile, the distance between the optical system  17  and the photoreceptor surface (the surface of the photosensitive drum  20 ) becomes greater as the deflection angle θ becomes greater. Therefore, in the second example of the optical scanning device  10 , it is possible to focus the beam B onto every point of the entire photoreceptor surface (the surface of the photosensitive drum  20 ). Thus, the second example of the optical scanning device  10  can achieve better image writing performance than the second comparative example. 
     Second Embodiment 
     Structure of the Optical Scanning Device 
     An optical scanning device  10  according to a second embodiment will be hereinafter described. The optical scanning device  10  according to the second embodiment is basically of the same structure as the optical scanning device  10  according to the first embodiment shown by  FIG. 1 . The difference in structure between the optical scanning device  10  according to the first embodiment and the optical scanning device  10  according to the second embodiment is that an axisymmetric aspherical lens  16 ′ is used in the optical scanning device  10  according to the second embodiment, while the free-form-surface lens  16  is used in the optical scanning device  10  according to the first embodiment. The other components of the optical scanning device  10  according to the second embodiment are the same as those of the optical scanning device  10  according to the first embodiment, and descriptions of the components are omitted. 
     Next, a third example of the optical scanning device  10 , which is an example according to the second embodiment, will be described below. In the third example of the optical scanning device  10 , the beam B 0  emitted from the light source  12  has a wavelength of 780 nm. The glass of the collimator lens  14  has a refractive index of 1.564, and the resin of the axisymmetric aspherical lens  16 ′ has a refractive index of 1.525. The polygon mirror of the deflector  18  is in the shape of an icosagon having an inscribed circle with a diameter of 30 mm. The deflection angle changes within the range from −15 degrees to 15 degrees. Table 6 shows the positional relationship among the collimator lens  14 , the axisymmetric aspherical lens  16 ′, the polygon mirror of the deflector  18  and the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                   
                   
                 Position of Origin of 
                 X-axis Vector in 
                 Y-axis Vector in 
               
               
                 Surface 
                 Name of 
                 Local Coordinate System 
                 Local Coordinate System 
                 Local Coordinate System 
               
             
          
           
               
                 Number 
                 Component 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
               
               
                   
               
             
          
           
               
                 1 
                 Collimator Lens 
                 119.09 
                 0.00 
                 10.42 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 2 
                   
                 116.10 
                 0.00 
                 10.16 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 3 
                 Axisymmetric 
                 99.24 
                 0.00 
                 8.68 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 4 
                 Aspherical Lens 
                 94.26 
                 0.00 
                 8.25 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 5 
                 Polygon Mirror 
                 0.00 
                 0.00 
                 0.00 
                 −1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 6 
                 Photoreceptor 
                 417.00 
                 0.00 
                 −37.00 
                 1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 1.0000 
                 0.0000 
               
               
                   
                 Surface 
               
               
                   
               
             
          
         
       
     
     Surface No. 1 denotes the surface of the collimator lens  14  closer to the light source  12 . Surface No. 2 denotes the surface of the collimator lens  14  closer to the axisymmetric aspherical lens  16 ′. Surface No. 3 denotes the surface of the axisymmetric aspherical lens  16 ′ closer to the collimator lens  14 . Surface No. 5 denotes the reflecting surface of the polygon mirror that reflects the beam B 0  at a deflection angle θ of 0 degrees. Surface No. 6 denotes the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     Surface No. 1 is a spherical surface and has a curvature of 4.33126×10 −3 . 
     Surface No. 2 is an axisymmetric aspherical surface and has a curvature of −6.68860×10 −2 . The shape of Surface No. 2 is expressed by the expression (1) above, and the coefficients are shown by Table 2 above. 
     Surface No. 3 is an axisymmetric aspherical surface and has a curvature of 3.66937×10 −3 . The shape of Surface No. 3 is expressed by the expression (1) above, and the coefficients are shown by Table 7. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Degree 
                 Coefficient 
               
               
                   
                   
               
             
             
               
                   
                 4 
                 −2.27726 × 10 −6   
               
               
                   
                 6 
                  1.36769 × 10 −7   
               
               
                   
                 8 
                 −3.09440 × 10 −9   
               
               
                   
                   
               
             
          
         
       
     
     All coefficients except for the coefficients shown in Tables 6 and 7 are 0. 
     Computer simulations were performed on the third example of the optical scanning device  10 . Here also, the optical scanning device used as the second comparative example was used for comparison. The second comparative example has been already described, and the description is not given here. 
     The above-described first computer simulation was performed.  FIG. 30  is a graph showing results of the first computer simulation performed on the third example of the optical scanning device  10 . The results of the first computer simulation performed on the second example are shown by  FIG. 21 .  FIG. 30  shows changes in the peak intensity with changes in the deflection angle θ only within the range from 0 degrees to 15 degrees. This is because changes in the peak intensity with changes in the deflection angle θ within the range from −15 degrees to 0 degrees are the same as the changes in the peak intensity with changes in the deflection angle θ within the range from 0 degrees to 15 degrees. 
     In the second comparative example, as is apparent from the graph of  FIG. 21 , the peak intensity largely changes with changes in the deflection angle θ. This shows that in an optical scanning device using an axisymmetric converging optical system that generates no aberrations on the axis, there exists a deflection angle θ that makes the convergence of the beam B very bad. In the third example of the optical scanning device  10 , on the other hand, as shown by  FIG. 30 , the peak intensity does not change so largely even with changes in the deflection angle θ. This shows that by using the optical system  17  including the axisymmetric aspherical lens  16 ′, degradation in the convergence of the beam B with changes in the deflection angle θ can be suppressed. 
     Next, the above-described second computer simulation was performed. The description of the second computer simulation is not given here.  FIG. 31  is a graph showing results of the second computer simulation performed on the third example of the optical scanning device  10 .  FIG. 31  shows the average main-scanning-direction image surface and the average sub-scanning-direction image surface of the whole rays of the beam B. The results of the second computer simulation performed on the second comparative example are shown by  FIG. 22 . 
     In the second comparative example, as shown by  FIG. 22 , the curve showing the image surface falls steeply with increases in the deflection angle θ. This shows that in the second comparative example, as the irradiation point of the photosensitive drum  20  with the beam B comes closer to either edge in y direction, it is not possible to image the beam B on the surface of the photosensitive drum  20  without moving the photosensitive drum  20  in the negative direction along x axis. 
     In the third example of the optical scanning device  10 , as shown by  FIG. 31 , the average main-scanning-direction image surface of the whole rays of the beam B does not curve so steeply even with increases in the deflection angle θ. In the third example of the optical scanning device  10 , the portion of the optical system  17  where the beam B passes depends on the deflection angle θ. Further, since the axisymmetric aspherical lens  16 ′ is used in the optical system  17 , the aberrations generated in the beam B depend on the portion of the optical system  17  where the beam B passes. As a result, as shown by  FIG. 31 , the average main-scanning-direction image surface of the whole rays of the beam B does not curve so steeply even with increases in the deflection angle θ. This shows that in the third example of the optical scanning device  10 , it is possible to focus the beam B in the main-scanning direction onto every point of the entire surface of the photosensitive drum  20  without moving the photosensitive drum  20  in x direction. 
     Surface No. 3 of the axisymmetric aspherical lens  16 ′ is axisymmetric. Changes in the aberrations generated in the beam B with changes in the position in the main-scanning direction of the axisymmetric aspherical lens  16 ′ where the beam B passes are the same as changes in the aberrations generated in the beam B with changes in the position in the sub-scanning direction of the axisymmetric aspherical lens  16 ′ where the beam B passes. Accordingly, with the axisymmetric aspherical lens  16 ′, it is impossible to control the main-scanning-direction image surface and the sub-scanning-direction image surface independently of each other. As shown by  FIG. 31 , therefore, in the third example of the optical scanning device  10 , the average sub-scanning-direction image surface of the whole spot of the beam B curves steeply with increases in the deflection angle θ. This shows that in the third example of the optical scanning device  10 , it is difficult to focus the beam B in the sub-scanning direction onto every point of the entire surface of the photosensitive drum  20  without moving the photosensitive drum  20  in x direction. Thus, compared with the second comparative example, the third example of the optical scanning device  10  can achieve better performance of image formation of the beam B on every point of the photosensitive drum  20 . Compared with the first example and the second example of the optical scanning device  10 , however, the third example of the optical scanning device  10  cannot achieve so good performance of image formation of the beam B on every point of the photosensitive drum  20 . From the viewpoint of cost, however, the axisymmetric aspherical lens  16 ′ is less expensive than the free-form-surface lens  16 , and accordingly, the third example of the optical scanning device  10  is cheaper to manufacture than the first example and the second example of the optical scanning device  10 . 
     Next, the above-described third computer simulation was performed. The description of the third computer simulation is not given here.  FIG. 32  shows the relationship between the vertical-line contrast and the deflection angle θ in the third example of the optical scanning device  10 .  FIG. 33  shows the relationship between the horizontal-line contrast and the deflection angle θ in the third example of the optical scanning device  10 . 
     As is apparent from  FIG. 32 , the vertical-line contrast in the third example of the optical scanning device  10  is less changeable with changes in the deflection angle θ than that in the second comparative example. The horizontal-line contrast in the third example of the optical scanning device  10  is, however, as changeable with changes in the deflection angle θ as that in the second comparative example. This is because the third example of the optical scanning device  10  uses the axisymmetric aspherical lens  16 ′. Thus, in the third example of the optical scanning device  10 , since the vertical-line contrast is less changeable with changes in the deflection angle θ, it is possible to write vertical lines of high picture quality. 
     Next, the above-described fourth computer simulation was performed. The description of the fourth computer simulation is not given here.  FIG. 34  shows results of the fourth computer simulation performed on the third example of the optical scanning device  10 . In  FIG. 34 , the vertical axis shows the curvature, and the horizontal axis shows the deflection angle θ. 
     In the third example of the optical scanning device  10 , as shown by  FIG. 34 , the average wavefront curvature in the main-scanning direction of the beam B becomes smaller with increases in the deflection angle θ. This means that the beam B is focused on a farther point from the optical system  17  as the deflection angle θ becomes greater. Meanwhile, the distance between the optical system  17  and the photoreceptor surface (the surface of the photosensitive drum  20 ) becomes greater as the deflection angle θ becomes greater. Therefore, in the third example of the optical scanning device  10 , it is possible to focus the beam B onto every point of the entire photoreceptor surface (the surface of the photosensitive drum  20 ). Thus, the third example of the optical scanning device  10  can achieve better image writing performance than the second comparative example. 
     In the third example of the optical scanning device  10 , the average wavefront curvature in the sub-scanning direction of the beam B does not change with changes in the deflection angle θ. This is because the third example of the optical scanning device  10  uses the axisymmetric aspherical lens  16 ′. 
     Third Embodiment 
     Structure of the Optical Scanning Device 
     An optical scanning device  10  according to a third embodiment will be hereinafter described.  FIG. 35  shows the structure of the optical scanning device according to the third embodiment. 
     The difference in structure between the optical scanning device  10  according to the second embodiment and the optical scanning device  10  according to the third embodiment is that only the axisymmetric aspherical lens  15  is used as the optical system  17  in the optical scanning device  10  according to the third embodiment, while the collimator lens  14  and the axisymmetrical aspherical lens  16 ′ are used as the optical system  17  in the optical scanning device  10  according to the second embodiment. Thus, in the optical scanning device  10  according to the third embodiment, the axisymmetric aspherical lens  15  serves as the collimator lens  14  and the axisymmetric aspherical lens  16 ′. The other components of the optical scanning device  10  according to the third embodiment are the same as those of the optical scanning device  10  according to the second embodiment, and descriptions of the components are omitted. 
     Fourth Example 
     Next, a fourth example of the optical scanning device  10 , which is an example according to the second embodiment, will be described below. In the fourth example of the optical scanning device  10 , the beam B 0  emitted from the light source  12  has a wavelength of 780 nm. The glass of the axisymmetric aspherical lens  15  has a refractive index of 1.564. The polygon mirror of the deflector  18  is in the shape of an icosagon having an inscribed circle with a diameter of 30 mm. The deflection angle θ changes within the range from −15 degrees to 15 degrees. Table 8 shows the positional relationship among the axisymmetric aspherical lens  15 , the polygon mirror of the deflector  18  and the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                   
                   
                 Position of Origin of 
                 X-axis Vector in 
                 Y-axis Vector in 
               
               
                 Surface 
                 Name of 
                 Local Coordinate System 
                 Local Coordinate System 
                 Local Coordinate System 
               
             
          
           
               
                 Number 
                 Component 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
                 x 
                 y 
                 z 
               
               
                   
               
             
          
           
               
                 1 
                 Axisymmetric 
                 119.09 
                 0.00 
                 10.42 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 2 
                 Aspherical Lens 
                 116.10 
                 0.00 
                 10.16 
                 −0.9962 
                 0.0000 
                 −0.0872 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 3 
                 Polygon Mirror 
                 0.00 
                 0.00 
                 0.00 
                 −1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 −1.0000 
                 0.0000 
               
               
                 4 
                 Photoreceptor 
                 417.00 
                 0.00 
                 −37.00 
                 1.0000 
                 0.0000 
                 0.0000 
                 0.0000 
                 1.0000 
                 0.0000 
               
               
                   
                 Surface 
               
               
                   
               
             
          
         
       
     
     Surface No. 1 denotes the surface of the axisymmetric aspherical lens  15  closer to the light source  12 . Surface No. 2 denotes the surface of the axisymmetric aspherical lens  15  closer to the deflector  18 . Surface No. 3 denotes the reflecting surface of the polygon mirror that reflects the beam B 0  at a deflection angle θ of 0 degrees. Surface No. 4 denotes the photoreceptor surface (the surface of the photosensitive drum  20 ). 
     Surface No. 1 is a spherical surface and has a curvature of 4.33126×10 −3 . 
     Surface No. 2 is an axisymmetric aspherical surface and has a curvature of −7.01834×10 −2 . The shape of Surface No. 2 is expressed by the expression (1) above, and the coefficients are shown by Table 9 below. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
               
                   
                 Degree 
                 Coefficient 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 4 
                 3.16227 × 10 −5       
               
               
                   
                 6 
                 1.22161 × 10 −10   
               
               
                   
                 8 
                 2.16396 × 10 −9       
               
               
                   
                 10 
                 2.15187 × 10 −11   
               
               
                   
                 12 
                 −2.55070 × 10 −13   
               
               
                   
                   
               
             
          
         
       
     
     All coefficients except for the coefficients shown in Tables 8 and 9 are 0. 
     Computer simulations were performed on the fourth example of the optical scanning device  10 . Here also, the optical scanning device used as the second comparative example was used for comparison. The second comparative example has been already described, and the description is not given here. 
     The above-described first to fourth computer simulations were performed on the fourth example of the optical scanning device  10 .  FIG. 36  shows results of the first computer simulation performed on the fourth example of the optical scanning device  10 .  FIG. 37  shows results of the second computer simulation performed on the fourth example of the optical scanning device  10 .  FIG. 38  shows the relationship between the vertical-line contrast and the deflection angle θ in the fourth example of the optical scanning device  10 .  FIG. 39  shows the relationship between the horizontal-line contrast and the deflection angle θ in the fourth example of the optical scanning device  10 .  FIG. 40  shows results of the fourth computer simulation performed on the fourth example of the optical scanning device. 
     As shown by  FIGS. 36 to 40 , the results of the first to fourth computer simulations performed on the fourth example of the optical scanning device  10  are similar to those of the simulations performed on the third example of the optical scanning device  10 . 
     Thus, the optical scanning devices  10  according to the embodiments above are less costly to manufacture. 
     Although the present invention has been described in connection with the preferred embodiments above, it is to be noted that various changes and modifications are possible to those who are skilled in the art. Such changes and modifications are to be understood as being within the scope of the present invention.