Patent Publication Number: US-6992689-B2

Title: Light scanning unit for use in image forming apparatus

Description:
The present application is a continuation of U.S. application Ser. No. 10/424,834, filed Apr. 29, 2003, the entire contents of which are incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   The present invention relates to a light scanning unit for use in, for example, a laser printer, a digital copier and the like and, particularly, to a light scanning unit of an over-illumination type in which a width in a main scanning direction of a luminous flux made incident on a polygon mirror (a direction along a rotary direction of the polygon mirror) is greater than a width in the main scanning direction, of reflective surfaces of the polygon mirror. 
   As the light scanning units of light scanning units of the over-illumination type invented by the present inventor, there are Jpn. Pat. Appln. KOKAI Publication No. 2002-328323 and U.S. Pat. No. 10/131,207 (filed Apr. 25, 2002) corresponding thereto. 
   The width in the main scanning direction of a light beam deflected by the polygon mirror is constant irrespective of a scanning angle (position angle) in a light scanning unit of under-illumination type though it is varied in accordance with a scanning angle in the above-mentioned light scanning unit of the over-illumination type. 
   In the present inventor&#39;s senior application, too, however, the problem that if the light beam made incident on the polygon mirror forms an angle with an optical axis of an image-forming optical system on a main scanning plane (if the light beam is made incident obliquely), irregularity beam diameter is laterally asymmetric about a center of the optical axis of the image-forming optical system, in the main scanning direction, is not solved completely. 
   When the beam diameter is irregular and laterally asymmetric about the center of the optical axis of the image-forming optical system, there is a problem that a latent image formed on a photosensitive body, i.e. an image density is varied at each scanning position. 
   Incidentally, if the light beam is made incident on an arbitrary reflective surface of the polygon mirror from a front face in the main scanning direction (in the vicinity) to reduce the irregularity in the beam diameter of the light beam on an image face (photosensitive body), the light beam traveling between a lens group, which is provided between the polygon mirror and the photosensitive body, and the arbitrary reflective surface of the polygon mirror forms an image within an image region of the photosensitive body and thereby causes degradation in image quality. The image quality is improved by the above proposal of the present inventor, but the degradation is not solved completely. 
   Even if a reflection prevention film is provided on the lens surface of the arbitrary lens to reduce the irregularity in the beam diameter of the light beam, the manufacturing costs of the lens are increased, profile irregularity of the lens surface is deteriorated and the optical characteristics are worsened as already disclosed by the present inventor. 
   BRIEF SUMMARY OF THE INVENTION 
   An object of the present invention is to provide a light scanning unit of an over-illumination type, capable of making density of an exposed image stable by restricting variation in a diameter of a light beam at all of scanning positions in a main scanning direction within a predetermined range. 
   According to an aspect of the present invention, the light scanning unit comprises a first optical system modifying a beam shape of a luminous flux emitted from a light source to a predetermined shape, a light deflecting unit having at least one reflective surface and deflecting the luminous flux whose beam shape is modified by the first optical system, in a predetermined first direction, a length of the deflected luminous flux in the first direction being greater than a length of the reflective surface along the first direction, a second optical system allowing the luminous flux deflected in the first direction by the light deflecting unit to form an image on an object to be scanned, and a sensor for detection of a write position, setting a timing to modulate an intensity of the luminous flux from the light source with image information. The sensor is positioned at an end of a side on which a beam diameter of the luminous flux is great, of a scanning end of the first direction on the object to be scanned. 
   According to another aspect of the present invention, the light scanning unit comprises an image-forming unit having a predetermined length in a first direction and a predetermined thickness in a direction orthogonal to the first direction, and forming an image of light made incident from directions orthogonal to the respective first and second directions, at a predetermined position of an object to be scanned, nearly linearly along the first direction, a light detector which detects the light whose image is formed nearly linearly along the first direction of the object to be scanned, by the image-forming unit, to set a timing to modulate an intensity of the light with image information, and which is positioned at any of one side end and the other side end of the first direction of the image-forming unit where a beam diameter of the light becomes great, a deflecting unit having at least one reflective surface that is elongated in the first direction, and continuously reflecting the light, along the first direction, toward a predetermined position of the image-forming unit, by varying the angle of the reflective surface, a length of the first direction of the light being greater than a length of the first direction of the reflective surface, and an optical unit modifying a beam shape of the light to be guided to the deflecting unit to a predetermined shape and guiding the light to the reflective surface of the deflecting unit. 
   According to yet another aspect of the present invention, the image forming apparatus comprises an image carrier capable of retaining an image corresponding to light distribution, wherein when light is applied to the image carrier in a state of being provided with a predetermined potential the potential is varied, an exposing unit, and a developing unit visualizing the image retained by the image carrier. The exposing unit comprises an image-forming unit having a predetermined length in a first direction and a predetermined thickness in a direction orthogonal to the first direction, and forming an image of light made incident in directions orthogonal to the respective first and second directions, at a predetermined position of an object to be scanned, nearly linearly along the first direction, a light detector which detects the light whose image is formed nearly linearly along the first direction of the object to be scanned, by the image-forming unit, to set a timing to modulate an intensity of the light with image information, and which is positioned at any of one side end and the other side end of the first direction of the image-forming unit where a beam diameter in the first direction of the light becomes great, a deflecting unit comprising at least one reflective surface that is elongated in the first direction, and continuously reflecting the light, along the first direction, toward a predetermined position of the image-forming unit, by varying the angle of the reflective surface, a length of the first direction of the light being greater than a length of the first direction of the reflective surface, and an optical unit modifying a beam shape of the light to be guided to the deflecting unit to a predetermined shape and guiding the light to the reflective surface of the deflecting unit. 
   Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention, and together with the general description given above and the detailed description of the embodiments given below, serve to explain the principles of the invention. 
       FIG. 1  is a schematic view showing an example of an image forming apparatus into which the light scanning unit according to an embodiment of the present invention is incorporated; 
       FIGS. 2A and 2B  are schematic views an example of the light scanning unit incorporated into the image forming apparatus shown in  FIG. 1 ; 
       FIG. 3  is a schematic block diagram showing an example of a drive circuit of a digital copier comprising the light scanning unit shown in  FIGS. 2A and 2B ; 
       FIG. 4  is a graph for explanation of a relationship between a beam diameter in the first direction of a light beam scanned by the light scanning unit shown in  FIGS. 2A and 2B  and a scanning position of the light beam; 
       FIGS. 5A and 5B  are schematic views showing an example of a light scanning unit which is different from the light scanning unit shown in  FIGS. 2A and 2B ; 
       FIG. 6  is a graph for explanation of a relationship between a beam diameter in the first direction of a light beam scanned by the light scanning unit shown in  FIGS. 5A and 5B  and a scanning position of the light beam; and 
       FIGS. 7A and 7B  are schematic views showing an example of applying the present invention to a light scanning unit having an image forming system using mirrors which are different from any mirror of the light scanning units shown in  FIGS. 2A and 2B , and  FIGS. 5A and 5B . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   An embodiment of the present invention will be described in detail with reference to the drawings.  FIG. 1  shows a digital copier which is an image forming apparatus comprising a light scanning unit according to this embodiment. 
   As shown in  FIG. 1 , a digital copier  1  comprises a scanner unit  10  serving as, for example, image reading means and a printer unit  20  serving as image forming means. 
   The scanner unit  10  includes a first carriage  11  formed to be movable in a direction of an arrow, a second carriage  12  driven to move by the movement of the first carriage  11 , an optical lens  13  which provides light from the second carriage  12  with predetermined image-forming characteristics, a photoelectric conversion element  14  which performs photoelectric conversion of the light to which the predetermined image-forming characteristics are provided by the optical lens  13  and outputs an electric signal, a document table  15  which retains a document D, a document fixing cover  16  which pushes the document D against the document table  15 , and the like. 
   A light source  17  which illuminates the document D and a mirror  18   a  which reflects the light applied from the light source  17  and reflected on the document D to the second carriage  12 , are provided at the first carriage  11 . 
   A mirror  18   b  which reflects the light from the mirror  18   a  of the first carriage  11  at 90 degrees and a mirror  18   c  which further reflects the light reflected by the mirror  18   b  at 90 degrees, are provided at the second carriage  12 . 
   The document D placed on the document table  15  is illuminated by the light source  17  to reflect light in which brightness and darkness of light corresponding to the presence and absence of an image are distributed. The reflected light of the document D is made incident on the optical lens  13  via the mirrors  18   a ,  18   b  and  18   c  as image information of the document D. The reflected light guided from the document D to the optical lens  13  is condensed on a light receiving surface of the photoelectric conversion element (CCD sensor)  14  by the optical lens  13 . 
   When start of image formation is input from an operation panel or external device (not shown), the first carriage  11  and the second carriage  12  are temporarily moved to home positions which are determined to have a predetermined positional relationship with the document table  15 , by drive of a carriage driving motor (not shown). Then the first carriage  11  and the second carriage  12  are moved along the document table  15  at a predetermined speed. Thus, the image information of the document D, i.e. the image light reflected from the document D, is cut out in a predetermined width along a direction in which the mirror  18   a  extends, i.e. the main scanning direction, and is reflected to the mirror  18   b . Then the image light is sequentially cut out by unit of the width which is cut out by the mirror  18   a , in a direction perpendicular to the direction in which the mirror  18   a  extends, i.e. a sub-scanning direction. Therefore all of image information items of the document D are guided to the CCD sensor  14  by moving the first carriage  11  along the longitudinal direction of the document D. An electric signal which is output from the CCD sensor  14  is an analog signal, which is converted into a digital signal by an A/D converter (not shown). The digital signal is temporarily stored in an image memory (not shown) as an image signal. 
   In the above manner, the image of the document D placed on the document table  15  is converted into, for example, a 8-bit digital image signal which represents light and shade of the image in an image processing unit (not shown) by each line along a first line in which the mirror  18   a  extends, by the CCD sensor  14 . 
   The printer unit  20  comprises a light scanning unit  21  which serves as an exposure unit to be explained later by referring to  FIGS. 2A ,  2 B and  3 , and an electrophotographic image-forming unit  22  capable of forming an image on recording paper P which is an image-formed medium. 
   A drum (cylinder)-like photosensitive body (hereinafter ‘photosensitive drum’)  23  which is rotated by a main motor to be explained by referring to  FIG. 3  such that an optional position is moved at a predetermined speed, and on which an electrostatic latent image corresponding to the image data, i.e. the image of the document D is formed by irradiation of a laser beam L from the light scanning unit  21 , is provided at a predetermined position of the image-forming unit  22 . The photosensitive body does not need to be shaped in a cylinder, but may be shaped in, for example, a belt. 
   A charging unit  24  which applies a surface potential of predetermined polarity to the surface of the photosensitive drum  23 , a developing unit  25  which selectively supplies toner as a visualizing agent to the electrostatic latent image formed on the photosensitive drum  23  by the light scanning unit and develops the image, a transfer unit  26  which applies a predetermined electric field to the toner image formed on an outer periphery of the photosensitive drum  23  by the developing unit  25  and transfers the toner image onto the recording paper P, a separating unit  27  which releases the recording paper P on which the toner image is transferred by the transferring unit and the toner between the recording paper P and the photosensitive drum  23  from electrostatic adsorption with the photosensitive drum  23  and separates them (from the photosensitive drum  23 ), a cleaning unit  28  which removes remaining toner left on the outer peripheral surface of the photosensitive drum  23  and returns the potential distribution of the photosensitive drum  23  to a state before the surface potential is supplied by the charging unit  24 , and the like are positioned around the photosensitive drum  23 . The charging unit  24 , the developing unit  25 , the transfer unit  26 , the separating unit  27  and the cleaning unit  28  are arranged in order, along a direction of an arrow in which the photosensitive drum  23  is rotated. The laser beam L from the light scanning unit  21  is applied onto a predetermined position X on the photosensitive drum  23  between the charging unit  24  and the developing unit  25 . 
   The image signal which is read from the document D by the scanner unit  10  is subjected to, for example, processing such as gray scale processing for halftone display or outline correction, and is converted into a printing signal, by an image processing unit (not shown). The printing signal is further converted into a laser modulation signal. The laser modulation signal causes the intensity of light of the laser beam applied from a semiconductor laser device which is provided at the light scanning unit  21  and which will be explained below to be varied to either intensity which allows an electrostatic latent image to be recorded on the outer periphery of the photosensitive drum  23  to which the predetermined surface potential is supplied by the charging unit  24  or intensity which allows no electrostatic latent images to be recorded thereon. 
   Each semiconductor laser device of the light scanning unit  21  to be explained below is intensity-modulated in accordance with the above-mentioned laser modulation signal, and emits light so as to record the electrostatic latent image at a predetermined position on the photosensitive drum  23  in response to predetermined image data. The light from the semiconductor laser device is deflected in a first direction that is the same as a reading line of the scanner unit  10  by a deflecting unit in the light scanning unit  21  which will be explained below, and is applied to a predetermined position X on the outer periphery of the photosensitive drum  23 . 
   Similarly, when the first carriage  11  and the second carriage  12  of the scanner unit  10  are moved along the document table  15  by rotating the photosensitive drum  23  in the direction of the arrow at a predetermined speed, the laser beam from the semiconductor laser device which is continuously deflected by the deflecting unit is focused in each line, at a predetermined interval, on the outer periphery of the photosensitive drum  23 . 
   Thus, the electrostatic latent image corresponding to the image signal is formed on the outer periphery of the photosensitive drum  23 . 
   The electrostatic latent image formed on the outer periphery of the photosensitive drum  23  is developed by toner from the developing unit  25  and moved to a position opposite to the transfer unit  26  by the rotation of the photosensitive drum  23 . A sheet of paper is taken out of a paper cassette  29  by a feed roller  30  and a separation roller  31 . The image is transferred onto recording paper P whose timing of feeding is adjusted by aligning rollers  32 , by an electric field from the transfer unit  26 . 
   The recording paper P onto which the toner image is transferred is separated therefrom together with the toner by the separating unit  27  and guided to a fixing unit  34  by a feeding unit  33 . 
   The recording paper P fed to the fixing unit  34  is ejected onto a tray  36  by ejection rollers  35  after the toner (toner image) is fixed by heat and pressure from the fixing unit  34 . 
   On the other hand, after the toner image (toner) is transferred onto the recording paper P by the transfer unit  26 , the photosensitive drum  23  is opposed to the cleaning unit  28  such that transfer residual toner (remaining toner) which is left on the outer periphery is removed, and is made to return to an initial state, i.e. a state before the surface potential is supplied by the charging unit  24  such that next image formation can be performed, as a result of continuous rotation. 
   Successive image formation can be performed by repeating the above process. 
   Thus, image information is read from the document D set on the document table  15  by the scanner unit  10 , the read image information is converted into the toner image, which is output onto the recording paper P, by the printer unit  20 , and copying is thereby performed. 
   In the above explanation of the image forming apparatus, a digital copier has been taken as an example. For example, however, a printer apparatus in which an image reading unit is not provided may also be taken. 
     FIGS. 2A and 2B  are schematic views of the structure of the light scanning unit shown in  FIG. 1 . 
     FIG. 2A  is a schematic plan view showing optical elements arranged between the light source (semiconductor laser device) included in the light scanning unit and the photosensitive drum (object to be scanned) as seen in a direction orthogonal to a main scanning direction (first direction) parallel to a direction in which the light beam passing from the light deflector (polygon mirror) to the photosensitive drum is scanned by the light deflector, and also showing the reflection made by the mirror.  FIG. 2B  is a schematically view showing a plane seen in a sub-scanning direction (second direction) that is orthogonal to the direction shown in  FIG. 2A , i.e. the main scanning direction. 
   As shown in  FIGS. 2A and 2B , the light scanning unit  21  includes a light source  41  which emits light of a predetermined wavelength, a light deflector  50  which deflects the light from the light source in a predetermined direction, a pre-deflection optical system  40  which guides the light from the light source to the light deflector  50 , and an image-forming optical system  60  which makes the light beam deflected by the light deflector  50  form an image on the photosensitive drum  23  under predetermined conditions. 
   The pre-deflection optical system  40  has at least one of a finite focal lens  42  which deforms a beam shape of a light beam L emitted from the light source  41  to a predetermined shape and size a collimator lens  42 , a lens  42  converts the light beam into divergent light, an aperture  43  which limits the quantity of light (luminous flux diameter) of the laser beam L passing through the finite focal-point lens or collimating lens or the lens  42  which converts the light beam into divergent light, to a predetermined magnitude, a cylindrical lens  44  which is provided with positive power in an only sub-scanning direction to deform the beam shape of the laser beam L whose quantity of light is limited by the aperture  43  to a predetermined beam shape, a mirror  45  which deflects the laser beam L having the beam shape deformed by the cylindrical lens  44  in a predetermined direction, and the like. The light source  41  is, for example, a semiconductor laser device which emits the laser beam (light beam) L of 780 nm. 
   The laser beam L which is provided with a predetermined beam shape by the pre-deflection optical system  40  is deflected (continuously reflected) to the photosensitive drum (scanned surface)  23  positioned at a subsequent stage, i.e. scanned nearly linearly along a predetermined direction, by the polygon mirror (light deflector)  50  in which at least one reflective surface and a polygon mirror motor  50 A capable of rotating the reflective surface at a predetermined speed are formed integrally. 
   The image-forming optical system  60  which forms an image of the laser beam L reflected continuously on each of the reflective surfaces of the polygon mirror  50 , nearly linearly along an axial direction of the photosensitive drum  23 , is provided between the polygon mirror  50  and the photosensitive drum  23 . 
   The image-forming optical system  60  comprises an image forming lens (generally called a fθ lens)  61  capable of providing convergence which is provided with a predetermined relationship on the basis of an angle at which the polygon mirror  50  is rotated, and a dust-proof glass  62  which prevents the toner, dust, paper dust and the like suspended in the image-forming unit  22  from intruding a housing (not shown) of the light scanning unit  21 , and the like. A horizontal synchronization sensor (sensor for detection of write position)  63  which monitors a timing of emitting the laser beam whose intensity is varied by the image signal from the light source  41  (timing of modulating the intensity of the light emitted from the light source  41  by image information), i.e. which monitors synchronization of the laser beam L in the main scanning direction, is provided at a predetermined position which will be explained below with reference to  FIG. 4 , of the laser beam L passed through the image focusing lens  61 . 
   A position on the photosensitive drum  23  as represented by exposure position X in  FIG. 1 , of the laser beam L reflected continuously on each of the reflective surfaces of the polygon mirror  50  when it is applied onto the photosensitive drum  23 , is made proportional to a rotation angle of each of the reflective surfaces of the polygon mirror  50 , the laser beam L is deformed to have a predetermined beam diameter, between an end of a longitudinal (axial) direction of the photosensitive drum  23  and the other end thereof, at any position on the photosensitive drum  23  in the longitudinal direction, and the laser beam L is made to form an image on the photosensitive drum  23 , by image-forming optical system  60 . At this time, the timing at which the laser beam L is modulated on the basis of the image information (timing of starting exposure in the main scanning direction) is set on the basis of the laser beam L in the main scanning direction monitored by the above-explained horizontal synchronization sensor  63 . 
   An optical path of the laser beam L from the semiconductor laser device  41  in the optical scanning unit  21  to the photosensitive drum  23  is deflected inside the housing (not shown) of the optical scanning unit  21 , by a plurality of mirrors or the like (not shown). The image forming lens  61  and any one of the mirrors (not shown) may be formed integrally by optimizing curvatures of the main scanning direction and the sub-scanning direction of the image forming lens  61  and the optical path between the polygon mirror  50  and the photosensitive drum  23 . 
   In the optical scanning unit shown in  FIGS. 2A and 2B , when each of an axis O I  along a main light ray of the incident laser beam directed to each of the reflective surfaces of the polygon mirror  50  and an optical axis O R  of the image-forming optical system  60  is projected to a main scanning plane, an angle α made by both of them is α=5°. In addition, an angle made by the incident laser beam and the optical axis O R  of the image-forming optical system is 2° as the optical scanning unit is seen from a sub-scanning cross-section. 
     FIG. 3  is a schematic block diagram showing an example of a drive circuit of a digital copier comprising the light scanning unit shown in  FIGS. 2A and 2B . 
   A ROM (read only memory)  102  which stores predetermined operation rules and initial data, a RAM  103  which temporarily stores input control data, a common (image) RAM  104  which maintains image data from the CCD sensor  14  or image data supplied from an external device and which outputs the image data to an image processing circuit to be explained below, an NVM (non-volatile memory)  105  which maintains stored data even if passage of electric current to the copier  1  is shut down with a battery backup, an image processing unit  106  which subjects the image data stored in the image RAM  104  to predetermined image processing and outputs the image data to a laser driver to be explained below, and the like, are connected to a CPU  101  serving as a main controller. 
   In addition, a laser driver  121  which allows the semiconductor laser device  41  of the light scanning unit  21  to emit light, a polygon motor driver  122  which drives the polygon motor  50 A rotating the polygon mirror  50 , a main motor driver  123  which drives the main motor  23 A driving the photosensitive drum  23 , the feeding mechanisms of the accompanying paper (transferred material), and the like, are also connected to the CPU  101 . A repetition period of the laser beam L in the main scanning direction monitored by the horizontal synchronization sensor  63  explained with reference to  FIG. 2A  is input to the laser driver  121  via the CPU  101  (under control of the CPU  101 ). 
   In the light scanning unit  21  shown in  FIGS. 2A and 2B , the beam shape of the divergent laser beam L emitted from the semiconductor laser device  41  is converted convergently or substantially parallel (or divergently in a rare case), by the finite focal-point lens or collimating lens or the lens  42  which performs conversion into divergent light. 
   The laser beam L whose beam shape is converted into a predetermined shape is passed through the aperture  43  such that the luminous flux width (luminous flux diameter) and the quantity of light are set to be optimum, and is provided with predetermined convergence in the only sub-scanning direction by the cylindrical lens  44 . Thus, the laser beam L is shaped in a line extended in the main scanning direction on each of the reflective surfaces of the polygon mirror  50 . 
   The polygon mirror  50  is, for example, a dodecahedron and an inscribed circle thereof is formed to have a diameter Dp of 29 mm. A width Wp in the main scanning direction, of each of the reflective surfaces (twelve surfaces) of the polygon mirror  50 , can be obtained from:
 
 Wp =tan(π/ N )× Dp 
 
where N represents the number of the reflective surfaces of the polygon mirror  50 . In this example, Wp is:
 
 Wp =tan(π/12)×29=7.77 mm.
 
   On the other hand, a beam width D L  in the main scanning direction, of the laser beam L applied to each of the reflective surfaces of the polygon mirror  50  is approximately 32 mm, i.e. set widely as compared with the width Wp=7.77 mm in the main scanning direction, of each of the reflective surfaces of the polygon mirror  50 . 
   The laser beam L guided to each of the reflective surfaces of the polygon mirror  50 , reflected continuously and then scanned (deflected) linearly by the rotation of the polygon mirror  50 , is provided with predetermined image-forming characteristics by the image forming lens  61  of the image-forming optical system  60  such that the beam diameter becomes nearly uniform, at least, in the main scanning direction, on the photosensitive drum  23  (image surface). The laser beam L is made to form an image, nearly linearly, on the surface of the photosensitive drum  23 . 
   The rotation angle of each of the reflective surfaces of the polygon mirror  50 , and the image-forming position, i.e. scanning position of the light beam made to form an image on the photosensitive drum  23 , are corrected to have a proportional relationship by the image forming lens  61 . Therefore, the speed of the light beam scanned linearly on the photosensitive drum  23  is constant in all the scanning regions, by the image forming lens  61 . The image forming lens  61  is provided with a curvature which can also correct displacement of the scanning position in the sub-scanning direction caused by the influence of the fact that each of the reflective surfaces of the polygon mirror  50  is individually non-parallel to the sub-scanning direction, i.e. slant occurs on each of the reflective surfaces. Furthermore, the image forming lens  61  also corrects a curvature of an image surface. To correct these optical characteristics, the curvature is varied by the scanning position. 
   The shape of the lens surface of the image forming lens  61  is defined by TABLE 1 described below and the following formula: 
             x   =           CUY   *     y   2       +     CUZ   *     z   2           1   +       1   -     AY   *     CUY   2     *     y   2       -     AZ   *     CUZ   2     *     z   2               +       ∑     n   =   0               ⁢       ∑     m   =   0               ⁢       A   mn     ⁢     y   m     ⁢     z     2   ⁢   n                       (   1   )             
 
where y represents the main scanning direction, z represents the sub-scanning direction and x represents the direction of the optical axis.
 
   
     
       
         
             
           
             
               TABLE 1 
             
             
                 
             
           
          
             
               Incident surface 
             
          
         
         
             
             
             
             
             
          
             
                 
               CUY 
               CYZ 
               AY 
               AZ 
             
             
                 
                 
             
             
                 
               −5.672E−03 
               −4.660E−03 
               1 
               1 
             
             
                 
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
          
             
                 
                 
               0 
               1 
               2 
               3 
               4 
               5 
             
             
                 
             
             
               n 
               0 
               0.000E+00 
                 2.787E−03 
                 1.980E−03 
               1.335E−07 
                 1.044E−07 
               −2.786E−11 
             
             
                 
               1 
               4.553E−03 
                 1.328E−06 
               −2.476E−07 
               5.778E−10 
                 9.129E−11 
               −1.236E−14 
             
             
                 
               2 
               5.619E−06 
               −7.489E−09 
               −8.817E−10 
               1.685E−12 
               −6.660E−14 
               −5.188E−16 
             
             
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
          
             
                 
                 
                 
               6 
               7 
               8 
               9 
               10 
             
             
                 
                 
             
             
                 
               n 
               0 
               −7.059E−12 
                 3.692E−15 
               1.841E−16 
               −6.741E−20 
               −1.779E−20 
             
             
                 
                 
               1 
               −7.811E−15 
               −2.800E−18 
               3.600E−19 
                 6.332E−22 
                 8.659E−24 
             
             
                 
                 
               2 
                 9.075E−18 
                 1.148E−19 
               5.498E−21 
               −5.670E−24 
               −3.951E−25 
             
             
                 
                 
             
          
         
         
             
          
             
               Emitting surface 
             
          
         
         
             
             
             
             
             
          
             
                 
               CUY 
               CYZ 
               AY 
               AZ 
             
             
                 
                 
             
             
                 
               5.092E−03 
               1.651E−02 
               1 
               1 
             
             
                 
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
          
             
                 
                 
               0 
               1 
               2 
               3 
               4 
               5 
             
             
                 
             
             
               n 
               0 
               0.000E+00 
               −1.071E−03 
               −8.388E−04 
               1.647E−07 
                 5.067E−08 
               −2.561E−11 
             
             
                 
               1 
               3.809E−03 
                 9.143E−07 
               −3.924E−07 
               5.036E−10 
                 4.401E−11 
               −2.248E−14 
             
             
                 
               2 
               2.945E−06 
               −4.016E−09 
               −1.720E−10 
               2.644E−13 
               −3.675E−14 
               −4.145E−17 
             
             
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
          
             
                 
                 
                 
               6 
               7 
               8 
               9 
               10 
             
             
                 
                 
             
             
                 
               n 
               0 
               −4.086E−12 
               1.397E−15 
                 1.539E−16 
               1.951E−19 
               −4.158E−20 
             
             
                 
                 
               1 
               −5.812E−16 
               4.130E−18 
               −1.228E−19 
               2.809E−22 
                 9.314E−24 
             
             
                 
                 
               2 
               −1.222E−17 
               1.238E−20 
                 3.609E−21 
               1.408E−24 
                 7.214E−26 
             
             
                 
                 
             
          
         
       
     
   
   The material of the image forming lens  61  is acryl (PMMA), and a refractive index n thereof is n=1.483987 for a laser beam whose wavelength is 780 nm. The thickness of the image forming lens  61  is 24 mm in the defocusing direction of the optical axis (direction in which the laser beam passes), and the height of the image forming lens  61  in the sub-scanning direction is 25 mm. 
   As a rotation angle θ of each of the reflective surfaces of the polygon mirror  50  is made nearly proportional to the position of the laser beam L whose image is made on the photosensitive drum  23  by using such an image forming lens  61 , the position of the laser beam L at which the image is formed on the photosensitive drum  23  can be corrected. 
   The image forming lens  61  can also correct displacement in the sub-scanning direction caused by deviation of the inclination in the sub-scanning direction of each of the reflective surfaces of the polygon mirror  50 , i.e. irregularity in the amount of surface slant. 
   To be more precise, even if the inclination defined between the arbitrary reflective surface of the polygon mirror  50  and the rotation axis thereof is varied (in each of the reflective surfaces), the displacement of the scanning position in the sub-scanning direction, of the laser beam L guided onto the photosensitive drum  23  can be corrected by nearly making a relationship of optical conjugate between the laser beam incident surface (polygon mirror  50  side) of the image forming lens  61  and the emission surface (photosensitive drum  23  side) thereof. 
   The beam diameter of the laser beam L depends on the wavelength of the light beam L emitted from the semiconductor laser device  41 . Thus, the beam diameter of the laser beam L can be made smaller by setting the wavelength of the laser beam L to be 650 nm or 630 nm or shorter. 
     FIG. 4  shows the variation in the beam diameter in the first direction of the laser beam whose image is formed on the photosensitive drum by the light scanning unit described with reference to  FIGS. 2A and 2B , in relation to the scanning position on the photosensitive drum ranging from −160 mm to 160 mm. 
   As shown in  FIG. 4 , it is confirmed that the beam diameter increases when the scanning position is on the scanning end of ‘+’ side. This occurs as the ‘+’ side of the scanning position is the scanning end opposite to the side where the laser beam L is made incident on the polygon mirror  50  and an F number is large. For example, if the image region of 300 mm is set to range from −160 mm to 140 mm (where the central value is −10 mm), the irregularity in the beam diameter is 8 μm. On the other hand, if the same image region is set to range from −140 mm to 160 mm (where the central value is +10 mm), the irregularity in the beam diameter reaches about 15 μm. 
   If the number of lenses is small, particularly, the ability to correct the irregularity in the beam diameter becomes small and, thus, the irregularity in the beam diameter at the scanning end can easily be greater. Furthermore, in the case of a plastic lens, the refractive index is small and the power is small. Thus, the ability to correct the beam diameter is small and the irregularity in the beam diameter at the scanning end can easily be greater. 
   Therefore, the irregularity in the beam diameter in the image region can be reduced by arranging the horizontal synchronization sensor (sensor for detection of write position)  63  shown in  FIG. 2A  at the position where the F number becomes large, i.e. the scanning position which is on the ‘+’ side from the center (an end portion of the side (upstream side) where the beam diameter of the laser beam becomes great, of the scanning end in the first direction on the object to be scanned, i.e. the photosensitive drum  23 ) (the influence from the variation in the beam diameter on the image can be restricted by assigning the region of the scanning position where the beam diameter in the first direction is irregular to the horizontal synchronization sensor). As the laser beam L whose beam diameter is great is made incident on the horizontal synchronization sensor  63 , inconvenience of being unable to sense the horizontal synchronization is solved. 
   In other words, where an angle obtained by projecting both the main light beam of the light incident on each of the reflective surfaces of the polygon mirror  50  and the optical axis of the image forming lens  61  onto the scanning plane is represented by α, the horizontal synchronization sensor  63  is positioned at a position where ‘α≠0’ is satisfied. The predetermined convergence that is provided to the laser beam L by the image forming lens  61  is maintained as it is and they are made incident on the horizontal synchronization sensor  63 . That is, especial characteristics of image formation are not further provided to the laser beam directed from the image forming lens  61  to the photosensitive drum  23  by a image forming (convergence/divergence) system such as a lens or the like, and the laser beam is guided to the horizontal synchronization sensor  63 . 
   That is, a problem arises that the irregularity in the beam diameter in the main scanning direction of the laser beam L whose image is formed on the photosensitive drum  23  becomes great in accordance with the scanning position in the main scanning direction, by using the image forming lens  61  whose angle is shifted from the optical axis in the direction of the main scanning plane or the sub-scanning cross-section, when the laser beam L scanned by each of the reflective surfaces of the polygon mirror  50  is made to form an image on the photosensitive drum  23 . However, the influence of the irregularity in the beam diameter on the image can be restricted by arranging the horizontal synchronization sensor  63  at the scanning end of the side where the beam diameter is increased. 
     FIGS. 5A and 5B  are schematic views for explanation of another embodiment of the light scanning unit shown in  FIGS. 2A and 2B . The same structures as those already explained with reference to  FIGS. 2A and 2B  will be denoted by the same reference numerals and their detailed explanations will be omitted. 
   A light scanning unit  221  shown in  FIGS. 5A and 5B  is composed of a pre-deflection optical system  70  comprising the semiconductor laser device  41 , the finite focal-point lens or collimating lens or the lens  42  which performs conversion into divergent light, the aperture  43 , the cylindrical lens  44 , etc., the polygon mirror  50  whose inscribed circle has a diameter of 25 mm and which is a dodecahedron, an image-forming optical system  80  comprising an image forming lens  81 , a dust-proof glass  82  and a horizontal synchronization sensor  83 , etc., and the like. The horizontal synchronization sensor  63  is provided on the ‘+’ side (upstream side) that includes the scanning position where the irregularity in the beam diameter is great is at the center, in the main scanning direction, in the same manner as explained with reference to  FIG. 2A . 
   In the light scanning unit  221  shown in  FIGS. 5A and 5B , the laser beam from the semiconductor laser device  41  is made incident on each of the reflective surfaces of the polygon mirror  50 , from the outside of the scanning region which makes a predetermined angle in the main scanning surface to the optical axis O R  of the system of the image-forming optical system  80 . The angle α between the optical axis O I  of the incident side in which the laser beam directed to the polygon mirror  50  should pass and the optical axis O R  of the image-forming optical system  80  is, for example, 46.42°. An angle between an incident laser beam Lo and the scanning plane (including the optical axis O R ) is 0° when both of the optical axes are seen from the sub-scanning cross-section. 
   The image forming lens  81  is formed of acryl, having a refractive index n=1.483987 and a thickness in the defocusing direction in the optical axis of 15 mm. A shape of the lens surface is defined by applying data of TABLE 2 shown below to the above-explained formula (2). 
   
     
       
         
             
           
             
               TABLE 2 
             
             
                 
             
           
          
             
               Incident surface 
             
          
         
         
             
             
             
             
             
          
             
                 
               CUY 
               CYZ 
               AY 
               AZ 
             
             
                 
                 
             
             
                 
               −0.0047 
               −0.0039 
               1 
               1 
             
             
                 
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
             
          
             
                 
                 
               0 
               1 
               2 
               3 
               4 
               5 
               6 
               7 
               8 
             
             
                 
             
             
               n 
               0 
               0.00E+00 
               −4.41E−03 
               −2.71E−04 
               4.32E−07 
               1.17E−07 
               −2.72E−11 
               −1.52E−12 
                 8.03E−16 
               −2.34E−18 
             
             
                 
               1 
               1.75E−02 
                 1.62E−06 
               −2.71E−06 
               3.57E−10 
               9.86E−11 
                 1.56E−14 
                 1.02E−15 
               −1.55E−18 
                 4.56E−20 
             
             
                 
             
          
         
         
             
          
             
               Emitting surface 
             
          
         
         
             
             
             
             
             
          
             
                 
               CUY 
               CYZ 
               AY 
               AZ 
             
             
                 
                 
             
             
                 
               0.0059 
               −0.0036 
               1 
               1 
             
             
                 
                 
             
          
         
         
             
             
          
             
                 
               m 
             
          
         
         
             
             
             
             
             
             
             
             
             
             
             
          
             
                 
                 
               0 
               1 
               2 
               3 
               4 
               5 
               6 
               7 
               8 
             
             
                 
             
             
               n 
               0 
               0.00E+00 
               5.70E−03 
               −4.30E−03 
                 4.60E−07 
                 7.22E−08 
               −1.58E−11 
               −7.62E−13 
               5.08E−16 
               −4.76E−17 
             
             
                 
               1 
               2.44E−02 
               3.38E−06 
               −1.69E−06 
               −3.36E−12 
               −7.89E−12 
                 8.52E−15 
                 1.07E−15 
               1.55E−18 
                 2.88E−19 
             
             
                 
             
          
         
       
     
   
     FIG. 6  shows a variation in the beam diameter of the scanning region (main scanning position) of the image surface in the light scanning unit shown in  FIGS. 5A and 5B . 
   As shown in  FIG. 6 , it is confirmed that the beam diameter increases on the scanning end where the scanning position is on the ‘+’ side. This occurs because the ‘+’ side of the scanning position is opposite to the side on which the laser beam L is made incident on the polygon mirror  50  and the F number is large. 
   That is, the irregularity in the beam diameter in the image region can be reduced by arranging the horizontal synchronization sensor  83  shown in  FIG. 5A  at the position where the F number becomes large, i.e. the scanning position which is on the ‘+’ side (upstream side) from the center, similarly to the case explained with reference to  FIG. 2A  (the influence from the variation in the beam diameter on the image can be restricted by assigning the region of the scanning position where the beam diameter in the first direction is irregular to the horizontal synchronization sensor). 
     FIGS. 7A and 7B  show a light scanning unit comprising an image forming system using mirrors which are different from any mirror of the light scanning units shown in  FIGS. 2A and 2B , and  FIGS. 5A and 5B . The side of the light source from the polygon mirror  50  is substantially the same as the light source side in the system explained above with reference to  FIGS. 5A and 5B , and its detailed description will be omitted. 
   In  FIGS. 7A and 7B , the laser beam reflected on an arbitrary reflective surface is provided with divergence in the sub-scanning direction by a first mirror  191  and convergence in the sub-scanning direction by a second mirror  192 , and made to form an image, nearly linearly, at a predetermined position of the photosensitive drum  23 . A horizontal synchronization sensor  193  is provided on the ‘+’ side (upstream side) centering on the scanning position at which the irregularity in the beam diameter is great, in the main scanning direction, similarly to the cases explained with reference to  FIGS. 2A and 5A . The irregularity in the beam diameter in the image region can be reduced by arranging the horizontal synchronization sensor (sensor for detection of write position)  193  shown in  FIG. 7A  at the position where the F number becomes large, i.e. the scanning position which is on the ‘+’ side from the center (an end portion of the side (upstream side) where the beam diameter of the laser beam in the first direction becomes great, of the scanning end in the first direction on the photosensitive drum  23 ) (the influence from the variation in the beam diameter on the image can be restricted by assigning the region of the scanning position where the beam diameter in the first direction is irregular to the horizontal synchronization sensor). 
   As the laser beam L whose beam diameter in the first direction is great is made incident on the horizontal synchronization sensor  193 , inconvenience of being unable to sense the horizontal synchronization is solved. 
   In other words, where an angle obtained by projecting both the main light beam of the light incident on each of the reflective surfaces of the polygon mirror  50  and the optical axis of the image forming lens  61  onto the scanning plane is represented by α, the horizontal synchronization sensor  193  is positioned at a position where ‘α≠0’ is satisfied. The predetermined convergence that is provided to the laser beam L by the second mirror  192  is maintained as it is and made incident on the horizontal synchronization sensor  193 . That is, especial characteristics of image formation are not further provided to the laser beam directed from the second mirror  192  to the photosensitive drum  23 , and the laser beam is guided to the horizontal synchronization sensor  63 . 
   It is apparent from  FIG. 7A  that the laser beam is scanned to have a scanning width ranging, for example, from −160 mm to 160 mm, on the photosensitive drum  23  in the main scanning direction, by the second mirror  192 . 
   The shape of the reflective surface of the first mirror  191  is represented by the following formula: 
       x   =       [       (     cuyy   2     )     /     {       1   /                 ⁢     (     1   -       aycuy   2     ⁢     y   2       -       azcuz   2     ⁢     z   2         )       }       ]     +     ∑       almy   1     ⁢   zm             
 
where cuy represents a free-form surface function, y represents a position of the main scanning direction, ay represents a coefficient, cuz represents a free-form surface function, z represents a position of the sub-scanning direction, az represents a coefficient, and aim represents a coefficient.
 
   The power in the main scanning direction, of the first mirror  191 , is negative (shaped in a convex) and the power in the main scanning direction, of the second mirror  192 , is positive (shaped in a concave). 
   Thus, in the light scanning unit composed of two mirrors shown in  FIGS. 7A and 7B , too, the irregularity in the beam diameter in the image region can be reduced by arranging the horizontal synchronization sensor  193  at the position where the F number becomes large, i.e. the scanning position which is on the ‘+’ side from the center (upstream side) (the influence from the variation in the beam diameter on the image can be restricted by assigning the region of the scanning position where the beam diameter is irregular to the horizontal synchronization sensor). As the laser beam L whose beam diameter is great is made incident on the horizontal synchronization sensor  193 , inconvenience of being unable to sense the horizontal synchronization is solved. 
   As explained above, the light scanning unit of the over-illumination type employs the image forming lens whose angle is shifted from the optical axis in the direction of the main scanning plane or the sub-scanning cross-section when the laser beam scanned on each of the reflective surfaces of the polygon mirror is made to form an image on the photosensitive drum. Thus, a problem arises that the irregularity in the beam diameter of the laser beam in the main scanning direction made to form an image on the photosensitive drum becomes great. However, the influence of the irregularity in the beam diameter on the image can be restricted by arranging the horizontal synchronization sensor at the scanning end side where the beam diameter increases. As the laser beam whose beam diameter is great is made incident on the horizontal synchronization sensor, inconvenience of being unable to sense the horizontal synchronization is solved. 
   Therefore, the light beam whose beam diameter variation is set in a predetermined range can be obtained at all the scanning positions of the main scanning direction and, as a result, irregularity of density of the exposed image can be restricted and the image quality can be improved. 
   Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.