Abstract:
An scanning lens to scan a document image includes a lens and a retainer to retain the lens bonded and fixed to the retainer by an adhesive. Conditional formula (1), or both conditional formula (2) and conditional formula (3) below are satisfied: 
     
       
         
           
             
               
                 
                   
                       
                   
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Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This patent application is based on and claims priority pursuant to 35 U.S.C. §119(a) to Japanese Patent Application No. 2015-145077, filed on Jul. 22, 2015, in the Japan Patent Office, the entire disclosure of which is hereby incorporated by reference herein. 
       BACKGROUND 
       [0002]    Technical Field 
         [0003]    Exemplary aspects of the present disclosure generally relate to a scanning lens, a scanning device, such as a scanner, and an image forming apparatus, such as a copier, a facsimile machine, a printer, or a multi-functional system including a combination thereof. 
         [0004]    Related Art 
         [0005]    In a scanning device for use in an image scanner, a facsimile machine, or a digital copier to scan a document image, a scanning lens forms a reduced optical image of the original image, and a solid-state image sensor, such as a charge-coupled device (CCD), images the reduced optical image and converts image data into an electronic image data. 
         [0006]    To scan original data as color images, a so-called three-line CCD sensor including three light receiving elements with the respective filters for colors, such as red, green, and blue, is employed as the solid image sensor. The three-line CCD sensor forms a reduced optical image of the original onto the light receiving surface of the CCD sensor to perform color separation into three colors, thereby converting the color image data into electrical signals. 
         [0007]    In the above-described scanning lens, there is a need for the image surface to have a high contrast in a high spatial frequency region and an aperture efficiency of approximately 100% up to the peripheral portion of the angle of view. In addition, to properly scan a color original document, there is a need for the image forming positions of the respective colors of red, green, and blue on the light receiving surface to coincide, with chromatic aberrations of the respective colors properly corrected. 
         [0008]    Such a widely used scanning lens, known as a Gauss lens, provides a relatively large diameter and high resolution. However, to achieve the high performance required in recent years in the configuration of the Gauss lens, the number of lenses increases and the optical system also unavoidably increases in size as a result. 
       SUMMARY 
       [0009]    In an aspect of this disclosure, there is provided an improved scanning lens to scan a document image, including a lens and a retainer to retain the lens bonded and fixed to the retainer by an adhesive, wherein conditional formula (1), or both conditional formula (2) and conditional formula (3) below are satisfied: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
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         [0010]    where, 
         [0000]    
       
         
           
             
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         [0011]    is a total volume of an adhesive protruding in a positive direction of a main scanning direction beyond a bonding portion between the retainer and the lens at at least one bonding location, in which the lens is bonded to the retainer by the adhesive, the main scanning direction including the positive direction and a negative direction opposite to the positive direction, 
         [0000]    
       
         
           
             
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         [0012]    is a total volume of an adhesive protruding beyond the bonding portion at the at least one bonding location in the negative direction, 
         [0013]    i is a number of bonding locations, 
         [0014]    α large  is a greater linear expansion coefficient between a linear expansion coefficient of the retainer and a linear expansion coefficient of the lens, 
         [0015]    α small  is a smaller linear expansion coefficient between the linear expansion coefficient of the retainer and the linear expansion coefficient of the lens, 
         [0016]    Va is a volume of the adhesive in the bonding portion between the retainer and the lens at the at least one bonding location, and 
         [0017]    Vb is a volume of the adhesive protruding beyond the bonding portion toward the lens at the at least one bonding location. 
         [0018]    In another aspect of this disclosure, there is provided another improved scanning device including an illumination system to illuminate a document, the scanning lens described above to form a reduced image of light reflected from the document illuminated by the illumination system to form an image of the document, and an image sensor to optically convert the image of the document formed by the scanning lens into image data. 
         [0019]    Further described are improved image forming apparatuses including the scanning device described above. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]    The aforementioned and other aspects, features, and advantages of the present disclosure will be better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
           [0021]      FIG. 1  is a schematic cross-sectional view of a scanning lens and a bonding location according to a first embodiment of the present disclosure; 
           [0022]      FIG. 2  is a view of the scanning lens viewed from the direction of the arrow in  FIG. 2 ; 
           [0023]      FIG. 3  is a schematic view of a scanning lens and a bonding location viewed from the side of an image sensor according to a second embodiment of the present disclosure; 
           [0024]      FIG. 4  is a view of a rear-group lens viewed from the direction of the arrow in  FIG. 3 ; 
           [0025]      FIG. 5  is a schematic view of a scanning lens and a bonding location viewed from the side of an image sensor according to a third embodiment of the present disclosure; 
           [0026]      FIG. 6  is a view of a rear-group lens viewed from the direction of the arrow in  FIG. 5 ; 
           [0027]      FIG. 7  is a schematic cross-sectional view of a scanning lens and a bonding location according to a fourth embodiment of the present disclosure; 
           [0028]      FIG. 8  is a view at a bonding location viewed from the direction of the arrow in  FIG. 7 ; 
           [0029]      FIG. 9  is a schematic cross-sectional view of a scanning device as one example according to an embodiment of the present disclosure; 
           [0030]      FIG. 10  is a schematic cross-sectional view of a scanning device as another example according to another embodiment of the present disclosure; and 
           [0031]      FIG. 11  is a schematic cross-sectional view of an image forming apparatus as one example according to an embodiment of the present disclosure. 
       
    
    
       [0032]    The accompanying drawings are intended to depict embodiments of the present disclosure and should not be interpreted to limit the scope thereof. The accompanying drawings are not to be considered as drawn to scale unless explicitly noted. 
       DETAILED DESCRIPTION 
       [0033]    In describing embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected and it is to be understood that each specific element includes all technical equivalents that have the same function, operate in a similar manner, and achieve similar results. 
         [0034]    Although the embodiments are described with technical limitations with reference to the attached drawings, such description is not intended to limit the scope of the disclosure and all of the components or elements described in the embodiments of this disclosure are not necessarily indispensable. 
         [0035]    A detailed description is provided of configurations according to embodiments of  FIG. 1  through  FIG. 11  of the present disclosure. 
         [0036]    (Scanning Lens) 
       First Embodiment 
       [0037]      FIG. 1  and  FIG. 2  illustrate a scanning lens  1  and a retainer  20  as a first embodiment of the present disclosure.  FIG. 1  is a schematic cross-sectional view of the scanning lens  1  and bonding locations according to the first embodiment.  FIG. 2  is a view of the scanning lens  1  viewed from the direction of the arrow A in  FIG. 1 . 
         [0038]    In the present embodiment, the scanning lens  1  includes a front-group lens  10 A disposed on the object side and a rear-group lens  10 B disposed on the image side. The front-group lens  10 A includes five lenses  11  through  15  including at least one positive lens and a negative lens. The rear-group lens  10 B includes one plastic negative lens  16 . Each of the lenses  11  through  15  in the front-group lens  10 A is retained by a front-group retainer  25 . The lens  16  of the rear-group lens  10 B is retained by the retainer  20 . 
         [0039]    The lens  16  includes an attachment portion  17 A and an attachment portion  17 B at the positive side and the negative side, respectively in the longitudinal direction (a main scanning direction) of the lens  16 . The attachment portions  17 A and  17 B allow the lens  16  to be fixed onto and retained by the retainer  20 . Each of the attachment portions  17 A and  17 B constitute a bonding location A 1  (A 2 ), at which the lens  16  is bonded to the retainer  20 . The retainer  20  includes an attachment portion  21 A and an attachment portion  21 B at the positive side and the negative side, respectively in the main scanning direction. The attachment portion  21 A and the attachment portion  21 B correspond to the attachment portion  17 A and the attachment portion  17 B, respectively. The attachment portion  17 A and the attachment portion  17 B are bonded to the attachment portion  21 A and the attachment portion  21 B, respectively with an adhesive  19 , so that the retainer  20  retains the lens  16 . Examples of the adhesive  19 , which in the present embodiment is an ultraviolet cure adhesive, include UVX-8204 (registered trademark) manufactured by Denka Company Limited, WORLDROCK 5342 (registered trademark) and WORLDROCK XVL-90T2 (registered trademark) manufactured by Kyoritsu Chemical &amp; Co., Ltd. It is to be noted that, a location, in which the attachment portion  17 A is bonded to the attachment portion  21 A by the adhesive  19 , is a bonding location A 1 , and a location, in which the attachment portion  17 B is bonded to the attachment portion  21 B by the adhesive  19 , is a bonding location A 2 . 
         [0040]    The retainer  20  is a base of the scanning lens  1 . The retainer  20  holds the front-group retainer  25  as well. 
         [0041]    It is to be noted that the symbol “D” in the figures refers to the distance between the retainer  20  and the lens  16 . The symbols “Vp 1 ” and “Vp 2 ” refer to the volumes of the adhesive  19  that protrude beyond bonding portions in the positive direction at the respective boding locations A 1  and A 2 . The symbols “Vm 1 ” and “Vm 2 ” refer to the volumes of the adhesive  19  that protrude beyond the bonding portions in the negative direction at the respective bonding locations A 1  and A 2 . In this case, the term “bonding portion” refers to a portion between the retainer  20  and the lens  16 , which is hidden and invisible when the lens  16  is viewed from the retainer  20  side in the vertical direction. That is, the bonding portion is a portion except for an adhesive portion protruding beyond the hidden portion at the bonding location. 
       Second Embodiment 
       [0042]      FIG. 3  and  FIG. 4  illustrate a scanning lens  1  and a retainer  20  according to a second embodiment of the present disclosure.  FIG. 3  is a schematic view of the scanning lens  1  and bonding locations A 1  and A 2  viewed from the side of an image sensor according to the second embodiment.  FIG. 4  is a view of a rear-group lens  10 B viewed from the direction of the arrow B in  FIG. 3 . It is to be noted that a description is omitted of the same aspects as those of the above-described embodiment. 
         [0043]    In the scanning lens  1  according to the second embodiment, the lens  16  of a rear-group lens  10 B includes attachment portions  17 A and  17 B on the bottom side (on a retainer  20  side) of the lens  16 . At the attachment portions  17 A and  17 B, the lens  16  is bonded to the retainer  20 . 
       Third Embodiment 
       [0044]      FIG. 5  and  FIG. 6  illustrate a scanning lens  1  and a retainer  20  according to a third embodiment of the present disclosure.  FIG. 5  is a schematic view of the scanning lens  1  and a bonding location viewed from the side of an image sensor according to the third embodiment.  FIG. 6  is a view of the rear-group lens  10 B viewed from the direction of the arrow C in  FIG. 5 . It is to be noted that a description is omitted of the same aspects as those of the above-described embodiment. 
         [0045]    In the scanning lens  1  according to the third embodiment, the lens  16  of the rear-group lens  10 B includes attachment portions  17 A and  17 B on the bottom side (on the retainer  20  side) of the lens  16 . At the attachment portions  17 A and  17 B, the lens  16  is bonded to the retainer  20 . 
         [0046]    It is to be noted that, the symbol “Vp” refers to the volume of an adhesive  19  protruding beyond a bonding portion at the bonding location in the positive direction, and the symbol “Vm” refers to the volume of the adhesive  19  protruding beyond a bonding portion at a bonding location in the negative direction. 
       Fourth Embodiment 
       [0047]      FIG. 7  and  FIG. 8  illustrate a scanning lens  1  and a retainer  25  according to a fourth embodiment of the present disclosure.  FIG. 7  is a schematic cross-sectional view of the scanning lens  1  and a bonding location according to the fourth embodiment.  FIG. 8  is a view of a front-group lens  10 A viewed from the direction of the arrow E in  FIG. 7 . 
         [0048]    The scanning lens  1  according to the fourth embodiment includes a lens  16  of a rear group  18 B with four legs  18  ( 18 A through  18 D), each extending toward the object side (the front-group lens side), and further includes a front-group retainer  25  to retain the front group lens  10 A. The legs  18 A through  18 D are bonded to the front-group retainer  25 . A bonding location A 1  is a location, in which the leg  18 A and the front-group retainer  25  are bonded to each other by an adhesive  19 . Similarly, bonding locations A 2  through A 4  are the respective locations, in which the legs  18 B through  18 D are bonded to the front-group retainer  25  by an adhesive  19 . 
         [0049]    It is to be noted that the symbols “Vp 1 ”, “Vp 2 ”, “Vp 3 ”, and “Vp 4 ” refer to the volumes of an adhesive  19  protruding beyond bonding portions at the respective bonding locations A 1  through A 4  in the positive direction. The symbols “Vm 1 ”, “Vm 2 ”, “Vm 3 ”, and “Vm 4 ” refer to the volumes of the adhesive  19  protruding beyond the bonding portions at the respective bonding locations A 1  through A 4  in the negative direction. 
         [0050]    [Conditional Formula] 
         [0051]    The scanning lens  1  according to the present embodiments, to scan a document image includes a retainer  20  and at least one lens (for example, the lens  16  of the rear-group lens  10 B) bonded to the retainer  20 . In the scanning lens  1  according to the present embodiment, no adhesive  19  protrudes beyond the bonding portion between the retainer  20  and the lens  16 . Alternatively, in the scanning lens  1  according to the present embodiments, the ratio of the amount (volume) of the adhesive  19  only at the bonding portion at each bonding location A 1 , A 2 , A 3 , or A 4  to the amount of the adhesive  19  protruding beyond the corresponding bonding portion is less than or equal to a predetermined value. In addition to this condition, the ratio of the linear expansion coefficient of the retainer  20  to the linear expansion coefficient of the lens  16  and the ratio of the amount of the adhesive  19  protruding beyond each bonding portion toward the main scanning direction satisfy a predetermined relation. 
         [0052]    Preferably, the scanning lens  1  satisfies conditional formula (1) in mathematical expression  2  below. Alternatively, the scanning lens  1  preferably satisfies conditional formula (2) and conditional formula (3). 
         [0000]    
       
         
           
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         [0053]    where, 
         [0000]    
       
         
           
             
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         [0054]    is the total volume or the adhesive protruding beyond a bonding portion at each bonding location in the positive direction of the main scanning direction encompassing the positive direction and the negative direction opposite to the positive direction, 
         [0000]    
       
         
           
             
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         [0055]    is the total volume of the adhesive protruding beyond a bonding portion at each bonding location in the negative direction, 
         [0056]    i is the number of bonding locations, 
         [0057]    α large  is a greater linear expansion coefficient between the linear expansion coefficient of the retainer and the linear expansion coefficient of the lens, 
         [0058]    α small  is a smaller linear expansion coefficient between the linear expansion coefficient of the retainer and the linear expansion coefficient of the lens, 
         [0059]    Va is the volume of the adhesive in a bonding portion between the retainer and the lens at each bonding location, and 
         [0060]    Vb is the volume of the adhesive protruding beyond a bonding portion to the lens at each bonding location. 
         [0061]    Such a configuration, as described in detail below, reduces a lens misalignment caused by the expansion and contraction of the adhesive  19  due to changes in temperature, thereby achieving a scanning lens that maintains successful image forming performance even with changes in temperature while reducing the number of man-hours involved for its construction. 
         [0062]    Conditional formula (1) defines the adhesive  19  not protruding beyond the bonding portion. 
         [0063]    Conditional formula (2) defines the relations between the ratio of the linear expansion coefficient of the retainer  20  retaining the scanning lens  1  to the linear expansion coefficient of the lens (hereinafter, referred to as lens  16 ) bonded to and retained by the retainer  20 , and the ratio of the amount of the adhesive  19  protruding toward the main scanning direction beyond the bonding portion at each bonding location. 
         [0064]    During changes in temperature, the lens  16  is subjected to a force from the bonding location due to the difference in the linear expansion coefficient between the lens  16  and the retainer  20 . With a low ratio in linear expansion coefficient between the retainer  20  and the lens  16 , the lens  16  is subjected to a small force from the retainer  20 , by nature. With extremely poor balance of the amount of the adhesive  19  protruding toward the main scanning direction at the entire bonding locations, however, a force applied in a direction, to which a balance between the lens  16  and the retainer  20  is inclined due to changes in temperature, to vary the position and posture of the lens  16  increases under the influence of the protruding adhesive  19 . As a result, the lens  16  moves more greatly during changes in temperature. 
         [0065]    With a high ratio of linear expansion coefficient between the retainer  20  and the lens  16 , even in the case of a little unbalanced ratio of the amount of the adhesive  19  protruding toward the main scanning direction at the entire bonding locations, an increased force is applied to the lens  16  due to the difference in linear expansion coefficient during changes in temperature as well as the poor balance between the lens  16  and the retainer  20 . As a result, the posture of the lens  16  greatly varies. This variation in the posture of the lens  16  deteriorates the image forming performance even with changes in temperature. 
         [0066]    Conditional formula (3) defines the ratio of the amount (volume) of the adhesive  19  at the bonding portion between the retainer  20  and the lens  16  at each bonding location A 1 , A 2 , A 3 , or A 4  to the amount of the adhesive protruding beyond the bonding portion, in the scanning lens  1 . 
         [0067]    With an excessively high ratio of the volume of the adhesive  19  protruding toward the lens  16  beyond the bonding portion to the volume of the adhesive  19  at the bonding portion, the ratio of contribution to the fixation of the lens  16  at the bonding portion decreases while the ratio of contribution to the fixation of the lens  16  at the adhesive protruding beyond the bonding portion increases. For example, when the entire volume of the protruding adhesive  19  in the entire protruding locations is greater than or equal to half of the volume of the adhesive  19  at the entire bonding locations, the influence of the adhesive  19  protruding beyond the bonding portion becomes dominant, which means that bonding of the lens  16  to the retainer is not controlled by the adhesive  19  at the bonding portion. 
         [0068]    The present inventor has found that satisfying conditional formulas (2) and (3) maintains a successful image forming performance even with changes in temperature. In addition, failing to satisfy conditional formulas (2) and (3) leads to a deterioration in the image forming performance with changes in temperature. 
         [0069]    In the scanning lens  1  according to the present embodiment, satisfying conditional formula (1) achieves no amount of the adhesive  19  protruding beyond the bonding portion. Alternatively, setting the permissible amount of the adhesive  19  adhering to an unintended place within the range of conditional formula (3) reduces the influence of the adhesive  19  protruding beyond the bonding portion. In addition, Conditional formula (2) defines the ratio of the linear expansion coefficient of the retainer  20  and the linear expansion coefficient of the lens  16 , and the balance ratio of the volume of the adhesive  19  protruding beyond the bonding portion at each bonding location. 
         [0070]    With such a configuration, a scanning lens  1  with a high performance, maintaining a successful image forming performance is obtained, such that the lens  16  does not shift or tilt toward the main scanning direction, in which a deterioration in the image forming performance increases even with changes in temperature. 
         [0071]    A description is provided of more favorable conditions of the scanning lens  1  below. 
         [0072]    In the scanning lens  1 , satisfying conditional formula (4) below further maintains a successful image forming performance: 
         [0000]      0≦D&lt;1.0  (4)
 
         [0073]    where, 
         [0074]    D denotes the distance (mm) between the retainer  20  and the lens  16  at the bonding portion. 
         [0075]    Conditional formula (4) defines the distance between the retainer  20  and the lens  16  at the bonding portion at the bonding location A 1 , A 2 , A 3 , or A 4 . With the value of D exceeding the upper limit defined by conditional formula (4), the distance between the retainer  20  and the lens  16  excessively increases, thereby increasing a variation in the position and posture of the lens  16  with changes in temperature when the balance of the amount of the adhesive  19  collapses. 
         [0076]    With changes in temperature, a force is applied to the lens  16  due to expansion and contraction. Further, with changes in temperature, the adhesive  19  between the retainer  20  and the lens  16  at the bonding location A 1 , A 2 , A 3  or A 4  bends toward a direction, in which the force is applied, while reacting against the force. The amount of variation in (bending of) the lens  16  increases with a thick adhesive  19  as compared to with a thin adhesive  19 . 
         [0077]    The same applies to the case, in which vibration force is applied. With an adhesive  19  having an increased thickness, variation in position and posture of the lens  16  more greatly increases. 
         [0078]    Accordingly, satisfying conditional formula (4) reduces the variation in the lens  16 , thereby maintaining a successful image forming performance. 
         [0079]    In the scanning lens  1 , satisfying conditional formula (5) below further maintains a successful image forming performance with changes in temperature: 
         [0000]      0≦ D ( D max− D min)/ D max&lt;0.5  (5),
 
         [0080]    where, 
         [0081]    Dmax denotes a maximum distance between the retainer  20  and the lens  16  at a bonding portion at a bonding location, and 
         [0082]    Dmin denotes a minimum distance between the retainer  20  and the lens  16  at a bonding portion at a bonding location. 
         [0083]    Conditional formula ( 5 ) defines the distance between the retainer  20  and the lens  16  at a bonding portion at a bonding location A 1 , A 2 , A 3 , or A 4 . With the value of (Dmax−Dmin)/Dmax exceeding the upper limit defined by conditional formula (5), the thickness of the adhesive  19  differs depending on a bonding portion at each bonding location, and thereby the relation in force of expansion and contraction between the lens  16  and the adhesive  19  according to changes in temperature varies depending on a position of a bonding portion, so that the posture of the lens  16  varies with changes in temperature. As a result, obtaining a successful image forming performance is difficult. 
         [0084]    Satisfying at least one of conditional formula (4) and conditional formula (5) more properly eliminates or reduces a lens misalignment due to expansion and contraction caused by changes in temperature, thereby achieving the scanning lens  1  with a high performance that maintains a successful image forming performance even even with changes in temperature. 
         [0085]    The scanning lens  1  according to the present embodiment preferably includes the front-group lens  10 A with a positive lens and three to five negative lenses, and the rear-group lens  10 B with a plastic negative lens. With such a configuration, a compact scanning lens with aberrations properly corrected is achieved. 
         [0086]    Further, in the scanning lens  1 , it is preferable for the rear-group lens  10 B to be bonded to the retainer  20 . A bonding location is easily formed on the rear-group lens  10 B because the rear-group lens  10 B is plastic. This facilitates bonding the rear-group lens  10 B (the lens  16 ) to the retainer  20 , thereby reducing the number of man-hours involved for its construction. Further, applying bonding to the end of the lens system his facilitates bonding, thereby reducing the number of man-hours involved for its construction. 
         [0087]    Further, in the scanning lens  1 , it is preferable for the rear-group lens  10 B to have at least one aspherical surface. Having the rear-group lens  10 B with at least one aspherical surface properly corrects distortion. 
         [0088]    Further, in the scanning lens  1 , it is preferable for the front-group lens  10 A to have at least one aspherical surface. Having the front-group lens  10 A with at least one aspherical surface properly corrects aberrations. 
         [0089]    In the scanning lens  1 , the rear-group lens  10 B may not have the outer shape of rotational symmetry with respect to the optical axis because a light receiving element array (image sensor) is disposed on the image surface. The rear-group lens  10 B may be of an elongated strip shape along the main scanning direction. 
         [0090]    With such a configuration with the light receiving element array, instead of increasing the diameter of lens of the rear-group lens  10 B to obtain quality with a high performance, a width for a light ray to pass through may be provided in only one direction, i.e., the main scanning direction that is the arrangement direction of the light receiving elements. Accordingly, the length (which corresponds to the height of the scanning lens  1 ) of the scanning lens  1  in a direction perpendicular to the arrangement direction of the light receiving element is reduced, thereby achieving a reduction in size of the scanning lens  1 . This further achieves a reduction in weight and cost. Alternatively, the rear-group lens  10 B may have the outer shape of rotational symmetry with respect to the optical axis. In this case, a configuration with an area sensor to simultaneously scan the whole viewing surface of an image is available. 
         [0091]    According to the scanning lens  1  according to the present embodiment described above, adopting the method of bonding described above reduces a lens misalignment due to expansion and contraction caused by changes in temperature, thereby achieving an scanning lens  1  that maintains a successful image forming performance even with changes in temperature, reducing the number of man-hours involved for its construction. 
         [0092]    (Scanning Device  1 ) 
         [0093]    Next, a description is provided of a scanning device.  FIG. 9  is a schematic cross-sectional view of a scanning device according to an embodiment of the present disclosure. 
         [0094]    In a scanning device  30 , a document  32  with a document image to be scanned is placed on the top surface of a document placing glass  31  in a planar manner. A first moving body  33  holds a mirror  33   c  with a mirror surface tilted by 45 degree with respect to a document placing surface of the document placing glass  31 . The first moving body  33  moves from a position of the first moving body  33  depicted by a solid line to a position of another first moving body  33 ′ depicted by a dotted line at a constant speed V along a longitudinal direction, which is a direction perpendicular to the drawing, as illustrated in  FIG. 9 . Another first moving body  33 ′ is a first moving body having moved. 
         [0095]    The first moving body  33  holds an illumination system, such as fluorescent lamp  33   a  and a reflector  33   b  elongating along the direction perpendicular to the drawing. The fluorescent lamp  33   a  emits light to illuminate the document  32  on the document placing glass  31  when the first moving body  33  starts to move to right in  FIG. 9 . Accordingly, during the movement of the first moving body  33  to the position (of the first moving body  33 ′) indicated by the dotted line, the document  32  is optically scanned. 
         [0096]    Examples of the fluorescent lamp  33   a  include a tube lamp, such as a halogen lamp, a xenon lamp, and a cold cathode tube, a light emitting diode (LED), in which point light sources are arranged in a row, a linear light source with a light guide body to convert a point light source into a linear light source, and a surface emitting light source, such as an organic electroluminescence (EL). 
         [0097]    A second moving body  34  elongates along the direction perpendicular to the drawing. The second moving body  34  holds a pair of mirror  34   a  and  34   b  with mirror surfaces respectively tilted to form an angle of 90°. The second moving body  34  moves from a position of the second moving body  34  depicted by a solid line to a position of another second moving body  34 ′ depicted by a dotted line at a constant speed V/2, in synchronization with movement of the first moving body  33 . Another second moving body  34 ′ is a second moving body having moved. 
         [0098]    When the document  32  is optically scanned, the reflected light from an illuminated area of the document  32  is reflected by the mirror  33   c  of the moving body  33 , and is sequentially reflected by the mirror  34   a  and the mirror  34   b  to enter the scanning lens  1  (image forming lens) as image-forming light rays. 
         [0099]    In this case, the ratio of the speed of the first moving body  33  to the speed of the second moving body  34  is 2:1. Accordingly, the optical path length from the illuminated area of the document  32  to the scanning lens  1  is maintained constant. 
         [0100]    The image forming light rays having entered the scanning lens  1  is subjected to the image forming operation of the scanning lens  1 , thereby forming a reduced image of the document  32  on the light receiving surface of an image sensor  36 . The image sensor  36  is a CCD line sensor, in which micro-photoelectric conversion parts are closely arranged in the direction perpendicular to the drawing. With the optical scanning over the document  32 , the image sensor  36  outputs an electric signal for a pixel unit regarding a document image. The output electric signal is subjected to signal processing, such as an analog-to-digital (A/D) conversion, converted to an image signal, and stored in a memory as needed. 
         [0101]    It is to be noted that the image sensor  36  separates the image forming image into three colors, red, green, and blue, to scan color data, and synthesizes the electric signals converted by the respective photoelectric conversion parts to scan a color document. 
         [0102]    In the scanning lens  1  of the scanning device  30  according to the present embodiment with the scanning lens  1  according to the present embodiments, adopting the method of bonding according to the present embodiment reduces a lens misalignment due to expansion and contraction caused by changes in temperature, thereby achieving an scanning device  30  including an scanning lens  1  with a high performance to maintain a successful image forming performance even with changes in temperature, reducing the number of man-hours involved for its construction. Such a configuration, as described below, reduces a lens misalignment caused by the expansion and contraction of the adhesive  19  due to changes in temperature, thereby achieving a scanning lens that maintains a successful image forming performance even with changes in temperature, reducing the number of man-hours involved for its construction. 
         [0103]    (Scanning Device  2 ) 
         [0104]      FIG. 10  illustrates a scanning device according to another embodiment.  FIG. 10  is a schematic cross-sectional view of the scanning device  40 . 
         [0105]    In the scanning device  40 , a document  42  with a document image to be scanned is placed on the top surface of a document placing glass  41  in a planar manner. A scanning unit  43  holds mirrors  43   e,    43   f,  and  43   g  with mirror surfaces respectively tilted to a document placing surface of the document placing glass  41 . The scanning unit  43  moves from a position of the scanning unit  43  depicted by a solid line to a position of another scanning unit  43  depicted by a dotted line at a constant speed V along a longitudinal direction, which is a direction perpendicular to the drawing, as illustrated in  FIG. 10 . Another scanning unit  43  is a scanning unit  43 ′ having moved. 
         [0106]    The scanning unit  43  holds an illumination system, such as fluorescent lamps  43   a  and  43   c  and reflectors  43   b  and  43   d  elongating along the direction perpendicular to the drawing. The fluorescent lamps  43   a  and  43   c  emit light to illuminate the document  42  on the document placing glass  41  when the scanning unit  43  moves to right in  FIG. 10 . Accordingly, during the movement of the scanning unit  43  to the position of the scanning unit  43 ′ indicated by the dotted line, the document  42  is optically scanned. 
         [0107]    When the document  42  is optically scanned, the reflected light from an illuminated area of the document  42  is sequentially reflected by the mirror  43   e,  the mirror  43   f,  and the mirror  43   g  to enter the scanning lens  1  (image forming lens) as image-forming light rays. In this case, all of the mirrors  43   e,    43   f,  and  43   g  are held by the scanning unit  43  in an integral manner. Accordingly, the optical path length from the illuminated area of the document  42  to the scanning lens  1  is maintained constant. 
         [0108]    The image forming light rays having entered the scanning lens  1  is subjected to the image forming operation of the scanning lens  1 , thereby forming a reduced image of the document  42  on the light receiving surface of an image sensor  45 . Then, same as in the scanning device  30  of  FIG. 9 , the formed reduced image is converted into electric signals to scan document data. 
         [0109]    In the scanning lens  1  of the scanning device  40  according to the present embodiment with the scanning lens  1  according to the present embodiments, adopting the method of bonding according to the present embodiment reduce a lens misalignment due to expansion and contraction caused by changes in temperature, thereby achieving an scanning device  40  including an scanning lens  1  with a high performance to maintain a successful image forming performance even with changes in temperature, reducing the number of man-hours involved for its construction. Such a configuration reduces a lens misalignment caused by expansion and contraction of the adhesive  19  due to changes in temperature, thereby achieving an scanning device  40  reduced in size, weight, and cost, having a high performance to maintain a successful image forming performance even with changes in temperature. 
         [0110]    (Image Forming Apparatus) 
         [0111]    Next, a description is provided of an image forming device.  FIG. 11  is a schematic cross-sectional view of an image forming apparatus  200 . 
         [0112]    The image forming apparatus  200  includes a scanning device  30  in the upper part of the image forming apparatus  200  and an image forming unit  100  below the scanning device  30 . In this case, a description is provided of a configuration with the scanning device  30  of  FIG. 9  as a scanning device. 
         [0113]    In the scanning device  30 , the image sensor  36  as the CCD line sensor of three lines outputs an image signal to an image processing unit  120  to convert the image signal into a writing signal for writing each color of yellow, magenta, cyan, and black. 
         [0114]    The image forming unit  100  includes a round photoconductor  110  having photoconductivity as a latent image bearer, a charging roller  111  as a charger, a revolver developing device  113 , a transfer belt  114 , and a cleaning device  115  around the photoconductor  110 . As the charger, instead of the charging roller  111 , a corona charger may be employed. 
         [0115]    In response to the writing signal from the image processing unit  120 , an optical scanner  117  optically scans the photoconductor  110  to write the colors. The optical scanning device  117  optically scans between the charging roller  111  and the developing device  113  on the photoconductor  110 . 
         [0116]    To form an image, the photoconductor  110  having a photoconductivity rotates in a clockwise direction at a constant speed, and the charging roller  111  uniformly charges the surface of the photoconductor  110 . The charged surface is exposed to an optical writing of a laser beam from the optical scanner  117  to form an electrostatic latent image on the surface of the photoconductor  110 . The formed electrostatic latent image is a negative latent image with an image portion exposed to light. 
         [0117]    To write an image, with rotation of the photoconductor  110 , a yellow image, a magenta image, a cyan image, and a black image are written in this recited order. The formed electrostatic latent image is reversely developed by a developing unit Y with a yellow toner, a developing unit M with a magenta toner, a developing unit C with a cyan toner, and a developing unit K with a black toner in sequence to form a visualized positive image. The resultant toner images of the respective colors are sequentially transferred onto the transfer belt  114  by a transfer voltage application roller  114 A such that the toner images of the respective colors are superimposed one atop the other, thereby forming a color image. 
         [0118]    A cassette  118  storing a transfer sheet S as a recording medium is detachably installable to the apparatus body. With the cassette  118  installed, a sheet on the top of the stack of the transfer sheet S stored is fed by a feed roller  122 , and the leading end of the transfer sheet S is captured by a registration roller pair  119 . 
         [0119]    The registration roller pair  119  sends the transfer sheet S to a transfer nip when the color image of toner on the transfer belt  114  starts to move to a position of transfer. Then, the color image is superimposed onto the transfer sheet S sent to the transfer nip, thus electrostatically transferring the color image onto the transfer sheet S at the transfer nip by a transfer roller  114 B. The transfer roller  114 B presses the transfer sheet S toward the color image on the transfer belt  114  during transfer. 
         [0120]    The transfer sheet S having the color image transferred is sent to a fixing device  116 . After fixing the color image onto the transfer sheet S in the fixing device  116 , the transfer sheet S passes through a conveyance path to be discharged onto an output tray  121  by an output roller pair. With every transfer of each toner image, the surface of the photoconductor  110  is cleaned by the cleaning device  115 , thereby removing the remaining toner and powder from the surface of the photoconductor  110 . 
         [0121]    Applying the scanning lens  1  described above to the scanning device  30  of the image forming apparatus  200  according to the present embodiment reduces a lens misalignment due to expansion and contraction of the adhesive  19  caused by changes in temperature, thereby achieving an image forming apparatus  200  including a scanning device  30  reduced in size, weight, and cost, with a high performance to maintain a successful image forming performance even with changes in temperature. 
         [0122]    It is to be noted that, although a multicolor image forming apparatus is taken as an example of the image forming apparatus  200 , a monochrome image forming apparatus is also applicable. 
         [0123]    In the image forming apparatus  200  including a sheet discharge space between the scanning device  30  and the image forming unit  100  inside a housing of the image forming apparatus  200 , employing the scanning device  30  with the scanning lens  1  described above reduces the height of the scanning device  30 , increasing the space between the scanning device  30  and the image forming unit  100 , to increase the visibility of the output transfer sheet S for an operator, facilitating the operation. 
         [0124]    Although the embodiments of the present disclosure have been described above, the present disclosure is not limited to the embodiments described above, and a variety of modifications can naturally be made within the scope of the present disclosure. 
         [0125]    For example, a round lens is employed in the embodiments described above. However, an oval lens with top and bottom are portions cut out may be used for the scanning lens  1 . 
       Examples 
       [0126]    A description is provided of Examples of the scanning lens  1  below. 
       Example 1 
       [0127]    As Example 1, Table 1 represents parameters and calculated results of the scanning lens  1  according to a first embodiment as illustrated in  FIGS. 1 and 2 . It is to be noted that “mm” is used as the unit of distance, and “mm 3 ” is used as the unit of volume. 
         [0000]    
       
         
               
               
               
             
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                   
                 A1 
                 A2 
               
               
                   
               
               
                 Va 
                 6   
                 5.5  
               
               
                 Va/2 
                 3   
                 2.75 
               
               
                 Vb 
                 1   
                 1.5  
               
               
                 D 
                 0.5 
                 0.4  
               
               
                   
               
               
                   
                   
                 TOTAL 
               
               
                   
               
               
                 Vp 1   
                 0.4 
                 0.8 
               
               
                 Vp 2   
                 0.4 
                   
               
               
                 Vm 1   
                 0.6 
                 1.7 
               
               
                 Vm 2   
                 1.1 
               
               
                   
               
               
                   
                 LENS 
                 RETAINER 
               
               
                   
               
               
                 α 
                 6.0E−05 
                 1.2E−05 
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       α 
                                       large 
                                     
                                     / 
                                     
                                       α 
                                       small 
                                     
                                   
                                   × 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             
                                               i 
                                                
                                               
                                                   
                                               
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                     / 
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             i 
                                           
                                         
                                         + 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   , 
                                   2 
                                   , 
                                   
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
                 1.8 
               
               
                   
               
               
                 (Dmax − Dmin)/Dmax 
                 0.2 
               
               
                   
               
             
          
         
       
     
       Example 2 
       [0128]    As Example 2, Table 2 represents parameters and calculated results of the scanning lens  1  according to a second embodiment as illustrated in  FIGS. 3 and 4 . 
         [0000]    
       
         
               
               
               
             
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                   
                 A1 
                 A2 
               
               
                   
               
               
                 Va 
                 12   
                 12   
               
               
                 Va/2 
                 6   
                 6   
               
               
                 Vb 
                 3   
                 3   
               
               
                 D 
                 0.8 
                 0.7 
               
               
                   
               
               
                   
                   
                 TOTAL 
               
               
                   
               
               
                 Vp 1   
                 1.5 
                 4 
               
               
                 Vp 2   
                 2.5 
                   
               
               
                 Vm 1   
                 1.5 
                 2 
               
               
                 Vm 2   
                 0.5 
               
               
                   
               
               
                   
                 LENS 
                 RETAINER 
               
               
                   
               
               
                 α 
                 8.0E−06 
                 6.0E−05 
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       α 
                                       large 
                                     
                                     / 
                                     
                                       α 
                                       small 
                                     
                                   
                                   × 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             
                                               i 
                                                
                                               
                                                   
                                               
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                     / 
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             i 
                                           
                                         
                                         + 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   , 
                                   2 
                                   , 
                                   
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
                 2.5  
               
               
                   
               
               
                 (Dmax − Dmin)/Dmax 
                 0.13 
               
               
                   
               
             
          
         
       
     
       Example 3 
       [0129]    As Example 3, Table 3 represents parameters and calculated results of the scanning lens  1  according to a third embodiment as illustrated in  FIGS. 5 and 6 . 
         [0000]    
       
         
               
               
             
               
               
               
             
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 Va 
                 14   
               
               
                 Va/2 
                 7   
               
               
                 Vb 
                 4   
               
               
                 D 
                 0.8 
               
               
                   
               
               
                 Vp 
                 1.5 
               
               
                 Vm 
                 2.5 
               
               
                   
               
             
          
           
               
                   
                 LENS 
                 RETAINER 
               
               
                   
               
               
                 α 
                 6.0E−05 
                 1.9E−05 
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       α 
                                       large 
                                     
                                     / 
                                     
                                       α 
                                       small 
                                     
                                   
                                   × 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             
                                               i 
                                                
                                               
                                                   
                                               
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                     / 
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             i 
                                           
                                         
                                         + 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   , 
                                   2 
                                   , 
                                   
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
                 0.79 
               
               
                   
               
               
                 (Dmax − Dmin)/Dmax 
                 0   
               
               
                   
               
             
          
         
       
     
       Example 4 
       [0130]    As Example 4, Table 4 represents parameters and calculated results of the scanning lens  1  according to a fourth embodiment as illustrated in  FIGS. 7 and 8 . 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
             
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                   
                 A1 
                 A2 
                 A3 
                 A4 
               
               
                   
               
               
                 Va 
                 8   
                 10   
                 9   
                 9   
               
               
                 Va/2 
                 4   
                 5   
                 4.5 
                 4.5 
               
               
                 Vb 
                 3   
                 1   
                 2   
                 2   
               
               
                 D 
                 0.3 
                 0.5 
                 0.4 
                 0.4 
               
               
                   
               
             
          
           
               
                   
                   
                 TOTAL 
               
               
                   
               
               
                 Vp 1   
                 1.2 
                 3.6 
               
               
                 Vp 2   
                 0.6 
                   
               
               
                 Vp 3   
                 0.7 
                   
               
               
                 Vp 4   
                 1.1 
                   
               
               
                 Vm 1   
                 1.8 
                 4.4 
               
               
                 Vm 2   
                 0.4 
                   
               
               
                 Vm 3   
                 1.3 
                   
               
               
                 Vm 4   
                 0.9 
               
               
                   
               
               
                   
                 LENS 
                 RETAINER 
               
               
                   
               
               
                 α 
                 7.0E−06 
                 2.3E−05 
               
               
                   
               
             
          
           
               
                 
                   
                     
                       
                           
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       α 
                                       large 
                                     
                                     / 
                                     
                                       α 
                                       small 
                                     
                                   
                                   × 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             
                                               i 
                                                
                                               
                                                   
                                               
                                             
                                           
                                         
                                         - 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                     / 
                                     
                                       ( 
                                       
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vp 
                                             i 
                                           
                                         
                                         + 
                                         
                                           
                                             ∑ 
                                             i 
                                             n 
                                           
                                            
                                           
                                             Vm 
                                             i 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                  
                               
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   , 
                                   2 
                                   , 
                                   
                                     … 
                                      
                                     
                                         
                                     
                                      
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
                 0.33 
               
               
                   
               
               
                 (Dmax − Dmin)/Dmax 
                 0.4  
               
               
                   
               
             
          
         
       
     
         [0131]    Numerous additional modifications and variations are possible in light of the above teachings. It is therefore to be understood that, within the scope of the above teachings, the present disclosure may be practiced otherwise than as specifically described herein. With some embodiments having thus been described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the scope of the present disclosure and appended claims, and all such modifications are intended to be included within the scope of the present disclosure and appended claims.