Patent Publication Number: US-9891549-B2

Title: Light scanning apparatus, image forming apparatus, and method of manufacturing light scanning apparatus

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a light scanning apparatus including a rotary polygon mirror, to an image forming apparatus including the light scanning apparatus, and to a method of manufacturing the light scanning apparatus. 
     Description of the Related Art 
     Hitherto, an electrophotographic image forming apparatus includes a light scanning apparatus. The light scanning apparatus is configured to deflect a light beam emitted from a light source with the use of a rotary polygon mirror. The deflected light beam is scanned on a photosensitive drum through an fθ lens, to thereby form an electrostatic latent image. 
     The image forming apparatus needs to determine an emitting start timing of a light beam in order to keep a writing start position of an image at a fixed position in a main scanning direction. In order to determine the emitting start timing of the light beam, the light scanning apparatus generally includes a light beam detector (hereinafter referred to as “BD”). The BD is configured to output a BD signal when the BD receives the light beam emitted from the light source and deflected by the rotary polygon mirror. The image forming apparatus is configured to determine the emitting start timing of the light beam based on the BD signal. However, in order to enable the BD to generate the BD signal, optical components such as a condeser lens and a slit configured to allow the light beam to enter the BD are required in addition to the BD. Therefore, there arises a problem in that the number of components and the assembly man-hours are increased, to thereby raise the cost. 
     In the aim of solving this problem, there is disclosed in U.S. Pat. No. 7,345,695 that the emitting start timing of the light beam is determined, without use of the BD, by detecting a reference mark arranged on the rotary polygon mirror or on a member integrally rotated with the rotary polygon mirror. 
     However, the arrangement of the reference mark and a detector configured to detect the reference mark still poses the problem in that the number of components and the assembly man-hours are increased, to thereby raise the cost. 
     SUMMARY OF THE INVENTION 
     In view of the above, the present invention provides a light scanning apparatus configured to determine an emitting start timing of a light beam based on a rotational position detection signal generated in accordance with rotation of a motor configured to rotate a rotary polygon mirror, an image forming apparatus including the light scanning apparatus, and a method of manufacturing the light scanning apparatus. 
     In order to solve the above-mentioned problems, according to one embodiment of the present invention, there is provided a light scanning apparatus, comprising:
         a light source configured to emit a light beam;   a rotary polygon mirror configured to deflect the light beam emitted from the light source so that the light beam scans on a surface of a photosensitive member in a main scanning direction;   a motor configured to rotate the rotary polygon mirror; and   a rotational position detection unit configured to detect a magnetic flux change caused by rotation of the motor to generate a rotational position detection signal,   wherein an emitting start timing of the light beam from the light source is determined based on the rotational position detection signal in order to maintain a writing start position of the light beam with respect to the photosensitive member in the main scanning direction.       

     According to one embodiment of the present invention, there is provided an image forming apparatus including the light scanning apparatus. 
     According to one embodiment of the present invention, there is provided a method of manufacturing the light scanning apparatus. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A ,  FIG. 1B , and  FIG. 1C  are explanatory views of a motor according to a first embodiment of the present invention. 
         FIG. 2  is an explanatory view of a light scanning apparatus according to the first embodiment. 
         FIG. 3  is a graph for showing variance in periods of FG signals according to a second embodiment of the present invention. 
         FIG. 4  is a block diagram of a writing start control portion according to a third embodiment of the present invention. 
         FIG. 5A  and  FIG. 5B  are timing charts for illustrating operations of the writing start control portion according to the third embodiment. 
         FIG. 6  is a block diagram of a configuration necessary for processing of generating phase data according to the third embodiment. 
         FIG. 7A  and  FIG. 7B  are timing charts for illustrating processing of generating the phase data according to the third embodiment. 
         FIG. 8  is a flowchart for illustrating processing of generating the phase data according to the third embodiment. 
         FIG. 9  is a block diagram of the writing start control portion according to a fourth embodiment of the present invention. 
         FIG. 10  is a timing chart for illustrating an operation of the writing start control portion according to the fourth embodiment. 
         FIG. 11  is a block diagram of the writing start control portion according to a fifth embodiment of the present invention. 
         FIG. 12  is a block diagram of an abnormal period detection circuit according to the fifth embodiment. 
         FIG. 13A  and  FIG. 13B  are timing charts for illustrating abnormality of a detection timing signal according to the fifth embodiment. 
         FIG. 14A  and  FIG. 14B  are timing charts for illustrating operations of the writing start control portion according to the fifth embodiment. 
         FIG. 15  is a block diagram of the writing start control portion according to a sixth embodiment of the present invention. 
         FIG. 16  is a graph for showing a relationship between a rotation speed setting value and an actual rotation speed of a motor according to the sixth embodiment. 
         FIG. 17A  and  FIG. 17B  are time charts for illustrating a relationship between a reference signal and phase data according to the sixth embodiment. 
         FIG. 18  is a flowchart for illustrating processing of generating a speed change coefficient according to the sixth embodiment. 
         FIG. 19  is a sectional view of an image forming apparatus according to the first embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Now, the embodiments of the present invention will be described referring to the accompanying drawings. 
     First Embodiment 
     Image Forming Apparatus 
     An electrophotographic image forming apparatus  1  according to a first embodiment will be described.  FIG. 19  is a sectional view of the image forming apparatus  1  according to the first embodiment. The image forming apparatus  1  includes light scanning apparatus  2  ( 2 Y,  2 M,  2 C, and  2 K), an image control portion  5 , an image reading portion  500 , an image forming portion  503  having photosensitive drums (photosensitive members)  25 , a fixing portion  504 , and a sheet feeding and conveying portion  505 . The image reading portion  500  is configured to illuminate an original placed on an original platen, optically read an image of the original, and convert the read image into image data (electric signal). The image control portion  5  is configured to receive the image data from the image reading portion  500  and convert the received image data into an image signal. The image control portion  5  is further configured to transmit the image signal to the light scanning apparatus  2  and control emission of light from the light scanning apparatus  2 . 
     The image forming portion  503  includes four image forming stations P (PY, PM, PC, and PK). The four image forming stations P are arranged in the order of yellow (Y), magenta (M), cyan (C), and black (K) along a rotation direction R 2  of an endless intermediate transfer belt (hereinafter referred to as “intermediate transfer member”)  511 . The image forming stations P include photosensitive drums (photosensitive members)  25  ( 25 Y,  25 M,  25 C, and  25 K), respectively, serving as image bearing members rotated in a direction indicated by arrows R 1 . Around the photosensitive drums  25 , there are arranged chargers (charging units)  3 , the light scanning apparatus  2 , developing devices (developing units)  4 , primary transfer members  6  ( 6 Y,  6 M,  6 C, and  6 K), and cleaning devices  7  ( 7 Y,  7 M,  7 C, and  7 K), respectively, along the rotation direction R 1 . 
     The chargers  3  ( 3 Y,  3 M,  3 C, and  3 K) are configured to uniformly charge surfaces of the rotating photosensitive drums  25  ( 25 Y,  25 M,  25 C, and  25 K), respectively. The light scanning apparatus  2  ( 2 Y,  2 M,  2 C, and  2 K) are configured to emit light beams modulated in accordance with image signals, to thereby form electrostatic latent images on the surfaces of the photosensitive drums  25  ( 25 Y,  25 M,  25 C, and  25 K). The developing devices  4  ( 4 Y,  4 M,  4 C, and  4 K) are configured to develop the electrostatic latent images formed on the photosensitive drums  25  ( 25 Y,  25 M,  25 C, and  25 K) with toner (developer) of respective colors, to thereby form toner images. The primary transfer members  6  ( 6 Y,  6 M,  6 C, and  6 K) are configured to perform primary transfer of the toner images on the photosensitive drums  25  ( 25 Y,  25 M,  25 C, and  25 K) sequentially onto the intermediate transfer member  511  to superimpose the images one on another. The cleaning devices  7  ( 7 Y,  7 M,  7 C, and  7 K) are configured to collect residual toner on the photosensitive drums  25  ( 25 Y,  25 M,  25 C, and  25 K) after the primary transfer. 
     A recording medium (hereinafter referred to as “sheet”) S is conveyed from a sheet feeding cassette  508  of the sheet feeding and conveying portion  505  or from a manual feeding tray  509  to a secondary transfer roller  510 . The secondary transfer roller  510  is configured to perform secondary transfer of collectively transferring the toner images on the intermediate transfer member  511  onto the sheet S. The sheet S having the toner images transferred thereon is conveyed to the fixing portion  504 . The fixing portion  504  is configured to heat and press the sheet S to melt the toner, to thereby fix the toner image onto the sheet S. With this, a full-color image is formed on the sheet S. The sheet S having the image formed thereon is delivered to a delivery tray  512 . 
     The light scanning apparatus  2  ( 2 Y,  2 M,  2 C, and  2 K) are configured to start emission of light beams for magenta, cyan, and black images sequentially from an emitting start timing of a light beam for a yellow image. The emitting start timings of the light scanning apparatus  2  in a sub-scanning direction are controlled so that a full-color toner image having no color misregistration is transferred onto the intermediate transfer member  511 . 
     (Light Scanning Apparatus) 
       FIG. 2  is an explanatory view of the light scanning apparatus  2  according to the first embodiment. The light scanning apparatus  2  includes a laser control portion  11 , a semiconductor laser (light source)  12 , a collimator lens  13 , a cylindrical lens  14 , a motor  15 , an fθ lens  17 , and a reflection mirror  18 . The motor  15  includes a rotor  15   b . A rotary polygon mirror  15   a  is integrally rotated with the rotor  15   b . In the embodiment, the image control portion  5  is arranged outside the light scanning apparatus  2  and inside a main body of the image forming apparatus  1 . The image control portion  5  and the light scanning apparatus  2  are electrically connected to each other. The image control portion  5  may be arranged in the light scanning apparatus  2 . Laser light (hereinafter referred to as “light beam”) L emitted from the semiconductor laser  12  passes through the collimator lens  13  and the cylindrical lens  14  to reach the rotary polygon mirror  15   a . The light beam L is deflected by the rotary polygon mirror  15   a , passes through the fθ lens  17  and the reflection mirror  18 , and is scanned on the photosensitive drum  25  in the main scanning direction indicated by an arrow X, to thereby form an electrostatic latent image. In the light scanning apparatus  2  according to the embodiment, a light beam detector (BD) configured to output a BD signal for controlling an emitting start timing of the light beam L for forming the electrostatic latent image in an image region on the photosensitive drum  25  is not arranged. 
     (Motor) 
       FIG. 1A ,  FIG. 1B , and  FIG. 1C  are explanatory views of the motor  15  according to the first embodiment.  FIG. 1A  is a transverse sectional view of the motor  15  according to the first embodiment. The motor (deflection unit)  15  is a three-phase six-pole brushless DC motor. The numbers of phases and poles of the motor  15  are not limited to three phases and six poles. The rotary polygon mirror  15   a  includes four reflection surfaces (deflection surfaces). The number of the reflection surfaces of the rotary polygon mirror  15   a  is not limited to four surfaces. 
     The rotary polygon mirror  15   a  and the rotor  15   b  are integrally fixed by a motor shaft  81 . In an interior of the rotor  15   b  as indicated by the broken lines in  FIG. 1A , magnets (permanent magnets)  15   d  having six pairs of magnetic poles arranged therein are mounted on an inner circumferential surface of the rotor  15   b . In  FIG. 1A , a position of the rotor  15   b  with respect to a motor control board  15   e  is illustrated as being higher than an actual position for convenience of description only. A motor shaft bearing  82  is configured to rotatably support the motor shaft  81  fixed to the rotor  15   b . A winding  15   c  includes three slots (coils) arranged on the motor control board  15   e  so as to drive a three-phase current. There is only one Hall element  16  illustrated in  FIG. 1A . However, in reality, Hall elements  16   a ,  16   b , and  16   c  corresponding to the number of (three) slots of the winding  15   c  are arranged as illustrated in  FIG. 1B . 
       FIG. 1B  is a view for illustrating the winding  15   c , the magnets  15   d , and the Hall elements (rotational position detection units)  16  ( 16   a ,  16   b , and  16   c ).  FIG. 1C  is a time chart for illustrating passing positions of the magnets  15   d , output of the Hall element  16   a , and rotational position detection signals (hereinafter referred to as “FG signal”)  22  when the rotor  15   b  is rotated in a clockwise direction. The Hall element  16   a  is configured to convert a magnetic flux change caused by rotation of the rotor  15   b  into an electric signal and generate a (+) output indicated by the solid line and a (−) output indicated by the broken line. The FG signals  22  illustrated in  FIG. 1C  can be obtained from differential output of the Hall element  16   a . The FG signals  22  can be determined from outputs of any one of the plurality of Hall elements  16   a ,  16   b , and  16   c . Thus, in the following description, any one of the plurality of Hall elements  16   a ,  16   b , and  16   c  is described as the Hall element  16 . In the embodiment, the Hall element  16  is used as a rotational position detection unit. However, instead of using the Hall element  16 , the FG signals  22  can also be generated through use of a magnetic pattern or a rectangular detection pattern for detection of the magnetic flux change caused by rotation of the rotor  15   b.    
     The FG signals  22  are output from the Hall element  16  arranged in the motor  15 . The motor control board  15   e  is configured to detect positions of the magnetic poles of the magnets  15   d  arranged in the rotor  15   b  based on the FG signals  22  and switch current flowed to the three slots of the winding  15   c , to thereby rotate the motor  15 . The image control portion  5  determines, based on the FG signal  22 , an emitting start timing (light exposure start timing) for starting emission of the light beam L from the semiconductor laser  12 . Herein, the emitting start timing is a timing at which the semiconductor laser  12  starts emission of the light beam L in accordance with an image signal  40  to keep a writing start position of an image at a fixed position in a main scanning direction X. The main scanning direction X is a direction parallel to a rotational axis line AL of the photosensitive drum  25 . The image control portion  5  is configured to output the image signal  40  to the laser control portion (light source control portion)  11  in accordance with the emitting start timing. That is, the image control portion  5  can sequentially output image signals  40  to the laser control portion  11  at timings of outputting the FG signals  22 . In the first embodiment, the FG signal serves as a synchronization signal for the light beam L in the main scanning direction to keep a writing start position of an image at a fixed position in the main scanning direction. 
     According to the first embodiment, the image control portion  5  can determine, based on the FG signal  22  output from the Hall element  16  of the motor  15 , the emitting starting timing at which the semiconductor laser  12  starts emission of the light beam L. According to the first embodiment, a BD and optical components configured to cause a light beam to enter the BD are not required, thereby being capable of reducing the cost. 
     Second Embodiment 
     Next, a second embodiment will be described. In the second embodiment, configurations which are the same as those of the first embodiment are denoted by the same reference symbols, and description thereof is omitted. The image forming apparatus  1 , the motor  15 , and the light scanning apparatus  2  according to the second embodiment are the same as those of the first embodiment, and hence description thereof is omitted.  FIG. 3  is a graph for showing variance in periods of the FG signals  22  according to the second embodiment. The solid line represents measured values of the periods of the FG signals  22  with respect to magnetic pole positions I, II, III, IV, V, and VI when the motor  15  is rotated at a predetermined rotation speed. The broken line represents a theoretical value for the periods of the FG signals  22  with respect to the magnetic pole positions I, II, III, IV, V, and VI. The measured values of the periods of the FG signals  22  with respect to the magnetic pole positions I, II, III, IV, V, and VI have a variance of about 1% due to variance in magnetized positions of the magnets  15   d . Thus, the magnetic pole positions I, II, III, IV, V, and VI can be identified by measuring each period of the FG signals  22 . 
     Measured values of the periods of the FG signals  22  with respect to the magnetic pole positions I, II, III, IV, V, and VI during rotation of the motor  15  at a predetermined rotation speed are stored in advance in a memory of the image control portion  5  as a period pattern of the FG signals  22 . During a preparation operation before starting image formation, the image control portion  5  can identify the magnetic pole positions I, II, III, IV, V, and VI by measuring the periods of the FG signals  22  and checking (matching) the measured periods against the period pattern stored in the memory (not shown). A relationship between the identified magnetic pole positions I, II, III, IV, V, and VI and orientations of certain reflection surfaces of the rotary polygon mirror  15   a  is determined in advance. The emitting start timing of the light beam with respect to each reflection surface of the rotary polygon mirror  15   a  can be identified in accordance with the relationship between the magnetic pole positions and the orientations of the reflection surfaces. 
     According to the second embodiment, the magnetic pole positions of the magnets  15   d  fixed to the rotor  15   b  can be identified by detecting the periods of the FG signal  22 . The emitting start timing of the light beam with respect to each of the plurality of reflection surfaces of the rotary polygon mirror  15   a  can be determined based on the identified magnetic pole positions. Thus, precision in the emitting start timing of the light beam to keep a writing start position of an image at a fixed position in the main scanning direction can be improved. 
     Third Embodiment 
     Next, a third embodiment will be described. In the third embodiment, configurations which are the same as those of the first embodiment have the same reference symbols allotted, and description thereof is omitted. The image forming apparatus  1 , the motor  15 , and the light scanning apparatus  2  according to the third embodiment are the same as those of the first embodiment, and hence description thereof is omitted.  FIG. 4  is a block diagram of a writing start control portion  31  according to the third embodiment. The writing start control portion  31  includes a face identifying portion (identifying unit)  34 , a reference signal generating portion (reference signal generating unit)  36 , and a data storage portion (storage unit)  37 . The motor  15  is configured to start rotation in accordance with a motor activation signal  41  output from the image control portion  5 . The Hall element  16  of the motor  15  is configured to generate the FG signals  22  in accordance with the rotation of the motor  15 . FG signals  22  are input to the face identifying portion  34  and the reference signal generating portion  36 . The face identifying portion  34  is configured to measure the periods of the FG signals  22 , identify the reflection surfaces based on a relationship between the measured periods and the reflection surfaces of the rotary polygon mirror  15   a , and generate a face identification signal  35 . Herein, the face identifying portion  34  serves as an identifying unit configured to identify the magnetic pole positions of the magnets  15   d  arranged in the rotor  15   b . The face identifying portion  34  is configured to identify the reflection surfaces (deflection surfaces) of the rotary polygon mirror  15   a  by identifying the magnetic pole positions of the magnet  15   d  and output the face identification signals  35  as an identification result for the reflection surfaces. The reference signal generating portion  36  is configured to generate reference signals  38  based on the face identification signals  35  and the FG signals  22 . The data storage portion  37  is configured to store phase data  39  having phase values representing a positional relationship of the reflection surfaces of the rotary polygon mirror  15   a  with respect to the reference signals  38 . It is preferred that the phase data  39  include a plurality of pieces of data corresponding to the number of the reflection surfaces of the rotary polygon mirror  15   a . It is preferred that the plurality of pieces of data included in the phase data  39  correspond to the plurality of reflection surfaces of the rotary polygon mirror  15   a , respectively. The image control portion  5  is configured to determine, based on the reference signals  38  and the phase data  39 , the emitting start timing for each reflection surface of the rotary polygon mirror  15   a  to keep a writing start position of an image at a fixed position in the main scanning direction. 
       FIG. 5A  and  FIG. 5B  are timing charts for illustrating operations of the writing start control portion  31  according to the third embodiment.  FIG. 5A  is a timing chart for illustrating an operation immediately after activation of the motor  15 .  FIG. 5B  is a timing chart for illustrating an operation during steady rotation of the motor  15 . 
     The face identifying portion  34  is configured to generate a detection timing signal  32 . The detection timing signal  32  is a signal which is output at a predetermined timing once every revolution of the motor  15  with the start of activation of the motor  15  as a starting point. A period of the detection timing signal  32  corresponds to one revolution period of the motor  15 . As illustrated in  FIG. 5A , the face identifying portion  34  is configured to start measurement for the periods of the FG signals  22  based on the detection timing signals  32 . In  FIG. 5A , the FG signals  22  start from the magnetic pole position I at the time of activation. However, the start timing differs each time when the motor  15  is activated. The face identifying portion  34  is configured to measure the periods of the FG signals  22  and is capable of identifying the magnetic pole positions I, II, III, IV, V, and VI based on the measured periods. For example, the measured values of the periods of the FG signals  22  are stored in advance as a period pattern in the data storage portion  37  at the time of assembling the light scanning apparatus  2 . In the embodiment, the periods of the FG signals  22  are stored as a period pattern in the order of the magnetic pole positions III, IV, V, VI, I, and II in the data storage portion  37 . The face identifying portion  34  is configured to measure the periods of the FG signals  22  at the time of image formation, check the measured periods against the period pattern, identify a period of the FG signal  22  matched with a reference value (stored period) of the magnetic pole position III, and generate the face identification signal  35 . In the embodiment, the face identification signal  35  identifies that the FG signal  22  having a period matched with the reference value stored in the data storage portion  37  corresponds to the magnetic pole position III. The reference value may represent one period selected from a plurality of periods of the FG signals  22  generated during one revolution of the motor  15  when the motor  15  is rotated at a predetermined rotation speed, or may be a period pattern of the FG signals  22  generated during one revolution of the motor  15 . At the time of activation in  FIG. 5A , the periods of the FG signals  22  may be fluctuated due to acceleration of the motor  15 , and hence the face identification signal  35  is not output. However, as illustrated in  FIG. 5B , when the motor  15  is in steady rotation at a predetermined rotation speed, the face identification signals  35  are stably output. According to the embodiment, there is no need to arrange another additional detector in order to identify the reflection surfaces of the rotary polygon mirror  15   a.    
     The reference signal generating portion  36  is configured to extract the FG signal  22  at any timing of being synchronized with the face identification signal  35  and generate the reference signal  38 . In  FIG. 5A  and  FIG. 5B , for example, the reference signal  38  is output in synchronization with falling of the FG signal  22  after one period of the face identification signal  35 . 
     The data storage portion  37  is configured to store the phase data  39  for determination of the emitting start timing during one revolution of the motor  15 . The phase data  39  includes time information (time t 1  to time t 4 ) representing respective intervals of the plurality of reflection surfaces of the rotary polygon mirror  15   a  to form a predetermined angle with respect to the reference signal  38 . In the case of the rotary polygon mirror  15   a  having four surfaces, four pieces of phase data  39  are stored in the data storage portion  37 . The image control portion  5  is configured to determine, based on the reference signal  38  and the phase data  39 , the emitting start timing of the light beam for each reflection surface of the rotary polygon mirror  15   a  to keep a writing start position of an image at a fixed position in the main scanning direction. The image control portion  5  sequentially outputs the image signals  40  to the laser control portion  11  at the timings of the phase data  39  with the reference signal  38  as a reference. A method of generating the phase data  39  will be described later. 
     The writing start control portion  31  is configured to generate the reference signal  38  based on the FG signal  22 . The image control portion  5  is configured to determine, based on the reference signal  38  and the phase data  39 , the emitting start timing of the light beam to keep a writing start position of an image at a fixed position in the main scanning direction. 
     (Method of Generating Phase Data) 
       FIG. 6  is a block diagram of a configuration necessary for processing of generating the phase data  39  according to the third embodiment. The portion surrounded by the broken lines is a tool  100  necessary for assembling of the light scanning apparatus  2 . The tool  100  includes a beam detector (hereinafter referred to as “tool BD”)  101 , an FG-BD phase measuring portion  103 , and a tool control portion  104 . The tool  100  is arranged with respect to the light scanning apparatus  2  when the phase data  39  is generated in a factory or the like before shipping of the image forming apparatus  1 . The tool  100  is removed from the light scanning apparatus  2  after the phase data  39  is generated. The light scanning apparatus  2  can be manufactured in such a manner. 
     In order to generate the phase data  39 , the tool BD  101  is arranged at a position corresponding to the writing start position of an image in the main scanning direction X of the photosensitive drum  25 . The tool control portion  104  outputs a motor activation signal  41  from the image control portion  5  to rotate the motor  15 . Then, the tool control portion  104  controls the laser control portion  11  arranged in the light scanning apparatus  2  to cause the semiconductor laser  12  to emit light. The light beam L emitted from the semiconductor laser  12  is deflected by the rotary polygon mirror  15   a  and enters the tool BD  101 . When the light beam L enters the tool BD  101 , the tool BD  101  outputs a beam detection signal (hereinafter referred to as “BD signal”)  102 . The FG-BD phase measuring portion  103  is configured to measure time differences (phase times) t 1 , t 2 , t 3 , and t 4  of the BD signal  102  with respect to the reference signal  38  and output a measurement result to the tool control portion  104 . 
       FIG. 7A  and  FIG. 7B  are timing charts for illustrating processing of generating the phase data  39  according to the third embodiment.  FIG. 7A  and  FIG. 7B  are each an illustration of a phase relationship between the reference signal  38  and the phase data  39 . The phase data  39  is determined based on the reference signal  38  and the BD signal  102 . The phase data  39  represents time differences of the BD signals  102  with respect to the reference signal  38 . That is, the phase data  39  represents times t 1 , t 2 , t 3 , and t 4  from the reference signal  38  to the BD signals  102  corresponding to the reflection surfaces of the rotary polygon mirror  15   a , respectively.  FIG. 7A  is an illustration of a case where the BD signal  102  corresponding to the time t 1  of the phase data  39  is close to the reference signal  38 . In this case, the rotation fluctuation (jitter) of the motor  15  may cause deviation of the FG signal  22  corresponding to the reference signal  38  in the time axis direction. In the case of the phase relationship between the BD signal  102  corresponding to the time t 1  and the reference signal  38  illustrated in  FIG. 7A , when the timing of generating the FG signal  22  corresponding to the reference signal  38  is fluctuated, a phase between the BD signal  102  corresponding to the time t 1  and the reference signal  38  may be inversed. Thus, as illustrated in  FIG. 7B , a BD signal  102   b  that is one period after a BD signal  102   a  close to the reference signal  38  may be set as the first time t 1  of the phase data  39 . With this, an error in the phase data  39  due to the rotation fluctuation (jitter) of the motor  15  can be reduced. 
       FIG. 8  is a flowchart for illustrating processing of generating the phase data  39  according to the third embodiment. First, the tool  100  is arranged with respect to the light scanning apparatus  2 . As illustrated in  FIG. 8 , the phase data  39  is generated by the following steps. The tool control portion  104  is configured to execute the processing of generating the phase data  39  in accordance with a program stored in a ROM (not shown). When the processing of generating the phase data  39  is started, the tool control portion  104  causes the motor  15  to rotate, to thereby output the FG signals  22  (S 101 ). The writing start control portion  31  generates the face identification signal  35  based on the FG signal  22  and generates the reference signal  38  based on the face identification signal  35  and the FG signal  22  (S 102 ). 
     The tool control portion  104  causes the semiconductor laser  12  to emit the light beam L. The light beam L is deflected by the rotary polygon mirror  15   a  and enters the tool BD  101 . When the light beam L enters the tool BD  101 , the tool BD  101  outputs the BD signal  102  (S 103 ). The FG-BD phase measuring portion  103  measures times t 1 , t 2 , t 3 , and t 4  between the reference signal  38  and the BD signals  102  (S 104 ). The tool control portion  104  stores the times (measurement results) t 1  to t 4  measured by the FG-BD phase measuring portion  103  in the data storage portion  37  as the phase data  39  (S 105 ). The processing of generating the phase data  39  is terminated. After that, the tool  100  is removed from the light scanning apparatus  2 . 
     According to the third embodiment, the emitting start timing can be determined from the reference signal  38  generated based on the FG signal  22  and from the phase data  39  stored in the data storage portion (storage unit)  37 . Thus, the emitting start timing is determined with high precision without arrangement of an additional detector, thereby being capable of keeping a writing start position of an image at a fixed position in the main scanning direction. 
     Fourth Embodiment 
     Next, a fourth embodiment will be described. In the fourth embodiment, configurations which are the same as those of the first embodiment have the same reference symbols allotted, and description thereof is omitted. The image forming apparatus  1 , the motor  15 , and the light scanning apparatus  2  according to the fourth embodiment are the same as those of the first embodiment, and hence description thereof is omitted.  FIG. 9  is a block diagram of the writing start control portion  31  according to the fourth embodiment. The writing start control portion  31  includes the face identifying portion (identifying unit)  34 , an extraction signal generating portion (extraction signal generating unit)  52 , the reference signal generating portion (reference signal generating unit)  36 , and the data storage portion (storage unit)  37 . The motor  15  is configured to rotate in accordance with the motor activation signal  41  output from the image control portion  5 , to thereby generate the FG signals  22 . The face identifying portion  34  is configured to measure periods of the FG signals  22  and generate the face identification signals  35 . The extraction signal generating portion  52  is configured to extract the FG signal  22  at any timing of being synchronized with rising of the face identification signal  35 , to thereby generate an extraction signal  51 . A period of the extraction signal  51  corresponds to one revolution period of the rotary polygon mirror  15   a . The reference signal generating portion  36  is configured to generate the reference signal  38  based on the period of the extraction signal  51  through the following calculation method. The data storage portion  37  is configured to store the phase data  39  including phase values of the reflection surfaces of the rotary polygon mirror  15   a  with respect to the reference signal  38 . The image control portion  5  is configured to determine the emitting start timing for each surface of the rotary polygon mirror  15   a  from the reference signal  38  and the phase data  39  to keep a writing start position of an image at a fixed position in the main scanning direction. The processing of generating the phase data  39  is the same as that of the third embodiment, and hence description thereof is omitted. 
     (Reference Signal/Calculation Method) 
     The reference signal generating portion  36  is configured to measure periods T k  between falling edges of the extraction signal  51  and sequentially determine, based on the calculation results, moving average values of the periods of the extraction signal  51  as presented in Expression 1, Expression 2, and Expression 3. Herein, “k” is an integer. In the embodiment, moving average values of four periods τ k , τ k+1 , τ k+2 , and τ k+3  are sequentially determined. The average values of the periods of the extraction signal  51  may be determined by averaging “n” (n≧2) periods of the extraction signal  51 . The number of periods of the extraction signal  51  to be averaged and the extraction signal  51  to be used for averaging may be arbitrarily selected. 
     
       
         
           
             
               
                 
                   
                     T 
                     1 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           τ 
                           1 
                         
                         + 
                         
                           τ 
                           2 
                         
                         + 
                         
                           τ 
                           3 
                         
                         + 
                         
                           τ 
                           4 
                         
                       
                       ) 
                     
                     4 
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
             
               
                 
                   
                     T 
                     2 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           τ 
                           2 
                         
                         + 
                         
                           τ 
                           3 
                         
                         + 
                         
                           τ 
                           4 
                         
                         + 
                         
                           τ 
                           5 
                         
                       
                       ) 
                     
                     4 
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
             
               
                 
                   
                     T 
                     n 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           τ 
                           n 
                         
                         + 
                         
                           τ 
                           
                             n 
                             + 
                             1 
                           
                         
                         + 
                         
                           τ 
                           
                             n 
                             + 
                             2 
                           
                         
                         + 
                         
                           τ 
                           
                             n 
                             + 
                             3 
                           
                         
                       
                       ) 
                     
                     4 
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
       FIG. 10  is a timing chart for illustrating an operation of the writing start control portion  31  according to the fourth embodiment. The FG signals  22  are output from the motor  15 . The detection timing signals  32  are generated by the face identifying portion  34  at a predetermined timing once every revolution of the motor  15  with the start of activation of the motor  15  as a starting point. The face identifying portion  34  starts measurement for the periods of the FG signals  22  based on the detection timing signals  32 . The face identification signals  35  are output from the face identifying portion  34  when the period of the FG signal  22  measured by the face identifying portion  34  matches with a reference value stored in the data storage portion  37 . In the embodiment, the face identification signal  35  identifies that the FG signal  22  having a period matched with the reference value stored in the data storage portion  37  corresponds to the magnetic pole position III. The face identification signals  35  and the FG signals  22  are input to the extraction signal generating portion  52 . The extraction signal generating portion  52  is configured to extract the FG signal  22  at any timing of being synchronized with the face identification signal  35  and generate the extraction signal  51 . The extraction signal  51  is input to the reference signal generating portion  36 . The reference signal generating portion  36  is configured to sequentially calculate moving average values (T 1 , T 2 , . . . Tn) of the period τ k  of the extraction signal  51  with the use of Expression 1, Expression 2, and Expression 3. Herein, “n” is an integer. The reference signal generating portion  36  is configured to generate the reference signal  38  at timing of the moving average value (T 1 , T 2 , . . . Tn) of the periods τ k  of the extraction signals  51  with the falling edge of the extraction signal  51  as a starting point. The reference signals  38  and the phase data  39  are input to the image control portion  5 . The phase data  39  represents times t 1 , t 2 , t 3 , and t 4  output from the data storage portion  37 . The image control portion  5  is configured to determine an emitting start timing for each surface of the rotary polygon mirror  15   a  based on the reference signal  38  and the phase data  39  to keep a writing start position of an image at a fixed position in the main scanning direction. The image control portion  5  is configured to sequentially output the image signals  40  to the respective laser control portions  11  for the light scanning apparatus  2   a ,  2   b ,  2   c , and  2   d  at the timings of the phase data  39  with the reference signal  38  as a starting point. 
     According to the fourth embodiment, the periods of the FG signals  22  are averaged, and hence an error in the periods of the FG signals due to the jitter of the motor  15  can be reduced. Thus, the emitting start timing is determined with high precision without arrangement of an additional detector, thereby being capable of keeping a writing start position of an image at a fixed position in the main scanning direction. 
     Fifth Embodiment 
     Next, a fifth embodiment will be described. In the fifth embodiment, configurations which are the same as those of the first embodiment have the same reference symbols allotted, and description thereof is omitted. The image forming apparatus  1 , the motor  15 , and the light scanning apparatus  2  according to the fifth embodiment are the same as those of the first embodiment, and hence description thereof is omitted.  FIG. 11  is a block diagram of the writing start control portion  31  according to the fifth embodiment. The writing start control portion  31  includes the face identifying portion (identifying unit)  34 , the extraction signal generating portion (extraction signal generating unit)  52 , the reference signal generating portion (reference signal generating unit)  36 , an abnormal period detection circuit (abnormal period detection unit)  53 , and the data storage portion (storage unit)  37 . The motor  15  is configured to be rotated in accordance with the motor activation signal  41  output from the image control portion  5 , to thereby generate the FG signal  22 . The face identifying portion  34  is configured to measure periods of the FG signals  22  and generate the face identification signals  35 . The face identification signals  35  are input to the extraction signal generating portion  52 . The extraction signal generating portion  52  is configured to extract the FG signal  22  at any timing of being synchronized with the face identification signal  35  and generate the extraction signal  51 . 
     Further, the face identifying portion  34  is configured to generate the detection timing signals  32 . The detection timing signals  32  are input to the abnormal period detection circuit  53 . The abnormal period detection circuit  53  is configured to measure periods of the detection timing signals  32 . When a period of the detection timing signal  32  falls outside of a range of thresholds (τerr_max and τerr_min) set in advance in the abnormal period detection circuit  53 , the abnormal period detection circuit  53  outputs an abnormality detection signal  54  to the reference signal generating portion  36 . When the reference signal generating portion  36  receives the abnormality detection signal  54 , the reference signal generating portion  36  removes the extraction signal  51  corresponding to the abnormality detection signal  54 . The reference signal generating portion  36  calculates a moving average value of the periods of the extraction signals  51  excluding the extraction signal  51  corresponding to the abnormality detection signal  54 . The reference signal generating portion  36  is configured to generate the reference signals  38  based on the extraction signals  51  and the moving average value of the periods of the extraction signals  51 . The data storage portion  37  is configured to store the phase data  39  representing phase values of the rotary polygon mirror  15   a  with respect to the reference signal  38 . The image control portion  5  is configured to determine an emitting start timing for each surface of the rotary polygon mirror  15   a  from the reference signal  38  and the phase data  39  to keep a writing start position of an image at a fixed position in the main scanning direction. The processing of generating the phase data  39  is the same as that of the third embodiment, and hence description thereof is omitted. 
     (Abnormal Period Detection Circuit) 
       FIG. 12  is a block diagram of the abnormal period detection circuit  53  according to the fifth embodiment. A first counter  62  and a second counter  65  are configured to count periods of the detection timing signals  32  with the use of a clock (CLK)  61 . Thresholds (τerr_max and τerr_min) set in advance are input by preset, and a carry out (carry output, hereinafter referred to as “CO”) is output in accordance with a result of counting. A first D-type flip-flop (hereinafter referred to as “first DFF”)  64  is configured to output an upper limit abnormality signal when a period of the detection timing signal  32  exceeds the upper limit threshold τerr_max. That is, the first DFF  64  is configured to output an upper limit abnormality signal in accordance with the CO output of the first counter  62  and the detection timing signal  32 . A second D-type flip-flop (hereinafter referred to as “second DFF”)  67  is configured to output a lower limit abnormality signal when a period of the detection timing signal  32  is equal to or less than the lower limit threshold τerr_min. That is, the second DFF  67  is configured to output a lower limit abnormality signal in accordance with the CO output of the second counter  65  and the detection timing signal  32 . The abnormality detection signal  54  is obtained from a result of subjecting the output of the first DFF  64  and the output of the second DFF  67  to a logical sum at an OR gate  68 . 
       FIG. 13A  and  FIG. 13B  are timing charts for illustrating abnormality of a detection timing signal according to the fifth embodiment.  FIG. 13A  is a timing chart for illustrating operations of the first counter  62  and the first DEF  64  when a period of the detection timing signal  32  is abnormally extended. The first counter  62  is configured to count the periods of the detection timing signals  32  with the clock (CLK)  61 . A count value of the first counter  62  is cleared and reset to zero at each time when the detection timing signal  32  is received. The first counter  62  is configured to determine whether or not the count value is larger than the upper limit threshold (τerr_max)  63 . The upper limit threshold (τerr_max)  63  is a value set in advance. The upper limit threshold (τerr_max)  63  is set to be, for example, a value which is longer than a target period by 5% in view of a jitter tolerance of the motor  15 . The first counter  62  is configured to reset a counter value for each period of the detection timing signal  32 . When the count value is not reset with a value equal to or less than the upper limit threshold (τerr_max)  63 , the first counter  62  outputs the CO. That is, when the period of the detection timing signal  32  exceeds the upper limit threshold (τerr_max)  63 , the first counter  62  outputs the CO as an abnormal period. The first DFF  64  is configured to output an H-level output voltage when the CO output is input by asynchronous preset. When the CO output is not input by asynchronous preset, the first DEF  64  outputs an L-level output voltage. When the H-level output voltage is input to the OR gate  68 , the OR gate  68  outputs an abnormality detection signal  54 . 
       FIG. 13B  is a timing chart for illustrating operations of the second counter  65  and the second DEF  67  when the period of the detection timing signal  32  is abnormally shortened. The second counter  65  has the structure which is the same as that of the first counter  62 . The second counter  65  is configured to count the periods of the detection timing signals  32  with the clock (CLK)  61 . The count value of the second counter  65  is cleared and reset to zero at each time when the detection timing signal  32  is received. The second counter  65  is configured to determine whether or not the count value is larger than the lower limit threshold (τerr_min)  66 . The lower limit threshold (τerr_min)  66  is set to a value shorter than a target period by about 5% based on the same idea as the upper limit threshold (τerr_max)  63 . The second counter  65  is configured to output the CO as a normal period when the period of the detection timing signal  32  exceeds the lower limit threshold (τerr_min)  66 . The second DFF  67  resets the CO output to an asynchronous state in the case of the normal period. When the period of the detection timing signal  32  is not reset with a value equal to or lower than the lower limit threshold (τerr_min)  66 , the second DFF  67  outputs an H-level output voltage as the abnormal period. When the H level output voltage is input to the OR gate  68 , the OR gate  68  outputs the abnormality detection signal  54 . 
       FIG. 14A  and  FIG. 14B  are timing charts for illustrating operations of the writing start control portion  31  according to the fifth embodiment.  FIG. 14A  is an illustration of the case where a period of the detection timing signal  32  is abnormally extended.  FIG. 14B  is an illustration of the case where a period of the detection timing signal  32  is abnormally shortened. The face identifying portion  34  starts measurement for periods of the FG signal  22  in accordance with the detection timing signals  32 . The face identification signals  35  are signals which are obtained by measuring the periods of the FG signals  22  with the face identifying portion  34  and specifying the FG signal  22  matched with the stored value of the data storage portion  37 . The reference signal  38  is output from the reference signal generating portion  36  at a timing of a moving average value (T 1 , T 2 , . . . Tn) of the periods of the extraction signals  51  with a falling edge of the extraction signal  51  as a starting point. Meanwhile, when the reference signal generating portion  36  receives the abnormality detection signal  54  from the abnormal period detection circuit  53 , the reference signal generating portion  36  outputs the reference signal  38  at a timing of T 1  obtained from a sequential moving average of periods excluding a period of the extraction signal  51  corresponding to the abnormality detection signal  54 . In the examples illustrated in  FIG. 14A  and  FIG. 14B , abnormality is detected at the period τ 3 . In this case, as represented by Expression 4, a moving average value is determined with use of periods τ 1 , τ 2 , τ 4 , and τ 5  excluding the period τ 3 . 
     
       
         
           
             
               
                 
                   
                     T 
                     1 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           τ 
                           1 
                         
                         + 
                         
                           τ 
                           2 
                         
                         + 
                         
                           τ 
                           4 
                         
                         + 
                         
                           τ 
                           5 
                         
                       
                       ) 
                     
                     4 
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     According to the fifth embodiment, abnormal data in the periods of the FG signals  22  is excluded, thereby being capable of reducing an error in a moving average value of the periods. Thus, precision in the emitting start timing to keep a writing start position of an image at a fixed position in the main scanning direction can be further improved. 
     Sixth Embodiment 
     Next, a sixth embodiment will be described. In the sixth embodiment, configurations which are the same as those of the first embodiment have the same reference symbols allotted, and description thereof is omitted. The image forming apparatus  1 , the motor  15 , and the light scanning apparatus  2  according to the sixth embodiment are the same as those of the first embodiment, and hence description thereof is omitted.  FIG. 15  is a block diagram of the writing start control portion  31  according to the sixth embodiment. The writing start control portion  31  includes the face identifying portion  34 , the extraction signal generating portion  52 , the reference signal generating portion (reference signal generating unit)  36 , the abnormal period detection circuit  53 , the data storage portion  37 , a speed change coefficient storage portion (speed change coefficient storage unit)  47 , and a phase difference calculating portion (speed change phase data generating unit)  48 . The motor  15  is rotated in accordance with the motor activation signal  41  output by the image control portion  5 , to thereby generate the FG signals  22 . The image control portion  5  is configured to perform activating/stopping control in accordance with the motor activation signal  41 , and concurrently output the image signals  40  to the laser control portion  11  in accordance with the speed change phase data  50  with the reference signal  38  output from the writing start control portion  31  as a starting point. 
     With reference to  FIG. 15 , the writing start control portion  31  according to the sixth embodiment will be described. The face identifying portion  34  starts measurement for the periods of the FG signals  22  based on the detection timing signals  32 . The face identifying portion  34  checks the measured periods of the FG signals  22  against a period pattern stored in advance in the data storage portion  37 . The face identifying portion  34  specifies a period of the FG signal  22  matched with the reference value of the period pattern stored in advance in the data storage portion  37  and generates the face identification signal  35 . The extraction signal generating portion  52  is configured to extract the FG signal  22  and generate an extraction signal  51  at any timing of being synchronized with rising of the face identification signal  35 . 
     The abnormal period detection circuit  53  is configured to measure the period of the detection timing signal  32 . When the period of the detection timing signal falls outside of the range of the threshold (τerr_max and τerr_min) set in advance in the abnormal period detection circuit  53 , the abnormal period detection circuit outputs the abnormality detection signal  54  to the reference signal generating portion  36 . Meanwhile, when the motor  15  is changed in speed, the image control portion  5  outputs a speed change signal  46  to the abnormal period detection circuit  53 . When the abnormal period detection circuit  53  receives the speed change signal  46  from the image control portion  5 , the abnormal period detection circuit  53  changes the thresholds (τerr_max and τerr_min) in accordance with the amount of speed change. 
     When the reference signal generating portion  36  receives the abnormality detection signal  54  from the abnormal period detection circuit  53 , the reference signal generating portion  36  excludes the extraction signal  51  corresponding to the abnormality detection signal  54 . The reference signal generating portion  36  is configured to calculate a moving average value of the periods of the extraction signals  51  excluding the extraction signal  51  corresponding to the abnormality detection signal  54 . The reference signal generating portion  36  is configured to generate the reference signal  38  based on the extraction signals  51  and the moving average value of the periods of the extraction signals  51 . 
     The phase difference calculating portion  48  is configured to calculate speed change phase data  50  from the phase data  39  stored in the data storage portion  37  and a speed change coefficient  49  stored in the speed change coefficient storage portion  47  in accordance with the speed change signal  46  output from the image control portion  5 . The speed change phase data  50  is corrected phase data obtained by correcting the phase data  39  based on the speed change coefficient  49 . The data storage portion  37  and the speed change coefficient storage portion  47  may be one memory which is, for example, an EEPROM. The image control portion  5  is configured to output the image signals  40  to the respective laser control portions  11  of the light scanning apparatus  2   a ,  2   b ,  2   c , and  2   d  sequentially at timings of the speed change phase data  50  with the reference signal  38  as a starting point. The processing of generating the phase data  39  is the same as that of the third embodiment, and hence description thereof is omitted. 
     (Countermeasure to Speed Change of Motor) 
     Next, countermeasure to a speed change of the motor  15  will be described.  FIG. 16  is a graph for showing a relationship between a rotation speed setting value and an actual rotation speed of the motor  15  according to the sixth embodiment. In  FIG. 16 , there are shown the cases where a motor A and a motor B having the same configuration are rotated at a first setting value of 15,000 rpm and a second setting value of 30,000 rpm. A theoretical value of the speed change coefficient from the first setting value of 15,000 rpm to the second setting value of 30,000 rpm is 2.000. However, the actual rotation speeds of the motor A and the motor B are different from the first setting value of 15,000 rpm and the second setting value of 30,000 rpm due to variance in components or other factors. At the first setting value of 15,000 rpm, the actual rotation speed of the motor A is 15,000 rpm, and the actual rotation speed of the motor B is 15,075 rpm. Further, at the second setting value of 30,000 rpm, the actual rotation speed of the motor A is 30,180 rpm, and the actual rotation speed of the motor B is 30,000 rpm. In this case, the speed change coefficient of the motor A is 1.990 (from 15,075 rpm to 30,000 rpm), whereas the speed change coefficient of the motor B is 2.012 (from 15,000 rpm to 30,180 rpm). It can be seen that there is an error of about 1% between the speed change coefficients of the motor A and the motor B. Herein, the speed change coefficient of the motor represents a ratio of the amount of change in the actual rotation speed with respect to the amount of change in the set rotation speed of the motor. 
       FIG. 17A  and  FIG. 17B  are time charts for illustrating a relationship between the reference signal  38  and the phase data  39  according to the sixth embodiment.  FIG. 17A  is an illustration of the reference signal  38  and the phase data  39  at the time of 15,000 rpm.  FIG. 17B  is an illustration of a result of calculation of the phase data  39  at the time of 30,000 rpm from the phase data  39  at the time of 15,000 rpm with use of the reference signal  38 , the phase data  39  (theoretical value), and the speed change coefficient at the time of 30,000 rpm. As illustrated in  FIG. 17B , it can be seen that the phase data  39  (t 4 ′) of the motor A calculated with use of the theoretical value of the speed change coefficient becomes longer than the theoretical value (t 4 ), and that the phase data  39  (t 4 ″) of the motor B calculated with use of the theoretical value of the speed change coefficient becomes shorter than the theoretical value (t 4 ). This error in the phase data may lead to degradation of precision in the writing start position. Therefore, in the sixth embodiment, a difference between the setting value of the rotation speed of the motor  15  and the actual rotation speed is measured, and the emitting start timing of the semiconductor laser  12  is changed in accordance with the rotation speed of the motor  15 . 
     Specifically, the speed change coefficient of the motor  15  is measured when the light scanning apparatus  2  is assembled, to thereby determine the speed change coefficient  49 . The speed change coefficient  49  is to be stored in the speed change coefficient storage portion  47 . The tool  100  for use in generating the speed change coefficient  49  is the same as the tool  100  of the third embodiment, and hence description thereof is omitted.  FIG. 18  is a flowchart for illustrating processing of generating the speed change coefficient  49  according to the sixth embodiment. The tool control portion  104  is configured to execute the processing of generating the speed change coefficient  49  in accordance with a program stored in a ROM (not shown). When the processing of generating the speed change coefficient  49  is started, the tool control portion  104  sets the rotation speed of the motor  15  (S 201 ). The tool control portion  104  causes the motor  15  to rotate, to thereby output the FG signals  22  (S 202 ). The writing start control portion  31  generates the face identification signal  35  from the FG signal  22 , to thereby generate the reference signals  38  (S 203 ). 
     The tool control portion  104  causes the semiconductor laser  12  to emit the light beam L. The light beam L is deflected by the rotary polygon mirror  15   a  and enters the tool BD  101 . When the light beam L enters the tool BD  101 , the tool BD  101  outputs BD signals  102 . The tool control portion  104  measures periods of the BD signals  102  (S 204 ). The FG-BD phase measuring portion  103  measures times t 1 , t 2 , t 3 , and t 4  from the reference signal  38  to the BD signals  102  corresponding to the respective reflection surfaces (S 205 ). The tool control portion  104  determines whether or not the measurement has been completed (S 206 ). When the measurement has not been completed (NO in S 206 ), the processing proceeds to S 201 , and another rotation speed is set. When the measurement has been completed (YES in S 206 ), the processing proceeds to S 207 . 
     The tool control portion  104  calculates the speed change coefficient  49  which is a period ratio from the period of the BD signals  102  obtained through rotation of the motor  15  at a plurality of rotation speeds (S 207 ). The tool control portion  104  stores the measurement result in the FG-BD phase measuring portion  103  as phase data  39  in the data storage portion  37  (S 208 ). The tool control portion  104  stores the speed change coefficient  49  obtained in S 207  in the speed change coefficient storage portion  47  (S 209 ). The tool control portion  104  terminates the processing of generating the speed change coefficient  49 . 
     According to the sixth embodiment, at the time of speed change of the motor  15 , the emitting start timing is determined based on the speed change coefficient  49  memorized in advance, and hence the precision in the image writing start position in the main scanning direction can be improved regardless of the variance in the motor  15 . 
     In the embodiment, the image forming apparatus  1  configured to form a color image is described. However, the present invention is also applicable to an image forming apparatus configured to form a monochromatic image. 
     According to the embodiment, the emitting start timing of the light beam can be determined based on the FG signals  22  output from the motor  15  without addition of another detector. Therefore, the cost for the light scanning apparatus can be reduced. 
     According to the above described embodiments, the emitting start timing of the light beam can be determined based on the rotational position detection signals generated in accordance with rotation of the motor configured to rotate the rotary polygon mirror. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2015-178208, filed Sep. 10, 2015, which is hereby incorporated by reference herein in its entirety.