Patent Publication Number: US-11652939-B2

Title: Position sensing apparatus, image forming apparatus, and position detection method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This patent application is based on and claims priority pursuant to 35 U.S.C. § 1.19(a) to Japanese Patent Application No. 2021-075407, filed on Apr. 27, 2021, in the Japan Patent Office, the entire disclosure of which is hereby incorporated by reference herein. 
     BACKGROUND 
     Technical Field 
     Embodiments of the present disclosure relate to a position sensing apparatus, an image forming apparatus, and a position detection method. 
     Background Art 
     In the related art, the position of a recording sheet tends to change in image forming apparatuses, and there are some cases in which the image on the recording sheet is displaced. 
     In the related art, technologies are known in the art that corrects the positional displacement of an image on a recording sheet. In such image forming apparatuses known in the art, the position of an invisible mark that is formed on a recording sheet is detected by irradiating the light outside the area of visibility, and the position at which the image is formed is corrected based on the detected position of the invisible mark. 
     SUMMARY 
     Embodiments of the present disclosure described herein provide a position sensing apparatus and a method of detecting a position. The position sensing apparatus includes a scanner configured to emit light to an object to scan an image of the object, and a position detector. In the position sensing apparatus, the scanner outputs a first result of scanning obtained by irradiating the object with visible light and a second result of scanning obtained by irradiating the object with invisible light to the position detector, and the position detector corrects the second result of scanning based on the first result of scanning, and to detect an invisible alignment image based on the corrected second result of scanning. The method includes emitting light to an object using a scanner, obtaining a first result of scanning as the scanner irradiates the object with visible light, obtaining a second result of scanning as the scanner irradiates the object with invisible light, correcting the second result of scanning based on the first result of scanning, using a position detector, and detecting an invisible alignment image based on the corrected second result of scanning, using the position detector. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of embodiments and the many attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings. 
         FIG.  1    is a basic configuration diagram of a position sensing apparatus according to a first embodiment of the present disclosure. 
         FIG.  2    is a diagram illustrating a configuration of a position sensing apparatus, according to an embodiment of the present disclosure. 
         FIG.  3    is a diagram illustrating a configuration of a sensor according to an embodiment of the present disclosure. 
         FIG.  4    is a diagram illustrating a configuration of an image on a recording sheet according to an embodiment of the present disclosure. 
         FIG.  5    is a diagram illustrating the spectral reflectance of an image formed on a recording sheet, according to an embodiment of the present disclosure. 
         FIG.  6    is a schematic diagram illustrating how the correction is performed by the image processing unit to distinguish a plurality of IR toner images from the other information, according to the first embodiment of the present disclosure. 
         FIG.  7    is a diagram illustrating a configuration or structure of an image forming apparatus according to a second embodiment of the present disclosure. 
         FIG.  8    is a diagram illustrating a configuration of the control blocks of an image forming apparatus according to an embodiment of the present disclosure. 
         FIG.  9    is a schematic diagram of a recording sheet on which a color visible image and a plurality of alignment images are printed, according to the second embodiment of the present disclosure. 
         FIG.  10 A  and  FIG.  10 B  are diagrams each illustrating the images of the first data and the second data that are obtained by scanning the recording sheet of  FIG.  9    with a position sensing apparatus, according to the second embodiment of the present disclosure. 
         FIG.  11 A ,  FIG.  11 B  &amp; and  FIG.  11 C  are diagrams each illustrating a method of generating a subtracted image, according to a second embodiment of the present disclosure. 
         FIG.  12    is a diagram illustrating a method of detecting a positional displacement using a controller, according to an embodiment of the present disclosure, 
         FIG.  13 A  is a diagram illustrating a method of detecting an alignment image according to the related art. 
         FIG.  13 B  is a diagram illustrating a method of detecting an alignment image according to a first modification of the second embodiment of the present disclosure. 
         FIG.  14    is a diagram illustrating an infrared image obtained as a result of treating the read value of scanning with invisible light as the level of the bare surface of a sheet, according to the first modification of the second embodiment of the present disclosure. 
         FIG.  15    is a diagram illustrating a configuration of the control blocks of an image forming apparatus according to a second modification of the second embodiments of the present disclosure. 
         FIG.  16 A  and  FIG.  16 B  are diagrams illustrating a case in which a K plate image of print data overlaps with an S plate image at a fixed position, according to a second modification of the second embodiment of the present disclosure. 
         FIG.  17    is a flowchart of the processes of changing the position of an image by a controller, according to the second modification of the second embodiment of the present disclosure. 
         FIG.  18 A ,  FIG.  18 B ,  FIG.  18 C , and  FIG.  18 D  are diagrams illustrating how the position of one of a plurality of infrared (IR) toner images changes when a K color toner image overlaps with the IR toner image, according to the second modification of the second embodiment of the present disclosure. 
         FIG.  19 A  and  FIG.  19 B  are diagrams illustrating the image-forming area determined by changing the positions of a plurality of IR toner images, according to the second modification of the second embodiment of the present disclosure. 
         FIG.  20    is a flowchart of the changing processes performed by a controller, according to a third modification of the second embodiment of the present disclosure. 
         FIG.  21 A  and  FIG.  21 B  are diagrams illustrating an effect of the positional change of an image when a K color toner image overlaps with an IR toner image, according to the second modification of the second embodiment of the present disclosure. 
     
    
    
     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 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “includes” and/or “including”, when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     In describing example embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the present disclosure 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 structure, operate in a similar manner, and achieve a similar result. 
     In the following description, illustrative embodiments will be described with reference to acts and symbolic representations of operations (e.g., in the form of flowcharts) that may be implemented as program modules or functional processes including routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types and may be implemented using existing hardware at existing network elements or control nodes. Such existing hardware may include one or more central processing units (CPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), computers or the like. These terms may be collectively referred to as processors. 
     Unless specifically stated otherwise, or as is apparent from the discussion, terms such as “processing” or “computing” or “calculating” or “determining” or “displaying” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical, electronic quantities within the computer system&#39;s registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices. 
     A position sensing apparatus, an image forming apparatus, and a position detection method according to an embodiment of the present disclosure are described below in detail with reference to the accompanying drawings. 
     First Embodiment 
       FIG.  1    is a basic configuration diagram of a position sensing apparatus according to a first embodiment of the present disclosure. 
     As illustrated in  FIG.  1   , the position sensing apparatus  1  includes a position detector  20  and a scanner  10  having a light source  11 . The light source  11  according to the present embodiment is a light source of the light that is emitted to an object. The light with which the subject is irradiated includes light in two ranges, i.e., visible light and light in a range outside the visible range. For example, infrared light may be selected as the light in a range outside the visible range. The light in a range outside the visible range that can be selected may be collectively referred to as invisible light in the following description. 
     The scanner  10  irradiates an object with light, and outputs a first result of scanning d 1  that is the result of scanning that is obtained by irradiating the object with visible light and a second result of scanning d 2  that is the result of scanning that is obtained by irradiating the object with invisible light. The scanner  10  according to the present embodiment includes a first scanner  12  and a second scanner  13 . The first scanner  12  scans the first data readable from a visible range, and outputs the first result of scanning d 1 . The second scanner  13  scans the second data readable from a range outside the visible range, and outputs the second result of scanning d 2 . 
     Regarding, the first result of scanning d 1  and the second result of scanning d 2 , the position detector  20  corrects the second result of scanning d 2  based on the first result of scanning d 1 , and detects alignment data that is invisible under visible light based on the corrected second result of scanning d 2 . In  FIG.  1   , the position detector  20  is included in the position sensing apparatus  1 . However, no limitation is indicated thereby, and an external device may be used as the position detector  20 . 
     A concrete example of a configuration and operation of the position sensing apparatus  1  according to embodiments of the present disclosure will be described below. In the following description, a recording sheet is used as an example of an object. The object may be, for example, a plastic, a film, a cloth, or other kinds of medium instead of a sheet of paper. Cases in which the first data and the second data are formed on a recording sheet using toner are described by way of example. As will be described later, no limitation is indicated to toner, and other materials may be used to form data on a recording sheet. 
       FIG.  2    is a diagram illustrating a configuration of the position sensing; apparatus  1 , according to the present embodiment. 
     The sensing apparatus  1  as illustrated in  FIG.  2    is provided with a visible-light source unit  401 , an infrared light source unit  402 , and a sensor  403 . As illustrated in  FIG.  2   , the position sensing apparatus  1  may include a background unit  500 . A reading device  400  according to the present embodiment includes the visible-light source unit  401 , the infrared light source unit  402 , and the sensor  403 , and scans and reads an image on the recording sheet P through a scanning window  404 . 
     The visible-light source unit  401  and the infrared light source unit  402  are the light source units used to emit visible light and invisible light, respectively, and are provided for the light source  11 . As illustrated in  FIG.  2   , the visible-light source unit  401  and the infrared light source unit  402  irradiate the recording sheet P with light, and the sensor  403  reads the light reflected by the recording sheet P. 
     The visible-light source unit  401  according to the present embodiment is a white light-emitting diode (LED) or a plurality of LEDs of multiple colors. The LEDs of multiple colors may be, for example, a red LED, a green LED, and a blue LED, A single LED may be used for each color, or a plurality of LEDs may be used for each color in combination. The infrared light source unit  402  is an infrared LED. 
     The arrangement of the visible-light source unit  401  and the infrared light source unit  402  as illustrated  FIG.  2    is given for the sake of explanatory convenience, and no limitation is indicated thereby. The visible light source unit  401  and the infrared light source unit  402  are not limited to LEDs, and run be any other kinds of light sources. 
       FIG.  3    is a diagram illustrating a configuration of the sensor  403  according to the present embodiment. 
     In the present embodiment described with reference to  FIG.  3   , a line sensor is used as the sensor  403 , The sensor  403  is provided with a first sensor  501  that includes a row of red pixels, a row of green pixels, and a row a blue pixels. The sensor  403  is provided with a second sensor  502  that includes a row of invisible (IV) pixels. The red pixels receive the light of red color, and convert the received red light into an electrical signal. The green pixels receive the light of green color, and convert the received green light into an electrical signal. The blue pixels receive the light of blue color, and convert the received bite light into an electrical signal. The invisible (IV) pixels receive infrared light, and convert the received infrared light into an electrical signal. 
     The first sensor  501  corresponds to the first scanner  12  that reads the first data, and the second sensor  502  corresponds to the second scanner  13  that reads the second data. 
     The sensor  403  is configured to be orthogonal to the direction of conveyance of the recording sheet. Due to such a configuration, the sensor  403  can read an image of the recording sheet on a line-by-line basis across the width of the recording sheet. The configuration or structure of the sensor  403  is not limited to such a configuration or structure. For example, the position sensing apparatus  1  may be provided with a main-scanning driving mechanism that drives the sensor  403  in the main scanning direction, and the sensor  403  may scan and read an image of the recording sheet on a line-by-line basis in the width direction of the recording sheet. 
     The rows of pixels of red, green, and blue (RGB) color are given by way of example, and no limitation is intended to those combinations. For example, when only a plurality of K color toner images are to be read, only one row of pixels of any one of RGB colors may be arranged. 
     The sensor  403  is not limited to a line sensor in which a row of pixels are arranged, and may be an image sensor. The image transmission mode of the sensor  403  may be a method or system using one of charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS). 
     The pixels of red, green, and blue (RUB) colors and the invisible (IV) pixels may be driven by the same drive system, or may be driven by different drive systems separately. 
       FIG.  2    illustrates a conveyance unit that conveys the recording sheet P to the scanning position of the sensor  403 . In  FIG.  2   , the recording sheet P is conveyed in the direction of conveyance by the rotation of the conveyance roller  600  of the conveyance unit, and in so doing, the sensor  403  scans the recording sheet P at the scanning position on a line-by-line basis. As described above, as the recording sheet P is conveyed, the sensor  403  scans the recording sheet P in the sub-scanning direction, i.e., the direction parallel to the length of the recording sheet P. 
     The background unit  500  is read as a background of the recording sheet P when the first scanner  12  reads the recording sheet P at the scanning position. The edges of the recording sheet P are detected from the result of scanning based on the differences in read values due to, for example, the differences in color or pattern between the recording sheet P and the background unit  500 . Some examples of the materials for the background unit  500  will be described later. 
     In this configuration, the visible light of the visible-light source unit  401  and the infrared light of the infrared light source unit  402  are emitted to the recording sheet P at the scanning position through the scanning window  404 , respectively. The result of scanning of the recording sheet P with the irradiation of visible light can be obtained from the first sensor  501  of the sensor  403 , and the result of scanning of the recording sheet P with the irradiation of infrared light can be obtained from the second sensor  502  of the sensor  403 . Scanning of the recording sheet P by irradiation with visible light may be referred to as scanning with visible light in the following description, and scanning of the recording sheet P by irradiation with invisible light such as infrared light may be referred to as scanning with invisible light in the following description. 
       FIG.  4    is a diagram illustrating a configuration of an image on a recording sheet P according to the present embodiment. 
     On the recording sheet P illustrated in  FIG.  4   , an image is formed using toner. Depending on the material used for the toner, an image that can be viewed by human eyes and an image that cannot be viewed by human eyes are formed on the recording sheet when illuminated with visible light. The former is a visible image, and the latter is an image for alignment to be detected by the position sensing apparatus  1 . 
     In  FIG.  4   , a plurality of K color toner images p 1  are formed as visible images on the recording sheet P, and a plurality of IR toner images p 2  are formed as images for alignment on the recording sheet P. The multiple IR toner images p 2  are formed by IR toner made of a material that absorbs infrared light. The alignment images are satisfactory as long as they are detected by the position sensing apparatus  1 . Accordingly, such alignment images may be formed of IR toner that is scanned with invisible light. 
     The material for forming an image on the recording sheet P is not limited to toner. The forming material may be other kinds of material such as ink. The alignment images are not limited to the cross-shaped mark illustrated by way of example in  FIG.  4   , and may be changed to any other shapes where appropriate. 
       FIG.  5    is a diagram illustrating the spectral reflectance of an image formed on a recording sheet P, according to the present embodiment. 
     By way of example, in  FIG.  3   , the spectral reflectance of a toner image that is formed on a piece of plain white paper is illustrated. The horizontal axis denotes the wavelength in nanometers (nm), and the vertical axis denotes the reflectivity of light in percentage (%). 
       FIG.  5    illustrates the spectral reflectance of color toner of cyan (C), color toner of magenta (M), color toner of yellow (Y), and black (K) toner, and infrared (IR) toner, according to an embodiment of the present disclosure. 
     As illustrated in the invisible area of  FIG.  5   , all of the light reflectivity of the color toner of cyan, magenta, and yellow (CMY) takes a larger value due to the irradiation with invisible light exceeding 780 nanometers (nm) approximately, but the light reflectivity of IR toner takes a small value. Accordingly, the IR toner images p 2  whose read value is small is detected in the second data that is the result of scanning obtained by the second sensor  502 . However, the light reflectivity of K color toner is also as low as the light reflectivity of the IR toner in the invisible area. Due to such a configuration, when the K color toner is used to form a visible image, the visible image in the second data tends to be detected with a read value as low as the read value of the IR toner images p 2 . In other words, the K color toner image p 1  is detected as an image in the first data that is the result of scanning or the first sensor  501 , and is detected as an image also in the second data without being distinguished from the IR toner images p 2 . 
     In this way, by the irradiation of the invisible light, when a material indicating the same characteristics as the IR toner in the invisible area is used in the visible image, the image in which such a material is used is detected as an image in both of the first data and the second data due to the irradiation with invisible light. 
     The first data and the second data that are read by the sensor  403  are output to, for example, an image processing unit, and are used for positional detection. The image processing unit according to the present embodiment may be functionally implemented by a control program that is stored in a memory such as a read only memory (ROM) and executed by a central processing unit (CPU) in a personal computer or one or more processors provided with the CPU, the ROM, and a random access memory (RAM). Alternatively, some of or all of these functions of the image processing unit may be configured by hardware such as an application-specific integrated circuit (ASIC). The image processing unit according to the present embodiment serves as the position detector  20 . The image processing unit may be arranged inside the position sensing apparatus  1  or may be provided for an external device capable of communicating with the position sensing apparatus  1 . 
     Regarding the first result of scanning d 1  and the second result of scanning d 2 , the image processing unit corrects the second result of scanning d 2  based on the first result of scanning d 1 , and detects the alignment data that is invisible under visible light based on the corrected second result of scanning d 2 . How the second result of scanning is corrected based on the first result of scanning is described below by way of example. 
       FIG.  6    is a schematic diagram illustrating how the correction is performed by the image processing unit to distinguish the multiple IR toner images p 2  from the other information, according to the first embodiment of the present disclosure. 
       FIG.  6   , an image that indicates the result of scanning is illustrated. The image D 1  scanned with visible light that is obtained by the scanning with visible light corresponds to the first data. The infrared image D 2  that is obtained by scanning with invisible light corresponds to the second data. As illustrated in  FIG.  6   , the infrared image D 2  includes a plurality of K color toner images p 1  of the image D 1  scanned with visible light in addition to a plurality of IR toner images p 2 . 
     In view of these circumstances, the image processing unit according to the present embodiment performs correcting processes by subtracting the elements in common between the infrared image D 2  and the image D 1  scanned with visible light. In other words, as schematically illustrated in  FIG.  6    with arithmetic symbols “−” and “=”, the image processing unit according to the present embodiment subtracts the differences between the infrared image D 2  and the image D 1  scanned with visible light to obtain a subtracted image D 3 . In the present embodiment, the image processing unit eliminates from the infrared image D 2  the K color toner images p 1  included in common between the infrared image D 2  and the image D 1  scanned with visible light. By so doing, correction is performed in such a manner that the IR toner images p 2  remain on the subtracted image D 3 . The image processing unit according to the present embodiment uses the subtracted image  133 , which is obtained as a result of correction performed as above, for alignment. 
     In the present embodiment, the image processing unit eliminates the differences between the infrared image D 2  and the image D 1  scanned with visible light to distinguish the IR toner images on the infrared image D 2 . However, no limitation is indicated thereby, and other kinds of processing may be adopted where appropriate. For example, as treatment in preparation for the elimination of these differences, the image processing unit according to the present embodiment may binarize the values read from each pixel, or may emphasize the K color toner images p 1  and the IR toner images p 2 , which are included in the infrared image D 2  and the image D 1  scanned with visible light. Alternatively, as treatment in preparation for the elimination of these differences, the image processing unit according to the present embodiment may remove images whose sizes are smaller than a predetermined area as noise. The image processing unit may use any correction method other than the above method in which differences are eliminated as long as the IR toner images p 2  can be distinguished as a result based on the infrared image D 2  and the image D 1  scanned with visible light. For example, the image processing unit according to the present embodiment may perform a comparison between a prescribed threshold value and a read value for each corresponding pixel or corresponding area between the infrared image D 2  and the image D 1  scanned with visible light, and may distinguish between pixels in common and the other pixels that are not in common, based on the results of the comparison. 
     As described above, the position sensing apparatus according to the first embodiment of the present disclosure can distinguish invisible alignment data from the other information based on the result of scanning obtained with the irradiation of visible light and the result of scanning obtained with the irradiation of invisible light. As it is not always necessary to perform, for example, arrangement of information that makes the visible image, reduction in the size of the visible image, changes in color, an image for alignment can be detected without depending on an image-forming area such as the visible image. 
     Second Embodiment 
     An image forming apparatus to which the position sensing apparatus according to the above embodiment of the present disclosure is applied is described below as a second embodiment of the present disclosure. 
       FIG.  7    is a diagram illustrating a configuration or structure of an image forming apparatus  2  according to a second embodiment of the present disclosure. 
     The image forming apparatus  2  as illustrated in  FIG.  7    includes a controller  30  (see  FIG.  8   ), an image forming device  50 , a fixing device  60 , and an operation panel  80 . 
     The operation panel  80  is a user interface of the image forming apparatus  2 , and includes an input device such as a touch panel or hardware keys that receive input operation of various kinds of settings or commands for execution and an output device such as a liquid crystal display used to display a setting operation screen and a notification screen. The output device may include, for example, a notification lamp and a loudspeaker. 
     The image forming device  50  includes an image forming unit, and uses the image forming unit to form an image on the recording sheet P.  FIG.  7    illustrates an electrophotographic configuration as the configuration of the image forming unit. The formed image in the second embodiment of the present disclosure includes a visible image that can be read under visible light and an invisible alignment image that cannot be read under visible light. The image forming device  50  does not necessarily form such an alignment image on the recording sheet P together with the visible image every time, and may form the alignment image on the recording sheet P at a prescribed timing as appropriate. For example, the controller  30  according to the second embodiment of the present disclosure may instruct the image forming device  50  to form an alignment image, for example, when a visible image is to be formed for the first time after the system is turned on, when a predetermined number of sheets have been printed with a visible image, or when a certain length of time has passed. Alternatively, the controller  30  may be configured to instruct the image forming device  50  to form a plurality of alignment images, for example, when the recording sheet P is to be replaced or when the changes in operating temperatures are detected. When the controller  30  instructs the image forming device  50  to form alignment images, the image forming device  50  may be operated to continuously form a plurality of alignment images for a predetermined number of sheets. In such cases, the controller  30  according to the present embodiment may compute and obtain the amount of correction of the position at which the image has been formed, based on, for example, an average value of the amounts of displacements of the multiple alignment images on each one of the recording sheets. 
     The configuration or structure of the image forming device  50  is described below in more detail. The image forming device  50  includes an optical writing device  51 , a plurality of image forming units  52  that uses a tandem system to form images of multiple plates, a plurality of transfer units  53 , an intermediate transfer belt  54 , a sheet feeder  55 , a conveyance path  56 , a secondary transfer roller  57 , and a sheet ejection belt  58 . 
     In addition to the photoconductor drums  52 - 1 ,  52 - 2 ,  52 - 3 , and  52 - 4  for Y, M, C, and K toners, respectively, one of the multiple image forming units  52  is provided with can S photoconductor drum  52 - 5 . The S photoconductor drum  52 - 5  is a photoconductor drum that forms an alignment image. By way of example, cases in which infrared (IR) toner is used as the toner of the S photoconductor drum  52 - 5  are described below. 
     For example, image forming elements including a charger, a developing device, a transfer unit, a cleaner, and a discharger are arranged around each one of the photoconductor drums  52 - 1 ,  52 - 2 ,  52 - 3 , and  52 - 4 , and the S photoconductor drum  52 - 5 . An intermediate transfer belt  54  is seamlessly stretched between the multiple transfer units  53  and the photoconductor drums  52 - 1 ,  52 - 2 ,  52 - 3 , and  52 - 4 , and the S photoconductor drum  52 - 5  and. The intermediate transfer belt  54  is stretched between a driving roller g 1  and a driven roller g 2 . 
     The optical writing device  51  writes the image on each one of the plates of yellow (Y), magenta (M), cyan (C), black (K), and S onto corresponding on of the photoconductor drums. The multiple image forming units  52  form toner images of the respective plates of Y, M, C, K, and S by performing an image forming process by the respective image forming elements in the respective photoconductor drums, and transfers the toner images of the respective plates of Y, M, C, K, and S onto an intermediate transfer belt  54  traveling in one direction by the respective transfer units  53 . As a result, the visible images that are the toner images of each one of the plates of Y, M, C, and K and the primarily-transferred images of the multiple alignment images that are the IR toner images of the S plate are formed on the intermediate transfer belt  54 . 
     When the intermediate transfer belt  54  further runs and the primarily-transferred image on the intermediate transfer belt  54  reaches the secondary transfer position, the primarily-transferred image is transferred onto the recording sheet P. In other words, the primarily-transferred image is secondary-transferred onto the recording sheet P. 
     The sheet feeder  55  accommodates a bundle of recording sheets P, and feeds the recording sheets P from an upper side of the bundle of recording sheets. A registration roller pair g 3  separates the recording sheets fed from the sheet feeder  55  on a one-piece-by-one-piece basis and supplies the recording sheet to the conveyance path  56 . 
     The conveyance path  56  conveys the recording sheet P fed from the sheet feeder  55  in the direction indicated by an arrow Y 1  (see  FIG.  7   ) as the conveyance roller  600  rotates. 
     The secondary transfer roller  57  is arranged at a secondary transfer position. The secondary transfer roller  57  transfers the primarily-transferred image on the intermediate transfer belt  54  onto the recording sheet P that is being conveyed through the conveyance path  56 . 
     The image forming device  50  sends the recording sheet P on which an image is formed to the fixing device  60  by the sheet ejection belt  58 . 
     The fixing device  60  fixes the image formed on the recording sheet P by the image forming device  50  onto the recording sheet P by pressure and drying. 
     The fixing device  60  is provided with a position sensing apparatus  61 . The position sensing apparatus  61  reads an image from the recording sheet P by the sensor after pressure bonding and drying, and transmits a result of scanning to the controller  30 . 
     The configuration or structure of the fixing device  60  is described below in more detail. The fixing device  60  includes, for example, the position sensing apparatus  61 , a cooling unit  62 , and a fixing unit  63 . The recording sheet P on which an image is formed by the image thrilling device  50  is sequentially sent to the fixing unit  63 , the cooling unit  62 , and the position sensing apparatus  61 . The fixing unit  63  heats and pressurizes the recording sheet P in order to fix an image on the recording sheet P. The cooling unit  62  cools the heated recording sheet P. The position sensing apparatus  61  scans an image from the recording sheet P, and sends the result of scanning to the controller  30 . It is not always necessary for the position sensing apparatus  61  to read the image every time. For example, when the image forming device  50  forms an alignment image on a recording sheet P, the position sensing apparatus  61  reads the image on the recording sheet P. The controller  30  detects the positional displacement based on the result of scanning fed hack from the position sensing apparatus  61  and instructs the image forming device  50  to correct the position at which the image has been formed. 
       FIG.  8    is a diagram illustrating a configuration of the control blocks of the image forming apparatus  2 , according to the present embodiment. 
     For example, the control processes of the controller  30  as illustrated in  FIG.  8    may be functionally implemented by a control program that is stored in a memory such as a ROM and executed by a CPU in a personal computer or one or more processors provided with the CPU, the ROM, and a RAM. Alternatively, some of or all of these functions of the control processes of the controller  30  as illustrated in  FIG.  8    may be configured by hardware such as an application-specific integrated circuit (ASIC). The controller  30  may include a functional unit or ASIC that serves as the image processing unit according to the present embodiment. 
     Upon receiving a print execution instruction from the operation panel  80 , the controller  30  outputs print data to the image forming engine  35  to execute printing. In the present embodiment, the source from which the print data is obtained is not limited to any particular source. The print data according to the present embodiment may be any predetermined data read from the storage unit  31  by the controller  30 , or may be the data that is sent from a counterpart and then is received by the controller  30  through a communication unit such as a network interface. 
     The image forming engine  35  drives the image forming device  50  and the fixing device  60  in response to a print execution instruction, forms an image on the recording sheet P fed from the sheet feeder  55  by an electrophotographic method, and fixes the image on the recording sheet P by the fixing device  60 . For example, the image forming engine  35  and the image forming device  50  serves as an image forming device. 
     The controller  30  corrects the position at which the image has been formed at a prescribed timing. For example, the controller  30  according to the present embodiment may correct the position at which the image has been formed when an operation for correction is received through the operation panel  80  by the user or when printing is to be performed for the first time after the system is turned on. Alternatively, the controller  30  according to the present embodiment may correct the position at which the image has been formed when a predetermined number of sheets have been printed or when a certain length of time has passed. For example, the number of printed sheets or the lapse of a certain length of time is counted by a counter  32  coupled to the controller  30 . Alternatively, the position at which the image has been formed may be corrected by the controller  30  when the sensor  33  detects the timing at which the recording sheet P is to be replaced or the changes in operating temperatures. 
     When the position at which the image has been formed is to be corrected, the controller  30  instructs the image forming engine  35  to form the alignment images on the S plate in addition to the formation of the images of the multiple plates of cyan, magenta, yellow and black (CMYK) colors of the print data. When instructed to form a plurality of alignment images, the image forming engine  35  outputs a plurality of fixed alignment images to the optical writing device  51 , and forms the multiple alignment images using the S photoconductor drum  52 - 5 . As a result, the alignment images for the fixed position are formed on the recording sheet P together with the visible image. 
       FIG.  9    is a schematic diagram of a recording sheet P on which a color visible image and a plurality of alignment images p 2  are primed, according to the present embodiment. 
     The term printing is used as a synonym for image formation. The term color printing refers to printing in which at least one of cyan, magenta, and yellow (CMY) is used. On the recording sheet P as illustrated in  FIG.  9   , a color visible tillage is formed by a C color toner image p 11 , an M color toner image p 12 , a Y color toner image p 13 , and a K color toner image p 14 . The C color toner image p 11 , the M color toner image p 12 , the Y color toner image p 13 , and the K color toner image p 14  are included in the schematic diagram of  FIG.  9   . The position, shape, and area of each color may be determined as desired. In a similar manner to the first embodiment of the present disclosure, the IR toner images p 2  according to the present embodiment are also indicated by cross-shaped marks. In the present embodiment, the multiple IR toner images p 2  are printed at fixed positions of the four corners of the recording sheet P. 
     As illustrated in  FIG.  8   , for example, the position sensing apparatus  61  according to the present embodiment operates in response to instructions for detection sent from the controller  30 , and scans and reads the recording sheet P on which a plurality of alignment images have been formed. Then, the read first data and second data are output to the controller  30 . 
       FIG.  10 A  and  FIG.  10 B  are diagrams each illustrating the images of the first data and the second data that are obtained by scanning the recording sheet P of  FIG.  9    with the position sensing apparatus  61 , according to the second embodiment of the present disclosure. 
     As illustrated in  FIG.  10 A  and  FIG.  10 B , the C color toner image p 11 , the M color toner image p 12 , the Y color toner image p 13 , and the K color toner image p 14  are included in an image D 11  scanned with visible light. Such an image scanned with visible light corresponds to the first data, and may be referred to as scanned color image the following description. In a similar manner to the first embodiments of the present disclosure, the multiple IR toner images p 2  and the K color toner image p 14  are included in an infrared image D 21  scanned with invisible light. Such an infrared image scanned with invisible light corresponds to the second data. 
     In  FIG.  8   , the controller  30  generates, based on the first data and the second data, an image in which the alignment images included in the second data are distinguished from the other images, and detects a positional displacement from the arrangement of the alignment images in the subtracted image. Such an image in which the alignment images are distinguished from the other images is, for example, a subtracted image. 
       FIG.  11 A , FIG. and  FIG.  11 C  are diagrams each illustrating a method of generating a subtracted image, according to the second embodiment of the present disclosure. 
       FIG.  11 A  illustrates an image on which an M color toner image p 12  and a plurality of K color toner images p 14  are formed as color visible images. Operation can be performed in a similar manner even when other colors are included. Accordingly, for the sake of explanatory convenience, in the present embodiment, cases of the M color toner image p 12  are described by way of example. 
     As illustrated in  FIG.  11 B  and  FIG.  11 C , the controller  30  performs predetermined pretreatment based on the scanned color image D 11  and the infrared image D 21 , and then calculating the difference between the two images. More specifically, firstly, as illustrated in  FIG.  11 B , the controller  30  performs pretreatment to extract the elements in common between the scanned color image D 11  and the infrared image D 21 . As illustrated in  FIG.  11 C , the controller  30  subtracts the elements in common on the image D 31 , which is the image of the elements in common obtained as a result of performing pretreatment, from the infrared image D 21 , and detects positional displacement based on the multiple IR toner images p 2  located at the four corners, which remain as a subtracted image D 32 . In other words, the controller  30  according to the present embodiment calculates a difference between two images, and detects positional displacement based on the obtained difference. 
     In  FIG.  8   , when the positional displacement is detected, a correction value for correcting the positional displacement of each of the multiple plates of cyan, magenta, yellow, and black (CMYK) colors is fed back from the controller  30  to the image forming engine  35 . The image forming engine  35  corrects the formation positions of the images of the respective CMYK plates based on the correction values. 
       FIG.  12    is a diagram illustrating a method of detecting positional displacement using the controller  30 , according to the present embodiment. 
     The controller  30  detects the positional displacement based on the subtracted image D 32 . For the sake of explanatory convenience, only one of the multiple IR toner images p 2  among the alignment images located at the four corners is illustrated in the schematic diagram of  FIG.  12   . The peripheral area of a recording-sheet image P 0  on the subtracted image D 32  is referred to as a background image P 50 . The background image P 50  is processed so as to remain on the subtracted image D 32 . For example, an infrared absorbing member may be used for the background unit  500 . The controller  30  may detect the boundary between the background image P 50  and the recording-sheet image P 0  based on the scanned color image  1311  or the infrared image D 21 , and may use the detected boundary position as an edge of the recording-sheet image P 0 . In  FIG.  12   , the boundary between the white area and the black area is an edge of the recording-sheet image P 0 . 
     In the subtracted image D 32 , the controller  30  checks the changes in the scanning level of pixels in the main scanning direction and the sub-scanning direction of the recording-sheet image P 0 , and detects a position where the scanning level exceeds a threshold value such as the level of the bare surface of a sheet. The main scanning direction corresponds to the width direction of the recording sheet P, and the sub-scanning direction corresponds to the length direction of the recording sheet P. In the present embodiment described with reference to  FIG.  12   , the controller  30  firstly detects the position where the scanning level changes from black to white in the normal direction of main scanning as an edge in the width direction of the recording sheet P, and then detects the pixels of the IR toner image p 2  where the scanning level changes as the correct detection position of the alignment image. With the method according to the second embodiment of the present disclosure, the K color toner image p 14  is not included in the subtracted image D 32 . Accordingly, the alignment image can be accurately detected. 
     The controller  30  according to the second embodiment of the present disclosure performs detection on the multiple alignment images at the four corners in the main scanning direction and the sub-scanning direction. As a result, the vertical lines and horizontal lines of the cross shape of the respective alignment images are detected. Note that such detection is performed from the edge side. In other words, the cross shape at the top-left corner is detected in the normal direction in the main scanning direction and is detected from above in the sub-scanning direction. Moreover, the cross shape at the top-right corner is detected in the reverse direction in the main scanning direction and is detected from above in the sub-scanning direction. The controller  30  according to the second embodiment of the present disclosure can detect, for example, displacements or bending in the position at which an image is formed, based on the four edges of the recording-sheet image P 0  and the results of detection of the positions of the vertical lines and horizontal lines of the multiple alignment images at the four corners. 
     In the second embodiment of the present disclosure, the processes to be performed when the position sensing apparatus  61  reads an image and the controller  30  detects a plurality of alignment images are described. However, no limitation is indicated thereby, and in some modifications of the above embodiments of the present disclosure, some of or all of the detection processes of a plurality of alignment images that are performed by the controller  30  in the second embodiment of the present disclosure may be performed by the position sensing apparatus  61 . 
     In a similar manner to the first embodiments of the present disclosure, also in the image forming apparatus according to the second embodiment of the present disclosure, the invisible alignment data can be distinguished from the other information based on the result of scanning obtained with the irradiation of visible light and the result of scanning obtained with the irradiation of invisible light. It is not always necessary to perform, for example, arrangement of information that makes u the visible image, reduction in the size of the visible image, change in color. Accordingly, an image for alignment can be detected without depending on an image-forming area such as the visible image. 
     First Modification of Second Embodiment 
     As a first modification of the second embodiment of the present disclosure, a method of detecting a plurality of alignment images adopting a method other than a method using a difference between two images is described below. For example, the controller  30  checks the scanning level of pixels of the color image D 11  scanned with visible light and the infrared image D 21  scanned with invisible light, as illustrated in  FIG.  10 A  and  FIG.  10 B , in each of the main scanning direction and the sub-scanning direction of the recording-sheet image. Regarding an area whose read level is smaller than the scanning level of the bare surface of a sheet in the scanning with visible light, the controller  30  treats the read value of the scanning with invisible light as the level of the bare surface of a sheet. By so doing, an alignment image cart be detected. 
       FIG.  13 A  is a diagram illustrating a method of detecting an alignment image according to the related art.  FIG.  13 B  is a diagram illustrating a method of detecting an alignment image according to the first modification of the second embodiment of the present disclosure. 
     For the sake of explanatory convenience, in  FIG.  13 A  and  FIG.  13 B , only one of the multiple IR toner images p 2  among the alignment images located at the four corners and the K and the K color toner image p 14  are illustrated as the infrared image D 21 . The peripheral area of the recording-sheet image P 0  on the infrared image D 21  is also referred to as the background image P 50 . 
     As illustrated in  FIG.  13 A , the controller  30  according to the related art firstly detects the position where the scanning level changes from black to white in the main scanning direction as an edge in the width direction of the recording sheet P, and then detects the area where the scanning level changes as the alignment image. In the detection method according to the related art described with reference to  FIG.  13 A , the K color toner image p 14  is located ahead of the IR toner image p 2 , which is an alignment image, in the main scanning direction. Accordingly, the K color toner image p 14  is detected as an alignment image. 
     By contrast, in the method according to the first modification of the second embodiment of the present disclosure as illustrated in  FIG.  13 B , regarding an area whose read level is smaller than the scanning level of the bare surface of a sheet in the scanning with visible light, the controller  30  treats the read value of the scanning with invisible light as the level of the bare surface of a sheet after the boundary is detected. Due to such a configuration, the controller  30  according to the first modification of the second embodiment of the present disclosure can detect an area of the IR toner image p 2  where the scanning level changes from the level of the bare surface of a sheet as the alignment image after an edge of an image scanned with invisible light is detected. 
       FIG.  14    is a diagram illustrating the infrared image D 21  obtained as a result of treating the read value of the scanning with invisible light as the level of the bare surface of a sheet, according to the first modification of the second embodiment of the present disclosure. 
     As illustrated in  FIG.  14   , the K color toner image p 14  is excluded from the object to be detected. The C color toner image p 11 , the M color toner image p 12 , and the Y color toner image p 13  are also set as objects not to be detected. Due to this configuration, the multiple IR toner images p 2  can be detected using the above-described method. 
     As described above, the controller  30  according to the first modification of the second embodiment of the present disclosure can also distinguish invisible alignment data from the other information based on the result of scanning obtained with the irradiation of visible light and the result of scanning obtained with the irradiation of invisible light. Due to such a configuration, the image for alignment can be detected without depending on the image-forming area. 
     Second Modification of Second Embodiment 
     Depending on the image data, when the image forming device  50  form the multiple IR toner images p 2 , some of the positions at which the multiple IR toner images p 2  are formed may overlap with the position at which the K color toner image p 14  is formed on the visible image. In order to handle such a situation, cases where the positions at which the multiple IR toner images p 2  are formed can be changed, according to a second modification of the second embodiment of the present disclosure, are described below. 
       FIG.  15    is a diagram illustrating a configuration of the control blocks of the image forming apparatus  2  according to a second modification of the second embodiments of the present disclosure. 
     In  FIG.  15   , the configuration or structure that is described as above with reference to  FIG.  8    is modified. The configuration or structure similar to that of the second embodiment described with reference to  FIG.  8    may be omitted where appropriate, and the configuration or structure that is different from that of the second embodiment described with reference to  FIG.  8    will be described. 
     The controller  30  according to the second modification of the second embodiment of the present disclosure is provided with an S-image determining unit  301 . The S-image determining unit  301  determines whether the image of the K plate of the print data overlaps the image of the S plate at the fixed position. When it is determined that the images overlap with each other, the S-image determining unit  301  changes the position of the image of the S plate to a position that does not overlap. 
       FIG.  16 A  and  FIG.  16 B  are diagrams illustrating a case in which a K plate image of the print data overlaps with an S plate image at a fixed position, according to the second modification of the second embodiment of the present disclosure. 
     As illustrated in  FIG.  16 A , the K color toner image p 14  of the K plate and the IR toner image p 2  of the S plate may overlap with each other. In the present modification of the second embodiment of the present disclosure, the entirety of the cross shape that serves as the alignment image p 2  overlaps with the K color toner image p 14 . However, no limitation is intended thereby, and some of the cross shape that serves as the alignment image p 2  may overlap with the K color toner image p 14 . Although it depends on the alignment method, basically, the alignment is performed using the entirety of the cross shape. For this reason, when at least some of the cross shape overlaps with the K color toner image p 14 , the position of the IR toner image p 2  that serves as an image for alignment is changed to a different position so as not to overlap with the K color toner image p 14 . When some specific portion of the cross shape is allowed to overlap with the K color toner image p 14  and such a specific portion of the cross shape overlaps with the K color toner image p 14 , it is not necessary to change the position of the cross shape. 
     In the case of the present modification of the second embodiment of the present disclosure as illustrated in  FIG.  16 A , the result of scanning is equivalent to each other between the scanning with visible light and the scanning with invisible light, and the cross shape of the IR toner image p 2  is hidden by the K color toner image p 14  as illustrated in  FIG.  16 B . In such cases, the alignment image p 2  cannot be detected from the results of scanning with visible light and the results of scanning with invisible light. In order to handle such a situation, the position of the IR toner image p 2  is changed. 
       FIG.  17    is a flowchart of the processes of changing the position of an image by the controller  30 , according to the second modification of the second embodiment of the present disclosure. 
     Firstly, in a step S 1 , the controller  30  according to the second modification of the second embodiment of the present disclosure obtains image data. Secondly, in a step S 2 , the controller  30  according to the second modification of the second embodiment of the present disclosure determines whether the K color toner image p 14  is formed on any one of the multiple IR toner images p 2  based on the obtained image data. 
     When it is determined that the K color toner image p 14  is not formed on none of the multiple IR toner images p 2  (“NO” in the step S 2 ), the controller  30  according to the second embodiment of the present disclosure terminates the processes of changing the position of the IR toner image p 2 , and instructs the image forming engine  35  to print the image. 
     On the other hand, when it is determined that the K color toner image p 14  is formed on one of the multiple IR toner images p 2  (“YES” in the step S 2 ), in a step S 3 , the controller  30  according to the second modification of the second embodiment of the present disclosure changes the position at which the IR toner image p 2  is to be formed. When the multiple IR toner images p 2  are formed at a plurality of positions, the controller  30  according to the second modification of the second embodiment of the present disclosure determines whether the K color toner image p 14  is formed on each one of the positions at which the multiple IR toner images p 2  are formed, and changes the position of the IR toner image p 2  on which the K color toner image p 14  is formed, on a one-by-one basis. When the image forming engine  35  is instructed to print an image, the controller  30  according to the second modification of the second embodiment of the present disclosure instructs the image forming engine  35  to change the position at which the IR toner image p 2  is to be formed. 
       FIG.  18 A ,  FIG.  18 B ,  FIG.  18 C , and  FIG.  18 D  are diagrams illustrating how the position of one of the multiple IR toner images changes when the K color toner image overlaps with the IR toner image, according to the second modification of the second embodiment of the present disclosure. 
       FIG.  18 A ,  FIG.  18 B ,  FIG.  18 C , and  FIG.  18 D  illustrate how the position changes with reference to the example arrangement described above with reference to  FIG.  16 A .  FIG.  18 A  illustrates a printing when the position of any image is not changed, according to the second modification of the second embodiment of the present disclosure.  FIG.  18 B  illustrates a printing when the position of an image is changed in the sub-scanning direction, according to the second modification of the second embodiment of the present disclosure.  FIG.  18 C  illustrates a printing when the position of an image is changed in the main scanning direction, according to the second modification of the second embodiment of the present disclosure.  FIG.  18 D  illustrates a printing when the position of an image is changed toward the center of the image data, according to the second modification of the second embodiment of the present disclosure. The arrows with dotted lines in these drawings indicate the moving direction of the position of the IR toner image set at the same position as the K color toner image. 
       FIG.  19 A  and  FIG.  19 B  are diagrams each illustrating the image forming area determined by changing the positions of a plurality of IR toner images p 2 , according to the second modification of the present embodiment of the present disclosure. 
     For the purposes of comparing with the embodiments of the present disclosure,  FIG.  19 A  illustrates an image-forming area with respect to an object when a position detection method according to the related art. The image-forming area is indicated by a rectangular area drawn by dotted lines. As illustrated in  FIG.  19 A , the image-forming area according to the related art is limited to the area within the rectangle formed by the four IR toner images p 2  printed at the four corners. The K color toner image p 14  is also arranged inside the image-forming area in the related art. By contrast, in the second modification of the second embodiment of the present disclosure as illustrated in  FIG.  19 B , some of the positions at which the multiple IR toner images p 2  are printed can be changed. Due to this configuration, the image-forming area that includes the areas at which the K color toner images p 14  are printed is substantially not limited. In other words, due to such a configuration, the image for alignment can be detected without depending on the image-forming area. As no dependency is present on the image-forming area according to the second modification of the second embodiment of the present disclosure, the image-forming area can be made wide. 
     Third Modification of Second Embodiment 
     In the second modification of the second embodiment of the present disclosure, as described above, when some of the positions at which the multiple IR toner images are formed overlaps with the position at which the K color toner image is formed on the visible image, the position at which the IR toner image is formed is changed. However, as the color of the K color toner is black, it is also possible to form a pseudo black image using the cyan, magenta, and yellow (CMY) color toner. In view of these circumstances, in the third modification of the second embodiment of the present disclosure, a C color toner image, an M color toner image, and a Y color toner image make up the K color toner image p 14  that is a black image in the visible range. In the third modification of the second embodiment of the present disclosure, when it is determined that the K color toner image p 14  is formed on one of the multiple IR toner images p 2 , the S-image determining unit  301  of the controller  30  does not give instructions to change the position of any image, but gives instructions to perform printing upon changing the K color toner image to the CMY color toner image. As the other configurations or structures are equivalent to the configuration or structure described above with reference to  FIG.  15   , the illustration and description of the control blocks are omitted. 
       FIG.  20    is a flowchart of the changing processes performed by the controller  30 , according to a third modification of the second embodiment of the present disclosure. 
     Firstly, in a step S 11 , the controller  30  according to the third modification of the second embodiment of the present disclosure obtains image data, and in a step S 12 , determines whether any K color toner image is formed on the IR toner image based on the obtained image data. 
     When it is determined that the K color toner image p 14  is not formed on one of the multiple IR toner images p 2  (“NO” in the step S 12 ), the controller  30  according to the third modification of the second embodiment of the present disclosure terminates the changing process, and instructs the image forming engine  35  to print an image based on the image data. 
     On the other hand, when it is determined that the K color toner image p 14  is formed on one of the multiple IR toner images p 2  (“YES” in the step S 12 ), in a step S 13 , the controller  30  according to the third modification of the second embodiment of the present disclosure performs control to form the K color toner image p 14  that is a black image, using cyan, magenta, and yellow (CMY) color toner. In other words, the controller  30  instructs the image forming engine  35  to form the K color toner image p 14 , using C color toner image, M color toner image, and Y color toner image. 
       FIG.  21 A  and  FIG.  21 B  are diagrams illustrating an effect of the positional change of an image when the K color toner image p 14  overlaps with the IR toner image p 2 , according to the second modification of the second embodiment of the present disclosure. 
       FIG.  21 A  illustrates a case in which no image is changed, according to the second modification of the second embodiment of the present disclosure.  FIG.  21 B  illustrates a case in which an image is changed, according to the second modification of the second embodiment of the present disclosure. 
     In  FIG.  21 A , no image is changed. Accordingly, the IR toner image p 2  and the K color toner image p 14  cannot be distinguished from each other based on the result of scanning. By contrast, in  FIG.  21 B , an image is changed. Accordingly, the IR toner image p 2  remains as the K color toner image p 14  is not included in the second result of scanning. As a result, the IR toner image p 2  can be distinguished from the K color toner image p 14 . 
     Other Modifications 
     In the above embodiments of the present disclosure or the modifications of those embodiments of the present disclosure, the image forming apparatus detects, for example, the displacement or bending of the position at which an image is formed in the main scanning direction and the sub-scanning direction, using the cross-shaped marks of the multiple alignment images p 2  at the four corners. However, such a detection method is given by way of example, and no limitation is intended thereby. As long as, for example, the displacement or bending of the position at which an image is formed can be detected, the number of cross-shaped marks may be reduced by changing, for example, the arrangement of those cross-shaped marks. Alternatively, the shape of the marks may be changed, or the scanning method may be modified. 
     In the above embodiments of the present disclosure or the modifications of those embodiments of the present disclosure, the image forming apparatuses each of which is provided with a tandem image forming unit are described. However, the image forming apparatuses are not limited to the ones provided with a tandem system, and may be, for example, image forming apparatuses each of which is provided with a rotary image forming unit. 
     In the second embodiment of the present disclosure, the position sensing apparatus is applied to the image forming apparatus  2  that serves as a printer. However, no limitation is indicated thereby, and the position sensing apparatus according to the above embodiments of the present disclosure and their modifications of those embodiments of the present disclosure may be applied to an image processing apparatus such as a multifunction peripheral (MFP) that has at least two of a photocopying function, a printing function, a scanning function, and a facsimile (FAX) function. 
     In the above description, some preferred embodiments of the present disclosure and the modifications of those embodiments of the present disclosure are described. However, the description of the above embodiments and the modifications of those embodiments is given by way of example, and no limitation is intended thereby. 
     Note that 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 appended claims, the embodiments of the present disclosure may be practiced otherwise than as specifically described herein. For example, elements and/or features of different illustrative embodiments may be combined with each other and/or substituted for each other within the scope of this disclosure and appended claims. 
     Any one of the above-described operations may be performed in various other ways, for example, in an order different from the one described above. 
     Each of the functions of the described embodiments may be implemented by one or more processing circuits or circuitry. Processing circuitry includes a programmed processor, as a processor includes circuitry. A processing circuit also includes devices such as an application specific integrated circuit (ASIC), digital signal processor (DSP), field programmable gate array (FPGA), and conventional circuit components arranged to perform the recited functions.