PATENT ABSTRACT
Example embodiments of the present invention relate to systems methods and computer program products for bend estimation. The system comprises a first and second light absorbers disposed at a substantially same position along an axis of a light guide and enabled to absorb first and second respective amounts of a plurality of wavelengths of a light transmitted along the light guide, a light detector enabled to detect respective intensities of the plurality of wavelengths of the light not absorbed by the first and second light absorbers, and a processor enabled to calculate a bend state of the light guide according to the detected intensities of the plurality of wavelengths of the light.

PATENT DESCRIPTION
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application is a continuation application of PCT Application No. PCT/JP2014/080270 filed Nov. 14, 2014, which is hereby incorporated by reference in its entirety. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to a bend information estimation system, method and computer program product that estimates bend information representing a bending state of an object having flexibility. 
       BACKGROUND 
       [0003]    In general, a device which is mounted in a flexible insertion portion of an insertion device (for example, an endoscope) and detects a bending state of the insertion portion has been known. For example, Japanese Patent Application Publication No. JP-A-2007-143600 discloses an endoscope shape detection probe using an optical fiber. 
       SUMMARY 
       [0004]    Example embodiments of the present invention relate to systems and methods for bend estimation. The system comprises a first and second light absorbers disposed at a substantially same position along an axis of a light guide and enabled to absorb first and second respective amounts of a plurality of wavelengths of a light transmitted along the light guide, a light detector enabled to detect respective intensities of the plurality of wavelengths of the light not absorbed by the first and second light absorbers, and a processor enabled to calculate a bend state of the light guide according to the detected intensities of the plurality of wavelengths of the light. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0005]    Objects, features, and advantages of embodiments disclosed herein may be better understood by referring to the following description in conjunction with the accompanying drawings. The drawings are not meant to limit the scope of the claims included herewith. For clarity, not every element may be labeled in every Figure. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments, principles, and concepts. Thus, features and advantages of the present disclosure will become more apparent from the following detailed description of exemplary embodiments thereof taken in conjunction with the accompanying drawings in which: 
           [0006]      FIG. 1  is a diagram schematically illustrating a configuration of an endoscope system including a bend information estimation device of a first embodiment. 
           [0007]      FIG. 2  is a diagram for describing an amount representing a bending state of a flexible portion. 
           [0008]      FIG. 3  is a block diagram illustrating an example of a configuration of a sensor. 
           [0009]      FIG. 4  is a diagram illustrating an example of a relationship between a wavelength and an intensity of light emitted from a light source. 
           [0010]      FIG. 5  is a diagram illustrating an example of a relationship between a wavelength of light incident to a light detector and detection sensitivity of the light detector. 
           [0011]      FIG. 6  is a sectional view including an optical axis of a light guiding member. 
           [0012]      FIG. 7  is a sectional view of the light guiding member in a radial direction thereof, which is taken along line A-A in  FIG. 6 . 
           [0013]      FIG. 8  is a diagram illustrating an example of a relationship between a wavelength and an absorption rate of light in a first light absorber and a second light absorber. 
           [0014]      FIG. 9A  is a diagram schematically illustrating transmission of light in a state in which a first detection target portion bends inward. 
           [0015]      FIG. 9B  is a diagram schematically illustrating transmission of light in a state in which the first detection target portion is in a straight line state. 
           [0016]      FIG. 9C  is a diagram schematically illustrating transmission of light in a state in which the first detection target portion bends outward. 
           [0017]      FIG. 10  is a diagram illustrating an example of a relationship between a wavelength and a reference light quantity. 
           [0018]      FIG. 11  is a diagram illustrating an example of bend characteristic information acquired with respect to a first wavelength. 
           [0019]      FIG. 12  is a diagram illustrating an example of bend characteristic information acquired with respect to a second wavelength. 
           [0020]      FIG. 13  is a diagram illustrating a state in which the flexible portion having a length of L, which includes a detection target portion group, bends at an angle θ and with curvature κ. 
           [0021]      FIG. 14  is a diagram illustrating an example of a detected light quantity in a bending state in  FIG. 13 . 
           [0022]      FIG. 15  is a diagram illustrating an example of a relationship between a wavelength and a change rate of a light quantity in the detection target portion group. 
           [0023]      FIG. 16  is a flowchart illustrating flow of a process in a control unit. 
           [0024]      FIG. 17  is a flowchart illustrating an example of acquisition of the bend characteristic information. 
           [0025]      FIG. 18  is a flowchart illustrating an example of acquisition of reference light quantity information. 
           [0026]      FIG. 19  is a flowchart illustrating an example of a bend information calculation process. 
           [0027]      FIG. 20  is a block diagram illustrating another example of a configuration of a sensor. 
           [0028]      FIG. 21  is a diagram illustrating another example of a relationship between a wavelength and an absorption rate of light in a first light absorber and a second light absorber. 
           [0029]      FIG. 22  is a block diagram illustrating another example of a configuration of a sensor. 
           [0030]      FIG. 23  is a diagram illustrating an example of a relationship between a wavelength and an emission intensity of the light source at a certain time point. 
           [0031]      FIG. 24  corresponds to  FIG. 23  and is a diagram illustrating a relationship between the wavelength of light incident to the light detector and detection sensitivity of the light detector. 
           [0032]      FIG. 25  is a block diagram illustrating an example of a bend information calculation unit according to a second embodiment. 
           [0033]      FIG. 26  is a diagram illustrating another example of a relationship between a wavelength and an absorption rate of light in a first light absorber and a second light absorber. 
           [0034]      FIG. 27  is a block diagram illustrating an example of a configuration of a sensor according to a third embodiment. 
           [0035]      FIG. 28  is a diagram illustrating another example of a relationship between a wavelength and an absorption rate of light in first, second, third, and fourth light absorbers. 
           [0036]      FIG. 29A  is a diagram illustrating a state in which a region having a length of L 1 , of a flexible portion, which includes a first detection target portion group, bends at an angle θ 1  and with curvature κ 1 . 
           [0037]      FIG. 29B  is a diagram illustrating a state in which a region having a length of L 2 , of a flexible portion, which includes a second detection target portion group, bends at an angle θ 2  and with curvature κ 2 . 
           [0038]      FIG. 30  is a diagram illustrating an example of bend characteristic information acquired with respect to a first wavelength associated with the second detection target portion group. 
           [0039]      FIG. 31  is a diagram illustrating an example of bend characteristic information acquired with respect to a second wavelength associated with the second detection target portion group. 
       
    
    
     DETAILED DESCRIPTION 
       [0040]    As described in Japanese Patent Application Publication No. JP-A-2007-143600, the detection probe includes the optical fiber that integrally bends with an insertion portion of an endoscope. The optical fiber is provided with two light modulating units substantially at the same positions in a longitudinal direction of the optical fiber. The light modulating unit detects curvature in two directions of, for example, an X direction and a Y direction. The light modulating unit modulates an intensity or the like of a wavelength component of light transmitting through the optical fiber. In the probe, the light modulating unit detects the curvature of the optical fiber and further curvature of the insertion portion that integrally bends with the optical fiber, based on the intensity or the like of the wavelength component obtained before and after light passes through the light modulating unit. 
         [0041]    However, the prior art does not disclose a specific method for calculating the curvatures in the two directions (magnitude of the bending) based on the intensity or the like of the wavelength component. In addition, a specific method for calculating a bending orientation of the optical fiber along with the curvature is not disclosed. 
         [0042]    Therefore, example embodiments of the present invention provide a bend information estimation device that is capable of estimating bend information (a bending orientation and a magnitude of bending), an endoscope system including the bend information estimation device, a bend information estimating method, and a program for estimating bend information. 
         [0043]    According to the present invention, it is possible to provide a bend information estimation device that is capable of estimating bend information, an endoscope system including the bend information estimation device, a bend information estimating method, and a program for estimating bend information. 
         [0044]      FIG. 1  is a diagram schematically illustrating a configuration of an endoscope system  1  including a bend information estimation device  10  (hereinafter, referred to as an estimation device  10 ) according to an example embodiment of the present invention. The endoscope system  1  includes an endoscope  810 , an endoscope control unit  820 , the estimation device  10 , a display unit  180 , and an input device  190 . 
         [0045]    The endoscope  810  includes an elongate insertion portion  812  that is inserted into an insertion target body, and a manipulating unit  814  connected to a base end side of the insertion portion  812 . The insertion portion  812  includes a hard front end portion  816 , a bending portion  817  provided on the base end side of the hard front end portion  816 , and a flexible tube portion  818  provided on the base end side of the bending portion  817 . The hard front end portion  816  is provided with an illumination optical system, an observation optical system, an imaging device, or the like, which are not illustrated in figures. The bending portion  817  bends in a desired direction in response to manipulation of the manipulating unit  814 . The flexible tube portion  818  freely bends. The manipulating unit  814  is used to perform various types of manipulation of the endoscope  810  including the bending manipulation described above. 
         [0046]    The endoscope control unit  820  controls various operations of the endoscope  810 . In addition, the endoscope control unit  820  includes an image processing unit  822  for performing processes on an image acquired by the observation optical system and the imaging device described above. 
         [0047]    The estimation device  10  is a device for estimating bend information representing a bending state of the insertion portion  812 , particularly, the bending portion  817  and the flexible tube portion  818  (hereinafter, referred to as a flexible portion  819 , as illustrated in  FIG. 2 ). The estimation device  10  includes a sensor  500  configured to have a sensor driving unit  300  and a sensor unit  400 , and a control unit  100  (described in greater detail below with reference to  FIG. 3 ). 
         [0048]    The display unit  180  may be a common display device (e.g., a liquid crystal display, a CRT display, and an organic EL display). The display unit  180  is connected to the endoscope control unit  820  and displays an image processed in the endoscope control unit  820 . In addition, the display unit  180  is connected to the control unit  100  and displays the bend information or the like obtained by the estimation device  10 . 
         [0049]    The input device  190  may be a common input device (e.g., a keyboard, a pointing device such as a mouse, a tag reader, a button switch, a slider, and a dial). The input device  190  is connected to the control unit  100 . The input device  190  is used to input various instructions such that a user operates the estimation device  10 . The input device  190  may be a storage medium. In this case, information stored in the storage medium is input to the control unit  100 . 
         [0050]      FIG. 2  is a diagram illustrating a bending state of a flexible portion according to an example embodiment of the present invention. As illustrated in  FIG. 2 , the flexible portion  819  has a length L, which is positioned to have a straight line shape from an origin P 0  (0, 0, 0) to a point P 1  (0, 0, L), is illustrated in a solid line according to an example embodiment of the present invention. The flexible portion  819  bends as illustrated in a dashed line in  FIG. 2 , and the point P 1  (0, 0, L) is shifted to a point P′ 1  (x, y, z). Here, the flexible portion  819  is described to bend to have an arc shape, for convenience. According to the example embodiment illustrated in  FIG. 2 , in order to describe a bending state of the flexible portion  819 , two items of information of a bending orientation (or bend orientation) and a magnitude of the bending (or bend magnitude) need to be obtained. The bend orientation and bend magnitude can comprise a bend state. The bending orientation is represented by, for example, an angle θ formed between an x axis and a straight line through the origin P 0  (0, 0, 0) and a point (x, y, 0) obtained by projecting the point P′ 1  (x, y, z) to an xy plane. In addition, the magnitude of the bending is represented by, for example, curvature κ, curvature radius r=κ −1 , a central angle φ=L/r=κL, or the like. As described above, according to example embodiments of the present invention, the bending orientation and the magnitude of the bending required to describe the bending state of the flexible portion  819  are referred to as the bend information. 
         [0051]      FIG. 3  is a block diagram illustrating an example of a configuration of the sensor  500  of the estimation device  10  configured to have a sensor driving unit  300  and a sensor unit  400  according to an example embodiment of the present invention. The sensor driving unit  300  includes a light source  310 , a light detector  320 , a light branching unit  330 , and an antireflective member  340 . The sensor unit  400  includes a light guiding member (also referred to herein as a light guide)  420  provided with a detection target portion group (also referred to herein as a detection target group)  410  including a plurality of detection target portions, and a reflective member  430 . 
         [0052]    The light source  310  may be a commonly known light emitting portion such as a lamp, an LED, or a laser diode. The light source  310  further may have a fluorescent substance for converting a wavelength, and the like. 
         [0053]      FIG. 4  is a diagram illustrating an example of a relationship between a wavelength and an intensity of light emitted from the light source  310 . The light source  310  emits light having an emission wavelength range including a first wavelength λ 1  and a second wavelength λ 2 . The first wavelength λ 1  is a characteristic wavelength of a spectrum that is absorbed by a light absorber (hereinafter, referred to as a first light absorber  424 ) of a first detection target portion  411  that configures the detection target portion group  410 . Here, the characteristic wavelength means a wavelength with which the highest absorption is performed, for example, (refer to  FIG. 8 ). Similarly, the second wavelength λ 2  is a characteristic wavelength of a spectrum that is absorbed by a light absorber (hereinafter, referred to as a second light absorber  425 ) of a second detection target portion  412  that configures the detection target portion group  410 . 
         [0054]    The light detector  320  includes an element such as a spectroscope or a color filter for dispersing light, and a light receiving element such as a photodiode. The light detector  320  detects an intensity of light of a predetermined wavelength range and outputs light quantity information. Here, the light quantity information is information representing a relationship between a specific wavelength in the predetermined wavelength range and a light intensity with the wavelength. 
         [0055]      FIG. 5  is a diagram illustrating an example of a relationship between a wavelength of light incident to the light detector  320  and detection sensitivity of the light detector  320 . The light detector  320  has detection sensitivity within a wavelength range including the first wavelength λ 1  and the second wavelength λ 2  described above. The light detector  320  outputs, to the control unit  100 , the light quantity information representing light intensity detected with the wavelengths λ 1  and λ 2 , for example. 
         [0056]    Note that the light detector is not limited to a light detector having spectral characteristics. The light source and the light detector include an example of a configuration in which a light source and a light detector are combined, thereby detecting a light quantity for each of a plurality of predetermined wavelength range. For example, the light source and the light detector include an example of configuration in which narrow-band light is emitted from the light source at time intervals in order, and light quantities in wavelength ranges are detected by a broad band light detector. 
         [0057]    With reference to  FIG. 3 , the light branching unit  330  is optically connected to the light source  310  and the light detector  320 . The light branching unit  330  includes an optical coupler, a half mirror, or the like. The light branching unit  330  guides the light emitted from the light source  310  to the light guiding member  420  and guides, to the light detector  320 , the light guided by the light guiding member  420 . 
         [0058]    The antireflective member  340  is optically connected to the light branching unit  330 . The antireflective member  340  prevents light, which is not incident to the light guiding member  420  of the light emitted from the light source  310 , from returning to the light detector  320 . 
         [0059]    The light guiding member  420  is, for example, an optical fiber and is flexible. A base end of the light guiding member  420  is connected to the light branching unit  330 . The light guiding member  420  is incorporated in the insertion portion  812  in a longitudinal direction thereof, as schematically illustrated in  FIG. 1 . The light guiding member  420  is provided with the detection target portion group  410  disposed on the flexible portion  819  at a position of the insertion portion  812 , which is considered to be necessary to have the calculated bend information. 
         [0060]    As illustrated in  FIG. 3 , the detection target portion group  410  includes at least the first detection target portion  411  and the second detection target portion  412 , and may further include an m-th detection target portion  41   m . Here, m is an arbitrary number. The detection target portions  411 ,  412 , . . . , and  41   m  are provided substantially at the same position of the light guiding member  420  in the longitudinal direction (optical axis direction) thereof. Hereinafter, the detection target portion group  410  is described to be configured to have the first detection target portion  411  and the second detection target portion  412 . 
         [0061]      FIG. 6  is a sectional view including an optical axis of the light guiding member  420  according to an example embodiment of the present invention.  FIG. 7  is a sectional view of the light guiding member  420  in a radial direction thereof, which is taken along line A-A in  FIG. 6 , according to an example embodiment of the present invention.  FIGS. 6 and 7  will be described in conjunction. 
         [0062]    The light guiding member  420  includes a core  423 , a clad  422  that surrounds the core  423 , and a jacket  421  that surrounds the clad  422 . A part of the jacket  421  and the clad  422  is removed and the core  423  is exposed such that the first detection target portion  411  is formed with the first light absorber  424  provided on the exposed core  423 . The second detection target portion  412  is provided substantially at the same position as the first detection target portion  411  in the longitudinal direction of the light guiding member  420  and at a position, for example, substantially orthogonal to the first detection target portion  411  in a cross section of the light guiding member  420  in a radial direction thereof. The second detection target portion  412  is formed with the second light absorber  425  provided in the same manner as the first detection target portion  411 . Note that, without limiting to the light absorber, it is possible to use an optical member having an effect on a spectrum of the guided light, and the optical member may be, for example, a wavelength converting member (e.g., fluorescent substance). 
         [0063]      FIG. 8  is a diagram illustrating an example of a relationship between a wavelength and an absorption rate of light in the first light absorber  424  and the second light absorber  425 . As illustrated in  FIG. 8 , the light absorbers  424  and  425  provided in different detection target portions  411  and  412  have a light absorption rate different for each wavelength (i.e., light absorption characteristics different from each other). 
         [0064]      FIGS. 9A to 9C  are diagrams schematically illustrating light guided to the vicinity of the first detection target portion  411  of the light guiding member  420 . It should be understood that a relationship exists between the bending states of the detection target portions  411  and  412  and a transmission amount of light guided through the light guiding member  420 . In  FIGS. 9A to 9C , the second detection target portion  412  is not illustrated. As illustrated in  FIG. 9B , in a case where the light guiding member  420  is in a straight line state, a part of light guided through the light guiding member  420  is absorbed into the light absorber  424 . In this respect, in a case where the light guiding member  420  bends such that the light absorber  424  is positioned inward as illustrated in  FIG. 9A , light reaching the light absorber  424  is reduced and, thus, an amount of light absorption by the light absorber  424  decreases. Hence, the transmission amount of light guided through the light guiding member  420  increases. On the other hand, in a case where the light guiding member  420  bends such that the detection target portion group  410  is positioned outward as illustrated in  FIG. 9C , light reaching the light absorber  424  increases, and thus an amount of light absorption by the light absorber  424  increases. Hence, the transmission amount of light guided through the light guiding member  420  decreases. 
         [0065]    As described above, an amount of light guided through the light guiding member  420  is changed depending on the bending state of the first detection target portion  411 . The same is true of the second detection target portion  412 . In the following description, the bending of the light guiding member  420  in a direction in which the transmission amount of light increases is referred to as the bending in a positive direction as illustrated in  FIG. 9A  and the bending of the light guiding member  420  in a direction in which the transmission amount of light decreases is referred to as the bending in a negative direction as illustrated in  FIG. 9C . 
         [0066]    With reference to  FIG. 3  again, the reflective member  430  is provided in an end portion of the light guiding member  420  on a side on which the end portion is not connected to the light branching unit  330  (i.e., a front end). The reflective member  430  reflects the light guided by the light guiding member  420  from the light branching unit  330  such that the light returns in a direction toward the light branching unit  330 . 
         [0067]    Next, the control unit  100  of the estimation device  10  will be described with reference to  FIG. 1  again. The control unit  100  can be configured of an electronic computer such as a personal computer. The control unit  100  includes a calculation unit  101 , an endoscope bend information computing unit  140 , a light detector driving unit  150 , and an output unit  160 . The calculation unit  101  is configured of a device or the like including a CPU, an ASIC, or the like. The calculation unit  101  includes an input unit  130 , a storage unit  120 , and a bend information calculation unit  110 . 
         [0068]    The light quantity information is input to the input unit  130  from the light detector  320  of the sensor driving unit  300 . The input unit  130  transmits the input light quantity information to the bend information calculation unit  110 . In addition, bend characteristic information of the detection target portion group  410 , which will be described below, is input to the input unit  130 . Further, information output from the endoscope control unit  820  is also input to the input unit  130 . The input unit  130  transmits the input information to the bend information calculation unit  110  or the light detector driving unit  150 . 
         [0069]    The storage unit  120  stores various items of information required in calculation performed in the bend information calculation unit  110 . The storage unit  120  can be a memory. The storage unit  120  stores a program including calculation algorithms and a light quantity estimation relationship including the bend characteristic information of the detection target portion group  410 , which will be described below, or the like. 
         [0070]    The bend information calculation unit  110  calculates the bend information of the detection target portion group  410  based on the light quantity information acquired via the input unit  130  and the light quantity estimation relationship stored in the storage unit  120 , which will be described below. The bend information calculation unit  110  includes an estimation value calculation unit  212 . The estimation value calculation unit  212  generates a light quantity estimation value, based on the light quantity estimation relationship stored in the storage unit  120 . The bend information calculation unit  110  calculates the bend information of the detection target portion group  410 , based on the light quantity information acquired via the input unit  130  and the generated light quantity estimation value. The bend information calculation unit  110  transmits the calculated bend information to the endoscope bend information computing unit  140  and the output unit  160 . In addition, the bend information calculation unit  110  outputs, to the light detector driving unit  150 , information related to an operation of the light detector  320 , such as a gain of the light detector  320 , which is required to calculate the bend information. 
         [0071]    The endoscope bend information computing unit  140  includes, for example, a CPU, an ASIC, or the like. The endoscope bend information computing unit  140  calculates bend information of the insertion portion  812  on which the detection target portion group  410  is disposed, based on the bend information of the detection target portion group  410 , which is calculated in the bend information calculation unit  110 . The calculated bend information is transmitted to the output unit  160 . Note that the endoscope bend information computing unit  140  may be incorporated in the bend information calculation unit  110 . 
         [0072]    The light detector driving unit  150  generates a drive signal of the light detector  320 , based on the information acquired from the input unit  130  or the bend information calculation unit  110 . In response to the drive signal, for example, the light detector driving unit  150  switches between on and off of the operation of the light detector  320 , based on an instruction from a user, which is acquired via the input unit  130 , or adjusts the gain of the light detector  320 , based on the information acquired from the bend information calculation unit  110 . In addition, the light detector driving unit  150  may be configured to also control the operation of the light source  310 . The light detector driving unit  150  transmits the generated drive signal to the output unit  160 . 
         [0073]    The output unit  160  outputs, to the display unit  180 , the bend information of the detection target portion group  410 , which is acquired from the bend information calculation unit  110 , or the bend information of the insertion portion  812 , which is acquired from the endoscope bend information computing unit  140 . In addition, the output unit  160  outputs the acquired bend information to the endoscope control unit  820 . In addition, the output unit  160  outputs, to the light detector  320 , the drive signal from the light detector driving unit  150 . 
         [0074]    Operations of the endoscope system  1  and the estimation device  10  are described according to an example embodiment of the present invention. 
         [0075]    A user inserts the insertion portion  812  of the endoscope  810  into the insertion target body. At this time, the insertion portion  812  bends to form a shape of the insertion target body. The endoscope  810  obtains an image signal from the observation optical system and the imaging device provided in the insertion portion  812 . The obtained image signal is transmitted to the image processing unit  822  of the endoscope control unit  820 . The image processing unit  822  generates an image of the inside of the insertion target body, based on the acquired image signal. The image processing unit  822  displays the generated image on the display unit  180 . 
         [0076]    When the user causes the bend information of the insertion portion  812  to be displayed on the display unit  180  or wants to cause the endoscope control unit  820  to perform various operations using the bend information of the insertion portion  812 , the user inputs such instructions into the control unit  100  via the input device  190 . At this time, the estimation device  10  operates. 
         [0077]    When the estimation device  10  operates, the light source  310  of the sensor driving unit  300  emits light in a predetermined emission wavelength range. The light emitted from the light source  310  is guided to the light guiding member  420  of the sensor unit  400  via the light branching unit  330 . The guided light is transmitted into the light guiding member  420  from the base end side to the front end side. At this time, a light quantity in the light guiding member  420  is changed, depending on the bending state of the detection target portion group  410  provided in the light guiding member  420  and, thus, a light quantity to be transmitted is changed for each wavelength. The light is reflected and returns from the reflective member  430  and is transmitted into the light guiding member  420  from the front end side to the base end side. The reflected light reaches the light detector  320  via the light branching unit  330 . The light detector  320  detects the intensity of the reflected light for each wavelength. 
         [0078]    The light detector  320  outputs, to the input unit  130  of the control unit  100 , the light quantity information about the wavelength and the intensity of the detected light. The bend information calculation unit  110  acquires the input light quantity information from the input unit  130 , and the bend information calculation unit  110  calculates the bend information of the detection target portion group  410 . 
         [0079]    The endoscope bend information computing unit  140  acquires the calculated bend information of the detection target portion group  410 . The endoscope bend information computing unit  140  calculates the bend information of the insertion portion  812  based on the acquired bend information. 
         [0080]    The endoscope control unit  820  acquires, via the output unit  160 , the bend information of the detection target portion group  410 , which is calculated in the bend information calculation unit  110 , or the bend information of the insertion portion  812 , which is calculated in the endoscope bend information computing unit  140 . The endoscope control unit  820  controls an operation of the endoscope  810  based on the acquired bend information. In addition, the bend information is displayed on the display unit  180  via the output unit  160 . 
         [0081]    Further, the light detector driving unit  150  acquires the information input to the input unit  130  and the bend information of the detection target portion group  410  which is calculated in the bend information calculation unit  110 . The light detector driving unit  150  transmits the drive signal to the light detector  320  via the output unit  160  based on the acquired information and controls the operation of the light detector  320 . 
         [0082]    As described above, according to the estimation device  10 , the bend information of the detection target portion group  410  is acquired by the calculation unit  101 . Further, the endoscope bend information computing unit  140  calculates the bend information of the insertion portion  812  based on the acquired bend information. In this manner, it is possible for the user to know the bend information of the detection target portion group  410  or the insertion portion  812  during the manipulation of the endoscope  810 . In addition, the endoscope control unit  820  is capable of controlling the operation of the endoscope  810  based on the bend information. 
         [0083]    The calculation performed in the calculation unit  101  in the estimation device  10  of the embodiment is described in detail. 
         [0084]    First, information prepared before use of the estimation device  10  is described. A detected light quantity (detected light quantity information) D λn  with respect to light having a wavelength λn, which is detected by the light detector  320 , is given by the following Expression (1). 
         [0000]        D   λn   =E   λn   ×A   λn   ×B   λn   ×C   λn   Expression (1)
 
         [0085]    Here, E λn  is an emitted light quantity with respect to the light having the wavelength λn which is emitted from the light source  310 , A λn , is an absorption rate of the light having the wavelength λn in the first light absorber  424 , B λn  is an absorption rate of the light having the wavelength λn in the second light absorber  425 , C λn  is an absorption rate of the light having the wavelength λn in a member other than the detection target portion group  410 , which is positioned on a light path through which the light is transmitted, such as the light branching unit  330 , the light guiding member  420 , the reflective member  430 , or the like in the sensor driving unit  300  and in the sensor unit  400 . 
         [0086]    The emitted light quantity E λn  and the absorption rate C λn  do not depend on a bending orientation or a magnitude of the bending of the detection target portion group  410 . Hence, Expression (1) representing the detected light quantity D λn  is rewritten as Expression (2), below. In other words, in a case where the detection target portion group  410  (detection target portions  411  and  412 ) has a predetermined shape as a reference (hereinafter, referred to as a reference bending state), a light quantity with respect to the light having the wavelength λn, which is detected by the light detector  320 , is obtained as a reference light quantity (or a reference light intensity value) I λn . In addition, when the detection target portion group  410  bends with respect to the reference bending state, a ratio of the reference light quantity I λn  and the light quantity with respect to the light having the wavelength λn, which is detected by the light detector  320 , is a change rate α λn  in the detection target portion group  410 . In other words, the change rate α λn  is a change rate of the light quantity at which the first detection target portion  411  and the second detection target portion  412  that configure the detection target portion group  410  absorb the light. Accordingly, the light quantity D λn  is given by the following Expression (2). 
         [0000]        D   λn   =I   λn ×α λn   Expression (2)
 
         [0087]    The absorption rate of the light in the light absorbers  424  and  425  of the detection target portion group  410  changes depending on the bending orientation (e.g., the angle θ described above) and the magnitude of the bending (e.g., the curvature θ) of the detection target portion group  410 . Hence, the change rate α λn  in the detection target portion group  410  is given in the following Expression (3). 
         [0000]      α λn   ≈f   λn (θ, κ)  Expression (3)
 
         [0000]    Here, the function f λn  is the bend characteristic information with respect to the detection target portion group  410 . 
         [0088]    The following Expression (4) is obtained by Expression (2) and Expression (3). In Expression (4), the left side represents the light quantity information in an arbitrary bending state, and the right side represents the light quantity estimation value obtained based on the reference light quantity (reference light quantity information) and the bend characteristic information. 
         [0000]        D   λn (θ, κ)≈ I   λn   ×f   λn (θ, κ)  Expression (4)
 
         [0089]    In the reference bending state for determining the reference light quantity I λn , for example, in a case where the detection target portion group  410  has the straight line shape (i.e., the curvature of the detection target portions  411  and  412  is 0), a case where the curvature radius is ∞ is employed. However, the reference bending state is not limited thereto and may have a shape other than the straight lint shape. Hereinafter, a case where the detection target portion group  410  has the straight line shape as the reference bending state is described. Note that the angle θ described above of the detection target portion group  410  having the straight line shape is 0 for convenience. 
         [0090]      FIG. 10  is a diagram illustrating an example of a relationship between the wavelength and the reference light quantity. When the detection target portion group  410  is in the reference bending state (i.e., θ=0, κ=0), the light quantity D λn (0, 0) is given by the following Expression (5), by definition. 
         [0000]        D   λn (0,0)= I   λn   Expression (5)
 
         [0091]    In other words, the reference light quantity is I λn  and f λn (0, 0)=1, by definition. 
         [0092]    In addition, the function f λn (θ, κ) is given by the following Expression (6) derived from Expression (4). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         f 
                          
                         
                             
                         
                       
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                      
                     
                       ( 
                       
                         θ 
                         , 
                         κ 
                       
                       ) 
                     
                   
                   ≈ 
                   
                     
                       
                         D 
                         
                           λ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         ( 
                         
                           θ 
                           , 
                           κ 
                         
                         ) 
                       
                     
                     
                       I 
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    The function f λn  as the bend characteristic information is acquired by changing the angle θ and the curvature κ in a range in which it is possible to obtain the angle θ and the curvature κ described above of the detection target portion group  410 . 
         [0093]      FIG. 11  is a diagram illustrating an example of bend characteristic information f λ1 (θ, κ 1 ) and bend characteristic information f λ1 (θ, κ 2 ) acquired with respect to the first wavelength λ 1 .  FIG. 12  is a diagram illustrating an example of bend characteristic information f λ2 (θ, κ 1 ) and bend characteristic information f λ2 (θ, κ 2 ) acquired with respect to the second wavelength λ 2 . As described above, an amplitude and a phase vary by the wavelength and, thereby, it is possible to derive the angle θ and the curvature κ.  FIGS. 11 and 12  illustrate bend characteristic information with respect to two curvatures κ 1  and κ 2 , respectively. However, the acquired bend characteristic information is not limited thereto and may be acquired as relationships between the angle θ in the emission wavelength range and the change rate α λn  in the detection target portion group  410  with respect to various curvatures κ. 
         [0094]    The function f λn  as the bend characteristic information can be represented by a periodic function and, for example, can be approximately represented by a sine function of the following Expression (7). 
         [0000]        f   λn (θ, κ)=α λn (κ)·sin └θ+ b   λn (κ)┘+ε λn (κ)  Expression (7)
 
         [0095]    Here, α λn  represents amplitude, b λn  represents a phase, and c λn  is an offset. Since the terms are all the functions of the curvature κ, for example, it is possible to express Expression (7) in a quadratic equation of the curvature κ as the following Expression (8). 
         [0000]        f   λn (θ, κ)=( a   2λn κ 2   +a   1λn    κ+a   0λn )sin [θ+( b   2λn κ 2   b   1λn   κ+b   0λn )]+( c   2λn κ 2   +c   1λn   κ+c   0λn )  Expression (8)
 
         [0096]    Note that the periodic function is not limited to an expression represented by a first-order sine wave and, for example, in a case of using a Fourier series obtained by combining high-order sine waves as the function f λn  accuracy thereof improves. 
         [0097]    In example embodiments of the present invention, the bend characteristic information and the reference light quantity information are acquired in advance, for example, at the time of manufacturing the endoscope system  1  or at the time of assembly of the endoscope system  1 , and are stored in the storage unit  120  in advance. Otherwise, in other example embodiments of the present invention, the bend characteristic information and the reference light quantity information may be acquired whenever the information is used. 
         [0098]    Next, the calculation performed in the calculation unit  101  during the operation of the estimation device  10  will be described in detail. As illustrated in FIG.  13 , the flexible portion  819  having the length L, which includes the detection target portion group  410 , bends at an angle θ and with curvature κ.  FIG. 14  is a diagram illustrating an example of the relationship between the wavelength and the detected light quantity in the bending state. 
         [0099]    By Expression (4), the detected light quantity D λn  detected by the light detector  320  is equal to the product of the reference light quantity information I λ  acquired in advance (which is illustrated in  FIG. 10 ) and the bend characteristic information f 2 (θ, κ) in the detection target portion group  410  (i.e., the change rate). 
         [0100]      FIG. 15  is a diagram illustrating an example of such a change rate (i.e., the change rate f λ (θ, κ)) with respect to the reference light quantity information in an arbitrary bending state. As illustrated in  FIG. 15 , in order to obtain the angle θ and the curvature κ in the detection target portion group  410 , a simultaneous equation represented by the following Expression (9) is solved, based on the detected light quantities D λ1  and D λ2  with the first wavelength λ 1  and the second wavelength λ 2  which are detected by the light detector  320 . 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               D 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 κ 
                               
                               ) 
                             
                           
                           = 
                           
                             
                               I 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             × 
                             
                               
                                 f 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               D 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                              
                             
                               ( 
                               
                                 θ 
                                 , 
                                 κ 
                               
                               ) 
                             
                           
                           = 
                           
                             
                               I 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                             
                             × 
                             
                               
                                 f 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
         [0101]    The reference light quantity information I λ1  and I λ2  and the bend characteristic information f λ1 (θ, κ) and f λ2 (θ, κ) are acquired in advance as described above and are stored in the storage unit  120 . Hence, it is possible to obtain the angle θ and the curvature κ of the detection target portion group  410  (i.e., the bending orientation and the magnitude of the bending thereof) based on the detected light quantities D λ1  and D λ2 . In other words, the light quantity estimation value is calculated based on a light quantity estimation relationship represented in a form of the function described above and, thereby, the bend information of the detection target portion group  410  is obtained. Note that the light quantity estimation relationship is not limited to the relationship represented by the form of the function described above and may be a relationship represented by a table (e.g., a lookup table) in which the relationship between the wavelength and the light quantity is stored. 
         [0102]    In addition, bend information estimating calculation using, as the curvature, a parameter representing the magnitude of the bending of the detection target portion group and the bend characteristic is described. However, it is possible to employ bend information estimating calculation using another parameter such as the curvature radius as the parameter representing the magnitude of the bending and the bend characteristic information corresponding thereto. 
         [0103]      FIG. 16  is a flowchart illustrating a process in the control unit  100  according to an example embodiment of the present invention. In Step S 1 , the control unit  100  determines whether or not the bend characteristic information is stored in the storage unit  120 . In a case of determining that the information is not stored (NO), the process proceeds to Step S 2  and the control unit  100  acquires the bend characteristic information (described below with reference to  FIG. 17 ). 
         [0104]    After the acquisition of the bend characteristic information in Step S 2 , or in a case where it is determined that the bend characteristic information is stored in the storage unit  120  in Step S 1  (YES), the process proceeds to Step S 3 . Note that a case where the determination is YES in Step S 1  means, for example, a case where the acquisition of the bend characteristic information is performed in the factory setting or at the time of assembly of the endoscope system  1 . 
         [0105]    In Step S 3 , the control unit  100  determines whether or not there is a request for reacquiring the reference light quantity information. In a case of determining that there is a request (YES), the process proceeds to Step S 4 . In Step S 4 , the control unit  100  acquires the reference light quantity information through a subroutine (Step S 21  below with reference to  FIG. 17  and Steps S 211  to S 213  described below with reference to  FIG. 18 ) for acquiring the reference light quantity information described above. Note that there is a request for such reacquisition, for example, in a case where connection to another control unit other than the control unit  100  described above is performed, or in a case where the sensor driving unit  300  and the sensor unit  400  are separated from each other and are reconnected to each other. 
         [0106]    The request for reacquisition of the reference light quantity information which is determined in Step S 3  is issued, for example, in a case where the light branching unit  330  of the sensor driving unit  300  and the light guiding member  420  of the sensor unit  400  are separated from each other or are reconnected to each other. The control unit  100  may be configured to determine whether the connection is maintained, that is, the separation and the reconnection are performed in this case. 
         [0107]    After the reference light quantity information I λ  is acquired in Step S 4 , or in a case of determining that there is no request in Step S 3  (NO), the process proceeds to Step S 5  and the calculation unit  101  of the control unit  100  performs the bend information calculation of the detection target portion group  410 . 
         [0108]    After the bend information calculation process in Step S 5  the process proceeds to Step S 6 . In Step S 6 , the control unit  100  determines whether or not calculation of the bend information is performed. In a case of determining that the calculation is performed (YES), the process returns to Step S 1 , and the processes from Step S 1  described above are repeated. In a case of determining that the calculation is not performed (NO) the process ends. 
         [0109]      FIG. 17  is a flowchart illustrating an example of acquisition of the bend characteristic information. In Step S 21 , the control unit  100  acquires the reference light quantity information I λ . In Step S 22 , the control unit  100  acquires the bend characteristic information f λn (θ, κ) of the detection target portion group  410 . For example, the acquired bend characteristic information is the bend characteristic information f λ1 (θ, κ 1 ) and f λ1 (θ, κ 2 ) illustrated in  FIG. 11 , and is the bend characteristic information f λ2 (θ, κ 1 ) and f λ2 (θ, κ 2 ) illustrated in  FIG. 12 . For example, it is possible to acquire the items of the bend characteristic information by manually changing the bending orientation with the curvatures κ 1  and κ 2  with respect to the characteristic wavelengths λ 1  and λ 2 , or mechanically changing by a bend setting mechanism not illustrated. Further, In Step S 23 , the acquired bend characteristic information is stored in the storage unit  120 . The acquisition of bend characteristic information ends. 
         [0110]      FIG. 18  is a flowchart illustrating an example of acquisition of the reference light quantity information. In Step S 211 , the control unit  100  sets that the detection target portion group  410  is in the reference bending state (a straight line shape in the embodiment). Note that, in a case where setting of the detection target portion group  410  in the reference bending state is manually performed, in Step S 211 , the control unit  100  checks whether or not the detection target portion group  410  is in the reference bending state. In Step S 212 , the control unit  100  acquires the light quantity information I λ  in the reference bending state (Expression (5)). In Step S 213 , the acquired reference light quantity information I λ  is stored in the storage unit  120 . The acquisition of the reference light quantity information I λ  is ended, and the process proceeds to Step S 22 . 
         [0111]      FIG. 19  is a flowchart illustrating an example of a bend information calculation process. In Step S 51 , the bend information calculation unit  110  reads, from the storage unit  120 , the reference light quantity information I λ  and the bend characteristic information f λn (θ, κ) of the detection target portion group  410 . In Step S 52 , the bend information calculation unit  110  acquires, via the input unit  130 , the detected light quantity information D λn  in an arbitrary bending state by the light detector  320 . Further, in Step S 53 , the bend information calculation unit  110  obtains the angle θ and the curvature κ in an above-mentioned manner, based on the detected light quantity information D λn , the reference light quantity information I λ , and the bend characteristic information f λn (θ, κ) (Expression (9)). In Step S 54 , the bend information calculation unit  110  transmits the obtained angle θ and the curvature κ to the output unit  160 . The bend information calculation is ended. 
         [0112]    Note that the bend characteristic information does not depend on the characteristics of the light source  310  or the light detector  320  but depends on only the light absorption characteristics of the light absorbers  424  and  425  of the detection target portion group  410 . Hence, components of the sensor driving unit  300  may be separated from one another and, for example, a light source that emits light in a predetermined emission wavelength range or a light detector having detection sensitivity over all of the wavelengths which are required by the control unit  100  may be used. In other words, it is possible to acquire the bend characteristic information by another light source or light detector or it is possible to perform replacement with another sensor driving unit. 
         [0113]    According to example embodiments of the present invention, the light guiding member  420  that configures the sensor unit  400  is provided with the detection target portion group  410  including the plurality of detection target portions formed substantially at the same position in the longitudinal direction of the light guiding member. Thus, in order to estimate the bend information of the detection target portion group  410 , the wavelengths are used and the number of wavelengths is greater than or equal to the number of detection target portions. The light quantity information for each wavelength in the detection target portion group  410  is detected by the light detector  320  of the sensor driving unit  300 . The bend information of the detection target portion group  410  or the insertion portion  812  is estimated based on the detected light quantity information and the light quantity estimation value calculated based on the light quantity estimation relationship including the bend characteristic information stored in advance in the storage unit  120 . As described above, according to the embodiment, it is possible to provide the bend information estimation device that is capable of estimating the bend information. 
         [0114]    In addition, according to example embodiments of the present invention, it is possible to obtain the bend information of the detection target portion group  410  without obtaining the bend information of the individual detection target portions that configure the detection target portion group  410 . 
         [0115]    In addition, according to example embodiments of the present invention, in order to obtain the bend information, the change rate of the light in the detection target portion group  410  is used. Hence, it is possible to perform the bend information calculation without depending on a spectrum of the light source  310  of the sensor driving unit  300  or spectral sensitivity of the light detector  320 . 
         [0116]    In addition, according to example embodiments of the present invention, information about a distance between the light source  310  and the detection target portion group  410  provided in the light guiding member  420  is not required in the bend information calculation. Hence, it is possible to perform the bend information calculation without considering a positional relationship between the light source  310  and the detection target portion group  410 . 
         [0117]    Further, according to example embodiments of the present invention, absorption or loss of the light in the light branching unit  330  of the sensor driving unit  300  and the reflective member  430  of the sensor unit  400  is constant regardless of the magnitude of the bending of the detection target portion group  410 . Hence, even the reference light quantity information is obtained in a state in which the loss is reflected in the calculation. Therefore, it is possible to perform computation without considering specifically the effects of the light branching unit  330  or the reflective member  430 . 
         [0118]      FIG. 20  is a block diagram illustrating an example configuration of the sensor  500 . As illustrated in  FIG. 20 , the sensor unit  400  includes a sensor storage unit  440 . The sensor storage unit  440  stores sensor identification information or the bend characteristic information in advance in factory setting or at the time of assembly of the device. The sensor identification information (i.e., ID information) is information for identifying types of or individual sensor units  400 , and the information is preferably unique. In addition, in acquisition of the bend characteristic information, the bend characteristic information is stored in the sensor storage unit  440  (e.g., Step S 213  in  FIG. 18 ). In this manner, even in a case where the sensor unit  400  is connected to another sensor driving unit other than the sensor driving unit  300 , it is possible to read the sensor identification information or the bend characteristic information from the sensor storage unit  440 . 
         [0119]    In addition, in the case of the connection to another control unit (in a case where the bend characteristic information is not present in the storage unit  120 ), the bend characteristic information is read from the sensor storage unit  440  instead of performing the acquisition of the bend characteristic information (e.g., Step S 22  in  FIG. 17 ). In this manner, even in the case where the sensor driving unit  300  is connected to another control unit the bend characteristic information does not need to be reacquired. 
         [0120]    According to an example embodiment using a plurality of sensor units, before Step S 1  and immediately after the start of the flow illustrated in  FIG. 16 , the control unit  100  may set a step of checking the sensor identification information of the connected sensor units  400 . Note that, in this example embodiment, as prerequisites, the bend characteristic information is associated with the sensor identification information and the bend characteristic information (i.e., bend characteristic information for each of the plurality of sensor units) is stored in the storage unit  120 . 
         [0121]    In the step of checking the sensor identification information, for example, the sensor identification information is input by the input device  190  from the input unit  130 . The sensor identification information may be engraved or attached on the sensor unit  400  or may be stored in a tag. The tag is preferably a non-contact tag such as RFID. Otherwise, the information may be stored in and read from the sensor storage unit  440  as described above or the information stored in another storage medium may be read. In addition, in a case of the sensor identification information that does not satisfy the prerequisites described above and is not stored in the storage unit  120 , the process may be performed along the flow in  FIG. 16 . 
         [0122]    According to an example embodiment of the present invention, because it is possible to extract the bend characteristic information from the sensor identification information it also is possible to extract the bend characteristic information from the sensor identification information even in the case of connection to another sensor unit. Hence, the bend characteristic information does not need to be reacquired. 
         [0123]    Expression (9) may be expressed by log and may be expressed as the following Expression (10). 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             log 
                              
                             
                                 
                             
                              
                             
                               
                                 D 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                           = 
                           
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 I 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                             + 
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 
                                   f 
                                   
                                     λ 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     , 
                                     κ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             log 
                              
                             
                                 
                             
                              
                             
                               
                                 D 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                           = 
                           
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 I 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                             + 
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 
                                   f 
                                   
                                     λ 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     , 
                                     κ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
         [0124]    Log is used and the right side of Expression (9) is expressed by addition. Therefore, it is possible to consider log of the change rate of the detection target portion group  410  as absorbance obtained from the reference light quantity information as a reference. In addition, the bend characteristic information of the detection target portion group  410  is represented by the following Expression (11) using log of Expression (3). 
         [0000]        F   λn (θ, κ)≈log  f   λn (θ, κ)  Expression (11)
 
         [0125]    The following Expression (12) is obtained from Expression (10) and Expression (11). 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             log 
                              
                             
                                 
                             
                              
                             
                               
                                 D 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                           = 
                           
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 I 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                             + 
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 
                                   F 
                                   
                                     λ 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     , 
                                     κ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             log 
                              
                             
                                 
                             
                              
                             
                               
                                 D 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                                
                               
                                 ( 
                                 
                                   θ 
                                   , 
                                   κ 
                                 
                                 ) 
                               
                             
                           
                           = 
                           
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 I 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   2 
                                 
                               
                             
                             + 
                             
                               log 
                                
                               
                                   
                               
                                
                               
                                 
                                   F 
                                   
                                     λ 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     , 
                                     κ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
         [0126]    According to an example embodiment of the present invention, because it is possible to rewrite a product of the reference light quantity information and the bend characteristic information into a sum thereof, it is possible to easily perform computation. 
         [0127]      FIG. 21  is a diagram illustrating an example of a relationship between the wavelength and the absorption rate of light in the first light absorber and the second light absorber. It should be understood that the wavelengths used to calculate the bend information are not limited to the specific wavelengths λ 1  and λ 2  and may be a first wavelength band d λ1  and a second wavelength band d λ2  having bandwidths, respectively, as illustrated in  FIG. 21 . For example, the first detection target portion  411  and the second detection target portion  412  may have the wavelength bands (i.e., characteristic absorption bands) as wavelength ranges having absorption wavelength characteristics different from each other (i.e., the absorption rates of the first light absorber and the second light absorber are different from each other) in a wavelength range in which both of the portions absorb light (i.e., both of the first light absorber and the second light absorber have the absorption rate in the wavelength range). In example embodiments of the present invention, the number of the wavelength bands is greater than or equal to the number of the detection target portions (i.e., two or more). 
         [0128]    According to an example embodiment of the present invention, because the wavelength that is used to calculate the bend information is not one specific wavelength but may have a bandwidth, the light detector  320  does not need to have high wavelength resolution. Hence, it is possible to manufacture the light detector  320  at low costs. In addition, because only a local wavelength is not used, the light detector is unlikely to be affected by noise. In addition, the wavelength band which is used may include a part of another wavelength band. For example, the first wavelength band and the second wavelength band may overlap each other. 
         [0129]      FIG. 22  is a block diagram illustrating an example of a configuration of the sensor driving unit  300  and the sensor unit  400 . The sensor driving unit  300  includes the light source  310  and the light detector  320 . In addition, the sensor unit  400  includes the light guiding member  420  which is provided with the detection target portion group  410 . The light branching unit  330 , the antireflective member  340 , and the reflective member  430  described above are not provided. The light source  310  is optically connected to the base end of the light guiding member  420 . In addition, the light detector  320  is optically connected to the front end of the light guiding member  420 . The light emitted from the light source  310  is guided to the light guiding member  420 . The guided light is transmitted into the light guiding member  420  from the base end side to the front end side, and then reaches the light detector  320 . In this example embodiment in which the light branching unit, the antireflective member, and the reflective member are not provided, it is possible to reduce the loss of the light due to these members. Therefore, it is possible to reduce the light quantity of the light source. 
         [0130]    In certain example embodiments of the present invention, the light detector  320  may be configured to be capable of detecting a plurality of predetermined wavelengths λ 1  and λ 2 , or the light quantities D λ1  and D λ2  of the wavelength bands d λ1  and d λ2 , respectively. For example, wavelength characteristics of emission intensity of the light guided to the light guiding member  420  is caused to change at a time, and a light quantity at the time is detected. 
         [0131]      FIG. 23  is a diagram illustrating an example of the relationship between the wavelength and the emission intensity of the light source at times t 1  and t 2 . In  FIG. 23 , a relationship at the time t 1  is illustrated in a solid line and a relationship at the time t 2  is illustrated in a dashed line. The light source  310  emits light having a peak in the wavelength λ 1  at time t 1  and light having a peak in the wavelength λ 2  at time t 2 , using a filter and the like. 
         [0132]      FIG. 24  corresponds to  FIG. 23  and is a diagram illustrating a relationship between the wavelength of light incident to the light detector and the detection sensitivity of the light detector. The light detector  320  includes a light receiving element (light receiving element that does not have a light dispersing function performed by a filter or the like) that has detection sensitivity with respect to the intensity of the light having peaks in the wavelengths λ 1  and λ 2 . According to this example embodiment of the present invention, the light quantities are detected from the light receiving element synchronized at the times t 1  and t 2  and, thereby, it is possible to obtain the light quantity information (detected light quantities of the wavelength bands). 
         [0133]    A further embodiment of the present invention is described with reference to  FIGS. 25 and 26  and, hereinafter, description of parts common to the previously described embodiments is omitted and only different parts are described. 
         [0134]      FIG. 25  is a block diagram illustrating an example of a bend information calculation unit  110   a  according to an example embodiment of the present invention. The bend information calculation unit  110   a  includes the estimation value calculation unit  212  and an evaluation value calculation unit  214  as an optimized calculation portion. As will be described below, the evaluation value calculation unit  214  performs calculation to optimize the bend information of the detection target portion group  410 . 
         [0135]    As illustrated in the example embodiment of  FIG. 25 , the bend information of the detection target portion group  410  is estimated by using the relationship between the wavelength and the absorption rate of the light in the first light absorber and the second light absorber similar to the embodiments described above, and further using detected light quantity information D λ3  in a third wavelength λ 3 , the reference light quantity information I λ3 , and bend characteristic information f λ3  of the detection target portion group  410 . 
         [0136]      FIG. 26  is a diagram illustrating an example of a relationship between the wavelength and the absorption rate of the light in the first light absorber and the second light absorber according to an example embodiment of the present invention. The third wavelength λ 3  is a wavelength having absorption rate of the light which is different from the first wavelength λ 1  and the second wavelength λ 2 . 
         [0137]    According to the example embodiment of  FIGS. 25 and 26 , a difference Δ λn  between the right side and the left side in Expression (9) is obtained (n=1, 2, and 3). In other words, the following Expression (13) represents a difference between a value of the light quantity information and an estimated light quantity value in an arbitrary bending state. 
         [0000]      Δ λn   =D   λn (θ, κ)− I   λn   ×f   λn (θ, κ)  Expression (13)
 
         [0138]    In the example embodiment of  FIGS. 25 and 26 , in Step S 53  in the flow illustrated in  FIG. 19 , the evaluation value calculation unit  214  optimizes the bend information of the detection target portion group  410  such that the difference between the value of the light quantity information and the estimated bend information is small. For example, an evaluation value J as a sum of squared differences Δ λn  in the wavelengths is obtained, and the bend information of the detection target portion group  410  is determined to have the minimum evaluation value J. The evaluation value J is given by the following Expression (14). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         J 
                         = 
                           
                          
                         
                           ∑ 
                           
                               
                           
                            
                           
                             
                               ( 
                               
                                 Δ 
                                 
                                   λ 
                                   n 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             Δ 
                             
                               λ 
                               1 
                             
                             2 
                           
                           + 
                           
                             Δ 
                             
                               λ 
                               2 
                             
                             2 
                           
                           + 
                           
                             Δ 
                             
                               λ 
                               3 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     14 
                     ) 
                   
                 
               
             
           
         
       
     
         [0139]    In addition, for example, as will be shown in the following Expression (15), in certain example embodiments, a weighting coefficient w n  may be applied and contribution of the evaluation value J for each wavelength or wavelength band may be adjusted. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         J 
                         = 
                           
                          
                         
                           ∑ 
                           
                             
                               
                                 w 
                                 n 
                               
                                
                               
                                 ( 
                                 
                                   Δ 
                                   
                                     λ 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               w 
                               1 
                             
                              
                             
                               Δ 
                               
                                 λ 
                                 1 
                               
                               2 
                             
                           
                           + 
                           
                             
                               w 
                               2 
                             
                              
                             
                               Δ 
                               
                                 λ 
                                 2 
                               
                               2 
                             
                           
                           + 
                           
                             
                               w 
                               3 
                             
                              
                             
                               Δ 
                               
                                 λ 
                                 3 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     15 
                     ) 
                   
                 
               
             
           
         
       
     
         [0140]    In setting of the weighting coefficient w n , for example, contribution of the wavelength or the wavelength band in which the maximum light absorption amount is obtained by the light absorbers of the detection target portion group  410  may be increased. 
         [0141]    According to the certain example embodiments, the evaluation value calculation unit  214  performs the optimized calculation, and thereby the bend information of the detection target portion group  410  is obtained with high accuracy. In addition, it is possible to provide the bend information estimation device that has redundancy and is unlikely to be affected by noise or the like. 
         [0142]    In addition, in some example embodiments, the optimized calculation can include a plurality of optimized calculations which are different in convergence. For example, a first optimized calculation is an overall optimized calculation with high accuracy and a second optimized calculation is a locally optimized calculation with higher convergence than the first optimized calculation. The overall optimized calculation means a method such as particle swarm optimization (PSO), differential evolution (DE), a genetic algorithm (GA), and a simulated annealing method (SA), which can derive an optimal solution without obtaining a local solution. The locally optimized calculation means a local search method such as Newton&#39;s method, a method of steepest descent, or a simplex method, which obtains a local solution. It is possible to configure the bend information estimation device such that a user can select whether to perform any calculation or to perform parallel calculations. As described above, the user can select accuracy and a speed of the calculation. For example, use of the parallel calculations enables to calculate the appropriate optimal solution rapidly. 
         [0143]    A further example embodiment of the present invention is described with reference to  FIGS. 27 to 31 . Hereinafter, description of parts common to the previous embodiments is omitted, and only different parts are described. 
         [0144]      FIG. 27  is a block diagram illustrating an example of a configuration of the sensor  500  configured to have the sensor driving unit  300  and the sensor unit  400 . The light guiding member  420  is provided with a first detection target portion group  410  including the first detection target portion  411  and the second detection target portion  412  and a second detection target portion group  450  including a third detection target portion  451  and a fourth detection target portion  452 . The second detection target portion group  450  is disposed at a different position from the first detection target portion group  410  in the longitudinal direction of the light guiding member  420 . The second detection target portion group  450  is formed in a similar way to the first detection target portion group  410 . The third detection target portion  451  is provided with a third light absorber and the fourth detection target portion  452  is provided with a fourth light absorber. A positional relationship between the third detection target portion  451  and the fourth detection target portion  452  is similar to the positional relationship between the first detection target portion  411  and the second detection target portion  412 . 
         [0145]      FIG. 28  is a diagram illustrating another example of the relationship between the wavelength and the absorption rate of light in first to fourth light absorbers. As illustrated in  FIG. 28 , the light absorbers provided in different detection target portions  411 ,  412 ,  451 , and  452  have a light absorption rate different for each wavelength, that is, have light absorption characteristics different from each other. 
         [0146]    Next, calculations performed in the calculation unit  101  of the estimation device  10  in order to estimate the bend information (angle θ α  and curvature κ α ) in the first detection target portion group  410  and the bend information (angle θ β  and curvature κ β ) in the second detection target portion group  450  are described. A length L 1  of the flexible portion  819  including the first detection target portion group  410  and a length L 2  thereof including the second detection target portion group  450  are considered to bend at angles θ 1  and θ 2  and with curvatures κ 1  and κ 2 , respectively, as illustrated in  FIGS. 29A and 29B . 
         [0147]    Note that, as illustrated in  FIGS. 29A and 29B , the angles θ 1  and θ 2  are represented by a local coordinate system (i.e., an x 1 y 1 z 1  coordinate system and an x 2 y 2 z 2  coordinate system) in the detection target portion groups  410  and  450 , respectively. Hence, the bending orientation is represented by, for example, the angle θ 1  formed between an x 1  axis and a straight line through the origin P 10  (0, 0, 0) and a point (x, y, 0) obtained by projecting a point P 11  (x, y, z) to an xy plane as illustrated in  FIG. 29A  and the angle θ 2  formed between an x 2  axis and a straight line through the origin P 20  (0, 0, 0) and a point (x, y, 0) obtained by projecting a point P′ 21  (x, y, z) to the xy plane as illustrated in  FIG. 29B . In addition, the magnitude of the bending is represented by, for example, the curvature κ 1  and the curvature κ 2 . 
         [0148]    Similar to Expression (2), by using the product of the reference light quantity I λn  and the change rates α λn  and β λn  in the detection target portion groups  410  and  450 , the detected light quantity D λn  detected by the light detector  320  is expressed as follows. 
         [0000]        D   λn   =I   λn ×α λn ×β λn   Expression (16)
 
         [0149]    The change rate α λn  is a ratio of the reference light quantity I λn  and the light quantity with respect to the light having the wavelength λn which is detected by the light detector  320  when only the first detection target portion group  410  bends with respect to the reference bending state (i.e., a change rate of the light quantity which is produced due to the absorption of the light by the first detection target portion  411  and the second detection target portion  412  that comprise the first detection target portion group  410 ). In addition, the change rate β λn  is a ratio of the reference light quantity I λn  and the light quantity with respect to the light having the wavelength λn which is detected by the light detector  320  when only the second detection target portion group  450  bends with respect to the reference bending state (i.e., a change rate of the light quantity which is produced due to the absorption of the light by the third detection target portion  451  and the fourth detection target portion  452  that comprise the second detection target portion group  450 ). 
         [0150]    Similar to the first embodiment, the change rates α λn  and β λn  are given in the following Expression (17) and Expression (18). 
         [0000]      α λn   ≈f   λn (θ α , κ α )  Expression (17)
 
         [0000]      β λn   ≈g   λn (θ β , κ β )  Expression (18)
 
         [0000]    Here, the function f λn  is the bend characteristic information in the first detection target portion group  410  and the function g λn  is the bend characteristic information in the second detection target portion group  450 . 
         [0151]    The following Expression (19) is obtained from Expression (16), Expression (17), and Expression (18). In Expression (19), the left side represents the light quantity information in an arbitrary bending state and the right side represents a light quantity estimation value generated based on a product of the reference light quantity (reference light quantity information) and the bend characteristic information of the first and second detection target portion groups. 
         [0000]        D   λn (θ α , κ α , θ β , κ β )≈ I   λn   ×f   λn (θ α , κ α )× g   λn (θ β , κ β )   Expression (19)
 
         [0152]    In the reference bending state for determining the reference light quantity I λn , for example, a case where both of the detection target portion groups  410  and  450  have the straight line shape (i.e., a case where the curvatures of the detection target portion groups  410  and  450  are 0) the curvature radius is ∞. Note that the angles θ α  and θ β  of the detection target portion groups  410  and  450  are 0, for convenience. When the detection target portion groups  410  and  450  are in the reference bending state, the light quantity D λn (0, 0, 0) is given by the following Expression (20), by definition. 
         [0000]        D   λn (0,0,0,0)= I   λn   Expression (20)
 
         [0000]    In other words, the reference light quantity is I λn , and f λn (0, 0)=g λn (0, 0)=1, by definition. 
         [0153]    In addition, the function f λn (θ α , κ α ) and the function g λn (θ β , κ β ) are given by the following Expression (21) and Expression (22) derived from Expression (19). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                      
                     
                       ( 
                       
                         
                           θ 
                           α 
                         
                         , 
                         
                           κ 
                           α 
                         
                       
                       ) 
                     
                   
                   ≈ 
                   
                     
                       
                         D 
                         
                           λ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         ( 
                         
                           
                             θ 
                             α 
                           
                           , 
                           
                             κ 
                             α 
                           
                           , 
                           0 
                           , 
                           0 
                         
                         ) 
                       
                     
                     
                       I 
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     21 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       g 
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                      
                     
                       ( 
                       
                         
                           θ 
                           β 
                         
                         , 
                         
                           κ 
                           β 
                         
                       
                       ) 
                     
                   
                   ≈ 
                   
                     
                       
                         D 
                         
                           λ 
                            
                           
                               
                           
                            
                           n 
                         
                       
                        
                       
                         ( 
                         
                           0 
                           , 
                           0 
                           , 
                           
                             θ 
                             β 
                           
                           , 
                           
                             κ 
                             β 
                           
                         
                         ) 
                       
                     
                     
                       I 
                       
                         λ 
                          
                         
                             
                         
                          
                         n 
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     22 
                     ) 
                   
                 
               
             
           
         
       
     
         [0154]    The function f λn  and the function g λn  as the bend characteristic information are acquired by changing the angles θ α  and θ β  and the curvatures κ α  and κ β  of the detection target portion groups  410  and  450  in a possible range, respectively. For example, the functions f λ1 (θ α , κ 1 ), f λ1 (θ α , κ 2 ). f λ2 (θ α , κ 1 ) and f λ2 (θ α , κ 2 ) as the bend characteristic information of the first detection target portion group  410  are the same as in  FIGS. 11 and 12 . 
         [0155]      FIG. 30  is a diagram illustrating an example of bend characteristic information g λ1 (θ β , κ 1 ) and bend characteristic information g λ1 (θ β , κ 2 ) acquired with respect to the first wavelength λ 1 .  FIG. 31  is a diagram illustrating an example of bend characteristic information g λ2 (θ β , κ 1 ) and bend characteristic information g λ2 (θ β , κ 2 ) acquired with respect to the second wavelength λ 2 .  FIGS. 30 and 31  will be described in conjunction. 
         [0156]    As described above, an amplitude and a phase vary depending on the wavelength and, thereby, it is possible to derive the angle θ β  and the curvature κ. The wavelengths used in the calculation in example embodiments are wavelengths λ 1 , λ 2 , λ 3 , and λ 4  which are absorbed by the detection target portions  411 ,  412 ,  451 , and  452 . Hence, for example, the bend characteristic information f λ1 (θ α , κ 1 ), f λ1 (θ α , κ 2 ), f λ2 (θ α , κ 1 ), f λ2 (θ α , κ 2 ), f λ3 (θ α , κ 1 ), f λ3 (θ α , κ 2 ), f λ4 (θ α , κ 1 ), and the bend characteristic information g λ1 (θ β , κ 1 ), g λ1 (θ β , κ 2 ), g λ2 (θ β , κ 1 ), g λ2 (θ β , κ 2 ), g λ3 (θ β , κ 1 ), g λ3 (κ β , κ 2 ), g λ4 (θ β , κ 1 ), and g λ4 (θ β , κ 2 ) are acquired. It is possible to acquire the items of the bend characteristic information by manually changing the bending orientation with the curvatures κ 1  and κ 2  with respect to the characteristic wavelengths λ 1 , λ 2 , λ 3 , and λ 4  or mechanically changing by a bend setting mechanism not illustrated. 
         [0157]    In example embodiments, in order to obtain the angles θ α  and θ β  and the curvatures κ α  and κ β  in the first detection target portion group  410  and the second detection target portion group  450 , a simultaneous equation represented by the following Expression (23) is solved based on the detected light quantities D λ1  to D λ4  in the first to fourth wavelengths λ 1  to λ 4  which are detected by the light detector  320 . 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               D 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   θ 
                                   α 
                                 
                                 , 
                                 
                                   κ 
                                   α 
                                 
                                 , 
                                 
                                   θ 
                                   β 
                                 
                                 , 
                                 
                                   κ 
                                   β 
                                 
                               
                               ) 
                             
                           
                           = 
                           
                             
                               I 
                               
                                 λ 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             × 
                             
                               
                                 f 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     θ 
                                     α 
                                   
                                   , 
                                   
                                     κ 
                                     α 
                                   
                                   , 
                                 
                                 ) 
                               
                             
                             × 
                             
                               
                                 g 
                                 
                                   λ 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     θ 
                                     β 
                                   
                                   , 
                                   
                                     κ 
                                     β 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     D 
                                     λ2 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         α 
                                       
                                       , 
                                       
                                         κ 
                                         α 
                                       
                                       , 
                                       
                                         θ 
                                         β 
                                       
                                       , 
                                       
                                         κ 
                                         β 
                                       
                                     
                                     ) 
                                   
                                 
                                 = 
                                 
                                   
                                     I 
                                     
                                       λ 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   × 
                                   
                                     
                                       f 
                                       
                                         λ 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           θ 
                                           α 
                                         
                                         , 
                                         
                                           κ 
                                           α 
                                         
                                         , 
                                       
                                       ) 
                                     
                                   
                                   × 
                                   
                                     
                                       g 
                                       
                                         λ 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                       
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           θ 
                                           β 
                                         
                                         , 
                                         
                                           κ 
                                           β 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           D 
                                           
                                             λ 
                                              
                                             
                                                 
                                             
                                              
                                             3 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               θ 
                                               α 
                                             
                                             , 
                                             
                                               κ 
                                               α 
                                             
                                             , 
                                             
                                               θ 
                                               β 
                                             
                                             , 
                                             
                                               κ 
                                               β 
                                             
                                           
                                           ) 
                                         
                                       
                                       = 
                                       
                                         
                                           I 
                                           
                                             λ 
                                              
                                             
                                                 
                                             
                                              
                                             3 
                                           
                                         
                                         × 
                                         
                                           
                                             f 
                                             
                                               λ 
                                                
                                               
                                                   
                                               
                                                
                                               3 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 α 
                                               
                                               , 
                                               
                                                 κ 
                                                 α 
                                               
                                               , 
                                             
                                             ) 
                                           
                                         
                                         × 
                                         
                                           
                                             g 
                                             
                                               λ 
                                                
                                               
                                                   
                                               
                                                
                                               3 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 β 
                                               
                                               , 
                                               
                                                 κ 
                                                 β 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           D 
                                           
                                             λ 
                                              
                                             
                                                 
                                             
                                              
                                             4 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               θ 
                                               α 
                                             
                                             , 
                                             
                                               κ 
                                               α 
                                             
                                             , 
                                             
                                               θ 
                                               β 
                                             
                                             , 
                                             
                                               κ 
                                               β 
                                             
                                           
                                           ) 
                                         
                                       
                                       = 
                                       
                                         
                                           I 
                                           
                                             λ 
                                              
                                             
                                                 
                                             
                                              
                                             4 
                                           
                                         
                                         × 
                                         
                                           
                                             f 
                                             
                                               λ 
                                                
                                               
                                                   
                                               
                                                
                                               4 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 α 
                                               
                                               , 
                                               
                                                 κ 
                                                 α 
                                               
                                               , 
                                             
                                             ) 
                                           
                                         
                                         × 
                                         
                                           
                                             g 
                                             
                                               λ 
                                                
                                               
                                                   
                                               
                                                
                                               4 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 β 
                                               
                                               , 
                                               
                                                 κ 
                                                 β 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     23 
                     ) 
                   
                 
               
             
           
         
       
     
         [0158]    As described above, it is possible to obtain the angles θ α  and θ β  and the curvatures κ α  and κ β  in the detection target portion groups  410  and  450  (i.e., the bend information) based on the detected light quantities D λ1  to D λ4 . Similarly, it is possible to obtain the bend information of three or more detection target portion groups. 
         [0159]    Throughout this description, an endoscope is described as an example of a device to which the bend information estimation device is applied, and the endoscope system is described; however, one of ordinary skill in the art will appreciate that a target in which the bend information estimation device is incorporated is not limited to an endoscope and may be any target for which bend estimation is desired (e.g., a catheter, a surgical robot, or the like, whether or not it is inserted into an insertion target body). 
         [0160]    As described above, example embodiments of the present invention are described with reference to the accompanying drawings. However, it should be noted that all of these drawings and descriptions are presented only as exemplary embodiments. The present invention is not limited to the embodiments described above, and alternative embodiments may be conceived that may have a structure and method disclosed as herein without departing from the principle of the disclosure as claimed in the present disclosure.