Abstract:
A technique for measuring displacement involves passing parallel laser light from a laser light source through a first diffraction grating to a semi-transparent semi-reflective mirror. A portion of the laser light is reflected as first reversed light, which passes through the first diffraction grating. The remainder of the parallel laser light proceeds to a total reflection mirror and is reflected as second reversed light that passes through the semi-transparent semi-reflective mirror and the first diffraction grating. The amount of refracted light of a predetermined order that is of the first and second reversed light and that results from the first diffraction grating is detected by a first optical sensor, and the amount of displacement is obtained from the interference band or a signal thereof corresponding to the amount of relative motion in the axial direction of the total reflection mirror with respect to the semi-transparent semi-reflective mirror.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of International Application No. PCT/JP2011/057560, filed on Mar. 28, 2011, entitled “Displacement Measurement Method, and Displacement Measuring Device,” which claims priority under 35 U.S.C. §119 to Application No. JP 2010-083537 filed on Mar. 31, 2010, entitled “Method and Apparatus for Measuring Displacement,” the entire contents of which are hereby incorporated by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a method and an apparatus for measuring a displacement, and more particularly to a method and an apparatus for measuring a displacement with an extended measurement range. 
     BACKGROUND 
     Recently, people who travel in automobiles are paying attention to electric power-assisted bicycles for their health and the environment. Among the electric power-assisted bicycles, a bicycle capable of energy regeneration and long distance travel with a single charging came into focus. Generally, a regenerative charging is performed after a braking is applied. However, energy efficiency is low when regenerative charging is performed after the braking is applied. Therefore, it is preferable that the regenerative charging starts once a brake lever is pulled before a mechanical brake is actually applied. In order to achieve this, means capable of detecting the pulling of the brake lever before the mechanical brake is actually applied, i.e., a tension of a brake wire, and capable of measuring a small amount of movement (displacement) proportional to the tension of the brake wire is necessary. 
       FIGS. 16A and 16B  show relationships between an amount of manipulation of a brake lever and a braking force in an electric power-assisted vehicle. For the electric power-assisted bicycle described above, it is necessary to measure the amount of manipulation of the brake lever corresponding to an amount the movement of the brake wire in an idle period shown in  FIG. 16A  when the pulling of the brake lever starts. Next, it is necessary to detect a point (an operation point P 1  of the mechanical braking) where a brake pad starts the mechanical braking of the bicycle by inhibiting the rotation of wheels based on the extension of the brake wire. This is due to the fact that rider(s) may feel as if the bicycle underwent an abrupt braking or the braking force were insufficient when a braking control between the regenerative braking and the mechanical braking is not performed smoothly before and after the braking. 
     In particular, an idle period of a brake in an electric power-assisted bicycle or the like can change by replacing braking wires or by adjusting the tension of the brake wire. Accordingly, as shown in  FIG. 16B , the amount of manipulation of the brake lever required for starting the mechanical braking may easily deviate from the operation point P 1  to another operation point P 2  of the mechanical brake. According to the prior art, only the amount of manipulation of the brake lever is detected, and start of the mechanical braking is determined when the detected amount of manipulation reaches a predetermined amount. Therefore, according to the prior art, since the start of mechanical braking cannot be accurately detected even when the operation point is changed to P 2  as described above, the braking control cannot be performed smoothly between the regenerative braking and the mechanical braking. In order to maximize the efficiency of the regenerative charging, a configuration is necessary wherein the start of mechanical braking is precisely detected by simultaneously or sequentially measuring both the amount of movement and an amount of the extension of the brake wire. 
     Conventionally, an optical interferometer is used to measure a minute displacement such as the amount of the movement or the amount of the extension of the brake wire. A Michelson interferometer  200  shown in  FIG. 17A  includes a laser light source  202 ; a collimating lens  204  configured to convert an incident beam of laser light into a parallel beam; a splitter  206  configured to divide a beam into two beams and direct one beam to a fixed minor  208  and the other beam to a movable mirror  210 ; and an optical sensor  212  configured to receive an interference beam of the two reflected beams. In the Michelson interferometer  200 , a detector detects two optical patterns of bright and dark bands when the movable mirror  210  moves one wavelength with respect to a fixed unit  214  in a direction of beam propagation. As shown in  FIG. 17B , these optical interference fringes are observed as interference patterns  216 . In this case, a displacement not greater than the one wavelength may be detected by detecting a voltage gradient of the interference fringe. In addition, a displacement greater than the one wavelength may be measured by counting the number of the interference fringes (i.e., the interference patterns). As shown in  FIG. 17C , the displacement may be calculated by equation: [displacement]=[the one wavelength]×[the number of interference fringes]×2 because path difference in round trip is twice the displacement of the movable mirror. Here, additional means are necessary to detect the direction of the movement of the brake wire. Techniques using optical interference such as a device and a method of detecting a phase difference described above are disclosed in the following Patent Document 1: Japanese Patent Laid-Open Publication No. 2007-271624. 
     SUMMARY 
     However, the above-described conventional interferometer has following disadvantages:
     (1) A measurement range is determined by the wavelength of light. That is, since the displacement is measured by counting the number of wavelengths of transmitted light, the displacement can be measured only within a range larger than or equal to a wavelength of light. As a result, it is not possible to achieve a resolution below the wavelength of light.   (2) Since the conventional interferometer is very sensitive to the positional precision of optical devices therein, the displacement sometimes cannot be measured due to a deviation in angle (order of 0.01°) or a deviation in position (order of sub-nm). As a result, it is necessary to prevent detection errors caused by environmental variables such as variations in temperature, humidity, external vibration and a lapse of time.   (3) It is difficult to miniaturize the interferometer because a collimating lens, a combination of mirrors, and a splitter are required.   (4) It is impossible to simultaneously or sequentially measure a displacement (e.g., the amount of movement and the amount of the extension of the brake wire in the electric power-assisted bicycle as described above) with different detection sensitivities or in different detection positions.   

     In order to solve the disadvantages, it is an object of the present invention to provide a method and apparatus for measuring displacement unaffected by a precision of an optical device, of a simple configuration, miniaturizable, highly robust to a positional deviation, and with adjustable optical resolution. It is another object of the present invention to provide a method and apparatus for measuring displacement capable of simultaneously or sequentially measuring a displacement with different detection sensitivities or in different detection positions. 
     According to a first aspect of the present invention, there is provided a method for measuring a displacement, the method comprising: generating a first reflected beam and a transmitted beam from an incidence of a parallel beam upon a first diffraction grating and a semi-reflective mirror in sequence, the first diffraction grating and the semi-reflective mirror being disposed along an optical axis, wherein the first reflected beam is generated by a reflection of the parallel beam by the semi-reflective mirror and the transmitted beam is generated by a transmission of the parallel beam by the semi-reflective mirror; generating a second reflected beam by a reflection of the transmitted beam by a total reflection mirror movable along the optical axis; dividing the first reflected beam into a first 0 th  order beam propagating in a direction same as that of the first reflected beam and a first ±n th  order beam having a diffraction angle with respect to the first 0 th  order beam by an incidence of the first reflected beam upon the first diffraction grating; dividing the second reflected beam into a second 0 th  order beam and a second ±n th  order beam having a diffraction angle with respect to the second 0 th  order beam by an incidence of the second reflected beam upon the first diffraction grating; and measuring a first displacement in a direction of the optical axis from a first light intensity obtained by receiving an interference beam of the first ±n th  order beam and the second ±n th  order beam. 
     According to a second aspect of the present invention, there is provided an apparatus for measuring a displacement, the apparatus comprising: a light source configured to generate a parallel beam; a total reflection mirror facing the light source, the total reflection mirror being movable along an optical axis of the parallel beam; a semi-reflective mirror disposed along the optical axis between the light source and the total reflection mirror; a first diffraction grating disposed along the optical axis between the light source and the semi-reflective mirror; and a first sensor configured to measure a light intensity, wherein the semi-reflective mirror generates a first reflected beam and a transmitted beam by reflecting and transmitting the parallel beam, respectively, the total reflection mirror generates a second reflected beam by reflecting the transmitted beam, the first diffraction grating divides the first reflected beam into a first 0 th  order beam propagating in a direction same as that of the first reflected beam and a first ±n th  order beam having a diffraction angle with respect to the first 0 th  order beam and the second reflected beam into a second 0 th  order beam and a second ±n th  order beam having a diffraction angle with respect to the second 0 th  order beam, and the first sensor measures a first light intensity by receiving an interference beam of the first ±n th  order beam and the second ±n th  order beam. 
     The foregoing and other objects, features and advantages of the present invention will be apparent from the detailed description and the accompanying drawings in the following. 
     According to the present invention, it is possible to provide a method and a device for measuring displacement which are unaffected by a precision of a diffraction grating, hardly affected by positional deviation in a plane on which the diffraction grating is placed, of a simple configuration, miniaturizable, and with adjustable optical resolution. In addition, a displacement at different positions can be measured with a single light source in accordance with the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a basic structure of an apparatus for measuring displacement according to a first embodiment of the present invention. 
         FIGS. 2A through 2E  are schematic diagrams of the apparatus for measuring displacement according to the first embodiment, wherein  FIG. 2A  is a schematic diagram of a basic structure of a wire extension detection unit,  FIGS. 2B and 2C  illustrate light paths L 4  and L 5 , respectively, and  FIGS. 2D and 2E  illustrate interferences between the light paths L 4  and L 5 . 
         FIG. 3  is a diagram qualitatively illustrating an operation principle of a displacement measurement by the wire extension detection unit. 
         FIGS. 4A and 4B  are diagrams quantitatively illustrating the operation principle of the displacement measurement by the wire extension detection unit. 
         FIG. 5  is a diagram qualitatively illustrating an operation principle of the displacement measurement by a wire movement detection unit according to the first embodiment. 
         FIG. 6A  is a diagram quantitatively illustrating the operation principle of the displacement measurement by the wire movement detection unit, and  FIGS. 6B through 6D  show images of interference fringes of an interference beam detected by an optical sensor. 
         FIG. 7  is a diagram of an overall configuration of an electric power-assisted bicycle using the apparatus for measuring displacement according to the first embodiment. 
         FIGS. 8A through 8C  are schematic diagrams of a brake mechanism in the electric power-assisted bicycle. 
         FIGS. 9A through 9C  are diagrams illustrating functions of the apparatus for measuring displacement and a braking operation of the electric power-assisted bicycle. 
         FIG. 10  depicts an example of a displacement measuring unit according to the first embodiment. 
         FIG. 11A  is a circuit diagram of a laser light source in the wire extension detection unit of the above example,  FIG. 11B  is a circuit diagram of an optical detection circuit in the wire extension detection unit,  FIG. 11C  is a signal waveform diagram of an output  1  of the optical detection circuit, and  FIG. 11D  is a block diagram schematically illustrating a process sequence of the output  1 . 
         FIG. 12A  illustrates a transition of dark spots detected by an optical sensor during an idle period in the wire movement detection unit of the above example, and  FIG. 12B  illustrates a transition of light intensity measured during a mechanical braking period by the optical sensor in the wire extension detection unit. 
         FIG. 13A  illustrates a relationship between an amount of manipulation of a brake lever and a wire tension, and  FIG. 13B  illustrates a relationship between the amount of manipulation and a braking force. 
         FIGS. 14A and 14B  illustrate an apparatus for measuring displacement according to a second embodiment of the present invention, wherein  FIG. 14A  illustrates a basic structure of the apparatus for measuring displacement, and  FIG. 14B  illustrates a circuit diagram of an optical detection circuit in the apparatus for measuring displacement. 
         FIGS. 15A and 15B  are signal waveform diagrams of outputs A and B of the optical detection circuit, respectively, according to the second embodiment, and  FIG. 15C  is a signal waveform diagram showing a result of an operation between the outputs A and B. 
         FIG. 16A  is a diagram for illustrating a relationship between an amount of manipulation of a brake lever and a braking force in an electric power-assisted vehicle, and  FIG. 16B  is a diagram illustrating a relationship between the amount of manipulation and the braking force when a brake operation point is changed. 
         FIGS. 17A through 17C  illustrate exemplary prior arts. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, the present invention will be described in detail with reference to the following embodiments. 
     First, a basic structure in accordance with a first embodiment of the present invention will be described with reference to  FIGS. 1 ,  6 A through  6 D,  7 , and  8 A through  8 C. In the first embodiment, a displacement measurement according to the present invention is applied to measurements of an amount of an extension and an amount of a movement of a brake wire in an electric power-assisted bicycle.  FIG. 1  is a schematic diagram of the basic structure according to the first embodiment,  FIG. 7  illustrates an overall configuration of the electric power-assisted bicycle, and  FIGS. 8A through 8C  are diagrams schematically illustrating a brake mechanism in the electric power-assisted bicycle. As shown in  FIG. 1 , an apparatus  10  for measuring displacement in accordance with the first embodiment includes a laser light source  12  such as a laser diode; a collimating lens  14  configured to convert laser light  13  emitted by the laser light source  12  into a parallel beam  15 ; first, second and third diffraction gratings  16 ,  18  and  20  disposed in order along an optical axis of the parallel beam  15 , a semi-reflective mirror  22 ; a total reflection mirror  24 ; and optical sensors  26  and  28 . The above elements except the total reflection mirror  24  may be configured as a displacement measuring unit  70  capable of moving as a single body as shown in  FIG. 6 . Further, as shown in  FIGS. 7 and 8A  through  8 C, an electric power-assisted bicycle  50  may include a handle  52 ; a brake mechanism having a brake lever  54 , a brake wire  56  covered by a tube  58 , a brake pad  60  and a rim  62 ; a controller  64 ; a motor  66 ; and a battery  68 . As shown in  FIG. 7 , the displacement measuring unit  70  may be installed, for example, near the brake lever  54  in the electric power-assisted bicycle  50 . 
     As shown in  FIG. 8A , the brake mechanism has a well-known configuration wherein a tension is applied to the brake wire  56  by manipulating the brake lever  54  to push the brake pad  60  against the rim  62 . In an idle period during which the pulling of the brake lever  54  starts, the brake wire  56  moves as shown in  FIG. 8B . In a mechanical braking period during which the brake pad  60  is in contact with the rim  62  in order to apply a mechanical braking, the brake wire  56  extends as shown in  FIG. 8C . in accordance with the first embodiment, a wire extension detection unit including the laser light source  12 , the collimating lens  14 , the second diffraction grating  18 , the third diffraction grating  20 , and the second optical sensor  26  detects an amount of extension of the brake wire  56  shown in  FIG. 8C , and measures an amount of manipulation of the brake corresponding to the amount of extension. 
     Further, a wire movement detection unit including the laser light source  12 , the collimating lens  14 , the first diffraction grating  16 , the semi-reflective mirror  22 , the total reflection mirror  24 , and the first optical sensor  28  detects an amount of movement of the brake wire  56  shown in  FIG. 8B , and measures the amount of manipulation of the brake. In accordance with the first embodiment, the two detection units are installed to enable simultaneous (or sequential) measurement of the amount of extension and the amount of movement of the brake wire using the single light source. Thus, an operation point P 1  or P 2  of the mechanical braking shown in  FIGS. 16A and 16B  can be accurately detected, and an efficiency of regenerative charging can be improved by maximizing a regeneration during the idle period. 
     Among the two detection units, the wire extension detection unit will now be described. The parallel beam  15  passed through the first diffraction grating  16 , the second diffraction grating  18  and the third diffraction grating  20  is divided into a 0 th  order beam (i.e., diffracted beam of 0 th  order) propagating in the same direction as the parallel beam  15  and ±n th  order beams (i.e., diffracted beams of ±n th  order, where n is a natural number) having a diffraction angle with respect to the 0 th  order beam by each diffraction grating. Hereinafter, the 0 th  order beam propagating in the same direction as the parallel beam  15  after passing through the first diffraction grating  16 , the second diffraction grating  18  and the third diffraction grating  20  will be referred to as a straight beam  30 . 
       FIG. 2A  is a schematic diagram of a basic structure of the wire extension detection unit,  FIGS. 2B and 2C  illustrate a light path L 4  and a light path L 5 , respectively, and  FIGS. 2D and 2E  illustrate interferences between the light paths L 4  and L 5 . In the wire extension detection unit, the second diffraction grating  18  divides the straight beam  30  passed through the first diffraction grating  16  into the straight beam  30  and a diffracted beam  32 . The third diffraction grating  20  has a grating pitch P equal to that of the second diffraction grating  18 . The third diffraction grating  20  faces the second diffraction grating  18  and is disposed to be movable with respect to the second diffraction grating  18  along the optical axis of the straight beam  30 . The third diffraction grating  20  divides the straight beam  30  passed through the second diffraction grating  18  into the straight beam  30  and the diffracted beam  34 . A photodiode or the like is used as the optical sensor  26 . More specifically, the diffracted beam  32  is obtained by the following: First, the parallel beam  15  incident upon the first diffraction grating  16  is divided into a first 0 th  order beam propagating in a direction same as that of the parallel beam  15  and a first ±n th  order beam having a diffraction angle with respect to the first 0 th  order beam. Thereafter, the first 0 th  order beam incident upon the second diffraction grating  18  is divided into a second 0 th  order beam propagating in a direction same as that of the first 0 th  order beam and a second ±n th  order beam having a diffraction angle with respect to the second 0 th  order beam. Finally, the second 0 th  order beam incident upon the third diffraction grating  20  is to obtain a third 0 th  order beam propagating in a direction same as that of the second 1 st  order beam as the diffracted beam  32 . In addition, the first 0 th  order beam and the second 0 th  order beam are obtained from the parallel beam  15  incident upon the first diffraction grating  16  and the second diffraction grating  18  in sequence, and the third 1 st  order beam is obtained from the second 0 th  order beam incident upon the third diffraction grating  20  as the diffracted beam  34 . Although 1 st  order beams are used in the first embodiment, the displacement may be measured using a diffracted beam of different order. 
     The second diffraction grating  18  and the third diffraction grating  20  include a plurality of grooves  18 A and a plurality of grooves  20 A having a predetermined pitch (i.e., the grating pitch P in  FIG. 2A ), respectively, and have the same diffraction direction. In addition, the optical sensor  26  detect an intensity of an interference beam  36  generated by an interference between the received diffracted beams  34  and  32  having the same order and the same optical axis. A signal representing an interference pattern such as “bright” and “dark” is generated in response to the detected intensity of the interference beam  36 . An axial displacement between the second diffraction grating  18  and the third diffraction grating  20 , i.e. an axial displacement of the parallel beam  15 , is measured from the signal representing the interference pattern corresponding to an amount of movement (a displacement X shown in  FIG. 2A ) of the third diffraction grating  20  relative to the second diffraction grating  18 . Here, an axial direction refers to a direction normal to a main surfaces of the second diffraction grating  18  and the third diffraction grating  20 . 
       FIG. 2B  illustrates the light path L 4  formed by the second diffraction grating  18 , and  FIG. 2C  illustrates the light path L 5  formed by the third diffraction grating  20 . Here, the light path L 4  shown in  FIG. 2B  is a path of the first 0 th  order beam which propagates straight after passing through the first diffraction grating  16 , the second ±n th  order beam (which is the second 1 st  order beam in the first embodiment) passed through the second diffraction grating  18 , and the third 0 th  order beam whose propagation direction remains unchanged after passing through the third diffraction grating  20  (the first 0 th  order beam→the second 1 st  order beam→the third 0 th  order beam). The light path L 5  shown in  FIG. 2C  is a path of the first 0 th  order beam and the second 0 th  order beam which propagate straight after passing through the first diffraction grating  16  and the second diffraction grating  18 , and the diffracted beam  34  (i.e., the third 1 st  order beam) which propagates in the same direction as the diffracted beam  32  shown in  FIG. 2B  after being diffracted by the third diffraction grating  20  (the first 0 th  order beam→the second 0 th  order beam→the third 1 st  order beam).  FIG. 2D  illustrates an overlapping of the light paths L 4  and L 5 . In accordance with the present invention, the displacement is measured by measuring the intensity of the interference beam  36  before and after the movement of the third diffraction grating  20  relative to the second diffraction grating  18 . Further, as shown in  FIG. 2E , the present invention utilizes characteristics that the light paths L 4  and L 5  share the same light path and the diffracted beams are hardly affected by an inclination of the diffraction gratings. In accordance with the present invention, the interference pattern is not adversely affected even when the third diffraction grating  20  vibrates due to, for example, tilting or external vibration. In addition, since the present invention does not require a splitter which is one of the largest element in the conventional optical system, the apparatus of the present invention can be miniaturized at a lower cost. 
     Next, an operation principle of the wire extension detection unit will be qualitatively described with reference to  FIG. 3 . First, the second diffraction grating  18  and the third diffraction grating  20  are disposed to face each other at a predetermined interval. The laser light source  12  emits a laser light, which passes through the collimating lens  14  to be converted to the parallel beam  15 . Thereafter, the parallel beam  15  passes through the first diffraction grating  16 . The straight beam  30 , which is a portion of the parallel beam  15  propagating straight after passing through the first diffraction grating  16 , is incident upon the second diffraction grating  18 . The straight beam  30  is then divided into a diffracted beam (path  1  and path  3 ) and a straight beam (the straight beam  30  shown in  FIG. 2A ) by the second diffraction grating  18 . Thereafter, the diffracted beam and the straight beam are incident upon the third diffraction grating  20 . The straight beam is then diffracted by the third diffraction grating  20  (path  2 ). The interference beam is generated by the interference between the diffracted beam diffracted by the fixed first diffraction grating  18  and the diffracted beam diffracted by the movable second diffraction grating  20 . Thereafter, the optical sensor  26  detects the intensity of the interference beam. When the third diffraction grating  20  moves in the axial direction from a position P 1  denoted by a solid line to a position P 2  denoted by a dotted line in  FIG. 3 , a position on the optical axis at which the beam propagating along the path  2  is diffracted is changed from the position P 1  to the position P 2 . An interference beam  1  without phase difference is generated by the interference between the diffracted beams of the paths  1  and  2  before the movement of the third diffraction grating  20 . However, an interference beam  2  with a phase difference shown in  FIG. 3  is generated by the interference between the diffracted beams of the paths  2  and  3  after the movement of the third diffraction grating  20 . As a result, the interference pattern corresponding to an amount of the movement, in which bright portion and dark portion are alternately repeated, is generated, and the amount of movement can be detected. 
     Next, an operation principle of the wire extension detection unit will be quantitatively described with reference to  FIGS. 4A and 4B . As shown in  FIG. 4A , a relationship between an incidence angle θ (=0° when a parallel beam is incident upon the third diffraction grating  20 ) of a transmissive diffraction grating (the third diffraction grating  20  in  FIGS. 4A and 4B ) and a diffraction angle φ is given by Equation 1, where λ is a wavelength and P is a diffraction grating pitch:
 
sin φ+sin θ=λ/ P   (1)
 
     As shown in  FIG. 4B , when the third diffraction grating  20  moves by Δd, a variation in length of the path  2  is Δd, and a variation Δd 2  in length of the path  3  is given by Equation 2.
 
Δ d 2=Δ d /cos φ  (2)
 
     If there is no path difference between the variable path  2  and the fixed path  1  before the movement, a path difference A between the path  2  and the path  3  after the movement is given by Equation 3.
 
Δ=Δ d 2 −Δd=Δd (1/cos φ−1)  (3)
 
     A specific example will be described based on the quantitative operation principle hereinafter. Assuming that the incidence angle θ of the transmissive diffraction grating is 0, the wavelength λ is 0.65 μm, and the grating pitch P is 1.6 μm, the diffraction angle φ is arc sin(0.65/1.6)=24.0° from Equation 1. In addition, since the diffraction angle φ is 24° for the diffraction grating, the path difference Δ between the paths  2  and  3  when the amount of movement of the third diffraction grating  20  is Δd can be calculated as Δ=Δd(1/cos(24°)−1)=0.094 Δd by Equation 3, and a single interference fringe is generated by the amount of movement of about 11 wavelengths. 
     In the conventional interference system, the interference fringe always occurs twice when the amount of movement is equal to one wavelength. However, in the first embodiment, the occurrence frequency of the interference pattern is dependent upon the diffraction angle φ, and a detection range may be increased by adjusting the diffraction angle φ. In addition, since the diffraction angle φ is determined by the grating pitch P and the wavelength λ, the occurrence frequency of the interference pattern is dependent upon the grating pitch P. Therefore, by reducing (narrowing) the grating pitches P of the second diffraction grating  18  and the third diffraction grating  20 , the displacement may be measured in order of less than one wavelength. By increasing the detection range in this manner, the displacement in a linear range can be measured, and the displacement widely ranging from sub-μm to about 20 mm can be measured. 
     Table 1 shows an exemplary relationship among the number of gratings (number/mm), the grating pitch P (μm), the diffraction angle φ (degrees), a magnification G and a detection range (μm) in the second diffraction grating  18  and third diffraction grating  20 . Assuming that the path difference between the paths  2  and  3  is Δ when the third diffraction grating  20  moves by Δd, Δ is obtained by Equation 3 above. The magnification G is Δd/Δ. When G is 1, the detection range is equal to one wavelength of light, and the detected intensity has a sinusoidal waveform. When the magnification G is greater than 1, the detection range is [wavelength λ]×[magnification G], and the displacement can be measured within the linear range by expanding the sine wave. 
     
       
         
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 μm Sensor 
                   
                 mm Sensor 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Gratings (numbers/mm) 
                 1350 
                 625 
                 300 
                 20.511 
                 10 
               
               
                 Grating pitch P (μm) 
                 0.74 
                 1.60 
                 3.33 
                 48.75 
                 100.00 
               
               
                 Diffraction angle Φ (°) 
                 61.34224 
                 23.96948 
                 11.24472 
                 0.763898 
                 0.372425 
               
               
                 Magnification G 
                 0.921513 
                 10.59581 
                 51.09213 
                 11250.5 
                 47335.78 
               
               
                 detection range (μm) 
                 0.299492 
                 3.443639 
                 16.60494 
                 3656.412 
                 15384.13 
               
               
                   
               
             
          
         
       
     
     Hereinafter, a wire movement detection unit according to the first embodiment will be described with reference to  FIGS. 5 and 6A  through  6 D. First, the configuration and the qualitative operation principle of the wire movement detection unit will be described with reference to  FIG. 5 . The wire movement detection unit includes the laser light source  12 , the collimating lens  14 , the first diffraction grating  16 , the semi-reflective mirror  22 , the total reflection mirror  24  and the first optical sensor  28 . The first diffraction grating  16  is disposed in the optical axis of the parallel beam  15 , and divides an incident beam into a straight 0 th  order beam (a beam of 0 th  order) and ±n th  order beams (diffracted beams of ±n th  order) having diffraction angles with respect to the 0 th  order beam. The semi-reflective mirror  22 , which is disposed between the second diffraction grating  18  and the third diffraction grating  20  in the optical axis of the straight beam  30 , is installed to face the first diffraction grating  16 . The semi-reflective mirror  22  reflects a portion of the straight beam (light path L 1 ) passed through the first diffraction grating  16  so that the straight beam is divided into a first beam (referred to as a first reflected beam Lrev 1 ) traveling along a light path L 2  to return to the first diffraction grating  16  and a second beam propagating straight along a light path L 3 . 
     The total reflection mirror  24  is disposed to be movable relative to the semi-reflective mirror  22  along the optical axis. The total reflection mirror  24  reflects the straight beam  30  (in the light path L 3 ) passed through the semi-reflective mirror  22  to generate a second reflected beam Lrev 2 . The second reflected beam Lrev 2  passes through the semi-reflective mirror  22 , and then returns to the first diffraction grating  16 . In addition, in the first embodiment, the second diffraction grating  18  and the third diffraction grating  20  are disposed between the first diffraction grating  16  and the semi-reflective mirror  22 . Thus, light propagating along the light path L 1  shown in  FIG. 5  includes a first 0 th  order beam passed through the first diffraction grating  16 , a second 0 th  order beam passed through the second diffraction grating  18  and a third 0 th  order beam passed through the third diffraction grating  20 . Similarly, the first reflected beam Lrev 1  (in the light path L 2 ) and the second reflected beam Lrev 2  include a first 0 th  order beam passed through the third diffraction grating  20  and a second 0 th  order beam passed through the second diffraction grating  18 . The first reflected beam Lrev 1  and the second reflected beam Lrev 2  are diffracted by the first diffraction grating  16 , and the optical sensor  28  receives diffracted beams of the first reflected beam Lrev 1  and the second reflected beam Lrev 2  to detect the intensity of the diffracted beams. A signal representing an interference pattern of the interference beam such as “bright” and “dark” is generated in response to the detected intensity by reception of the interference beam. An axial displacement of the total reflection mirror  24  (displacement Y shown in  FIG. 5A ) with respect to the semi-reflective mirror  22  is measured from the signal representing the interference pattern corresponding to an amount of movement. A photodiode may be used as the optical sensor  28 . Although the wire movement detection unit according to the first embodiment is configured in a manner that the optical sensor  28  receives a 1 st  order beam diffracted by the first diffraction grating  16 , a diffracted beam of a predetermined order other than 1 may also be used to detect the displacement Y similar to the wire extension detection unit. 
     Hereinafter, the operation principle of the wire movement detection unit will be quantitatively described with reference to  FIGS. 6A through 6D .  FIG. 6A  illustrates an operation of the wire movement detection unit, and  FIGS. 6B through 6D  show images of interference patterns detected by the optical sensor  28 . Specifically,  FIG. 6A  illustrates an example where all of the elements, except for the total reflection mirror  24 , of the apparatus  10  for measuring displacement in accordance with the first embodiment are made into a single body as the displacement measuring unit  70  movable relative to the total reflection minor  24 . As shown in  FIG. 6A , when the displacement of the total reflection minor  24  relative to the semi-reflective minor  22  (or the displacement of the displacement measuring unit  70  relative to the total reflection minor  24 ) is Y, a path difference between the first reflected beam Lrev 1  and the second reflected beam Lrev 2  is  2 Y. If an optical brightness detected by the optical sensor  28  before the movement is “bright” (the inside of a frame F 1  in  FIG. 6B ), and an oscillation wavelength of the laser light source  12  is λ, the brightness detected by the optical sensor  28  changes from “bright” to “dark” (the inside of a frame F 3  in  FIG. 6D ) when Y=λ/4×(2n+1), where n is an integer. When 0&lt;Y&lt;λ/4×(2n+1), which corresponds to a transient state from “bright” to “dark”, the brightness detected by the optical sensor  28  is in intermediate level (the inside of a frame F 2  in  FIG. 6C ). Further, when the light intensity throughout the whole range shown in  FIGS. 6B through 6D  is detected, a detection sensitivity deteriorates because the light intensity changes only in a small amount in response to a change in the interference pattern. In order to prevent this, the light intensity is measured only within a part of the range indicated by the frames F 1  through F 3  in  FIGS. 6B through 6D , respectively, thereby achieving a high detection sensitivity in accordance with first embodiment. 
     Next, a specific example of the first embodiment will be described with reference to  FIGS. 9A to 13B .  FIGS. 9A through 9C  illustrate braking operations of the electric power-assisted bicycle and functions of the apparatus for measuring displacement, and  FIG. 10  illustrates a specific example of the displacement measuring unit according to the first embodiment.  FIG. 11A  is a circuit diagram of a laser light source of the specific example,  FIG. 11B  is a circuit diagram of an optical detection circuit of the wire extension detection unit,  FIG. 11C  is a signal waveform diagram of an output  1  of the optical detection circuit, and  FIG. 11D  is a schematic block diagram showing the processing sequence of the output  1 .  FIG. 12A  illustrates a transition of dark spots detected by the optical sensor  28  in the wire movement detection unit during an idle period in accordance with the specific example, and 
       FIG. 12B  illustrates a transition of light intensity measured by the optical sensor  26  in the wire extension detection unit during a mechanical braking period.  FIG. 13A  illustrates a relationship between an amount of manipulation of the brake lever and the wire tension, and  FIG. 13B  illustrates a relationship between the amount of manipulation and the braking force. In addition, the electric power-assisted bicycle  50  and the brake mechanism therein are constituted as described above. 
     The displacement measuring unit  70 , which is movable with the brake wire  56  by means of a guide shaft (not shown) for example, is installed near the brake lever  54  in a housing  11  fixed to the brake handle (bicycle handle)  52 . In addition, the total reflection mirror  24  is fixed on a surface of a side  11 B of the housing  11 . The brake wire  56  penetrates from a side  11 A of the housing  11  to the side  11 B. As shown in  FIG. 10 , the displacement measuring unit  70  is constituted by the laser light source  12 , the collimating lens  14 , the first through third diffraction gratings  16 ,  18  and  20 , the semi-reflective mirror  22  and the optical sensors  26  and  28  accommodated in a transparent resin molded body  72 . A through-hole  74  extending from a side  72 A to a side  72 B for passing through the brake wire  56  is disposed in an upper portion of the transparent resin molded body  72 . The brake wire  56  is fixed to the transparent resin molded body  72  at two points by means of screws  76 A and  76 B. 
     Furthermore, the laser light source  12  is inserted in a circular recessed portion (not shown) formed at the side  72 A, and is connected to a laser driver circuit  78  installed outside of the transparent resin molded body  72 . In addition, the collimating lens  14  is disposed in a space  80 A in the transparent resin molded body  72 , and an outer edge of the collimating lens  14  is fixed by an adhesive for example. The space  80 A may be formed by cutting. Further, the first diffraction grating  16  is disposed in a space  80 B, and the second diffraction grating  18  and third diffraction grating  20  are disposed in a space  80 C. Rear surfaces of the first through third diffraction gratings  16 ,  18 , and  20  are fixed by a transparent adhesive for example. Furthermore, the semi-reflective mirror  22  is disposed in a space  80 D, the optical sensor  26  is disposed in a space  80 E, and the optical sensor  28  is disposed in a space  80 F. 
     The transparent resin molded body  72  further has a spaces (not shown) serving as a light path, a slit  86 A located above the second diffraction grating  18  and a slit  86 B located above the third diffraction grating  20 . The slit  86 A extends from the space  80 C. The slit  86 A and the slit  86 B provide elasticity for the transparent resin molded body  72  such that the transparent resin molded body  72  can expand and contract (denoted by an arrow F 10  in  FIG. 10 ) along with the brake wire  56  in the axial direction near a boundary between the second diffraction grating  18  and the third diffraction grating  20 . In the first embodiment, the third diffraction grating  20  is movable horizontally relative to the second diffraction grating  18  by the slit  86 A and the slit  86 B. Thus, the amount of movement can be measured precisely. In addition, the transparent resin molded body  72  is not bendable in a direction of thickness. The optical sensor  26  and the optical sensor  28  are connected to an I/V conversion circuit  82  and an I/V conversion circuit  84 , respectively, installed outside of the transparent resin molded body  72 . 
     A transparent resin such as acryl and polycarbonate having a dimension of 15 mm (W) by 5 mm (H) may be used as the transparent resin molded body  72 . Further, a laser diode (LD) having a small emergence angle, a wavelength of 650 nm and an output of 5 mW may be used as the laser light source  12 . The optical axis may be arranged in a direction parallel to the grooves  18 A and  20 A in the diffraction grating  18  and the diffraction grating  20 . A collimating lens having a numerical aperture (NA) of 0.65, an effective diameter of 4 mm and a thickness of 1.5 mm may be used as the collimating lens  14 . A diffraction grating having a grating pitch of 0.72 nm and a grating groove depth of 216 nm may be used as the first diffraction grating  16 . In addition, a diffraction grating having a grating pitch P of 1.6 nm, a groove depth of 150 nm, and a groove width of 0.5 nm may be used as the second diffraction grating  18  and the third diffraction grating  20 . 
     Preferably, the diffraction angle of the second diffraction grating  18  is same as that of the third diffraction grating  20 , and a distance between the diffraction grating  18  and the diffraction grating  20  is within a coherence length (about 1 mm) of the laser light source  12 . This is because an interference characteristics deteriorates and a larger diameter of an incident beam is required when the distance between the diffraction grating  18  and the diffraction grating  20  increases. In addition, a mirror having 50% transmittance and 50% reflectivity is preferable as the semi-reflective mirror  22 , and a mirror having 100% reflectivity is preferable as the total reflection mirror  24 . An optical sensor having a size suitable for receiving at least a portion of the interference beam  36  is preferable as the optical sensor  26  serving as a light receiving device, and an optical sensor having a size suitable for receiving at least a portion of the interference beam of the first reflected beam Lrev 1  and the second reflected beam Lrev 2  are preferable as the optical sensor  28 . 
     To detect the extension of the brake wire  56 , the displacement measuring unit  70  is configured as in the following. The transparent resin molded body  72  can be divided into two parts by a boundary line (denoted by a dotted line in  FIG. 10 ) between the second diffraction grating  18  and the third diffraction grating  20 . The two divided parts are fixed to the brake wire  56  by the screws  76 A and  76 B, respectively, and are elastically connected to each other about the slit  86 A and the slit  86 B. As shown in  FIG. 9C , when the brake wire  56  is extended, an interval I varies in response to the extension of the brake wire  56  with the two diffraction gratings  18  and  20  remaining parallel to each other. Thus, the amount of extension (the displacement X) can be detected. Further, as shown in  FIG. 9B , the displacement measuring unit  70  moves along with the brake wire  56 , and a change occurs in the distance between the total reflection mirror  24  and the semi-reflective mirror  22  when compared to a state before the start of the manipulation of the brake lever shown in  FIG. 9A . Thus, the amount of movement (the displacement Y) of the brake wire  56  can be detected. 
       FIG. 11A  illustrates a circuit configuration of the laser light source  12 . In the present example, a laser diode LD is used in the laser light source  12 . The laser diode LD is connected to a power supply via a current limiting resistor R 1 . In addition,  FIG. 11B  illustrates the optical detection circuit in the wire extension detection unit according to the example. In the example, a photodiode PD is used in the optical sensor  26 . The photodiode PD generates a current according to the intensity of the received interference beam. The generated current is inputted to an inverting input terminal of an operational amplifier OP to be converted into a voltage, and the voltage is outputted as the output  1 . That is, the operational amplifier OP is equivalent to the I/V converter circuit  82 . In addition, two resistors R 2  and R 3  are installed in the circuit shown in  FIG. 11B . The resistor R 2  sets an operation point (an output voltage when there is no incident beam upon the photodiode PD) of the output of the operational amplifier OP. The resistor R 3  whose terminals are both connected to the operational amplifier OP sets a gain of the output voltage in response to the intensity of the incident beam of the optical sensor  26  (the photodiode PD). If the light intensity remains constant, the output voltage increases as the resistance of the resistor R 3  increases. 
       FIG. 11C  illustrates a waveform of the output  1  produced by the operational amplifier OP. In  FIG. 11C , the abscissa represents the displacement X, and the ordinate represents a detected voltage. As shown in  FIG. 11C , the displacement X may be obtained from an amplitude of the output  1  having a sine wave shape. Specifically, as shown in  FIG. 11D , the output  1  is amplified by an amplifier circuit  90  and then binarized by a slicer  92 . Further, clocks are counted by a clock counter  94 . Thereafter, an arithmetic unit  96  calculates [the count]×[the wavelength λ] by an arithmetic firmware to obtain the displacement X. An entire range of the amplitude of the sine wave shown in  FIG. 11C  can be used to obtain the displacement X. However, in order to prepare against a deviation in a detection range caused by a calibration error of the optical sensor  26 , it is preferable to have about 20% margin and use a detection range of about ±80% amplitude. The optical detection circuit, the output waveform and the operation process of the optical sensor  28  in the wire movement detection unit are same as those of the optical sensor  26 . 
     In the displacement measuring unit  70  described above, when the pulling of the brake lever  54  starts while in the states shown in  FIG. 8A  and  FIG. 9A , the brake wire  56  moves as shown in  FIG. 8B . At the same time, the displacement measuring unit  70  moves together with the brake wire  56  as shown in  FIG. 9B , resulting in the displacement Y. By measuring the amount of movement of the brake wire  56  based on the displacement Y which is the amount of movement of the total reflection mirror  24  relative to the semi-reflective mirror  22 , the amount of manipulation of the brake lever  54  corresponding to the amount of movement can be measured in order of millimeters. Based on the change in the interval I between the second diffraction grating  18  and third diffraction grating  20  shown in  FIG. 9C , the displacement measuring unit  70  measures the extension (the displacement X) of the brake wire  56  caused by the manipulation of the brake lever  54  shown in  FIG. 8C  in order of micrometers. The displacement measuring unit  70  detects a transition from the idle period to the mechanical braking period of the electric power-assisted bicycle  50 . Further, the controller  64  in the electric power-assisted bicycle  50  determines an optimum regenerative braking force based on the output of the displacement measuring unit  70 , and controls the motor  66  to perform an optimum regenerative braking control. The motor  66  generates an electric power for charging the battery  68 . In addition, the controller  64  detects a performance and conditions of the battery  68 . 
     The electric power-assisted bicycle  50  including the apparatus  10  for measuring displacement can detect a minute deformation of the brake wire  56  caused by a tension. Therefore, the electric power-assisted bicycle  50  can charge the battery  68  by regenerative braking using the motor  66  as a generator during the idle period of the conventional brake shown in  FIG. 13A . Further, as shown in  FIG. 13B , an efficiency may be enhanced since the regenerative braking is performed in parallel during the mechanical braking period (during which the brake pad is in contact with wheels). According to the first embodiment, even when the operation point of the mechanical braking changes, for example, from the operation point P 1  to the operation point P 2  in  FIG. 16B  as a result of the brake adjustment, the changed operation point can be accurately detected. Thus, it is possible to maintain a high regeneration efficiency. 
     The transition from the idle period to the mechanical braking period is detected as below. During the idle period, only the interference pattern detected by the optical sensor  28  in the wire movement detection unit changes while the interference pattern detected by the optical sensor  26  in the wire extension detection unit remains unchanged.  FIG. 12A  shows a transition of the number of dark spots detected by the optical sensor  28  during the idle period. In  FIG. 12A , the abscissa represents the amount of movement (the displacement Y (nm)) of the displacement measuring unit  70 , and the ordinate represents the number of the dark spots. As shown in  FIG. 12A , the amount of movement (the displacement Y) can be detected in order of micrometers or millimeters by counting the dark spots detected by the optical sensor  28 . During the mechanical braking period, the interference pattern detected by the optical sensor  26  changes. In  FIG. 12B , the abscissa represents the amount of movement (the displacement X) of the wire extension detection unit, and the ordinate represents a light intensity.  FIG. 12B  illustrates a variation in the light intensity measured by the optical sensor  26  during the mechanical braking period. A start of mechanical braking can be detected from the variation in the light intensity shown in  FIG. 12B  based on the quantitative principle described above. 
     According to the first embodiment, the following effects can be achieved:
     (1) The first diffraction grating  16 , the semi-reflective mirror  22  and the total reflection mirror  24  are disposed in order along the optical axis of a parallel straight beam emitted from the laser light source  12 . The parallel straight beam incident upon the semi-reflective mirror  22  through the first diffraction grating  16  is divided into the straight beam  30  headed toward the total reflection mirror  24  and the first reflected beam Lrev 1  returning to the first diffraction grating  16 . The straight beam  30  is reflected by the total reflection mirror  24  as the second reflected beam Lrev 2  returning to the first diffraction grating  16  through the semi-reflective mirror  22 . The first reflected beam Lrev 1  and the second reflected beam Lrev 2  are then diffracted by the first diffraction grating  16  and the light intensity of the diffracted beam of a predetermined order is measured by the optical sensor  28 . In such manner, the amount of movement (the displacement) of the brake wire  56  can be detected based on the change in the relative position of the total reflection mirror  24  with respect to the semi-reflective mirror  22 .   (2) Since the displacement is detected by a light path sharing scheme, an influence of tilt can be suppressed. Thus, a detection error caused by an external force (vibration) can be prevented.   (3) Since a splitter is not required, the number of components can be reduced. Therefore, miniaturization and low-cost fabrication is facilitated. In addition, owing to a simple configuration, the device is highly robust to positional deviation.   (4) The measurement range can be expanded to be greater than one wavelength. Thus, a displacement ranging from less than one wavelength to greater than one wavelength can be continuously measured and an optical resolution can be adjusted by the pitch of the diffraction grating.   (5) The second diffraction grating  18  and the third diffraction grating  20  having the same grating pitch P, which are movable relative to each other along the optical axis, are disposed between the first diffraction grating  16  and the semi-reflective mirror  22 . Among the beams diffracted by the second diffraction grating  18  and the third diffraction grating  20 , the beam diffracted by the second diffraction grating  18  having a predetermined order is received by the optical sensor  26  by which the light intensity is measured. In addition, based on the signal representing the interference pattern, the displacement corresponding to the amount of axial movement (the displacement X) of the third diffraction grating  20  relative to the second diffraction grating  18  is detected so as to measure the amount of extension of the brake wire  56 . Thus, the displacement may be simultaneously or sequentially measured at different positions in the optical axis using a single light source. In the first embodiment, the starting point of mechanical braking can be accurately detected based on the two displacements measured as above. Thus, the efficiency of regenerative charging is enhanced.   

     Hereinafter, a second embodiment of the present invention will be described with reference to  FIGS. 14A through 15C  wherein like reference numerals indicate like elements of the first embodiment. The second embodiment is a modified example of the wire extension detection unit of the first embodiment.  FIG. 14A  illustrates a basic structure of a wire extension detection unit according to the second embodiment of the present invention, and  FIG. 14B  is a circuit diagram of an optical detection circuit according to the second embodiment.  FIGS. 15A and 15B  are signal waveform diagrams depicting outputs A and B produced by the optical detection circuit, and  FIG. 15C  is a signal waveform diagram depicting a signal waveform obtained from an arithmetic operation between the outputs A and B. In accordance with the second embodiment, a third diffraction grating includes a stepped portion, and one of the two outputs of a dual optical sensor is divided by the other output of the two outputs of the dual optical sensor so that the detection position remains unchanged even when the light intensity of the laser light source changes and that the detection characteristic of the light intensity is linear rather than a sine wave. 
     As shown in  FIG. 14A , the apparatus  10  for measuring displacement has a configuration same as that of the first embodiment except that a phase plate  104  is disposed on a third diffraction grating  102  to form the stepped portion and that a dual optical sensor  106  is used instead of the single optical sensor  26  of the first embodiment. The phase plate  104  has a thickness d of about 3 μm, and is formed by cutting or molding the stepped portion with a material same as that of the third diffraction grating  102 . The straight parallel beam which emitted from the laser light source  12  and then collimated by the collimating lens  14  is incident upon the fixed second diffraction grating  18  through the first diffraction grating  16 . The beam incident upon the second diffraction grating  18  is divided into a diffracted beam and a straight beam, and the straight beam is then incident upon the movable third diffraction grating  102 . A portion of the straight beam directly incident upon onto the third diffraction grating  102  without passing through the phase plate  104  is diffracted at a surface of the third diffraction grating  102  (indicated by a thick solid line in  FIG. 14A ). A portion of the straight beam incident upon the phase plate  104  passes through the phase plate  104  and is diffracted at the surface of the third diffraction grating  102  (indicated by a dot and dash line in FIG.  14 A). In the second embodiment, the dual optical sensor includes two photodiodes PD 1  and PD 2 . 
     In a two-phase shift scheme, two interference patterns with a path difference of Δ=λ/4×(1/cos φ−1) are generated, and the generated interference patterns are interpreted by a mathematical operation to obtain a displacement. In this case, the thickness d of the stepped portion is given by the following Equation 4:
 
 d={λ (1/cos φ−1)}×{( n− 1)/4},  (4)
 
where n is a refractive index of the material of the stepped portion.
 
     By substituting, for example, the wavelength λ with 0.65 μm and the refractive index n with 1.58, the thickness d of the stepped portion is d={λ/(1/cos φ−1)}/{n−1)/4}={10.65/0.094}/{(1.58−1)/4}=2.98 (μm). 
     The beam is incident upon the dual optical sensor  106  after passing through the phase plate  104  having a thickness d obtained from Equation 4 above and also the third diffraction grating  102 . Thereafter, as shown in  FIG. 14B , a current is generated in response to the intensity of the interference beam received by the photodiode PD 1  in the dual optical sensor  106 . The generated current is inputted to an inverting input terminal of the operational amplifier OP 1  to be converted into a voltage. The voltage is outputted by the operational amplifier OP 1  as the output signal A. As shown in  FIG. 15A , the output signal A has a sinusoidal waveform. In addition, when the photodiode PD 2  receives the interference beam, a current is generated in response to the intensity of the received interference beam. The generated current is inputted to the inverting input terminal of the operational amplifier OP 2  to be converted into a voltage. The voltage is outputted as an output signal B. The output signal B has a sinusoidal waveform whose phase is shifted by 90° compared to the output signal A, i.e., a cosine waveform shown in  FIG. 15B . That is, the output signal A is sin(X) and the output signal B is cos(X) for the displacement X. Functions of resistors R 4  to R 7  shown in  FIG. 14B  are the same as those of the resistors R 2  and R 3  in the first embodiment. 
     The output signal A divided by the output signal B is equal to tan(X). Therefore, the displacement X is obtained by calculating arc tan (denoted as tan −1 ) of the division as expressed by the Equation 5:
 
 X =tan −1 ( A/B )  (5)
 
     The output signals A and B are inputted to an arithmetic unit  108  shown in  FIG. 14B . The arithmetic unit  108  performs the above calculation by subjecting the output signals A and B to an analog-to-digital conversion and a digital signal processing. A result of the calculation is shown in  FIG. 15C . Similar to the first embodiment, it is preferable to use a detection range of about ±80% of the amplitude. According to the second embodiment, the phase plate  104  having the thickness d is disposed on the movable third diffraction grating  102 , and the interference beam is received by the dual optical sensor  106 . Thus, the detection characteristic can be linearized by using a phase shift. 
     In addition, the present invention is not limited to the foregoing embodiments, and various changes may be made therein without departing from the scope of the invention.
     (1) The shapes, dimensions, and materials described in the above embodiments are mere examples, and may be changed appropriately as required as long as the same effects are achieved. In the displacement measuring unit  70  of the second embodiment, the transparent resin molded body  72  is provided with elasticity by the slit  86 A near the second diffraction grating  18  and the slit  86 B near the third diffraction grating  20 . However, this is merely an example, and the design may be changed appropriately within a scope where the same effects are achieved. The transparent resin molded body  72  may also be provided with elasticity by installing a slit (not shown) near a middle portion between the two diffraction gratings  18  and  20 , for example.   (2) In the first embodiment, the displacement is measured by using the 0 th  order beams and the 1 st  order beams. However, this is merely an example and the displacement may also be measured using diffracted beams of a certain order (e.g., second-order beams) instead of the 1 st  order beam.   (3) In the above-described embodiments, the laser light source  12  is employed as a light source. However, this is merely an example and a low cost light emitting diode (low coherence) may also be used. When a low cost light source other than a semiconductor laser whose coherence length is about 1 mm such as a light emitting diode whose coherence length is about 10 nm or less is used, it is preferable to set a diffraction angle φ shown in  FIGS. 4A and 4B  smaller. The path difference shown in  FIG. 4B  is given by Equation 3. Therefore, in a configuration of a sensor with detection range of 3.6 mm for example, the path difference Δ is 0.36 nm when Δd is 3.6 mm and the diffraction angle φ is 0.76°. That is, since the path difference between two interfering beams is less than the minimum distance of 10 μm for interference (spatial coherence length), the path difference falls within a measurable limit, and can be measured. In addition, as described above, the diffraction angle φ can be changed by changing the grating pitch P.   (4) In accordance with the first embodiment, the braking force is detected by measuring the displacement made by the extension (tension) of the brake wire in the electric power-assisted bicycle  50 . However, this is merely an example. The displacement measuring unit  70  may be inserted in the tube  58  holding the brake wire  56 , and the braking force may be detected based on a stress applied to the displacement measuring unit  70  in a lengthwise direction of the brake wire  56 .   (5) The first embodiment includes two displacement detection units: the wire movement detection unit including the first diffraction grating  16 , the semi-reflective mirror  22 , the total reflection mirror  24  and the optical sensor  28 ; and the wire extension detection unit including the second diffraction grating  18 , the third diffraction grating  20  and the optical sensor  26 . However, the second displacement detection unit may be provided only when necessary.   (6) In accordance with the first embodiment, both of the amount of extension and the amount of movement of the brake wire  56  are detected to perform a regenerative braking of the electric power-assisted bicycle  50  efficiently. However, this is merely an example. The present invention may also be applied to a measurement of a minute displacement such as measurement of distortions in a mechanical system and a calibration of a micro-measurement instrument. For instance, detection of positions required for zooming or focusing of a camera are currently performed by a mechanical switch array. However, the present invention may also be applied thereto to enable flexible and small-sized position detecting devices. In addition, since the present invention can expand the detection range, a displacement greater than one wavelength can be detected linearly. Therefore, the present invention can also be applied to optical microphones for example. Further, a minute vibration can be detected according to the present invention, which can also be applied to vibration sensors for example.   

     According to the first aspect of the present invention, the relative displacement of the total reflection mirror about the optical axis of the parallel beam widely ranging from sub-μm to about 20 mm can be measured. Thus, an apparatus for measuring displacement capable of measuring minute displacement can be provided. Particularly, since the displacement can be precisely measured without compensating for changes in temperature or environment, distortion or torsion of a mechanical system can be measured. Further, it is preferable that the present invention is used to detect the amount of movement or the amount of extension of the brake wire in the electric power-assisted bicycle. 
     In addition, by combining the second aspect of the present invention to the first aspect of the present invention, the displacement of the total reflection mirror about the optical axis of the parallel beam can be measured. Further, the displacement between a pair of the diffraction gratings can be measured simultaneously or sequentially by using a single light source, and measuring positions and detection sensitivities can be changed from those of the above-described displacement measurement of the total reflection mirror. Therefore, the present invention is preferably applied to measuring multiple displacements such as the amount of extension and the amount of movement of the brake wire in the electric power-assisted bicycle. 
     
       
         
               
             
               
               
             
           
               
                   
               
               
                 List of reference signs: 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  10: apparatus for measuring displacement 
                  11: housing 
               
               
                 11A, 11B: side 
                  12: laser light source 
               
               
                  13: convert laser light 
                  14: collimating lens 
               
               
                  15: parallel beam 
                  16: first diffraction grating 
               
               
                  18: second diffraction grating 
                  18A: grooves 
               
               
                  20: third diffraction grating 
                  22: semi-reflective mirror 
               
               
                  24: total reflection mirror 
                  26, 28: optical sensor 
               
               
                  30: straight beam 
                  32, 34: diffracted beam 
               
               
                  36: interference beam 
                  50: electric power-assisted 
               
               
                   
                   bicycle 
               
               
                  52: brake handle (bicycle handle) 
                  54: brake lever 
               
               
                  56: brake wire 
                  58: tube 
               
               
                  60: brake pad 
                  62: rim 
               
               
                  64: controller 
                  66: motor 
               
               
                  68: battery 
                  70: displacement measuring 
               
               
                   
                   unit 
               
               
                  72: transparent resin molded body 
                 72A, 72B: side 
               
               
                  74: through-hole 
                 76A, 76B: screws 
               
               
                  78: laser driver circuit 
                 80A~80F: space 
               
               
                 82, 84: I/V conversion circuit 
                 86A, 86B: slit 
               
               
                  90: amplifier circuit 
                  92: slicer 
               
               
                  94: clock counter 
                  96: arithmetic unit 
               
               
                 102: third diffraction grating 
                 104: phase plate 
               
               
                 106: dual optical sensor 
                 108: arithmetic unit 
               
               
                 200: Michelson interferometer 
                 202: laser light source 
               
               
                 204: collimating lens 
                 206: splitter 
               
               
                 208: fixed mirror 
                 210: movable mirror 
               
               
                 212: optical sensor 
                 214: fixed unit 
               
               
                 216: interference patterns 
                 F1~F3: frame 
               
               
                 L1~L5: light path 
                 Lrev1, Lrev2: reflected beam 
               
               
                 LD: laser diode 
                 OP, OP1, OP2: operational 
               
               
                   
                 amplifier 
               
               
                 PD, PD1, PD2: photodiode 
                 R1: current limiting resistor 
               
               
                 R2~R7: resistors