Abstract:
A method and equipment based on multi-core fiber Bragg grating (FBG) probe for measuring structures of a micro part are provided. The provided method relates to how to accomplish measuring structures of a micro part by transforming two or three-dimensional contact displacements into spectrum shifts of the multi-core FBG probe, and to reconstruct the structure geometry of a micro part. The provided equipment can be used to bring the spherical tip of the multi-core FBG probe into contact with a micro part, to determine coordinates of contact points, and to reconstruct the structure geometry of a micro part. The provided method and equipment feature high sensitivity, low probing force, high inspecting aspect ratio and immunity to environment interference.

Description:
FIELD OF INVENTION 
       [0001]    The invention relates to a method based on multi-core FBG probe for measuring structures of a micro part, wherein structure measurement of a micro part is accomplished by transforming two or three-dimensional contact displacements into spectrum shifts of the multi-core FBG probe and the structure geometry of a micro part is reconstructed. The invention also relates to an equipment based on multi-core FBG probe for measuring structures of a micro part, and the equipment consists of a coordinate measuring instrument system, a photoelectric probing system and a measurement computer, wherein the spherical tip of the multi-core FBG probe is brought into contact with a micro part, and contact points of a micro part can be calculated from coordinates of the multi-core FBG probe relative to the coordinate measuring instrument system and contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position measured directly using the photoelectric probing system. 
       DESCRIPTION OF PRIOR ART 
       [0002]    With fast development of manufacturing technologies, more and more structures of micro parts with dimensions of 0.1˜1 mm and aspect ratios of more than 10:1 are now used in an increasing number of applications, including ink-jet printer nozzles, microgroove arrays in aerospace propulsion engines, cooling vents in turbine blades, diesel fuel injection holes and devices of binary optics, which present challenges to the measurement precision and inspecting depth of existing probing systems. Therefore, it is of great significance to develop a precise probing system for measuring structures of a micro part, especially for one with a miniaturized size and high inspecting aspect ratio. 
         [0003]    Much work has been done on this particular aspect in recent years. For example, Gaoliang Dai, Sebastian Bütefisch, Frank Pohlenz and Hans-Ulrich Danzebrink et al. invented a small silicon probe based on MEMS fabrication process, which consists of a silicon chip membrane and integrated piezoresistive elements. The piezoresistive elements are etched onto the silicon membrane to detect three-dimensional deformation, and the stylus is attached to the center of the silicon membrane. The probe tip is less than 300 μm in diameter, and the probing force achieved by the membrane system is about 100 mN. However, the fabrication process of their probe is complex and the production cost is high. 
         [0004]    Owing to the low production cost, immune to electromagnetic interference and interruption and compact in size, more and more fiber probes have been developed in recent year for dimensional measurement. H. Schwenke, F. Wäldele, C. Weiskirch, H. Kunzmann invented a fiber probe with a fiber spherical tip to backscatter light. The stylus of this probe is 15 μm in diameter, and the spherical tip is 25 μm in diameter. The laser beam enters through the fiber and lights the fiber spherical tip. The back scattered light is imaged using a CCD camera, and contact displacements in xy-direction is thus transformed into movements of the center of the light spot in a CCD camera. This probe can further be extended to a three-dimensional system by attaching a fiber sphere to the stylus and the image of the spherical tip is reflected on a second CCD camera using a mirror. But due to shadowing effect, a CCD camera cannot obtain enough light energy to create an image, and the inspecting depth achievable with this probe is thus limited. 
         [0005]    Jiubin Tan and Jiwen Cui invented a spherical coupling optical fiber probe. The spherical coupling optical fiber probe consists of incident fiber, effluent fiber and a spherical coupler combining double fibers fixed on the probe tip. The laser beam passes through the coupling lens to enter the coupler and comes out from the effluent fiber in the reverse direction. The return light passes through an object lens and is captured by a CCD camera with an objective lens. This probe extends the range of inspecting depth, but how to realize three-dimensional measurement and fabricate a smaller fiber coupler with a high coupling efficiency is still an open issue. 
         [0006]    So, Jiubin Tan, Fei Wang and Jiwen Cui invented a fiber probe based on micro focal-length collimation to further extend the inspecting depth. A cylindrical lens with a focal length in micrometers is formed by a thin glass fiber stylus without coating. A parallel light source is focused by an objective lens to form a point light source. Then, the point light source is collimated by the cylindrical lens and the image fringe is acquired by a linear or area array CCD camera. This probing system has a displacement magnification of more than 10,000 because the focal length of the fiber cylindrical lens is very short. Light propagates outside high aspect ratio structures of a micro part and the inspecting depth can thus be extended. However, limitations of this approach include that the z-displacement is detected by buckling, which is not stable and may be hard to achieve true three-dimensional measurements. 
         [0007]    For fiber probes, it is a challenge to make them sensitive to the z-displacement until a FBG probe was invented by H Ji, H-Y Hsu, L X Kong and A B Wedding. Their probe comprises FBG in the fiber stylus, and contact displacements are transformed into shifts of the center wavelength of FBG&#39;s reflection spectrum. This probe cannot be affected by shadow effect; theoretically, light can disregard the aspect ratio of structures of a micro part and propagate in the stylus of this probe. The size of this probe and probing system is also miniaturized. When the probe gets contact with a micro part in the z-direction, FBG is subjected to compression stress and the z-displacement can be readily measured. However, this probe is not sensitive to radial contact displacements because FBG is located in the neutral stress plane when it is deflected. 
         [0008]    Above all, fiber probes have been widely applied in measuring structures of a micro part and become more suitable for its optical and mechanical features of optical conductivity, easy miniaturization and low probing force. Different methods have been designed for sensing contact displacements of fiber probes, and the followings are some of their drawbacks: 
         [0009]    1. The inspecting depth is restricted by shadow effect. For some probes based on light backscatter, the emission light is easily obstructed or reflected by the sidewall, and a large range of the emission angle allows few particles of light to reach the photo-detector. 
         [0010]    2. Bulk size of the probing system can hardly meet the requirement of the probing space and limits its application for measuring structures on a complex-shaped micro part with limited probing space. 
         [0011]    3. Absence of multi-dimensional tactile sense and multi-dimension-decoupling capacity makes the measurement process complex and time-consuming. A real-time application can hardly be achieved. 
         [0012]    4. The inspecting resolutions of fiber probes are hard to be further enhanced. Most of fiber probes have sub-micrometer resolutions only. The displacement sensitivities are too low to achieve precise measurement. 
       SUMMARY OF INVENTION 
       [0013]    One purpose of the present invention is to propose a method based on multi-core FBG probe for measuring structures of a micro part, which consists of following steps: 
         [0014]    Step 1. 
         [0015]    Providing a multi-core FBG probe, which comprises a spherical tip and a multi-core fiber stylus inscribed FBGs in its cores. The multi-core fiber stylus, cantilevered at one end and with the spherical tip fixed on the other, serves as the multi-core FBG probe. The multi-core fiber utilized to fabricate the multi-core fiber stylus should have one or more cores located out of the center of the multi-core fiber; 
         [0016]    Step 2. 
         [0017]    Providing a photoelectric probing system, which consists of the multi-core FBG probe mentioned in step 1, an optical path for the operation of the multi-core FBG probe, and an interrogation unit (consisting of a demodulation unit and a signal processing unit) for detecting and processing the sensing signal of the multi-core FBG probe. When a micro part is measured, the spherical tip of the multi-core FBG probe is brought into contact with a micro part and spectra of FBGs comprised in the multi-core fiber stylus shift accordingly. The optical path supplies the multi-core FBG probe with energy and ensures the sensing signal containing spectrum shifts of FBGs in the multi-core fiber stylus and the reference FBG can reach the interrogation unit. The interrogation unit detects the sensing signal, transforms it into spectrum shifts of FBGs, and then calculates contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position; 
         [0018]    Step 3. 
         [0019]    Combining the photoelectric probing system mentioned in step 2 with a coordinate measuring instrument system to form an equipment based on multi-core FBG probe for measuring structures of a micro part, contact displacements of the spherical tip of the multi-core FBG probe and coordinates of the multi-core FBG probe relative to the coordinate measuring instrument system are acquired in real time and are processed by a measurement computer, wherein coordinates of contact points can be calculated from coordinates of the multi-core FBG probe relative to the coordinate measuring instrument system and contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position measured directly using the photoelectric probing system; 
         [0020]    Step 4. 
         [0021]    A micro part measured is fastened to the measurement table of the equipment based on multi-core FBG probe for measuring structures of a micro part mentioned in step 3. The motion of the measurement table and the multi-core FBG probe fixed on the sleeve of the equipment is controlled by manual operation or a measurement program. Relative motion between the multi-core FBG probe and a micro part occurs and the motion track is accurately designed to bring the spherical tip of the multi-core FBG probe into contact with a certain point of a micro part. Coordinates of a contact points can be calculated in the measurement computer mentioned in step 3; 
         [0022]    Step 5. 
         [0023]    Repeat the measurement process in step 4 to obtain coordinates of more contact points and the structure geometry of a micro part measured can be reconstructed from coordinates of these contact points. 
         [0024]    The second purpose of the present invention is to propose equipment based on multi-core FBG probe for measuring structures of a micro part. 
         [0025]    According to the second aspect of the invention, the equipment for measuring structures of a micro part consists of a coordinate measuring instrument system which is used to implement the whole measuring process and determine accurate coordinates of the multi-core FBG probe relative to the coordinate measuring instrument, a photoelectric probing system which makes the multi-core FBG probe working, demodulates the sensing signal and extracts contact displacements of the spherical tip of the multi-core FBG probe, a measurement computer which receives results of the coordinate measuring instrument system and the photoelectric probing system, calculates coordinates of contact points of a micro part being measured using according results above, plans measuring process and sends motion signal to a Computer Numerical Control (CNC) controller of the coordinate measuring instrument system. 
         [0026]    The coordinate measuring instrument system is of standard design, which consists of a crosspiece, a sleeve adjustable in the X and Z direction, a measurement table movable in the Y direction, an instrument basement, a XYZ-counter, a CNC controller. The crosspiece and the sleeve adjustable in the X and Z direction, the crosspiece and the instrument basement, the measurement table movable in the Y direction and the instrument basement are linked with mechanical structures, respectively. The sleeve adjustable in the X and Z direction and the XYZ-counter, the measurement table movable in the Y direction and the XYZ-counter, the instrument basement and the CNC controller, the XYZ-counter and the measurement computer, and the CNC controller and the measurement computer are linked with electric cable, respectively. 
         [0027]    The equipment based on multi-core FBG probe for measuring structures of a micro part features a photoelectric probing system, which consists of a light source, an optical circulator, a multi-channel optical switch, a multi-core fiber fan-out (which makes single mode fiber access to every core of multi-core fiber), multi-core fiber, a multi-core FBG probe consisting of a multi-core fiber stylus and a spherical tip, a reference FBG, a demodulation unit and a signal processing unit. The light source and the optical circulator, the optical circulator and the multi-channel optical switch, the multi-channel optical switch and the multi-core fiber fan-out, the multi-channel optical switch and the reference FBG, and the optical circulator and the demodulation unit are linked with single mode fiber, respectively. The multi-core fiber fan-out and the multi-core fiber stylus of the multi-core FBG probe are linked with the multi-core fiber. The multi-channel optical switch and the measurement computer, the demodulation unit and the signal processing unit, and the signal processing unit and the measurement computer are linked with electric cable, respectively. 
         [0028]    The light source can be a broadband ASE source. When the light source is a broadband ASE source, the reflected light signal is reflection spectra of FBGs and the demodulation unit can be an optical spectrum analysis device. 
         [0029]    The light source can be a broadband ASE source. When the light source is a broadband ASE source, the reflected light signal is reflection spectra of FBGs and the demodulation unit can be also a matching FBG pair demodulation system which consists of a 50:50 coupler, a demodulation FBG and a multi-channel optical power measuring device. 
         [0030]    The light source can be a narrowband laser source whose wavelength is located in the range of reflection spectra of FBGs comprised in the multi-core FBG probe and the reference FBG. When the light source is a narrowband laser source, the reflected light signal is reflectivity of the spectra of FBGs at current wavelength of the narrowband laser source and the demodulation unit can be a multi-channel optical power measuring device. 
         [0031]    The multi-core FBG probe is fabricated by inscribing FBG in the multi-core fiber etched by hydrofluoric acid or machining to reduce its diameter served as the multi-core fiber stylus. A spherical tip, fabricated by electric discharge machining, oxy-hydrogen flame machining or micro ball assembly technique, fixed on the free end of the multi-core fiber stylus. The diameter D of the multi-core fiber without coating used to fabricate the multi-core fiber stylus is usually in the range of 50 μm to 400 μm. The radii of the multi-core fiber&#39;s cores are r, and r is normally 4 μm to 6 μm. The distance d from cores of to the center of the multi-core fiber should ensure that the multi-core fiber contains the cores, that is d should be less than 0.5D−r. The diameter ratio of the spherical tip to the multi-core fiber stylus is normally in the range of 1.2˜1.5. The other end of the multi-core fiber stylus is fastened to the sleeve of the coordinate measuring instrument system. The multi-core FBG probe can be 3˜10 mm long, so a maximum aspect ratio of 200:1 can be achieved. 
         [0032]    The multi-core fiber stylus of the multi-core FBG probe can be a section of eccentric single-core fiber, and wherein said multi-core fiber is the eccentric single-core fiber. The core is located on the negative direction of horizontal axis with a distance of d to the center of the eccentric single-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0033]    The multi-core fiber stylus of the multi-core FBG probe can be a section of dual eccentric core fiber, and wherein said multi-core fiber is the dual eccentric core fiber. The first cores and the second core are located on the negative direction of horizontal axis and vertical axis with a distance of d to the center of the dual eccentric core fiber, respectively. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0034]    The multi-core fiber stylus of the multi-core FBG probe can be a section of eccentric two-core fiber, and wherein said multi-core fiber is the eccentric two-core fiber. The first core is located on the negative direction of horizontal axis with a distance of d to the center of the eccentric two-core fiber; the second core is located in the center of the eccentric two-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0035]    The multi-core fiber stylus of the multi-core FBG probe can be a section of two-core fiber, and wherein said multi-core fiber is the two-core fiber. The first core and the second core are located on the negative and positive direction of horizontal axis with a distance of d to the center of the two-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0036]    The multi-core fiber stylus of the multi-core FBG probe can be a section of eccentric three-core fiber, and wherein said multi-core fiber is the eccentric three-core fiber. The first core and the second core are located on the negative direction of horizontal axis and vertical axis with a distance of d to the center of the eccentric three-core fiber, respectively; the third core is located in the center of the eccentric three-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0037]    The multi-core fiber stylus of the multi-core FBG probe can be a section of three-core fiber, and wherein said multi-core fiber is the three-core fiber. The three cores are located out the center of the three-core fiber with a distance of d to its center; the lines from the first core and the second core to the center of the three-core fiber are beveled at an angle of 30 degree and 150 degree to the negative direction of horizontal axis, respectively; the third core is located on the negative direction of vertical axis. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0038]    The multi-core fiber stylus of the multi-core FBG probe can be a section of eccentric four-core fiber, and wherein said multi-core fiber is the eccentric four-core fiber. The first core, the second core and the third core are located out the center of the eccentric four-core fiber with a distance of d to its center; the lines from the first core and second core to the center of the eccentric four-core fiber are beveled at an angle of 30 degree and 150 degree to the negative direction of horizontal axis, respectively; the third core is located on the negative direction of vertical axis; the fourth core is located in the center of the eccentric four-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0039]    The multi-core fiber stylus of the multi-core FBG probe can be a section of four-core fiber, and wherein said multi-core fiber is the four-core fiber. The first core and the second core are located on the negative and positive direction of horizontal axis with a distance of d to the center of the four-core fiber, respectively; the third core and the fourth core are located on the negative and positive direction of vertical axis with a distance of d to the center of the four-core fiber, respectively. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0040]    The multi-core fiber stylus of the multi-core FBG probe can be a section of five-core fiber, and wherein said multi-core fiber is the five-core fiber. The first core and the second core are located on the negative and positive direction of horizontal axis with a distance of d to the center of the five-core fiber, respectively; the third core and the fourth core are located on the negative and positive direction of vertical axis with a distance of d to the center of the five-core fiber, respectively; the fifth core is located in the center of the five-core fiber. The horizontal and vertical axes are in the section of the multi-core fiber stylus, and the origin of horizontal and vertical axes is at the center of the multi-core fiber stylus. 
         [0041]    The present invention has following advantages: 
         [0042]    (1). High Radial Sensitivity. 
         [0043]    Thanks to the cores located out of the center of the multi-core fiber, FBGs comprised in the multi-core fiber stylus are subjected to stress several hundreds of times larger than that in a normal single core FBG probe (such as the probe invented by H Ji et al.) with a same radial contact displacement and structure parameters. Therefore, the radial sensitivity of the multi-core FBG probe is increased by several hundreds of times. 
         [0044]    (2) High Inspecting Aspect Ratio. 
         [0045]    The inspecting depth is not affected by the shadowing effect by guiding optical signals propagating in the probe and separating the signal processing device from the probe. The minimum dimension of structures of a micro part to be measured can go up to 50 μm for the limit imposed by the spherical tip of the multi-core fiber, and the inspecting aspect ratio is up to 200:1. 
         [0046]    (3) Very Low Probing Force. 
         [0047]    The contact measurement is achieved by deflecting a thin optical fiber. The probing force is less than several tens of mN. 
         [0048]    (4) Immunity to Environment Interference. 
         [0049]    Optical fiber is immune to electromagnetic interference, and temperature drifts can be compensated using a reference FBG. 
     
    
     
       BRIEF DESCRIPTION OF ACCOMPANYING DRAWINGS 
         [0050]      FIG. 1 : a schematic illustration of the multi-core FBG probe subjected to a radial contact displacement; 
           [0051]      FIG. 2 : a schematic illustration of the multi-core FBG probe subjected to an axial contact displacement; 
           [0052]      FIG. 3 : an illustration of the fiber with a core located out the center; 
           [0053]      FIG. 4 : an illustration of the fiber with a core located in the center; 
           [0054]      FIG. 5 : construction of equipment based on multi-core FBG probe for measuring structures of a micro part; 
           [0055]      FIG. 6 ( a ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric single-core fiber; 
           [0056]      FIG. 6 ( b ) : a section A 1 -A 1  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric single-core FBG probe; 
           [0057]      FIG. 6 ( c ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a dual eccentric core FBG probe; 
           [0058]      FIG. 6 ( d ) : a section A 2 -A 2  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a dual eccentric core FBG probe; 
           [0059]      FIG. 6 ( e ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric two-core FBG probe; 
           [0060]      FIG. 6 ( f ) : a section A 3 -A 3  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric two-core FBG probe; 
           [0061]      FIG. 6 ( g ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a two-core FBG probe; 
           [0062]      FIG. 6 ( h ) : a section A 4 -A 4  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a two-core FBG probe; 
           [0063]      FIG. 6 ( i ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric three-core FBG; 
           [0064]      FIG. 6 ( j ) : a section A 5 -A 5  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric three-core FBG; 
           [0065]      FIG. 6 ( k ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a three-core FBG; 
           [0066]      FIG. 6 ( l ) : a section A 6 -A 6  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a three-core FBG; 
           [0067]      FIG. 6 ( m ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric four-core FBG probe; 
           [0068]      FIG. 6 ( n ) : a section A 7 -A 7  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as an eccentric four-core FBG probe; 
           [0069]      FIG. 6 ( o ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a four-core FBG probe; 
           [0070]      FIG. 6 ( p ) : a section A 8 -A 8  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a four-core FBG probe; 
           [0071]      FIG. 6 ( q ) : a cross-sectional view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a five-core FBG probe; 
           [0072]      FIG. 6 ( r ) : a section A 9 -A 9  view of the multi-core FBG probe when the multi-core fiber stylus is embodied as a five-core FBG probe; 
           [0073]      FIG. 7 ( a ) : a schematic illustration of the demodulation unit embodied as an optical spectrum analysis device when the light source is a broadband ASE source; 
           [0074]      FIG. 7 ( b ) : a schematic illustration of demodulation unit embodied as a matching FBG pair demodulation system when the light source is the light source is a broadband ASE source; 
           [0075]      FIG. 7 ( c ) : a schematic illustration of demodulation unit embodied as a multi-channel optical power measuring device when the light source is the light source is a narrowband laser source. 
       
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0076]    A method based on multi-core FBG probe for measuring structures of a micro part includes following steps: 
         [0077]    Step 1. 
         [0078]    Providing a multi-core FBG probe, which comprises a spherical tip and a multi-core fiber stylus inscribed FBGs in its cores. The multi-core fiber stylus, cantilevered at one end and with the spherical tip fixed on the other, serves as the multi-core FBG probe. The multi-core fiber utilized to fabricate the multi-core fiber stylus should have one or more cores located out of the center of the multi-core fiber; 
         [0079]    In step 1, the multi-core fiber comprised FBG in its cores with a special structure is served as the multi-core FBG probe stylus. When the spherical tip of the multi-core FBG probe is subjected to a radial contact displacement, for example in axis x as shown in  FIG. 1 , the multi-core FBG probe can be simplified into a cantilever and the distribution of strain in the multi-core FBG probe can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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                       ( 
                       l 
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                   = 
                   
                     
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                             ( 
                             
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                            
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         [0080]    where, l is the coordinate along the multi-core FBG probe, l=0 at the fixed end, l=L at the free end, v r  is the contact displacement, d is the eccentric distance from the core to the neutral plane and L is the length of the multi-core FBG probe, respectively. 
         [0081]    FBGs comprised in the multi-core fiber stylus are subjected to strain due to a radial contact displacement and shifts of their reflection spectra can be express as: 
         [0000]      Δλ=λ(1− p   e )ε  (2)
 
         [0082]    where, λ is the Bragg wavelength of FBG, p e  is the effective photoelastic constant typically 0.213 for a common FBG, and ε is the strain caused by the contact deformation, respectively. It can be concluded from Eq. (1) and Eq. (2) that the distribution of strain in the multi-core fiber stylus caused by a radial contact displacement along axis x is not uniform. FBGs in the multi-core fiber stylus are transformed into linear chip FBGs, and shifts of reflection spectra of linear chip FBGs are the average of shifts of reflection spectra of local FBGs at both ends of the multi-core FBG probe. By substituting Eq (1) into Eq. (2), shifts of reflection spectra of FBGs can be given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δλ 
                     r 
                   
                   = 
                   
                     
                       - 
                       
                         λ 
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                           ( 
                           
                             1 
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                         d 
                       
                       
                         2 
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                           L 
                           2 
                         
                       
                     
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                       v 
                       r 
                     
                   
                 
               
               
                 
                   ( 
                   3 
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         [0083]    The remarkable difference between multi-core fiber and normal fiber used to fabricate the fiber stylus of a FBG probe is the cores located out of the center of the fiber stylus. It can be concluded from Eq. (3) that the reflection spectrum of FBG comprised in the core located out of the center of the fiber stylus has significant changes and can be serviced as sensing signal as a result of the eccentric distance from the core to the neutral plane as shown in  FIG. 3 . However, the shift of the reflection spectrum of FBG comprised in the core located in the center of fiber stylus approximates to zero as a result of d=0 as shown in  FIG. 4 . The structure of the core located out of the center of fiber stylus significantly improves the radial sensitivity of a FBG probe. 
         [0084]    As shown in  FIG. 2 , when the multi-core FBG probe is compressed through an axial contact along axis z and uniform strain in the multi-core FBG probe can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     ɛ 
                     a 
                   
                   = 
                   
                     - 
                     
                       
                         v 
                         a 
                       
                       L 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0085]    where, v a  is the contact displacement along axis z. 
         [0086]    By substituting Eq (4) into Eq. (2), shifts of reflection spectra of FBGs can be given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δλ 
                     a 
                   
                   = 
                   
                     
                       - 
                       
                         λ 
                          
                         
                           ( 
                           
                             1 
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                           ) 
                         
                       
                     
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                         v 
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                   5 
                   ) 
                 
               
             
           
         
       
     
         [0087]    It can be concluded from Eq. (5) that the axial sensitivity of the core located out of and in the center of the multi-core fiber stylus is the same. 
         [0088]    Step 2. 
         [0089]    Providing a photoelectric probing system, which consists of the multi-core FBG probe mentioned in step 1, an optical path for the operation of the multi-core FBG probe, and an interrogation unit (consisting of a demodulation unit and a signal processing unit) for detecting and processing the sensing signal of the multi-core FBG probe. When a micro part is measured, the spherical tip of the multi-core FBG probe is brought into contact with a micro part and the spectra of FBGs comprised in the multi-core fiber stylus shift accordingly. The optical path supplies the multi-core FBG probe with energy and ensures the sensing signal containing spectrum shifts of FBGs in the multi-core fiber stylus and the reference FBG can reach the interrogation unit. The interrogation unit detects the sensing signal, transforms it into spectrum shifts of FBGs, and then calculates contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position; 
         [0090]    In step 2, the photoelectric probing system can be embodied in three ways: 
         [0091]    The light source can be a broadband ASE source. When the light source is a broadband ASE source, the reflected light signal is reflection spectra of FBGs, and the demodulation unit can be an optical spectrum analysis device. The optical spectrum analysis device has an optical input port and an electric output port. Shifts of reflection spectra of FBGs detected by the optical spectrum analysis device are transformed into electric signal; the electric signal is send to the signal processing unit to calculate contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position. 
         [0092]    The light source can be a broadband ASE source. When the light source is a broadband ASE source, the reflected light signal is reflection spectra of FBGs and the demodulation unit can be also a matching FBG pair demodulation system which consists of a 50:50 coupler, a demodulation FBG and a multi-channel optical power measuring device. The matching FBG pair demodulation system has an optical input port and an electric output port. Reflection spectra of FBGs comprised in the multi-core fiber stylus of the multi-core FBG probe and the reference FBG is reflected and enters the demodulation unit. The demodulation FBG is not affected by the measurement process. Therefore, the spectrum overlap between the reflected light signal and the demodulation FBG just changes according to the spectrum shift of the reflected light signal. The optical power ratio of the reflected light signal and the spectrum overlap between the reflected light signal and the demodulation FBG is transformed into electric signal by the multi-channel optical power measuring device; the electric signal is send to the signal processing unit to calculate contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position. 
         [0093]    The light source can be a narrowband laser source whose wavelength is located in the range of reflection spectra of FBGs comprised in the multi-core fiber stylus of the multi-core FBG probe and the reference FBG. When the light source is a narrowband laser source, the reflected light signal is the reflectivity of the spectra of FBGs at current wavelength of the narrowband laser source and the demodulation unit can be a multi-channel optical power measuring device. The power of the reflected light signal is in related to the reflectivity of the spectra of FBGs at the wavelength of the narrowband laser source, and it changes according to shifts of reflection spectra of FBGs comprised in the multi-core fiber stylus of the multi-core FBG probe and the reference FBG. The optical power ratio of the reflected light signal and the narrowband laser source is transformed into electric signal by the multi-channel optical power measuring device; the electric signal is send to the signal processing unit to calculate contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position. 
         [0094]    Step 3. 
         [0095]    Combining the photoelectric probing system mentioned in step 2 with a coordinate measuring instrument system to form an equipment based on multi-core FBG probe for measuring structures of a micro part, contact displacements of the spherical tip of the multi-core FBG probe and coordinates of the multi-core FBG probe relative to the coordinate measuring instrument system are acquired in real time and are processed by a measurement computer, wherein coordinates of contact points can be calculated from coordinates of the multi-core FBG probe relative to the coordinate measuring instrument system and contact displacements of the spherical tip of the multi-core FBG probe relative to its zero-force position measured directly using the photoelectric probing system; 
         [0096]    In step 3, a type of equipment based on multi-core FBG probe for measuring structures of a micro part is formed, in which coordinates of the coordinate measuring instrument system and changes of the photoelectric probing system will be recorded in real time with a high speed. The photoelectric probing system is used as a trigger and the coordinate measuring instrument system offers a precise three-dimensional movement and feedback. The movement of the coordinate measuring instrument system will be stopped as soon as the spherical tip of the multi-core FBG probe contacts a micro part. Coordinates of contact points can be calculated using a program embedded within the measurement computer. 
         [0097]    Step 4. 
         [0098]    A micro part measured is fastened to a measurement table of the equipment based on multi-core FBG probe for measuring structures of a micro part mentioned in step 3. The motion of the measurement table and the multi-core FBG probe fixed on the sleeve of the equipment is controlled by manual operation or a measurement program. Relative motion between the multi-core FBG probe and a micro part occurs and the motion track is accurately designed to bring the spherical tip of the multi-core FBG probe into contact with a certain point of a micro part. Coordinates of a contact point can be calculated in the measurement computer mentioned in step 3; 
         [0099]    In step 4, coordinates of a contact point of a micro part can be manually or automatically acquired using the coordinate measurement method mentioned in step 3. 
         [0100]    Step 5. 
         [0101]    Repeat the measurement process in step 4 to obtain coordinates of more contact points and the structure geometry of a micro part measured can be reconstructed from coordinates of these contact points. 
         [0102]    In step 5, coordinates of a micro part are acquired using the measurement process mentioned in step 4 and the structure geometry of a micro part measured can be reconstructed according to contact points. 
         [0103]    According to the second purpose of the present invention, equipment based on multi-core FBG probe for measuring structures of a micro part can be set up in the following ways: 
         [0104]    As shown in  FIG. 5 , the equipment based on multi-core FBG probe  519  for measuring structures of a micro part consists of a coordinate measuring instrument system  51 , a photoelectric probing system  58 , and a measurement computer  520 . 
         [0105]    The coordinate measuring instrument system  51  consists of a crosspiece  52 , a sleeve  53  adjustable in the X and Z direction, a measurement table  54  movable in the Y direction, an instrument basement  55 , a XYZ-counter  56 , a CNC controller  57 . The crosspiece  52  and the sleeve  53  adjustable in the X and Z direction, the crosspiece  52  and the instrument basement  55 , the measurement table  54  movable in the Y direction and the instrument basement  55  are linked with mechanical structures, respectively. The crosspiece  52  supports the sleeve  53  adjustable in the X and Z direction. The instrument basement  55  supports the crosspiece  52  and the measurement table  54  movable in the Y direction. The instrument basement  55  drives the measurement table  54  directly and the sleeve  53  indirectly through the crosspiece  52 . The multi-core FBG probe  519  for sensing contact displacements is fixed on the sleeve  53  and can be adjustable in the X and Z direction. A micro part being measured is fastened to the measurement table  54  movable in the Y direction. The sleeve  53  adjustable in the X and Z direction and the XYZ-counter  56 , the measurement table  54  movable in the Y direction and the XYZ-counter  56 , the instrument basement  55  and the CNC controller  57 , the XYZ-counter  56  and the measurement computer  520 , and the CNC controller  57  and the measurement computer  520  are linked with electric cable, respectively. The XYZ-counter  56  is used to determine coordinate values X, Y, Z of the multi-core FBG probe  519  relative to the coordinate measuring instrument system  51 , and to send coordinate values to measurement computer  520 . The CNC controller  57  receives the signal from the measurement computer  520 , and controls the motion of the sleeve  53  and the measurement table  54 . Relative motion between the multi-core FBG probe  519  and a micro part is controlled by the CNC-controller  57  to implement CNC operations and measurement processes, and the motion track is accurately designed to bring the spherical tip  515  of the multi-core FBG probe  519  into contact with a certain point of a micro part. 
         [0106]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part features the photoelectric probing system  58 , which consists of a light source  59 , an optical circulator  510 , a multi-channel optical switch  511 , a multi-core fiber fan-out  512 , multi-core fiber  513 , a multi-core FBG probe  519  consisting of a multi-core fiber stylus  514  and a spherical tip  515 , a reference FBG  516 , a demodulation unit  517  and a signal processing unit  518 . The light source  59  and the optical circulator  510 , the optical circulator  510  and the multi-channel optical switch  511 , the multi-channel optical switch  511  and the multi-core fiber fan-out  512 , the multi-channel optical switch  511  and the reference FBG  516 , and the optical circulator  510  and the demodulation unit  517  are linked with single mode fiber, respectively. The light coming from the light source  59  goes through single mode fiber into a core of the multi-core fiber stylus  514  of the multi-core FBG probe  519  or the reference FBG  516  and then is reflected by FBGs within them. The reflected light signal as the sensing signal enters the demodulation unit  517  through the multi-core fiber  513 , the multi-core fiber fan-out  512 , the multi-channel optical switch  511  and the optical circulator  510 , respectively. The multi-channel optical switch  511  and the measurement computer  520  are linked with electric cable. The multi-channel optical switch  511  is controlled by the measurement computer  520  and the time-division-multiplexing measurement optical paths are formed by switching among FBGs in cores of the multi-core fiber stylus  514  and the reference FBG  516 . When the spherical tip  515  of the multi-core FBG probe  519  gets contact with a micro part, the multi-core FBG probe  519  deforms and consequent stress distributed along the multi-core fiber stylus  514  shifts reflection spectra of FBGs comprised in the multi-core fiber stylus  514 . The reflected light signal is thus changed. The demodulation unit  517  and the signal processing unit  518 , the signal processing unit  518  and the measurement computer  520  are linked with electric cable, respectively. The reflected light signal of FBGs in cores of the multi-core fiber stylus  514  of the multi-core FBG probe  519  and the reference FBG  516  is transformed into electric signal by the demodulation unit  517 ; the electric signal is processed to achieve contact displacements ΔX 1 , ΔY 1  and ΔZ 1  of the spherical tip  515  of the multi-core FBG probe  519  relative to its zero-force position uncoupled with environmental temperature drifts by the differential processing in the signal processing unit  518 , and then send to the measurement computer  520  and there linked to coordinate values X, Y, Z of the multi-core FBG probe  519  relative to the coordinate measuring instrument system  51 , which are determined using the XYZ-counter  56 . Coordinates of contact points can be calculated from coordinate values X, Y, Z of the multi-core FBG probe  519  relative to the coordinate measuring instrument system  51  and contact displacements ΔX 1 , ΔY 1  and ΔZ 1  of the spherical tip  515  of the multi-core FBG probe  519  relative to its zero-force position measured directly using the photoelectric probing system  58 . From the values computed in this way, structure geometry of a micro part is determined. 
         [0107]    The diameter D of the multi-core fiber without coating used to fabricate the multi-core fiber stylus  514  is usually in the range of 50 μm to 400 μm. The radii of the multi-core fiber&#39;s cores are r, and r is normally 4 μm to 6 μm. The distance d from the cores to the center of the multi-core fiber should ensure that the multi-core fiber contains the cores, that is d should be less than 0.5D−r. The multi-core FBG probe  519  can be 3˜10 mm long. The diameter ratio of the spherical tip  515  to the multi-core fiber stylus  514  is normally in the range of 1.2˜1.5. The horizontal axis is axis x, the vertical axis is axis y, and the axial direction along the multi-core fiber stylus  514  is axis z. The axes x and y are in the section of the multi-core fiber stylus  514 , and the origin of axes x and y is at the center of the multi-core fiber stylus  514 . 
         [0108]    The multi-core FBG probe  519  can be embodied in way 1: 
         [0109]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of eccentric single-core fiber  61 , and the multi-core fiber  513  is the eccentric single-core fiber  61 . As shown in  FIGS. 6 ( a ) and ( b ) , the core  62  is located on the negative direction of axis x with a distance of d to the center of the eccentric single-core fiber  61 . The multi-core FBG probe  519  fabricated by the eccentric single-core fiber  61  has a two-dimensional measurement capacity in axes z and x. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
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                                       Δλ 
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                   ( 
                   6 
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         [0110]    where, λ is the Bragg wavelength of FBG comprised in the core  62  of the eccentric single-core fiber  61  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P  is the spectrum shift of FBG comprised in the core  62  of the eccentric single-core fiber  61  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the core  62  to the center of the eccentric single-core fiber  61 ; p e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x  and v z  is contact displacements in axes x and z, respectively. 
         [0111]    It can be concluded form Eq. (6) that sensing signal of v x  is coupled with v z  in the multi-core FBG probe  519  fabricated by the eccentric single-core fiber  61 . Contact displacements in axes x and z can be measured in a time-division-multiplexing way using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of the spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0112]    The multi-core FBG probe  519  can be embodied in way 2: 
         [0113]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of dual eccentric core fiber  63 , and the multi-core fiber  513  is the dual eccentric core fiber  63 . As shown in  FIGS. 6 ( c ) and ( d ) , the first core  64  and the second core  65  are located on the negative and direction of axes x and y with a distance of d to the center of the dual eccentric core fiber  63 , respectively. The multi-core FBG probe  519  fabricated by the dual eccentric core fiber  63  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
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         [0114]    where, λ is the Bragg wavelength of FBGs comprised in the first core  64  and the second core  65  of the dual eccentric core fiber  63  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1  and Δλ P2  is spectrum shifts of FBGs comprised in the first core  64  and the second core  65  of the dual eccentric core fiber  63  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  64  and the second core  65  to the center of the dual eccentric core fiber  63 ; p e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. 
         [0115]    It can be concluded form Eq. (7) that v x  and v y  can be measured simultaneously. However, sensing signal of v x  and v y  are coupled with v z  in the multi-core FBG probe  519  fabricated by the dual eccentric core fiber  63 . Contact displacements in axes x, y and z can be measured in a time-division-multiplexing way using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0116]    The multi-core FBG probe  519  can be embodied in way 3: 
         [0117]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of eccentric two-core fiber  66 , and the multi-core fiber  513  is the eccentric two-core fiber  66 . As shown in  FIGS. 6 ( e ) and ( f ) , the first core  67  is located on the negative direction of axis x with a distance of d to the center of the eccentric two-core fiber  66 ; the second core  68  is located in the center of the eccentric two-core fiber  66 . The multi-core FBG probe  519  fabricated by the eccentric two-core fiber  66  has a two-dimensional measurement capacity in axes z and x. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
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                   ( 
                   8 
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         [0118]    where, λ is the Bragg wavelength of FBGs comprised in the first core  67  and the second core  68  of the eccentric two-core fiber  66  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1  and Δλ P2  is spectrum shifts of FBGs comprised in the first core  67  and the second core  68  of the eccentric two-core fiber  66  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  67  to the center of the eccentric two-core fiber  66 ; p e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x  and v z  is contact displacements in axes x and z, respectively. 
         [0119]    It can be concluded form Eq. (8) that v x  and v z  is not coupled with each other. Contact displacements in axes x and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0120]    The multi-core FBG probe  519  can be embodied in way 4: 
         [0121]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of two-core fiber  69 , and the multi-core fiber  513  is the two-core fiber  69 . As shown in  FIGS. 6 ( g ) and ( h ) , the first core  610  and the second core  611  are located on the negative and positive direction of axis x with a distance of d to the center of the two-core fiber  69 . The multi-core FBG probe  519  fabricated by the two-core fiber  69  has a two-dimensional measurement capacity in axes z and x. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
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                   9 
                   ) 
                 
               
             
           
         
       
     
         [0122]    where, λ is the Bragg wavelength of FBGs comprised in the first core  610  and the second core  611  of two-core fiber  69  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1  and Δλ P2  is spectrum shifts of FBGs comprised in the first core  610  and the second core  611  of two-core fiber  69  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  610  and the second core  611  to the center of the two-core fiber  69 ; p e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x  and v z  is contact displacements in axes x and z, respectively. 
         [0123]    It can be concluded form Eq. (9) that v x  and v z  is not coupled with each other. Contact displacements in axes x and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0124]    The multi-core FBG probe  519  can be embodied in way 5: 
         [0125]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of eccentric three-core fiber  612 , and the multi-core fiber is the eccentric three-core fiber  612 . As shown in  FIGS. 6 ( i ) and ( j ) , the first core  613  and the second core  614  are located on the negative direction of axes x and y axis with a distance of d to the center of the eccentric three-core fiber  612 , respectively; the third core  615  is located in the center of the eccentric three-core fiber  612 . The multi-core FBG probe  519  fabricated by the eccentric three-core fiber  612  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               2 
                                
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     R 
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             y 
                           
                           = 
                           
                             
                               2 
                                
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     R 
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             z 
                           
                           = 
                           
                             - 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         3 
                                       
                                     
                                     - 
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         λ 
                                         R 
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 L 
                               
                               
                                 λ 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0126]    where, λ is the Bragg wavelength of FBGs comprised in the first core  613 , the second core  614  and the third core  615  of the eccentric three-core fiber  612  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1 , Δλ P2  and Δλ P3  is spectrum shifts of FBGs comprised in the first core  613 , the second core  614  and the third core  615  of the eccentric three-core fiber  612  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the fiber cores  613  and  614  to the center of the eccentric three-core fiber  612 ; P e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. 
         [0127]    It can be concluded form Eq. (10) that v x , v y  and v z  is not coupled with each other. Contact displacements in axes x, y and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0128]    The multi-core FBG probe  519  can be embodied in way 6: 
         [0129]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of three-core fiber  616 , and the multi-core fiber is the three-core fiber  616 . As shown in  FIG. 6 ( k )  and (l), the first core  617 , the second core  618  and the third core  619  are located out the center of the three-core fiber  616  with a distance of d to its center; the lines from the first core  617  and the second core  618  to the center of the three-core fiber  616  are beveled at an angle of 30 degree and 150 degree to the negative direction of axis x, respectively; the third core  619  is located on the negative direction of axis y. The multi-core FBG probe  519  fabricated by the three-core fiber  616  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               
                                 3 
                               
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             y 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         1 
                                       
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         3 
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             z 
                           
                           = 
                           
                             - 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         1 
                                          
                                         
                                             
                                         
                                          
                                         or 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         or 
                                          
                                         
                                             
                                         
                                          
                                         3 
                                       
                                     
                                     - 
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         λ 
                                         R 
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 L 
                               
                               
                                 λ 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0130]    where, λ is the Bragg wavelength of FBGs comprised in the first core  617 , the second core  618  and the third core  619  of the three-core fiber  616  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1 , Δλ P2  and Δλ P3  is spectrum shifts of FBGs comprised in the first core  617 , the second core  618  and the third core  619  of the three-core fiber  616  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  617 , the second core  618  and the third core  619  to the center of the three-core fiber  616 , respectively; p e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. 
         [0131]    It can be concluded form Eq. (11) that v x  and v y  can be measured simultaneously. However, sensing signal of v x  and v y  are coupled with v z  in the multi-core FBG probe  519  fabricated by the three-core fiber  616 . Contact displacements in axes x, y and z can be measured in a time-division-multiplexing way using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0132]    The multi-core FBG probe  519  can be embodied in way 7: 
         [0133]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of eccentric four-core fiber  620 , and the multi-core fiber is the eccentric four-core fiber  620 . As shown in  FIGS. 6 ( m ) and ( n ) , the first core  621 , the second core  622  and the third core  623  are located out the center of the eccentric four-core fiber  620  with a distance of d to its center; the lines from the first core  621  and the second core  622  to the center of the eccentric four-core fiber  620  are beveled at an angle of 30 degree and 150 degree to the negative direction of axis x, respectively; the third core  623  is located on the negative direction of axis y; the fourth core  624  is located in the center of the eccentric four-core fiber  620 . The multi-core FBG probe  519  fabricated by the eccentric four-core fiber  620  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               
                                 3 
                               
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             y 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         1 
                                       
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                   + 
                                   
                                     2 
                                      
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         3 
                                       
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             z 
                           
                           = 
                           
                             - 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Δλ 
                                       
                                         P 
                                          
                                         
                                             
                                         
                                          
                                         4 
                                       
                                     
                                     - 
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         λ 
                                         R 
                                       
                                     
                                   
                                   ) 
                                 
                                  
                                 L 
                               
                               
                                 λ 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0134]    where, λ is the Bragg wavelength of FBGs comprised in the first core  621 , the second core  622 , the third core  623  and the fourth core  624  of the eccentric four-core fiber  620  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1 , Δλ P2 , Δλ P3  and Δλ P4  is spectrum shifts of FBGs comprised in the first core  621 , the second core  622 , the third core  623  and the fourth core  624  of the eccentric four-core fiber  620  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  621 , the second core  622  and the third core  623  to the center of the eccentric four-core fiber  620 , respectively; P e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. 
         [0135]    It can be concluded form Eq. (12) that v x , v y  and v z  is not coupled with each other. Contact displacements in axes x, y and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0136]    The multi-core FBG probe  519  can be embodied in way 8: 
         [0137]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of four-core fiber  625  and the multi-core fiber is the four-core fiber  625 . As shown in  FIGS. 6 ( o ) and ( p ) , the first core  626  and the second core  627  are located are located on the negative and positive direction of axis x with a distance of d to the center of four-core fiber  625 , respectively; the third core  628  and the fourth core  629  are located on the negative and positive direction of axis y with a distance of d to the center of the four-core fiber  625 , respectively. The multi-core FBG probe  519  fabricated by the four-core fiber  625  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             z 
                           
                           = 
                           
                             - 
                             
                               
                                 
                                   [ 
                                   
                                     
                                       
                                         1 
                                         4 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             Δλ 
                                             
                                               P 
                                                
                                               
                                                   
                                               
                                                
                                               1 
                                             
                                           
                                           + 
                                           
                                             Δλ 
                                             
                                               P 
                                                
                                               
                                                   
                                               
                                                
                                               2 
                                             
                                           
                                           + 
                                           
                                             Δλ 
                                             
                                               P 
                                                
                                               
                                                   
                                               
                                                
                                               3 
                                             
                                           
                                           + 
                                           
                                             Δλ 
                                             
                                               P 
                                                
                                               
                                                   
                                               
                                                
                                               4 
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       Δ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         λ 
                                         R 
                                       
                                     
                                   
                                   ] 
                                 
                                  
                                 L 
                               
                               
                                 λ 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0138]    where, λ is the Bragg wavelength of FBGs comprised in the first core  626 , the second core  627 , the third core  628  and the fourth core  629  of the four-core fiber  625  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1 , Δλ P2 , Δλ P3  and Δλ P4  is spectrum shifts of FBGs comprised in the first core  626 , the second core  627 , the third core  628  and the fourth core  629  of the four-core fiber  625  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  626 , the second core  627 , the third core  628  and the fourth core  629  to the center of the four-core fiber  625 , respectively; P e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. It can be concluded form Eq. (13) that v x , v y  and v z  is not coupled with each other. Contact displacements in axes x, y and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0139]    The multi-core FBG probe  519  can be embodied in way 9: 
         [0140]    The multi-core fiber stylus  514  of the multi-core FBG probe  519  can be a section of five-core fiber  630  and the multi-core fiber is the five-core fiber  630 . As shown in  FIGS. 6 ( q ) and ( r ) , the first core  631 , the second core  632  are located on the negative and positive direction of axis x with a distance of d to the center of the five-core fiber  630 , respectively; the third core  633  and the fourth core  634  are located on the negative and positive direction of axis y with a distance of d to the center of the five-core fiber  630 , respectively; the fifth core  635  is located in the center of the five-core fiber  630 . The multi-core FBG probe  519  fabricated by the five-core fiber  630  has a three-dimensional measurement capacity in axes x, y and z. The relationship between spectrum shifts and contact displacements can be analyzed using the theory mentioned in the first purpose of the present invention and expressed as: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
                                       e 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             v 
                             x 
                           
                           = 
                           
                             
                               
                                 ( 
                                 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       3 
                                     
                                   
                                   - 
                                   
                                     Δλ 
                                     
                                       P 
                                        
                                       
                                           
                                       
                                        
                                       4 
                                     
                                   
                                 
                                 ) 
                               
                                
                               
                                 L 
                                 2 
                               
                             
                             
                               3 
                                
                               λ 
                                
                               
                                   
                               
                                
                               
                                 d 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       p 
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         [0141]    where, λ is the Bragg wavelength of FBGs comprised in the first core  631 , the second core  632 , the third core  633 , the fourth core  634  and the fifth core  635  of the five-core fiber  630  served as the multi-core fiber stylus  514  and the reference FBG  516 ; Δλ P1 , Δλ P2 , Δλ P3 , Δλ P4  and Δλ P5  is spectrum shifts of FBGs comprised in the first core  631 , the second core  632 , the third core  633 , the fourth core  634  and the fifth core  635  of the five-core fiber  630  served as the multi-core fiber stylus  514  due to contact displacements and environmental temperature drifts, respectively; Δλ R  is the spectrum shift of FBG comprised in the reference FBG  516  due to environmental temperature drifts; d is the eccentric distance from the first core  631 , the second core  632 , the third core  633  and the fourth core  634  to the center of the five-core fiber  630 , respectively; P e  is the effective photoelastic constant, typically 0.213 for a common FBG; L is the length of the multi-core FBG probe  519 ; v x , v y  and v z  is contact displacements in axes x, y and z, respectively. 
         [0142]    It can be concluded form Eq. (14) that v x , v y  and v z  is not coupled with each other. Contact displacements in axes x, y and z can be measured simultaneously using the demodulation unit  517  and the signal processing unit  518 . What is more, the differential calculation of spectrum shifts of FBGs comprised in the multi-core fiber stylus  514  and the reference FBG  516  can compensate common-mode environmental temperature drifts to ensure measurement results are not influenced by environment. 
         [0143]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part can be embodied in way 1: 
         [0144]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part is shown in  FIG. 5 . The light source  59  can be a broadband ASE source. When the light source  59  is a broadband ASE source, the reflected light signal is reflection spectra of FBGs and the demodulation unit  517  can be an optical spectrum analysis device  71  as shown in  FIG. 7 ( a ) . 
         [0145]    The optical spectrum analysis device  71  has an optical input port  72  and an electric output port  73 . The reflected spectra of FBGs comprised in the multi-core FBG probe  519  and the reference FBG  516  are analyzed by the optical spectrum analysis device  71 , and the spectrum signal is transformed into electric signal; the electric signal is received and processed in the signal processing unit  518  using the Eq. (6)˜(14) according to the embodiments of the multi-core FBG probe  519  to achieve contact displacements ΔX 1 , ΔY 1  and ΔZ 1  of the spherical tip  515  of the multi-core FBG probe  519  relative to its zero-force position uncoupled with environmental temperature drifts. 
         [0146]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part can be embodied in way 2: 
         [0147]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part is shown in  FIG. 5 . The light source  59  can be a broadband ASE source. When the light source  59  is a broadband ASE source, the reflected light signal is reflection spectra of FBGs and the demodulation unit  517  can be also a matching FBG pair demodulation system  74  which consists of a 50:50 coupler  75 , a demodulation FBG  76  and a multi-channel optical power measuring device  77  as shown in  FIG. 7 ( b ) . The matching FBG pair demodulation system  74  has an optical input port  78  and an electric output port  79 . 
         [0148]    When the measured spectrum  710  enters the optical input port  78  of the matching FBG pair demodulation system  74 , the measured spectrum  710  is divided by the  50 : 50  coupler  75  into two parts, one part  711  is received by a detector of the multi-channel optical power measuring device  77 , and the other part  711 ′ enters the demodulation FBG  76  with a fixed reflection spectrum  712 . The spectrum  711 ′ is filtered and then reflected by the demodulation FBG  76 , and the spectrum overlap  713  of the spectrum  711 ′ and the spectrum  712  enters the other detector of the multi-channel optical power measuring device  77 . When the measured spectrum shifts to  714 , the optical power ratio of the spectrum overlap  713  and  716  of the spectrum  715 ′ and the spectrum  712  to the spectrum  715  related to the measured spectrum  714  changes and is not affect by the input optical power. Therefore, the optical power ratio of the multi-channel optical power measuring device  77  can be used to measure the shift of the measured spectrum. Reflected spectra of FBGs comprised in the multi-core fiber stylus  514  of the multi-core FBG probe  519  and the reference FBG  516  are analyzed by the matching FBG pair demodulation system  74 , and the spectrum signal is transformed into electric signal; the electric signal is received and processed in the signal processing unit  518  using the Eq. (6)˜(14) according to the embodiments of the multi-core FBG probe  519  to achieve contact displacements ΔX 1 , ΔY 1  and ΔZ 1  of the spherical tip  515  of the multi-core FBG probe  519  relative to its zero-force position uncoupled with environmental temperature drifts. 
         [0149]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part can be embodied in way 3: 
         [0150]    The equipment based on multi-core FBG probe  519  for measuring structures of a micro part is shown in  FIG. 5 . The light source  59  can be a narrowband laser source. When the light source  59  is a narrowband laser source, the demodulation unit  517  can be a multi-channel optical power measuring device  717  as shown in  FIG. 7 ( c ) . The multi-channel optical power measuring device  717  has two optical input ports  718  and  719 , and an electric output port  720 . The spectrum  721  of the narrowband laser source  59  is located in the range of reflection spectra of FBGs comprised in the multi-core fiber stylus  514  of the multi-core FBG probe  519  and the reference FBG  516 . 
         [0151]    The light spectrum  721  of the narrowband laser source  59  is reflected by the measured FBG spectrum  722  and enters the multi-channel optical power measuring device  717  through the port  718 . A part of light coming from the narrowband laser source  59  enters the multi-channel optical power measuring device  717  through the port  719  for optical power reference. The optical power of the reflected light signal is in related to the reflectivity of the measured FBG at the spectrum wavelength  721  of the narrowband laser source, and varies with the spectrum shift of the measured FBG from  722  to  723 . Therefore, the optical power ratio of the multi-channel optical power measuring device  717  can be used to measure the shift of the measured spectrum. Reflected spectra of FBGs comprised in the multi-core fiber stylus  514  of the multi-core FBG probe  519  and the reference FBG  516  are analyzed by the multi-channel optical power measuring device  717 , and the spectrum signal is transformed into electric signal; the electric signal is received and processed in the signal processing unit  518  using the Eq. (6)˜( 14 ) according to the embodiments of the multi-core FBG probe  519  to achieve contact displacements ΔX 1 , ΔY 1  and ΔZ 1  of the spherical tip  515  of the multi-core FBG probe  519  relative to its zero-force position uncoupled with environmental temperature drifts.