Assembled Cantilever Fiber Touch Trigger Probe for Three-Dimensional Measurement of Microstructures

sensors

Article Assembled Cantilever Fiber Touch Trigger Probe for Three-Dimensional Measurement of Microstructures

Limin Zou *, He Ni, Peng Zhang and Xuemei Ding

Department of Automatic Test and Control, Harbin Institute of Technology, Harbin 150080, China; [email protected] (H.N.); [email protected] (P.Z.); [email protected] (X.D.) * Correspondence: [email protected]; Tel.: +86-0451-86412041 (ext. 814)

Received: 17 October 2017; Accepted: 14 November 2017; Published: 20 November 2017

Abstract: In this paper, an assembled cantilever fiber touch trigger probe was developed for three-dimensional measurements of clear microstructures. The probe consists of a shaft assembled vertically to an optical fiber cantilever and a probing sphere located at the free end of the shaft. The laser is emitted from the free end of the fiber cantilever and converges on the photosensitive surface of the camera through the lens. The position shift of the light spot centroid was used to detect the performance of the optical fiber cantilever, which changed dramatically when the probing sphere touched the objects being measured. Experimental results indicated that the sensing system has sensitivities of 3.32 pixels/µm, 1.35 pixels/µm, and 7.38 pixels/µm in the x, y, and z directions, respectively, and resolutions of 10 nm, 30 nm, and 5 nm were achieved in the x, y, and z, respectively. An experiment on micro slit measurement was performed to verify the high aspect ratio measurement capability of the assembled cantilever fiber (ACF) probe and to calibrate the effective two-point diameter of the probing sphere. The two-point probe sphere diameter was found to be 174.634 µm with a standard uncertainly of 0.045 µm.

Keywords: ﬁber optics probe; touch trigger probe; three-dimensional metrology; micro/nano coordinate measurement machine (CMM)

1. Introduction With the rapid development of the semiconductor industry, precision engineering industry, micro-system technology, and materials science, many microstructures must be measured with higher precision. The size of these nano- and microstructures ranges from nanometers to hundreds of micrometers [1]. Significant measurement problems arise because the existing surface and coordinate measuring techniques are not fully suitable for the measurement of microstructures [2,3]. The coordinate measurement machine (CMM) is composed of two main parts: the precision positioning machine and the probe. The current positioning machine has achieved sub-nano positioning resolution in the range of several tens of millimeters [4]. Therefore, the main challenge in microstructure measurement is the development of micro-CMM probes with nanoscale measurement resolution and three-dimensional (3D) measurement capability. The tactile probing system has been widely used for the measurement of microstructures [5,6]. In 1999, National Physical Laboratory (NPL) developed a small probe that had a light structure [7]. The sensors consist of a floating plane, sensitive beams, a stylus, and a probe tip. The floating plane is suspended by the cross-shape sensitive beams, and the stylus and probe tip are fabricated on the floating plane. The deflections of the stylus and probing sphere are transformed into voltage by capacitive sensors on the sensitive beams. Combined with Micro-Electro-Mechanical System (MEMS) machining techniques, some compact probes have been developed based on the floating plane structure [8–10]. The tactile probe can help achieve high-sensitivity 3D measurement. The probe

Sensors 2017, 17, 2652; doi:10.3390/s17112652 www.mdpi.com/journal/sensors Sensors 2017, 17, 2652 2 of 18 developed by METAS [11,12], based on a parallel kinematic structure of flexure hinges, has a resolution of less than 1 nm. The translational motion is separated into its XYZ components, measured by three inductive sensors. However, the probing systems generate large contact probing force, and may cause plastic deformation damage during the probing process. To reduce the contact probing force, the probing system should be adequately flexible. A novel tactile probe with variable stiffness was developed by Kinnell et al. [13]. However, a practical limitation of the probing system is the length of time required, at 20 s, to reach a steady state when the controller switches to flexible mode. Some vibrating micro-CMM probes with minimal contact force have been developed. A micro-CMM probe is driven by six piezoelectric (PZT) actuators distributed on three suspending arms [14]. Intersection with the measurement surface produces a vibration amplitude change that can be detected by sensor PZTs. Though the performance of this probing system is satisfactory, fabricating the stylus is difficult. The probe manufacturing process is intricate and requires several rounds of electroplating, lithography, and high assembly accuracy. If the micro probe is not precisely attached to the center of the floating plate, the dissymmetrical structure will result in output non-linearity. The vibration can also be produced by a quartz tuning fork [15,16]. The optical fiber, about 1 mm long, is mounted on the sensing arm as the probe tip [15]. The resonance parameters of the quartz tuning fork are extremely sensitive to external forces. The probe has achieved sub-nanometer resolution in three directions. Since the probe is working in a vibrating state, the length of the probe should not be too long to ensure that the probe can vibrate stably. So, the length of the fiber limits its measurement range along the z-axis and it has difficultly measuring a high aspect ratio microstructure. A 700:1 high aspect ratio probe made by carbon fiber with diameter of 7 µm was developed [16]. However, the probe shanks need to be carefully aligned with the direction of oscillation of the tuning fork to achieve a planar oscillatory motion, making the probe system set up difficult. Some micro-CMM probes with high precision, based on reflected beam detection, have been applied to 3D measurement [17–19]. A reflective plane is fabricated at the end of the probe stylus. The tilt measuring system and the interferometer are used to detect the deflection of the mirror and thus of the probe stylus. The detection method, based on detecting reflected light, can achieve high nanoscale measurement resolution, but manufacturing a reflected membrane on a small probe is challenging. Additionally, the entire system is complicated, and the optical path calibration is difficult. Dai et al. developed an ultra-precision reflected light detection method based on an atom force microscope (AFM). The AFM achieves 3D measurement with a shaft fabricated on the AFM cantilever beam [20,21]. The detection principle of the micro-CMM probe system is the same as a commercial AFM, meaning both have the same measurement resolution. The advantage of the assembled cantilever structure is that its detection optical path is located above the objects to be measured, and the structures of the objects have little effect on measurement. Although the probing system has an excellent measurement performance, the measurement range for depth is still limited by the length of the shaft, which is 0.2 to 2 mm. Optical fiber has been widely applied in the field of microstructure measurement as its advantages include small measuring force, low cost, and easy processing. Some high-precision fiber probes have already been commercialized [22]. In 2001, Physikalisch-Technische Bundesanstalt (PTB) developed an opto-tactile sensor [23]. However, due to the shadowing effect, this probe cannot detect high aspect ratio structures. Based on the probe, a fiber probe that can measure the inner-dimensions of microstructures was developed [24]. To obtain higher resolution and 3D detection capability, this probe was later combined with fiber Bragg grating [25]. However, the fiber Bragg grating probe is expensive and difficult to manufacture. Stone et al. [26] reported a fiber deflection probing (FDP) method for CMM to inspect the profile of micro cavities. To achieve extremely high optical path magnification in limited measurement space, a fiber probe based on micro focal-length collimation, in which an optical fiber stylus acts as a micro focal-length cylindrical lens, was proposed in 2010 [27]. The method was then improved to include 3D measurement capability [28,29]. The probing system is capable of Sensors 2017, 17, 2652 3 of 18 decoupling 3D tactility, but the devices are too complicated to set up. The setup and calibration of the optical path requires high precision. Sensors 2017, 17, 2652 3 of 18 Many probing systems perform satisfactorily in probing experiments, but most of them have complicatedMany structures probing systems or detection perform systems. satisfactorily To address in probing this issue,experiments, an ACF but probe most is of proposed them have in this paper.complicated The ACF probestructures has or high detection detection systems. performance To address and this isissue, compact, an ACF inexpensive, probe is proposed easy toin fabricate,this and haspaper. a high The ACF signal probe to noise has high ratio detection (SNR) comparedperformance to and the is other compact, probes. inexpensive, easy to fabricate, and has a high signal to noise ratio (SNR) compared to the other probes. 2. Principle 2. Principle The structure of the ACF touch trigger probe is shown in Figure1. The ACF probe consists of a fixed block,The an structure optical of fiber the ACF cantilever, touch trigger a shaft, probe and is a shown probing in Figure sphere. 1. TheThe ACF shaft probe is glued consists to an of opticala fixed block, an optical fiber cantilever, a shaft, and a probing sphere. The shaft is glued to an optical fiber cantilever. The probing sphere is located at the free end of the shaft, which can be glued to the fiber cantilever. The probing sphere is located at the free end of the shaft, which can be glued to the shaft or directly fabricated on the shaft through melting. The advantage of the assembled cantilever shaft or directly fabricated on the shaft through melting. The advantage of the assembled cantilever structurestructure of the of probethe probe is that is that its detectionits detection optical optical path path is is located located above above thethe objectsobjects to be measured, and the structureand the structure of the objects of the hasobjects little has effect little oneffect the on measurement the measurement result. result. Accordingly, Accordingly, the the probe probe system can measuresystem can high-aspect-ratio measure high-aspect-ratio microstructures. microstructures.

Figure 1. Structure and measurement principle of the assembled cantilever fiber (ACF) probe. Figure 1. Structure and measurement principle of the assembled cantilever fiber (ACF) probe. The ACF touch trigger probe optical path is simple. The laser beam is coupled into the optical Thefiber ACFcantilever touch and trigger transmitted probe from optical the path fiber isca simple.ntilever. TheThe lasertransmitted beam beam is coupled converges into on the the optical fiberphotosensitive cantilever and surface transmitted of the charge from couple the fiber device cantilever. (CCD) camera The transmitted by lens. The beamfree end converges of the fiber on the cantilever generates a displacement when the probing sphere touches the object to be measured. photosensitive surface of the charge couple device (CCD) camera by lens. The free end of the fiber Therefore, the deflections of the shaft and probing sphere are transformed into the displacement of cantilever generates a displacement when the probing sphere touches the object to be measured. the centroid of the light spot, which can be measured by the CCD camera. The detection method can Therefore,be applied the deflections to measure ofmicrostruc the shafttures and without probing complicated sphere are transformedoperation and into its signal the displacement to noise ratio of the centroid(SNR) of is the high. light The spot, transfer which function canbe of measuredthe optical path by the can CCD be expressed camera. as: The detection method can be applied to measure microstructures without complicated operation and its signal to noise ratio (SNR) SSc=/ is high. The transfer function of the optical pathCCD can op be free expressed p , as: (1)

where, SCCD is the centroid position displacement of the light spot image of CCD, Sfree is the SCCD = βop · Sfree/cp, (1) displacement of the free end of the fiber cantilever, and op is the magnifying transfer coefficient of where, S is the centroid position displacement of the light spot image of CCD, S is the the opticalCCD path, which can be expressed as op=/ll 2 1 . Therein, l1 is the distance of the free endfree of displacement of the free end of the fiber cantilever, and βop is the magnifying transfer coefficient of the the cantilever to the lens, and l2 is the distance of the lens to CCD camera photosensitive. cp is the optical path, which can be expressed as βop = l2/l1. Therein, l1 is the distance of the free end of the cantileverpixel size to theof the lens, CCD and camera.l2 is the Here, distance cp is 3.75 of the μm/pixel. lens to CCD camera photosensitive. cp is the pixel size of theFor CCD the ACF camera. probe Here, systemcp isto 3.75haveµ highm/pixel. displacement sensitivity, it requires a large magnifying Fortransfer the coefficient. ACF probe However, system the to have increase high in displacementthe magnifying sensitivity,transfer coefficient it requires results a in large the volume magnifying transferenlargement coefficient. of the However, measuring the system. increase To achieve in the magnifying high displacement transfer sensitivity coefficient with results a size limitation, in the volume enlargementthe lens with of the a micro measuring focal length system. should To achievebe applied high in the displacement ACF probe system. sensitivity with a size limitation, the lens with a micro focal length should be applied in the ACF probe system.

Sensors 2017, 17, 2652 4 of 18 Sensors 2017, 17, 2652 4 of 18 Sensors 2017, 17, 2652 4 of 18 3.3. Analysis Analysis and and Design Design of of the the Probe Probe 3. Analysis and Design of the Probe 3.1.3.1. Displacement Displacement Transfer Transfer Function Function of of the the Probe Probe 3.1. Displacement Transfer Function of the Probe ForFor the ACFACF probe,probe, different different directions directions of contactof contac forcet force result result in different in different deflections deflections of the probingof the probingsphereFor and spherethe fiber ACF and cantilever. probe, fiber cantilever.different Therefore, directions Therefore, analyzing of analyz the contac effectingt force ofthe the effect result 3D contactof inthe different 3D force contact acting deflections force on the acting probing of theon theprobingsphere probing of sphere the sphere shaft and of is fiber essential.the cantilever.shaft is essential. Therefore, analyzing the effect of the 3D contact force acting on the probingTheThe structure structure sphere diagramof diagram the shaft and and is photo essential. photo of of the the probe probe are are shown shown in in Figure Figure 22,, where aa isis the the distance distance betweenbetweenThe the thestructure shaft shaft and diagram the fixedfixed and endend photo ofof the theof fiberthefiber probe cantilever, cantilever, are shownb bis is the the in length lengthFigure of of2, the thewhere fiber fiber cantilever,a cantilever,is the distance and andl is lbetween theis the length length the of shaft the of shaft. theand shaft.the As fixed shown As endshown in Figureof thein fiberFigure2a, the cantilever, contact2a, the forcecontact b is the along forcelength the along threeof the orthogonalthe fiber three cantilever, orthogonal directions and directionslof is x,the y, andlength of zx, are y,of and loadedthe zshaft. are on loaded theAs shown probing on the in probin sphere, Figureg andsphere, 2a, anythe and othercontact any direction otherforce directionalong of the the contactof three the contact forceorthogonal can force be candirectionssynthesized be synthesized of withx, y, and these with z are threethese loaded directions.three on directions. the probin g sphere, and any other direction of the contact force can be synthesized with these three directions.

(a) (b) (a) (b) Figure 2. Structure of the probe: (a) structure diagram of the ACF probe; and (b) photograph of the Figure 2. Structure of the probe: (a) structure diagram of the ACF probe; and (b) photograph of the ACFFigure probe. 2. Structure of the probe: (a) structure diagram of the ACF probe; and (b) photograph of the ACF probe. ACF probe. To determine the relationship between the displacement of the probe and the contact force, the ACF ToprobeTo determine determine was divided the the relationship relationship into two parts between between for analysis: the the displa displacement oncemente part is of ofthe the the shaft probe probe (Figure and and the the3b), contact contact and the force, force, other the the is theACFACF cantilever probe probe was was beam divided divided (Figure into into 3c). two two In partsparts Figure for for 3, analysis: analysis: the solid on one arrowse part part isrepresent is the the shaft shaft the (Figure (Figure direction 33b),b), of and the the force, other the is dashedthethe cantilever cantilever arrows beam beamindicate (Figure (Figure the direction 33c).c). In Figure of the 33, ,displa thethe solidsocement,lid arrowsarrows the representcurverepresent arrows thethe directionrepresentdirection of ofthe thethe direction force,force, thethe of thedasheddashed moment, arrows arrows and indicate indicate the broken the the directiondirection line indicates of of the the the displa displacement, deflectioncement, of the the the curve curve probe. arrows arrows represent represent the the direction direction of of thethe moment, moment, and and the the broken broken line line indicates indicates the the deflection deﬂection of of the probe.

(a) (b)(c) (a) (b)(c) Figure 3. The ACF probe was split and analyzed separately: (a) the contact force along the x-axis subjectFigure to3. probingThe ACF sphere; probe (wasb) the split deflection and analyzed of the shaft; separately: and (c )( thea) the deflection contact offorce the cantilever.along the x-axis Figure 3. The ACF probe was split and analyzed separately: (a) the contact force along the x-axis subject to probing sphere; (b) the deflection of the shaft; and (c) the deflection of the cantilever. Thesubject relationship to probing between sphere; (b displacement) the deflection ofand the force shaft; in and the (c x) thedirection deflection was of analyzed. the cantilever. For the shaft of theThe ACF relationship probe, it can between be treated displacement as a traditio andnal force single-ended in the x direction fixed fiber was cantilever analyzed. beam For the and shaft the forceof the Thein ACF the relationship probe,x direction it can between is be subject treated displacement to as the a traditio free and endnal force of single-ended the in theshaft x direction(Figure fixed fiber3b). was The analyzed.cantilever displacement Forbeam the and shaftof the of forcethe ACF in the probe, x direction it can be is treated subject as to a traditionalthe free end single-ended of the shaft fixed (Figure fiber 3b). cantilever The displacement beam and the of force the probing sphere dx,x1 can be obtained by applying deflection equation of cantilever beam: probing sphere dx,x1 can be obtained by applying deflection equation of cantilever beam:

Sensors 2017, 17, 2652 5 of 18 in the x direction is subject to the free end of the shaft (Figure3b). The displacement of the probing sphere ∆dx,x1 can be obtained by applying deﬂection equation of cantilever beam:

F l3 ∆d = x , (2) x,x1 3EI where E and I are the Young’s modules and polar moment of the inertia of the fiber, respectively. The polar moment of the inertia of the fiber is I = πd4/64, where d is the fiber diameter. For the cantilever of the ACF probe, it can also be treated as a traditional single-ended fixed fiber cantilever beam while the moment Mx is subjected to the free end. Mx can be expressed as Mx = Fx · l. The moment Mx is located on the fixed point between the shaft and the cantilever. As shown in Figure3c, the moment leads to a displacement ∆Dx,z of the free end of the cantilever and thus leads to 0 a rotation θ and a displacement ∆dx,z of the shaft along the z-axis. By applying deflection equation of 0 cantilever, the displacement ∆Dx,z, ∆dx,z , and rotation θ can be expressed as:

F la2 ∆d 0 = x , (3) x,z 2EI F la a ∆D = x (b − ), (4) x,z EI 2 F la θ = x . (5) EI The rotation of the shaft will lead to a displacement along the x-axis of the probing sphere:

F l2a ∆d = θ × l = x . (6) x,x2 EI The total displacement of the probing sphere consists of two parts. One is obtained by analyzing the shaft, the other is obtained by analyzing the cantilever. The total displacement of the probing sphere and the free end of the cantilever can be expressed as:   ∆D = 0 ∆d = ∆d + ∆d  x,x  x,x x,x1 x,x2 ∆Dx,y = 0 ∆dx,y = 0 . (7)   0  ∆Dx,z = ∆Dx,z  ∆dx,z = ∆dx,z

According to Equations (2) and (7), the relationship between the displacement and force along the x-axis can be expressed as:

  3 2 ∆D = 0 ∆d = Fxl + Fxl a  x,x  x,x 3EI EI ∆Dx,y = 0 ∆dx,y = 0 , (8) F la 2  ∆D = x (b − a )  Fxla x,z EI 2 ∆dx,z = 2EI where ∆Di,j is the displacement of the free end of the cantilever along axis j (j = x, y, or z) in the situation of force being applied to the probing sphere along axis i (i = x, y, or z). ∆di,j is the displacement of the probing sphere along axis j (j = x, y or z) when force is loaded on the probing sphere along axis i (i = x, y, or z). The derivation method can also be applied to analyze the displacement of the probing sphere and free end of the cantilever when force is loaded on probing sphere along the y- or z-axis. The relationship between the displacement and the contact along the y-axis can be expressed as:    ∆Dy,x = 0  ∆dy,x = 0  2  3 3 2 Fy a Fy a Fyl Fyl a(1+υ) ∆Dy,y = (3b − a) ∆dy,y = + + . (9)  6EI  3EI 3EI EI  ∆Dy,z = 0  ∆dy,z = 0 Sensors 2017, 17, 2652 6 of 18

The relationship between the displacement and the contact force along the z-axis can be expressed as:   ∆D = 0 ∆d = 0  z,x  z,x ∆Dz,y = 0 ∆dz,y = 0 . (10) 2 3  Fz a  Fz a ∆Dz,z = 6EI (3b − a) ∆dz,z = 3EI In reality, the contact force can be expressed as a stack of these three directions. Therefore, according to Equations (8)–(10), the relationship function between the probing sphere and contact force can be expressed as Equation (11), and the relationship function between the displacement of the free end of the cantilever and contact force can be expressed as Equation (12).

   3 2   ∆dx 2l + 6l a 0 0 Fx   1  3 3 2    ∆dy  =  0 2a + 2l + 6l a(1 + v) 0  Fy , (11) 6EI 2 3 ∆dz 3a l 0 2a Fz      0 0 0 0 Fx   1  2    ∆Dy  =  0 a (3b − a) 0  Fy , (12) 6EI 2 ∆Dz al(6b − 3a) 0 a (3b − a) Fz T T where ∆dx ∆dy ∆dz is the displacement of the probing sphere, 0 ∆Dy ∆Dz is the displacement of T the free end of the fiber cantilever, Fx Fy Fz is the contact force along the three axes to which the probing sphere is subjected, and v is the Poisson ratio of the fiber. Because the deflection of the fiber cantilever along the axis x is small, we considered that the displacement of the free end of the cantilever only exists in the y-z plane, and thus, the displacement of T the free end of the fiber cantilever can be expressed as 0 ∆Dy ∆Dz . The displacement of the probe tip in the x, y, and z directions transforms into the displacement of the free end of the fiber cantilever in the y and z directions. The detection system makes it impossible to distinguish between a displacement along the x axis or the z axis, meaning it can only be used as a touch trigger probe. However, the ACF probe can sense the force from three directions and can be used for 3D measurement. In most cases, the basic profiles of the samples are already known, according to the blueprints or observation. So, the contact directions can be predicted when the ACF probe, combined with a 3D positioning stage, is applied to measure the objects. Although the trigger signal cannot distinguish the contact direction, it has little influence when measuring objects with clear structures. From Equations (11) and (12), the displacement transfer function between the probing sphere and the free end of the cantilever can be expressed as:     0 0 0   0 ∆dx 2 3   =  0 3a b−a 0    ∆Dy   2a3+2l3+6l2a(1+v)  ∆dy . (13)  3a(b−a)  ∆Dz b a − ∆dz 4l2+12la 0 1.5 / 0.5

From Equation (13), the displacement transfer function is only related to the structure parameters of the probe.

3.2. Finite Element Analysis of the Probe A ﬁnite element analysis for the probe has also been performed to verify the correctness of the Equation (13). The parameters listed in Table1 have been used, where, the theoretical transfer coefﬁcients are calculated by substituting the structure parameters v, b, a and l into the Equations (11) and (12). Sensors 2017, 17, 2652 7 of 18

Table 1. The parameters of the probe.

Parameter Value E Young’s modulus of the optical fiber (Gpa) 80 d Diameter of the optical fiber (µm) 125 b (mm) 4 a (mm) 2 l (mm) 2 Diameter of the probing sphere (µm) 150 Contact force (µN) 20 v Poisson ratio of the fiber 0.16 Theoretical transfer coefficient (∆Dz/∆dx) 0.1875 Theoretical transfer coefficient (∆Dy/∆dy) 0.4562 Theoretical transfer coefficient (∆Dz/∆dz) 2.500

The contact force is applied to the probing sphere in the x, y and z directions. The displacement of the probing sphere and the free end of the ﬁber cantilever is calculated by ﬁnite element simulation, therefore, the simulation displacement transfer function between the probing sphere and the free end of the cantilever can be expressed as:      0 0 0 0 ∆dx       ∆Dy  =  0 0.4568 0  ∆dy . (14) ∆Dz 0.1879 0 2.502 ∆dz

Compared with the theoretical transfer coefficient in Table1, it can be found that the simulation results are very close to the theoretical calculation. Thus, the correctness of Equation (13) can been verified. The reason for the small discrepancy between the simulation and the theoretical solution is that the contact point is on the sphere surface and not in the middle of the fiber in the simulation. By loading a step-increasing displacement to the probing sphere, the displacement relationship between the probing sphere and the free end of the cantilever is shown in Figure4. It is obvious that the transfer coefficient along the axis z is the highest, and the transfer coefficient along axis y is the lowest. It also indicates that the detection sensitivity is highest in the z direction and the lowest in the ySensors direction. 2017, 17, 2652 8 of 18

FigureFigure 4. 4.The The displacement displacement relationship relationship of of the the probing probing sphere sphere and and the the free free end end of of the the ﬁber fiber cantilever cantilever obtainedobtained by by ﬁnite finite element element analysis. analysis.

3.3. Optimal Design of the Probe To obtain high detection sensitivity, the ACF probe structure was optimized. The effects of the structure parameters were analyzed, mainly including the distance between the shaft and the fixed end of the cantilever (a), the length of the cantilever (b), and the length of the shaft (l). T According to Equation (11), when the contact force is Fx 0 0 , the probing sphere has a displacement along axes x and z, the displacement of the two axes can be expressed as 32 2 dllaFx,x(2  6 ) x and dalFx,z3 x , respectively, and their relationship can be expressed as:

3a2 dd= . (15) x,z26lla2  x According to Equations (1), (13) and (15), the total displacement transfer function and transfer coefficients can be expressed as:

Sdcx,z=/ op x x p  Sdcy,yopyyp=/ , (16)  Sdcz,z=/ op z z p

 32mm x  2  26nnm  mm2 3  y  33 2 , (17)  226(1)mnmnv   31m  z   2

where Si,j the centroid position displacement of the light spot image of the CCD along axis j (j = x

or z), when the force is loaded on the probing sphere along axis i (i = x, y, or z); i is the transfer coefficient along axis i (i = x, y or z); m is the relative position of the shaft fixing point; and n is the relative length of the shaft, and they can be expressed as m = a/b and n = l/b. The two parameters m

Sensors 2017, 17, 2652 8 of 18

3.3. Optimal Design of the Probe To obtain high detection sensitivity, the ACF probe structure was optimized. The effects of the structure parameters were analyzed, mainly including the distance between the shaft and the ﬁxed end of the cantilever (a), the length of the cantilever (b), and the length of the shaft (l). T According to Equation (11), when the contact force is [Fx 0 0] , the probing sphere has a displacement along axes x and z, the displacement of the two axes can be expressed as 3 2 2 ∆dx,x = (2l + 6l a)Fx and ∆dx,z = 3a lFx, respectively, and their relationship can be expressed as:

3a2 ∆d = ∆d . (15) x,z 2l2 + 6la x

According to Equations (1), (13) and (15), the total displacement transfer function and transfer coefﬁcients can be expressed as:  ∆S = β β ∆d /c  x,z op x x p ∆Sy,y = βopβy∆dy/cp , (16)   ∆Sz,z = βopβz∆dz/cp

 3m(2−m)  βx = 2  2n +6nm m2(3−m) βy = 3 3 2 , (17)  2m +2n +6mn (1+v)  3/m−1 βz = 2 where ∆Si,j the centroid position displacement of the light spot image of the CCD along axis j (j = x or z), when the force is loaded on the probing sphere along axis i (i = x, y, or z); βi is the transfer coefficient along axis i (i = x, y or z); m is the relative position of the shaft fixing point; and n is the relative length of the shaft, and they can be expressed as m = a/b and n = l/b. The two parameters m and n are quite important, as they determine the sensitivity of the probe. The relationship curve between transfer coefficient βi and m and n are shown in Figure5. Figure5a,b show that a small value of n results in high radial sensitivity of the ACF probe. However, the value of n cannot be set as small as possible. To ensure the depth of the microstructures can be detected, the value of l is determined. Considering that n = l/b, the value of b will increase with the decrease in n, which decreases the natural frequency of the ACF probing. Figure5a,b also indicate that optimal solutions exist for βx and βy in the interval of m from 0 to 1. The appropriate value of m should be selected according to the measurement process. If the measurement process requires high sensitivity along the x-axis, the corresponding values of m and n should be selected according to the relationship curve in Figure5a. Figure5c indicates that the axial transfer coefficient βz is approximately inversely proportional to the value of m, so that a decrease in the value of m leads to an increase in axial detection sensitivity. Another important parameter of the ACF probe is the diameter of the probing sphere that determines the measurable diameter of the micro-hole. A smaller sphere diameter can be obtained by etching the fiber to expand the measuring range. Sensors 2017, 17, 2652 9 of 18

and n are quite important, as they determine the sensitivity of the probe. The relationship curve Sensors 2017, 17, 2652 9 of 18 between transfer coefficient i and m and n are shown in Figure 5.

(a)

(b)

(c)

Figure 5. The relationship between parameters m, n, and the transfer coefficient: (a) the curve of the Figure 5. The relationship between parameters m, n, and the transfer coefficient: (a) the curve of the x-axis transfer coefficient; (b) the curve of the y-axis transfer coefficient; and (c) the curve of the z-axis x-axis transfer coefficient; (b) the curve of the y-axis transfer coefficient; and (c) the curve of the z-axis transfer coefficient. transfer coefficient.

Sensors 2017, 17, 2652 10 of 18

4. Experiment

4.1. Fabrication of the ACF Probe The single mode fiber with an operating wavelength of 532 nm was used to fabricate the ACF probe. A melting probing sphere was fabricated using electric discharge machining (AV6471A, The 41st Institute of China Electronics Technology Group Corporation, Qingdao, China) at the end of the fiber whose coating layer had been stripped. The optical fiber, with its end cut flat, was placed between the discharge electrodes. The high voltage discharges generated by the electrodes break down the air to create a high temperature arc, and the instantaneous high temperature melted the end of the fiber. The melted fiber ends condensed into a sphere under surface tension. The process factors during the fabrication of the probe sphere were as follows: pre-melting time of 85 ms, melting time of 85 ms, pre-melting current of 40 mA, and melting current of 40 mA. Then, the fiber with the sphere was cut to a length of 5 mm using a fiber cleaver as the shaft. The shaft was assembled vertically to the cantilever using cyanoacrylate adhesive. The distance between the fixed point and the free end of the cantilever was 5 mm. Assembly operation was performed under a video measuring instrument. After the glue was completely cured, the probe was carefully fixed on the mechanical part, and the distance between the fixing point and the free end of the cantilever was about 10 mm. The last step was to fabricate the fiber patch cables on the other end of the cantilever to connect the fiber laser, finishing the fabrication of the ACF probe. The length of parameters b, a, and l of the probe were 10 mm, 5 mm, and 5 mm, respectively, and thus m = 0.5 and n = 0.5. The glue used in the fabrication process of the ACF probe was chosen carefully because the elasticity of the glue influences the displacement of the shaft. In Figure6, the blue line illustrates the influence of Young’s modulus of the curved glue on the x-axis transfer coefficient, and other two axes have similar curves. The red line indicates the transfer coefficient of ideal structure of the ACF probe. The ideal structure refers to the cantilever beam and the shaft being integrated without glue. The parameters listed in Table1 were used for finite element analysis. By loading the same displacement along the x-axis to the probing sphere of the probe with different glues, the transfer coefficient was calculated using finite element simulation. From Figure6, when the Young’s modulus of the cured glue is larger than 3000 MPa, the x-axis transfer coefficient is stable and is close to the coefficient of the probe with the ideal structure. The cyanoacrylate adhesive (V-100, Tong Shen Enterprise Co., Ltd, Kaohsiung, China) that was used in experiments has a Young’s modulus between 3000 and 5000 MPa. Assuming that the Young’s modulus of the glue is 3000 MPa, the x-axis transfer coefficient of the probe is 1.04 by finite element analysis, while the x-axis transfer coefficient is 1.07. Because the value of the two coefficients are close, the cyanoacrylate adhesive was used to glue the Sensors 2017, 17, 2652 11 of 18 shaft and the cantilever.

Figure 6. The relationship between the Young’s modulus of the cured glue. Figure 6. The relationship between the Young’s modulus of the cured glue.

4.2. Experimental Setup The ACF probe system was set up. All experimental equipment were placed on the vibration isolation platform. A glass cover was used to reduce the influence of air. The wavelength of the fiber- couple laser source was 532 nm. The CCD camera with 1288 × 964 pixels and pixel size of 3.75 μm (FL3-GE-13S2M-C, FLIR Inc., Wilsonville, OR, USA) were used to detect the shift in the light spot. The mechanical structure was designed to be used in conjunction with the ACF probe for measurement. The objective lens with an effective focal length (EFL) of 18 mm and numerical aperture (NA) of 0.25 (RMS10X, Olympus Corporation, Tokyo, Japan) was screwed into the

mechanical structure, and could obtain an optical magnifying coefficient op of around 11. A micro displacement stage was constructed, in which large range coarse positioning was achieved with a 3D micrometer screw mechanism, and nanometer positioning was achieved with a 3D piezoelectric nano positioning stage, assembled using a z nano positioning stage (PZ-38, piezosystem jena GmbH, Jena, Germany) and x-y nano positioning stages (PXY-100, piezosystem jena GmbH, Jena, Germany). The z stage was stacked onto the x-y stage. The precision gauge block was fixed onto the nano positioning stage to touch the ACF probe. The experimental set-up was configured as shown in Figure 7.

(a) (b)

Sensors 2017, 17, 2652 11 of 18

Sensors 2017, 17, 2652 Figure 6. The relationship between the Young’s modulus of the cured glue. 11 of 18

4.2. Experimental Setup 4.2. Experimental Setup The ACF probe system was set up. All experimental equipment were placed on the vibration The ACF probe system was set up. All experimental equipment were placed on the vibration isolation platform. A glass cover was used to reduce the influence of air. The wavelength of the fiber- isolation platform. A glass cover was used to reduce the influence of air. The wavelength of the couple laser source was 532 nm. The CCD camera with 1288 × 964 pixels and pixel size of 3.75 μm fiber-couple laser source was 532 nm. The CCD camera with 1288 × 964 pixels and pixel size of (FL3-GE-13S2M-C, FLIR Inc., Wilsonville, OR, USA) were used to detect the shift in the light spot. 3.75 µm (FL3-GE-13S2M-C, FLIR Inc., Wilsonville, OR, USA) were used to detect the shift in the The mechanical structure was designed to be used in conjunction with the ACF probe for light spot. The mechanical structure was designed to be used in conjunction with the ACF probe measurement. The objective lens with an effective focal length (EFL) of 18 mm and numerical for measurement. The objective lens with an effective focal length (EFL) of 18 mm and numerical aperture (NA) of 0.25 (RMS10X, Olympus Corporation, Tokyo, Japan) was screwed into the aperture (NA) of 0.25 (RMS10X, Olympus Corporation, Tokyo, Japan) was screwed into the mechanical mechanical structure, and could obtain an optical magnifying coefficient op of around 11. A micro structure, and could obtain an optical magnifying coefficient βop of around 11. A micro displacement stagedisplacement was constructed, stage was in constructed, which large in range which coarse large positioning range coarse was positioning achieved was with achieved a 3D micrometer with a 3D screwmicrometer mechanism, screw and mechanism, nanometer and positioning nanometer was positioning achieved was with achieved a 3D piezoelectric with a 3D piezoelectric nano positioning nano stage,positioning assembled stage, using assembled a z nano using positioning a z nano stagepositi (PZ-38,oning stage piezosystem (PZ-38, piezosystem jena GmbH, jena Jena, GmbH, Germany) Jena, andGermany) x-y nano and positioning x-y nano stagespositioning (PXY-100, stages piezosystem (PXY-100, piezosystem jena GmbH, Jena,jena GmbH, Germany). Jena, The Germany). z stage was The stackedz stage ontowas stacked the x-y onto stage. the The x-y precision stage. The gauge precisio blockn gauge was fixedblock ontowas fixed the nano onto positioningthe nano positioning stage to touchstage theto touch ACF probe.the ACF The probe. experimental The experimental set-up was set-up configured was configured as shown as in shown Figure7 in. Figure 7.

(a) (b)

Figure 7. Experimental setup of the ACF probing system: (a) experimental schematic diagram of the probing system; and (b) experimental setup of the ACF probing system.

4.3. Probe Performance Experiment Experiments were performed to evaluate the performance of the ACF ﬁber probe. The precision gauge block moves along three directions to touch the probing sphere. The output response curves of the probe along the x, y, and z axes are shown in Figure8. The sampling frequency of the CCD camera was one frame per 10 nm. The size of the light spot on the CCD camera was more than 200 × 200 pixels and the spot shape was round with good quality. The center-of-gravity algorithm was applied to calculate the position of the light spot centroid and a 0.01-pixel resolution of the CCD camera output was achieved. In Figure8, section I shows when the block has not yet touched the probing sphere. At this time, the ACF probe is in the non-triggered state, and the centroid position Sensors 2017, 17, 2652 12 of 18

Figure 7. Experimental setup of the ACF probing system: (a) experimental schematic diagram of the probing system; and (b) experimental setup of the ACF probing system.

4.3. Probe Performance Experiment Sensors 2017Experiments, 17, 2652 were performed to evaluate the performance of the ACF fiber probe. The precision12 of 18 gauge block moves along three directions to touch the probing sphere. The output response curves ofof the the light probe spot along remains the x, constant. y, and z Inaxes section are shown II, the in outputs Figure of8. theThe CCD sampling camera frequency change suddenly,of the CCD causedcamera by was the one interfacial frame per adhesive 10 nm. force. The size The of interfacial the light spot adhesive on the force CCD resulted camera fromwas more the co-action than 200 × of200 the pixels van der and Waals the spot force, shape capillary was round force, andwith other good micro-forces quality. The [9center-of-gravity]. In section III, algorithm the centroid was positionapplied of to the calculate light spot the changed position linearly of the light with thespot increasing centroid and displacement a 0.01-pixel of theresolution nano positioning of the CCD stage.camera Now, output the probe was wasachieved. in the over-triggeredIn Figure 8, section state. I The shows detection when sensitivity the block washas determinednot yet touched by the the curveprobing slope sphere. of the curveAt this fitted time, line the inACF section probe III. is The in th detectione non-triggered sensitivity state, of and the probethe centroid along the position x-axis of wasthe 3.32 light pixels/ spot remainsµm, and constant. the sensitivity In section of the II, probethe outputs along of the the y andCCD z camera axes were change 1.35 suddenly, pixels/µm caused and 7.38by pixels/the interfacialµm, respectively. adhesive force. What The is more, interfacial the probe adhesive has a force long linearresulted trigger from range the co-action more than of the 4 µ mvan thatder is Waals large enoughforce, capillary for the touchforce, and trigger other measurement. micro-forces The[9]. In sensitivities section III, of the the centroid probe wereposition highest of the inlight the z spot direction changed and linearly the lowest with in the the increasing y direction, disp correspondinglacement of the to nano the displacement positioning stage. relationship Now, the curvesprobe shown was in in the Figure over-triggered4. state. The detection sensitivity was determined by the curve slope of theThe curve position fitted ofline the in touch section trigger III. The point detection is so important sensitivity that of it shouldthe probe be determined along the x-axis as accurately was 3.32 aspixels/ possible.μm, Byand adopting the sensitivity the linear of fittingthe probe method, along the the effect y and of z the axes position were 1.35 vibration pixels/ ofμ them and touch 7.38 triggerpixels/ pointμm, wasrespectively. eliminated. What The is centroid more, the position probe ofhas the a non-triggeredlong linear trigger state range and the more centroid than position4 μm that ofis the large over-triggered enough for the were touch fitted trigger to two measurement. straight lines, The and sensitivities the intersection of the ofprobe the twowere straight highest lines in the wasz direction seen as the and touch the lowest trigger in point. the y Asdirection, shown corre in Figuresponding8, the to green the displacement solid circle is therelationship trigger point curves calculatedshown in using Figure the 4. linear fitting method. TheThe repeatability position of ofthe the touch ACF trigger probe point along is the so x,important y, and z axesthat wasit should also tested.be determined At the beginning as accurately of thisas experiment,possible. By the adopting gauge blockthe linear was controlledfitting method, to move the to effect the non-triggered of the position state, vibration corresponding of the touch to sectiontrigger I inpoint Figure was8, andeliminated. then was The moved centroid along position each direction of the to non-triggered touch the probe state repeatedly and the withcentroid a displacementposition of the of 2over-triggeredµm. Figure9 showswere fitted the repeatability to two straight results lines, of and 20 repetitionsthe intersection along of the the x,two y, andstraight z axes.lines The was vertical seen as axis the indicates touch trigger the offsets point. from As shown the average in Figure displacement 8, the green value solid of circle the trigger is the point.trigger Thepoint standard calculated deviations using ofthe the linear x, y, fitting and z directionsmethod. were 20.6 nm, 54.4 nm, and 9.4 nm, respectively.

(a)

Figure 8. Cont.

Sensors 2017, 17, 2652 13 of 18

Sensors 2017, 17, 2652 13 of 18 Sensors 2017, 17, 2652 13 of 18

(b)

(c)

Figure 8. Output response curves of the probe: (a) Gauge block moves along the x-axis; (b) Gauge block moves along the y-axis; and (c) Gauge block moves along the z-axis.

The repeatability of the ACF probe along the x, y, and z axes was also tested. At the beginning of this experiment, the gauge block was controlled to move to the non-triggered state, corresponding to section I in Figure 8, and then was moved along(c )each direction to touch the probe repeatedly with a displacementFigure 8. Output of 2 μ responsem. Figure curves 9 shows of the the probe: repeatability (a) Gauge result blocks moves of 20 repetitionsalong the x-axis; along (b the) Gauge x, y, and Figure 8. Output response curves of the probe: (a) Gauge block moves along the x-axis; (b) Gauge z axes.block The moves vertical along axis the indicates y-axis; and the ( coffsets) Gauge from block the moves average along displace the z-axis.ment value of the trigger point. Theblock standard moves deviations along the y-axis; of the and x, y, (c )and Gauge z directions block moves were along 20.6 the nm, z-axis. 54.4 nm, and 9.4 nm, respectively. The repeatability of the ACF probe along the x, y, and z axes was also tested. At the beginning of this experiment, the gauge block was controlled to move to the non-triggered state, corresponding to section I in Figure 8, and then was moved along each direction to touch the probe repeatedly with a displacement of 2 μm. Figure 9 shows the repeatability results of 20 repetitions along the x, y, and z axes. The vertical axis indicates the offsets from the average displacement value of the trigger point. The standard deviations of the x, y, and z directions were 20.6 nm, 54.4 nm, and 9.4 nm, respectively.

Figure 9. Repeatability results along the x, y, and z axes.

The stability of the probe system in the y and z axes was tested. The Figure 10 shows the stability test results of the probe. The total drift of the light spot in the y and z axes were about 130 nm and

Sensors 2017, 17, 2652 14 of 18

Sensors 2017, 17, 2652 14 of 18 Figure 9. Repeatability results along the x, y, and z axes. Figure 9. Repeatability results along the x, y, and z axes. The stability of the probe system in the y and z axes was tested. The Figure 10 shows the stability Sensors 2017, 17, 2652 14 of 18 test Theresults stability of the of probe. the probe The systemtotal drift in theof they and light z axes spot was in the tested. y and The z Figureaxes were 10 shows about the130 stability nm and test100 resultsnm for of a theduration probe. of The one total hour, drift respectively. of the light Thespot drift in the of ythe and light z axes spot were was about mainly 130 caused nm and by 100100environmental nmnm forfor aa durationduration factors ofof such oneone hour,hour,as vibration respectively.respectively. of the TheThe experiment driftdrift ofof thethe lightlightplatform, spotspot waswasair mainlymainlydisturbances, causedcaused and byby environmentalenvironmentaltemperature changes. factorsfactors such Observing such as vibrationas thevibration probe of the alongof experiment the the experimentx, y, platform, and z axes, pl airatform, the disturbances, equivalent air disturbances,and area temperature in the y-axisand changes.temperaturewas the Observinglargest. changes. So, the the Observing probe ACF alongprobe the thein probe the x, y, y-axis andalong z is axes,the mo x,re the y, sensitive and equivalent z axes, to external areathe equivalent in the forces, y-axis area and was inespecially the the largest. y-axis to So,wasair the disturbances,the ACF largest. probe So, than in the the theACF y-axis other probe is two more in axes, the sensitive y-axis which is to is mo externalwhrey sensitivethe forces,y-axis to andstability external especially of forces, the toACF and air probe disturbances, especially is larger to thanairthan disturbances, the the other z-axis. two than axes, the which other is two why axes, the which y-axis stabilityis why the of y-axis the ACF stability probe of is largerthe ACF than probe the z-axis.is larger than the z-axis.

(a) (b)

Figure 10. Stability experiment(a) result of the probe system. (a) The drift of light(b) spot along the z-axis, Figure 10. Stability experiment result of the probe system. (a) The drift of light spot along the z-axis, and (b) the drift of the light spot along the y-axis. andFigure (b) 10. the Stability drift of the experiment light spot result along of the the y-axis. probe system. (a) The drift of light spot along the z-axis, and (b) the drift of the light spot along the y-axis. An experiment using the same conditions as the repeatability test was completed to investigate An experiment using the same conditions as the repeatability test was completed to investigate the Anresolution experiment of the using probe, the sameand conditionsthe results asare the shown repeatability in Figure test was11. Atcompleted the beginning to investigate of this the resolution of the probe, and the results are shown in Figure 11. At the beginning of this experiment, theexperiment, resolution the of gauge the probe, block wasand controlledthe results to are move shown it to linearin Figure response 11. At section, the beginning corresponding of this to the gauge block was controlled to move it to linear response section, corresponding to section III experiment,section III in the Figure gauge 8, blockand then was was controlled moved toin moveregula itr tosteps. linear The response horizontal section, axis ofcorresponding Figure 11 is theto in Figure8, and then was moved in regular steps. The horizontal axis of Figure 11 is the number sectionnumber III of in steps Figure of 8, the and nano then positioning was moved stage in regula and rthe steps. vertical The horizontalaxis is the axis shift of of Figure the CCD 11 is spotthe of steps of the nano positioning stage and the vertical axis is the shift of the CCD spot centroid. numbercentroid. of The steps minimum of the nano moving positioning step that stage the and probe the systemvertical couldaxis isresolve the shift is ofthe the displacement CCD spot The minimum moving step that the probe system could resolve is the displacement resolution in centroid.resolution The in thisminimum direction. moving The resolution step that of the the prACFobe probing system systemcould alongresolve axes is x,the y, displacementand z were 10 this direction. The resolution of the ACF probing system along axes x, y, and z were 10 nm, 30 nm, resolutionnm, 30 nm, in and this 5 direction. nm, respectively. The resolution of the ACF probing system along axes x, y, and z were 10 and 5 nm, respectively. nm, 30 nm, and 5 nm, respectively.

(a) (a)

Figure 11. Cont.

Sensors 2017, 17, 2652 15 of 18 Sensors 2017, 17, 2652 15 of 18

(b)

(c)

Figure 11. Resolution of the ACF probe: (a) along the x-axis, (b) along the y-axis; and (c) along the z- Figure 11. Resolution of the ACF probe: (a) along the x-axis, (b) along the y-axis; and (c) along axis. the z-axis.

4.4. Calibration Experiments and Uncertainty Analyses 4.4. Calibration Experiments and Uncertainty Analyses There were two purposes to the micro-slit experiment: to verify the high aspect ratio There were two purposes to the micro-slit experiment: to verify the high aspect ratio measurement measurement capability of the ACF probe and to calibrate the diameter of the probing sphere [30]. capability of the ACF probe and to calibrate the diameter of the probing sphere [30]. The diameter The diameter of probing sphere, measured by the video measurement system, was 174.4 ± 2.8 μm. of probing sphere, measured by the video measurement system, was 174.4 ± 2.8 µm. Poor Poor sphere-diameter accuracy makes performing high precision measurements impossible. So, the sphere-diameter accuracy makes performing high precision measurements impossible. So, the diameter diameter of the sphere had to be calibrated. The coordinates of the ACF probe, gauge blocks, and of the sphere had to be calibrated. The coordinates of the ACF probe, gauge blocks, and nano nano positioning stage were carefully aligned to reduce the alignment error. A precision feeler gauge, positioning stage were carefully aligned to reduce the alignment error. A precision feeler gauge, with a with a thickness of 250 μm grade K referred to as a calibrated gauge, was placed in the middle of the thickness of 250 µm grade K referred to as a calibrated gauge, was placed in the middle of the two two support gauge blocks with grade K to achieve a micro slit to qualify the probe system. As shown support gauge blocks with grade K to achieve a micro slit to qualify the probe system. As shown in in Figure 12a, neodymium iron boron (Nd2Fe14B) magnets were used to fasten the two gauge blocks. Figure 12a, neodymium iron boron (Nd Fe B) magnets were used to fasten the two gauge blocks. Figure 12b shows the measurement results2 14 of the number one and number two trigger point Figure 12b shows the measurement results of the number one and number two trigger point positions. positions.

Sensors 2017, 17, 2652 16 of 18 Sensors 2017, 17, 2652 16 of 18

(a)

(b)

Figure 12. Measurement of the silt: (a) photograph of the micro slit and (b) the measurement results Figure 12. Measurement of the silt: (a) photograph of the micro slit and (b) the measurement results of theof twothe two trigger trigger points. points.

To avoid the influence of the edge chamfers of the gauge blocks, the probe sphere was aligned To avoid the inﬂuence of the edge chamfers of the gauge blocks, the probe sphere was aligned inside the gap with a depth of more than 100 μm from the top surface of the gauge blocks. The micro inside the gap with a depth of more than 100 µm from the top surface of the gauge blocks. The micro slit was moved back and forth along the x-axis to touch the probing sphere twice, then was moved slit was moved back and forth along the x-axis to touch the probing sphere twice, then was moved along the y-axis in a 2-μm step. The total displacement along the y-axis was 100 μm. This detection along the y-axis in a 2-µm step. The total displacement along the y-axis was 100 µm. This detection method avoids the low resolution drawback of the y-axis. The mean trigger point position of the methodnumber avoids one position the low was resolution 8.713 μm, drawback and that of of the the y-axis.number The two mean position trigger was point 84.079 position μm. The of mean the µ µ numbervalue and one positionthe standard was 8.713 deviationm, and of thatthe ofmeasured the number micro two silt position were was75.366 84.079 μm andm. The0.023 mean μm, µ µ valuerespectively. and the standard The standard deviation deviation of the of measured the measurem micro siltent wereresult 75.366 was mainlym and caused 0.023 bym, the respectively. interfacial Theadhesive standard force deviation and the of repeatability the measurement of the resultx-y nano was positioning mainly caused stage. by According the interfacial to the adhesive measurement force andresult, the repeatabilitythe mean value of the of the x-y effective nano positioning two-poin stage.t probe According sphere diameter to the measurement was evaluated result, at 174.634 the mean μm with a standard deviation of 0.023 μm.

Sensors 2017, 17, 2652 17 of 18 value of the effective two-point probe sphere diameter was evaluated at 174.634 µm with a standard deviation of 0.023 µm. Uncertainty analyses were completed according to GUM (ISO Guide to the Expression of Uncertainty in Measurement). The 0.023-µm standard deviation of measurement result is one of the sources of uncertainty. The corresponding uncertainty was estimated to be 0.014 µm. In addition, the length deviation limit of the calibrated feeler gauge and the supporting gauge blocks were 50 nm. So, the uncertainty of both the calibrated feeler gauge and the supporting gauges block were estimated to be 0.029 µm. The wringing error between the two gauge blocks and feeler gauge had to be considered. A wringing error of 10 nm occurred on each side, according to the data sheet of the gauge block, contributing to an uncertainty of 0.012 µm. The cosine error, Abbe error, and alignment error could also be uncertainty sources in the experiment. However, they are relatively small in the experiment and have little inﬂuence on the combined uncertainly. Therefore, the combined uncertainty of the measurement was estimated to be 0.045 µm. Notably, the primary motivation of this paper was to propose a novel probe system. Detailed discussion and improvement of the measurement uncertainty will be completed in future work.

5. Conclusions An assembled cantilever optical ﬁber touch trigger probe for 3D measurement of microstructures was developed, fabricated, and tested. The experimental results showed that the ACF probe has the potential to achieve nanoscale measurement resolution in 3D measurements of microstructures. The probe has the powerful capability to meet the 3D precision measurement requirements. Furthermore, the ACF probe system has many advantages, such as being inexpensive, easy to fabricate, compact, with high SNR. In the future, a lens with a micro focal length will be used for ultra-high sensitivities.

Acknowledgments: This work is supported by the National Natural Science Foundation of China under Grant 51575142 and the Natural Science Foundation of Heilongjiang Province under Grant E201423. Author Contributions: Limin Zou wrote the paper; He Ni invented this probe and designed the experiments; Peng Zhang performed the experiments and analyzed the data; Xuemei Ding contributed analysis tools and revised the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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