With the fast development of micro-machining, there is an increasing demand for the precision measurement of micro parts or microstructure arrays, such as holes of fuel injection, ink-jet printer nozzles, micro lens array, and binary optics lens [1,2]. But it is a challenge to realize the measurement of these micro parts because of their tiny features, high aspect ratio, and limited probing space [3].

Much work has been done in recent years by employing optical fiber probes to solve this problem. For example, Kao and Shih proposed in 2007 a fiber probe based on detecting the feeler element optically [4], and Tutsch et al. proposed in 2010 three different approaches for extending the sensitivity of the fiber probe in axis Z [5], but their aspect ratios are limited by the shadowing effect. Tan and co-workers proposed in 2011 a fiber probe based on spherical coupling for the measurement of micro holes [6], but to further improve its resolution is difficult because of the excessive loss of effluent light in the coupler. Depiereux et al. proposed in 2007 a fiber probe based on a white-light interferometer [7], and then Pfeifer et al. proposed in 2011 a fiber probe grinded fiber tip [8], but these two probes only have measurable capability in one dimension. Muralikrishnan et al. reported in 2006 a fiber probe by measuring the deflection of the fiber [9], but a low optical magnification affects its sensitivity. Wang and co-workers proposed in 2010 a fiber deflection probing method that uses fiber as a cylindrical lens [10], but it lacks measurable capability in the axis Z. Cui et al. proposed in 2014 a fiber Bragg grating (FBG)-based double-fiber probe [11], and breaks though the drawback of the FBG probes that lack radial measuring capability [12,13], but it still has a shortcoming in the radial resolution. It is therefore of great significance to find a probing method that can overcome the drawbacks and limitations above to achieve the measurement of micro parts with high-aspect ratios.

In this Letter, a fiber probe based on micro focal-length collimation (MFL-collimation), in which a FBG-inscribed fiber stylus acts as a micro focal-length cylindrical lens (MFLC-lens), is proposed to realize the three-dimensional (3D) metrology of micro parts with high-aspect ratios (shown in Fig. 1). The probing system consists of two mutually orthogonal MFL-collimation optical paths for the radial (axes X and Y) tactile-probing measurement and a matched FBG pair interrogation system for the axial (axis Z) tactile-probing measurement. Within such arrangement, optical signals of the MFL-collimation optical paths propagate outside the part being measured, and the optical signal of the FBG pair interrogation system transmits in the optical fiber, so the shadowing effect is completely avoided, and the probing space is significantly expanded. Another outstanding advantage of the probe is that it has two operating modes: deflection mode and compression mode, and the capability of decoupling the 3D tactility.

 

Fig. 1. Schematic diagram of the 3D probing system.

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Figure 2(a) shows the arrangement of MFL-collimation optical path. A laser beam from the laser diode (LD) goes through the reflective objective lens (ROL) and converges into an annular point light source at the focus. Meanwhile, the annular point light source located at the focus of the fiber stylus acting as a MFLC-lens is collimated into a fringe image by the MFLC-lens, and then the fringe image of the collimated light is detected by a CCD camera. The centroid position of the zero-order fringe image extracted from the fringe image is used to locate the position of the fringe image for the benefit of a higher signal-to-noise ratio. An advantage of the MFL-collimation optical path is that the centroid position of the fringe image is sensitive to the lateral defocus of the MFLC-lens but insensitive to the longitudinal defocus of the MFLC-lens, so the orthogonal lateral defocus of the MFLC-lens in the two mutually orthogonal MFL-collimation optical paths are decoupled.

 

Fig. 2. Measurement principle of MFL-collimation optical path (a) free status, (b) bending of probe in radial contact status, and (c) centroid shift of the zero-order fringe image in radial contact status.

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When the probe tip is moved to contact the micro parts in a radial direction, the probe operates in deflection mode. Due to the decoupling capability of the orthogonal lateral defocus of the MFLC-lens, a radial displacement along the X–Y plane can be decomposed into components along axes X and Y that can be measured through the MFL-collimation optical path of the corresponding axis.

As shown in Fig. 2(b), the radial displacement of the probe tip along the axis X is transformed into the radial deflection of the fiber stylus at the observation point (OP) with a deflection transfer coefficient, which can be expressed as

As shown in Fig. 2(c), $s_{o,j}$, which is actually a lateral defocus displacement of the MFLC-lens, is then transformed into a shift of the zero-order fringe image with a magnifying transfer coefficient, which can be expressed as

Therefore, the radial displacement of the probe tip is transformed into the centroid position shift of the zero-order fringe image with a transfer function, which can be expressed as

The FBG pair interrogation system integrated in the probing system is shown in Fig. 1. A measuring FBG (M-FBG) comprised in the fiber stylus and an external reference FBG (R-FBG) compose a matched FBG pair. A broadband light source from the amplified spontaneous-emission (ASE) light source enters the fiber stylus, and a narrow band Bragg spectrum reflected by the M-FBG passes through the circulator and transmits into the coupler. This reflected spectrum is then divided into two parts by the coupler, and one part of the power spectrum reflected by the M-FBG is received by the optical power meter 1 (PM1); the other part of the power spectrum entering the R-FBG, is filtered and reflected by the R-FBG, and finally the overlapping power spectrum between M-FBG and R-FBG is received by the optical power meter 2 (PM2). As a result of the M-FBG located in the neutral plane of the fiber stylus, the FBG pair interrogation system is sensitive to the axial compression of the fiber stylus but insensitive to the radial deflection of the fiber stylus, which is an advantage of the probing system and realizes the third dimensional measurement capability along the axis Z without sensing coupling along the axes X and Y.

When the probe tip is moved to contact the micro parts in the axial direction, the probe works in compression mode. It is shown in Fig. 3 that the axial displacement of the probe tip along the axis Z causes an equivalent compression of the fiber stylus, and this compression of the fiber stylus is transformed into a Bragg wavelength shift with a transfer function, which can be expressed as

 

Fig. 3. Measurement principle of the matched FBG pair interrogation system (a) axial compression of the probe in axial contact status and (b) shift of Bragg wavelength and variation of power ratio caused by the axial compression of the probe.

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In order to achieve the linear and most sensitive mode, the best-matched initial condition is applied to the interrogation system. The best-matched initial condition is expressed as [11]

Finally, by substituting Eqs. (4) and (6) into Eq. (5), the transfer function between the power ratio of PM2 to PM1 and the contact displacement of the probe tip along the axis Z is expressed as

Experimental setups are as follows. The annular beam light source is achieved using a normal LD and a ROL with a numerical aperture of 0.28 and a working distance of 24.5 mm. The focal length of the fiber stylus $f$ is $\sim 93\mathrm{\mu m}$. A linear CCD camera is utilized to capture the fringe image. The distance of the fiber stylus to the detection screen of the CCD camera $l_2$ is $\sim 125\mathrm{mm}$. The clearest image is obtained by adjusting the distance between the fiber stylus and the ROL. The initial Bragg wavelength ${\lambda }_M$ and ${\lambda }_R$ of the M-FBG and R-FBG is 1549.005 nm and 1539.034 nm, respectively. The FWHM ${\lambda }_{W,M}$ and ${\lambda }_{W,R}$ of the M-FBG and R-FBG is 0.1989 nm and 0.231 nm, respectively. As a result of Eq. (6), the initial Bragg wavelength of the R-FBG is turned to 1548.8756 nm to match best-matched initial condition. The available working space of the probe is expanded more than the method of Ref. [10], but due to the above configuration, it is still limited as a result that the micro part should not have mechanical interference with ROL-X, ROL-Y, CCD-X, and CCD-Y.

The probe is made of an optical fiber comprising FBG in its core. The optical fiber etched by hydrofluoric acid can be used to make a probe with different diameters by melting balls at the ends of the fiber stylus. The working length of the fiber stylus is about 2–5 mm, and the probe tip is about 50–200 μm in diameter. Thus the aspect ratio of the probe is about 10:1–100:1, which can be used to achieve high measurable aspect ratio. Here, a probe was fabricated with a fiber stylus length of 15 mm and a probe tip diameter of 131.52 μm.

Experiments are made to evaluate the performance of the 3D fiber probe. A glass cover is used to reduce the influence of air. All the devices are deposited on an active self-leveling isolation system (Thorlabs PTR52514 and PTS602). A plane gauge block is moved forward along the axes X, Y, and Z to touch the probe tip. It is shown in Fig. 4 that the output of CCDX has no response to the radial and axial displacement of the probe tip along the axes Y and Z, and a linear response to the radial displacement of the probe tip along the axis X with a sensitivity of 88 pixel/μm; similarly, the output of CCDY has no response to the radial and axial displacement of the probe tip along the axes X and Z, and a linear response to the radial displacement of the probe tip along the axis Y with a sensitivity of 83 pixel/μm; the power ratio of PM2 to PM1 has no response to the radial displacement of the probe tip along the axes X and Y, and a linear response to the axial displacement of the probe tip along the axis Z with a sensitivity of 4.9%/μm. It is clear that the 3D fiber probe is decoupled in 3D-probing measurement.

 

Fig. 4. Output response curve of 3D probing system (a) radial probing along axis X, (b) radial probing along axis Y, and (c) axial probing along axis Z.

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The resolution of the 3D fiber probe is verified. It is shown in Fig. 5 that the radial resolutions along the axes X and Y reach 5 nm, while the axial resolution along the axis Z reaches 8 nm. It is believed that the high-precision dimensional metrology of micro parts can be guaranteed.

 

Fig. 5. Resolution of 3D fiber probe (a) radial resolution along axis X, (b) radial resolution along axis Y, and (c) axial resolution along axis Z.

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As shown in Fig. 6(a), three ring gauges with nominal diameters of 500.91 μm (No. 1), 600.62 μm (No. 2), and 699.08 μm (No. 3) with an expanded measurement uncertainty of 0.15 μm for $k=2$ at a depth of 1000 μm are measured to verify the measurement capability of the 3D fiber probe. The test results of the diameters obtained by the 3D fiber probe are 501.01 μm (No. 1), 600.41 μm (No. 2), and 698.93 μm (No. 3) with standard deviations less than 0.05 μm.

 

Fig. 6. (a) Measurement of the ring gauges and (b) measurement of the ceramic circular disc.

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Measurement of micro holes on a ceramic circular disc is illustrated in Fig. 6(b). Three micro holes are selected to be measured at a depth of 500 μm. The diameters measured in this experiment are 300.60 μm (No. 4), 500.43 μm (No. 5), and 683.20 μm (No. 6). The standard deviations of these measurements are 0.058 μm, 0.035 μm, and 0.022 μm, respectively.

A 3D fiber probe is proposed, fabricated and tested. The probe has a capability of decoupling the 3D tactility, which benefits from the two mutually orthogonal MFL-collimation optical paths and the matched FBG pair interrogation system. The fiber stylus acts as a MFLC-lens in the two MFL-collimation optical paths, and the best-matched initial condition is implemented to optimize the FBG pair interrogation system working in the linear and most-sensitive mode. Experimental results indicate that a radial resolution of 5 nm and an axial resolution of 8 nm can be achieved. The probe is easily applied in the measurement of micro parts because of its high precision; low cost (made from a single mode fiber with FBG in its core); high measurable aspect ratio; and capability of decoupling the 3D tactility.