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Abstract
Surface metrology is an essential operation to determine whether the quality of manufactured surfaces meets the design requirements. In order to improve the surface accuracy and machining efficiency in the manufacturing of optical freeform surfaces, in-situ surface measurement without re-positioning the workpiece is considered as a promising technique in advanced manufacturing. In this study, a displacement laser scanner is integrated into an ultra-precision fly-cutting machine in order to perform as a coordinate measuring machine. However, some inevitable errors such as motion errors of the machine tool, thermal drift, vibrations, and errors of the laser sensor are introduced due to the manufacturing environment. To improve the performance of the measurement system, calibration of the main error sources is investigated with consideration of the characteristics of the built laser scanner system. Hence, the relationship between the moving speed of the laser scanner and the vibration of the tested signals is studied. Following that, the errors of the z-axis scale could be corrected by measuring a four-step heights artefact. Furthermore, volumetric positioning errors are identified by the proposed modified chi-square method and Gaussian processing prediction method. Simulation and measurement experiments are conducted, and the results indicate that the calibrated measuring system can measure ultra-precision freeform surfaces with micrometre form accuracy.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface topography measurement plays a key role in the ultra-precision manufacturing field for quality control and further machining process improvement. A large variety of off-line surface metrology instruments which are typically set in a well-controlled environment are used to acquire surface information, such as coordinate measuring machine (CMM), stylus profiles [1] and non-contact optical instruments [2]. With the increasing geometric complexity of ultra-precision freeform surfaces, such as manufacturing micro/nano-structured surfaces [3], off-line surface measurement cannot meet the requirements. This is particularly true when the same workpiece needs to be re-mounted to carry out the measurement of and compensation for machining errors. In order to ensure the surface quality of the workpiece, an in-situ measurement system that incorporates measurement sensors into ultra-precision machine tools provides a promising solution, which not only avoids post-process inspection, but also makes compensation machining easy to be carried out. However, due to the measurement sensors always moving along the axes of the machine tool, the spindle and slide error motions, vibration of the integrated measuring components and the machine tool itself, thermal drift and also the errors of the sensor adversely affect the uncertainty of the in-situ measurement applications.
Recently, many researchers have paid attention to the development of in-situ measuring instruments for precision machine tools. Li et al. [4] developed an in-situ autostereoscopy-based 3D measuring system to measure the micro-structured surfaces on an ultra-precision turning lathe. The system consisted of a microlens, a CCD sensor and a group of LED light bars to acquire the 3D raw information and extract disparity data from an established 3D digital model under different working environments. One limitation of this study was the resolution of measurement. Zhang et al. [5] employed a fringe deflectometry system both on a five-axis ultra-precision machine and a Taylor Hobson 1250GPI profilemeter. By using the fringe patterns, the phase similarity and phase range of the fringes were used to identify the position information. The linear and tilted positioning accuracy can be lowered to 5 µm and 0.005°, respectively. The measurement results were influenced by the fringe pattern accuracy as well as the positions between the light screen and the camera but there is still not adequate knowledge to address these problems.
In addition, a scanning tunnelling microscope was integrated into a diamond machine to manufacture and characterize the pyramid array surface [6]. The uncertainty of this in-situ measurement system was also analyzed. Li et al. [7,8] presented an interferometric on-machine probing system on a three-axis diamond turning machine. System errors such as kinematic error and vibration of the machine tool were also investigated and calibrated. Some contact probes with low measuring force were also applied to inspect the optical surface. The in-situ displacement probes were usually supported by an air bearing, so the displacement could be measured by a linear variable differential transformer (LVDT) [9–11]. Xu et al. [12] studied the LVDT on a three-axis ultra-precision machine tool and measured the sinusoidal surface. They successfully carried out the surface compensation process and achieved good results. Ito et al. [13] mounted a specular laser triangulation sensor on an ultra-precision grinding machine tool to measure the ceramic parts and the measurement errors including motion errors, tilt error and stability error. Chen et al. [14] designed a new chromatic confocal configuration to divide the reflected laser beam into two sub-beams so that the spectral non-smoothness of the mode-locked laser source can be eliminated. Seewig et al. [15] proposed that the use of scattered light sensors can be a powerful technique to measure form accuracy and surface roughness for in-line measurement. Tereschenko et al. [16] presented a passive vibration compensation method by integrating a high-resolution distance measuring interferometer into the white-light interferometer so that the measured deviations from the depth-scanning can be used to correct the measurement by the white-light interferometer.
Most of these studies focused on the task of in-situ measurement such as evaluation of the manufactured surface, compensation process, etc. On the contrary, separation and reduction of the additional error sources of these sensors as well as the related calibration in each type of in-situ measurement system have received little attention. As a result, this paper presents an in-situ displacement probing system which is integrated on a five-axis ultra-precision machine. It shows the calibration strategy for the volumetric errors, z-axis scale errors as well as the vibration influence.
2. Calibration of the integrated in-situ probing system
2.1 Development of the in-situ displacement probing (ISDP) system
In this study, a laser displacement probe was integrated onto a 5-axis ultra-precision fly-cutting machine (Precitech Freeform 705G, USA) including three linear axes and two rotary axes to perform as a coordinate measuring machine (x, y, z information). The high quality of the displacement sensor (Keyence, LK-G5000), with 20 nm measurement repeatability and ± 0.02% linearity in terms of the 2 mm measuring range with a 25 µm spot diameter at standard distance [17] provides the feasibility of measurement in ultra-precision technology. In this study, the measurement information was achieved by inspecting the positions of the three moving linear axes of the ultra-precision machine and the signals were loaded from the displacement sensor in the z direction.
As shown in Fig. 1, the displacement laser sensor is mounted on the spindle so that it can move along the x axis and y axis and obtain the displacement information in the z axis direction. To improve the measurement preference, the direction of the laser light should be aligned to the z direction of the z axis on the machine tool as accurately as possible although the measurement results are different from the reference distance which is determined by the sampling frequency of the sensor. In addition, the relative position distance of the laser sensor and the fly-cutting centre was set as about 40 mm, 5 mm, and 5 mm in the x, y, and z directions respectively so as to avoid interference when the length of the machined workpiece is less than 40 mm and the height difference (z direction) is larger than 5 mm simultaneously. To further ensure the alignment of the laser scanner, a transformation matrix [18] was identified with measurement of a few known surfaces so as to unify the coordinate frame of the sensor and the tool tip. In order to ensure the working space of the ISDP system, the space centre of the machine tool was set as the start point in the machine tool coordinate frame. Furthermore, the z-axis does not move in the whole measurement process after the stand distance is identified. Considering the one-dimensional property of the laser scanner, only a uni-directional scanning tool path as shown in Fig. 1 was selected so that the x, y positions could be consistent with the z displacement.
According to the configuration of the developed ISDP system, only the z direction is of interest because the x direction and the y direction can be guaranteed by the ultra-precision linear scale feedback with as small as 14 nm and 6 nm resolution [19], respectively. In order to evaluate the performance of the ISDP system, three factors that can influence the measurement accuracy including vibration of the integrated measuring components and the z axis scale errors and volumetric errors of the machine tool, they were determined and calibrated as compared with the corresponding results measured on the off-line measurement instrument.
2.2 Errors of the volumetric positioning
The developed ISDP system moves along the axes of the machine in order to carry out the metrology task. It is inevitable that measurement errors occur due to errors stemming from the geometric errors of the machine tool, inaccuracies in assembly, wear of the components, the errors of the probing system and so on. It is quite complex to identify the individual errors from one to the other. The comprehensive effect of all these errors are considered as volumetric positioning error. To obtain the combined errors in the machine tool, a fiducial-aided positioning method [18] was employed. A reconfigurable calibrated fiducial-aided artefact was measured in a relatively high-precision machine tool and it was amounted in the working space of the machine tool. The nominal positions of these fiducials were assured to be ${T_{np}}$, read from the numerical control system in the machine tool coordinate frame. However, due to the volumetric errors, these positions did not coincide with the calculated positions ${T_{cp}}$ which are regarded as actual positions transformed from the calibrated positions. Hence, the volumetric errors of the machine tool can be defined by the bias between the transformed positions of the calibrated fiducials and the measured positions in the machine tool coordinate frame, as given in Eq. (1):
It is assumed that the volumetric errors are determined by the mean values along the x, y and z axes of the measuring system, the errors were set as ${\varepsilon _{mX}}$, ${\varepsilon _{mY}}$, ${\varepsilon _{mZ}}$, and a root sum square approach was used to obtain the volumetric error:
For the calibrated fiducial-aided artefact, it is considered that the errors between the position of the calibrated fiducials and the real positions of the fiducials in the calibrated measuring coordinate frame are much smaller than the errors obtained in the in-situ measuring system. However, these errors still need to be considered. Similarly, the combined errors are set as ${\varepsilon _{rX}}$, ${\varepsilon _{rY}}$and ${\varepsilon _{rZ}}$ along the three moving axes. The relationship among those three coordinate frames and the definition of the several errors are shown in Fig. 2.
2.3 Modified chi-square volumetric error identification
A reconfigurable calibrated fiducial-aided artefact composed of a set of standard spheres was mounted on the machine tool. The individual spheres, ${S_i}$, $i = 1,2 \cdots n$, set the calibrated positions as (${X_{ri}},{Y_{ri}},{Z_{ri}}$), so the positions of these spheres (${X_{ci}},{Y_{ci}},{Z_{ci}}$) in the machine tool could be transformed from the calibrated coordinate frame and determined as follows:
For easy reading of the equations, the $\sum$ and the subscript are dropped, for instance, ${z_r} = \sum\nolimits_{i = 1}^N \,{Z_{ri}}$, $z_r^2 = \sum\nolimits_{i = 1}^N \,Z_{ri}^2$ and ${y_r}{z_r} = \sum\nolimits_{i = 1}^N \,({Y_{ri}}{Z_{ri}})$. It is clear that Eq. (7) can be easily solved by using Cramer’s Rule. From the above equations, it is obvious that the obtained best fitted parameters propagate new errors in the transforming process. A set of the errors of the 12 best fitted parameters are ${\varepsilon _{{D_j}}}$, $j = 1, \cdots 9,x,y,z$. The errors of these parameters can be defined by:
As studied in previous work [20], the errors of the fitted parameters can be obtained by determining the inverse matrix B, and they could be very small and up to 0.016 µm.
The relationship among different Cartesian coordinate systems is confirmed by the built mathematical model by using a number of fiducials. To check the accuracy of the proposed mathematical model, a Monte Carlo simulation method [22,23]was used to check how many fiducials could achieve better performance with a relatively high accuracy. Figure 3 shows the mean value and standard deviation of the simulated volumetric errors after 3,000 repeated experiments with different fiducials.
As shown in Fig. 3, the volumetric errors are almost equal to zero when using three or four fiducials but the values are significantly increased with an increasing number of fiducials from five to 13, and a slow increase can be seen when the number of fiducials increase to 20. After that, the values of the volumetric errors display a stable trend. It is obviously shown that the volumetric errors may be hidden if less than four fiducials are used but the volumetric errors are measured if more than 20 fiducials are used. It was concluded that 24 fiducials could achieve good results in the assessment of the volumetric error in this study.
2.4 Prediction and compensation of the volumetric errors in the working space
In the developed mathematical model, the volumetric errors can only be obtained at several measurement points. The other errors in the remaining positions can be determined by interpolation. To generate numerous spatial measurements that cover the entire working space, a Gaussian Process (GP) modelling method was used to predict the volumetric positioning errors with high accuracy. The GP modelling method is a powerful tool in machine learning, and it provides a Bayesian nonparametric approach to smoothing and interpolation [24].
It was assumed that the calculated volumetric errors at the nominal position $p = (x,y,z)$ is ${V_e}$, and these nominal positions and their errors were set as the input and output parameters of the GP model. A linear system with Gaussian distribution error with zero mean and ${\sigma _n}$ standard deviation is given in Eq. (12):
Then the ‘real’ volumetric errors $f(p)$ can be defined by a mean function $\mu (p)$ and a covariance function $K(p,p)$ in the GP model: So the ${V_e}$ can be determined by the input positions as: where I is the identity matrix. So the joint distribution over the calculated ${V_e}$ at the training position $p$, and the predicted $V_e^ \ast$ at the test position ${p^ \ast }$ is thus given by Eq. (14):A simulation study was carried out to check the accuracy of the GP-based prediction model. A total of 24 arbitrary points were generated and a standard error of 0.2 µm was added in three directions so that these points could be simulated as the calibrated points. The measured points could be obtained by adding several errors in the three directions, including probing errors (0.2,0.2,0.5)µm, and determining the centre of the standard sphere (0.3,0.3,0.5)µm, geometric error (0.5,0.5,0.8)µm, and thermal error (0.1,0.1,0.1)µm, by transforming the calculated points with an arbitrary transformation matrix. Hence, the volumetric errors of these 24 positions were determined by substituting them into Eq. (7). After setting the measured points and volumetric errors as input and output of the GP model, respectively, the prediction errors in the entire working space could be modelled. Finally, the compensation process was finished by changing the tool path in the new measurements. Figure 5 shows the results of the predicted volumetric errors and the calculated errors at the same position after 100 repeated simulations.
According to the results of Fig. 5, the deviation between the two datasets was drawn as shown in Fig. 6. The mean value of the prediction errors and the calculated errors are both 1.5 µm and the maximum value of the deviation is less than 0.0096 µm. These results show that the GP model has relatively high accuracy regarding the prediction of volumetric errors.
2.5 Vibration estimation of the measuring system
There are three main types of machine tool vibrations [25] including random vibrations due to impulsive loading of the machine tool, forced vibrations due to spindle imbalance and electric motors, and self-induced vibrations due to the feed motion or cutting process. These vibrations have a significant influence on ultra-precision freeform surface machining and the measuring process. It is necessary to reduce or eliminate them with consideration of the sampling strategies [26].
For the developed measuring system, the vibrations are due to interaction of the dynamic behaviour of the measuring process, which means that these two parameters – feed rate of the scanning speed and sampling frequency of the sensor − should be tested and optimized according to the measured surface. In order to avoid aliasing, it is necessary to have the sampling frequency two times more than the vibration frequency of the machine tool [27]. In addition, according to the analysis of the vibrations in an interferometric measuring system [8], it is suggested that the feature frequency of the measuring surface of interest should be lower than the vibration frequency. In this study, the vibration source was mainly considered as the dynamic behaviour of the developed on-machine device. It is important to find the relationship between the scanning speed and the vibration.
2.6 Calibration of z-axis scale errors
Due to the environmental effects, especially temperature and metrological characteristics between the ideal quantity and measured quantity, the amplification coefficient and linearity of the z-axis scale need to be considered. Matthias et al. [28,29] proposed manufacturing of new roughness standard for the linearity of the vertical axis and they achieved a good result. However, this method needs to measure the surface roughness which is not applicable for the displacement sensor. In this study, the instrument response curve [30] method as shown in Fig. 7 was used to correct the amplification coefficient and linearity of the sensor at the z-axis. The amplification coefficient was defined as the first-order poly-fit value of the response curve, and the linearity was obtained from the maximum local deviation of the response curve. To achieve enough information about the z-axis response curve, a step artefact with different heights can establish the relationship between the instrument response curve and the ideal one.
As shown in Fig. 8, a step surface with four different heights (0.2, 2, 5, 11) µm was designed and manufactured with an ultra-precision machining system from Moore Nanotech 350FG, USA. The manufactured step artefact was calibrated with a white light interferometer named Zygo Nexview, 5×.
The range of the z-axis of the displacement sensor is about 2 mm. The ISDP measurement results were compared to the calibrated multi-step artefacts. In order to ensure that all the measured positions were within the range of the instrument, the multi-step was measured in 50% of the instrument’s working range. A total of five measurement tasks were performed to reduce the random measurement errors.
3. Experiments and discussion
3.1 Vibration evaluation of the in-situ measurement system
In order to check the influence of the vibrations caused by the dynamic behaviour in the measuring process, a series of tests was carried out with a calibrated flat surface along the raster axis (x-axis in this research). The laser probe can provide a scanning sampling frequency ranging from 1 kHz to 200 kHz. Considering the avoidance of any alias of the signals of interest and the measurement accuracy of the laser probe with different sampling frequencies, a relatively high frequency of 20 kHz was used to obtain the scanned workpiece and 1000 Hz was selected to analyze the signals.
Figure 9 shows the signal vibrations with different scanning speeds. f = 0 mm/min means that the signals were measured when the on-machine measurement system was in its static condition. As shown in Fig. 9, the vibration values for each scanning speed can be summarized as its standard deviation, which are listed in Table 1. The in-situ static vibration was less than 20 nm, but the values were significantly increased when the laser scanner was moved along the machine axis at a low speed which was up to almost 10 times the static value. On the contrary, it seems that the vibrations exhibited a sharp decrease down to 10 nm when the feed rate was increased to 2 mm/min. After that, the standard values ranged over a very small scale until the feed rate was increased to 8 mm/min. The vibration amplitude becomes large when the feed rate is increased to 8 mm/min, which may be caused by the integrated mechanical structure. The fixture which was used for holding the sensor was made of aluminium alloy, which is light in weight but has relatively lower stiffness compared with the material of the machine axes. It may cause vibration when the machine axes are moved at a high feed rate. According to the spectrum analysis of the vibration signal at different feed rates as shown in Fig. 10, the vibration amplitude was increased dramatically in the low frequency area (lower than 20 Hz) when the feed rate ranged from 0.5 to 8 mm/min. Furthermore, the spectrum analysis also indicated that the frequencies of the vibration signals were less than approximately 40 Hz. Hence, combining the consideration of values in the two figures (Fig. 9, Fig. 10) and the table (Table 1), the scanning speed would be better at about 6 mm/min, and the analyzed sampling frequency should be larger than 80 Hz on the condition that the requirement of surface feature frequency of the measured workpiece was met.
Table 1. Standard deviation of the vibration signals with different moving speeds
3.2 Calibration of the z-axis scale errors
After obtaining the scanning speed of the on-machine system, a step surface with four steps was used to check the z-axis scale errors. The scanning speed was set as 6 mm/min along the x-axis and three repeated measurements were carried out from −16 mm to 16 mm. A fitted curve with different step heights is shown in Fig. 11, and the deviations between the measurement values obtained from the in-situ laser scanner and the off-machine Zygo Nexview are also listed in Table 2.
Table 2. Measurement results of the step heights with both in-situ and off-machine methods
By using the different step heights artefact and combining the measured results by the Zygo as a reference, the corrected amplification coefficient of the z-axis scale of the in-situ measurement system was about 0.9754, and the linearity deviation was less than 0.15 µm.
3.3 Volumetric error identification
Several experiments were conducted to check the developed mathematical model of volumetric positioning errors of the on-machine measurement system and the GP-based error prediction and compensation approach. The maximum measurement volume was approximately 200 mm × 40 mm × 50 mm. In order to ensure that the accuracy of the measurement was far less than the volumetric error, a total of 20 points were sampled uniformly in a 6 mm × 6 mm area and they were inspected three times.
As discussed before, 24 fiducials assembled on a fixture were randomly mounted in a 200 mm × 40 mm × 50 mm workspace. The fiducials were made of Si3N4 and acquired from the market. The positions of the fiducials were then calibrated in a multi-sensor Coordinate Measuring Machine named Werth Videocheck from Germany in a thermally controlled laboratory. The calibrated fiducial diameters were 9.997 ± 0.0002 mm, which indicated that the errors in the calibrated points were 0.2 µm. In the in-situ measurement system, the fixture with the calibrated fiducials was randomly mounted in the machine tool workspace. Hence, the positions of the fiducials were measured by the laser probe. After using the built chi-square volumetric error identification method, GP-based volumetric error prediction was used by setting the positions of the 24 fiducials and their volumetric position errors as the input. Figure 12 shows the measured positions of the fiducials and their volumetric errors. To improve the performance of the in-situ measurement system, the fixture with fiducials was controlled to move to 10 random positions in the machine tool.
Fig. 12. (a) Positions of randomly selected 24 fiducials and their volumetric positioning errors (magnified 2,500 times).
Figure 13(a) shows the predicted 3D errors in the entire working space. Figures 13(b)–13(d) contain the other views of the volumetric errors. The mean value of the volumetric positioning errors is 1.2 µm and the prediction value is about 1.6 µm in the entire working space. These results indicate that the developed volumetric error prediction method can identify errors with high precision and error compensation followed by this method which can be easily carried out by modifying the tool path. It is worth noting that only a few measured points are needed but relatively high-accuracy results can be achieved.
Fig. 13. (a) GP-based 3D volumetric error prediction in the working space (magnified 5,000 times) and (b) xy view (c) xz view (d) yz view.
3.4 Freeform surface in-situ measurement
Two freeform surfaces were measured by the developed in-situ probing system. In order to check the accuracy of the probing system, a comparison with the measurement results obtained from the CMM (Werth Videocheck) was also carried out. The uncertainty of the CMM is (0.25 + L/300) µm with a 0.2 mm fibre probe in a temperature range of 20 ± 0.2°C. In order to reduce the effect of temperature, the in-house temperature was also set at 20°C.
A relatively flat freeform F-theta surface and a sinusoidal surface with an amplitude of 0.5 mm as shown in Eq. (20) and Eq. (21) were employed to check the inspections. The two freeform surfaces were both machined by a fly-cutting machine tool as shown in Fig. 1.
The characterized results of the two surfaces are illustrated in the 3D form error maps shown in Fig. 14. To present the whole measured surfaces, the 3D form error maps were reconstructed using the B-spline method. The compared results of the two surfaces are also summarized in Table 3.
Fig. 14. (a) and (d) Workpiece of F-theta lens surface and sinusoidal surface, (b) and (e) 3D form error map of the dataset measured by CMM, (c) and (f) 3D form error map of the dataset measured by laser scanner, respectively.
Table 3. Summary of the two measured surfaces
As shown in Figs. 14(b), 14(c), 14(e) and 14(f), form errors of the in-situ measurement were almost consistent with that of the CMM inspections. However, according to Table 3, there was an increase of larger than 13.6% in $\textrm{RMS}$ and $\textrm{PV}$ values for both freeform surfaces. In addition, the measurement results at the relatively flat F-theta freeform surface had higher accuracy compared with those of the sinusoidal surface, and the increase of $\textrm{RMS}$ of the former surface was up to 24.8% but the latter exhibited an almost 60% rise. The uncertainty of these measurement results may be caused by the reflection of the laser light at the steep slope of the surface, transformation errors between the machine tool coordinate frame and the in-situ measurement system as well as the imperfection of the laser scanner fixture and accuracy of the laser sensor. It is clear that higher measurement error occurs when a relatively complex surface is measured for the developed in-situ measurement although the volumetric error of the measurement system was compensated for. From these in-situ measurements, the calibrated in-situ coordinate measuring system exhibited compatible performance in measuring freeform surface as compared with those of the high-accuracy CMM. These results may be enhanced by utilizing a more accurate laser sensor or better designed fixture.
4. Conclusion
This paper presents a calibration strategy for an integrated in-situ displacement probing (ISDP) system on an ultra-precision fly-cutting machine tool. Three main error sources were analyzed and identified by both simulations and experiments. Two freeform surfaces were measured on the in-situ displacement probing system and the measured surface form errors demonstrate compatible performance of the developed ISDP system compared with traditional off-line measurement systems. The following observations can be drawn:
- (i) Dynamic vibrations of the in-situ probing system are influenced by the scanning speed of the moving axes. Experimental studies show that most of the vibration frequencies were lower than 20 Hz when the feed rate ranged from 0 mm/min to 8 mm/min so that an optimized scanning speed and sampling frequency can be determined.
- (ii) Volumetric positioning errors of the ultra-precision fly-cutting machine can be identified using a calibrated fiducial-aided artefact. Simulation showed that the optimized number of fiducials was 24.
- (iii) Volumetric positioning error in the entire working space can be predicted by the proposed Gaussian process method. Simulations and experiments proved that the accuracy of the prediction model was lower than 0.0096 µm. The main error was about 1.6 µm in a 200 mm × 40 mm × 50 mm workspace.
- (iv) Measurement of the multi-step heights was used to correct the z-axis scale errors; the corrected amplification coefficient was found to be about 0.9754 and the linearity error was less than 0.15 µm.
- (v) Compared with the results measured on the high-precision multi-sensor CMM for the two freeform surfaces, the in-situ inspection exhibited greater measurement uncertainty. Moreover, the developed ISDP system appears to have better performance if the surface has relatively low geometric complexity.
Funding
National Key Research and Development Program of China (2017YFE0191300); Hong Kong Polytechnic University (BBX7); Research Grants Council, University Grants Committee (15202814).
Acknowledgments
The work described in this paper was supported by a grant from the National Key Research and Development Program of China (Project Code: 2017YFE0191300) and a grant from the Research Grants Council of the Government of the Hong Kong Special Administrative Region, China (Project No.: 15202814). The authors would also like to express their sincere thanks to the financial support provided by the Research Office of The Hong Kong Polytechnic University (Project No.: BBX7).
Disclosures
The authors declare no conflicts of interest.
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