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Traditional off-line measuring systems find it difficult to measure micro-structured workpieces which have a large volume and heavy weight, such as micro-structured patterned precision roller drums. This paper proposes an autostereoscopy-based three-dimensional (3D) measuring method and develops an innovative measuring system for the 3D on-machine measurement of the micro-structured surfaces, an Autostereoscopy-based Three-Dimensional On-machine Measuring (ATDOM) system. The ATDOM system is compact and capable of fast data acquisition and high accuracy in 3D computational reconstruction of complex surfaces under different measuring environments. A prototype ATDOM system is experimentally verified through a series of measurement experiments conducted on a precision machine tool. The results indicate that the ATDOM system provides an important means for efficient and reliable on-machine measurement of micro-structured surfaces.
© 2014 Optical Society of America
1. Introduction
The application of micro-structured surfaces has already stepped into and changed our lives. The geometrical complexity and high accuracy requirement of micro-structured surfaces imposes a lot of challenges in the measurement and characterization of micro-structured surfaces. This makes three-dimensional (3D) measurement the most desirable measuring process. Many coordinate measurement instruments developed in recent years for the measurement of micro-structured surfaces come under traditional off-line measurement processes [1–3], which are not amenable for measuring workpieces of a relatively large size and heavy weight. Moreover, there is a lack of efficiency and measurement traceability. In this sense, it is more amenable to directly measure workpieces during the manufacturing process which can be achieved by on-machine measurement.
Although many ultra-precision coordinate measuring instruments have already been developed in recent years for the measurement of micro-structured surfaces, even for 3D measurement [4–6], these measuring systems have their own defects. A probe that has mechanical contact with the workpiece is used to determine its actual size. Normally, the probe-type contact measurement machine makes use of interferometry to precisely detect the tiny movement of the probe [7]. Many commercial contact measurement systems can generate a 3D surface profile of freeform surface, which are also known as 3D profilometers, such as the New Form Talysurf PGI series developed by Talyor Hobson Ltd. The two biggest limitations [8] of the contact measurement system are that the contact probe can cause scratches and damage the workpiece and an error source is induced because the radius of the probe can result in discord between the track of the probe and actual surface profile.
Due to these limitations, different non-contact 3D measuring methods have been vigorously developed. The light scattering method [1] [9–11] is one of the most commonly used in this field. The sensor receives the light signal scattered from the test surface to obtain the profile information of the surface. Structured light measurement which can be categorized as the light scattering method and has been developed into a very mature method for 3D measurement. In order to increase the accuracy of the measurement, the light is usually coded into certain patterns. Xu et al. [12] used the composite pattern based on the binary stripe pattern to realize real-time 3D profile measurement. Moreover, the accuracy of the calibration of a point’s image coordinates directly influences the system's measurement accuracy. Xue et al. [13] developed a procedure to eliminate the errors in the calibration image for 3D measurement with structured light. Chen [14] developed a digital grating projection and proposed non-contact 3D measurement by using digital grating phase-shift, combined with height-phase mapping and self-lattice calibrating. The biggest limitation of the structure light method is the limited size of the stripe width which cannot easily meet the high requirements of the measurement.
Another universal method that can realize 3D measurement was inspired by the principle of human Binocular Stereo Vision. A stereovision 3D measuring method is based on a system with two cameras whose location in the space is known. According to their acquired images, the specific spatial information of the object can be determined. It is also extensively used in the Geographic Information System as a photogrammetry method. Zhao et al. [15] introduced a 3D measurement system based on the stereovision and phase-shifting method combined with CNC machine tools, which can measure the 3D profile of the machining workpieces between the key machining processes.
Moreover, triangulation with structured light projection is a well-established measurement technique. However, as an indispensable process for such system, all the existing calibration methods need to consider the influence of lens distortion and perspective error. Based on speckle projection, Zhu et al. [16] proposed a system for deformation measurement that is developed with a telecentric lens. The photogrammetry-based measuring technology has a complicated calibration process of coordinates which makes it very difficult to perform on machine measurement.
Focal variance is a well-developed method which has already been commercialized, especially in the micro and nano range, such as InfiniteFocus Series from Alicona. However, focal variance-based measuring systems usually have a rather low efficiency during the measurement. Helmli et al. [17] presented an optical measurement device based on the Focus Variation principle that is able to perform 3D measurements with 4 million measurement points within one second. Nevertheless, applying a focal variance-based measuring system to a fabricating machine to perform on-machine measurement is still a huge challenge. Another 3D reconstruction method named holography can visualize the microscopic phase objects in three dimensions and it can be used to measure their morphological parameters [18]. However, due to the complexity of the holographic system, it is difficult to meet the extremely rigorous requirements of the environment as imposed in the in situ measurement of 3D surfaces by the attachment of a holographic 3D system to a machining system.
Integral imaging, as a display-oriented technology, is a kind of autostereoscopic technology, which was initially proposed by G. Lippmann in 1908 [19]. The technology rapidly developed recently, including in fields other than displays. The three-dimensional information acquisition technology in integral imaging is actually a transformation of traditional three-dimensional information acquisitions. This technology provides more perspectives through the single image capturing of one camera. In the extraction of three-dimensional information [20], the depth is the first information extracted and is found by detecting the disparity, which means the relative distance to the exact same point of the object viewed from different perspectives. These same points are named corresponding points [21] and this process is called a stereo matching process. Moreover, based on that, the three-dimensional digital appearance of an object can be acquired by this methodology [22].
Being inspired by that, this paper innovatively proposes an autostereoscopy-based 3D measuring method and correspondingly developed the Autostereoscopy-based Three-Dimensional On-machine Measuring (ATDOM) System for measuring micro-structured surfaces. To our knowledge, this display-oriented technology developed as a measuring method was a new pioneering attempt. With one snapshot of the object scene, it has a fast data acquisition process. With a simple and compact system setup, it is adaptable for different measuring environments. With the accuracy of 3D computational reconstruction, it is a precise method as a measurement methodology. All the above makes the ATDOM system an effective 3D on-machine measuring system for micro-structured surfaces.
2. Autostereoscopy-based 3D measuring method
The Autostereoscopy-based 3D measuring method inherits the advantages of the autostereoscopic 3D display technology. It not only provides a fast and effective data acquisition process but also allows direct extraction of disparity information from the elemental images (EIs) without any additional error source sneaked into. The specific digital information of objects can be precisely reconstructed according to the geometrical relationship of the ray optics.
A. Autostereoscopy-based 3D measuring theory
Since human eyes provide the most direct way of experiencing the 3D world, stereoscopy is believed to be the most intuitive way to realize 3D displays. By providing a pair of images with slight differences and ensuring each of the eyes can receive its own image independently, the observer can receive a 3D image due to the processing by the human brain. Autostereoscopy, as a development of stereoscopy can provide real 3D images to the observer without any physical or mental aid. Similar to the theories proposed later, such as light field theory [23] and plenoptic functions, all of them are based on the elements that can provide multiple images with different angels of the same scene, such as inserting a micro lens array (MLA) into the optical path of a traditional imaging system. The 3D information of the objects scene is stored in the slight differences among a series of 2D images which are named elemental images.
The autostereoscopy-based 3D measuring method can be divided into two steps: the recording process and reconstruction process as shown in Fig. 1.Through the aid of ray optics, the MLA is analyzed as the pinhole array for clear illustration and effective analysis. Since the spatial locations of the elemental lenses are different, the acquired elemental images are slightly different. These differences between elemental images are called the disparities [24].
Fig. 1 Recording process and reconstruction process of the autostereoscopy-based 3D measuring method. Three sample points with different depths are recorded with disparities in the recording process (left figure), and these sample points can be precisely reconstructed in the reconstruction process (right figure) if the two process are symmetrical.
Specifically, the circle point A located on a certain depth plane and optical axis of the MLA is selected for easy demonstration. It is supposed that the half scale of MLA in one dimension is n which makes the whole scale of MLA 2n-1. Hence, the disparity of the circle point A between the nth elemental lens and the central elemental lens of MLA can be expressed as:
which DEI is the pitch of elemental images, n is the serial number of the elemental lens counting from the one that is facing the object point, SD is the recording distance which directly represents the depth information, g is the distance between the sensor and the MLA, and ΔDR(n,0) is the disparity.Accordingly, for the object points which are located on the same depth plane, their disparities in different elemental images are the same (the red solid lines and blue dashed lines as shown in Fig. 1 on the left) based on the simple geometrical relationship:
where DP is the abbreviation for lens pitch which is normally the same as DEI, and DB, DR are the absolute distance between the blue square and red circle corresponding points [21] in different elemental images.Based on the analysis made above, the object points on different depth planes can be quantitatively depicted on the elemental image plane under certain system parameters. As the system setup is ensured, the only factor that can determine the disparity is the depth information. The 3D information of the object space is stored in these disparities.
After the elemental images with 3D information stored are obtained during the recording process, these elemental images are directly used in the reconstruction process. Based on the reversibility of the optic rays, the two processes become symmetrical by using the same MLA and system setup, which means the object space can be precisely reconstructed, as shown in Fig. 1. This nature of autostereoscopy theory is the foundation of the autostereoscopy-based measurement method.
Specifically, the disparity information is represented by the number of pixels and single pixel size which is determined by the basic theory of machine vision-based measuring systems. In the reconstruction process of the proposed autostereoscopy-based 3D measuring method, one certain disparity ΔD is supposed to be approximately determined by the number of pixels Np and single pixel size p as expressed by Eq. (3) below:
A quantitative relationship between the number of pixels and the to-be-measured value, which is the dimensions of the targets, can be established in both the lateral and axial direction. They satisfy the fundamental theory of any indirect metrology system.For the lateral direction, considering the disparity information, the depth information of the plane can be confirmed by Eq. (1). Based on this depth information, the reconstructed lateral distance between two focused target points which is also the measured value between them in the lateral direction can be calculated. The image points denoted by a circle and square in the nth elemental image can be taken as a simple illustration as shown in the right part of Fig. 1. The measured value along the lateral direction can be expressed as:
where DsEI is the distance between two image points in single Elemental Image (EI) as shown as the distance of two focused elemental image points of the circle point and the square point in the nth elemental image in Fig. 1, SD is the depth information of the plane which is determined by the known disparity information, g is the distance between the elemental images and the MLA according to the system setup, and Dl is the measured value of two target points as shown as the measured value between the two reconstructed image points (circle point and square point) in Fig. 1.For axial direction, the circle point A and the cross point C as shown in Fig. 1 are used as a simple illustration. The distance between two depth planes which is also the measured value in the axial direction can be found from:
where SD1 and SD2 are the abstract axial positions of two depth planes, which are shown as the depth plane of the circle point and cross point in Fig. 1, n is the nth elemental image; ΔD1(n,0), and ΔD2(n,0) are the disparities information of different depth information in the nth elemental image which are shown as the disparity information of the circle point and cross point between the nth elemental images and the central elemental image in Fig. 1, g is also the distance between the elemental images and the MLA according to the system setup, and Depth is the measured value between two depth planes in the axial direction.The above equations (i.e. Equations (1)-(5)) quantitatively express the basic measuring theory of the proposed method, and build up the relationship between pixels and measured quantity, which is the theoretical foundation of the autostereoscopy-based 3D measuring method. Based on this, other specialties of the method, such as digital refocusing and disparity information direct extraction, can make the proposed method more effective when dealing with 3D measurement.
B. Digital refocusing
Image refocusing is the prominent feature of autostereoscopy-based 3D measuring theory. It is determined by the abundant information generated by every micro lens during the recording process. The captured information is spatially converged in the reconstruction space at different levels, which manifests as a series of continuous 2D images located axially with the focus changed continuously. Moreover, based on the property of symmetry between the two processes of the autostereoscopy-based 3D measuring method, the focal information is located at symmetrical positions of the object space in the reconstruction space with a scale which is not changed. This provides a solid basis for the purpose of being a measuring method.
The digital refocusing process is more likely to be the superposition and re-arrangement of the pixels layer by layer [25]. The acquired information is extracted and summed up to form different reconstructed planes. After the recording process, image points with disparities are located in every single elemental image. As shown on the right side of Fig. 1, the reconstruction process can reconstruct the information with different depths simultaneously. The reason for this is that disparity is a parameter which can only be determined by the depth information and can only be focused on its related depth during the reconstruction process.
The disparity of a certain depth plane of the object space is identical which can be easily discovered based on the geometrical relationship as shown in Eq. (2). These elemental image points with the same disparity can be relocated through the MLA to the reconstruction space at separated depths, with different degrees of superposition. Only the disparities with different depth information planes are varied. The theory of digital refocusing process is shown in Fig. 2.
Fig. 2 Digital refocusing. Sample points with different depth information can only be focally reconstructed on the depth plane to which they belong; information other than this is blurrily reconstructed.
The difference between the focused and defocused information is the degree of convergence of these elemental image points which can be very different foe every depth plane of the reconstruction space. Elemental image points with identical disparity can be converged into a focused reconstructed point on the depth plane where they are supposed to be attributed to that depth in the reconstruction space, such as the focus of blue dashed line and red solid line rays on the left reconstruction plane and green dashed and dotted line rays on the right reconstruction plane. Other elemental image points with different disparities can only be reconstructed into a defocused spot on that depth plane, such as the green defocused spot (shown as stripe pattern) in the left section view and blue and red defocused spot in the right section view. These phenomena happen in all the reconstruction planes other than the belonging depth plane, only with different defocused levels. That is how different depths of the reconstruction space can have different focal information simultaneously, which provides the possibility to axially reconstruct a continuous series of 2D images with its own specific focal information. This means 3D information of the object to be measured can be precisely and continuously reconstructed through the 2D focused information in a series of images along the axial direction. However, the focused information is affected by the other defocused information which causes a lot of difficulties for targeting the information needed by the measurement. This is the reason why focal information needs to be precisely extracted for the further measuring process.
C. Direct extraction of disparity information
According to the digital refocusing theory, based on a certain system setup, there exists only one disparity information pattern concerning a certain depth, which can be directly extracted from the elemental images and converged at its related focused plane. All the other information from the elemental images is eliminated. This extracted disparity information of different depth planes is essential to the measurement process because it can form the focused information on their related depth planes continuously along the axial direction with the scale which is unchanged. They provide sharp targets for measuring the dimensions of the object.
A direct extraction algorithm for the disparity information is developed based on the theory of digital refocusing and autostereoscopic information matching algorithm. Through the virtual setup of the MLA, a reconstruction process can be virtually built up according to the system setup of the recording process. In this sense, the information of the reconstruction space is identical to the object space according to the property of symmetry of autostereoscopy-based 3D measuring theory.
Based on the analysis of the recording process in part A of this section, the disparity map of a certain depth plane can be achieved, which is the core of the algorithm to extract the focused information. In the meantime, the defocused information is completely eliminated through an autostereoscopic information matching algorithm. The flowchart is shown in Fig. 4. After the recording process, the acquired elemental images are directly input into the program. According to the certain axial coordinate value, the disparity map can be calculated. The disparity map is used as a filter to screen all the pixels in the elemental images. With the aid of the matching algorithm [26,27] for autostereoscopic information in terms of grayscale information or color information, the criteria concerning the statistical characteristic quantities are applied to the pixels which are passed through the filter. Pixels with disparities that are not related to that axial coordinate value are ruled out. This is a single loop concerning one certain axial coordinate value. By inputting continuous axial values, their corresponding pixels are screened out and the focused information of its related reconstructed plane is determined. Combining the 2D focused information and the quantitative axial information of every processed image plane, the whole 3D object scene can be precisely and digitally reconstructed slice by slice as shown in Fig. 3.
Fig. 3 3D information of the digital reconstruction of the object space. Only the focused informaion of the related depth plane is processed. This information is digitally reconstructed along the axis to form the 3D information of the object. The sketch shows the 3D information of a spheroid which is reconstructed by several slices of the focused oval-shape information which is the section view of the spheroid.
This algorithm is completely based on the principle of recording process of autostereoscopic 3D display theory. No other error resources are imported in the whole process, which provides a solid basis to meet the requirements of a credible measuring process.
D. Error source analysis, reference, and calibration
As a machine vision-based measuring method, in order to make the acquired data valid, analyzing the error source and introducing a reference to perform the calibration are prerequisite.
Although the autostereoscopy-based 3D measuring method can precisely reconstruct the 3D information of the object space, the practical setup of the measuring system can unavoidably introduce errors into the measurement results. External error sources such as vibration of the manufacturing machine, different illumination status of the objects and different measurement posture of the system are introduced as random error sources. Through multiple measurement processes for a single target, these random error sources can eventually be eliminated.
Like any machine vision measuring system, the aberration of the optical system is the main systematical error source. Using a standard component with known data as a reference to perform the calibration can effectively eliminate this systematical error. Moreover, an important part of the autostereoscopy-based 3D measuring method is the dimensional transformation. The minimum operation unit of the measuring process is a pixel. The size of pixel in dimension of length is the key to the dimensional transformation from pixel to length. In this sense, like any machine vision-based measurement method, the outputs are in dimensions of length originating from the number of pixels.
A measuring process of reference is conducted through the proposed ATDOM system. For the calibration of the lateral direction, an Olympus reference with a pair of slits the distance between which is already known is input into the ATDOM system. Since the total pixel number between the two slits is available in different images with different system magnification, the single pixel size can be determined. Accordingly, the real lateral size of the object to be measured can be calculated through counting the number of pixels and multiplying by the single pixel size.
Due to the specialty of the theoretical basis of the autostereoscopy-based measuring method, the object can be reconstructed with the same scale if the two processes have the same system parameters. In this sense, if the lateral direction is calibrated, the axial direction is calibrated simultaneously based on the geometrical optics theory of the autostereoscopy-based measuring method. Accordingly, the ATDOM system is fully calibrated. So far, this is the whole autostereoscopy-based 3D measuring method, which is first proposed.
3. 3D on-machine measuring system
As shown in Fig. 5, a compact measuring system was built which consists of a CCD sensor, a micro-lens array (MLA), a zoom tube, an objective lens, and a group of LED light bars located in the shape of a square. The light is emitted from the squared light bars and is reflected by the workpiece to be measured. The light signal is propagated through the objective lens system and MLA, and is received by the sensor. The elemental images with disparities are captured and transferred to a computer immediately for further processing through the purposely-built measuring program.
Fig. 5 ATDOM system sketch and ATDOM system picture. The components in the ATDOM system correspond to each other in the upper and lower pictures. In the system sketch, WD is the working distance of objective lens, and fobj and fMLA are the focal length of the objective lens and MLA.
The F-number of the objective lens and MLA should be close enough to guarantee the efficient use of the light [23]. The MLA is positioned at the focal plane of the main lens, after which it is the image sensor that is placed at the MLA’s focal plane. The total size and scale of the MLA are of great importance to the performance [28,29] of the measuring system. The total size determines the measuring field and it should fit the CCD sensor. The scale and size of the elemental lens of the MLA possesses an inversely proportional relationship once the total size of the MLA is settled down. Moreover, these two parameters have a paradoxical relationship affecting the system performance. A bigger elemental lens can enhance the lateral measuring resolution. However, the larger size of elemental lens results in a smaller scale of the MLA which will lower the axial resolution of the measuring system and vice versa. These parameters of the MLA are balanced so as to achieve the desired measuring system performance. The specific parameter of the system is shown in Table 1.
Table 1. Specification of the ATDOM System
A calibration process of the ATDOM system using the standard optical slits is performed before the measuring process. After that, a theoretical performance analysis is provided based on the voxel model to represent the lateral and axial resolving ability of the measurement. The voxel model [21] is a verified model for the reconstruction process by analyzing the case of corresponding overlapping pixels, which is useful for the evaluation and optimization of integral imaging systems and this represents the limits of the ideal resolving ability of the measurement. Moreover, half of a pixel is the minimum unit that can be distinguished by the developed measuring program. This can improve the axial resolving ability twice as compared to the results of the voxel model analysis. Based on the analysis above, the theoretical resolving ability of the ATDOM system under 20X system magnification is around 0.36 um in the lateral direction and 0.07 um in the axial direction. This shows the potential of the best performance that the ATDOM system can achieve. Considering the limits of a recording system and real optical system, the practical resolving ability is around 10 um in the axial direction and around 0.5 um in the lateral direction.
4. Experiments for 3D on-machine measurement
In order to verify the feasibility of the system for on-machine measurement, this system was installed on a 3-axis ultra-precision machine named the Nanoform 350 FG. A series of measurement experiments was conducted for on-machine measurement of a machined 3D-micro-structured surface. Based on the analysis of the system performance, the on-machine measurement focused on the form accuracy measurement of the sub-millimeter-scale micro-structured surfaces. After the on-machine measurement, the measuring data of the dimensions of the pyramid structure is shown in Table 2.Edge A and Edge B in the lateral direction and Height in the axial direction are compared with that for the designed data as shown in Fig. 6.A compensation strategy is designed and the compensation process is conducted on the same machine without taking the workpiece down.
Table 2. Measuring data of dimensions of pyramid structure through the ATDOM System
Fig. 6 Original design of the pyramid micro-structured surface. The side-view and front-view of the workpiece are shown in the left side and right side of the upper part, and the 3D view of the workpiece is shown in the lower part of the figure.
As the ATDOM system is mounted on the ultra-precision machine which is shown in Fig. 7, a series of elemental images of the workpiece is captured by the CCD sensor through the MLA and objective lens in one single shot and the image data is instantly transferred to a computer for further processing. By processing the data via the purposely developed measurement program, the digital refocusing results of the object space along different axial positions can be acquired. Moreover, the focal information of the reconstructed planes is extracted to form the 3D measurement result of the object.
Fig. 7 ATDOM system conducting an on-machine measurement with the fabricating machine in order to perform the compensation process of a workpiece with the micro-structure of pyramids subsequently
The dimensions of the pyramid structure can be acquired by the dimensional transformation from the number of pixels counting from the focused margin and the size of a single pixel. After this, the axial digital information can also be confirmed due to the geometrical optics theory of the proposed autostereoscopy-based 3D measuring method.
Figure 8 shows a series of results of the pyramid sample with different foci along the Z axis through the computation by the purposely developed measuring program. Due to the advantageous features of the proposed method, these pictures show the information of different depth planes from top of the pyramid structure to the bottom vividly. Moreover, the information was obtained with the precise location of the Z axis as calculated by the calibration of the ATDOM system.
Fig. 8 Digital refocusing results. A series of pyramid structures with different foci from top to bottom and digital depth information is shown.
Based on the results processed from digital refocusing, the disparity information is directly extracted by the purposely developed measuring program. The isolated focused information can be obtained, which is the foundations to form the digital 3D information of the pyramid structure to be measured. The lateral size of the target in different reconstruction planes can be confirmed according to the number of pixels between the focused margins and the pixel size. Combining with the calibrated axial length information, the 3D information of the target can be measured.
In order to eliminate the random errors during the measurement, multiple measuring processes for the single pyramid structure are conducted. In the meantime, the multiple targets are measured through the ATDOM system in order to test the technical feasibility. The full data analysis results are shown in Table 2.
In order to conduct a comparison and benchmarking, a scanning electron microscope (SEM) was used in this experiment as the verification tool to provide the true value of the pyramid micro-structure. After the data processing and analysis, it was interesting to note that the 3D measurement data of the dimensions of the pyramid structure acquired from the ATDOM system and its related measuring program was valid.
5. Conclusion and future work
Freeform optical surface is a rather controversial concept with wide definitions since there exist different definitions in different research areas, including aspherical surfaces, non-rotationally symmetrical surfaces and traditional surfaces with microstructure regarding it. This paper proposed a novel on-machine measurement method named an autostereoscopy-based 3D measuring method. Hence an Autostereoscopy-based Three-Dimensional On-machine Measuring (ATDOM) system was established which is capable of performing 3D on-machine measurement for micro-structured surfaces. It is highly needed due to the geometrical complexity of micro-structured surfaces and convenience of manufacturing process. Experimental results show that the proposed ATDOM system is capable of performing 3D on-machine measurement by incorporating it into ultra-precision fabricating machines. It is believed that the proposed autostereoscopy-based 3D measuring method and the associated ATDOM system will definitely allow further development of ultra-precision manufacturing technology with an effective and efficient measuring process.
However, as the pioneering work of a potential research field, one of the dominant limitations of the ATDOM system is its measuring resolution as compared with the analyzed resolving ability limit and experimental results. In order to perform 3D on-machine measurement with higher accuracy and precision, future research work will focus on the amelioration of system parameters and the improvement of system performance. Moreover, detailed research analyzing the measuring performance of the system, and research regarding calibration, traceability, and uncertainty as a measuring instrument will also be explored in the future.
Acknowledgment
The authors would like to express their sincere thanks to the Research Committee of The Hong Kong Polytechnic University and the Innovation and Technology Commission (ITC) of the Government of the Hong Kong Special Administrative Region (HKSAR) for the financial support of the research work under project no. GHP/045/10SZ. The work was also supported by a PhD studentship (project account code RTK7) from The Hong Kong Polytechnic University.
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