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Surface characterization of a diamond turned XY sinusoidal grating
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ProcediaProcedia Engineering 00 (2012) 000–000 Engineering 19 (2011) 337 – 342
Procedia Engineering www.elsevier.com/locate/procedia
1st CIRP Conference on Surface Integrity (CSI)
Surface characterization of a diamond turned XY sinusoidal grating Y. Shimizua*, S. Osawaa ,T. Meguroa, W. Lua, W. Gao a a
Tohoku University, 6-6-01, Aoba, Aramaki-Aza, Aoba-ku, Sendai 980-8579, Japan
Abstract Surface characterization of an XY sinusoidal grating, which is fabricated by FTS (fast tool servo) on a diamond turning machine, is presented. The grating has a three dimensional micro-structured surface, which is a superposition of sinusoidal waves in the X- and Y-direction. The pitches and amplitudes of the sine waves are 10 µm and 0.4 µm, respectively. The surface form of the grating is imaged by a confocal microscope, a white light interference microscope and an atomic force microscope. The 3D images from the microscopes are compared with each other to distinguish the measurement uncertainties. The microscope images are analyzed by the two-dimensional discrete Fourier transform technique, which perfectly matches the nature of sinusoidal waves. The spatial spectrum of the grating surface is employed to identify the specific error factors introduced in the diamond turning process.
© 2012 Published by Elsevier Ltd. Selection and peer-review under responsibility of Prof. E. Brinksmeier Keywords: Metrology, Topography, Accuracy, Sinusoidal grating
1. Introduction 1.1. Background of this study The importance of the micro-structured array such as micro lens array, refractive grating and so on is increasing rapidly. Such micro structures array often have repetitive 3D profiles with high aspect ratios; namely, short pitch and large amplitude. Performances of such micro components would be decided by the accuracy of the three-dimensional (3D) profile. The measurement techniques which allow profile measurements with a high accuracy and a high resolution are therefore required [1-3] not only for quality
* Corresponding author. Tel.: +81-22-795-6950; fax: +81-22-795-6950. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.122
338 2
Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 Y. Shimizu et al./ Procedia Engineering 00 (2012) 000–000
inspection but also for feedback to the design and fabrication processes of these micro structures. Currently there are several measurement instruments for three-dimensional profile measurement. Each measurement instruments has advantages and disadvantages for its performance; vertical or horizontal measurement resolution, measurement range, measurement throughput, and so on. Generally speaking, optical methods provide us non-contact, wide-range and high throughput measurement with a good measurement resolution and accuracy. On the other hand, the contact-type methods such as SPM, which use a small and sharp stylus, provide us better measurement resolution although the measurement throughput and the measurement range would be limited by actuators in the measurement systems. In this paper, the 3D images from several measurement instruments are compared with each other to distinguish these performances. Microscope images of a XY sinusoidal grating, which has repetitive 3D structures on its surface, are analyzed by the two-dimensional discrete Fourier transform technique. 1.2. XY sinusoidal grating Figure 1 shows a schematic of the XY sinusoidal grating. The grating was fabricated by using fast tool servo (FTS) technology on an ultra-precision diamond turning machine [4-5]. The grating has a three dimensional micro-structured surface, which is a superposition of sinusoidal waves in the X- and Ydirection. The form profile of the grating can be expressed as
2π 2π zi (x i , y i ) = AX sin x i + AY sin y i λX λY
(1)
where AX, AY are the amplitudes of the sine functions in the X- and Y-directions, respectively. λX and λY are the corresponding spatial wavelengths. In the experiment described in the following, both AX and AY are set to be 0.2 µm, resulting in peak-to-valley amplitude of 0.4 µm. Both λX and λY are set to be 10 µm. The XY sinusoidal grating is used in the surface encoder system [6], which enables us to detect multidegree-of freedom motion when being used with two-dimensional optical angle sensors. The grating is precisely fabricated by FTS on an ultra-precision lathe. The measurement resolution of the surface encoder would be dominated by the pitch length of the grating, and its accuracy would be affected by the accuracy of the pitch length of the XY waveform and its profile. 1.3. Measurement instruments used in this study In this paper, a confocal microscope (VK9500, Keyence corporation), a white light interference microscope (New View 100, ZYGO corporation) and an atomic force microscope (Caliber AFM, Veeco corporation) were employed to image the surface form of the XY sinusoidal grating shown in previous section. Table 1 compares the performance of each measurement instruments.
Fig. 1. Schematic of the profile of a XY-sinusoidal grating
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Y.Y. Shimizu et et al.al./ / Procedia – 342 Shimizu ProcediaEngineering Engineering1900(2011) (2012)337 000–000
Table 1. Specification of the profile measurement instruments used in this paper
Horizontal resolution Vertical resolution
Confocal microscope (Keyence VK9500) 0.07 µm 0.01 µm
White light interference microscope (ZYGO New View 100) 0.27 µm 0.10 nm
Atomic force microscope (Veeco Caliber) 0.05 µm 0.60 nm
Measured area (Number of points)
50 µm × 70 µm (768 pt × 1024 pt)
120 µm × 160 µm (480 pt × 720 pt)
50 µm × 50 µm (1000 pt × 1000 pt)
2. Experiment Figure 2 shows a schematic of the measured grating. The two-dimensional sinusoidal pattern was fabricated on the top surface of the cylinder; the diameter of the grating area is 20 mm. The profile of the XY grating was evaluated at (A) nearly center position, (B) Mid-radial position, (3) Outer-radial position of the grating area. For a fair comparison, the same area should be measured by each measurement instruments. However, it was difficult to observe the same area because of a limitation of measurement setup. On the other hand, from the viewpoint of the turning process, characteristics of profile errors of portions A, B, C, along the circumference direction should be similar, and the result can be compared when the radial position was properly adjusted at each measurement. Figures 3 show the profiles of the XY grating acquired by the confocal microscope. The confocal microscope repeats capturing the images of the measurement surface while shifting the objective lens. The confocal microscope generates the profile image by processing the series of the acquired images; the focus positions at each pixel would be used as Z-directional data. Therefore, precise tilt angle adjustment is not necessary for the measurement process in the confocal microscope. However, it should be noted that the grating profile could not be observed without the proper tilt adjustment. A software adjustment is useful so that the proper profile can be acquired. Figures 4 show the profiles of the XY grating acquired by the white light interference microscope. The field of view was approximately 120 µm × 140 µm. The white light interference microscope repeats capturing the images of the optical interference fringe while shifting the objective lens. The interference fringe should be adjusted to be “null” by adjusting tilts and the light intensity should be adjusted carefully to carry out the profile measurement successfully, especially for the profile with a high-aspect ratio. In addition, we applied an averaging technique and low-pass filter to eliminate the influence of light scattering, which is considered to be due to the roughness / microwaviness on the XY grating. Figures 5 show the profile acquired by the atomic force microscope. A contact mode was employed to measure the grating profile; small tip of the AFM cantilever traces the grating surface while the cantilever motion is monitored to acquire Z-directional data. The field of view was approximately 50 µm × 50 µm, which is the maximum range of our AFM setup. The tilt angles of the measured profile were eliminated in 20 mm A Base
XY grating
B C
Measured position A: Center B: Mid C: Outer
50 mm
Fig. 2. Fabricated XY-sinusoidal grating (amplitude: 0.2 µm, pitch: 10 µm)
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Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 Y. Shimizu et al./ Procedia Engineering 00 (2012) 000–000
(a) Center (b) Mid-radius Fig. 3. Measured profile of the XY-grating by confocal microscope
(c) Outer radius
(a) Center (b) Mid-radius Fig. 4. Measured profile of the XY-grating by the white light interference microscope
(c) Outer radius
(a) Center (b) Mid-radius Fig. 5. Measured profile of the XY-grating by the AFM
(c) Outer radius
(a) Confocal microscope (b) White-light interference microscope Fig. 6. Measured profile of the XY-grating by each microscope 14 12 10 8 6 4 2 0
White light Confocal microscope interferometer
AFM
Amplitude (µm)
Pitch in Y-axis (µm)
Pitch in X-axis (µm)
14 12 10 8 6 4 2 0
Confocal White light microscope interferometer
AFM
(a) Pitch in X direction (b) Pitch in Y direction Fig. 7 Measured pitch and amplitude of the XY grating
(c) AFM 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
White light Confocal microscope interferometer
AFM
(c) Amplitude
the AFM software after the measurements. Figures 6 summarize the grating profile acquired by each instruments. The fields of view of each instruments were different, therefore, the data from the same size of the measurement are plotted off-line by using raw data of the profiles. The AFM has better horizontal resolution so that the distortion of the
Y.Y. Shimizu et et al.al./ / Procedia – 342 Shimizu ProcediaEngineering Engineering1900(2011) (2012)337 000–000
grating profile was observed clearer than the other microscope in our experiments. Although each measured profile showed that the XY grating was successfully fabricated with uniform amplitude, it was observed that the fabricated XY grating has a surface form distorted from the ideal sinusoidal curve, especially around the top and bottom of each grating pattern. Fig. 7 summarizes the measured pitch and amplitude of the sinusoidal pattern on XY grating. The data from white-light interference microscope showed slightly larger pitch deviation, which is due to the influence of light scattering. In addition, data from AFM showed smaller amplitude than the other two instruments; which is due to both the high aspect ratio of the XY grating and an influence of the AFM tip geometry. 3. Analysis by using two-dimensional discrete Fourier transform The grating profiles shown in previous section were analyzed by using the two-dimensional discrete Fourier transform (2D-DFT) to evaluate surface form error in spatial-frequency domain [6]. The DFT spectrum is effective in identifying periodical components in the profile of the sinusoidal pattern. Figures 8 through 10 summarize the 2D-DFT results of each measured profiles shown in Fig. 4 through 6. The 2D-DFT analyses were carried out by using MATLAB®, and the results were plotted in 3D contour images. The number of the data points acquired at each measurement instruments were different, therefore, XY axis of these DFT results were adjusted for fair comparison. In each figures, four
(a) Center
(b) Mid-radius
(c) Outer radius
Fig. 8. Results of 2D-DFT analyses of the measured grating profile by confocal microscope
(a) Center
(b) Mid-radius
(c) Outer radius
Fig. 9. Results of 2D-DFT analyses of the measured grating profile by the white light interference microscope
(a) Center
(b) Mid-radius
Fig. 10. Results of 2D-DFT analyses of the measured grating profile by the AFM
(c) Outer radius
341 5
Center Mid Outer
10
12
FFT power
12
FFT power
Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 14 14 Y. Shimizu et al./ Procedia Engineering Cener 00 (2012) 000–000
8 6 4
8 6 4
2
2
0
0
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
12
Mid Outer
10
FFT power
342 14 6
10
Center Mid Outer
8 6 4 2
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
(a) Confocal microscope (b) White-light interference microscope Fig. 11 Cross-section profiles of the 2D-DFT
0
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
(c) AFM
large peaks were observed around the center of the 2D-DFT results, at the special frequency of about 0.1 µm-1, which corresponds to the spatial wavelengths of the XY grating. The results with the white-light interferometer in Figs. 9 showed a low noise floor, which is due to the data processing with low-pass filter. In Figs. 10, frequency peak lower than the main peak was observed, especially in the results from the center of the grating area as shown in Fig. 10(a). The low frequency portion is considered to be due to center-alignment error at the mirror-finishing process before the grating fabrication [5]. Figures 11 show the cross-section profile of the 2D-DFT in X-direction. Both the DFT results with the confocal microscope and the white-light interference microscope showed a peak around 0.2 µm-1, which indicate the form error from the ideal sinusoidal form of the fabricated XY grating. It is considered that the form error was caused by the round nose geometry of the diamond tool used in FTS [5]. In AFM results, the peak around 0.2 µm-1 was not observed because of (1) the influence of the interaction between sinusoidal pattern of XY grating and AFM tip geometry and (2) the poor resolution of special frequency. 4. Conclusion A surface characterization of an XY sinusoidal grating, which surface form is a superposition of sinusoidal waves in the X- and Y-direction and its pitches and amplitudes of the sine waves are 10 µm and 0.2 µm, respectively, was successfully measured by using the confocal microscope, the white-light interferometer and the AFM. The AFM showed the grating profiles with higher resolution, whereas the AFM data showed smaller amplitude than the other two instruments due to both the high aspect ratio of the XY grating and an influence of the AFM tip geometry. The microscope images are analyzed by the two-dimensional discrete Fourier transform (2D-DFT) technique, and the spatial spectrum of the grating surface was employed to identify the specific error factors introduced in the diamond turning process. 2DDFT results of the white-light interference microscope and the confocal microscope indicated that the fabricated XY grating has a certain amount of form error, which is considered to be due to the round nose geometry of the diamond tool used in FTS. References [1] Leach RK. Fundamental Principles of Engineering Nanometrology. William Andrew Publishing Oxford; 2010, p. 115-175 [2] Dai G, Pohlenz F, Xu M, Koenders L, Danzebrink HU, Wilkening G. Accurate and traceable measurement of nano- and microstructures. Measurement Science and Technology; 2006, 17-3, p.545-552 [3] Bos EJC. Aspects of tactile probing on the micro scale. Precision Engineering; 2011, 35-2, p. 228-240 [4] Kouno K. A fast response piezoelectric actuator for servo correction of systematic errors in precision machining. Annals of CIRP; 1984, 33-1, p. 369-372 [5] Gao W, Araki T, Kiyono S, Okazaki Y, Yamanaka M. Precision nano-fabrication and evaluation of a large area sinusoidalgrid surface for a surface encoder. Precision Engineering; 2003, 27-3, p. 289-298 [6] Gao W. Precision Nanometrology –Sensors and Measurement Systems for Nanomanufacturing-, Springer London; 2010, ISBN 978-1-84996-253-7
ProcediaProcedia Engineering 00 (2012) 000–000 Engineering 19 (2011) 337 – 342
Procedia Engineering www.elsevier.com/locate/procedia
1st CIRP Conference on Surface Integrity (CSI)
Surface characterization of a diamond turned XY sinusoidal grating Y. Shimizua*, S. Osawaa ,T. Meguroa, W. Lua, W. Gao a a
Tohoku University, 6-6-01, Aoba, Aramaki-Aza, Aoba-ku, Sendai 980-8579, Japan
Abstract Surface characterization of an XY sinusoidal grating, which is fabricated by FTS (fast tool servo) on a diamond turning machine, is presented. The grating has a three dimensional micro-structured surface, which is a superposition of sinusoidal waves in the X- and Y-direction. The pitches and amplitudes of the sine waves are 10 µm and 0.4 µm, respectively. The surface form of the grating is imaged by a confocal microscope, a white light interference microscope and an atomic force microscope. The 3D images from the microscopes are compared with each other to distinguish the measurement uncertainties. The microscope images are analyzed by the two-dimensional discrete Fourier transform technique, which perfectly matches the nature of sinusoidal waves. The spatial spectrum of the grating surface is employed to identify the specific error factors introduced in the diamond turning process.
© 2012 Published by Elsevier Ltd. Selection and peer-review under responsibility of Prof. E. Brinksmeier Keywords: Metrology, Topography, Accuracy, Sinusoidal grating
1. Introduction 1.1. Background of this study The importance of the micro-structured array such as micro lens array, refractive grating and so on is increasing rapidly. Such micro structures array often have repetitive 3D profiles with high aspect ratios; namely, short pitch and large amplitude. Performances of such micro components would be decided by the accuracy of the three-dimensional (3D) profile. The measurement techniques which allow profile measurements with a high accuracy and a high resolution are therefore required [1-3] not only for quality
* Corresponding author. Tel.: +81-22-795-6950; fax: +81-22-795-6950. E-mail address: [email protected].
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.11.122
338 2
Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 Y. Shimizu et al./ Procedia Engineering 00 (2012) 000–000
inspection but also for feedback to the design and fabrication processes of these micro structures. Currently there are several measurement instruments for three-dimensional profile measurement. Each measurement instruments has advantages and disadvantages for its performance; vertical or horizontal measurement resolution, measurement range, measurement throughput, and so on. Generally speaking, optical methods provide us non-contact, wide-range and high throughput measurement with a good measurement resolution and accuracy. On the other hand, the contact-type methods such as SPM, which use a small and sharp stylus, provide us better measurement resolution although the measurement throughput and the measurement range would be limited by actuators in the measurement systems. In this paper, the 3D images from several measurement instruments are compared with each other to distinguish these performances. Microscope images of a XY sinusoidal grating, which has repetitive 3D structures on its surface, are analyzed by the two-dimensional discrete Fourier transform technique. 1.2. XY sinusoidal grating Figure 1 shows a schematic of the XY sinusoidal grating. The grating was fabricated by using fast tool servo (FTS) technology on an ultra-precision diamond turning machine [4-5]. The grating has a three dimensional micro-structured surface, which is a superposition of sinusoidal waves in the X- and Ydirection. The form profile of the grating can be expressed as
2π 2π zi (x i , y i ) = AX sin x i + AY sin y i λX λY
(1)
where AX, AY are the amplitudes of the sine functions in the X- and Y-directions, respectively. λX and λY are the corresponding spatial wavelengths. In the experiment described in the following, both AX and AY are set to be 0.2 µm, resulting in peak-to-valley amplitude of 0.4 µm. Both λX and λY are set to be 10 µm. The XY sinusoidal grating is used in the surface encoder system [6], which enables us to detect multidegree-of freedom motion when being used with two-dimensional optical angle sensors. The grating is precisely fabricated by FTS on an ultra-precision lathe. The measurement resolution of the surface encoder would be dominated by the pitch length of the grating, and its accuracy would be affected by the accuracy of the pitch length of the XY waveform and its profile. 1.3. Measurement instruments used in this study In this paper, a confocal microscope (VK9500, Keyence corporation), a white light interference microscope (New View 100, ZYGO corporation) and an atomic force microscope (Caliber AFM, Veeco corporation) were employed to image the surface form of the XY sinusoidal grating shown in previous section. Table 1 compares the performance of each measurement instruments.
Fig. 1. Schematic of the profile of a XY-sinusoidal grating
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Y.Y. Shimizu et et al.al./ / Procedia – 342 Shimizu ProcediaEngineering Engineering1900(2011) (2012)337 000–000
Table 1. Specification of the profile measurement instruments used in this paper
Horizontal resolution Vertical resolution
Confocal microscope (Keyence VK9500) 0.07 µm 0.01 µm
White light interference microscope (ZYGO New View 100) 0.27 µm 0.10 nm
Atomic force microscope (Veeco Caliber) 0.05 µm 0.60 nm
Measured area (Number of points)
50 µm × 70 µm (768 pt × 1024 pt)
120 µm × 160 µm (480 pt × 720 pt)
50 µm × 50 µm (1000 pt × 1000 pt)
2. Experiment Figure 2 shows a schematic of the measured grating. The two-dimensional sinusoidal pattern was fabricated on the top surface of the cylinder; the diameter of the grating area is 20 mm. The profile of the XY grating was evaluated at (A) nearly center position, (B) Mid-radial position, (3) Outer-radial position of the grating area. For a fair comparison, the same area should be measured by each measurement instruments. However, it was difficult to observe the same area because of a limitation of measurement setup. On the other hand, from the viewpoint of the turning process, characteristics of profile errors of portions A, B, C, along the circumference direction should be similar, and the result can be compared when the radial position was properly adjusted at each measurement. Figures 3 show the profiles of the XY grating acquired by the confocal microscope. The confocal microscope repeats capturing the images of the measurement surface while shifting the objective lens. The confocal microscope generates the profile image by processing the series of the acquired images; the focus positions at each pixel would be used as Z-directional data. Therefore, precise tilt angle adjustment is not necessary for the measurement process in the confocal microscope. However, it should be noted that the grating profile could not be observed without the proper tilt adjustment. A software adjustment is useful so that the proper profile can be acquired. Figures 4 show the profiles of the XY grating acquired by the white light interference microscope. The field of view was approximately 120 µm × 140 µm. The white light interference microscope repeats capturing the images of the optical interference fringe while shifting the objective lens. The interference fringe should be adjusted to be “null” by adjusting tilts and the light intensity should be adjusted carefully to carry out the profile measurement successfully, especially for the profile with a high-aspect ratio. In addition, we applied an averaging technique and low-pass filter to eliminate the influence of light scattering, which is considered to be due to the roughness / microwaviness on the XY grating. Figures 5 show the profile acquired by the atomic force microscope. A contact mode was employed to measure the grating profile; small tip of the AFM cantilever traces the grating surface while the cantilever motion is monitored to acquire Z-directional data. The field of view was approximately 50 µm × 50 µm, which is the maximum range of our AFM setup. The tilt angles of the measured profile were eliminated in 20 mm A Base
XY grating
B C
Measured position A: Center B: Mid C: Outer
50 mm
Fig. 2. Fabricated XY-sinusoidal grating (amplitude: 0.2 µm, pitch: 10 µm)
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Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 Y. Shimizu et al./ Procedia Engineering 00 (2012) 000–000
(a) Center (b) Mid-radius Fig. 3. Measured profile of the XY-grating by confocal microscope
(c) Outer radius
(a) Center (b) Mid-radius Fig. 4. Measured profile of the XY-grating by the white light interference microscope
(c) Outer radius
(a) Center (b) Mid-radius Fig. 5. Measured profile of the XY-grating by the AFM
(c) Outer radius
(a) Confocal microscope (b) White-light interference microscope Fig. 6. Measured profile of the XY-grating by each microscope 14 12 10 8 6 4 2 0
White light Confocal microscope interferometer
AFM
Amplitude (µm)
Pitch in Y-axis (µm)
Pitch in X-axis (µm)
14 12 10 8 6 4 2 0
Confocal White light microscope interferometer
AFM
(a) Pitch in X direction (b) Pitch in Y direction Fig. 7 Measured pitch and amplitude of the XY grating
(c) AFM 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
White light Confocal microscope interferometer
AFM
(c) Amplitude
the AFM software after the measurements. Figures 6 summarize the grating profile acquired by each instruments. The fields of view of each instruments were different, therefore, the data from the same size of the measurement are plotted off-line by using raw data of the profiles. The AFM has better horizontal resolution so that the distortion of the
Y.Y. Shimizu et et al.al./ / Procedia – 342 Shimizu ProcediaEngineering Engineering1900(2011) (2012)337 000–000
grating profile was observed clearer than the other microscope in our experiments. Although each measured profile showed that the XY grating was successfully fabricated with uniform amplitude, it was observed that the fabricated XY grating has a surface form distorted from the ideal sinusoidal curve, especially around the top and bottom of each grating pattern. Fig. 7 summarizes the measured pitch and amplitude of the sinusoidal pattern on XY grating. The data from white-light interference microscope showed slightly larger pitch deviation, which is due to the influence of light scattering. In addition, data from AFM showed smaller amplitude than the other two instruments; which is due to both the high aspect ratio of the XY grating and an influence of the AFM tip geometry. 3. Analysis by using two-dimensional discrete Fourier transform The grating profiles shown in previous section were analyzed by using the two-dimensional discrete Fourier transform (2D-DFT) to evaluate surface form error in spatial-frequency domain [6]. The DFT spectrum is effective in identifying periodical components in the profile of the sinusoidal pattern. Figures 8 through 10 summarize the 2D-DFT results of each measured profiles shown in Fig. 4 through 6. The 2D-DFT analyses were carried out by using MATLAB®, and the results were plotted in 3D contour images. The number of the data points acquired at each measurement instruments were different, therefore, XY axis of these DFT results were adjusted for fair comparison. In each figures, four
(a) Center
(b) Mid-radius
(c) Outer radius
Fig. 8. Results of 2D-DFT analyses of the measured grating profile by confocal microscope
(a) Center
(b) Mid-radius
(c) Outer radius
Fig. 9. Results of 2D-DFT analyses of the measured grating profile by the white light interference microscope
(a) Center
(b) Mid-radius
Fig. 10. Results of 2D-DFT analyses of the measured grating profile by the AFM
(c) Outer radius
341 5
Center Mid Outer
10
12
FFT power
12
FFT power
Y. Shimizu et al. / Procedia Engineering 19 (2011) 337 – 342 14 14 Y. Shimizu et al./ Procedia Engineering Cener 00 (2012) 000–000
8 6 4
8 6 4
2
2
0
0
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
12
Mid Outer
10
FFT power
342 14 6
10
Center Mid Outer
8 6 4 2
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
(a) Confocal microscope (b) White-light interference microscope Fig. 11 Cross-section profiles of the 2D-DFT
0
0
0.2 0.4 0.6 0.8 Spatial frequency µm-1
1
(c) AFM
large peaks were observed around the center of the 2D-DFT results, at the special frequency of about 0.1 µm-1, which corresponds to the spatial wavelengths of the XY grating. The results with the white-light interferometer in Figs. 9 showed a low noise floor, which is due to the data processing with low-pass filter. In Figs. 10, frequency peak lower than the main peak was observed, especially in the results from the center of the grating area as shown in Fig. 10(a). The low frequency portion is considered to be due to center-alignment error at the mirror-finishing process before the grating fabrication [5]. Figures 11 show the cross-section profile of the 2D-DFT in X-direction. Both the DFT results with the confocal microscope and the white-light interference microscope showed a peak around 0.2 µm-1, which indicate the form error from the ideal sinusoidal form of the fabricated XY grating. It is considered that the form error was caused by the round nose geometry of the diamond tool used in FTS [5]. In AFM results, the peak around 0.2 µm-1 was not observed because of (1) the influence of the interaction between sinusoidal pattern of XY grating and AFM tip geometry and (2) the poor resolution of special frequency. 4. Conclusion A surface characterization of an XY sinusoidal grating, which surface form is a superposition of sinusoidal waves in the X- and Y-direction and its pitches and amplitudes of the sine waves are 10 µm and 0.2 µm, respectively, was successfully measured by using the confocal microscope, the white-light interferometer and the AFM. The AFM showed the grating profiles with higher resolution, whereas the AFM data showed smaller amplitude than the other two instruments due to both the high aspect ratio of the XY grating and an influence of the AFM tip geometry. The microscope images are analyzed by the two-dimensional discrete Fourier transform (2D-DFT) technique, and the spatial spectrum of the grating surface was employed to identify the specific error factors introduced in the diamond turning process. 2DDFT results of the white-light interference microscope and the confocal microscope indicated that the fabricated XY grating has a certain amount of form error, which is considered to be due to the round nose geometry of the diamond tool used in FTS. References [1] Leach RK. Fundamental Principles of Engineering Nanometrology. William Andrew Publishing Oxford; 2010, p. 115-175 [2] Dai G, Pohlenz F, Xu M, Koenders L, Danzebrink HU, Wilkening G. Accurate and traceable measurement of nano- and microstructures. Measurement Science and Technology; 2006, 17-3, p.545-552 [3] Bos EJC. Aspects of tactile probing on the micro scale. Precision Engineering; 2011, 35-2, p. 228-240 [4] Kouno K. A fast response piezoelectric actuator for servo correction of systematic errors in precision machining. Annals of CIRP; 1984, 33-1, p. 369-372 [5] Gao W, Araki T, Kiyono S, Okazaki Y, Yamanaka M. Precision nano-fabrication and evaluation of a large area sinusoidalgrid surface for a surface encoder. Precision Engineering; 2003, 27-3, p. 289-298 [6] Gao W. Precision Nanometrology –Sensors and Measurement Systems for Nanomanufacturing-, Springer London; 2010, ISBN 978-1-84996-253-7