- Email: [email protected]
Surface profile measurement using a unique microtube-based system
1 September 1999
Optics Communications 168 Ž1999. 1–6 www.elsevier.comrlocateroptcom
Surface profile measurement using a unique microtube-based system Shizhuo Yin ) , Jiang Li, Minho Song Department of Electrical Engineering, The PennsylÕania State UniÕersity, UniÕersity Park, PA 16802, USA Received 29 April 1999; received in revised form 17 June 1999; accepted 17 June 1999
Abstract A unique method for surface profile measurement is described. A microtube attached with an objective microlens is used to scan the sample surface so that the surface profile can be obtained. The unique features of using a microtube are low alignment requirement and high robustness. With different focal lengths of microlenses, we could get a depth measurement range from 10 to 400 mm with a submicron to nm range depth resolution. To verify the feasibility of the proposed system, a profile obtained by this method is compared with the result obtained by using conventional stylus measurement. The results from the two methods are consistent. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.30.Wb; 07.60.y j; 42.87.y d; 07.79.Fc Keywords: Surface roughness measurement; Surface profile measurement; Confocal microscope; Microtube array; Microlens array
1. Introduction Generally, the national and international standards of the assessment of surface roughness are based on the profile of a surface traced by a suitable stylus. However, the contact between the stylus and the surface profile wears away the surface. This effect limits its application, especially for optically processed surfaces. The measurement of surface topography using non-contact technology has been the subject of study for a long time w1–7x. A number of surface measurement techniques have been developed, which are based on techniques such as projected fringes w1x, holographic interferometry w2x, ) Corresponding author. Fax: q1-814-865-7065; e-mail: [email protected]
shearing interferometry w3x, phase stepped polarization technique w4x, and the confocal microscopy w5–7x. Of these techniques, confocal microscopy is one of the best established ones. Its main advantage is depth discriminating capability obtained by placing an objective lens and a pinhole in front of a photodetector. By blocking the light flux reflected from out-of-focus planes, the surface profile information is converted into intensity variation at the photodetector. This optical-sectioning capability with high contrast permits three-dimensional Ž3-D. images to be built up from a series of image sections that can be obtained by scanning point by point at different depths. However, because of its scanning process, the confocal system is complicated in its structure and usually expensive. To reduce the cost and measurement time, in Ref. w7x, Tiziani and Uhde proposed a microlens
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 3 3 4 - X
2
S. Yin et al.r Optics Communications 168 (1999) 1–6
array confocal arrangement that showed the feasibility of multi-aperture confocal microscopy. By deploying a lens array, they could measure 3-D topography without lateral scanning, which greatly relaxed system requirements and decreased the measuring time and cost. However, in this case, the lens in front of the small pinhole aperture must be finely aligned, so that the light spots reflected from the object points can be focused to a small spot along the axis. The small limiting pinhole aperture as a spatial filter needs to be placed in the back focal plane of the lens. Only in this way can the light from out-of-focus planes be effectively blocked. In addition, when the surface-under-test has scattering grains in the scale of the focused beam spot, the reflected light flux will contain stray light. This increases crosstalk between different imaging lens channels and may degrade image contrast and resolution. To alleviate these limitations, in this paper, we developed a new device for microsurface profile measurement. We placed a microtube just behind the objective microlens, and fixed them together. The inside wall of the microtube was finished with black material that has rare reflectance, which can absorb most of the stray light. Such a structure can alleviate the alignment difficulties of previous confocal systems, and enhance the robustness of the system. Furthermore, the individually isolated channels will eliminate the crosstalk between the channels when the tube array is used for non-scanning 2-D measurements in the future.
2. Principle of microtube based measurement Fig. 1 shows the system structure of our proposed method. The collimated incoming light was directed into the microtube using a beam splitter. The microtube was made of aluminum and anodized black. Two aluminum planes were made optically polished. Half circles were then grooved on the aluminum plates. After being anodized, the two plates were bound together to form the microtube. In this way, the microtubes could be packed as closely as about 200 mm, so as to be used with a lens array in future work. In this system, only the collimated light beam could pass through the microtube without suffering
Fig. 1. Schematic diagram of the proposed surface profiling system.
severe attenuation. The input end of the tube block was angle finished, as shown in Fig. 1, to prevent reflected bias signals from reaching the photodetector, which greatly enhances system sensitivity. Furthermore, the adjustment of the lens mounted in front of the CCD could eliminate all the stray light from outside end of the microtube. This structure is much better than that of a regular confocal system, because in the regular confocal system the light reflected from any planes along the light direction will be received with the valuable signal light. In our system, the microlens was fixed at the other end of the microtube. If the light beam is focused on the surface-under-test as shown in Fig. 2Ža., the reflected light will also be collimated after passing the microlens so that it can pass through the microtube without severe attenuation. However in out-of-focus states, the reflected light will be diverging or converging after passing through the microlens again and the intensity at the photodetector will be substantially decreased by the low reflectance of the inside
S. Yin et al.r Optics Communications 168 (1999) 1–6
Fig. 2. Transformation of surface profiles to intensity variation using a microtube: Ža. light is focused on the object surface; Žb. underfocused; and Žc. overfocused.
wall surface. The surface height information was converted to intensity variation at the detector plane. The detector signal was stored and used to determine the profile of the surface-under-test using personal computer based subsequent data acquisition and analyzing electronics. This working principle is nearly the same as that of the confocal microscope except for the use of the microtube substituting for pinhole optics. The robust tube structure can greatly relax the alignment and stability requirements of conventional confocal systems, therefore it is very suitable for
3
low-cost, non-scanning array configurations with the use of a CCD Žcharge coupled device. instead of the photodetector. To achieve the best performance, the confocal microscope can be optimized by controlling parameters such as pinhole size, diameter and numerical aperture of the objective lens, etc., to get the best resolution while maintaining the efficiency w8x. Similarly, to obtain good lateral resolution and depth-discrimination capability in our designed system, we needed to optimize the dimensions and properties of the microlens, the microtube, and the relationship between them. For the purpose of simplicity, the required parameters are estimated by the well-known Rayleigh’s criterion w9x. The radius of minimum resolvable spot r is rf
1.22 l D
f,
Ž 1.
where l, D, and f are the wavelength, the diameter of the lens, and the focal length, respectively. Note that D is also the diameter of microtube in our system. To achieve the optimum performance, similar to the pinhole camera case, this diffraction limited spot size should be approximately equal to the
Fig. 3. Normalized light intensity as a function of axial defocus distance.
S. Yin et al.r Optics Communications 168 (1999) 1–6
4
Table 1 FWHM for the lenses with different focal lengths. In all cases, microtube diameter and length were 0.2 and 80 mm, respectively Focal length Žmm.
FHWM Žmm.
0.2
0.5
1.0
2.0
10
33
160
400
size of image of the input end of microtube formed by the microlens. Since the length of the microtube, L, is much greater than the focal length, f Ži.e. L 4 f ., the size of the image is approximately fDrL. Therefore, the condition to achieve optimum performance is
l 1.22
D
ff
f L
D.
Ž 2.
Then, the relationship between the length and the diameter of the microtube can be expressed as D f '1.22 l L .
Ž 3.
Note that, for the sloped surface, the reflected incident light may be away from the microtube axis, which in turn can reduce the output light intensity due to the absorption by the internal surface of the microtube. Thus, the detected light beam intensity
will depend on not only the distance between the microlens and the surface, which is directly related to the depth information, but also the direction of the slope. In other words, for the same height, one may get different output light intensities for slopes that have different directions. To solve this problem caused by the direction of the slope, during the scanning process, at each lateral position, the sample is also scanned axially by moving the microtube and microlens along the axial direction and the axial location that corresponds to the highest output light intensity is recorded. Fortunately, for each lateral position, this ‘highest peak’ axial location, which corresponds to the focal length of the microlens, is independent of the direction of the slope. In other words, for each lateral position, the slope of the surface only causes the change of the scale of the axial output light intensity distribution during the axial scanning process, but it does not change the axial peak location of the light intensity distribution. Therefore, by introducing axial scanning, the depth information of the surface can be obtained without being affected by the direction of the slope. This axial scanning method works fine for the sloped surface as long as the output light intensity from the sloped surface is still detectable. This, in general, is not a problem due to the high photosensitivity of
Fig. 4. Picture of S-22 comparator.
S. Yin et al.r Optics Communications 168 (1999) 1–6
current photodetectors, which is confirmed by our experimental results to be described in Section 3.
3. Experimental results In the experiment, considering the system dimension and controllability of the tube structure, an 80 mm length microtube and a 670 nm wavelength laser diode were used. Then, based on Eq. Ž3., the diameter of the microtube should be less than 256 mm. To make it simple, we chose 200 mm as the tube diameter. In addition, a set of 200 mm diameter microlenses made by Research Associates was also used as the microlenses. The depth discriminating performance of this technique was evaluated by scanning the sample in the vertical axial direction. To calibrate the system, at first, a standard optical mirror was scanned. Note that, in terms of light source, although low coherent broadband light is suitable to decrease the coherent noise level in the photodetector signal, to get the spatially homogeneous light distribution with simple optics, in the experiment, we used a laser diode at 670 nm wavelength as the light source. When the mirror was scanned in the vertical axial direction, the intensity via the defocus distance was measured as shown in Fig. 3. The peak in the figure corresponds to the focal length of the used microlens, that is, zero defocus distance. We tried several different lenses and Fig. 3 was obtained using a microlens of focal length 200 mm. The full width at half maximum ŽFWHM. of the curve of Fig. 3 was measured as about 10 mm. With a lens having a 2.0 mm focal length, the FWHM went up to 400 mm. Because we used an 8 bit analog-to-digital converter, the minimum axial movement of the mirror that can be detected by using the photodetector and the data acquisition board was 40 and 1560 nm for 200 mm and 2.0 mm focal length lenses, respectively. Table 1 summarizes the measured FWHM results for different microlenses. There is an apparent tradeoff between the working distance and the depth resolution. To examine the performance of the proposed technique, a standard S-22 roughness comparator, as shown in Fig. 4, was selected as a standard testing surface. The experimental parameters were chosen as follows: the focal length of the microlens was 200
5
mm, the diameter of the microtube was also 200 mm, and the length of the microtube was 80 mm. The measured surface was a 125 M ŽM s milled. surface within the S-22 Microfinish comparator. A personal computer controlled 2-axis scanning stage was used to scan the comparator along both the vertical Ži.e. axial. and lateral directions. At each lateral position, the comparator was scanned axially, and the axial location of the highest peak was chosen as the height of the comparator at that location. Fig. 5Ža. shows the result of the measurement. To verify this result, we also measured the surface profile of the sample by using the standard stylus profiler, and the result is given in Fig. 5Žb.. From Fig. 5Ža. and Fig. 5Žb., one can see that the profiles from the two measurements agree well. Of course, similar to the stylus method,
Fig. 5. Reconstructed profile of the sample comparator using: Ža. proposed microtube structure; and Žb. stylus profiler.
6
S. Yin et al.r Optics Communications 168 (1999) 1–6
there is a tradeoff between the resolution and dynamic range for our measurement system. 4. Discussion A new way for measuring the surface profile of mm scale 3-D structures using microtube based confocal scanning was developed. Using microlenses having 200 ; 2000 mm focal lengths, we could obtain 40 ; 1560 nm depth resolutions, respectively. Because of the simple and robust microtube structure, this system may be more suitable for harsh environments and low-cost applications that require moderate resolution performance. In addition, when the microtube array is used, this system will show much higher measurement speed and lower-crosstalk among array channels. Due to these advantages, it will find applications in mechanical engineering and microelectronics for high signal-to-noise ratio surface characterization. Acknowledgements The partial financial support of this research project from the US Army Research Office, ŽGrant
Number: P-34711-OH-YIP. is gratefully acknowledged. We also acknowledge Mr. Chung-Chen Kuo’s help during the measurement of the surface profile with stylus profiler. We also would like to thank Mr. Dana Anderson for his help with editing the manuscript. References w1x J.L. Dorty, Projection Moire for remote contour analysis, J. Opt. Soc. Am. 73 Ž1983. 366–372. w2x R. Dandliker, R. Thalmann, Heterodyne and quasi-heterodyne holographic interferometry, Opt. Eng. 24 Ž1985. 824–831. w3x T. Yatagai, T. Kanou, Aspherical surface testing with shearing interferometry using fringe scanning detection method, Opt. Eng. 23 Ž1984. 357–360. w4x R. Smythe, R. Moore, Instantaneous phase measuring interferometry, Opt. Eng. 23 Ž1984. 361–364. w5x M. Petran, M. Hadravsky, M.D. Egger, R. Galambos, Tandem-scanning reflected-light microscope, J. Opt. Soc. Am. 58 Ž1968. 661–664. w6x K. Carlsson, N. Aslund, Confocal imaging for 3-D digital microscopy, Appl. Opt. 26 Ž1987. 3232–3238. w7x H.J. Tiziani, H.-M. Uhde, Three-dimensional analysis by a microlens-array confocal arrangement, Appl. Opt. 33 Ž1994. 567–572. w8x T. Wilson, A.R. Carlini, Size of the detector in confocal imaging systems, Opt. Lett. 12 Ž1987. 227–229. w9x E. Heght, Optics, 2nd ed., Addison-Wesley, Reading, MA, 1990, p. 422.
Optics Communications 168 Ž1999. 1–6 www.elsevier.comrlocateroptcom
Surface profile measurement using a unique microtube-based system Shizhuo Yin ) , Jiang Li, Minho Song Department of Electrical Engineering, The PennsylÕania State UniÕersity, UniÕersity Park, PA 16802, USA Received 29 April 1999; received in revised form 17 June 1999; accepted 17 June 1999
Abstract A unique method for surface profile measurement is described. A microtube attached with an objective microlens is used to scan the sample surface so that the surface profile can be obtained. The unique features of using a microtube are low alignment requirement and high robustness. With different focal lengths of microlenses, we could get a depth measurement range from 10 to 400 mm with a submicron to nm range depth resolution. To verify the feasibility of the proposed system, a profile obtained by this method is compared with the result obtained by using conventional stylus measurement. The results from the two methods are consistent. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.30.Wb; 07.60.y j; 42.87.y d; 07.79.Fc Keywords: Surface roughness measurement; Surface profile measurement; Confocal microscope; Microtube array; Microlens array
1. Introduction Generally, the national and international standards of the assessment of surface roughness are based on the profile of a surface traced by a suitable stylus. However, the contact between the stylus and the surface profile wears away the surface. This effect limits its application, especially for optically processed surfaces. The measurement of surface topography using non-contact technology has been the subject of study for a long time w1–7x. A number of surface measurement techniques have been developed, which are based on techniques such as projected fringes w1x, holographic interferometry w2x, ) Corresponding author. Fax: q1-814-865-7065; e-mail: [email protected]
shearing interferometry w3x, phase stepped polarization technique w4x, and the confocal microscopy w5–7x. Of these techniques, confocal microscopy is one of the best established ones. Its main advantage is depth discriminating capability obtained by placing an objective lens and a pinhole in front of a photodetector. By blocking the light flux reflected from out-of-focus planes, the surface profile information is converted into intensity variation at the photodetector. This optical-sectioning capability with high contrast permits three-dimensional Ž3-D. images to be built up from a series of image sections that can be obtained by scanning point by point at different depths. However, because of its scanning process, the confocal system is complicated in its structure and usually expensive. To reduce the cost and measurement time, in Ref. w7x, Tiziani and Uhde proposed a microlens
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 3 3 4 - X
2
S. Yin et al.r Optics Communications 168 (1999) 1–6
array confocal arrangement that showed the feasibility of multi-aperture confocal microscopy. By deploying a lens array, they could measure 3-D topography without lateral scanning, which greatly relaxed system requirements and decreased the measuring time and cost. However, in this case, the lens in front of the small pinhole aperture must be finely aligned, so that the light spots reflected from the object points can be focused to a small spot along the axis. The small limiting pinhole aperture as a spatial filter needs to be placed in the back focal plane of the lens. Only in this way can the light from out-of-focus planes be effectively blocked. In addition, when the surface-under-test has scattering grains in the scale of the focused beam spot, the reflected light flux will contain stray light. This increases crosstalk between different imaging lens channels and may degrade image contrast and resolution. To alleviate these limitations, in this paper, we developed a new device for microsurface profile measurement. We placed a microtube just behind the objective microlens, and fixed them together. The inside wall of the microtube was finished with black material that has rare reflectance, which can absorb most of the stray light. Such a structure can alleviate the alignment difficulties of previous confocal systems, and enhance the robustness of the system. Furthermore, the individually isolated channels will eliminate the crosstalk between the channels when the tube array is used for non-scanning 2-D measurements in the future.
2. Principle of microtube based measurement Fig. 1 shows the system structure of our proposed method. The collimated incoming light was directed into the microtube using a beam splitter. The microtube was made of aluminum and anodized black. Two aluminum planes were made optically polished. Half circles were then grooved on the aluminum plates. After being anodized, the two plates were bound together to form the microtube. In this way, the microtubes could be packed as closely as about 200 mm, so as to be used with a lens array in future work. In this system, only the collimated light beam could pass through the microtube without suffering
Fig. 1. Schematic diagram of the proposed surface profiling system.
severe attenuation. The input end of the tube block was angle finished, as shown in Fig. 1, to prevent reflected bias signals from reaching the photodetector, which greatly enhances system sensitivity. Furthermore, the adjustment of the lens mounted in front of the CCD could eliminate all the stray light from outside end of the microtube. This structure is much better than that of a regular confocal system, because in the regular confocal system the light reflected from any planes along the light direction will be received with the valuable signal light. In our system, the microlens was fixed at the other end of the microtube. If the light beam is focused on the surface-under-test as shown in Fig. 2Ža., the reflected light will also be collimated after passing the microlens so that it can pass through the microtube without severe attenuation. However in out-of-focus states, the reflected light will be diverging or converging after passing through the microlens again and the intensity at the photodetector will be substantially decreased by the low reflectance of the inside
S. Yin et al.r Optics Communications 168 (1999) 1–6
Fig. 2. Transformation of surface profiles to intensity variation using a microtube: Ža. light is focused on the object surface; Žb. underfocused; and Žc. overfocused.
wall surface. The surface height information was converted to intensity variation at the detector plane. The detector signal was stored and used to determine the profile of the surface-under-test using personal computer based subsequent data acquisition and analyzing electronics. This working principle is nearly the same as that of the confocal microscope except for the use of the microtube substituting for pinhole optics. The robust tube structure can greatly relax the alignment and stability requirements of conventional confocal systems, therefore it is very suitable for
3
low-cost, non-scanning array configurations with the use of a CCD Žcharge coupled device. instead of the photodetector. To achieve the best performance, the confocal microscope can be optimized by controlling parameters such as pinhole size, diameter and numerical aperture of the objective lens, etc., to get the best resolution while maintaining the efficiency w8x. Similarly, to obtain good lateral resolution and depth-discrimination capability in our designed system, we needed to optimize the dimensions and properties of the microlens, the microtube, and the relationship between them. For the purpose of simplicity, the required parameters are estimated by the well-known Rayleigh’s criterion w9x. The radius of minimum resolvable spot r is rf
1.22 l D
f,
Ž 1.
where l, D, and f are the wavelength, the diameter of the lens, and the focal length, respectively. Note that D is also the diameter of microtube in our system. To achieve the optimum performance, similar to the pinhole camera case, this diffraction limited spot size should be approximately equal to the
Fig. 3. Normalized light intensity as a function of axial defocus distance.
S. Yin et al.r Optics Communications 168 (1999) 1–6
4
Table 1 FWHM for the lenses with different focal lengths. In all cases, microtube diameter and length were 0.2 and 80 mm, respectively Focal length Žmm.
FHWM Žmm.
0.2
0.5
1.0
2.0
10
33
160
400
size of image of the input end of microtube formed by the microlens. Since the length of the microtube, L, is much greater than the focal length, f Ži.e. L 4 f ., the size of the image is approximately fDrL. Therefore, the condition to achieve optimum performance is
l 1.22
D
ff
f L
D.
Ž 2.
Then, the relationship between the length and the diameter of the microtube can be expressed as D f '1.22 l L .
Ž 3.
Note that, for the sloped surface, the reflected incident light may be away from the microtube axis, which in turn can reduce the output light intensity due to the absorption by the internal surface of the microtube. Thus, the detected light beam intensity
will depend on not only the distance between the microlens and the surface, which is directly related to the depth information, but also the direction of the slope. In other words, for the same height, one may get different output light intensities for slopes that have different directions. To solve this problem caused by the direction of the slope, during the scanning process, at each lateral position, the sample is also scanned axially by moving the microtube and microlens along the axial direction and the axial location that corresponds to the highest output light intensity is recorded. Fortunately, for each lateral position, this ‘highest peak’ axial location, which corresponds to the focal length of the microlens, is independent of the direction of the slope. In other words, for each lateral position, the slope of the surface only causes the change of the scale of the axial output light intensity distribution during the axial scanning process, but it does not change the axial peak location of the light intensity distribution. Therefore, by introducing axial scanning, the depth information of the surface can be obtained without being affected by the direction of the slope. This axial scanning method works fine for the sloped surface as long as the output light intensity from the sloped surface is still detectable. This, in general, is not a problem due to the high photosensitivity of
Fig. 4. Picture of S-22 comparator.
S. Yin et al.r Optics Communications 168 (1999) 1–6
current photodetectors, which is confirmed by our experimental results to be described in Section 3.
3. Experimental results In the experiment, considering the system dimension and controllability of the tube structure, an 80 mm length microtube and a 670 nm wavelength laser diode were used. Then, based on Eq. Ž3., the diameter of the microtube should be less than 256 mm. To make it simple, we chose 200 mm as the tube diameter. In addition, a set of 200 mm diameter microlenses made by Research Associates was also used as the microlenses. The depth discriminating performance of this technique was evaluated by scanning the sample in the vertical axial direction. To calibrate the system, at first, a standard optical mirror was scanned. Note that, in terms of light source, although low coherent broadband light is suitable to decrease the coherent noise level in the photodetector signal, to get the spatially homogeneous light distribution with simple optics, in the experiment, we used a laser diode at 670 nm wavelength as the light source. When the mirror was scanned in the vertical axial direction, the intensity via the defocus distance was measured as shown in Fig. 3. The peak in the figure corresponds to the focal length of the used microlens, that is, zero defocus distance. We tried several different lenses and Fig. 3 was obtained using a microlens of focal length 200 mm. The full width at half maximum ŽFWHM. of the curve of Fig. 3 was measured as about 10 mm. With a lens having a 2.0 mm focal length, the FWHM went up to 400 mm. Because we used an 8 bit analog-to-digital converter, the minimum axial movement of the mirror that can be detected by using the photodetector and the data acquisition board was 40 and 1560 nm for 200 mm and 2.0 mm focal length lenses, respectively. Table 1 summarizes the measured FWHM results for different microlenses. There is an apparent tradeoff between the working distance and the depth resolution. To examine the performance of the proposed technique, a standard S-22 roughness comparator, as shown in Fig. 4, was selected as a standard testing surface. The experimental parameters were chosen as follows: the focal length of the microlens was 200
5
mm, the diameter of the microtube was also 200 mm, and the length of the microtube was 80 mm. The measured surface was a 125 M ŽM s milled. surface within the S-22 Microfinish comparator. A personal computer controlled 2-axis scanning stage was used to scan the comparator along both the vertical Ži.e. axial. and lateral directions. At each lateral position, the comparator was scanned axially, and the axial location of the highest peak was chosen as the height of the comparator at that location. Fig. 5Ža. shows the result of the measurement. To verify this result, we also measured the surface profile of the sample by using the standard stylus profiler, and the result is given in Fig. 5Žb.. From Fig. 5Ža. and Fig. 5Žb., one can see that the profiles from the two measurements agree well. Of course, similar to the stylus method,
Fig. 5. Reconstructed profile of the sample comparator using: Ža. proposed microtube structure; and Žb. stylus profiler.
6
S. Yin et al.r Optics Communications 168 (1999) 1–6
there is a tradeoff between the resolution and dynamic range for our measurement system. 4. Discussion A new way for measuring the surface profile of mm scale 3-D structures using microtube based confocal scanning was developed. Using microlenses having 200 ; 2000 mm focal lengths, we could obtain 40 ; 1560 nm depth resolutions, respectively. Because of the simple and robust microtube structure, this system may be more suitable for harsh environments and low-cost applications that require moderate resolution performance. In addition, when the microtube array is used, this system will show much higher measurement speed and lower-crosstalk among array channels. Due to these advantages, it will find applications in mechanical engineering and microelectronics for high signal-to-noise ratio surface characterization. Acknowledgements The partial financial support of this research project from the US Army Research Office, ŽGrant
Number: P-34711-OH-YIP. is gratefully acknowledged. We also acknowledge Mr. Chung-Chen Kuo’s help during the measurement of the surface profile with stylus profiler. We also would like to thank Mr. Dana Anderson for his help with editing the manuscript. References w1x J.L. Dorty, Projection Moire for remote contour analysis, J. Opt. Soc. Am. 73 Ž1983. 366–372. w2x R. Dandliker, R. Thalmann, Heterodyne and quasi-heterodyne holographic interferometry, Opt. Eng. 24 Ž1985. 824–831. w3x T. Yatagai, T. Kanou, Aspherical surface testing with shearing interferometry using fringe scanning detection method, Opt. Eng. 23 Ž1984. 357–360. w4x R. Smythe, R. Moore, Instantaneous phase measuring interferometry, Opt. Eng. 23 Ž1984. 361–364. w5x M. Petran, M. Hadravsky, M.D. Egger, R. Galambos, Tandem-scanning reflected-light microscope, J. Opt. Soc. Am. 58 Ž1968. 661–664. w6x K. Carlsson, N. Aslund, Confocal imaging for 3-D digital microscopy, Appl. Opt. 26 Ž1987. 3232–3238. w7x H.J. Tiziani, H.-M. Uhde, Three-dimensional analysis by a microlens-array confocal arrangement, Appl. Opt. 33 Ž1994. 567–572. w8x T. Wilson, A.R. Carlini, Size of the detector in confocal imaging systems, Opt. Lett. 12 Ž1987. 227–229. w9x E. Heght, Optics, 2nd ed., Addison-Wesley, Reading, MA, 1990, p. 422.