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Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers Toshiaki Matsuura , Kazuaki Udaka, Yasushi Oshikane, Haruyuki Inoue, Motohiro Nakano, Kazuto Yamauchi, Toshihiko Kataoka 2-1 Yamadaoka, Suita, Osaka, 565-0871, Japan
a r t i c l e in fo
abstract
Available online 29 December 2009
A phase-shifting point diffraction interferometer (PS/PDI) with two optical fibers has been developed. This system consists of high numerical aperture optics and it forms an interferogram on a CCD without using imaging optics. The positions of the fiber cores were determined by an iterative method for analyzing interferograms. The surface figure of a test mirror was obtained from the measured amplitude and phase by digital holography. The surface figure of a spherical concave mirror was measured at two different axial orientations of the mirror. The difference between the two results had a peak-to-valley value of 2 nm and a root-mean-square (rms) value of 0.85 nm. When the moire´ pattern, which is main cause for the difference, is eliminated, the measurement accuracy has an rms =0.15 nm. This procedure can also be used to measure aspherical mirrors. The measurement accuracy when measuring an aspherical mirror is expected to be the same as that when measuring a spherical mirror. & 2009 Elsevier B.V. All rights reserved.
Keywords: Point diffraction interferometer Phase-shifting method Optical fibers Digital holography Surface figure measurement Aspherical mirror
1. Introduction Extreme ultraviolet lithography (EUVL) requires focusing mirrors that have been finished to an accuracy within a rootmean-square (rms) value of 0.2 nm for the long-range figure error for a numerical aperture (NA) of 0.2 [1]. This requirement is derived from the Rayleigh criterion. A point diffraction interferometer (PDI) has been developed for measuring the absolute surface figure [2]. Its reference is a spherical wavefront generated by diffraction at a point aperture, the deviation of which from an ideal spherical shape is less than 10 5l for an NA of over 0.2 [3]. Precise measurements are performed by analyzing a series of interferograms by the phase-shifting (PS) method [4]. This combination of a PDI and the PS method is called a PS/PDI. A single-mode optical fiber core or a pinhole is applied to the point aperture in a PDI [1,3]. However, the NA of a test mirror is limited to half the diffracted wavefront because the wavefront is used both as the measurement and reference wavefronts. To perform measurements on high-NA mirrors, we have developed a PS/PDI that employs two single-mode optical fiber cores as point apertures [5]. One core is the measurement wavefront source and the other core is the reference wavefront source. This system can measure a test mirror that is the same size as the wavefront and an interferogram is formed on a CCD without using imaging optics, which generates aberrations. In this PS/PDI, accurate
Corresponding author. Tel./fax: + 81 6 6879 7278.
E-mail address: [email protected] (T. Matsuura). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.12.031
knowledge of the positions of the two cores is critical for analyzing interferograms. The core positions can be determined by an iterative method, in which the measurement and reference wavefronts are assumed to ideal spherical wavefronts [5]. PS/PDIs are suitable for measuring spherical concave mirrors because the diffracted wavefront is spherical. However, aspherical mirrors are also required for EUVL. To measure an aspherical mirror using a PS/PDI, measurement results are stitched [6] or the measurement wavefront on the test mirror is reconstructed by a numerical reconstruction method that uses digital holography [7]. We have used the numerical reconstruction method. We have demonstrated that a surface figure within a 1 mm radius can be measured by numerical simulations [8]. Thus, the measurement accuracy for spherical mirrors has been improved. In this present study, a spherical concave mirror was measured using the PS/PDI with two optical fibers at two different axial orientations. The positions of the optic components were determined and the wavefront was reconstructed. The spherical mirror measurement accuracy was evaluated. Since the procedure employed is the same as that used for aspherical mirror measurements, the accuracy of aspherical mirror measurements using the PS/PDI is expected to be the same.
2. PS/PDI system with two optical fibers and experimental procedure Fig. 1 shows a schematic diagram of the PS/PDI system used for spherical concave mirror measurements. All the optical
ARTICLE IN PRESS 234
T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
components were installed on a vibration isolation table to minimize mechanical vibrations. In addition, with the exception of the He Ne laser, all the optics were housed in a heat insulating box in a temperature-controlled room to suppress air currents. A He Ne laser that produced linearly polarized 632.8 nm light was used as the light source; it was coupled to an optical isolator to stabilize the output laser power. The polarization of the laser light was adjusted using a half-wave plate (HWP 1) before using a polarization beam splitter (PBS) to split the light into two beams. The s-polarized beam was reflected by the PBS. The p-polarized beam passed through the PBS and a quarter-wave plate (QWP) and was reflected by an aluminum mirror, M2, on a piezo stage (PZT). The PS method was implemented by varying the relative optical path length before the optical fibers. The beam reflected by M2 passed through the QWP again where it was converted into an s-polarized beam. As a result, two s-polarized beams were emitted from the PBS and were launched into two single-mode optical fibers, F1 and F2, by objective lenses, L1 and L2, respectively. The polarization of the beam in F1 was adjusted by HWP2 to maximize the contrast of the interferogram. Each singlemode optical fiber with a core size of 4 mm emitted a diffracted spherical wave. A spherical concave mirror (diameter: 200 mm, radius of curvature: 1500 mm) was tested. The tip of L2, which is the point light source of the measurement wavefront, was set at a position which is slightly shifted relative to the center of curvature. The measurement wavefront was reflected by the test mirror and focused. The tip of L1, which is the point light source of the reference wavefront, was set near the focal point. As a result, an interferogram was formed on the CCD. The protective glass plate of the CCD was removed to prevent interference from being generated by light being reflected in it. The CCD had 1200 1000 imaging pixels and the dimensions of each pixel were 6.45 6.45 mm2. 32 interferograms were continuously obtained and averaged to reduce random noise in the CCD. A preliminary phase map was obtained using averaged interferograms acquired by the seven-bucket PS method. An initial phase map was obtained by averaging 100 initial phase maps to reduce random noise caused by mechanical vibrations and air currents. This initial phase map represents the deviation between the measurement and reference wavefronts on the CCD. Additionally, the positions of the point light source of the reference wavefront and the CCD were obtained from the initial phase by an iterative method. They must be determined to within 5 mm to achieve a
Fig. 1. Schematic diagram of the PS/PDI system for spherical concave mirror measurements.
measurement accuracy of rms=0.1 nm. Finally, the phase map of the measurement wavefront containing only the surface figure profile was obtained on the CCD. To obtain the surface figure, the measurement wavefront on the test mirror was reconstructed with the data measured by the PS/PDI. The amplitude and phase maps of the measurement wavefront were measured on the CCD and discretized into 1200 1000 pixels. The center domain of 1000 1000 pixels was increased to 5000 5000 pixels by an interpolation method for precise integration. The measurement wavefront on the test mirror was numerically reconstructed by using the data on the CCD. Subsequently, amplitude and phase maps for an area equivalent to 200 200 pixels on the test mirror, the spatial wavelength of which was 1 mm, were reconstructed. The reconstructed phase map gave the surface figure of the test mirror. 3. Spherical concave mirror measurement To assess the accuracy of measurements by the PS/PDI with two optical fibers, the surface figure of a spherical concave mirror was measured at two different axial orientations. Fig. 2 shows the measurement results at 01. Fig. 2(a) shows the amplitude map of the measurement wavefront on the CCD, which was reflected by the test mirror and includes the surface figure profile. Some circular fringes caused by diffraction at the edge of the test mirror are visible. The upper region of the test mirror was shielded to prevent the mirror from falling and the bottom of the CCD image was cut off in Fig. 2. Fig. 2(b) shows a typical interferogram. Some vertical fringes are generated by the small interval between the focal point of the reflected measurement wavefront and the point light source of the reference wavefront. Fig. 2(c) shows the phase map of the measurement wavefront on the CCD. It contains only the surface figure profile and is the deviation from the ideal spherical shape. However, the phase map differs from the surface figure. The surface figure of the test mirror is obtained from the amplitude and phase maps of the measurement wavefront on the CCD by digital holography. This method simulates wavefront propagation, allowing the wavefront to be reconstructed at any position. However, the position of the test mirror, on which the measurement wavefront was reconstructed, was unknown. To determine its position, the center of curvature of the test mirror was taken to be the focal point of the reflected measurement wavefront and the radius of curvature was taken to be 1500 mm, which is its designed value. This procedure was performed for the following reason. The amplitude map of the reflected measurement wavefront at the focal point in the experiment was calculated by digital holography from the measurement data and is shown in Fig. 3(a). The ideal amplitude map at the focal point was obtained by performing a numerical simulation and it is shown in Fig. 3(b), in which the test mirror is assumed to be an ideal spherical concave mirror. Comparison of the amplitude maps at the focal point demonstrates that the measurement wavefront was sufficiently focused in the experiment. Based on this, the center of curvature of the test mirror was taken to be the focal point. The surface figure of the test mirror at 01 was obtained by digital holography and is shown in Fig. 4(a) as the deviation from the ideal spherical shape. The test mirror shown in Fig. 4 is 170 mm in diameter. Some circular fringe errors such as fringes in Fig. 3(a) appear due to diffraction from the edge of the test mirror. These errors can be eliminated if numerical simulation by digital holography is performed perfectly. Thus, the digital holography procedure used needs to be improved. The test mirror was rotated axially by approximately 901 and it was remeasured. The discrepancy between the two results is shown in Fig. 4(b). The difference between the results has a peak-to-valley value of 2 nm and an rms value of 0.85 nm.
ARTICLE IN PRESS T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
235
Fig. 2. Measurement results for a spherical concave mirror: (a) amplitude map of the measurement wavefront; (b) a typical interferogram; (c) phase map of the measurement wavefront on the CCD.
Fig. 3. Amplitude maps and the sections in Y= 0 of the measurement wavefront at the focal point: (a) in the experiment (b) in a numerical simulation.
A characteristic long-range fluctuation caused by not determining the positions of the optics accurately does not appear in Fig. 4(b). The main reason for observed difference is the moire´ pattern caused by the digitization of the digital holography. The numerical reconstruction was performed by a discrete integral and the discretization error appeared as a periodic pattern. In addition, the reconstructed wavefront on the test mirror was discretized into 200 200 pixels. The pattern and the pixels on the test mirror formed a moire´ pattern because of aliasing effects. The moire´ pattern can be suppressed by increasing the number of discretized points on the CCD and the test mirror. When the wavefront on the center of the mirror of 100 100 mm was
reconstructed into 200 200 pixels, the resolution of which is twice the former reconstruction, the moire´ pattern was suppressed. Using FFT, the moire´ pattern was separated at some level. The measurement accuracy is up to rms 0.15 nm. 4. Conclusion A PS/PDI with two optical fibers has been developed for largeaperture mirror measurements. The positions of the optics were determined by an iterative method for analyzing interferograms. The measurement wavefront was reconstructed on the test mirror to obtain the surface figure. A spherical concave mirror was
ARTICLE IN PRESS 236
T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
Fig. 4. Measurement results of spherical concave mirror. (a) The surface figure of the test mirror at 01 axially. (b) The deviation of the two results, which was measured at axial angles of 01 and 901.
measured at two different axial orientations. If the moire´ pattern is eliminated, a measurement accuracy of rms =0.15 nm can be obtained. This procedure is also applied measure aspherical mirrors. Thus, the measurement accuracy for aspherical mirrors is expected to be the same accuracy. Reference [1] K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, S. Okazaki, J. Vac. Sci. Technol. B 20 (2002) 2449.
[2] R.N. Smartt, Jpn. J. Appl. Phys. Vol. 14 (Suppl. 14-1) (1975) 351. [3] G.E. Sommargren, D. Kania, OSA TOPS on Extreme Ultraviolet Lithography, vol. 4, Optical Society of America, Washington DC, 1996, p. 108. [4] P. de Groot, Appl. Opt. Vol. 34 (1995) 4723. [5] T. Matsuura, S. Okagaki, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, Surf. Interface Anal. Vol. 40 (2008) 1028. [6] K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, S. Okazaki, Proc. SPIE 4343 (2001) 543. [7] I. Yamaguchi, T. Ida, M. Yokota, K. Yamashita, Appl. Opt. Vol. 45 (2006) 7610. [8] T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, Opt. Rev. Vol. 14 (2007) 401.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers Toshiaki Matsuura , Kazuaki Udaka, Yasushi Oshikane, Haruyuki Inoue, Motohiro Nakano, Kazuto Yamauchi, Toshihiko Kataoka 2-1 Yamadaoka, Suita, Osaka, 565-0871, Japan
a r t i c l e in fo
abstract
Available online 29 December 2009
A phase-shifting point diffraction interferometer (PS/PDI) with two optical fibers has been developed. This system consists of high numerical aperture optics and it forms an interferogram on a CCD without using imaging optics. The positions of the fiber cores were determined by an iterative method for analyzing interferograms. The surface figure of a test mirror was obtained from the measured amplitude and phase by digital holography. The surface figure of a spherical concave mirror was measured at two different axial orientations of the mirror. The difference between the two results had a peak-to-valley value of 2 nm and a root-mean-square (rms) value of 0.85 nm. When the moire´ pattern, which is main cause for the difference, is eliminated, the measurement accuracy has an rms =0.15 nm. This procedure can also be used to measure aspherical mirrors. The measurement accuracy when measuring an aspherical mirror is expected to be the same as that when measuring a spherical mirror. & 2009 Elsevier B.V. All rights reserved.
Keywords: Point diffraction interferometer Phase-shifting method Optical fibers Digital holography Surface figure measurement Aspherical mirror
1. Introduction Extreme ultraviolet lithography (EUVL) requires focusing mirrors that have been finished to an accuracy within a rootmean-square (rms) value of 0.2 nm for the long-range figure error for a numerical aperture (NA) of 0.2 [1]. This requirement is derived from the Rayleigh criterion. A point diffraction interferometer (PDI) has been developed for measuring the absolute surface figure [2]. Its reference is a spherical wavefront generated by diffraction at a point aperture, the deviation of which from an ideal spherical shape is less than 10 5l for an NA of over 0.2 [3]. Precise measurements are performed by analyzing a series of interferograms by the phase-shifting (PS) method [4]. This combination of a PDI and the PS method is called a PS/PDI. A single-mode optical fiber core or a pinhole is applied to the point aperture in a PDI [1,3]. However, the NA of a test mirror is limited to half the diffracted wavefront because the wavefront is used both as the measurement and reference wavefronts. To perform measurements on high-NA mirrors, we have developed a PS/PDI that employs two single-mode optical fiber cores as point apertures [5]. One core is the measurement wavefront source and the other core is the reference wavefront source. This system can measure a test mirror that is the same size as the wavefront and an interferogram is formed on a CCD without using imaging optics, which generates aberrations. In this PS/PDI, accurate
Corresponding author. Tel./fax: + 81 6 6879 7278.
E-mail address: [email protected] (T. Matsuura). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.12.031
knowledge of the positions of the two cores is critical for analyzing interferograms. The core positions can be determined by an iterative method, in which the measurement and reference wavefronts are assumed to ideal spherical wavefronts [5]. PS/PDIs are suitable for measuring spherical concave mirrors because the diffracted wavefront is spherical. However, aspherical mirrors are also required for EUVL. To measure an aspherical mirror using a PS/PDI, measurement results are stitched [6] or the measurement wavefront on the test mirror is reconstructed by a numerical reconstruction method that uses digital holography [7]. We have used the numerical reconstruction method. We have demonstrated that a surface figure within a 1 mm radius can be measured by numerical simulations [8]. Thus, the measurement accuracy for spherical mirrors has been improved. In this present study, a spherical concave mirror was measured using the PS/PDI with two optical fibers at two different axial orientations. The positions of the optic components were determined and the wavefront was reconstructed. The spherical mirror measurement accuracy was evaluated. Since the procedure employed is the same as that used for aspherical mirror measurements, the accuracy of aspherical mirror measurements using the PS/PDI is expected to be the same.
2. PS/PDI system with two optical fibers and experimental procedure Fig. 1 shows a schematic diagram of the PS/PDI system used for spherical concave mirror measurements. All the optical
ARTICLE IN PRESS 234
T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
components were installed on a vibration isolation table to minimize mechanical vibrations. In addition, with the exception of the He Ne laser, all the optics were housed in a heat insulating box in a temperature-controlled room to suppress air currents. A He Ne laser that produced linearly polarized 632.8 nm light was used as the light source; it was coupled to an optical isolator to stabilize the output laser power. The polarization of the laser light was adjusted using a half-wave plate (HWP 1) before using a polarization beam splitter (PBS) to split the light into two beams. The s-polarized beam was reflected by the PBS. The p-polarized beam passed through the PBS and a quarter-wave plate (QWP) and was reflected by an aluminum mirror, M2, on a piezo stage (PZT). The PS method was implemented by varying the relative optical path length before the optical fibers. The beam reflected by M2 passed through the QWP again where it was converted into an s-polarized beam. As a result, two s-polarized beams were emitted from the PBS and were launched into two single-mode optical fibers, F1 and F2, by objective lenses, L1 and L2, respectively. The polarization of the beam in F1 was adjusted by HWP2 to maximize the contrast of the interferogram. Each singlemode optical fiber with a core size of 4 mm emitted a diffracted spherical wave. A spherical concave mirror (diameter: 200 mm, radius of curvature: 1500 mm) was tested. The tip of L2, which is the point light source of the measurement wavefront, was set at a position which is slightly shifted relative to the center of curvature. The measurement wavefront was reflected by the test mirror and focused. The tip of L1, which is the point light source of the reference wavefront, was set near the focal point. As a result, an interferogram was formed on the CCD. The protective glass plate of the CCD was removed to prevent interference from being generated by light being reflected in it. The CCD had 1200 1000 imaging pixels and the dimensions of each pixel were 6.45 6.45 mm2. 32 interferograms were continuously obtained and averaged to reduce random noise in the CCD. A preliminary phase map was obtained using averaged interferograms acquired by the seven-bucket PS method. An initial phase map was obtained by averaging 100 initial phase maps to reduce random noise caused by mechanical vibrations and air currents. This initial phase map represents the deviation between the measurement and reference wavefronts on the CCD. Additionally, the positions of the point light source of the reference wavefront and the CCD were obtained from the initial phase by an iterative method. They must be determined to within 5 mm to achieve a
Fig. 1. Schematic diagram of the PS/PDI system for spherical concave mirror measurements.
measurement accuracy of rms=0.1 nm. Finally, the phase map of the measurement wavefront containing only the surface figure profile was obtained on the CCD. To obtain the surface figure, the measurement wavefront on the test mirror was reconstructed with the data measured by the PS/PDI. The amplitude and phase maps of the measurement wavefront were measured on the CCD and discretized into 1200 1000 pixels. The center domain of 1000 1000 pixels was increased to 5000 5000 pixels by an interpolation method for precise integration. The measurement wavefront on the test mirror was numerically reconstructed by using the data on the CCD. Subsequently, amplitude and phase maps for an area equivalent to 200 200 pixels on the test mirror, the spatial wavelength of which was 1 mm, were reconstructed. The reconstructed phase map gave the surface figure of the test mirror. 3. Spherical concave mirror measurement To assess the accuracy of measurements by the PS/PDI with two optical fibers, the surface figure of a spherical concave mirror was measured at two different axial orientations. Fig. 2 shows the measurement results at 01. Fig. 2(a) shows the amplitude map of the measurement wavefront on the CCD, which was reflected by the test mirror and includes the surface figure profile. Some circular fringes caused by diffraction at the edge of the test mirror are visible. The upper region of the test mirror was shielded to prevent the mirror from falling and the bottom of the CCD image was cut off in Fig. 2. Fig. 2(b) shows a typical interferogram. Some vertical fringes are generated by the small interval between the focal point of the reflected measurement wavefront and the point light source of the reference wavefront. Fig. 2(c) shows the phase map of the measurement wavefront on the CCD. It contains only the surface figure profile and is the deviation from the ideal spherical shape. However, the phase map differs from the surface figure. The surface figure of the test mirror is obtained from the amplitude and phase maps of the measurement wavefront on the CCD by digital holography. This method simulates wavefront propagation, allowing the wavefront to be reconstructed at any position. However, the position of the test mirror, on which the measurement wavefront was reconstructed, was unknown. To determine its position, the center of curvature of the test mirror was taken to be the focal point of the reflected measurement wavefront and the radius of curvature was taken to be 1500 mm, which is its designed value. This procedure was performed for the following reason. The amplitude map of the reflected measurement wavefront at the focal point in the experiment was calculated by digital holography from the measurement data and is shown in Fig. 3(a). The ideal amplitude map at the focal point was obtained by performing a numerical simulation and it is shown in Fig. 3(b), in which the test mirror is assumed to be an ideal spherical concave mirror. Comparison of the amplitude maps at the focal point demonstrates that the measurement wavefront was sufficiently focused in the experiment. Based on this, the center of curvature of the test mirror was taken to be the focal point. The surface figure of the test mirror at 01 was obtained by digital holography and is shown in Fig. 4(a) as the deviation from the ideal spherical shape. The test mirror shown in Fig. 4 is 170 mm in diameter. Some circular fringe errors such as fringes in Fig. 3(a) appear due to diffraction from the edge of the test mirror. These errors can be eliminated if numerical simulation by digital holography is performed perfectly. Thus, the digital holography procedure used needs to be improved. The test mirror was rotated axially by approximately 901 and it was remeasured. The discrepancy between the two results is shown in Fig. 4(b). The difference between the results has a peak-to-valley value of 2 nm and an rms value of 0.85 nm.
ARTICLE IN PRESS T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
235
Fig. 2. Measurement results for a spherical concave mirror: (a) amplitude map of the measurement wavefront; (b) a typical interferogram; (c) phase map of the measurement wavefront on the CCD.
Fig. 3. Amplitude maps and the sections in Y= 0 of the measurement wavefront at the focal point: (a) in the experiment (b) in a numerical simulation.
A characteristic long-range fluctuation caused by not determining the positions of the optics accurately does not appear in Fig. 4(b). The main reason for observed difference is the moire´ pattern caused by the digitization of the digital holography. The numerical reconstruction was performed by a discrete integral and the discretization error appeared as a periodic pattern. In addition, the reconstructed wavefront on the test mirror was discretized into 200 200 pixels. The pattern and the pixels on the test mirror formed a moire´ pattern because of aliasing effects. The moire´ pattern can be suppressed by increasing the number of discretized points on the CCD and the test mirror. When the wavefront on the center of the mirror of 100 100 mm was
reconstructed into 200 200 pixels, the resolution of which is twice the former reconstruction, the moire´ pattern was suppressed. Using FFT, the moire´ pattern was separated at some level. The measurement accuracy is up to rms 0.15 nm. 4. Conclusion A PS/PDI with two optical fibers has been developed for largeaperture mirror measurements. The positions of the optics were determined by an iterative method for analyzing interferograms. The measurement wavefront was reconstructed on the test mirror to obtain the surface figure. A spherical concave mirror was
ARTICLE IN PRESS 236
T. Matsuura et al. / Nuclear Instruments and Methods in Physics Research A 616 (2010) 233–236
Fig. 4. Measurement results of spherical concave mirror. (a) The surface figure of the test mirror at 01 axially. (b) The deviation of the two results, which was measured at axial angles of 01 and 901.
measured at two different axial orientations. If the moire´ pattern is eliminated, a measurement accuracy of rms =0.15 nm can be obtained. This procedure is also applied measure aspherical mirrors. Thus, the measurement accuracy for aspherical mirrors is expected to be the same accuracy. Reference [1] K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, S. Okazaki, J. Vac. Sci. Technol. B 20 (2002) 2449.
[2] R.N. Smartt, Jpn. J. Appl. Phys. Vol. 14 (Suppl. 14-1) (1975) 351. [3] G.E. Sommargren, D. Kania, OSA TOPS on Extreme Ultraviolet Lithography, vol. 4, Optical Society of America, Washington DC, 1996, p. 108. [4] P. de Groot, Appl. Opt. Vol. 34 (1995) 4723. [5] T. Matsuura, S. Okagaki, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, Surf. Interface Anal. Vol. 40 (2008) 1028. [6] K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, S. Okazaki, Proc. SPIE 4343 (2001) 543. [7] I. Yamaguchi, T. Ida, M. Yokota, K. Yamashita, Appl. Opt. Vol. 45 (2006) 7610. [8] T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, T. Kataoka, Opt. Rev. Vol. 14 (2007) 401.