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An instrument for manufacturing zone-plates by using a lathe
An instrument for manufacturing zone-plates by using a lathe Takashi Nomura,* Kazuhide Kamiya,* Hiroshi Miyashiro,* Kazuo Yoshikawa,t Hatsuzo Tashiro,t Masane Suzuki,$ Shigeo Ozono,§ Fumio Kobayashi, jl and Masao Usuki ~ *Department of Mechanical Systems Engineering, Toyama Prefectural University, Toyama, Japan tDepartment of Mechanical Systems Engineering, Toyama University, Toyama, Japan tNagoya College of Creative Art, Okusa, Komaki, Aichi, Japan §Department of Precision Machinery Engineering, University of Tokyo, Tokyo, Japan 11Fuji Photo Optical Co., Ltd., Uetake-machi, Ohmiya, Saitama, Japan ¶Nachi-Fujikoshi Co., Ltd., Ohkake, Namerikawa, Toyama, Japan A laser writing system is developed in order to manufacture precise and inexpensive zone-plates. The zone-plates are a key component of an interferometer that measures shape error of spherical or aspherical mirrors on an ultraprecision lathe. The laser writer is mounted on the sliding table of the lathe. A glass plate coated with photoresist is attached to a chuck of the lathe and rotated. The zone-plate grating is written on the glass plate by a focused laser beam. Zone-plate writing is sped up by reducing the necessary number of computer instructions, causing no loss in the accuracy of the zone-plate. The accuracy of the zone-plate obtained by this inexpensive method is O. I I~m and the same as that achieved by an electron beam writer.
Keywords: zone-plate; manufacture of zone-plate; zone-plate interferometer; laser beam; ultraprecision lathe
Introduction Common path interferometers incorporating zoneplates 1-6 are used to measure shape error of rotationally symmetric mirrors. Wavefronts diffracted through the zone-plates are used as reference surfaces to test spherical and aspherical mirrors. For accurate measurements, precise zone-plates corresponding to the designed shapes must be manufactured. This article describes a system for manufacturing zoneplates adequate for the zone-plate interferometers. Three methods are commonly used to manufacture zone-plates. The first method is the two-beam interference method, using optical elements. 1"2 Because the zone-plates obtained by this method have narrow grating pitches and generate diffracted wavefronts with large diverging angles, the shape error of mirrors with a large numerical aperture (NA) can be measured. However, it is difficult to Address reprint requests to Takashi Nomura, Department of Mechanical Systems Engineering, Toyama Prefectural University, Kosugi-machL Toyama, 939-03 Japan. @ 1994 Butterworth-Heinemann
290
fabricate zone-plates to test aspherical mirrors. In addition, the accuracy of the zone-plates is low because alignment of the optical elements is difficult. The second method is the photoreduction method. 3-6 Zone-plates are patterned by reducing large original zone-plate images written with a computer. Zone-plates for aspherical mirrors are produced by this method. However, gratings with narrow pitches are difficult to manufacture because the pitch is limited by spatial resolution of a camera lens. It is difficult to measure the shape error of mirrors with a large NA. The minimum pitch of the grating was about 10/~m and the maximum NA was 0.16 in our experience. The third method is the direct writing method using an electron beam writer. Because narrow gratings are written on photo plates by the electron beam with a spot diameter of 0.1 #m, the shape error of mirrors with large NA can be measured. The writer produces high-accuracy zone-plates for testing spherical and aspherical mirrors. However, the electron beam writer is expensive. Because many users of the zone-plate interferometer have to order the OCTOBER 1994 VOL 16 NO 4
Nomura et al.: Manufacturing zone-plates on a lathe
precision positioning accuracy. Figures 2 and 3 are a schematic diagram and photograph of the instrument. The dimensions of the instrument are 450 x 350 x 200 mm. A glass plate coated with photoresist is attached to the chuck and rotated. The sliding table travels radially with respect to the spindle by 0.1 pm Photo plate
3
M:Mirrors L:Lenses ZP:Zone-plate BS:Bea msplitters Figure 1 Zone-plate interferometer zone-plates from large corporations that have this expensive system, delivery time of the zone-plates usually ranges from 5 to 6 months. To overcome this problem, we developed a system for manufacturing zone-plates adequate for our newly developed zone-plate interferometer shown in Figure 1. Our system is based on the following two ideas: (1) Because the zone-plate gratings are concentric, they can be written quickly by revolving a photo plate attached to a chuck of a lathe and by moving a laser beam spot perpendicularly to the revolving axis of the photo plate. Buynov et al. used a similar technique for writing circular gratings, 7 although the accuracy was low (10 #m). (2) The gratings can be written more quickly by reducing the number of instructions from a computer to the lathe. The time for the instructions and for their verification occupies 80% of the writing time of the zone-plate gratings. In this article, an instrument for manufacturing zone-plates is presented. Interferograms of a spherical mirror obtained by a zone-plate manufactured with the instrument are compared with those obtained by the other zone-plate manufactured with the electron beam writer. A parabolic mirror with an NA of 0.36 is measured with a zone-plate manufactured with the instrument.
Ar laser
I
AOM,driver,
~tor I
Figure 2 Scheme of instrument for manufacturing zone- plates
M e t h o d and instrument for manufacturing zone-plate Precise positioning accuracy is necessary for writing zone-plate gratings. A laser beam writer is mounted on a sliding table of hydrostatic type with highPRECISION ENGINEERING
Figure 3
Instrument for manufacturing zone-plates 291
Nomura et al. Manufacturing zone-plates on a lathe according to computer instructions. Grating lines are written on the glass plates by overlapping a focused laser beam. The overlapping displacement is determined by the diameter of laser beam. We determine that the displacement is half the beam diameter. When a beam with a very small diameter is used, the writing time of the gratings is long because the instrument must be moved many times. The optimum beam diameter is determined according to the minimum pitch of the grating lines. The beam diameter is generally less than half the minimum pitch. Highprecision grating lines require a beam diameter of one-quarter the minimum pitch. The instrument writes one ring by overlapping the laser beam and moves to the next outer ring not with a constant displacement but with the minimum combination of the following 10 displacements [0.1 x 2n#m (n = 0, 1,2 . . . . . 9)]: 0.1 #m, 0.2 Fm, 0.4#m, 0.8/~m, 1.6/~m, 3.2/~m, 6.4 #m, 12.8/~m, 25.6/~m, and 51.2/~m. The light source of the instrument is an air-cooled Ar laser model 1223-15VLYVW manufactured by Uniphase Co., Ltd. The small size laser is suitable for mounting on the sliding table of the lathe. The maximum power of the laser is 15mW and its wavelength is 0.458/~m. The laser beam must fulfill the following two conditions. First, the laser beam is flashed on and off in order to write the grating lines of the zone-plate. Second, the intensity of the beam is proportional to the radius of the grating lines because the exposed energy per unit area of the grating lines must be uniform on the zone-plate. The intensity is modulated by an acoustic-optic light modulator (AOM) model A-160 manufactured by Hoya Co., Ltd. Figure 4 shows the relation between the input voltage to the AOM driver and the output power of the laser from the AOM when the laser beam radiates at the maximum power. The AOM is controlled by a computer. The beam spot size is adjusted by defocusing the laser beam or by changing the aperture 2 shown in Figure 2. Focal position of the beam is determined by measuring the intensity detected by the photo transistor with a pinhole. Figure 5 shows a photograph of the instrument for manufacturing zone-plates mounted on the ultraprecision lathe.
E
4.0
0 <
E £
3.0
E e~
2.0 ~q ¢13
O
~ 1.0 4-a
o
0
J 0
0.25
0.50
0.75
1.00
Input voltage to AOM driver (V) Figure 4 Relation between input voltage to AOM driver and output power of laser beam from AOM
Spot size of laser beam The zone-plates should meet the requirement for the newly developed zone-plate interferometer. The zone-plate interferometer shown in Figure 1 can measure the shape error of mirrors to the maximum NA of 0.36. NA is expressed as D
N A - 2 f -~
D
r,
a pitch P is expressed as follows: (1)
where D, f, and r are a diameter, a focal length, and a radius of curvature of the mirror as shown in Figure 6. The zone-plate is illuminating another laser beam. A diffracted angle e of laser beam from a grating with 292
Figure 5 Instrument for manufacturing zone-plates and an ultraprecision lathe
sin ~?- 2 i
D P-2L"
(2)
where 2i is the wavelength of the illumination beam and L is the distance between the zone-plate and the mirror. For example, when the wavelength of the OCTOBER 1994 VOL 16 NO 4
Nomura et aL : Manufacturing zone-plates on a lathe
!
Illumination beam
Mirror
Z ° n ~ L e ~
ns
Figure 6 Optical layout of the zone-plate interferometer illumination beam is 0.633/~m and a spherical concave mirror with a diameter of 50 mm and an NA of 0.36 is measured by using an optical configuration shown in Figure 6, the minimum grating pitch of the zone-plate is 4.6/~m. Therefore, the instrument must draw grating with less pitch than 4.6/~m. The beam radiating the Ar laser is collimated with lenses 1 and 2 and is focused on a photo plate with lens 3 (object glass, NAo = 0.55, x40) shown in Figure 2. When a beam with a uniform intensity distribution is used, the radius W of the beam spot is expressed as follows8: W = 0.61 - NA o '
(3)
where ;~ is the wavelength of the beam and NA o is a numerical aperture of the object glass. When a laser beam with a wavelength ~, of 0.458/~m is exposed on a high-contrast photoresist, the radius of the laser beam written on the photoresist is 0.51 and its diameter is about 1 #m. When the minimum grating pitch of the zone-plate is taken as two times the diameter of the beam spot, the minimum grating pitch is 2 #m. When the gratings of the zone-plate are written to the minimum pitch of 2.0/~m and are illuminated by a He-Ne laser with a wavelength of 0.633/~m, a mirror with a diameter of 114 mm and an NA of 0.81 is measurable by the optical arrangement shown in Figure 6. Because the maximum NA is 0.36 for the developed zone-plate interferometer, the condition meets our requirements. Because the minimum grating pitch is 4.6 #m in our requirements, the diameter of the beam spot is limited to a maximum of 2.3 #m. We determine that the grating lines are written on the photo plate by the beam spot with a diameter of 1.2/~m in our experiments.
Manufacturing accuracy of the zone-plate The laser writer is mounted on a sliding table of an ultraprecision lathe and is positioned from the axis of the spindle of the lathe to the outside. The positioning accuracy of the sliding table is 0.1 #m. For a grating pitch of the zone-plate of 4.6 #m, the positioning accuracy of the sliding table is 1/46 the grating pitch. PRECISION ENGINEERING
Figure 7
Loci of laser beam spots on a p h o t o plate
Because a manufacturing error of one pitch of the grating corresponds to a measurement error of )li/2, the measurement error obtained by the zone-plate remains less than 2i/92. Figure 7 s h o w s loci of the laser keam spots written on a glass plate coated with a photoresist. A solid circle shows a locus of the laser beam spot when the photo plate is revolved and the instrument is stopped. A solid line shows a locus of the beam spot when the photo plate is stopped and the instrument is moved. When the height error and the position of the beam are defined as Ah and x', the radius x of the circle is expressed as follows: x = (x '2 + Ah2) 1/2. (4)
The height of the beam spot is arranged by screws attached to the writing instrument. The height error remains because the arrangement accuracy of the height is lower than that of the sliding table. The height error Ah is measured on a microscope, and the precise position x of the instrument is calculated by Equation (4).
Experiments and experimental results Glass plates with a diameter of 50.0mm and a thickness of 3.00 mm were used as substrate of glass plates. The transmission accuracy of wavefronts through the photo plates was better than 4;/10 (=0.06/~m). The glass plates were coated with 1.5/~m of positive photoresist HPR-204D (Fuji-Hant Co., Ltd.) and were used as photo plates. The photo plates were revolved at 400 rpm. The photo plates exposed by an Ar laser beam were developed with MIF (Fuji-Hant Co., Ltd.). The zone-plates made by this treatment are of phase type. The grating lines were written on the photo plate by the beam spot with a diameter of 1.2/~m in these experiments. In order to confirm a minimum spot size of the laser beam, grating lines with a pitch of 2.0/~m were written. Figure 8 shows a photograph of the grating lines. 293
Nomura et al. : Manufacturing zone-plates on a lathe
produced by the two zone-plates. Because the zone-plates written by the laser beam are of phase type, the visibility of the moir6 fringes is very low. We observed the moir6 fringes by using an ultravioletsensitive photoresist. Figure 9 shows the moir6 fringes. Because the moir~ fringes of the figure are straight, the accuracy of both zone-plates is the same; that is, the accuracy of the zone-plate manufactured with the laser writer is 0.1 l~m. A spherical concave mirror with a radius of curvature of 140mm and a diameter of 30mm ( N A = 0 . 2 1 ) was measured by using both zoneplates. Figures 10 and 11 show these interferograms. When the shape error of the mirror is very small, a
Figure 8
Grating lines with a pitch of 2.01~m
A zone-plate with a diameter of 16 mm and a minimum grating pitch of 4.1 /~m was manufactured with the writing instrument. The overlapping displacement of the Ar laser beam was 0.6/~m. The writing time of the zone-plate was 3 hours by using a technique combining 10 movement displacements. When a constant displacement of 0.1 /=m is used, the writing time is 28 hours. Time written by an electron beam is not available to the public because of company secrets. In order to test the accuracy of the zone-plate, it was compared with a standard zone-plate manufactured by an electron beam writer. The accuracy of the standard zone-plate is 0.1 #m. Moir6 fringes are
F i g u r e 10 Interferogram of a spherical mirror obtained by using the zone-plate manufactured with the instrument
!
Figure 9 Moir~ pattern between a zone-plate manufactured with the instrument and another zone-plate manufactured with an electron beam writer 294
~!!
i
Figure 11 Interferogram of a spherical mirror obtained by using the zone-plate manufactured with the electron beam writer OCTOBER 1994 VOL 16 NO 4
Nomura et aL : Manufacturing zone-plates on a lathe
experiments. When a laser beam with a diameter of 1.2/~m was used to draw a zone-plate, the manufacturing time of the zone-plate with a diameter of 1 6 m m was 3 hours. Spherical and aspherical mirrors were measured by using the zone-plates. The accuracy of the zone-plate manufactured with the instrument was 0.1 /~m and the same as that achieved using an electron beam writer.
Acknowledgment This research was conducted with the cooperation of the research group "In-Process Measurement and Control of the Machine" of the Japan Society for Precision Engineering. We thank the Society and the group members for their support, and Professor T. Kohno of Tokyo Metropolitan Institute of Technology and Professor T. Honda of Chiba University for many helpful suggestions. Figure 12 Interferogram of a parabolic mirror obtained by using the zone-plate manufactured with the instrument fringe pattern obtained by shifting the zone-plate interferometer perpendicularly to the optical axis is straight because the fringes show a lateral shearing interference between the reference wavefronts and the surface of the mirror. These figures show that the interferograms obtained by the two different zoneplates have the same quality. These fringes were analyzed by a Fourier transform method. 9 The results indicated that the shape error of the mirror was less than ,~/10. In order to examine the measurable maximum NA of the zone-plate interferometer, the following parabolic mirror was measured by using a zone-plate adequate for the mirror: diameter of 50 mm and focal length of 70 mm (NA = 0.36). The interferogram of the mirror is shown in Figure 12.
Conclusions A laser beam with a wavelength of 0.458/~m and an object glass with an NAo of 0.55 was used in
PRECISION ENGINEERING
References 1 Murty, M. V. "Common path interferometer using Fresnel zone plates," J Opt Soc Am 1963, 53, 568-570 2 Smartt, R. N. "Zone plate interferometer," Appl Opt 1974, 13, 1093-1099 3 Tanigawa, H., Nakajima, K. and Matsuura, S., "Modified zone-plate interferometer for testing aspherical surfaces," Opt Acta 1980, 27, 1327-1334 4 Ohyama, N., Yamaguchi, I., Ichimura, I., Honda, T. and Tsujiuchi, J. "A dynamic zone plate interferometer for measuring aspherical surfaces," Opt Commun 1985, 54, 275-261 5 Nomura,T., Yoshikawa, K., Tashiro, H., Suzuki, M., Usuki, M. and Tsujiuchi, J. "A measuring method of a concave mirror by moving a zone-plate," J Jpn Soc Prec Eng 1988, 64, 1771-1775 (in Japanese) 6 Nomura,T., Yoshikawa, K., Tashiro, H., Suzuki, M., Kobayashi, F. and Usuki, M. "'Shape measurement of workpiece surface with zone-plate interferometer,'" Prec Eng 1993, 15, 86-92 7 Buynov,G. N., Larionov, N. P., Lukin, A. V., Mustafin, K. S. and Rafikov, R. A., "Holographic interferometric inspection of aspherical surfaces," Soy J Opt Technol 1971, 38, 194-197 8 Born, M. and Wolf, E. Princip/es of Optics. 5th ed., Elmsford, NY: Pergamon Press, 1975, p. 415 9 Takeda, M., Ina, H. and Kobayashi, S. "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,'" J Opt Soc Am 1982, 72, 156-160
295
Keywords: zone-plate; manufacture of zone-plate; zone-plate interferometer; laser beam; ultraprecision lathe
Introduction Common path interferometers incorporating zoneplates 1-6 are used to measure shape error of rotationally symmetric mirrors. Wavefronts diffracted through the zone-plates are used as reference surfaces to test spherical and aspherical mirrors. For accurate measurements, precise zone-plates corresponding to the designed shapes must be manufactured. This article describes a system for manufacturing zoneplates adequate for the zone-plate interferometers. Three methods are commonly used to manufacture zone-plates. The first method is the two-beam interference method, using optical elements. 1"2 Because the zone-plates obtained by this method have narrow grating pitches and generate diffracted wavefronts with large diverging angles, the shape error of mirrors with a large numerical aperture (NA) can be measured. However, it is difficult to Address reprint requests to Takashi Nomura, Department of Mechanical Systems Engineering, Toyama Prefectural University, Kosugi-machL Toyama, 939-03 Japan. @ 1994 Butterworth-Heinemann
290
fabricate zone-plates to test aspherical mirrors. In addition, the accuracy of the zone-plates is low because alignment of the optical elements is difficult. The second method is the photoreduction method. 3-6 Zone-plates are patterned by reducing large original zone-plate images written with a computer. Zone-plates for aspherical mirrors are produced by this method. However, gratings with narrow pitches are difficult to manufacture because the pitch is limited by spatial resolution of a camera lens. It is difficult to measure the shape error of mirrors with a large NA. The minimum pitch of the grating was about 10/~m and the maximum NA was 0.16 in our experience. The third method is the direct writing method using an electron beam writer. Because narrow gratings are written on photo plates by the electron beam with a spot diameter of 0.1 #m, the shape error of mirrors with large NA can be measured. The writer produces high-accuracy zone-plates for testing spherical and aspherical mirrors. However, the electron beam writer is expensive. Because many users of the zone-plate interferometer have to order the OCTOBER 1994 VOL 16 NO 4
Nomura et al.: Manufacturing zone-plates on a lathe
precision positioning accuracy. Figures 2 and 3 are a schematic diagram and photograph of the instrument. The dimensions of the instrument are 450 x 350 x 200 mm. A glass plate coated with photoresist is attached to the chuck and rotated. The sliding table travels radially with respect to the spindle by 0.1 pm Photo plate
3
M:Mirrors L:Lenses ZP:Zone-plate BS:Bea msplitters Figure 1 Zone-plate interferometer zone-plates from large corporations that have this expensive system, delivery time of the zone-plates usually ranges from 5 to 6 months. To overcome this problem, we developed a system for manufacturing zone-plates adequate for our newly developed zone-plate interferometer shown in Figure 1. Our system is based on the following two ideas: (1) Because the zone-plate gratings are concentric, they can be written quickly by revolving a photo plate attached to a chuck of a lathe and by moving a laser beam spot perpendicularly to the revolving axis of the photo plate. Buynov et al. used a similar technique for writing circular gratings, 7 although the accuracy was low (10 #m). (2) The gratings can be written more quickly by reducing the number of instructions from a computer to the lathe. The time for the instructions and for their verification occupies 80% of the writing time of the zone-plate gratings. In this article, an instrument for manufacturing zone-plates is presented. Interferograms of a spherical mirror obtained by a zone-plate manufactured with the instrument are compared with those obtained by the other zone-plate manufactured with the electron beam writer. A parabolic mirror with an NA of 0.36 is measured with a zone-plate manufactured with the instrument.
Ar laser
I
AOM,driver,
~tor I
Figure 2 Scheme of instrument for manufacturing zone- plates
M e t h o d and instrument for manufacturing zone-plate Precise positioning accuracy is necessary for writing zone-plate gratings. A laser beam writer is mounted on a sliding table of hydrostatic type with highPRECISION ENGINEERING
Figure 3
Instrument for manufacturing zone-plates 291
Nomura et al. Manufacturing zone-plates on a lathe according to computer instructions. Grating lines are written on the glass plates by overlapping a focused laser beam. The overlapping displacement is determined by the diameter of laser beam. We determine that the displacement is half the beam diameter. When a beam with a very small diameter is used, the writing time of the gratings is long because the instrument must be moved many times. The optimum beam diameter is determined according to the minimum pitch of the grating lines. The beam diameter is generally less than half the minimum pitch. Highprecision grating lines require a beam diameter of one-quarter the minimum pitch. The instrument writes one ring by overlapping the laser beam and moves to the next outer ring not with a constant displacement but with the minimum combination of the following 10 displacements [0.1 x 2n#m (n = 0, 1,2 . . . . . 9)]: 0.1 #m, 0.2 Fm, 0.4#m, 0.8/~m, 1.6/~m, 3.2/~m, 6.4 #m, 12.8/~m, 25.6/~m, and 51.2/~m. The light source of the instrument is an air-cooled Ar laser model 1223-15VLYVW manufactured by Uniphase Co., Ltd. The small size laser is suitable for mounting on the sliding table of the lathe. The maximum power of the laser is 15mW and its wavelength is 0.458/~m. The laser beam must fulfill the following two conditions. First, the laser beam is flashed on and off in order to write the grating lines of the zone-plate. Second, the intensity of the beam is proportional to the radius of the grating lines because the exposed energy per unit area of the grating lines must be uniform on the zone-plate. The intensity is modulated by an acoustic-optic light modulator (AOM) model A-160 manufactured by Hoya Co., Ltd. Figure 4 shows the relation between the input voltage to the AOM driver and the output power of the laser from the AOM when the laser beam radiates at the maximum power. The AOM is controlled by a computer. The beam spot size is adjusted by defocusing the laser beam or by changing the aperture 2 shown in Figure 2. Focal position of the beam is determined by measuring the intensity detected by the photo transistor with a pinhole. Figure 5 shows a photograph of the instrument for manufacturing zone-plates mounted on the ultraprecision lathe.
E
4.0
0 <
E £
3.0
E e~
2.0 ~q ¢13
O
~ 1.0 4-a
o
0
J 0
0.25
0.50
0.75
1.00
Input voltage to AOM driver (V) Figure 4 Relation between input voltage to AOM driver and output power of laser beam from AOM
Spot size of laser beam The zone-plates should meet the requirement for the newly developed zone-plate interferometer. The zone-plate interferometer shown in Figure 1 can measure the shape error of mirrors to the maximum NA of 0.36. NA is expressed as D
N A - 2 f -~
D
r,
a pitch P is expressed as follows: (1)
where D, f, and r are a diameter, a focal length, and a radius of curvature of the mirror as shown in Figure 6. The zone-plate is illuminating another laser beam. A diffracted angle e of laser beam from a grating with 292
Figure 5 Instrument for manufacturing zone-plates and an ultraprecision lathe
sin ~?- 2 i
D P-2L"
(2)
where 2i is the wavelength of the illumination beam and L is the distance between the zone-plate and the mirror. For example, when the wavelength of the OCTOBER 1994 VOL 16 NO 4
Nomura et aL : Manufacturing zone-plates on a lathe
!
Illumination beam
Mirror
Z ° n ~ L e ~
ns
Figure 6 Optical layout of the zone-plate interferometer illumination beam is 0.633/~m and a spherical concave mirror with a diameter of 50 mm and an NA of 0.36 is measured by using an optical configuration shown in Figure 6, the minimum grating pitch of the zone-plate is 4.6/~m. Therefore, the instrument must draw grating with less pitch than 4.6/~m. The beam radiating the Ar laser is collimated with lenses 1 and 2 and is focused on a photo plate with lens 3 (object glass, NAo = 0.55, x40) shown in Figure 2. When a beam with a uniform intensity distribution is used, the radius W of the beam spot is expressed as follows8: W = 0.61 - NA o '
(3)
where ;~ is the wavelength of the beam and NA o is a numerical aperture of the object glass. When a laser beam with a wavelength ~, of 0.458/~m is exposed on a high-contrast photoresist, the radius of the laser beam written on the photoresist is 0.51 and its diameter is about 1 #m. When the minimum grating pitch of the zone-plate is taken as two times the diameter of the beam spot, the minimum grating pitch is 2 #m. When the gratings of the zone-plate are written to the minimum pitch of 2.0/~m and are illuminated by a He-Ne laser with a wavelength of 0.633/~m, a mirror with a diameter of 114 mm and an NA of 0.81 is measurable by the optical arrangement shown in Figure 6. Because the maximum NA is 0.36 for the developed zone-plate interferometer, the condition meets our requirements. Because the minimum grating pitch is 4.6 #m in our requirements, the diameter of the beam spot is limited to a maximum of 2.3 #m. We determine that the grating lines are written on the photo plate by the beam spot with a diameter of 1.2/~m in our experiments.
Manufacturing accuracy of the zone-plate The laser writer is mounted on a sliding table of an ultraprecision lathe and is positioned from the axis of the spindle of the lathe to the outside. The positioning accuracy of the sliding table is 0.1 #m. For a grating pitch of the zone-plate of 4.6 #m, the positioning accuracy of the sliding table is 1/46 the grating pitch. PRECISION ENGINEERING
Figure 7
Loci of laser beam spots on a p h o t o plate
Because a manufacturing error of one pitch of the grating corresponds to a measurement error of )li/2, the measurement error obtained by the zone-plate remains less than 2i/92. Figure 7 s h o w s loci of the laser keam spots written on a glass plate coated with a photoresist. A solid circle shows a locus of the laser beam spot when the photo plate is revolved and the instrument is stopped. A solid line shows a locus of the beam spot when the photo plate is stopped and the instrument is moved. When the height error and the position of the beam are defined as Ah and x', the radius x of the circle is expressed as follows: x = (x '2 + Ah2) 1/2. (4)
The height of the beam spot is arranged by screws attached to the writing instrument. The height error remains because the arrangement accuracy of the height is lower than that of the sliding table. The height error Ah is measured on a microscope, and the precise position x of the instrument is calculated by Equation (4).
Experiments and experimental results Glass plates with a diameter of 50.0mm and a thickness of 3.00 mm were used as substrate of glass plates. The transmission accuracy of wavefronts through the photo plates was better than 4;/10 (=0.06/~m). The glass plates were coated with 1.5/~m of positive photoresist HPR-204D (Fuji-Hant Co., Ltd.) and were used as photo plates. The photo plates were revolved at 400 rpm. The photo plates exposed by an Ar laser beam were developed with MIF (Fuji-Hant Co., Ltd.). The zone-plates made by this treatment are of phase type. The grating lines were written on the photo plate by the beam spot with a diameter of 1.2/~m in these experiments. In order to confirm a minimum spot size of the laser beam, grating lines with a pitch of 2.0/~m were written. Figure 8 shows a photograph of the grating lines. 293
Nomura et al. : Manufacturing zone-plates on a lathe
produced by the two zone-plates. Because the zone-plates written by the laser beam are of phase type, the visibility of the moir6 fringes is very low. We observed the moir6 fringes by using an ultravioletsensitive photoresist. Figure 9 shows the moir6 fringes. Because the moir~ fringes of the figure are straight, the accuracy of both zone-plates is the same; that is, the accuracy of the zone-plate manufactured with the laser writer is 0.1 l~m. A spherical concave mirror with a radius of curvature of 140mm and a diameter of 30mm ( N A = 0 . 2 1 ) was measured by using both zoneplates. Figures 10 and 11 show these interferograms. When the shape error of the mirror is very small, a
Figure 8
Grating lines with a pitch of 2.01~m
A zone-plate with a diameter of 16 mm and a minimum grating pitch of 4.1 /~m was manufactured with the writing instrument. The overlapping displacement of the Ar laser beam was 0.6/~m. The writing time of the zone-plate was 3 hours by using a technique combining 10 movement displacements. When a constant displacement of 0.1 /=m is used, the writing time is 28 hours. Time written by an electron beam is not available to the public because of company secrets. In order to test the accuracy of the zone-plate, it was compared with a standard zone-plate manufactured by an electron beam writer. The accuracy of the standard zone-plate is 0.1 #m. Moir6 fringes are
F i g u r e 10 Interferogram of a spherical mirror obtained by using the zone-plate manufactured with the instrument
!
Figure 9 Moir~ pattern between a zone-plate manufactured with the instrument and another zone-plate manufactured with an electron beam writer 294
~!!
i
Figure 11 Interferogram of a spherical mirror obtained by using the zone-plate manufactured with the electron beam writer OCTOBER 1994 VOL 16 NO 4
Nomura et aL : Manufacturing zone-plates on a lathe
experiments. When a laser beam with a diameter of 1.2/~m was used to draw a zone-plate, the manufacturing time of the zone-plate with a diameter of 1 6 m m was 3 hours. Spherical and aspherical mirrors were measured by using the zone-plates. The accuracy of the zone-plate manufactured with the instrument was 0.1 /~m and the same as that achieved using an electron beam writer.
Acknowledgment This research was conducted with the cooperation of the research group "In-Process Measurement and Control of the Machine" of the Japan Society for Precision Engineering. We thank the Society and the group members for their support, and Professor T. Kohno of Tokyo Metropolitan Institute of Technology and Professor T. Honda of Chiba University for many helpful suggestions. Figure 12 Interferogram of a parabolic mirror obtained by using the zone-plate manufactured with the instrument fringe pattern obtained by shifting the zone-plate interferometer perpendicularly to the optical axis is straight because the fringes show a lateral shearing interference between the reference wavefronts and the surface of the mirror. These figures show that the interferograms obtained by the two different zoneplates have the same quality. These fringes were analyzed by a Fourier transform method. 9 The results indicated that the shape error of the mirror was less than ,~/10. In order to examine the measurable maximum NA of the zone-plate interferometer, the following parabolic mirror was measured by using a zone-plate adequate for the mirror: diameter of 50 mm and focal length of 70 mm (NA = 0.36). The interferogram of the mirror is shown in Figure 12.
Conclusions A laser beam with a wavelength of 0.458/~m and an object glass with an NAo of 0.55 was used in
PRECISION ENGINEERING
References 1 Murty, M. V. "Common path interferometer using Fresnel zone plates," J Opt Soc Am 1963, 53, 568-570 2 Smartt, R. N. "Zone plate interferometer," Appl Opt 1974, 13, 1093-1099 3 Tanigawa, H., Nakajima, K. and Matsuura, S., "Modified zone-plate interferometer for testing aspherical surfaces," Opt Acta 1980, 27, 1327-1334 4 Ohyama, N., Yamaguchi, I., Ichimura, I., Honda, T. and Tsujiuchi, J. "A dynamic zone plate interferometer for measuring aspherical surfaces," Opt Commun 1985, 54, 275-261 5 Nomura,T., Yoshikawa, K., Tashiro, H., Suzuki, M., Usuki, M. and Tsujiuchi, J. "A measuring method of a concave mirror by moving a zone-plate," J Jpn Soc Prec Eng 1988, 64, 1771-1775 (in Japanese) 6 Nomura,T., Yoshikawa, K., Tashiro, H., Suzuki, M., Kobayashi, F. and Usuki, M. "'Shape measurement of workpiece surface with zone-plate interferometer,'" Prec Eng 1993, 15, 86-92 7 Buynov,G. N., Larionov, N. P., Lukin, A. V., Mustafin, K. S. and Rafikov, R. A., "Holographic interferometric inspection of aspherical surfaces," Soy J Opt Technol 1971, 38, 194-197 8 Born, M. and Wolf, E. Princip/es of Optics. 5th ed., Elmsford, NY: Pergamon Press, 1975, p. 415 9 Takeda, M., Ina, H. and Kobayashi, S. "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,'" J Opt Soc Am 1982, 72, 156-160
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