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Discussions on on-machine measurement of aspheric lens-mold surface
Optik 124 (2013) 4406–4411
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Discussions on on-machine measurement of aspheric lens-mold surface Yongjian Zhu a,b,∗ , Jingxin Na b , Weiqing Pan a , Yanan Zhi c a
Zhejiang University of Science and Technology, Hangzhou 310023, PR China State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, PR China c Shanghai Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, PR China b
a r t i c l e
i n f o
Article history: Received 25 September 2012 Accepted 10 January 2013
Keywords: On-machine measurement Aspheric lens mold Ultra-precision machining Instantaneous shearing interferometry
a b s t r a c t At present, regarding to the machining of aspheric lens mold, there are two major methods to carry out the on-machine measurement (OMM) — contacting method (CM) and non-contacting method (NCM). Here such two methods are reviewed in detail. CM is mainly based on the contacting probe which is scratching aspheric surface of lens mold to achieve profile data. To be efficient, an idea with 45◦ tilt of probe is proposed for OMM of lens mold by Suzuki. But generally speaking, the contacting OMM is not so efficient and can only deal with axisymmetric aspheric lens mold. On the contrary, NCM mostly uses laser to achieve aspheric profile without any contact. On ultra-precision lathe, laser scanning system or laser interferometer is mounted on the frame of lathe and transfers measurement data to machining system efficiently. However, most NCMs need stable environment and low working noise except instantaneous phase-shifting shearing interferometry (IPSSI). Therefore, a new idea about IPSSI is proposed in this paper to realize OMM of lens molds. Unfortunately, it’s also difficult to test the high numerical aperture aspheric or free-form lens molds. By comparison, the newly-developed fringe reflection (FR) method is becoming the promising method because it features the high efficiency and high accuracy. However, this method has not been used for OMM system yet. Much research should be conducted for FR OMM technology. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Classical polishing methods used for spherical surfaces of lens mold are not applicable to general aspheres and freeforms [1]. So currently, the aspheric lens-mold shape are formed mainly by computer-controlled local polishing method, magneto-rheological finishing process (MRF), single point diamond turning (SPDT) or precision diamond grinding method. In every manufacturing process, the achievable precision is only as good as the measurement method. For a high-end aspheric optics processing environment, important characteristics of a measurement method are: (a) high accuracy; (b) universal; (c) non-contact; (d) large measurement volume; (e) short measurement time [2]. That is to say, the onmachine measurement (OMM) of aspheric lens mold should be highly efficient, accurate and universal. Up to now, there are two major kinds of OMM methods: probe contacting method [3–12,14–16] and laser-based non-contacting method [13,17–30]. The contacting method uses the stylus or probe to scratch the surface of lens mold to achieve the section profile. In this case, the probe will damage the smoothness of lens-mold surface to
∗ Corresponding author at: Zhejiang University of Science and Technology, Hangzhou 310023, PR China. E-mail address: [email protected] (Y. Zhu). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.01.106
some degree. Suzuki [5] proposed a 45 degrees tilted OMM system for small optical parts, by which the contact angle between the probe axis and the contact surface is kept constant. The probe friction force on lens-mold surface is changed smoothly so that the damage on the surface of lens mold becomes much less. Anyway, the contact between the probe and lens-mold surface is unavoidable. Therefore, the laser-based non-contacting OMM method is proposed to avoid the disadvantages of contacting method. References [18–28] have proposed some non-contacting OMM methods based the laser interferometry or laser holographic technology to realize the nondestructive testing. The other non-contacting OMM methods include the laser-triangle method [17], the laser-scanning method [2] and the fringe reflection (FR) method [29,30]. All the non-contacting OMM methods share the common advantages of non-destruction and high accuracy. But they are very different in efficiency and universal. The OMM laser interferometry is highly limited in measuring different shapes of aspheric lens molds. Meanwhile, most of non-contacting measurement systems need the stable environment and low working noise except the instantaneous phase-shifting shearing interferometry (IPSSI). Here a new concept about IPSSI is proposed in this paper to realize the OMM of lens molds. Unfortunately, it’s also difficult to test the high numerical aperture (NA) aspheric or free-form lens molds. Comparatively speaking, the laser-scanning OMM method is highly universal and accurate, but not so satisfactory in efficiency, especially its cost
Y. Zhu et al. / Optik 124 (2013) 4406–4411
Fig. 1. Contacting OMM system by Mohammad (from Ref. [4]).
should be considered carefully. The newly developed FR method is becoming a promising OMM method to be used to seek the balance among high efficiency, high accuracy and universal. 2. Probe-contacting OMM method As for the probe-contacting OMM methods, Mohammad [4] has developed a fully functional 4 axis CNC ELID grinding machine and an OMM system to measure the ground aspheric surface profile and diameter of grinding wheel. The OMM system was based on coordinate measurement machine (CMM) principle and checked the ground surface profile during machining. At the same time, the wheel wear could be also measured at some regular interval. Fig. 1 shows the OMM system. In 2011, Huang [3] proposed a machining error compensation method using OMM system in 3-axis aspheric grinding. It aimed to providing the compensating profile data for large aspheric grinding. By use of this OMM system, the machining errors were reduced dramatically and the accuracy was improved by more than 45%, compared with the non-compensation machining. Additionally, Suzuki [5] proposed a 45◦ tilted contacting OMM system for small aspheric optics, especially for the large NA optics with steep surface angle. A air slider made of SIALON was adopted for the measurement probe and it was tilted for 45◦ against the aspheric workpiece axis so as to reduce the change in the probe friction force. Fig. 2 showed the real setup of OMM system and the conventional system. Through experiments, it proved that the measuring accuracy was much improved as compared to the conventional method. Kim [7] realized diamond turning of large off-axis aspheric mirrors with OMM, and the machine axis errors were compensated in real time by using a fast tool servo. Its results showed that the proposed approach was capable of fabricating aluminum mirrors of 620 mm diameter with form accuracy of 0.7 m in peakto-valley (PV). On the other hand, Arai [10] presented a novel probe-scanning system to achieve the precise profile measurement of micro-aspheric mold. Fig. 3 showed the Arai’s new OMM
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Fig. 3. Arai’s scanning probe OMM system (from Ref. [10]).
system. It consisted of a scanning stage and a sensor unit. The probe’s contact force is less than 2.3 mN. Its experiments proved that the measurement repeatability of micro-aspheric scanning were smaller than ±20 nm. Chen [9] also developed a compensation method based on the OMM to conducting the grinding of tungsten carbide (WC) aspheric lens mold. The form error after grinding was achieved by subtracting the target profile from the actual ground profile. The experiments showed that the aspheric surface had an accuracy of 177 nm (PV) and roughness of 1.7 nm (Ra) after 3 compensation cycles. Yongjian [11] developed a low-cost OMM method used in fine grinding of large aspheric mirror. The OMM method was carried out on a common digital-controlled lapping machine tool and its accuracy was better than 5 m. To improve the accuracy of OMM, Yoshikazu [12] put forward an accurate two-probe method to measure an aspheric lens on an ultra-precision grinding machine. Its results showed that the deviation of tested profile from the designed value was confirmed to be 0.35 m. In addition, Changyu [15] provided an OMM method aiming at solving the complex aspheric surface. Its experiments showed that the measuring method had high accuracy, universal utility in the aspheric machining and measurement. Zhifang [16] had also made an OMM of aspheric workpiece surface by using a precise-calibrated, lowforce and air-bearing LVDT. According to the investigations of OMM methods, the probe contacting method is still popular for the ultra-precision machining although the scanning efficiency of probe is much limited. Its profile accuracy can be on the order of submicron. However, on the most cases, it’s only suitable for the axisymmetric aspheric surface of lens mold.
3. Non-contacting OMM method 3.1. Laser triangle method
Fig. 2. the 45 degrees OMM method compared to conventional one (from Ref. [5]); (a) Conventional OMM method; (b) the 45 degrees tilted OMM method.
Gao [17] firstly developed an in-process form error measurement device to deal with the opaque barrier and vibration. It was based on a single laser sensor of 50 nm resolution together with a damping technique and a moving average one. Fig. 4 showed the prototype for the OMM optical setup by Gao. In Fig. 4, the proposed damping technique was able to improve vibration attenuation by nearly 21 times compared to the natural attenuation, and its moving average method was able to reduce errors by seven to ten times with no change of form errors. For a workpiece sample, the overall system measurement error could be as low as 0.3 m.
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Fig. 4. Prototype for the OMM optical setup by Y. Gao (from Ref. [17]).
Fig. 7. The scheme of OMM system with polishing machine, test tower and interfero-meter by Christopher W. King (from Ref. [19]).
Fig. 5. The OMM system by Mauro Melozzi (from Ref. [18]).
3.2. Integrated interferometer-based method To improve the efficiency of OMM, Mauro Melozzi [18] realized a digital interferometer for measuring the shape of optical surfaces in an unstable environment. It was based on the spatialcarrier phase-shifting technique. The system had been mounted over a polishing machine and used for the OMM of aspheric mirror surfaces. It was shown in Fig. 5. A compact Twyman-Green interferometer is mounted on a frame, and fixed near the curvature center of aspheric surface, which is vertically facing the polishing machine. Fig. 6 showed the principle scheme of this interferometer. Through experiments, the form error tested by the optical OMM system was about /8 in PV and /35 rms. King Christopher [19] also used a 6 Fizeau interferometer to develop an integrated solution for polishing and measuring moderately large concave optics up to 1 m in diameter. It was based on the combination of a Zeeko polishing machine and a
5-axis motorized stage housing Fizeau interferometer. The OMM system was still equipped with a CGH holder to install different CGH elements. Fig. 7 showed the scheme of OMM system with polishing machine, test tower and interferometer. The measurement results proved that the aspheric form error was at the /8 PV level. Wang[25] and Li [26] proposed a real-time OMM interferometric method to test the weak aspheric surfaces, respectively. The former used a sphere mirror as the reference surface and measured a aspheric mirror of ˚350 mm. The tested results were the PV and RMS of 0.387 and 0.048, respectively. The latter modified the ZYGO interferometer and used it to test the weak aspheric surfaces in real time. The testing error is 0.16 ± 0.014 of PV. 3.3. Synthetic aperture interferometry In 2003, Richard Tomlinson [24] proposed a synthetic aperture interferometry to realize the OMM of aspheric optics. It used a scanning probe consisting of a source and receiving fiber pair to measure the phase difference. In contrast with classical interferometers, the method did not need test or null plates and had the potential to be integrated into the manufacturing process [24]. But afterward, it was found that this fiber probe did not have sufficient NA to measure steep surfaces and that simply increasing the NA decreases the light gathering efficiency substantially [21]. So Amiya Biswas [21] introduced supplementary optics to increase the NA, and the light gathering efficiency had been increased by adopting an anamorphic probe design. Therefore, this OMM method could measure steep aspheric lens molds by increasing the NA of probe. The measurement results showed that the OMM system was capable of measuring surface form to submicron accuracy. 3.4. Method of holographic interferometry
Fig. 6. Twyman-Green interferometer by Mauro Melozzi: the waveform generator was used to introduce forced mechanical vibrations (from Ref. [18]).
Based on the holographic interferometry, Dil Jan [20] developed an OMM method of measuring the steep aspheric surfaces, which could be a convex or concave aspheric lens mold with a high NA. The maximum aspheric slope could be 1200 waves/rad. The
Y. Zhu et al. / Optik 124 (2013) 4406–4411
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Fig. 8. The holographic interferometer for testing the reproducibility of the fabrication of aspheres; M1, 2 are mirrors, B is the beam splitter, l1 –15 are lenses, P is the photographic plate, S is the observing screen. (from Ref. [20]).
measurement process was divided into two steps: First, a standard measurement was performed to obtain a reference surface. Second, the reproducibility of the fabrication of aspheric surfaces was tested by means of a holographic comparison method. The experiments demonstrated that the measuring shape error is smaller than 0.1 m. Fig. 8 is the optical scheme of measurement principle. Xiang [27] proposed another holographic interferometer for real-time OMM of aspheric surfaces as well. It aimed at solving the testing problems during the rough machining and finish machining of aspheric optics. 3.5. Laser scanning method Henselmans [2] invented a non-contacting OMM prototype for freeform optics with the laser scanning distance probe. It was said that the OMM system was capable of universal, non-contact and fast measurement of freeform optics up to ˚500 mm, with an uncertainty of 30 nm (2). Fig. 9 (a) showed the real setup of OMM system, (b) was the optical principle scheme. 3.6. Shearing interferometry Both Kohno [22] and Ming [28] proposed the OMM methods based on the radial shearing interferometry. The former used two zone plates to measure a concave mirror figure. The on-machine experiments showed that the method was stable and compact enough to be applicable to on-machine measurement for diamond turning at about 0.06 m in PV accuracy. The latter also developed a small OMM setup based on two zone plates, and its experiments proved that the method could realize the OMM of weak aspheric surfaces and its accuracy reached /5 in PV and /10 in RMS. Additionally, Nomura [23] invented a common path lateral-shearing interferometer for machine running combining
Fig. 9. the OMM setup by Rens Henselmans—1: -axis, 2: aspheric lens, 3: spindle, 4 and 5: light path of -axis position interferometry, 6 and 7: reference mirrors, 8: metrology frame, 9: capacitive probes, 10: lower metrology frame (from Ref. [2]); (a) the real setup of OMM system; (b) the optical principle scheme.
Fig. 10. The scheme diagram of lateral-shearing interferometer by Takashi Nomura (from Ref. [23]).
with fringe-scanning method, which was little affected by mechanical vibrations and air turbulence. Fig. 10 was the scheme diagram of lateral-shearing interferometer by Takashi Nomura. The experimental results of a parabolic concave mirror agreed well with those measured by a Fizeau interferometer. According to the analysis, it’s known that there are some common advantages such as high accuracy, high speed and high NA measurement for the present interferometric methods. But when the interferometer is mounted on the machine, the unstable factors should be considered such as vibration and environment noise. In this case, the instantaneous phase-shifting shearing interferometry (IPSSI) should be introduced. Therefore, a new concept about IPSSI has proposed in this paper to realize the OMM of lens molds. Fig. 11 showed the scheme diagram of new double-frequency radial shearing interferometer which was based on instantaneous phase shifting. The key elements were the two optical semi-circle wedge pairs, which consisted of two optical wedges with the same small angle (on the scale of arcmin). In each wedge pair, the narrow ends were placed oppositely. The final fringe patterns were divided into upper and lower parts with different fringe periods, which could be solved to achieve the aspheric shapes according to the differential theory. However, this method could only deal with the OMM of axisymmetric aspheric lens mold. So the double-frequency radial shearing interferometer could be modified by replacing the semi-circle
Fig. 11. The optical scheme diagram of double-frequency interferometer.
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of lens molds. Unfortunately, it’s also hard to test the high NA aspheric molds or free-form lens molds. Through investigation, the newly-developed FR method could be the most promising method to conduct the OMM. It features the high efficiency and high accuracy. Furthermore, the FR method can almost measure all aspheric surfaces including non-axisymmetric and free-form one. Up to now, this method is not used for OMM system yet. Much study should be carried out for the FR OMM system.
Acknowledgements
Fig. 12. The structure of fringe-reflection measurement setup (from Ref. [29]).
wedges with full-circle ones. But the other symmetric light path should be added along the transmitting direction of light through Jamin Plate 7. Generally speaking, this method had a good antivibration ability and could realize the OMM of most aspheric lens molds, but failed to measure the free-form molds and its cost was not low enough compared to the following FR method. 3.7. Fringe reflection method At present, the FR method was proposed to test the specular surfaces [30]. Later on, Tang [29] used it to test the aspheric mirrors. Fig. 12 was the principal structure of FR measurement setup. It adopted a liquid crystal display (LCD) screen to display sinusoidal fringe patterns and a camera to record the fringe patterns reflected via the tested mirror, and through the movement of LCD and camera along the optical axis of tested mirror, each pixel could find a corresponding point on the tested mirror and got its coordinate and slope. At last, the 3D shape of the tested mirror can be reconstructed by integration. Theoretically, FR method could measure the most aspheric mirrors including the non-axisymmetric and free form. Furthermore, this method also featured high efficiency, strong antinoise ability and low cost. Now it needs to be further improved in order to suit for the OMM during the ultra-precision machining. 4. Conclusions Aspheric lens mold could be processed through polishing, diamond turning or grinding by computer-controlled machine tools. During the machining of aspheric lens mold, the OMM has become an indispensable tool to achieve the final form. An accurate OMM system could provide the precision data for the compensation machining. In this paper, two kinds of OMM methods are discussed and reviewed in detail. The probe-based contacting method is still popular in aspheric optics processing. But it’s not satisfactory in measurement time and versatility. In the most cases, it can only measure the axisymmetric aspheric surface with relatively low efficiency. Especially the probe will scratch the surface of soft-metal lens mold to some degree. So many non-contacting OMM methods have been proposed to solve the scratching problems. The laser-based interferometry becomes the mainstream in OMM system. Through the interferometry, one can achieve the 3D data quickly on one time. Its accuracy is comparable to the probe-contacting method. But laser interferometry is equally limited to the versatility in measuring various types of optical surface. In addition, most of laser interferometric methods need the stable environment and low working noise except IPSSI. Therefore, a new idea on IPSSI is proposed here to realize the OMM
This work was supported by the National Natural Science Foundation of China (Grant No.51005212 & No.61275110); the Public-Service Technology Research Plan of Zhejiang Province (No.2011C21003); the open fund of Key Laboratory of Space Laser Communication and Testing Technology from Chinese Academy of Sciences; China Postdoctoral Science Foundation (No.2011M500936 & No.2012T50274) and Foundation of State Key Laboratory of Automotive Simulation and Control (No.20111114).
References [1] H.H. Karow, Fabrication Methods for Precision Optics, Wiley Interscience, U.S., 1993, ISBN 0-471-51222-2. [2] R. Henselmans, Non-contact measurement machine for freeform optics, Eindhoven University of Technology, Ph.D. Thesis, 2009. [3] H. Huang, X. Lei, J. Wang, et al., A Machining error compensation method using on-machine profile measurement in 3-axis aspheric grinding, Adv. Mater. Res. 154/155 (2011) 390–395. [4] M.S. Rahman, Design and development of an on-machine profile measurement system for an Elid grinding machine, Thesis of Master Degree, National University of Singapore, 2007. [5] H. Suzuki, T. Onishi, T. Moriwaki, et al., Development of a 45 degrees tilted on-machine measuring system for small optical parts, Ann. CIRP 57 (1) (2008) 414–417. [6] M. Sazedur Rahman, T. Saleh, H.S. Lim, Development of an on-machine profile measurement system in ELID grinding for machining aspheric surface with software compensation, Int. J. Mach. Tool Manuf. 48 (2008) 887–895. [7] H. Kim, E. Kim, B. Song, Diamond turning of large off-axis aspheric mirrors using a fast tool servo with on-machine measurement, J. Mater. Process. Technol. 146 (2004) 349–355. [8] H. Kim, K. Lee, K. Lee, Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement, Int. J. Mach. Tool Manuf. 49 (2009) 991–997. [9] F.J. Chen, S.H. Yin, H. Huang, Profile error compensation in ultra-precision grinding of aspheric surfaces with on-machine measurement, Int. J. Mach. Tool Manuf. 50 (2010) 480–486. [10] Y. Arai, A. Shibuya, Y. Yoshikawa, Online measurement of micro-aspheric surface profile with compensation of scanning error, Key Eng. Mater. 381/382 (2008) 175–178. [11] Y. Wan, B. Fan, J. Yuan, An on-line measuring technique for lapping large aspherical mirror, Opto-Electron. Eng. 32 (1) (2005) 1–4. [12] A. Yoshikazu, G. Wei, S. Hiroki, On-machine measurement of aspherical surface profile, Nanotechnol. Precis. Eng. 2 (3) (2004) 210–216. [13] G. Li, Design and research of ultra-precision measurement of aspheric mirror and error analysis system, Guangdong University of Technology, Thesis of Master Degree, 2007. [14] Y. Guo, J. Guo, X. Ke, System error separation and revision for aspheric lens on-machine measurement, Nanotechnol. Precis. Eng. 8 (5) (2010) 414–421. [15] C. Xu, C. Pang, Precision on-machine measurement technology of rational complex aspheric surface, Aviat. Precis. Manuf. Technol. 46 (2) (2010) 9–13. [16] Z. He, J. Zhang, W. Liu, On-line measurement of aspheric workpiece surface accuracy in precision machining, Aviat. Precis. Manuf. Technol. 39 (1) (2003) 5–8. [17] Y. Gao, X. Huang, Y. Zhang, An in-process form error measurement system for precision machining, Meas. Sci. Technol. 21 (2010) 1–8. [18] M. Melozzi, L. Pezzati, A. Mazzoni, In process optical metrology for aspheric surfaces, SPIE 2210 (1994) 625–630. [19] W. King Christopher, Integrated on-machine metrolsystems, UCL, Optic Technium, UK, 2010, ogy http://www.jspe.or.jp/english/sympo/2010a/2010a-2-4.pdf [20] G. Dil Jan, F. Greve Peter, Mesman Wichert, Measurement of steep aspheric surfaces, Appl. Opt. 17 (4) (1978) 553–557. [21] A. Biswas, J. Coupland, Measurement of steep aspheric surfaces using an anamorphic probe, Appl. Opt. 47 (11) (2008) 1705–1710. [22] T. Kohno, D. Matsumoto, T. Yazawa, Radial shearing interferometer for inprocess measurement of diamond turning, Opt. Eng. 39 (10) (2000) 2696–2699.
Y. Zhu et al. / Optik 124 (2013) 4406–4411 [23] T. Nomura, K. Kamiya, H. Miyashiro, Shape measurements of mirror surfaces with a lateral shearing interferometer during machine running, Precis. Eng. 22 (4) (1998) 185–189. [24] M. Richard Tomlinson, Coupland Jeremy and Jon Petzing, Synthetic aperture interferometry: in-process measurement of aspheric optics, Appl. Opt. 42 (4) (2003) 701–707. [25] X. Wang, L. Wang, X. Zhang, Testing of weak aspheric surface by real-time interferometry, Precis. Eng. 16 (2) (2008) 184–189. [26] B. Li, Real-time interferometric testing of weak aspheric surfaces, Thesis of Master Degree, Changchun Institute of Optics, Fine Mechanics and Physics, 2005.
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[27] Y. Xiang, A holographic interferometric setup of aspheric measurement in real time, Changchun Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, China Invention Patent, CN1080405A (1994). [28] M. Wang, B. Zhang, S. Nie, A small online radial shearing interferometer and its measurement of aspheric optics, Nanjing Normal University, China Invention Patent, CN1529120A (2004). [29] Y. Tang, X. Su, Y. Liu, 3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry, Opt. Exp. 16 (19) (2008) 15090–15096. [30] T. Bothe, W.S. Li, C. von Kopylow, et al., High-resolution 3D shape measurement on specular surfaces by fringe reflection, Proc. SPIE 5457 (2004) 411–422.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Discussions on on-machine measurement of aspheric lens-mold surface Yongjian Zhu a,b,∗ , Jingxin Na b , Weiqing Pan a , Yanan Zhi c a
Zhejiang University of Science and Technology, Hangzhou 310023, PR China State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130025, PR China c Shanghai Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, PR China b
a r t i c l e
i n f o
Article history: Received 25 September 2012 Accepted 10 January 2013
Keywords: On-machine measurement Aspheric lens mold Ultra-precision machining Instantaneous shearing interferometry
a b s t r a c t At present, regarding to the machining of aspheric lens mold, there are two major methods to carry out the on-machine measurement (OMM) — contacting method (CM) and non-contacting method (NCM). Here such two methods are reviewed in detail. CM is mainly based on the contacting probe which is scratching aspheric surface of lens mold to achieve profile data. To be efficient, an idea with 45◦ tilt of probe is proposed for OMM of lens mold by Suzuki. But generally speaking, the contacting OMM is not so efficient and can only deal with axisymmetric aspheric lens mold. On the contrary, NCM mostly uses laser to achieve aspheric profile without any contact. On ultra-precision lathe, laser scanning system or laser interferometer is mounted on the frame of lathe and transfers measurement data to machining system efficiently. However, most NCMs need stable environment and low working noise except instantaneous phase-shifting shearing interferometry (IPSSI). Therefore, a new idea about IPSSI is proposed in this paper to realize OMM of lens molds. Unfortunately, it’s also difficult to test the high numerical aperture aspheric or free-form lens molds. By comparison, the newly-developed fringe reflection (FR) method is becoming the promising method because it features the high efficiency and high accuracy. However, this method has not been used for OMM system yet. Much research should be conducted for FR OMM technology. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Classical polishing methods used for spherical surfaces of lens mold are not applicable to general aspheres and freeforms [1]. So currently, the aspheric lens-mold shape are formed mainly by computer-controlled local polishing method, magneto-rheological finishing process (MRF), single point diamond turning (SPDT) or precision diamond grinding method. In every manufacturing process, the achievable precision is only as good as the measurement method. For a high-end aspheric optics processing environment, important characteristics of a measurement method are: (a) high accuracy; (b) universal; (c) non-contact; (d) large measurement volume; (e) short measurement time [2]. That is to say, the onmachine measurement (OMM) of aspheric lens mold should be highly efficient, accurate and universal. Up to now, there are two major kinds of OMM methods: probe contacting method [3–12,14–16] and laser-based non-contacting method [13,17–30]. The contacting method uses the stylus or probe to scratch the surface of lens mold to achieve the section profile. In this case, the probe will damage the smoothness of lens-mold surface to
∗ Corresponding author at: Zhejiang University of Science and Technology, Hangzhou 310023, PR China. E-mail address: [email protected] (Y. Zhu). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.01.106
some degree. Suzuki [5] proposed a 45 degrees tilted OMM system for small optical parts, by which the contact angle between the probe axis and the contact surface is kept constant. The probe friction force on lens-mold surface is changed smoothly so that the damage on the surface of lens mold becomes much less. Anyway, the contact between the probe and lens-mold surface is unavoidable. Therefore, the laser-based non-contacting OMM method is proposed to avoid the disadvantages of contacting method. References [18–28] have proposed some non-contacting OMM methods based the laser interferometry or laser holographic technology to realize the nondestructive testing. The other non-contacting OMM methods include the laser-triangle method [17], the laser-scanning method [2] and the fringe reflection (FR) method [29,30]. All the non-contacting OMM methods share the common advantages of non-destruction and high accuracy. But they are very different in efficiency and universal. The OMM laser interferometry is highly limited in measuring different shapes of aspheric lens molds. Meanwhile, most of non-contacting measurement systems need the stable environment and low working noise except the instantaneous phase-shifting shearing interferometry (IPSSI). Here a new concept about IPSSI is proposed in this paper to realize the OMM of lens molds. Unfortunately, it’s also difficult to test the high numerical aperture (NA) aspheric or free-form lens molds. Comparatively speaking, the laser-scanning OMM method is highly universal and accurate, but not so satisfactory in efficiency, especially its cost
Y. Zhu et al. / Optik 124 (2013) 4406–4411
Fig. 1. Contacting OMM system by Mohammad (from Ref. [4]).
should be considered carefully. The newly developed FR method is becoming a promising OMM method to be used to seek the balance among high efficiency, high accuracy and universal. 2. Probe-contacting OMM method As for the probe-contacting OMM methods, Mohammad [4] has developed a fully functional 4 axis CNC ELID grinding machine and an OMM system to measure the ground aspheric surface profile and diameter of grinding wheel. The OMM system was based on coordinate measurement machine (CMM) principle and checked the ground surface profile during machining. At the same time, the wheel wear could be also measured at some regular interval. Fig. 1 shows the OMM system. In 2011, Huang [3] proposed a machining error compensation method using OMM system in 3-axis aspheric grinding. It aimed to providing the compensating profile data for large aspheric grinding. By use of this OMM system, the machining errors were reduced dramatically and the accuracy was improved by more than 45%, compared with the non-compensation machining. Additionally, Suzuki [5] proposed a 45◦ tilted contacting OMM system for small aspheric optics, especially for the large NA optics with steep surface angle. A air slider made of SIALON was adopted for the measurement probe and it was tilted for 45◦ against the aspheric workpiece axis so as to reduce the change in the probe friction force. Fig. 2 showed the real setup of OMM system and the conventional system. Through experiments, it proved that the measuring accuracy was much improved as compared to the conventional method. Kim [7] realized diamond turning of large off-axis aspheric mirrors with OMM, and the machine axis errors were compensated in real time by using a fast tool servo. Its results showed that the proposed approach was capable of fabricating aluminum mirrors of 620 mm diameter with form accuracy of 0.7 m in peakto-valley (PV). On the other hand, Arai [10] presented a novel probe-scanning system to achieve the precise profile measurement of micro-aspheric mold. Fig. 3 showed the Arai’s new OMM
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Fig. 3. Arai’s scanning probe OMM system (from Ref. [10]).
system. It consisted of a scanning stage and a sensor unit. The probe’s contact force is less than 2.3 mN. Its experiments proved that the measurement repeatability of micro-aspheric scanning were smaller than ±20 nm. Chen [9] also developed a compensation method based on the OMM to conducting the grinding of tungsten carbide (WC) aspheric lens mold. The form error after grinding was achieved by subtracting the target profile from the actual ground profile. The experiments showed that the aspheric surface had an accuracy of 177 nm (PV) and roughness of 1.7 nm (Ra) after 3 compensation cycles. Yongjian [11] developed a low-cost OMM method used in fine grinding of large aspheric mirror. The OMM method was carried out on a common digital-controlled lapping machine tool and its accuracy was better than 5 m. To improve the accuracy of OMM, Yoshikazu [12] put forward an accurate two-probe method to measure an aspheric lens on an ultra-precision grinding machine. Its results showed that the deviation of tested profile from the designed value was confirmed to be 0.35 m. In addition, Changyu [15] provided an OMM method aiming at solving the complex aspheric surface. Its experiments showed that the measuring method had high accuracy, universal utility in the aspheric machining and measurement. Zhifang [16] had also made an OMM of aspheric workpiece surface by using a precise-calibrated, lowforce and air-bearing LVDT. According to the investigations of OMM methods, the probe contacting method is still popular for the ultra-precision machining although the scanning efficiency of probe is much limited. Its profile accuracy can be on the order of submicron. However, on the most cases, it’s only suitable for the axisymmetric aspheric surface of lens mold.
3. Non-contacting OMM method 3.1. Laser triangle method
Fig. 2. the 45 degrees OMM method compared to conventional one (from Ref. [5]); (a) Conventional OMM method; (b) the 45 degrees tilted OMM method.
Gao [17] firstly developed an in-process form error measurement device to deal with the opaque barrier and vibration. It was based on a single laser sensor of 50 nm resolution together with a damping technique and a moving average one. Fig. 4 showed the prototype for the OMM optical setup by Gao. In Fig. 4, the proposed damping technique was able to improve vibration attenuation by nearly 21 times compared to the natural attenuation, and its moving average method was able to reduce errors by seven to ten times with no change of form errors. For a workpiece sample, the overall system measurement error could be as low as 0.3 m.
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Fig. 4. Prototype for the OMM optical setup by Y. Gao (from Ref. [17]).
Fig. 7. The scheme of OMM system with polishing machine, test tower and interfero-meter by Christopher W. King (from Ref. [19]).
Fig. 5. The OMM system by Mauro Melozzi (from Ref. [18]).
3.2. Integrated interferometer-based method To improve the efficiency of OMM, Mauro Melozzi [18] realized a digital interferometer for measuring the shape of optical surfaces in an unstable environment. It was based on the spatialcarrier phase-shifting technique. The system had been mounted over a polishing machine and used for the OMM of aspheric mirror surfaces. It was shown in Fig. 5. A compact Twyman-Green interferometer is mounted on a frame, and fixed near the curvature center of aspheric surface, which is vertically facing the polishing machine. Fig. 6 showed the principle scheme of this interferometer. Through experiments, the form error tested by the optical OMM system was about /8 in PV and /35 rms. King Christopher [19] also used a 6 Fizeau interferometer to develop an integrated solution for polishing and measuring moderately large concave optics up to 1 m in diameter. It was based on the combination of a Zeeko polishing machine and a
5-axis motorized stage housing Fizeau interferometer. The OMM system was still equipped with a CGH holder to install different CGH elements. Fig. 7 showed the scheme of OMM system with polishing machine, test tower and interferometer. The measurement results proved that the aspheric form error was at the /8 PV level. Wang[25] and Li [26] proposed a real-time OMM interferometric method to test the weak aspheric surfaces, respectively. The former used a sphere mirror as the reference surface and measured a aspheric mirror of ˚350 mm. The tested results were the PV and RMS of 0.387 and 0.048, respectively. The latter modified the ZYGO interferometer and used it to test the weak aspheric surfaces in real time. The testing error is 0.16 ± 0.014 of PV. 3.3. Synthetic aperture interferometry In 2003, Richard Tomlinson [24] proposed a synthetic aperture interferometry to realize the OMM of aspheric optics. It used a scanning probe consisting of a source and receiving fiber pair to measure the phase difference. In contrast with classical interferometers, the method did not need test or null plates and had the potential to be integrated into the manufacturing process [24]. But afterward, it was found that this fiber probe did not have sufficient NA to measure steep surfaces and that simply increasing the NA decreases the light gathering efficiency substantially [21]. So Amiya Biswas [21] introduced supplementary optics to increase the NA, and the light gathering efficiency had been increased by adopting an anamorphic probe design. Therefore, this OMM method could measure steep aspheric lens molds by increasing the NA of probe. The measurement results showed that the OMM system was capable of measuring surface form to submicron accuracy. 3.4. Method of holographic interferometry
Fig. 6. Twyman-Green interferometer by Mauro Melozzi: the waveform generator was used to introduce forced mechanical vibrations (from Ref. [18]).
Based on the holographic interferometry, Dil Jan [20] developed an OMM method of measuring the steep aspheric surfaces, which could be a convex or concave aspheric lens mold with a high NA. The maximum aspheric slope could be 1200 waves/rad. The
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Fig. 8. The holographic interferometer for testing the reproducibility of the fabrication of aspheres; M1, 2 are mirrors, B is the beam splitter, l1 –15 are lenses, P is the photographic plate, S is the observing screen. (from Ref. [20]).
measurement process was divided into two steps: First, a standard measurement was performed to obtain a reference surface. Second, the reproducibility of the fabrication of aspheric surfaces was tested by means of a holographic comparison method. The experiments demonstrated that the measuring shape error is smaller than 0.1 m. Fig. 8 is the optical scheme of measurement principle. Xiang [27] proposed another holographic interferometer for real-time OMM of aspheric surfaces as well. It aimed at solving the testing problems during the rough machining and finish machining of aspheric optics. 3.5. Laser scanning method Henselmans [2] invented a non-contacting OMM prototype for freeform optics with the laser scanning distance probe. It was said that the OMM system was capable of universal, non-contact and fast measurement of freeform optics up to ˚500 mm, with an uncertainty of 30 nm (2). Fig. 9 (a) showed the real setup of OMM system, (b) was the optical principle scheme. 3.6. Shearing interferometry Both Kohno [22] and Ming [28] proposed the OMM methods based on the radial shearing interferometry. The former used two zone plates to measure a concave mirror figure. The on-machine experiments showed that the method was stable and compact enough to be applicable to on-machine measurement for diamond turning at about 0.06 m in PV accuracy. The latter also developed a small OMM setup based on two zone plates, and its experiments proved that the method could realize the OMM of weak aspheric surfaces and its accuracy reached /5 in PV and /10 in RMS. Additionally, Nomura [23] invented a common path lateral-shearing interferometer for machine running combining
Fig. 9. the OMM setup by Rens Henselmans—1: -axis, 2: aspheric lens, 3: spindle, 4 and 5: light path of -axis position interferometry, 6 and 7: reference mirrors, 8: metrology frame, 9: capacitive probes, 10: lower metrology frame (from Ref. [2]); (a) the real setup of OMM system; (b) the optical principle scheme.
Fig. 10. The scheme diagram of lateral-shearing interferometer by Takashi Nomura (from Ref. [23]).
with fringe-scanning method, which was little affected by mechanical vibrations and air turbulence. Fig. 10 was the scheme diagram of lateral-shearing interferometer by Takashi Nomura. The experimental results of a parabolic concave mirror agreed well with those measured by a Fizeau interferometer. According to the analysis, it’s known that there are some common advantages such as high accuracy, high speed and high NA measurement for the present interferometric methods. But when the interferometer is mounted on the machine, the unstable factors should be considered such as vibration and environment noise. In this case, the instantaneous phase-shifting shearing interferometry (IPSSI) should be introduced. Therefore, a new concept about IPSSI has proposed in this paper to realize the OMM of lens molds. Fig. 11 showed the scheme diagram of new double-frequency radial shearing interferometer which was based on instantaneous phase shifting. The key elements were the two optical semi-circle wedge pairs, which consisted of two optical wedges with the same small angle (on the scale of arcmin). In each wedge pair, the narrow ends were placed oppositely. The final fringe patterns were divided into upper and lower parts with different fringe periods, which could be solved to achieve the aspheric shapes according to the differential theory. However, this method could only deal with the OMM of axisymmetric aspheric lens mold. So the double-frequency radial shearing interferometer could be modified by replacing the semi-circle
Fig. 11. The optical scheme diagram of double-frequency interferometer.
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of lens molds. Unfortunately, it’s also hard to test the high NA aspheric molds or free-form lens molds. Through investigation, the newly-developed FR method could be the most promising method to conduct the OMM. It features the high efficiency and high accuracy. Furthermore, the FR method can almost measure all aspheric surfaces including non-axisymmetric and free-form one. Up to now, this method is not used for OMM system yet. Much study should be carried out for the FR OMM system.
Acknowledgements
Fig. 12. The structure of fringe-reflection measurement setup (from Ref. [29]).
wedges with full-circle ones. But the other symmetric light path should be added along the transmitting direction of light through Jamin Plate 7. Generally speaking, this method had a good antivibration ability and could realize the OMM of most aspheric lens molds, but failed to measure the free-form molds and its cost was not low enough compared to the following FR method. 3.7. Fringe reflection method At present, the FR method was proposed to test the specular surfaces [30]. Later on, Tang [29] used it to test the aspheric mirrors. Fig. 12 was the principal structure of FR measurement setup. It adopted a liquid crystal display (LCD) screen to display sinusoidal fringe patterns and a camera to record the fringe patterns reflected via the tested mirror, and through the movement of LCD and camera along the optical axis of tested mirror, each pixel could find a corresponding point on the tested mirror and got its coordinate and slope. At last, the 3D shape of the tested mirror can be reconstructed by integration. Theoretically, FR method could measure the most aspheric mirrors including the non-axisymmetric and free form. Furthermore, this method also featured high efficiency, strong antinoise ability and low cost. Now it needs to be further improved in order to suit for the OMM during the ultra-precision machining. 4. Conclusions Aspheric lens mold could be processed through polishing, diamond turning or grinding by computer-controlled machine tools. During the machining of aspheric lens mold, the OMM has become an indispensable tool to achieve the final form. An accurate OMM system could provide the precision data for the compensation machining. In this paper, two kinds of OMM methods are discussed and reviewed in detail. The probe-based contacting method is still popular in aspheric optics processing. But it’s not satisfactory in measurement time and versatility. In the most cases, it can only measure the axisymmetric aspheric surface with relatively low efficiency. Especially the probe will scratch the surface of soft-metal lens mold to some degree. So many non-contacting OMM methods have been proposed to solve the scratching problems. The laser-based interferometry becomes the mainstream in OMM system. Through the interferometry, one can achieve the 3D data quickly on one time. Its accuracy is comparable to the probe-contacting method. But laser interferometry is equally limited to the versatility in measuring various types of optical surface. In addition, most of laser interferometric methods need the stable environment and low working noise except IPSSI. Therefore, a new idea on IPSSI is proposed here to realize the OMM
This work was supported by the National Natural Science Foundation of China (Grant No.51005212 & No.61275110); the Public-Service Technology Research Plan of Zhejiang Province (No.2011C21003); the open fund of Key Laboratory of Space Laser Communication and Testing Technology from Chinese Academy of Sciences; China Postdoctoral Science Foundation (No.2011M500936 & No.2012T50274) and Foundation of State Key Laboratory of Automotive Simulation and Control (No.20111114).
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