Investigation of Error Separation for Three Dimensional Profile Rotary Measuring System

Bo Chen

Professor Min Xu, Doctor Xiangchao Zhang

Department of Optical Science and engineering, Fudan University

Abstract. High precision 3D profile rotary measuring systems for large diameter workpieces are urgently needed in precision engineering. Error separation is critical for improving the system accuracy. In order to obtain higher precision for 3D profile rotary measuring systems, the variable and systematic errors are analyzed and separated in this report. In the measuring system, roll and pitch caused by the probe tilt violate the Abbe principle and are removed in the same manner. The radial run-out and the perpendicular error between the probe and the spindle axis are compensated by a two-probe-two-step method carried out on a standard hemisphere artifact. When implementing the error separation, the form error of the artifact mixes with the perpendicular error, and the least-squares method is applied to fit the hemisphere and work out the perpendicular error and the profile error of the hemisphere. Finally, numerical validation is presented by Matlab program to confirm the effectiveness and correctness of the proposed method.

References:

[1] S. Osawa, K. Busch, M. Franke, and H. Schwenke, Precis. Eng. 29, 56 (2005).

[2] M.M.P.A. Vermeulen, P.C.J.N. Rosielle, and P.H.J. Schellekens, CIRP Ann.-Manuf. Techn. 47, 447(1998).

[3] G. Jäger, T. Hausotte, E. Manske, H.J. Büchner, R. Mastylo, N. Dorozhovets, and N. Hofmann, Measurement, 43, 1099 (2010).

[4] J.G. Salsbury, Precis. Eng. 27, 189 (2003).

[5] O. Horikawa, N. Maruyama, and M. Shimada, Precis. Eng. 25, 200 (2001).

[6] T. Sun, Meas. Sci. Technol. 7, 1563 (1996).

[7] M. Neugebauer, Meas. Sci. Technol. 12, 68 (2001).

[8] D.G. Chetwynd and G.J. Siddall, J. Phys. E: Sci. Instrum. 9, 537 (1976).

[9] L.X. Cao, J. Phys. E: Sci. Instrum. 22, 903 (1989)

[10]B. Muralikrishnan, S. Venkatachalam, J. Raja, and M. Malburg, Precis. Eng. 29, 257 (2005).

[11] X.Q. Lei, J.S Li, Y. Li, Y.W. Zhou, Y.J. Xue, and X.Z. Ren, Proc. 2006 IEEE Int. Conf. Mechatronics and Automation, 2006, p. 89.

[12] C.K. Chen and S.C. Wu, Meas. Sci. Technol. 10, 76 (1999).

[13] W.Q. Zhao, Z. Xue, J.B. Tan, and Z.B. Wang, Int. J. Mach. Tool Manu. 46, 1869 (2006).

[14] C. J. Evans, R. J. Hocken, and W. T. Estler, CIRP Ann.-Manuf. Techn. 45, 617 (1996).

[15] J.F. Tu, B. Bossmanns, and S.C.C. Hung, Precis. Eng. 21, 90 (1997).

[16] W. Gao, S. Kiyono, and T. Sugawara, Precis. Eng. 21, 123 (1997).

[17] W. Gao, J. Yokoyama, H. Kojima, and S. Kiyono, Precis. Eng. 26, 279 (2002).

[18] A.C. Okafor and Y.M. Ertekin, Int. J. Mach. Tool Manu. 40, 1199 (2000).

[19] M. Jung, K.J. Cross, J.W. McBride, and M. Hill, Precis. Eng. 24, 127 (2000).

[20] Å. Björck, Numerical Methods for Least Squares Problems, (PA: SIAM, Philadelphia, 1996).

[21] J. Pujol, Geophysics. 72, W1-W16 (2007).

[22] L.N. de Castro, Fundamentals of Natural Computing---Basic Concepts, Algorithms, and Applications, (Chapman & Hall/CRC, Boca Raton, 2006).

[23] K. Falconer, Fractal geometry---mathematical foundations and Applications, (John Wiley& Sons, Chichester, 1990).

The electronic and optical properties of silicon nanocrystals embedded

 in SiO₂: Density functional theory calculations

           Guoqing Yue

Supervisor: Songyou Wang

Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China

Abstract::Silicon nanocrystals have been studied intensely for over a decade for their potential application in silicon photonics , especially as efficient room temperature light emitters. Given that the Si light emitters, especially, lasers, are not commercially available, research in the field of Si photonics is to find a low-loss active medium that can be used for achieving optical gain and waveguiding in order to pave the way for fabricating a silicon laser in the wavelength of interest. However, bulk crystalline silicon is a poor light emitter at room temperature, mainly due to its indirect band gap structure. During the 1990s, many different strategies were employed to overcome the problem. Silicon nanocrystals are considered to be the preferable strategy for improving the light emission properties of silicon. Embedding silicon nanocrystals in a silica matrix is considered as a very promising candidate for such an active medium.

In this work , we present first-principles calculations of the structural, electronic, and optical properties of silicon nanocrystals of different atom number (respectively ten, seventeen, thirty and thirty-five atoms) embedded in a SiO₂ matrix. The band gap of those materials is 1.84eV, 2.65eV, 1.47eV, 1.1eV in turn with the increase of atom number of silicon nanocrystals. The analysis of the band gap region is obtained by calculating the contribution of atoms respectively located in the core, interface and matrix on the electronic density. The projected density of state for silicon nanocrystals of seventeen atoms is shown. we can see that the valence band top and the bottom of conduction band is entirely dominated by the density of state of the core atom of silicon nanocrystals and the atoms of the interface together. The effects generated by the surrounding matrix on the optical properties of the nanocrystals also are studies. A strong dependence of optical properties on the size of silicon nanocrystals is observed, but do not strictly obey quantum confinement effect.

Reference:

[1] L. Ding, T. P. Chen, Y. Liu, M. Yang, and J. I. Wong, J. Appl. Phys. 101,103525(2007)

[2] K senio, F Bechstedt, and P Kroll, Nanotechnology 20,135702(2009) 

[3] R. Guerra, I. Marri, R. Magri, and L. M. Samos, Phys. Rev. B 79, 155320(2009)

[4] R. Guerra, E. Degoli, and S. Ossicini, Phys. Rev. B 80, 155332(2009)

[5] P. Loper, R.Muller, D.Hiller, T. Barthel, E.Malguth, S. Janz, J. C. Goldschmidt, M. Hermle, and M. Zacharias, Phys. Rev. B 84, 195317(2011)

Polishing Large-Aperture Mirror Using Ultra-Precise Bonnet

Wei Wang

Department of Optical Science and engineering, Fudan University

ABSTRACT: As the development of modern optical technology, especially space optical science, more high precision mirrors with large apertures are needed. But it is difficult to manufacture high precision large aperture optical components. The method of optical polishing using an ultra-precise bonnet is based upon the technology of computer controlled optical surfacing. A bonnet filled with air is applied as a precise polishing tool which is flexible and able to adapt itself well to the shape of the part, which is superior to other polishing methods. A material removing model of bonnet precessed polishing is established according to kinematic principle based on the Preston equation. The model is modified in terms of Hertz contact theory using the physical characteristics of polishing bonnet tools. A satisfactory result was obtained for one of the surfaces of a wedge mirror with a diameter of 570mm. The resulted PV and RMS parameters are 1/8 λ and 1/75 λ respectively.

REFERENCES

[1]R. G. Bingham, D. D. Walker, D-H. Kim, et al. A novel automated process for aspheric surfaces[C]. Proc. SPIE, 2000, 4093: 445-450.

[2]D. D. Walker, A. Beaucamp, D. Brooks, et al. Novel CNC Polishing Process for Control of Form and Texture on Aspheric Surfaces[C]. Proc. SPIE, 2002, 4767: 99-106

[3]D. D. Walker, A. Beaucamp, D. Brooks, etc. New Results from the Precessions Polishing Process Scaled to Larger Sizes[C]. Proc. SPIE, 2004, 5494: 71-81

[4]D. D. Walker, A. Beaucamp, V. Doubrovski, etc. Automated Optical Fabrication-First results From the New Precessions 1.2m CNC polishing machine[C]. Proc. SPIE, 2006, 6273: 91-98

[5]Quantang Fan，Jiangqiang Zhu，Bao’an Zhang. Effect of the geometry of workpiece on polishing velocity in free annular polishing [J]. Chin. Opt. Lett. , 2007，5(5): 298～300

[6]K. L. Johnson. Contact Mechanics[M]. Beijing: Higher Education Pres. 1992: 72～77

[7] Li Hongyu, Zhang Wei, Yu Guoyu, ACTA OPTICA SINICA, Vol 29, No.3 March, 2009, P811-817.