Abstract

A new surface probing technique using the circular motion of an optically-trapped microsphere is proposed for a nanocoordinate measuring system. The probe sphere is oscillated circularly in the plane perpendicular to the probe axis and the circular orbit of the probe sphere is monitored for the detection of the position and normal vector direction of the surface. The principle of detection is based on changes in the circular orbit of the microsphere. When the probe approaches a work surface, the orbit of the probe sphere becomes elliptical. The minor-axis length and the minor-axis angle of the ellipse are then used as parameters to detect the position and normal vector direction of the surface, respectively. In this study, the circular motion probe is shown to have a resolution of position detection of 39nm, and the accuracy of measuring a normal vector to the surface is on the order of 3°.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
    [CrossRef]
  2. T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
    [CrossRef]
  3. R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
    [CrossRef]
  4. U. Brand and J. Kirchhoff, “A micro-CMM with metrology frame for low uncertainty measurements,” Meas. Sci. Technol. 16, 2489-2497 (2005).
    [CrossRef]
  5. M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
    [CrossRef]
  6. A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
    [CrossRef]
  7. M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
    [CrossRef]
  8. S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” CIRP Annals 50, 357-360 (2001).
    [CrossRef]
  9. M. Gruhlke and H. Rothe, “Combining coordinate measurement and nanometrology for large-range nanoscale metrology,” Proc. SPIE 6648, 66480I (2007).
    [CrossRef]
  10. S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
    [CrossRef]
  11. H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.
  12. Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
    [CrossRef]
  13. A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
    [CrossRef]
  14. A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
    [CrossRef]
  15. IBS Precision Engineering: http://www.ibspe.com/.
  16. G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
    [CrossRef]
  17. H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
    [CrossRef]
  18. H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
    [CrossRef]
  19. F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.
  20. K. Hidaka, “Study of a small-sized ultrasonic probe,” CIRP Annals 55, 567-570 (2006).
    [CrossRef]
  21. ISO 10360-1 (2000).
  22. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  23. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. 94, 4853-4860 (1997).
    [CrossRef] [PubMed]
  24. R. C. Gauthier, R. N. Tait, H. Mende, and C. Pawlowicz, “Optical selection, manipulation, trapping, and activation of a microgear structure for applications in micro-optical-electromechanical systems,” Appl. Opt. 40, 930-937 (2001).
    [CrossRef]
  25. M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863-865 (2001).
    [CrossRef]
  26. E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
    [CrossRef] [PubMed]
  27. L. P. Ghislain and W. W. Webb, “Scanning-force microscope based on an optical trap,” Opt. Lett. 18, 1678-1680 (1993).
    [CrossRef] [PubMed]
  28. M. E. J. Friese, A. G. Truscott, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Three-dimensional imaging with optical tweezers,” Appl. Opt. 38, 6597-6603 (1999).
    [CrossRef]
  29. M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
    [CrossRef]
  30. Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
    [CrossRef]
  31. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  32. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]
  33. W. H. Wright, G. J. Sonek, and M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735-1748 (1994).
    [CrossRef] [PubMed]
  34. Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
    [CrossRef]
  35. Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).
  36. M. E. J. Friese, A. G. Truscott, H. R. Dunlop, and N. R. Heckenberg, “Determination of the force constant of a single-beam gradient trap by measurement of backscattered light,” Appl. Opt. 35, 7112-7116 (1996).
    [CrossRef] [PubMed]
  37. Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
    [CrossRef]
  38. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
    [CrossRef]
  39. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer, 1983).
  40. R. Omori, T. Kobayashi, and A. Suzuki, “Observation of a single-beam gradient-force optical trap for dielectric particles in air, ” Opt. Lett. 22, 816-818 (1997).
    [CrossRef] [PubMed]

2008 (1)

M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
[CrossRef]

2007 (2)

M. Gruhlke and H. Rothe, “Combining coordinate measurement and nanometrology for large-range nanoscale metrology,” Proc. SPIE 6648, 66480I (2007).
[CrossRef]

A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
[CrossRef]

2006 (3)

A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
[CrossRef]

K. Hidaka, “Study of a small-sized ultrasonic probe,” CIRP Annals 55, 567-570 (2006).
[CrossRef]

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

2005 (3)

U. Brand and J. Kirchhoff, “A micro-CMM with metrology frame for low uncertainty measurements,” Meas. Sci. Technol. 16, 2489-2497 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

2004 (2)

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

2003 (1)

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

2002 (1)

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

2001 (7)

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” CIRP Annals 50, 357-360 (2001).
[CrossRef]

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
[CrossRef]

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

R. C. Gauthier, R. N. Tait, H. Mende, and C. Pawlowicz, “Optical selection, manipulation, trapping, and activation of a microgear structure for applications in micro-optical-electromechanical systems,” Appl. Opt. 40, 930-937 (2001).
[CrossRef]

M. P. MacDonald, L. Paterson, W. Sibbett, K. Dholakia, and P. E. Bryant, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26, 863-865 (2001).
[CrossRef]

2000 (1)

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

1999 (4)

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

M. E. J. Friese, A. G. Truscott, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Three-dimensional imaging with optical tweezers,” Appl. Opt. 38, 6597-6603 (1999).
[CrossRef]

G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
[CrossRef]

Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
[CrossRef]

1998 (1)

M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
[CrossRef]

1997 (3)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. 94, 4853-4860 (1997).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

R. Omori, T. Kobayashi, and A. Suzuki, “Observation of a single-beam gradient-force optical trap for dielectric particles in air, ” Opt. Lett. 22, 816-818 (1997).
[CrossRef] [PubMed]

1996 (1)

1994 (1)

1993 (1)

1992 (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1986 (1)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. 94, 4853-4860 (1997).
[CrossRef] [PubMed]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Berg-Sørensen, K.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

Berns, M. W.

Bieri, M.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Bjorkholm, J. E.

Bottinelli, S.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Brand, U.

U. Brand and J. Kirchhoff, “A micro-CMM with metrology frame for low uncertainty measurements,” Meas. Sci. Technol. 16, 2489-2497 (2005).
[CrossRef]

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Breguet, J. M.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Brenner, H.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer, 1983).

Brocher, B.

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

Bryant, P. E.

Butefischa, S.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Buttgenbach, S.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Cao, S.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Carneiro, K.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

Chu, S.

Clavel, R.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

De Chiffre, L.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

Dejima, S.

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

Dholakia, K.

Ding, Z.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Dunlop, H. R.

Dussler, G.

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

Dziedzic, J. M.

Estler, T.

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

Feifer, T. P.

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

Florin, E. L.

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

Fracheboud, M.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Freudenberg, R.

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

Friese, M. E. J.

Gauthier, R. C.

Ghislain, L. P.

Gruhlke, M.

M. Gruhlke and H. Rothe, “Combining coordinate measurement and nanometrology for large-range nanoscale metrology,” Proc. SPIE 6648, 66480I (2007).
[CrossRef]

Haitjema, H.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
[CrossRef]

Hansen, H. N.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

Happel, J.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer, 1983).

Hartig, F.

H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.

Hayashi, T.

M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
[CrossRef]

Haycocks, J.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Heckenberg, N. R.

Hidaka, K.

K. Hidaka, “Study of a small-sized ultrasonic probe,” CIRP Annals 55, 567-570 (2006).
[CrossRef]

Hoffmann, J.

A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
[CrossRef]

Hoffmann, W.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Hörber, J. K. H.

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Imai, K.

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

Jackson, K.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Jakl, P.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

JeZek, J.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

Jonas, A.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

Kim, S. W.

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” CIRP Annals 50, 357-360 (2001).
[CrossRef]

Kirchhoff, J.

U. Brand and J. Kirchhoff, “A micro-CMM with metrology frame for low uncertainty measurements,” Meas. Sci. Technol. 16, 2489-2497 (2005).
[CrossRef]

Kleine-Besten, T.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Kobayashi, T.

Kung, A.

A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
[CrossRef]

Kunzmann, H.

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

Lai, G.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Leach, R.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Lewis, A.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Lewis, A. J.

G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
[CrossRef]

Liska, M.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

MacDonald, M. P.

McMurtry, D.

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

Meli, F.

A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
[CrossRef]

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Mende, H.

Michihata, M.

M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
[CrossRef]

Miyoshi, T.

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
[CrossRef]

Oldfield, S.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
[CrossRef]

Omori, R.

Paterson, L.

Pawlowicz, C.

Peggs, G.

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

Peggs, G. N.

A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
[CrossRef]

G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
[CrossRef]

Pralle, A.

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Pri, W. O.

H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
[CrossRef]

Rosielle, P. C. J. N.

M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
[CrossRef]

Rothe, H.

M. Gruhlke and H. Rothe, “Combining coordinate measurement and nanometrology for large-range nanoscale metrology,” Proc. SPIE 6648, 66480I (2007).
[CrossRef]

Rubinsztein-Dunlop, H.

Sakakibara, T.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Schellekens, P. H. J.

H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
[CrossRef]

M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
[CrossRef]

Schwenke, H.

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.

Seryab, M.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

Shimizu, H.

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

Shinohara, S.

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

Sibbett, W.

Sonek, G. J.

Stelzer, E. H. K.

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Suzuki, A.

Tait, R. N.

Takahashi, S.

Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
[CrossRef]

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

Takaya, Y.

M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
[CrossRef]

Thalmann, R.

A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
[CrossRef]

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

Truscott, A. G.

Vermeulen, M. M. P. A.

M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
[CrossRef]

Waldele, F.

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.

Webb, W. W.

Weckenmann, A.

A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
[CrossRef]

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

Weiskirch, C.

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

Wendt, K.

H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.

Wright, W. H.

Yacoot, A.

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Zemtnek, P.

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

Appl. Opt. (4)

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

CIRP Annals (11)

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Nano-position sensing using optically motion-controlled microprobe with PSD based on the laser trapping technique,” CIRP Annals 54, 467-470 (2005).
[CrossRef]

K. Hidaka, “Study of a small-sized ultrasonic probe,” CIRP Annals 55, 567-570 (2006).
[CrossRef]

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, “Dimensional micro- and nano-metrology,” CIRP Annals 55, 721-743 (2006).
[CrossRef]

M. M. P. A. Vermeulen, P. C. J. N. Rosielle, P. H. J. Schellekens, “Design of a high-precision 3D-coordinate measuring machine,” CIRP Annals 47, 447-450 (1998).
[CrossRef]

M. Michihata, Y. Takaya, and T. Hayashi, “Development of the nano-probe system based on the laser trapping technique,” CIRP Annals 57, 493-496 (2008).
[CrossRef]

S. W. Kim, “New design of precision CMM based upon volumetric phase-measuring interferometry,” CIRP Annals 50, 357-360 (2001).
[CrossRef]

Y. Takaya, S. Takahashi, and T. Miyoshi, “Development of the nano-CMM probe based on laser trapping technology,” CIRP Annals 48, 421-424 (1999).
[CrossRef]

A. Weckenmann, T. Estler, G. Peggs, and D. McMurtry, “Probing systems in dimensional metrology,” CIRP Annals 53, 657-684 (2004).
[CrossRef]

G. N. Peggs, A. J. Lewis, and S. Oldfield, “Design for a compact high-accuracy CMM,” CIRP Annals 48, 417-420 (1999).
[CrossRef]

H. Haitjema, W. O. Pri, and P. H. J. Schellekens, “Development of a silicon-based nanoprobe system for 3-D measurements,” CIRP Annals 50, 365-368 (2001).
[CrossRef]

H. Schwenke, F. Waldele, C. Weiskirch, and H. Kunzmann, “Opto-tactile sensor for 2D and 3D measurement of small structures on coordinate measuring machines,” CIRP Annals 50, 361-364 (2001).
[CrossRef]

J. Appl. Phys. (1)

Z. Ding, G. Lai, T. Sakakibara, and S. Shinohara, “Determination of the spring constant of an optical trap by external sinusoidal excitation and lock-in detection,” J. Appl. Phys. 88, 737-741 (2000).
[CrossRef]

J. Struct. Biol. (1)

E. L. Florin, A. Pralle, J. K. H. Hörber, and E. H. K. Stelzer, “Photonic force microscope based on optical tweezers and two-photon excitation for biological applications,” J. Struct. Biol. 119, 202-211 (1997).
[CrossRef] [PubMed]

Meas. Sci. Technol. (3)

U. Brand and J. Kirchhoff, “A micro-CMM with metrology frame for low uncertainty measurements,” Meas. Sci. Technol. 16, 2489-2497 (2005).
[CrossRef]

A. Weckenmann, G. N. Peggs, and J. Hoffmann, “Probing systems for dimensional micro- and nano-metrology,” Meas. Sci. Technol. 17, 504-509 (2006).
[CrossRef]

A. Kung, F. Meli, and R. Thalmann, “Ultraprecision micro-CMM using a low force 3D touch probe,” Meas. Sci. Technol. 18, 319-327 (2007).
[CrossRef]

Measurement (2)

T. P. Feifer, R. Freudenberg, G. Dussler, and B. Brocher, “Quality control and process observation for the micro assembly process,” Measurement 30, 1 (2001).
[CrossRef]

Y. Takaya, H. Shimizu, S. Takahashi, and T. Miyoshi, “Fundamental study on the new probe technique for the nano-CMM based on laser trapping and a mirau interferometer,” Measurement 25, 9-18 (1999).
[CrossRef]

Microsystem Technologies (1)

S. Cao, U. Brand, T. Kleine-Besten, W. Hoffmann, H. Schwenke, S. Butefischa, and S. Buttgenbach, “Recent developments in dimensional metrology for microsystem components,” Microsystem Technologies 8, 3-6 (2002).
[CrossRef]

Nanotechnology (1)

R. Leach, J. Haycocks, K. Jackson, A. Lewis, S. Oldfield, and A. Yacoot, “Advances in traceable nanometrology at the National Physical Laboratory,” Nanotechnology 12, R1-R6 (2001).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Proc. Natl. Acad. Sci. (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Proc. Natl. Acad. Sci. 94, 4853-4860 (1997).
[CrossRef] [PubMed]

Proc. SPIE (3)

M. Seryab, P. Jakl, J. JeZek, A. Jonas, P. Zemtnek, and M. Liska, “The use of an optically trapped microprobe for scanning details of surface,” Proc. SPIE 5259, 166-169 (2003).
[CrossRef]

Y. Takaya, K. Imai, S. Dejima, and T. Miyoshi, “Dynamic properties measurement of vibrating microprobe for nano-position sensing using radiation pressure control,” Proc. SPIE 5930, 223-230 (2005).

M. Gruhlke and H. Rothe, “Combining coordinate measurement and nanometrology for large-range nanoscale metrology,” Proc. SPIE 6648, 66480I (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594-612(2004).
[CrossRef]

Other (5)

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer, 1983).

H. Schwenke, F. Hartig, K. Wendt, and F. Waldele, “Future challenges in coordinate metrology: addressing metrological problems for very small and very large parts,” presented at the International Display Workshop, Knoxville, Tennessee, 7-10 May 2001.

IBS Precision Engineering: http://www.ibspe.com/.

F. Meli, M. Fracheboud, S. Bottinelli, M. Bieri, R. Thalmann, J. M. Breguet, and R. Clavel, “High precision, low force 3D touch probe for measurements on small objects,” in EUSPEN International Topical Conference on Precision Engineering, Micro Technology, Measurement Techniques and Equipment 2003. Proceedings. Vol. 2, M. Weck, ed. (Voerde, 2003), pp. 411-414.

ISO 10360-1 (2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Proposed microprobe: (a) typical probe [15]; (b) probe controlled by optical radiation pressure.

Fig. 2
Fig. 2

Concept of the circular motion probe.

Fig. 3
Fig. 3

Theoretical viscosities impinging on the probe near a wall.

Fig. 4
Fig. 4

Theoretically estimated oscillation amplitude of the probe near a wall.

Fig. 5
Fig. 5

Schematic of the experimental setup.

Fig. 6
Fig. 6

Detected probe signals: (a) oscillating signals along the X and Y axis; (b) orbit of the probe sphere motion.

Fig. 7
Fig. 7

Viscosities impinging on the probe near a wall.

Fig. 8
Fig. 8

Oscillation amplitude of the probe near a wall.

Fig. 9
Fig. 9

Orbits of the probe motion near a wall.

Fig. 10
Fig. 10

Minor-axis length on the elliptical orbit of the probe.

Fig. 11
Fig. 11

CCD image of the approach experiment.

Fig. 12
Fig. 12

Minor-axis angles on the elliptical orbit of the probe. The legend means a inclined angle of the work.

Tables (1)

Tables Icon

Table 1 Experimental Results of Measuring Normal Vector Angle of the Inclined Surface.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

θ = 1 2 tan 1 2 A x A y cos ϕ A x 2 A y 2 .
[ x y ] = R θ [ x y ] , R θ = [ cos θ sin θ sin θ cos θ ] .
m x ¨ + D x ˙ + k ( x A sin 2 π f t ) = F ( t ) ,
x = X exp [ ( i ( 2 π f t ϕ ) ] .
X = f n 2 ( f n 2 f 2 ) 2 + ( D 2 π m f ) 2 A ,
m x ¨ + D x x ˙ + k x ( x A sin 2 π f t ) = F x ( t ) ,
m y ¨ + D y y ˙ + k y ( y A cos 2 π f t ) = F y ( t ) ,
D = 6 π η r ,
D = 6 π r H ,
H = η 1 9 16 ( r h ) + 1 8 ( r h ) 3 45 256 ( r h ) 4 1 16 ( r h ) 5 ,
D = 6 π r H ,
H = 4 3 η sinh α n = 1 n ( n + 1 ) ( 2 n 1 ) ( 2 n + 3 ) × [ 2 sinh ( 2 n 1 ) α + ( 2 n 1 ) sinh 2 α 4 sinh 2 ( n + 1 / 2 ) α ( 2 n + 1 ) 2 sinh 2 α 1 ] ,
α = cosh 1 ( h r ) = ln { h r + [ ( h r ) 2 1 ] 1 / 2 } ,

Metrics