Error analysis of a plane mirror interferometer based on geometric optical paths

doi:10.1364/OE.20.005108

Error analysis of a plane mirror interferometer based on geometric optical paths

Shanzhi Tang, Zhao Wang, Lihong Zhong, Jianmin Gao, and Junjie Guo »View Author Affiliations

Optics Express, Vol. 20, Issue 5, pp. 5108-5118 (2012)
http://dx.doi.org/10.1364/OE.20.005108

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Abstract
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Abstract

Plane mirror interferometer is a common way for the precision displacement measurement. However, during the measurement, it still suffers from disturbances such as misalignments, rotations and air refractive index fluctuations, which lead to poor accuracy. Traditional error analysis is rather limited in the static state and separation of the disturbances. In this paper, displacement measurement errors are analyzed, which are caused by the disturbed factors for a plane mirror interferometer. Then error modeling, which based on the geometric optical paths, is carried out by the partial differentiation theory. Moreover, the characteristics of the error are discussed by using this model. It is suggested that this model can release the measurement accuracy reduction brought by coupling effects between adjustment factor of the optical paths and the rotary error of the measured object (e. g. a guideway).

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4640) Instrumentation, measurement, and metrology : Optical instruments

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 9, 2011
Revised Manuscript: December 31, 2011
Manuscript Accepted: January 2, 2012
Published: February 16, 2012

Citation
Shanzhi Tang, Zhao Wang, Lihong Zhong, Jianmin Gao, and Junjie Guo, "Error analysis of a plane mirror interferometer based on geometric optical paths," Opt. Express 20, 5108-5118 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5108

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References

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing (ISAM 2011), 1–6 (2011).
F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE4401, 227–233 (2001). [CrossRef]
W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng.30(1), 96–103 (2006). [CrossRef]
I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum.81(4), 045103 (2010). [CrossRef] [PubMed]
H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol.17(4), 746–752 (2006). [CrossRef]
Z. Zhang and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum.78(8), 083107 (2007). [CrossRef] [PubMed]
F. G. P. Peeters, “Interferometer with added flexibility in its use,” Opt. Eng.35(7), 1953–1956 (1996). [CrossRef]
N. Bobroff, “Critical alignments in plane mirror interferometry,” Proc. SPIE1673, 63–67 (1992). [CrossRef]
N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993). [CrossRef]
H. Zhang, T. Xu, W. Jing, D. Jia, F. Tang, K. Liu, and Y. Zhang, “Influence of angle misalignment on detection polarization coupling in white light interferometer,” Proc. SPIE6829(68290E), 1–9 (2007).
D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl. Opt.36(18), 4034–4042 (1997). [CrossRef] [PubMed]
S. Awtar and A. H. Slocum, “Target block alignment error in XY stage metrology,” Precis. Eng.31(3), 185–187 (2007). [CrossRef]
H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol.16(11), 2155–2166 (2005). [CrossRef]
K. R. Koops, M. G. A. van Veghel, G. J. W. L. Kotte, and M. C. Moolmen, “Calibration strategies for scanning probe metrology,” Meas. Sci. Technol.18(2), 390–394 (2007). [CrossRef]
J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol.15(12), 1879–1884 (2009). [CrossRef]
L. A. Kivioja, “The EDM corner reflector constant is not constant,” Surveying and Mapping6, 143–149 (1978).
J. Huang, H. Xian, W. Jiang, and X. Li, “The reflected beam’s phase aberration induced by the fabrication errors of corner cube retroreflector,” Acta Opt. Sin.29(7), 1951–1955 (2009). [CrossRef]

Arai, Y.
Awtar, S.
Bobroff, N.
Bosse, H.
Büchner, H. J.
Cohen, D. L.
Gao, W.
Goullioud, R.
Hahn, I.
Huang, J.
Jäger, G.
Jeanmonod, N.
Jia, D.
Jiang, W.
Jing, W.
Kivioja, L. A.
Kiyono, S.
Koops, K. R.
Kotte, G. J. W. L.
Lee, D. Y.
Lee, M. Y.
Li, X.
Liu, K.
Meil, F.
Menq, C. H.
Moolmen, M. C.
Park, C. H.
Park, J.
Peeters, F. G. P.
Shibuya, A.
Slocum, A. H.
Tang, F.
Thalmann, R.
Thiess, C.
van Veghel, M. G. A.
Wang, X.
Weilert, M.
Wilkening, G.
Xian, H.
Xu, T.
Zhang, H.
Zhang, Y.
Zhang, Z.

Acta Opt. Sin.

J. Huang, H. Xian, W. Jiang, and X. Li, “The reflected beam’s phase aberration induced by the fabrication errors of corner cube retroreflector,” Acta Opt. Sin.29(7), 1951–1955 (2009). [CrossRef]

Appl. Opt.

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl. Opt.36(18), 4034–4042 (1997). [CrossRef] [PubMed]

Meas. Sci. Technol.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993). [CrossRef]
H. Bosse and G. Wilkening, “Developments at PTB in nanometrology for support of the semiconductor industry,” Meas. Sci. Technol.16(11), 2155–2166 (2005). [CrossRef]
K. R. Koops, M. G. A. van Veghel, G. J. W. L. Kotte, and M. C. Moolmen, “Calibration strategies for scanning probe metrology,” Meas. Sci. Technol.18(2), 390–394 (2007). [CrossRef]
H. J. Büchner and G. Jäger, “A novel plane mirror interferometer without using corner cube reflectors,” Meas. Sci. Technol.17(4), 746–752 (2006). [CrossRef]

Microsyst. Technol.

J. Park, M. Y. Lee, and D. Y. Lee, “A nano-metrology system with a two-dimensional combined optical and X-ray interferometer and an atomic force microscope,” Microsyst. Technol.15(12), 1879–1884 (2009). [CrossRef]

Opt. Eng.

F. G. P. Peeters, “Interferometer with added flexibility in its use,” Opt. Eng.35(7), 1953–1956 (1996). [CrossRef]

Precis. Eng.

W. Gao, Y. Arai, A. Shibuya, S. Kiyono, and C. H. Park, “Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage,” Precis. Eng.30(1), 96–103 (2006). [CrossRef]
S. Awtar and A. H. Slocum, “Target block alignment error in XY stage metrology,” Precis. Eng.31(3), 185–187 (2007). [CrossRef]

Proc. SPIE

H. Zhang, T. Xu, W. Jing, D. Jia, F. Tang, K. Liu, and Y. Zhang, “Influence of angle misalignment on detection polarization coupling in white light interferometer,” Proc. SPIE6829(68290E), 1–9 (2007).
F. Meil, N. Jeanmonod, C. Thiess, and R. Thalmann, “Calibration of a 2D reference mirror system of a photomask measuring instrument,” Proc. SPIE4401, 227–233 (2001). [CrossRef]
N. Bobroff, “Critical alignments in plane mirror interferometry,” Proc. SPIE1673, 63–67 (1992). [CrossRef]

Rev. Sci. Instrum.

Z. Zhang and C. H. Menq, “Laser interferometric system for six-axis motion measurement,” Rev. Sci. Instrum.78(8), 083107 (2007). [CrossRef] [PubMed]
I. Hahn, M. Weilert, X. Wang, and R. Goullioud, “A heterodyne interferometer for angle metrology,” Rev. Sci. Instrum.81(4), 045103 (2010). [CrossRef] [PubMed]

Surveying and Mapping

L. A. Kivioja, “The EDM corner reflector constant is not constant,” Surveying and Mapping6, 143–149 (1978).

Other

S. Tang, Z. Wang, Z. Jiang, J. Gao, and J. Guo, “A new measuring method for circular motion accuracy of NC machine tools based on dual-frequency laser interferometer,” in Proceedings of IEEE International Symposium on Assembly and Manufacturing (ISAM 2011), 1–6 (2011).

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