Monte Carlo evaluation of periodic error uncertainty

Precision Engineering

Volumn 31, Issue 3, 2007, Pages 251-259

  Schmitz, Tony L ^a   Kim, Hyo Soo ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

Displacement; Interferometry; Nonlinearity; Uncertainty

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; INTERFEROMETERS; MONTE CARLO METHODS; NONLINEAR SYSTEMS; THERMAL EFFECTS;

ANALYTICAL DISPLACEMENT EQUATION; HETERODYNE INTERFEROMETER; PERIODIC ERROR EXPRESSION; WAVELENGTH STABILITY;

UNCERTAIN SYSTEMS;

EID: 34248403752     PISSN: 01416359     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.precisioneng.2006.10.001     Document Type: Article

References (39)

1. Fedotova G. Analysis of the measurement error of the parameters of mechanical vibrations. Measure Techn 23 7 (1980) 577-580
2. Quenelle R. Nonlinearity in interferometric measurements. Hewlett-Packard J 34 4 (1983) 10
3. Sutton C. Nonlinearity in length measurements using heterodyne laser Michelson interferometry. J Phys E: Sci Instrumen 20 (1987) 1290-1292
4. Barash V., and Fedotova G. Heterodyne interferometer to measure vibration parameters. Measure Techn 27 7 (1984) 50-51
5. Bobroff N. Residual errors in laser interferometry from air turbulence and nonlinearity. Appl Optics 26 13 (1987) 2676-2682
6. Rosenbluth A., and Bobroff N. Optical sources of nonlinearity in heterodyne interferometers. Precis Eng 12 1 (1990) 7-11
7. Stone J., and Howard L. A simple technique for observing periodic nonlinearities in Michelson interferometers. Precis Eng 22 4 (1998) 220-232
8. Patterson S., and Beckwith J. Reduction of systematic errors in heterodyne interferometric displacement measurement. Proceedings of the Eighth International Precision Engineering Seminar (IPES) (1995), Compiegne, France 101-104
9. Badami V., and Patterson S. A frequency domain method for the measurement of nonlinearity in heterodyne interferometry. Precis Eng 24 1 (2000) 41-49
10. Badami V., and Patterson S. Investigation of nonlinearity in high-accuracy heterodyne laser interferometry. Proceedings of the 12th Annual American Society for Precision Engineering (ASPE) Conference. Norfolk, VA (1997) 153-156
11. Wu C., and Deslattes R. Analytical modeling of the periodic nonlinearity in heterodyne interferometry. Appl Optics 37 28 (1998) 6696-6700
12. Wu C., and Su C. Nonlinearity in measurements of length by optical interferometry. Measure Sci Technol 7 (1996) 62-68
13. Hou W., and Wilkening G. Investigation and compensation of the nonlinearity of heterodyne interferometers. Precis Eng 14 2 (1992) 91-98
14. Hou W., and Zhao X. Drift of nonlinearity in the heterodyne interferometer. Precis Eng 16 1 (1994) 25-35
15. Howard L., and Stone J. Computer modeling of heterodyne interferometer errors. Precis Eng 12 1 (1995) 143-146
16. Tanaka M., Yamagami T., and Nakayama K. Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels. IEEE Trans Instrument Measure 38 2 (1989) 552-554
17. Bobroff N. Recent advances in displacement measuring interferometry. Measure Sci Technol 4 (1993) 907-926
18. Steinmetz C. Sub-micron position measurement and control on precision machine tools with laser interferometry. Precis Eng 12 1 (1990) 12-24
19. Cretin B., Xie W., Wang S., and Hauden D. Heterodyne interferometers: practical limitations and improvements. Optics Commun 65 3 (1988) 157-162
20. Petru F., and Cip O. Problems regarding linearity of data of a laser interferometer with a single-frequency laser. Precis Eng 23 1 (1999) 39-50
21. Augustyn W., and Davis P. An analysis of polarization mixing errors in distance measuring interferometers. J Vacuum Sci Technol B 8 6 (1990) 2032-2036
22. Xie Y., and Yu Y. Zeeman laser interferometer errors for high precision measurements. Appl Optics 31 7 (1992) 881-884
23. De Freitas J., and Player M. Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry. Measure Sci Technol 4 (1993) 1173-1176
24. De Freitas J., and Player M. Polarization effects in heterodyne interferometry. J Modern Optics 42 9 (1995) 1875-1899
25. De Freitas J. Analysis of laser source birefringence and dichroism on nonlinearity in heterodyne interferometry. Measure Sci Technol 8 (1997) 1356-1359
26. Li B., and Liang J. Effects of polarization mixing on the dual-wavelength heterodyne interferometer. Appl Optics 36 16 (1997) 3668-3672
27. Park B., Eom T., and Chung M. Polarization properties of cube-corner retroreflectors and their effects on signal strength and nonlinearity in heterodyne interferometers. Appl Optics 35 22 (1996) 4372-4380
28. Wu C., Lawall J., and Deslattes R. Heterodyne interferometer with subatomic periodic nonlinearity. Appl Optics 38 19 (1999) 4089-4094
29. Oldham N., Kramar J., Hetrick P., and Teague E. Electronic limitations in phase meters for heterodyne interferometry. Precis Eng 15 3 (1993) 173-179
30. Schmitz T., and Beckwith J. An investigation of two unexplored periodic error sources in differential-path interferometry. Precis Eng 27 3 (2002) 311-322
31. Chu D., and Ray A. Nonlinearity measurement and correction of metrology data from an interferometer system. Proceedings of Fourth Euspen International Conference (2004), Glasgow, Scotland (UK) 300-301
32. Donaldson R. Error budgets. In: Hocken R. (Ed). Technology of machine tools. Machine tool accuracy vol. 5 (1980), Machine Tool Task Force (UCRL-52960-5)
33. Slocum A. Precision machine design (1992), Prentice Hall, Englewood Cliffs, NJ
34. Schmitz T., Evans C., Davies A., and Estler W.T. Displacement uncertainty in interferometric radius measurements. Ann CIRP 51 1 (2002) 451-454
35. International Organization for Standardization (ISO). Guide to the Expression of Uncertainty in Measurement. Geneva 1995.
36. Taylor B, Kuyatt C. NIST Technical Note 1297 Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. Gaithersburg, MD 1994.
37. Cosijns S., Haitjema H., and Schellekens P. Modeling and verifying non-linearities in heterodyne displacement interferometry. Precis Eng 26 (2002) 448-455
38. Oldham N., Kramar J., Hetrick P., and Teague E. Electronic limitations in phase meters for heterodyne interferometry. Precis Eng 15 3 (1993) 173-179
39. Estler W.T. High-accuracy displacement interferometry in air. Appl Optics 24 (1985) 808-815