A new laser differential confocal radius measurement (DCRM) is proposed for high precision measurement of radius. Based on the property of an axial intensity curve that the absolute zero precisely corresponds to the focus of the objective in a differential confocal system (DCS), DCRM uses the zero point of the DCS axial intensity curve to precisely identify the cat's-eye and confocal positions of the test lens, and measures the accurate distance between the two positions to achieve the high-precision measurement of radius of curvature (ROC). In comparison with the existing measurement methods, DCRM proposed has a high measurement precision, a strong environmental anti-interference capability and a low cost. The theoretical analyses and preliminary experimental results indicate that DCRM has a relative measurement error of better than 5ppm.

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1. P. Becker, H. Friedrich, and K. Fujii, “W. Giardini, G Mana, A Picard, H-J Pohl, H. Riemann and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 1–20 (2009).
2. D. Malacara, “Optical Shop Testing, 2nd edition,” (Wiley-Interscience, 1992), Chap17.
3. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992). [CrossRef]
4. Y. Xiang, “Focus retrocollimated interferometry for long-radius-of-curvature measurement,” Appl. Opt. 40(34), 6210–6214 (2001). [CrossRef]
5. Y. Pi and P. J. Reardon, “Determining parent radius and conic of an off-axis segment interferometrically with a spherical reference wave,” Opt. Lett. 32(9), 1063–1065 (2007). [CrossRef] [PubMed]
6. U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of sphere with interferometry,” Ann. CIRP 53(1), 451–454 (2004). [CrossRef]
7. Q. Hao, Q. Zhu, and Y. Hu, “Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts,” Opt. Lett. 34(8), 1288–1290 (2009). [CrossRef] [PubMed]
8. T. L. Schmitz, C. J. Evans, A. D. Davies and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technology, 51, 451–454 (2002).
9. T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius-of-curvature,” Proc. SPIE 4451, 432–447 (2001). [CrossRef]
10. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12(21), 5013–5021 (2004). [CrossRef] [PubMed]
11. W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005). [CrossRef]
12. L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).
13. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 9.
14. A. Davies and T. L. Schmitz, “Correcting for stage error motions in radius measurements,” Appl. Opt. 44(28), 5884–5893 (2005). [CrossRef] [PubMed]
15. T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47(36), 6692–6700 (2008). [CrossRef] [PubMed]

Acta Phys. Sin.

• L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

Ann. CIRP

• U. Griesmann, J. Soons, Q. Wang, and D. DeBra, “Measuring form and radius of sphere with interferometry,” Ann. CIRP 53(1), 451–454 (2004). [CrossRef]

Appl. Opt.

• Y. Xiang, “Focus retrocollimated interferometry for long-radius-of-curvature measurement,” Appl. Opt. 40(34), 6210–6214 (2001). [CrossRef]
• A. Davies and T. L. Schmitz, “Correcting for stage error motions in radius measurements,” Appl. Opt. 44(28), 5884–5893 (2005). [CrossRef] [PubMed]
• T. L. Schmitz, N. Gardner, M. Vaughn, K. Medicus, and A. Davies, “Improving optical bench radius measurements using stage error motion data,” Appl. Opt. 47(36), 6692–6700 (2008). [CrossRef] [PubMed]

Meas. Sci. Technol.

• P. Becker, H. Friedrich, and K. Fujii, “W. Giardini, G Mana, A Picard, H-J Pohl, H. Riemann and S. Valkiers, “The Avogadro constant determination via enriched silicon-28,” Meas. Sci. Technol. 20, 1–20 (2009).

Opt. Eng.

• L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992). [CrossRef]

Opt. Express

• W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12(21), 5013–5021 (2004). [CrossRef] [PubMed]

Opt. Lett.

• Q. Hao, Q. Zhu, and Y. Hu, “Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts,” Opt. Lett. 34(8), 1288–1290 (2009). [CrossRef] [PubMed]
• Y. Pi and P. J. Reardon, “Determining parent radius and conic of an off-axis segment interferometrically with a spherical reference wave,” Opt. Lett. 32(9), 1063–1065 (2007). [CrossRef] [PubMed]

Proc. SPIE

• T. L. Schmitz, A. D. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius-of-curvature,” Proc. SPIE 4451, 432–447 (2001). [CrossRef]

Sens. Actuators A Phys.

• W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005). [CrossRef]

Other

• M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 9.
• T. L. Schmitz, C. J. Evans, A. D. Davies and W. T. Estler, “Displacement Uncertainty in Interferometric Radius Measurements,” CIRP Annals - Manufacturing Technology, 51, 451–454 (2002).
• D. Malacara, “Optical Shop Testing, 2nd edition,” (Wiley-Interscience, 1992), Chap17.

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