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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 13 — May. 1, 2012
  • pp: 2379–2387

Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses

Long Li, Cuifang Kuang, Ding Luo, and Xu Liu  »View Author Affiliations

Applied Optics, Vol. 51, Issue 13, pp. 2379-2387 (2012)

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Spot distortion caused by astigmatism effect in orthogonal cylindrical lenses is utilized to measure axial displacement with 30 nm resolution, strong noise immunity, and compact experiment setup. Axial displacement of the sample surface is determined by four-quadrant difference processing of distorted laser spots’ energy distribution images received by CCD. Four-quadrant difference processing results indicate an applicable measuring range of 5.6 μm (cubic fitting r=0.9988) with a highly linear range of 1.2 μm (linear fitting r=0.9996). Factors affecting measuring range and sensitivity are analyzed by theoretical deduction and numerical simulation. This technique has potential applications in drifting sample tracking and measurement in advanced microscopy.

© 2012 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(220.4830) Optical design and fabrication : Systems design

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: January 5, 2012
Manuscript Accepted: February 20, 2012
Published: April 26, 2012

Long Li, Cuifang Kuang, Ding Luo, and Xu Liu, "Axial nanodisplacement measurement based on astigmatism effect of crossed cylindrical lenses," Appl. Opt. 51, 2379-2387 (2012)

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  1. Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).
  2. X. Li, “Displacement measurement based on the Moire fringe,” Proc. SPIE 8321, 832148 (2011). [CrossRef]
  3. S. L. Yeh, S. T. Lin, and Y. H. Chang, “Precise displacement measurement for a local surface,” Opt. Lett. 34, 3406–3408 (2009). [CrossRef]
  4. I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).
  5. K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012). [CrossRef]
  6. K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011). [CrossRef]
  7. P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001). [CrossRef]
  8. K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).
  9. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993). [CrossRef]
  10. W.-S. Sun, K.-D. Liu, J.-W. Pan, C.-L. Tien, and M.-S. Hsieh, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express 17, 2235–2246 (2009). [CrossRef]
  11. H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).
  12. C.-H. Liu and Z.-H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47, 3968–3972 (2008). [CrossRef]
  13. H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011). [CrossRef]
  14. K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001). [CrossRef]
  15. A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995). [CrossRef]
  16. L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, “Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device,” Opt. Express 13, 9003–9013(2005). [CrossRef]
  17. L. S. Pedrotti and F. L. Pedrotti, Optics and Vision (Prentice Hall, 1998).
  18. J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969). [CrossRef]
  19. A. E. Attard, “Matrix optical analysis of skew rays in mixed systems of spherical and orthogonal cylindrical lenses,” Appl. Opt. 23, 2706–2709 (1984). [CrossRef]
  20. L. Te-Tan, “A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces,” Optik 119, 713–722 (2008). [CrossRef]
  21. K. Chen, H. Yang, L. Sun, and G. Jin, “Generalized method for calculating astigmatism of the unit-magnification multipass system,” Appl. Opt. 49, 1964–1971 (2010). [CrossRef]
  22. G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994). [CrossRef]
  23. ASAP Reference Manual Version 7.5.0 (Breault Research Organization, 2003).
  24. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986). [CrossRef]
  25. M. R. Beversluis, G. W. Bryant, and S. J. Stranick, “Effects of inhomogeneous fields in superresolving structured-illumination microscopy,” J. Opt. Soc. Am. A 25, 1371–1377 (2008). [CrossRef]

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