OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 7 — Aug. 1, 2013

Coherence scanning interferometry: linear theory of surface measurement

Jeremy Coupland, Rahul Mandal, Kanik Palodhi, and Richard Leach  »View Author Affiliations


Applied Optics, Vol. 52, Issue 16, pp. 3662-3670 (2013)
http://dx.doi.org/10.1364/AO.52.003662


View Full Text Article

Enhanced HTML    Acrobat PDF (349 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The characterization of imaging methods as three-dimensional (3D) linear filtering operations provides a useful way to compare the 3D performance of optical surface topography measuring instruments, such as coherence scanning interferometry, confocal and structured light microscopy. In this way, the imaging system is defined in terms of the point spread function in the space domain or equivalently by the transfer function in the spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable to weakly scattering objects; however, for the case of surface scattering, the system is linear if multiple scattering is assumed to be negligible and the Kirchhoff approximation is assumed. A difference between the filter characteristics derived in each case is found. However this paper discusses these differences and explains the equivalence of the two approaches when applied to a weakly scattering object.

© 2013 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(090.0090) Holography : Holography
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(180.0180) Microscopy : Microscopy
(240.0240) Optics at surfaces : Optics at surfaces
(290.0290) Scattering : Scattering

ToC Category:
Scattering

History
Original Manuscript: December 21, 2012
Revised Manuscript: April 4, 2013
Manuscript Accepted: April 15, 2013
Published: May 22, 2013

Virtual Issues
Vol. 8, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Jeremy Coupland, Rahul Mandal, Kanik Palodhi, and Richard Leach, "Coherence scanning interferometry: linear theory of surface measurement," Appl. Opt. 52, 3662-3670 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-52-16-3662


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. B. S. Lee and T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990). [CrossRef]
  2. L. Deck and P. De Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994). [CrossRef]
  3. R. K. Leach, Optical Measurement of Surface Topography (Springer, 2011), 187–208.
  4. G. S. Kino and S. S. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990). [CrossRef]
  5. F. Gao, R. K. Leach, J. Petzing, and J. M. Coupland, “Surface measurement errors using commercial scanning white light interferometers,” Meas. Sci. Technol. 19, 015303 (2008). [CrossRef]
  6. C. L. Giusca and R. K. Leach, “Calibration of the scales of areal surface topography measuring instruments: Part 2—Amplification coefficient, linearity and squareness,” Meas. Sci. Technol. 23, 065005 (2012). [CrossRef]
  7. J. N. Petzing, J. M. Coupland, and R. K. Leach, “The measurement of rough surface topography using coherence scanning interferometry,” in Good Practice Guide No. 116, (National Physical Laboratory, 2010), pp. 92–112.
  8. W. Hillmann, “Surface profiles obtained by means of optical methods—are they true representations of the real surface,” CIRP Ann. 39, 581–583 (1990). [CrossRef]
  9. K. Palodhi, J. M. Coupland, and R. K. Leach, “A linear model of fringe generation and analysis in coherence scanning interferometry,” presented at the ASPE Summer Topical Meeting on Precision Interferometric Metrology, Asheville, North Carolina, 23–25 June2010.
  10. K. Palodhi, J. M. Coupland, and R. K. Leach, “Determination of the point spread function of a coherence scanning interferometer,” in Proceedings of the 13th International Conference on Metrology and Properties of Engineering Surfaces (NPL, 2011), pp. 199–202.
  11. R. Mandal, K. Palodhi, J. M. Coupland, R. K. Leach, and D. Mansfield, “Application of linear systems theory to characterize coherence scanning interferometry,” Proc. SPIE 8430, 84300T (2012). [CrossRef]
  12. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). [CrossRef]
  13. R. Dandliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970). [CrossRef]
  14. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985). [CrossRef]
  15. C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990). [CrossRef]
  16. A. F. Fercher, H. Bartelt, H. Becker, and E. Wiltschko, “Image formation by inversion of scattered field data: experiments and computational simulation,” Appl. Opt. 18, 2427–2439 (1979). [CrossRef]
  17. J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 07010 (2008). [CrossRef]
  18. P. D. Ruiz, J. M. Huntley, and J. M. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 13, 453–465 (2010). [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999), 695–734.
  20. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Artech House, 1987), 17–33.
  21. R. J. Wombellan and J. A. DeSanto, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991). [CrossRef]
  22. E. I. Thorsosand and D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991). [CrossRef]
  23. C. J. Raymond, “Milestones and future directions in applications of optical scatterometry,” Proc. SPIE CR72, 147–177 (1999). [CrossRef]
  24. C. J. R. Sheppard and M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992). [CrossRef]
  25. C. J. R. Sheppard, “Imaging of random surfaces and inverse scattering in the Kirchhoff approximation, waves in random media,” Waves Random Media 8, 53–66 (1998).
  26. J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, 1978), p. 56.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited