OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 8 — Mar. 10, 2014
  • pp: 1554–1563

Coherence scanning interferometry: measurement and correction of three-dimensional transfer and point-spread characteristics

Rahul Mandal, Jeremy Coupland, Richard Leach, and Daniel Mansfield  »View Author Affiliations

Applied Optics, Vol. 53, Issue 8, pp. 1554-1563 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1565 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



When applied to the measurement of smooth surfaces, coherence scanning interferometry can be described by a three-dimensional linear filtering operation that is characterized either by the point-spread function in the space domain or equivalently by the transfer function (TF) in the spatial frequency domain. For an ideal, aberration-free instrument, these characteristics are defined uniquely by the numerical aperture of the objective lens and the bandwidth of the illumination source. In practice, however, physical imperfections such as those in lens aberrations, reference focus, and source alignment mean that the instrument performance is not ideal. Currently, these imperfections often go unnoticed as the instrument performance is typically only verified using rectilinear artifacts such as step heights and lateral grids. If an object of varying slope is measured, however, significant errors are often observed as the surface gradient increases. In this paper, a new method of calibration and adjustment using a silica micro-sphere as a calibration artifact is introduced. The silica microsphere was used to compute the point-spread and TF characteristics of the instrument, and the effect of these characteristics on instrument performance is discussed. Finally, a straightforward method to correct for phase and amplitude imperfections in the TF is described using a modified inverse filter.

© 2014 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(180.6900) Microscopy : Three-dimensional microscopy
(180.1655) Microscopy : Coherence tomography

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: January 24, 2014
Revised Manuscript: January 24, 2014
Manuscript Accepted: January 28, 2014
Published: March 5, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Rahul Mandal, Jeremy Coupland, Richard Leach, and Daniel Mansfield, "Coherence scanning interferometry: measurement and correction of three-dimensional transfer and point-spread characteristics," Appl. Opt. 53, 1554-1563 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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, Characterisation of Areal Surface Texture (Springer-Verlag, 2013).
  4. 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]
  5. T. V. Vorburger, H. G. Rhee, T. B. Renegar, J.-F. Song, and A. Zheng, “Comparison of optical and stylus methods for measurement of surface texture,” Int. J. Adv. Manuf. Technol. 33, 110–118 (2007). [CrossRef]
  6. R. K. Leach, C. L. Giusca, and K. Naoi, “Development and characterisation of a new instrument for traceable measurement of areal surface texture,” Meas. Sci. Technol. 20, 125102 (2009). [CrossRef]
  7. W. Xie, P. Lehmann, and J. Niehues, “Lateral resolution and transfer characteristics of vertical scanning white-light interferometers,” Appl. Opt. 51, 1795–1803 (2012). [CrossRef]
  8. P. De Groot and X. C. Lega, “Interpreting interferometric height measurements using the instrument transfer function,” in Fringe 2005: The 5th International Workshop on Automatic Processing of Fringe Patterns, W. Osten, ed. (Springer, 2006), pp. 30–37.
  9. G. Häusler and S. Ettl, “Limitations of optical 3D-sensors,” in Optical Measurement of Surface Topography, R. Leach, ed. (Springer-Verlag, 2011), pp. 23–48.
  10. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), pp. 456–520.
  11. J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008). [CrossRef]
  12. M. R. Foreman, C. L. Giusca, J. M. Coupland, P. Török, and R. K. Leach, “Determination of the transfer function for optical surface topography measuring systems—a review,” Meas. Sci. Technol. 24, 052001 (2013). [CrossRef]
  13. J. M. Coupland, R. Mandal, K. Palodhi, and R. K. Leach, “Coherence scanning interferometry: linear theory of surface measurement,” Appl. Opt. 52, 3662–3670 (2013). [CrossRef]
  14. K. Palodhi, J. M. Coupland, and R. K. Leach, “A linear model of fringe generation and analysis in coherence scanning interferometry,” presented at the American Society of Precision Engineering Summer Topical Meeting on Precision Interferometric Metrology, Asheville, North Carolina, June 23–25, 2010.
  15. C. L. Giusca, R. K. Leach, and F. Helery, “Calibration of the scales of surface topography measuring instruments: part 2. Amplification, linearity and squareness,” Meas. Sci. Technol. 23, 065005 (2012). [CrossRef]
  16. A. Henning, C. Giusca, A. Forbes, I. Smith, R. K. Leach, J. M. Coupland, and R. Mandal, “Correction for lateral distortion in coherence scanning interferometry,” CIRP Ann. 62, 547–550 (2013). [CrossRef]
  17. J. W. Gates, “Fringe spacing in interference microscopes,” J. Sci. Instrum. 33, 507 (1956). [CrossRef]
  18. 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]
  19. Y. Zhou, Y. Ghim, A. Fard, and A. Davies, “Application of the random ball test for calibrating slope-dependent errors in profilometry measurements,” Appl. Opt. 52, 5925–5931 (2013). [CrossRef]
  20. W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, 2001), pp. 351–354.
  21. P. De Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995). [CrossRef]

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