Abstract

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef]
  2. P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
    [CrossRef]
  3. P. Ettl, “Über die Signalentstehung bei Weisslichtinterferometrie,” Ph.D. dissertation (University Erlangen–Nuremberg, 2001).
  4. 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.
  5. P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
    [CrossRef]
  6. A. Pförtner and J. Schwider, “Dispersion error in white-light Linnik interferometers and its implication for evaluation procedures,” Appl. Opt. 40, 6223–6228 (2001).
    [CrossRef]
  7. G. Häusler, “Ubiquitous coherence: boon and bale of the optical metrologist,” Proc. SPIE 4933, 48–52 (2003).
    [CrossRef]
  8. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.
  9. J. W. Goodman, “Speckle with finite number of steps,” Appl. Opt. 47, A111–A118 (2008).
    [CrossRef]
  10. T. Dresel, “Grundlagen und Grenzen der 3D-Datengewinnung mit dem Kohärenzradar,” Master’s thesis (University Erlangen–Nuremberg, 1991).
  11. P. Pavliček and J. Soubusta, “Theoretical measurement uncertainty of white-light interferometry on rough surfaces,” Appl. Opt. 42, 1809–1813 (2003).
    [CrossRef]
  12. P. Pavliček and O. Hýbl, “White-light interferometry on rough surfaces—measurement uncertainty caused by surface roughness,” Appl. Opt. 47, 2941–2949 (2008).
    [CrossRef]
  13. 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]
  14. N. George and A. Jain, “Speckle reduction using multiple tones of illumination,” Appl. Opt. 12, 1202–1212(1973).
    [CrossRef]

2008 (2)

2003 (2)

P. Pavliček and J. Soubusta, “Theoretical measurement uncertainty of white-light interferometry on rough surfaces,” Appl. Opt. 42, 1809–1813 (2003).
[CrossRef]

G. Häusler, “Ubiquitous coherence: boon and bale of the optical metrologist,” Proc. SPIE 4933, 48–52 (2003).
[CrossRef]

2002 (1)

2001 (1)

1998 (1)

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

1995 (1)

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]

1992 (1)

1973 (1)

Colonna de Lega, X.

de Groot, P.

P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
[CrossRef]

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]

Deck, L.

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]

Dresel, T.

T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
[CrossRef]

T. Dresel, “Grundlagen und Grenzen der 3D-Datengewinnung mit dem Kohärenzradar,” Master’s thesis (University Erlangen–Nuremberg, 1991).

Ettl, P.

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

P. Ettl, “Über die Signalentstehung bei Weisslichtinterferometrie,” Ph.D. dissertation (University Erlangen–Nuremberg, 2001).

Ettl, S.

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.

George, N.

Goodman, J. W.

J. W. Goodman, “Speckle with finite number of steps,” Appl. Opt. 47, A111–A118 (2008).
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.

Häusler, G.

G. Häusler, “Ubiquitous coherence: boon and bale of the optical metrologist,” Proc. SPIE 4933, 48–52 (2003).
[CrossRef]

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
[CrossRef]

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.

Hýbl, O.

Jain, A.

Kramer, J.

Laszlo, I.

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

Pavlicek, P.

Pförtner, A.

Schenk, M.

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

Schmidt, B.

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

Schwider, J.

Soubusta, J.

Turzhitsky, M.

Venzke, H.

Appl. Opt. (7)

J. Mod. Opt. (1)

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]

Proc. SPIE (2)

G. Häusler, “Ubiquitous coherence: boon and bale of the optical metrologist,” Proc. SPIE 4933, 48–52 (2003).
[CrossRef]

P. Ettl, B. Schmidt, M. Schenk, I. Laszlo, and G. Häusler, “Roughness parameters and surface deformation measured by coherence radar,” Proc. SPIE 3407, 133–140 (1998).
[CrossRef]

Other (4)

P. Ettl, “Über die Signalentstehung bei Weisslichtinterferometrie,” Ph.D. dissertation (University Erlangen–Nuremberg, 2001).

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.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1984), pp. 9–75.

T. Dresel, “Grundlagen und Grenzen der 3D-Datengewinnung mit dem Kohärenzradar,” Master’s thesis (University Erlangen–Nuremberg, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Schematic of WLI on a rough surface.

Fig. 2.
Fig. 2.

Six arbitrarily chosen correlograms from different pixels (different speckles). Note the big variation of the correlogram position.

Fig. 3.
Fig. 3.

Profile of a rough surface, measured 10 times. Highlighted are a dark speckle and a bright speckle.

Fig. 4.
Fig. 4.

Sketch of the observation pupil with the images of four light sources.

Fig. 5.
Fig. 5.

a, SNR histogram of correlograms, for standard WLI (black), the “best-of-two” (dashed) and the “best-of-four” speckles (gray). b, SNR histogram of correlograms from Fig. 5a, in detail, for standard WLI (one pattern) and the best-of-four method. With the best-of-four method, there is only a very small number of pixels with a SNR of less than 4.

Fig. 6.
Fig. 6.

Fraction of pixels with a SNR<4 for the best-of-n speckle patterns.

Fig. 7.
Fig. 7.

Accumulated probability distributions P1c for standard WLI and P4c for the best-of-four, both measured with the coherence radar. For comparison, the calculated distribution P4 for the best-of-four, derived from Eq. (6), is given as well. The best-of-four method improves the SNR significantly, as shown experimentally and theoretically.

Fig. 8.
Fig. 8.

Measurement of a two-Euro coin with one speckle pattern (left side) and best-of-four speckle patterns (right side).

Fig. 9.
Fig. 9.

Surface roughness Rac measured by coherence radar of roughness standard no. 2 from Table 1. The measurement was done with one of the four light sources from Fig. 4.

Tables (1)

Tables Icon

Table 1. Measurement of the Surface Roughness Parameter Ra of Three Roughness Standards with the Coherence Radar, with One Pattern, and with the Best-of-Four Speckle Patternsa

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

uexp[i2kz(x,y)].
usmooth1+i2kz(x,y).
uroughexp[i2kz(x,y)].
σzc(I)=12IIσo.
σR=σB2+σ22+σ32+σ422>σB2.
Pn=[P1]n.

Metrics