Abstract

A model has been developed that predicts the effective optical path through a thick, refractive specimen on a reflective substrate, as measured with a scanning confocal interference microscope equipped with a high-numerical-aperture objective. Assuming that the effective pinhole of the confocal microscope has an infinitesimal diameter, only one ray in the illumination bundle (the magic ray) contributes to the differential optical path length (OPL). A pinhole with finite diameter, however, allows rays within a small angular cone centered on the magic ray to contribute to the OPL. The model was incorporated into an iterative algorithm that allows the measured phase to be corrected for refractive errors by use of an a priori estimate of the sample profile. The algorithm was validated with a reflected-light microscope equipped with a phase-shifting laser-feedback interferometer to measure the interface shape and the 68° contact angle of a silicone-oil drop on a coated silicon wafer.

© 2000 Optical Society of America

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Corrections

David G. Fischer and Ben Ovryn, "Interfacial shape and contact-angle measurement of transparent samples with confocal interference microscopy: a publisher’s erratum," Opt. Lett. 25, 862-862 (2000)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-25-11-862

References

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  1. P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
    [CrossRef]
  2. S. Calixto and M. Ornelas-Rodriquez, Opt. Lett. 24, 1212 (1999).
    [CrossRef]
  3. R. Grunwald, H. Mischke, and W. Rehak, Appl. Opt. 38, 4117 (1999).
    [CrossRef]
  4. B. T. Teipen and D. L. MacFarlane, Appl. Opt. 38, 2040 (1999).
    [CrossRef]
  5. Z. L. Liau, D. W. Nam, and R. G. Waarts, Appl. Opt. 33, 7371 (1994).
    [CrossRef] [PubMed]
  6. E. Sackmann, Science 271, 43 (1996).
    [CrossRef] [PubMed]
  7. G. Wiegand, K. R. Neumaier, and E. Sackmann, Appl. Opt. 37, 6892 (1998).
    [CrossRef]
  8. T. R. Scheuerman, A. K. Camper, and M. A. Hamilton, J. Colloid Interface Sci. 208, 23 (1998).
    [CrossRef] [PubMed]
  9. K. R. Willson and S. Garoff, Colloids Surf. A 89, 263 (1994).
    [CrossRef]
  10. B. Ovryn and J. H. Andrews, ASME, (American Society of Mechanical Engineers, New York, 1997), p. 1.
  11. T. Young, Philos. Trans. 95, 65 (1805).
    [CrossRef]
  12. Rayleigh, Proc. R. Soc. London Ser. A 92, 184 (1915).
    [CrossRef]
  13. F. Bashforth and J. C. Adams, An Attempt to Test the Theories of Capillary Action (Cambridge U. Press, Cambridge, 1883).
  14. P. Concus, J. Fluid Mech. 34, 481 (1968).
    [CrossRef]
  15. The laser feedback interferometer is based on a He–Ne cw laser λ=632.8 nm. The spot size for the 0.8-NA objective is 290 nm, and the sampling step size is 290 nm/pixel. See B. Ovryn and J. H. Andrews, Opt. Lett. 23, 1078 (1998); Appl. Opt. 38, 1959 (1999).
    [CrossRef]
  16. C. W. Extrand, J. Colloid Interface Sci. 157, 72 (1993).
    [CrossRef]
  17. D. G. Fischer and B. Ovryn, Proc. SPIE 3782, 378 (1999).
    [CrossRef]
  18. C. J. R. Sheppard and K. G. Larkin, Appl. Opt. 34, 4731 (1995).
    [CrossRef] [PubMed]

1999 (4)

1998 (3)

1996 (1)

E. Sackmann, Science 271, 43 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (1)

C. W. Extrand, J. Colloid Interface Sci. 157, 72 (1993).
[CrossRef]

1985 (1)

P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
[CrossRef]

1968 (1)

P. Concus, J. Fluid Mech. 34, 481 (1968).
[CrossRef]

1915 (1)

Rayleigh, Proc. R. Soc. London Ser. A 92, 184 (1915).
[CrossRef]

1805 (1)

T. Young, Philos. Trans. 95, 65 (1805).
[CrossRef]

Adams, J. C.

F. Bashforth and J. C. Adams, An Attempt to Test the Theories of Capillary Action (Cambridge U. Press, Cambridge, 1883).

Andrews, J. H.

Bashforth, F.

F. Bashforth and J. C. Adams, An Attempt to Test the Theories of Capillary Action (Cambridge U. Press, Cambridge, 1883).

Calixto, S.

Camper, A. K.

T. R. Scheuerman, A. K. Camper, and M. A. Hamilton, J. Colloid Interface Sci. 208, 23 (1998).
[CrossRef] [PubMed]

Concus, P.

P. Concus, J. Fluid Mech. 34, 481 (1968).
[CrossRef]

de Gennes, P. G.

P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
[CrossRef]

Extrand, C. W.

C. W. Extrand, J. Colloid Interface Sci. 157, 72 (1993).
[CrossRef]

Fischer, D. G.

D. G. Fischer and B. Ovryn, Proc. SPIE 3782, 378 (1999).
[CrossRef]

Garoff, S.

K. R. Willson and S. Garoff, Colloids Surf. A 89, 263 (1994).
[CrossRef]

Grunwald, R.

Hamilton, M. A.

T. R. Scheuerman, A. K. Camper, and M. A. Hamilton, J. Colloid Interface Sci. 208, 23 (1998).
[CrossRef] [PubMed]

Larkin, K. G.

Liau, Z. L.

MacFarlane, D. L.

Mischke, H.

Nam, D. W.

Neumaier, K. R.

Ornelas-Rodriquez, M.

Ovryn, B.

Rayleigh,

Rayleigh, Proc. R. Soc. London Ser. A 92, 184 (1915).
[CrossRef]

Rehak, W.

Sackmann, E.

Scheuerman, T. R.

T. R. Scheuerman, A. K. Camper, and M. A. Hamilton, J. Colloid Interface Sci. 208, 23 (1998).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Teipen, B. T.

Waarts, R. G.

Wiegand, G.

Willson, K. R.

K. R. Willson and S. Garoff, Colloids Surf. A 89, 263 (1994).
[CrossRef]

Young, T.

T. Young, Philos. Trans. 95, 65 (1805).
[CrossRef]

Appl. Opt. (5)

Colloids Surf. A (1)

K. R. Willson and S. Garoff, Colloids Surf. A 89, 263 (1994).
[CrossRef]

J. Colloid Interface Sci. (2)

C. W. Extrand, J. Colloid Interface Sci. 157, 72 (1993).
[CrossRef]

T. R. Scheuerman, A. K. Camper, and M. A. Hamilton, J. Colloid Interface Sci. 208, 23 (1998).
[CrossRef] [PubMed]

J. Fluid Mech. (1)

P. Concus, J. Fluid Mech. 34, 481 (1968).
[CrossRef]

Opt. Lett. (2)

Philos. Trans. (1)

T. Young, Philos. Trans. 95, 65 (1805).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

Rayleigh, Proc. R. Soc. London Ser. A 92, 184 (1915).
[CrossRef]

Proc. SPIE (1)

D. G. Fischer and B. Ovryn, Proc. SPIE 3782, 378 (1999).
[CrossRef]

Rev. Mod. Phys. (1)

P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
[CrossRef]

Science (1)

E. Sackmann, Science 271, 43 (1996).
[CrossRef] [PubMed]

Other (2)

F. Bashforth and J. C. Adams, An Attempt to Test the Theories of Capillary Action (Cambridge U. Press, Cambridge, 1883).

B. Ovryn and J. H. Andrews, ASME, (American Society of Mechanical Engineers, New York, 1997), p. 1.

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Figures (4)

Fig. 1
Fig. 1

Ray traces when a high-NA beam is scanned from the left into a spherical drop. (a) xS=-4.55 µm, (b) xc=-2.30 µm, (c) xS=7.51 µm. The two rays shown by the arrows in (b) and (c) represent magic rays, which after reflection from the substrate follow paths that are coincident with ray paths in the incident cone.

Fig. 2
Fig. 2

Optical path of the magic ray for the transverse scan position xS. The scan position is the point that is conjugate to the pinhole of the confocal microscope.

Fig. 3
Fig. 3

Two-dimensional phase image before the data were unwrapped. The visibility and the phase along the delineated region are shown in insets (a) and (b), respectively. Only those data points to the left of the arrow in (b) were unwrapped and used for the fit in Fig. 4. The maximum of the visibility was 0.3.

Fig. 4
Fig. 4

(a) Superposition of (solid curve) the predicted shape of the fluid drop and + the measured shape after correction of the data by use of the magic-ray model. The difference between the two is shown in (b) +. Also shown is the difference between the corrected data and a high-order polynomial fit to the data. The abscissa is normalized by the contact radius of the drop.

Equations (2)

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ϕxS=4π/λnhxR-hxR2+xS-xR21/2,
fr=secθ1-1-r2 cos2θ1/2,

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