Abstract

We show by analytical and numerical calculations that the phase change on reflection that occurs in interference microscopy is almost independent of the numerical aperture of the objective. The shift of the microscope interferogram response due to the phase change on reflection, however, increases with the numerical aperture. Measurements of the interferogram shift are made with a Linnik interference microscope equipped with various numerical-aperture objectives and are reported and compared with theory.

© 2004 Optical Society of America

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  1. B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurements of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
    [CrossRef] [PubMed]
  2. F. Laeri, T. C. Strand, “Angström resolution optical profilometry for microscopic objects,” Appl. Opt. 26, 2245–2249 (1987).
    [CrossRef] [PubMed]
  3. K. Creath, Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988).
  4. J. M. Bennett, “Precise method for measuring the absolute phase change on reflection,” J. Opt. Soc. Am. 54, 612–624 (1964).
    [CrossRef]
  5. T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
    [CrossRef]
  6. T. Doi, K. Toyoda, Y. Tanimura, “Effect of phase changes on reflection and their wavelength dependence in optical profilometry,” Appl. Opt. 36, 7157–7161 (1997).
    [CrossRef]
  7. K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
    [CrossRef]
  8. J. F. Biegen, “Determination of the phase change on reflection from two-beam interference,” Opt. Lett. 19, 1690–1693 (1994).
    [CrossRef] [PubMed]
  9. S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
    [CrossRef]
  10. C. W. See, M. G. Somekh, R. D. Holmes, “Scanning optical microellipsometer for pure surface profiling,” Appl. Opt. 35, 6663–6668 (1996).
    [CrossRef] [PubMed]
  11. G. D. Feke, D. P. Snow, R. D. Grober, P. J. Groot, L. Deck, “Interferometric back focal plane microellipsometry,” Appl. Opt. 37, 1796–1802 (1998).
    [CrossRef]
  12. K. Leonhardt, U. Droste, H. J. Tiziani, “Topometry for locally changing materials,” Opt. Lett. 23, 1772–1774 (1998).
    [CrossRef]
  13. M. Born, E. Wolf, Principle of Optics, 6th ed. (Pergamon, New York, 1989).
  14. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).
  15. A. Dubois, J. Selb, L. Vabre, A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (2000).
    [CrossRef]
  16. G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
    [CrossRef] [PubMed]
  17. F. C. Chang, G. S. Kino, “325-nm interference microscope,” Appl. Opt. 37, 3471–3479 (1998).
    [CrossRef]
  18. H. Mykura, G. E. Rhead, “Errors in surface topography measurements with wide-aperture interference microscopies,” J. Sci. Instrum. 40, 313–317 (1963).
    [CrossRef]
  19. C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. A 4, 1354–1360 (1987).
    [CrossRef]
  20. J. F. Biegen, “Calibration requirements for Mirau and Linnik microscope interferometers,” Appl. Opt. 28, 1972–1974 (1989).
    [CrossRef] [PubMed]
  21. K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 333–341 (1989).
    [CrossRef]
  22. G. Schulz, K.-E. Elssner, “Errors in phase-measurements interferometry with high numerical aperture,” Appl. Opt. 30, 4500–4505 (1991).
    [CrossRef] [PubMed]
  23. A. Dubois, “Phase map measurements by interferometry with sinusoidal phase modulation and four integrating buckets,” J. Opt. Soc. A. 18, 1972–1979 (2001).
    [CrossRef]

2001 (1)

A. Dubois, “Phase map measurements by interferometry with sinusoidal phase modulation and four integrating buckets,” J. Opt. Soc. A. 18, 1972–1979 (2001).
[CrossRef]

2000 (1)

1998 (3)

1997 (1)

1996 (1)

1995 (1)

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

1994 (1)

1991 (2)

K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
[CrossRef]

G. Schulz, K.-E. Elssner, “Errors in phase-measurements interferometry with high numerical aperture,” Appl. Opt. 30, 4500–4505 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (2)

J. F. Biegen, “Calibration requirements for Mirau and Linnik microscope interferometers,” Appl. Opt. 28, 1972–1974 (1989).
[CrossRef] [PubMed]

K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 333–341 (1989).
[CrossRef]

1987 (2)

F. Laeri, T. C. Strand, “Angström resolution optical profilometry for microscopic objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. A 4, 1354–1360 (1987).
[CrossRef]

1985 (1)

1964 (1)

1963 (1)

H. Mykura, G. E. Rhead, “Errors in surface topography measurements with wide-aperture interference microscopies,” J. Sci. Instrum. 40, 313–317 (1963).
[CrossRef]

Bennett, J. M.

Bhushan, B.

Biegen, J. F.

Boccara, A. C.

Born, M.

M. Born, E. Wolf, Principle of Optics, 6th ed. (Pergamon, New York, 1989).

Chandler-Horowitz, D.

T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
[CrossRef]

Chang, F. C.

Chim, S. S. C.

Creath, K.

K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 333–341 (1989).
[CrossRef]

K. Creath, Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988).

Deck, L.

Doi, T.

Droste, U.

Dubois, A.

A. Dubois, “Phase map measurements by interferometry with sinusoidal phase modulation and four integrating buckets,” J. Opt. Soc. A. 18, 1972–1979 (2001).
[CrossRef]

A. Dubois, J. Selb, L. Vabre, A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (2000).
[CrossRef]

Elssner, K.-E.

Feke, G. D.

Grober, R. D.

Groot, P. J.

Holmes, R. D.

Jordan, H. J.

K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
[CrossRef]

Juskaitis, R.

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Kino, G. S.

Koliopoulos, C. L.

Laeri, F.

Leonhardt, K.

K. Leonhardt, U. Droste, H. J. Tiziani, “Topometry for locally changing materials,” Opt. Lett. 23, 1772–1774 (1998).
[CrossRef]

K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
[CrossRef]

Matthews, H. J.

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. A 4, 1354–1360 (1987).
[CrossRef]

McWaid, T.

T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
[CrossRef]

Mykura, H.

H. Mykura, G. E. Rhead, “Errors in surface topography measurements with wide-aperture interference microscopies,” J. Sci. Instrum. 40, 313–317 (1963).
[CrossRef]

Rhead, G. E.

H. Mykura, G. E. Rhead, “Errors in surface topography measurements with wide-aperture interference microscopies,” J. Sci. Instrum. 40, 313–317 (1963).
[CrossRef]

Schulz, G.

See, C. W.

Selb, J.

Shatalin, S.

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. A 4, 1354–1360 (1987).
[CrossRef]

Snow, D. P.

Somekh, M. G.

Song, J. F.

T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
[CrossRef]

Strand, T. C.

Tan, J. B.

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Tanimura, Y.

Tiziani, H. J.

K. Leonhardt, U. Droste, H. J. Tiziani, “Topometry for locally changing materials,” Opt. Lett. 23, 1772–1774 (1998).
[CrossRef]

K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
[CrossRef]

Toyoda, K.

Vabre, L.

Vorburger, T.

T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
[CrossRef]

Wilson, T.

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principle of Optics, 6th ed. (Pergamon, New York, 1989).

Wyant, J. C.

Appl. Opt. (11)

K. Creath, “Calibration of numerical aperture effects in interferometric microscope objectives,” Appl. Opt. 28, 333–341 (1989).
[CrossRef]

G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 29, 3775–3783 (1990).
[CrossRef] [PubMed]

G. D. Feke, D. P. Snow, R. D. Grober, P. J. Groot, L. Deck, “Interferometric back focal plane microellipsometry,” Appl. Opt. 37, 1796–1802 (1998).
[CrossRef]

F. C. Chang, G. S. Kino, “325-nm interference microscope,” Appl. Opt. 37, 3471–3479 (1998).
[CrossRef]

A. Dubois, J. Selb, L. Vabre, A. C. Boccara, “Phase measurements with wide-aperture interferometers,” Appl. Opt. 39, 2326–2331 (2000).
[CrossRef]

C. W. See, M. G. Somekh, R. D. Holmes, “Scanning optical microellipsometer for pure surface profiling,” Appl. Opt. 35, 6663–6668 (1996).
[CrossRef] [PubMed]

B. Bhushan, J. C. Wyant, C. L. Koliopoulos, “Measurements of surface topography of magnetic tapes by Mirau interferometry,” Appl. Opt. 24, 1489–1497 (1985).
[CrossRef] [PubMed]

F. Laeri, T. C. Strand, “Angström resolution optical profilometry for microscopic objects,” Appl. Opt. 26, 2245–2249 (1987).
[CrossRef] [PubMed]

G. Schulz, K.-E. Elssner, “Errors in phase-measurements interferometry with high numerical aperture,” Appl. Opt. 30, 4500–4505 (1991).
[CrossRef] [PubMed]

T. Doi, K. Toyoda, Y. Tanimura, “Effect of phase changes on reflection and their wavelength dependence in optical profilometry,” Appl. Opt. 36, 7157–7161 (1997).
[CrossRef]

J. F. Biegen, “Calibration requirements for Mirau and Linnik microscope interferometers,” Appl. Opt. 28, 1972–1974 (1989).
[CrossRef] [PubMed]

J. Microsc. (1)

S. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

J. Opt. Soc. A (1)

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. A 4, 1354–1360 (1987).
[CrossRef]

J. Opt. Soc. A. (1)

A. Dubois, “Phase map measurements by interferometry with sinusoidal phase modulation and four integrating buckets,” J. Opt. Soc. A. 18, 1972–1979 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Sci. Instrum. (1)

H. Mykura, G. E. Rhead, “Errors in surface topography measurements with wide-aperture interference microscopies,” J. Sci. Instrum. 40, 313–317 (1963).
[CrossRef]

Opt. Commun. (1)

K. Leonhardt, H. J. Jordan, H. J. Tiziani, “Micro-ellipso height profilometry,” Opt. Commun. 80, 205–209 (1991).
[CrossRef]

Opt. Lett. (2)

Other (4)

M. Born, E. Wolf, Principle of Optics, 6th ed. (Pergamon, New York, 1989).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

K. Creath, Progress in Optics XXVI, E. Wolf, ed. (Elsevier, New York, 1988).

T. McWaid, T. Vorburger, J. F. Song, D. Chandler-Horowitz, “The effect of thin films on interferometric step height measurements,” in Interferometry: Surface Characterization and Testing, K. Creath, J. E. Greivenkamp, eds., Proc. SPIE1776, 2–13 (1992).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Phase changes of light on reflection air and copper versus incidence angle for the s- and p-polarization components and for unpolarized light. ϕ s (θ), ϕ p (θ), and ϕ(θ) are calculated modulo π by use of Eq. (3), Eq. (4), and Eq. (7), respectively, at a wavelength of 650 nm. The refractive indices of copper are n = 0.224 and k = 3.63.14

Fig. 2
Fig. 2

(a) Numerical calculation of the interferogram response M(z) with different numerical apertures [see Eq. (15)]. The object is a copper surface, with a phase change on reflection ϕ(θ) calculated with Eq. (7). (b) Magnification of the peaks of both curves in (a) to show the shift of the interferogram with numerical aperture when the phase change on reflection is not zero.

Fig. 3
Fig. 3

Experimental setup: MO, coverslip-corrected microscope objectives (for various numerical apertures); BS, beam splitter; and PZT, piezoelectric transducer. The interference filter is centered at λ = 650 nm, with a bandwidth Δλ = 10 nm.

Tables (2)

Tables Icon

Table 1 Theoretical Shift of the Central Fringe as a Function of Numerical Aperture for Copper at λ = 650 nma

Tables Icon

Table 2 Measurement of the Central Fringe Shift with Various Numerical Apertures for Copper at λ = 650 nm

Equations (23)

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

|rsθ|=N2+K2-2N cos θ+cos2 θN2+K2+2N cos θ+cos2 θ1/2,
|rpθ|=|rsθ|N2+K2-2N sin θ tan θ+sin2 θ tan2 θN2+K2+2N sin θ tan θ+sin2 θ tan2 θ1/2,
tan ϕsθ=-2K cos θN2+K2-cos2 θ,
tan ϕpθ=2K cos θN2+K2-sin2 θN2+K2-n2+k22 cos2 θ,
N=12n2-k2-sin2 θ2+4n2k21/2+n2-k2-sin2 θ,
K=12n2-k2-sin2 θ2+4n2k2]1/2-n2-k2-sin2 θ.
ϕθ=arg|rs|expiϕs+|rp|expiϕp.
|rpθ|=|rsθ|1-γθ2+Oθ4,
ϕsθ=ϕ0+εθ2+Oθ4,
ϕpθ=ϕ0-εθ2+Oθ4,
γ=2nn2+k2,
ε=kn2+k2,
ϕ0=arctan2k1-n2+k2  modulo π.
ϕθ=ϕ0+Oθ4.
Mz=0θmaxcos4πσz cos θ+ϕθcos θ sin θdθ.
12σ<Λ<12σ cos θmax,
-ϕ04πσ<z0<-ϕθmax4πσ cos θmax.
Mz=VzcosΦz,
Vz  sinπσzθmax2/πσzθmax2,
Φz=4πσαz+ϕ0,
α=1-θmax2/4.
Λ=12ασ=121-θmax2/4σ.
z0=-ϕ04πασ=-ϕ04π1-θmax2/4σ.

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