Abstract

A white-light Fizeau interferometer is described. Commonly, white-light fringes can be produced only by using a virtual wedge instrument such as a Michelson interferometer. By use of a series arrangement of a Fabry–Perot interferometer in front of a two-beam Fizeau interferometer, white-light fringes can be produced. For white-light fringes to be obtained, the thickness of the air gap between the Fizeau plates has to be adjusted to the same thickness as the air gap between the Fabry–Perot plates (or in more general terms to a rational multiple of this value). The contrast of the two-beam type of Fizeau fringes depends on the reflectivity of the Fabry–Perot plates.

© 1997 Optical Society of America

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References

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  1. P. de Groot, L. Deck, “Surface profiling by analysis of white light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
    [CrossRef]
  2. T. Dresel, G. Häusler, H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef] [PubMed]
  3. J. Schwider, L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19, 995–996 (1994).
    [CrossRef] [PubMed]
  4. C. Koliopoulos, “Low coherent noise interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 396 (1995).
  5. J. Schwider, O. Falkenstörfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34, 2972–2975 (1995).
    [CrossRef]
  6. G. Schulz, “Zweistrahlinterferenz in Planspiegelanordnungen,” Opt. Acta 11, 43–60, 89–99, 131–143 (1964).
    [CrossRef]
  7. A. Perot, C. Fabry, “Sur la mesure optique de la difference de deux epaisseurs,” C. R. Acad. Sci. 138, 676–678 (1904).
  8. C. Candler, Modern Interferometers (Hilger and Watts, London, 1951).
  9. J. Schwider, “Superposition fringes as a measuring tool in optical testing,” Appl. Opt. 18, 2364–2367 (1979).
    [CrossRef] [PubMed]
  10. G. Schulz, J. Schwider, “Zweistrahlinterferometer Licht-quellenbildtransformation als Schraubung und neue Effekte an Interferenzstreifen,” Optik 21, 587–597 (1964).
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).
  12. W. Gröbner, N. Hofreiter, Integraltafeln II/Bestimmte Integrale (Springer-Verlag, Wien, 1961), p. 113.

1995

P. de Groot, L. Deck, “Surface profiling by analysis of white light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

J. Schwider, O. Falkenstörfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34, 2972–2975 (1995).
[CrossRef]

1994

1992

1979

1964

G. Schulz, J. Schwider, “Zweistrahlinterferometer Licht-quellenbildtransformation als Schraubung und neue Effekte an Interferenzstreifen,” Optik 21, 587–597 (1964).

G. Schulz, “Zweistrahlinterferenz in Planspiegelanordnungen,” Opt. Acta 11, 43–60, 89–99, 131–143 (1964).
[CrossRef]

1904

A. Perot, C. Fabry, “Sur la mesure optique de la difference de deux epaisseurs,” C. R. Acad. Sci. 138, 676–678 (1904).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Candler, C.

C. Candler, Modern Interferometers (Hilger and Watts, London, 1951).

de Groot, P.

P. de Groot, 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, 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.

Fabry, C.

A. Perot, C. Fabry, “Sur la mesure optique de la difference de deux epaisseurs,” C. R. Acad. Sci. 138, 676–678 (1904).

Falkenstörfer, O.

J. Schwider, O. Falkenstörfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34, 2972–2975 (1995).
[CrossRef]

Gröbner, W.

W. Gröbner, N. Hofreiter, Integraltafeln II/Bestimmte Integrale (Springer-Verlag, Wien, 1961), p. 113.

Häusler, G.

Hofreiter, N.

W. Gröbner, N. Hofreiter, Integraltafeln II/Bestimmte Integrale (Springer-Verlag, Wien, 1961), p. 113.

Koliopoulos, C.

C. Koliopoulos, “Low coherent noise interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 396 (1995).

Perot, A.

A. Perot, C. Fabry, “Sur la mesure optique de la difference de deux epaisseurs,” C. R. Acad. Sci. 138, 676–678 (1904).

Schulz, G.

G. Schulz, “Zweistrahlinterferenz in Planspiegelanordnungen,” Opt. Acta 11, 43–60, 89–99, 131–143 (1964).
[CrossRef]

G. Schulz, J. Schwider, “Zweistrahlinterferometer Licht-quellenbildtransformation als Schraubung und neue Effekte an Interferenzstreifen,” Optik 21, 587–597 (1964).

Schwider, J.

J. Schwider, O. Falkenstörfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34, 2972–2975 (1995).
[CrossRef]

J. Schwider, L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19, 995–996 (1994).
[CrossRef] [PubMed]

J. Schwider, “Superposition fringes as a measuring tool in optical testing,” Appl. Opt. 18, 2364–2367 (1979).
[CrossRef] [PubMed]

G. Schulz, J. Schwider, “Zweistrahlinterferometer Licht-quellenbildtransformation als Schraubung und neue Effekte an Interferenzstreifen,” Optik 21, 587–597 (1964).

Venzke, H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Zhou, L.

Appl. Opt.

C. R. Acad. Sci.

A. Perot, C. Fabry, “Sur la mesure optique de la difference de deux epaisseurs,” C. R. Acad. Sci. 138, 676–678 (1904).

J. Mod. Opt.

P. de Groot, L. Deck, “Surface profiling by analysis of white light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Opt. Acta

G. Schulz, “Zweistrahlinterferenz in Planspiegelanordnungen,” Opt. Acta 11, 43–60, 89–99, 131–143 (1964).
[CrossRef]

Opt. Eng.

J. Schwider, O. Falkenstörfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34, 2972–2975 (1995).
[CrossRef]

Opt. Lett.

Optik

G. Schulz, J. Schwider, “Zweistrahlinterferometer Licht-quellenbildtransformation als Schraubung und neue Effekte an Interferenzstreifen,” Optik 21, 587–597 (1964).

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

W. Gröbner, N. Hofreiter, Integraltafeln II/Bestimmte Integrale (Springer-Verlag, Wien, 1961), p. 113.

C. Koliopoulos, “Low coherent noise interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 396 (1995).

C. Candler, Modern Interferometers (Hilger and Watts, London, 1951).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the white-light Fizeau interferometer.

Fig. 2
Fig. 2

Experimental white-light interferogram with l = 1 produced by an arrangement from Fig. 1.

Fig. 3
Fig. 3

Same as Fig. 2, but an interference filter with dλ = 10 nm at λ = 575 nm was used.

Fig. 4
Fig. 4

Line scan through interferograms of Figs. 2 (left) and 3 (right).

Equations (15)

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I=I01+RlV cos Φ,
Φ=ΔFiz-lδFP=2kT-lt.
u=u01-R1-Reiδ,
u1=u101-R1-Reiδ, u2=u201-R1-ReiδexpiΔ+π,
I=u102+u202-2 u102u202 cos Δ1+R2-2R cos δ1-R2,
I=1-R2u102+u2021-V cos Δ1+R2-2R cos δ.
I¯Δk=k0k0+ΔkIkdk=constk0k0+Δk1-V cos Δk1+R2-2R cos δkdk,
I¯Δk=const0Δk1-V cos Δk1+R2-2R cos δkdk.
Δk=lδk+Φ=2ltk+Φ,
I¯Δk0Δkdk1+R2-2R cos 2tk-V cos Φ0Δkcos 2ltk dk1+R2-2R cos 2tk+V sin Φ0Δksin 2ltk dk1+R2-2R cos 2tk.
02πIψdψ02πdψ1+R2-2R cos ψ-V cos Φ02πcos lψdψ1+R2-2R cos ψ+V sin Φ02πsin lψdψ1+R2-2R cos ψ.
I¯Δk=const A1+DAV  cosΦ-Θ
02πdψ1+R2-2R cos ψ=A; 02πcos lψdψ1+R2-2R cos ψ=B; 02πsin lψdψ1+R2-2R cos ψ=C.
A=2π1-R2; B=2πRl1-R2; C=0l is a positive wholenumber.
I¯Δk=I¯0Δk1+VRl  cos  Φ,

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