Abstract

Superposition fringes are suitable for making highly accurate measurements of the thicknesses of air layers. A combination of a multiple beam interferometer (Fabry-Perot) and a two-beam interferometer is discussed. In this case the contrast degradation is small. Two possible applications are discussed to some extent: the first deals with the adjustment of air gaps between lenses or other optical elements, and the second is a special spherical Fizeau interferometer. This interferometer makes possible surface testing of spheres with the help of interference colors or rings as is usual with the proof glass method, with radius differences of several centimeters. The latter application seems especially promising.

© 1979 Optical Society of America

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References

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  1. J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).
  2. C. Fabry, H. Buisson, J. Phys. 9, 189 (1919).
  3. J. Schwider, Opt. Appl. 9, 33, 39 (1979).
  4. M. Born, E. Wolf, Principles of Optics (PergamonLondon, 1959).
  5. R. A. Patten, Appl. Opt. 10, 2717 (1971).
    [Crossref] [PubMed]
  6. G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).
  7. D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, New York, 1973, p. 39).
  8. In the case of a plate distance of F.P. of 1 mm and a bandwidth of 100 nm, about 700 frequencies can pass.
  9. W. Gröbner, N. Hofreiter, Integraltafeln II Bestimmte Int. (Springer, Vienna1961, pp. 113, 114).
  10. R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1968).
  11. J. S. Harris, Thesis, U. Reading, England (1971), p. 247.
  12. O. Candler, Modern Interferometers ((Hilger, London, 1951).
  13. G. Schulz, J. Schwider, Progress in Optics, Vol. 13, (North-Holland, Amsterdam, 1976), pp. 95–167.
    [Crossref]
  14. It should be mentioned that the described technique could also be used for FECO applications in transmitted light [see, e.g., S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948)]. Here, the thickness of the air layer between the Fizeau plates can be several mm’s without loss of resolution in the spectroscopic evaluation, because the superposition fringes are widely spaced.

1979 (1)

J. Schwider, Opt. Appl. 9, 33, 39 (1979).

1971 (1)

1967 (1)

G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).

1919 (1)

C. Fabry, H. Buisson, J. Phys. 9, 189 (1919).

1913 (1)

J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).

Benoit, J. R.

J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).

Born, M.

M. Born, E. Wolf, Principles of Optics (PergamonLondon, 1959).

Buisson, H.

C. Fabry, H. Buisson, J. Phys. 9, 189 (1919).

Candler, O.

O. Candler, Modern Interferometers ((Hilger, London, 1951).

Champeney, D. C.

D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, New York, 1973, p. 39).

Fabry, C.

C. Fabry, H. Buisson, J. Phys. 9, 189 (1919).

J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).

Gröbner, W.

W. Gröbner, N. Hofreiter, Integraltafeln II Bestimmte Int. (Springer, Vienna1961, pp. 113, 114).

Harris, J. S.

J. S. Harris, Thesis, U. Reading, England (1971), p. 247.

Hesse, G.

G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).

Hofreiter, N.

W. Gröbner, N. Hofreiter, Integraltafeln II Bestimmte Int. (Springer, Vienna1961, pp. 113, 114).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1968).

Patten, R. A.

Perot, A.

J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).

Ross, W.

G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).

Schulz, G.

G. Schulz, J. Schwider, Progress in Optics, Vol. 13, (North-Holland, Amsterdam, 1976), pp. 95–167.
[Crossref]

Schwider, J.

J. Schwider, Opt. Appl. 9, 33, 39 (1979).

G. Schulz, J. Schwider, Progress in Optics, Vol. 13, (North-Holland, Amsterdam, 1976), pp. 95–167.
[Crossref]

Tolansky, S.

It should be mentioned that the described technique could also be used for FECO applications in transmitted light [see, e.g., S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948)]. Here, the thickness of the air layer between the Fizeau plates can be several mm’s without loss of resolution in the spectroscopic evaluation, because the superposition fringes are widely spaced.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (PergamonLondon, 1959).

Zöllner, F.

G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).

Appl. Opt. (1)

J. Phys. (1)

C. Fabry, H. Buisson, J. Phys. 9, 189 (1919).

Opt. Appl. (1)

J. Schwider, Opt. Appl. 9, 33, 39 (1979).

Trav. Mem. Bur. Int. Poids Mes. (1)

J. R. Benoit, C. Fabry, A. Perot, Trav. Mem. Bur. Int. Poids Mes. 15, 1 (1913).

Z. Exp. Techn. Phys. (1)

G. Hesse, W. Ross, F. Zöllner, Z. Exp. Techn. Phys. 15, 5 (1967).

Other (9)

D. C. Champeney, Fourier Transforms and Their Physical Applications (Academic, New York, 1973, p. 39).

In the case of a plate distance of F.P. of 1 mm and a bandwidth of 100 nm, about 700 frequencies can pass.

W. Gröbner, N. Hofreiter, Integraltafeln II Bestimmte Int. (Springer, Vienna1961, pp. 113, 114).

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1968).

J. S. Harris, Thesis, U. Reading, England (1971), p. 247.

O. Candler, Modern Interferometers ((Hilger, London, 1951).

G. Schulz, J. Schwider, Progress in Optics, Vol. 13, (North-Holland, Amsterdam, 1976), pp. 95–167.
[Crossref]

It should be mentioned that the described technique could also be used for FECO applications in transmitted light [see, e.g., S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948)]. Here, the thickness of the air layer between the Fizeau plates can be several mm’s without loss of resolution in the spectroscopic evaluation, because the superposition fringes are widely spaced.

M. Born, E. Wolf, Principles of Optics (PergamonLondon, 1959).

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Figures (4)

Fig. 1
Fig. 1

Arrangement for producing superposition fringes in a Fizeau interferometer formed by two arbitrary surfaces. The light of a white light source is collimated, filtered by a F.P. interferometer, and reflected at the two surfaces of the Fizeau interferometer. The observation makes use of a spectroscope to watch the Edser-Butler fringes during adjustment. B1, B2, stops; O1,O2, objectives; RSH, rotational symmetric synthetic hologram.

Fig. 2
Fig. 2

Edser-Butler fringes for a spherical lens combined with a plane surface. A small misalignment was introduced to show the interference fringes.

Fig. 3
Fig. 3

Schema of a spherical Fizeau interferometer on the basis of superposition fringes. As reference normal one surface of a concentric meniscus was used.

Fig. 4
Fig. 4

Test interferograms obtained with an arrangement according to Fig. 3: Left, white light fringes; right, same fringes but interference filter (573 nm) inserted.

Equations (13)

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i = i 1 + i 2 + 2 ( i 1 i 2 ) 1 / 2 γ 12 ( r ) ( Δ ) ,
u 1 = u 10 1 - R 1 - R exp ( i δ ) u 2 = u 20 1 - R 1 - R exp ( i δ ) exp [ i ( Δ + π ) ] ,
i = u 1 + u 2 2 = ( 1 - R ) 2 ( u 10 2 + u 20 2 ) 1 - V cos Δ 1 + R 2 - 2 R cos δ
i ¯ = k 0 k 0 + Δ k ˜ i ( k ) d k = a k 0 k 0 + Δ k ˜ 1 - V cos Δ ( k ) 1 + R 2 - 2 R cos δ ( k ) d k ,
Δ ( k ) = N δ ( k ) + Δ ¯ .
Δ = k g ,
i ¯ = a { k 0 k 0 + Δ k ˜ d k 1 + R 2 - 2 R cos δ ( k ) - k 0 k 0 + Δ k ˜ V cos N δ ( k ) 1 + R 2 - 2 R cos δ ( k ) d k cos Δ ¯ + k 0 k 0 + Δ k ˜ V sin N δ ( k ) 1 + R 2 - 2 R cos δ ( k ) d k sin Δ ¯ } .
i ¯ = a { 0 Δ k ˜ d k 1 + R 2 - 2 R cos δ ( k ) - 0 Δ k ˜ V cos N δ ( k ) d k 1 + R 2 - 2 R cos δ ( k ) cos Δ ¯ + 0 Δ k ˜ V sin N δ ( k ) 1 + R 2 - 2 R cos δ ( k ) d k sin Δ ¯ } .
i ¯ = a { 0 2 π d ψ 1 + R 2 - 2 R cos ψ - 0 2 π V cos N ψ d ψ 1 + R 2 - 2 R cos ψ cos Δ ¯ + 0 2 π V sin N ψ 1 + R 2 - 2 R cos ψ d ψ sin Δ ¯ } .
i ¯ = a A [ 1 + ( D / A ) cos ( Δ ¯ - θ ) ] ,
D = ( B 2 + C 2 ) 1 / 2 ,             θ = arctan ( C / B ) , and A = 0 2 π d ψ 1 + R 2 - 2 R cos ψ , B = - V 0 2 π cos N ψ 1 + R 2 - 2 R cos ψ d ψ , C = V 0 2 π sin N ψ 1 + R 2 - 2 R cos ψ d ψ .
A = 2 π 1 - R 2 ;             B = - V 2 π R N 1 - R 2 ;             C = 0.
i ¯ = i 0 ( 1 + V R N cos Δ ¯ ) .

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