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References

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  1. G. Hansen, Z. Instrumentenk. 61, 411 (1941).
  2. P. Connes, Rev. Opt. 35, 37 (1956).
  3. L. Mertz, Transformations in Optics (Wiley, New York1965).
  4. P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).
  5. R. L. Hilliard, Ph.D. Thesis, University of Saskatchewan (1964).
  6. R. L. Hilliard, G. G. Shepherd, J. Opt. Soc. Amer. 56, 362 (1966).
    [CrossRef]
  7. W. D. Johnston, Appl. Opt. 7, 357 (1968).
    [CrossRef] [PubMed]
  8. R. L. Hilliard, G. G. Shepherd, Planet. Space Sci. 14, 383 (1966).
    [CrossRef]
  9. H. H. Zwick, G. G. Shepherd, Planet. Space Sci. in press.
  10. W. H. Steel, in Interferometry (Cambridge U.P., London, 1967), p. 64.
  11. M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1962).
  12. C. S. Williams, Appl. Opt. 5, 1084 (1966).
    [CrossRef] [PubMed]
  13. M. Abramawitz, I. Stegun, Handbook of Mathematical Functions, Applied Math. Series 55 (U.S. Govt. Printing Office, Washington, 1964), p. 304.

1968 (1)

1966 (3)

R. L. Hilliard, G. G. Shepherd, Planet. Space Sci. 14, 383 (1966).
[CrossRef]

C. S. Williams, Appl. Opt. 5, 1084 (1966).
[CrossRef] [PubMed]

R. L. Hilliard, G. G. Shepherd, J. Opt. Soc. Amer. 56, 362 (1966).
[CrossRef]

1963 (1)

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

1956 (1)

P. Connes, Rev. Opt. 35, 37 (1956).

1941 (1)

G. Hansen, Z. Instrumentenk. 61, 411 (1941).

Abramawitz, M.

M. Abramawitz, I. Stegun, Handbook of Mathematical Functions, Applied Math. Series 55 (U.S. Govt. Printing Office, Washington, 1964), p. 304.

Bouchareine, P.

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

Cagnet, M.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1962).

Connes, P.

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

P. Connes, Rev. Opt. 35, 37 (1956).

Françon, M.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1962).

Hansen, G.

G. Hansen, Z. Instrumentenk. 61, 411 (1941).

Hilliard, R. L.

R. L. Hilliard, G. G. Shepherd, J. Opt. Soc. Amer. 56, 362 (1966).
[CrossRef]

R. L. Hilliard, G. G. Shepherd, Planet. Space Sci. 14, 383 (1966).
[CrossRef]

R. L. Hilliard, Ph.D. Thesis, University of Saskatchewan (1964).

Johnston, W. D.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York1965).

Shepherd, G. G.

R. L. Hilliard, G. G. Shepherd, J. Opt. Soc. Amer. 56, 362 (1966).
[CrossRef]

R. L. Hilliard, G. G. Shepherd, Planet. Space Sci. 14, 383 (1966).
[CrossRef]

H. H. Zwick, G. G. Shepherd, Planet. Space Sci. in press.

Steel, W. H.

W. H. Steel, in Interferometry (Cambridge U.P., London, 1967), p. 64.

Stegun, I.

M. Abramawitz, I. Stegun, Handbook of Mathematical Functions, Applied Math. Series 55 (U.S. Govt. Printing Office, Washington, 1964), p. 304.

Thrierr, J. C.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1962).

Williams, C. S.

Zwick, H. H.

H. H. Zwick, G. G. Shepherd, Planet. Space Sci. in press.

Appl. Opt. (2)

J. Opt. Soc. Amer. (1)

R. L. Hilliard, G. G. Shepherd, J. Opt. Soc. Amer. 56, 362 (1966).
[CrossRef]

J. Phys. Rad. (1)

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

Planet. Space Sci. (1)

R. L. Hilliard, G. G. Shepherd, Planet. Space Sci. 14, 383 (1966).
[CrossRef]

Rev. Opt. (1)

P. Connes, Rev. Opt. 35, 37 (1956).

Z. Instrumentenk. (1)

G. Hansen, Z. Instrumentenk. 61, 411 (1941).

Other (6)

M. Abramawitz, I. Stegun, Handbook of Mathematical Functions, Applied Math. Series 55 (U.S. Govt. Printing Office, Washington, 1964), p. 304.

L. Mertz, Transformations in Optics (Wiley, New York1965).

R. L. Hilliard, Ph.D. Thesis, University of Saskatchewan (1964).

H. H. Zwick, G. G. Shepherd, Planet. Space Sci. in press.

W. H. Steel, in Interferometry (Cambridge U.P., London, 1967), p. 64.

M. Cagnet, M. Françon, J. C. Thrierr, Atlas of Optical Phenomena (Springer-Verlag, Berlin, 1962).

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Figures (3)

Fig. 1
Fig. 1

The geometrical arrangement for a WAMI. The beam-splitting cube is coupled to a back-surfaced mirror M1 of thickness t and refractive index n. The hypothetical mirror at a depth t/n is mirrored at M1′. The second mirror M2 is defocused a distance e from M1′.

Fig. 2
Fig. 2

Twelve photographs of the Haidinger rings formed by the WAMI. Beginning at the upper left, each photograph is for a successively lower value of defocusing, beginning at positive and ending in negative values. The photographs are numbered horizontally with 1 in the top left-hand corner and 12 in the bottom right-hand corner.

Fig. 3
Fig. 3

The solid curves illustrate the calculated change in path difference as a function of off-axis angle for defocusing values ranging from +200 μ in 40-μ steps. The experimental points shown are derived from photographs 1, 7, and 12 of Fig. 2.

Equations (13)

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Δ = 2 n t cos φ n - 2 t cos φ .
t tan φ n = t tan φ .
t = t / n
Δ 0 = 2 t ( n - 1 / n ) .
δ Δ = m λ = Δ - Δ 0 = e φ 2 + ( Δ 0 / 8 n 2 ) φ 4 ,
e = - ( Δ 0 / 8 n 2 ) φ c 2 .
i = 2 I 0 [ 1 + area cos ( 2 π σ Δ ) d A / area d A ] ,
d A = 2 π f 2 φ d φ
A = π f 2 φ M 2 .
V = ( M 2 + N 2 ) 1 2 .
M = c · cos ( b 2 / a ) { C [ ( g / b ) · d ] - C ( g ) } + c · sin ( b 2 / a ) { S [ ( g / b ) · d ] - S ( g ) } ,
N = c · cos ( b 2 / a ) { S [ ( g / b ) · d ] - S ( g ) } - c · sin ( b 2 / a ) { C [ ( g / b ) · d ] - C ( g ) } ,
a = π σ Δ 0 / 4 n 2 , d = a φ M 2 + b , b = π σ e , g = ( 2 / a π ) 1 2 · b , c = ( 1 / φ M 2 ) · ( π / 2 a ) 1 2 , C ( x ) = 0 x ( 2 / π ) 1 2 cos x 2 d x , S ( x ) = 0 x ( 2 / π ) 1 2 sin x 2 d x .

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