Abstract

The instrument function of a wide angle Michelson interferometer spectrometer is derived in terms of known or easily measured functions using a novel method of computing the phase difference between the two beams. The interferometer essentially achieves immersion with solid materials and has the advantages of a larger field of view and fewer reflecting interfaces. A set of instrument functions is plotted in which either the field of view or the wavelength, with the other held fixed, may be interpreted as the parameter. The allowable field of view is found to increase linearly with the index of refraction of the cube material. A simple working model yielded both white light and mercury green light fringes.

© 1968 Optical Society of America

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References

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  1. J. B. Saunders, Appl. Opt. 6, 1581 (1967).
    [CrossRef] [PubMed]
  2. P. Bouchereine, P. Connes, J. Phys. Radium 24, 134 (1963).
  3. L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), p. 19.
  4. J. Connes, Rev. Optique 40, 63 (1961).
  5. J. Connes, J. Phys. Radium 19, 187 (1958).
    [CrossRef]

1967 (1)

1963 (1)

P. Bouchereine, P. Connes, J. Phys. Radium 24, 134 (1963).

1961 (1)

J. Connes, Rev. Optique 40, 63 (1961).

1958 (1)

J. Connes, J. Phys. Radium 19, 187 (1958).
[CrossRef]

Bouchereine, P.

P. Bouchereine, P. Connes, J. Phys. Radium 24, 134 (1963).

Connes, J.

J. Connes, Rev. Optique 40, 63 (1961).

J. Connes, J. Phys. Radium 19, 187 (1958).
[CrossRef]

Connes, P.

P. Bouchereine, P. Connes, J. Phys. Radium 24, 134 (1963).

Mertz, L.

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), p. 19.

Saunders, J. B.

Appl. Opt. (1)

J. Phys. Radium (2)

P. Bouchereine, P. Connes, J. Phys. Radium 24, 134 (1963).

J. Connes, J. Phys. Radium 19, 187 (1958).
[CrossRef]

Rev. Optique (1)

J. Connes, Rev. Optique 40, 63 (1961).

Other (1)

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), p. 19.

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Figures (4)

Fig. 1
Fig. 1

a, transmitting half-cubes; b, plane mirrors; c, beam splitter coating; f, line of relative motion; g, surface of potential total internal reflection; h, incident radiation; i, composite radiation to be focused by parabolic mirror, e, onto detector, d.

Fig. 2
Fig. 2

(a) Half-cubes of solid Michelson interferometer. (b) Mercury green light fringes.

Fig. 3
Fig. 3

Path of a plane wave through the instrument.

Fig. 4
Fig. 4

Plots of the instrument function. The dotted curve is sin∊τ/∊τ for comparison.

Equations (9)

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ψ = x arm k ( x ) d x = y arm k ( x ) d x = 2 π λ ( 2 δ ( n 2 - sin 2 θ ) 1 2 + t 0 { 2 1 2 ( n 2 - sin 2 θ ) 1 2 + n 0 2 - n 2 + 1 2 [ sin θ cos ϕ + ( n 2 - sin 2 θ ) 1 2 ] 2 + n 0 2 - n 2 + 1 2 [ sin θ cos ϕ - ( n 2 - sin 2 θ ) 1 2 ] 2 } - t 1 [ 2 ( n 2 - sin 2 θ ) 1 2 + n 1 2 - n 2 + 1 2 [ sin θ cos ϕ + ( n 2 - sin 2 θ ) 1 2 ] 2 + n 1 2 - n 2 + 1 2 [ sin θ cos ϕ - ( n 2 - sin 2 θ ) 1 2 ] 2 ) ,
ψ = 2 π λ 2 δ ( n 2 - sin 2 θ ) 1 2 2 π λ 2 δ n [ 1 - θ 2 2 n 2 + θ 4 + ( 1 6 n 2 - 1 8 n 4 ) ]
ψ ( θ M ) - ψ ( 0 ) = - π , or θ M = ( n λ / 2 δ M ) 1 2
h ( ν , δ ) = A π θ M 2 sin ( π ν δ θ M 2 / n ) π ν δ θ M 2 / n cos { 4 π n ν δ [ 1 - θ M 2 / 4 n 2 ] } .
B m ( ν ) = 0 B ( ν ) f ( ν , ν ) d ν .
f ( ν , ν ) = F t ω [ F ω t - 1 { T ( ω ) F t ω [ h ( ν , t ) R ( t ) ] } R ( t ) ] ,
h ¯ ( ν , ω ) = ( A π 2 θ M 2 / 2 r ) [ R r ( ω - s ) + R r ( ω + s ) ] ,
f ( ν , ν ) = A π θ M 2 r ( π / 2 ) 1 2 - [ R r ( ω - s ) + R r ( ω + s ) ] × sin ( ω - ω ) τ ( ω - ω ) d ω
= ( A n / ν v ) ( π / 2 ) 1 2 ( Si { [ ω - ( s - r ) ] τ } - Si { [ ω - ( s + r ) ] τ } + Si { [ ω + ( s - r ) ] τ } - Si { [ ω + ( s + r ) ] τ } ) ,

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