Abstract

A novel type of interferometer, the moving-mirror-pair interferometer, is presented, and its principle and properties are studied. The new interferometer is built with three flat mirrors, which include two flat moving mirrors fixed as a single moving part by a rigid structure and one flat fixed mirror. The optical path difference (OPD) is obtained by the straight reciprocating motion of the double moving mirror, and the OPD value is four times the physical shift value of the double moving mirror. The tilt tolerance of the double moving mirror of the novel interferometer is systematically analyzed by means of modulation depth and phase error. Where the square aperture is concerned, the formulas of the tilt tolerance were derived. Due to the novel interferometer’s large OPD value and low cost, it is very applicable to the high-spectral-resolution Fourier-transform spectrometers for any wavenumber region from the far infrared to the ultraviolet.

© 2008 Optical Society of America

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References

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  1. J. K. Kauppinen, I. K. Salomaa, and J. O. Partanen, “Carousel interferometer,” Appl. Opt. 34, 6081-6085 (1995).
    [CrossRef] [PubMed]
  2. D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl.Opt. 36, 4034-4042 (1997).
    [CrossRef] [PubMed]
  3. G. W. Stroke, “Photoelectric fringe signal information and range in interferometers with moving mirrors,” J. Opt. Soc. Am. 47, 1097-1103 (1957).
    [CrossRef]
  4. J. Connes and P. Connes, “Near-infrared planetary spectra by Fourier spectroscopy. I. Instruments and results,” J. Opt. Soc. Am. 56, 896-910 (1966).
    [CrossRef]
  5. J. Kauppinen and V.-M. Horneman, “Large aperture cube corner interferometer with a resolution of 0.001 cm−1,” Appl. Opt. 30, 2575-2578 (1991).
    [CrossRef] [PubMed]
  6. J. Kauppinen and P. Saarinen, “Line-shape distortions in misaligned cube corner interferometers,” Appl. Opt. 31, 69-74 (1992).
    [CrossRef] [PubMed]
  7. R. Beer and D. Marjaniemi, “Wavefronts and construction tolerances for a cat's-eye retroreflector,” Appl. Opt. 5, 1191-1197 (1966).
    [CrossRef] [PubMed]
  8. M. V. R. K. Mutry, “Some more aspects of the Michelson interferometer with cube corners,” J. Opt. Soc. Am. 50, 7-10 (1960).
    [CrossRef]
  9. R. L. White, “Performance of an FT-IR with a cube-corner interferometer,” Appl. Spectrosc. 39, 320-326 (1985).
    [CrossRef]
  10. J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99-129 (2004).
    [CrossRef]

2004 (1)

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99-129 (2004).
[CrossRef]

1997 (1)

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl.Opt. 36, 4034-4042 (1997).
[CrossRef] [PubMed]

1995 (1)

1992 (1)

1991 (1)

1985 (1)

1966 (2)

1960 (1)

1957 (1)

Beer, R.

Cohen, D. L.

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl.Opt. 36, 4034-4042 (1997).
[CrossRef] [PubMed]

Connes, J.

Connes, P.

Heinonen, J.

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99-129 (2004).
[CrossRef]

Horneman, V.-M.

Kauppinen, I.

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99-129 (2004).
[CrossRef]

Kauppinen, J.

Kauppinen, J. K.

Marjaniemi, D.

Mutry, M. V. R. K.

Partanen, J. O.

Saarinen, P.

Salomaa, I. K.

Stroke, G. W.

White, R. L.

Appl. Opt. (4)

Appl. Spectrosc. (1)

Appl. Spectrosc. Rev. (1)

J. Kauppinen, J. Heinonen, and I. Kauppinen, “Interferometers based on the rotational motion,” Appl. Spectrosc. Rev. 39, 99-129 (2004).
[CrossRef]

Appl.Opt. (1)

D. L. Cohen, “Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series,” Appl.Opt. 36, 4034-4042 (1997).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (3)

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Figures (6)

Fig. 1
Fig. 1

Optics of the moving-mirror-pair interfero meter.

Fig. 2
Fig. 2

Equivalent sketch maps of the light path (a) with the tilted double moving mirror and (b) when the tilt angle of moving mirror 1 is θ and that of moving mirror 2 is θ + β (the angle between the two moving mirrors is β).

Fig. 3
Fig. 3

Sketch of the integral of the interference intensity for a square aperture.

Fig. 4
Fig. 4

Optical path difference x created by a moving-mirror-pair interferometer of typical dimensions (a) ( L = 10 mm , x 0 = 20 mm ) and (b) ( L = 20 mm , x 0 = 40 mm )as a function of the tilt angle θ ( θ [ π / 180 , π / 180 ] , i.e., θ [ 1 ° , 1 ° ] ).

Fig. 5
Fig. 5

Optical path difference x created by a moving-mirror-pair interferometer (a) of typical dimensions ( L 1 = 290 mm , L 2 = 310 mm , β = π / 10 , 800 ) as a function of the tilt angle θ ( θ [ π / 150 , π / 180 ] , i.e. θ [ 1 . 2 ° , 1 ° ] ) and (b) of typical dimensions ( L 1 = 290 mm , L 2 = 310 mm , β = π / 2160 ) as a function of the tilt angle θ ( θ [ π / 90 , π / 180 ] , i.e., θ [ 2 ° , 1 ° ] ).

Fig. 6
Fig. 6

Optics of the moving-mirror-pair interferometer with a compensating plate and a plane-parallel plate of glass.

Equations (42)

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I ( x ) = B ( σ ) [ 1 + cos ( 2 π σ x ) ] ,
x c = L cos 2 θ L = 2 L sin 2 θ cos 2 θ ,
m = m 2 m 1 = ( L 2 L 1 ) tan 2 θ = L tan 2 θ ,
L = L 2 L 1 ,
m 1 = L 1 tan 2 θ ,
m 2 = L 2 tan 2 θ ,
S = S 1 + S 2 .
S = D ( D m 1 ) ,
I ( x 0 ) = 1 S s 1 B ( σ ) { 1 + cos [ 2 π σ ( x 0 + x c + δ x ) ] } · d S 1 + 1 S s 2 B ( σ ) d S 2 ,
δ x = ( ξ m 2 d ) tan θ · ( 1 + 1 cos 2 θ ) ( ξ m 1 d ) tan θ · ( 1 + 1 cos 2 θ ) = m tan 2 θ ,
I ( x 0 ) = 1 S s 1 B ( σ ) { 1 + cos { 2 π σ [ x 0 + x c m tan 2 θ ] } } · d S 1 + 1 S s 2 B ( σ ) d S 2 .
I ( x 0 ) = B ( σ ) + 1 S s 1 B ( σ ) · cos { 2 π σ [ x 0 + x c m tan 2 θ ] } · d S 1 .
I ( x 0 ) = B ( σ ) { 1 + D m 2 D m 1 cos [ 2 π σ ( x 0 + x c m tan 2 θ ) ] } .
I ( x 0 ) = B ( σ ) { 1 + D L 2 tan 2 θ D L 1 tan 2 θ cos { 2 π σ [ x 0 + 2 L sin 2 θ cos 2 θ L tan 2 2 θ ] } } .
M ( D , L 1 , L 2 , θ ) = D L 2 tan 2 θ D L 1 tan 2 θ ,
φ ( L , θ ) = 2 π σ ( 2 L sin 2 θ cos 2 θ L tan 2 2 θ ) ,
x = x 0 + 2 L sin 2 θ cos 2 θ L tan 2 2 θ = 2 L + 2 L sin 2 θ cos 2 θ L tan 2 2 θ .
x c = L 2 cos 2 ( θ + β ) L 1 cos 2 θ ( L 2 L 1 ) = L 2 cos 2 ( θ + β ) L 1 cos 2 θ + L 1 L 2 ,
δ x = ( ξ d ) tan ( θ + β ) · ( 1 + 1 cos 2 ( θ + β ) ) ( ξ d ) tan θ · ( 1 + 1 cos 2 θ ) = ( ξ d ) [ tan 2 ( θ + β ) tan 2 θ ] ,
m 1 = L 1 tan 2 θ ,
m 2 = L 2 tan 2 ( θ + β ) ,
δ x = ( ξ m 2 d ) tan 2 ( θ + β ) ( ξ m 1 d ) tan 2 θ .
I ( x 0 ) = B ( σ ) + 1 S s 1 B ( σ ) · cos { 2 π σ [ x 0 + x c + δ x ] } · d S 1 .
I ( x 0 ) = B ( σ ) + 1 S s 1 B ( σ ) · cos { 2 π σ [ x 0 + x c + ( ξ m 2 d ) tan 2 ( θ + β ) ( ξ m 1 d ) tan 2 θ ] } · d S 1 .
I ( x 0 ) = B ( σ ) { 1 + 1 D m 1 · 1 2 π σ · [ tan 2 ( θ + β ) tan 2 θ ] { sin { 2 π σ [ x 0 + x c + ( ξ m 2 d ) tan 2 ( θ + β ) ( ξ m 1 d ) tan 2 θ ] } } m 2 D 2 D 2 } .
{ sin { 2 π σ [ x 0 + x c + ( ξ m 2 d ) tan 2 ( θ + β ) ( ξ m 1 d ) tan 2 θ ] } } m 2 D 2 D 2 = 2 sin { π σ ( D m 2 ) [ tan 2 ( θ + β ) tan 2 θ ] } cos { 2 π σ [ x 0 + x c ( d + m 2 2 ) tan 2 ( θ + β ) + ( d + m 1 m 2 2 ) tan 2 θ ] } ,
I ( x 0 ) = B ( σ ) { 1 + D m 2 D m 1 · sin { π σ ( D m 2 ) [ tan 2 ( θ + β ) tan 2 θ ] } π σ ( D m 2 ) [ tan 2 ( θ + β ) tan 2 θ ] cos { 2 π σ [ x 0 + x c + ( d + m 1 m 2 2 ) tan 2 θ ( d + m 2 2 ) tan 2 ( θ + β ) ] } } .
I ( x 0 ) = B ( σ ) { 1 + D L 2 tan 2 ( θ + β ) D L 1 tan 2 θ · sin { π σ [ D L 2 tan 2 ( θ + β ) ] [ tan 2 ( θ + β ) tan 2 θ ] } π σ [ D L 2 tan 2 ( θ + β ) ] [ tan 2 ( θ + β ) tan 2 θ ] cos { 2 π σ [ x 0 + L 2 cos 2 ( θ + β ) L 1 cos 2 θ + L 1 L 2 + ( d + L 1 tan 2 θ L 2 tan 2 ( θ + β ) 2 ) tan 2 θ ( d + L 2 tan 2 ( θ + β ) 2 ) tan 2 ( θ + β ) ] } } .
M ( D , L 1 , L 2 , θ , β ) = D L 2 tan 2 ( θ + β ) D L 1 tan 2 θ · sin { π σ [ D L 2 tan 2 ( θ + β ) ] [ tan 2 ( θ + β ) tan 2 θ ] } π σ [ D L 2 tan 2 ( θ + β ) ] [ tan 2 ( θ + β ) tan 2 θ ] ,
φ ( d , L 1 , L 2 , θ , β ) = 2 π σ [ L 2 cos 2 ( θ + β ) L 1 cos 2 θ + L 1 L 2 + ( d + L 1 tan 2 θ L 2 tan 2 ( θ + β ) 2 ) tan 2 θ ( d + L 2 tan 2 ( θ + β ) 2 ) tan 2 ( θ + β ) ] ,
x = x 0 + L 2 cos 2 ( θ + β ) L 1 cos 2 θ + L 1 L 2 + ( d + L 1 tan 2 θ L 2 tan 2 ( θ + β ) 2 ) tan 2 θ ( d + L 2 tan 2 ( θ + β ) 2 ) tan 2 ( θ + β ) = L 2 L 1 + L 2 cos 2 ( θ + β ) L 1 cos 2 θ + ( d + L 1 tan 2 θ L 2 tan 2 ( θ + β ) 2 ) tan 2 θ ( d + L 2 tan 2 ( θ + β ) 2 ) tan 2 ( θ + β ) .
M ( D , L 1 , L 2 , θ ) = D L 2 tan 2 θ D L 1 tan 2 θ = 0.9 .
θ = 1 2 arctan D 10 ( L 2 0.9 L 1 ) .
θ max = 1 2 arctan D 10 ( L 2 max 0.9 L 1 min ) .
| δ x k | = | x θ k x k | λ SNR .
{ 2 π σ x k = ( 2 k + 1 2 ) π 2 π σ ( x θ k + 2 L sin 2 θ cos 2 θ L tan 2 2 θ ) = ( 2 k + 1 2 ) π { x k = 4 k + 1 4 λ x θ k = 4 k + 1 4 λ ( 2 L sin 2 θ cos 2 θ L tan 2 2 θ ) ,
| 2 L sin 2 θ cos 2 θ L tan 2 2 θ | λ SNR .
| 2 L θ 2 | λ SNR .
θ λ 2 · | L | · SNR .
θ λ 2 · | L 2 L 1 | · SNR .
θ max = λ 2 · | L max | · SNR = λ | Δ max | · SNR ,
θ max = λ 4 · | l max | · SNR .

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