Abstract

A new type of interferometer, the moving-optical-wedge interferometer, is presented, and its principle and properties are studied. The novel interferometer consists of one beam splitter, two flat fixed mirrors, two fixed compensating plates, one fixed optical wedge, and one moving optical wedge. The optical path difference (OPD) as a function of the displacement of the moving optical wedge from the zero path difference position is accomplished by the straight reciprocating motion of the moving optical wedge. A large physical shift of the moving optical wedge corresponds to a very short OPD value of the new interferometer if the values of the wedge angle and the refractive index of the two optical wedges are given properly. The new interferometer is not so sensitive to the velocity variation of the moving optical wedge and the mechanical disturbances compared with the Michelson interferometer, and it is very applicable to low-spectral-resolution application for any wavenumber region from the far infrared down to the ultraviolet.

© 2008 Optical Society of America

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References

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  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]
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    [CrossRef] [PubMed]
  3. D. L. Cohen, “Performance degradation of a Michelson interferometer due to random sampling errors,” Appl. Opt. 38, 139-151 (1999).
    [CrossRef]
  4. A. S. Zachor and S. M. Aaronson, “Delay compensation: its effect in reducing sampling errors in Fourier spectroscopy,” Appl. Opt. 18, 68-75 (1979).
    [CrossRef] [PubMed]
  5. L. Palchetti and D. Lastrucci, “Spectral noise due to sampling errors in Fourier-transform spectroscopy,” Appl. Opt. 40, 3235-3243 (2001).

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Figures (4)

Fig. 1
Fig. 1

Optics of the moving-optical-wedge interferometer.

Fig. 2
Fig. 2

The light path of ray I transmitted through the two optical wedges.

Fig. 3
Fig. 3

Relationship between the factor F and the refractive index n ( α = 20 ° ).

Fig. 4
Fig. 4

Relationship between the factor F and the wedge angle α ( n = 1.51637 ).

Equations (41)

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l = u t ,
I ( x ) = B ( σ ) [ 1 + cos ( 2 π σ x ) ] ,
sin α = n sin θ 1 ,
n sin θ 2 = sin θ 3 = n sin θ 4 ,
n sin θ 5 = sin θ 6 = sin θ 6 ,
α = θ 1 + θ 2 = θ 4 + θ 5 ,
s = l tan α cos α = l sin α .
θ 1 = θ 5 = arcsin ( sin α / n ) ,
sin θ 2 = sin θ 4 = sin ( α θ 1 ) ,
θ 6 = θ 6 = α ,
sin θ 3 = n sin ( α θ 1 ) .
| D E ¯ | = s / cos θ 5 .
x = 2 ( | P Q ¯ | + | Q R ¯ | n + | R A ¯ | + | A B ¯ | n + | B C ¯ | + | C E ¯ | n + | E G ¯ | ) 2 ( | P L ¯ | n + | L M ¯ | + | M N ¯ | n + | N F ¯ | ) = 2 ( | P Q ¯ | + | Q R ¯ | n + | R A ¯ | + | A B ¯ | n + | B C ¯ | + | C E ¯ | n + | E G ¯ | ) 2 ( | P Q ¯ | + | Q R ¯ | n + | R A ¯ | + | A B ¯ | n + | B C ¯ | + | C D ¯ | n + | D H ¯ | ) = 2 ( | C E ¯ | | C D ¯ | ) n + 2 ( | E G ¯ | | D H ¯ | ) = 2 | D E ¯ | n 2 | D E ¯ | cos ( θ 6 θ 5 ) = 2 | D E ¯ | [ n cos θ 6 cos θ 5 sin θ 6 sin θ 5 ] .
x = 2 l sin α 1 ( sin α n ) 2 [ n cos α 1 ( sin α n ) 2 sin α sin α n ] = 2 sin α ( n 2 sin 2 α cos α ) l .
x = 2 sin α ( n 2 sin 2 α cos α ) u t .
I ( x ) = B ( σ ) { 1 + cos [ 2 π σ 2 sin α ( n 2 sin α cos α ) l ] } .
I ( x ) = B ( σ ) { 1 + cos [ 2 π σ 2 sin α ( n 2 sin 2 α cos α ) u t ] } .
x = F l ,
F = 2 sin α ( n 2 sin 2 α cos α ) .
F = 2 sin 20 ° ( n 2 ( sin 20 ° ) 2 cos 20 ° ) ,
F = 2 sin α ( 1 . 51637 2 sin 2 α cos α ) ,
sin 45 ° = n sin β ,
| O P ¯ | = | P L ¯ | = | Q R ¯ | = s / cos β ,
| A B ¯ | = d 1 / cos ( α θ 1 ) ,
| B C ¯ | = d 2 / cos θ 3 ,
| C D ¯ | = d 3 / cos θ 4 ,
| D H ¯ | = d 4 .
Δ 0 = | P Q ¯ | + | Q R ¯ | n + | R A ¯ | + | A B ¯ | n + | B C ¯ | + | C D ¯ | n + | D H ¯ | = d 5 + s cos β n + d 0 + d 1 cos ( α θ 1 ) n + d 2 cos θ 3 + d 3 cos θ 4 n + d 4 .
cos β = 1 sin 2 β = 1 ( sin 45 ° n ) 2 = 1 1 2 n 2 = 4 n 2 2 2 n ,
cos ( α θ 1 ) = cos α n n 2 sin 2 α + sin 2 α n ,
cos θ 3 = 1 sin 2 θ 3 = 1 [ n · sin ( α θ 1 ) ] 2 = 1 sin 2 α · ( n 2 sin 2 α cos α ) 2 ,
cos θ 4 = 1 sin 2 θ 4 = 1 sin 2 ( α θ 1 ) = 1 n n 2 sin 2 α ( n 2 sin 2 α cos α ) 2 .
Δ 0 = 2 s n 2 4 n 2 2 + d 5 + d 0 + d 4 + n 2 d 1 cos α n 2 sin 2 α + sin 2 α + d 2 1 ( n 2 sin 2 α cos α ) 2 sin 2 α + n 2 d 3 n 2 ( n 2 sin 2 α cos α ) 2 sin 2 α .
Δ 2 = 2 s n 2 4 n 2 2 + d 5 + d 0 + d 4 + n 2 d 1 cos α n 2 sin 2 α + sin 2 α + d 2 1 ( n 2 sin 2 α cos α ) 2 sin 2 α + n 2 d 3 n 2 ( n 2 sin 2 α cos α ) 2 sin 2 α
Δ 2 = | P L ¯ | n + | L M ¯ | + | M N ¯ | n + | N F ¯ | .
| L M ¯ | + | M N ¯ | n + | N F ¯ | = d 5 + d 0 + d 4 + n 2 d 1 cos α n 2 sin 2 α + sin 2 α + d 2 1 ( n 2 sin 2 α cos α ) 2 sin 2 α + n 2 d 3 n 2 ( n 2 sin 2 α cos α ) 2 sin 2 α .
| M N ¯ | n = | A B ¯ | n + | C D ¯ | n .
| M N ¯ | = s 0 / cos θ 1 .
s 0 = | M N ¯ | cos θ 1 = ( | A B ¯ | + | C D ¯ | ) cos θ 1 .
s 0 = ( d 1 cos ( α θ 1 ) + d 3 cos θ 4 ) 1 sin 2 θ 1 .
s 0 = ( d 1 cos α n n 2 sin 2 α + sin 2 α n + d 3 1 n n 2 sin 2 α ( n 2 sin 2 α cos α ) 2 ) 1 ( sin α n ) 2 = ( d 1 cos α n 2 sin 2 α + sin 2 α + d 3 n 2 sin 2 α ( n 2 sin 2 α cos α ) 2 ) n 2 sin 2 α .

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