Abstract

Symmetrical sampling of an interferogram with respect to zero path difference is usually difficult to achieve in Michelson interferometers while off-center sampled interferograms require double-sided exponential Fourier transformation which is costly in computation time and degrades SNR. Several correction methods have been suggested by other authors that attempt to replace this transformation by an equivalent single-sided cosine transform. One such method utilizing a change of origin in the interferogram has been shown to lead to distorted spectra because of the effect of overlapping aliases. This distortion becomes particularly important for data involving smoothly varying spectra where over-all shape is important.

© 1972 Optical Society of America

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References

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  1. R. M. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).
  2. J. Connes, Rev. Opt. 40, 45, 101, 157, 213 (1961).
  3. M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Am. 56, 59 (1966).
    [CrossRef]
  4. E. V. Loewenstein, Appl. Opt. 2, 491 (1963).
    [CrossRef]
  5. J. E. Gibbs, H. A. Gebbie, Infra-Red Phys. 5, 187 (1965).
    [CrossRef]

1966 (1)

1965 (1)

J. E. Gibbs, H. A. Gebbie, Infra-Red Phys. 5, 187 (1965).
[CrossRef]

1963 (1)

1961 (1)

J. Connes, Rev. Opt. 40, 45, 101, 157, 213 (1961).

Bracewell, R. M.

R. M. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).

Connes, J.

J. Connes, Rev. Opt. 40, 45, 101, 157, 213 (1961).

Forman, M. L.

Gebbie, H. A.

J. E. Gibbs, H. A. Gebbie, Infra-Red Phys. 5, 187 (1965).
[CrossRef]

Gibbs, J. E.

J. E. Gibbs, H. A. Gebbie, Infra-Red Phys. 5, 187 (1965).
[CrossRef]

Loewenstein, E. V.

Steel, W. H.

Vanasse, G. A.

Appl. Opt. (1)

Infra-Red Phys. (1)

J. E. Gibbs, H. A. Gebbie, Infra-Red Phys. 5, 187 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

Rev. Opt. (1)

J. Connes, Rev. Opt. 40, 45, 101, 157, 213 (1961).

Other (1)

R. M. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).

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Figures (3)

Fig. 1
Fig. 1

Periodicity of Fourier transforms.

Fig. 2
Fig. 2

Interferogram sampled off-center.

Fig. 3
Fig. 3

Effect of change of origin on Fourier transform.

Equations (18)

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I ( x ) = 2 0 E ( k ) ( 1 + cos 2 π k x ) d k = 1 2 I ( 0 ) + 2 0 E ( k ) cos 2 π k x d x ,
F ( x ) = + E ( k ) exp ( 2 π i k x ) d k .
E ( k ) = + F ( x ) exp ( + 2 π i k x ) d x .
f ( k ) = 2 x 0 sinc ( 2 k x 0 ) = ( sin 2 π k x 0 ) / π k ,
F ( x ) = F ( x ) · III ( x / δ x ) .
F . . [ F ( x ) ] = F . . [ F ( x ) ] * III ( k δ x )
E ( k ) = E ( x ) * III ( k δ x ) ,
F ( x ) = F ( x + ) .
E ( k ) = + F ( x ) exp [ 2 π i k ( x + ) ] d x
E ( k ) = + F ( u ) exp ( 2 π i k u ) d u .
E ( k ) = 2 0 F ( u ) cos 2 π k u d u = 2 F ( x ) cos 2 π k ( x + ) d x .
E ( k ) = F ( 0 ) cos ( 2 π k ) δ x + 2 δ x n = 1 N F ( n δ x ) cos 2 π k ( + n δ x ) ,
x = 0 , δ x , 2 δ x , N δ x
u = , + δ x , + 2 δ x , + N δ x
F ( u ) = F ( u ) · A ( u ) · III [ ( u ) / δ x ] .
F . . [ III ( u δ x ) ] = δ x exp ( 2 π i k ) · III ( k δ x )
s ( k ) exp [ ( 2 π i n ) / δ x ] .
δ ( x ) · F ( 0 ) · cos 2 π k ( / 2 ) .

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