Abstract

A method is given of correcting the asymmetry of an interferogram, caused by either defects in the interferometer or off-center sampling. The method makes use of the phase error, which can be derived from the central portion of the interferogram or from a separate calibration. The technique avoids the disadvantages of the double-sided transform, normally used to derive the spectrum from such interferograms.

© 1966 Optical Society of America

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References

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  1. J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).
  2. J. Connes and P. Connes (private communication).
  3. J. Connes and V. Nozal, J. Phys. Radium 22, 359 (1961).
    [Crossref]

1961 (2)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

J. Connes and V. Nozal, J. Phys. Radium 22, 359 (1961).
[Crossref]

Connes, J.

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

J. Connes and V. Nozal, J. Phys. Radium 22, 359 (1961).
[Crossref]

J. Connes and P. Connes (private communication).

Connes, P.

J. Connes and P. Connes (private communication).

Nozal, V.

J. Connes and V. Nozal, J. Phys. Radium 22, 359 (1961).
[Crossref]

J. Phys. Radium (1)

J. Connes and V. Nozal, J. Phys. Radium 22, 359 (1961).
[Crossref]

Rev. Opt. (1)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).

Other (1)

J. Connes and P. Connes (private communication).

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Figures (5)

Fig. 1
Fig. 1

Correction of a slightly asymmetric interferogram. (a) Recorded interferogram. (b) Interferogram after filtering and correction for a phase error derived from the center of the interferogram. (c) The interferogram corrected for a phase error derived from a separate calibration of the interferometer.

Fig. 2
Fig. 2

Correction for a very asymmetric interferogram. (a) Recorded interferogram. (b) Interferogram after one application of correction technique; asymmetry is still present. (c) Interferogram after two corrections; the symmetry is improved.

Fig. 3
Fig. 3

Phase curves φ(ν) for the interferograms of Fig. 2. Full curve—uncorrected phase, broken curve—after first correction, dotted curve—after second correction.

Fig. 4
Fig. 4

Uncorrected and corrected interferograms for an N + NO reaction.

Fig. 5
Fig. 5

Spectra corresponding to the interferograms of Fig. 4; (a) spectrum obtained by double-sided transform, (b) cosine transform of uncorrected interferogram, (c) cosine transform of corrected interferogram.

Equations (15)

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M ( t ) = 2 0 B ( ν ) cos 2 π ν t d ν ,
M ( t ) = - + B ( ν ) e - 2 π i v t d ν ,
B ( ν ) = m ( ν ) = 2 0 M ( t ) cos 2 π ν t d t ,
M ( t ) = 2 0 B ( ν ) cos [ 2 π ν t + φ ( ν ) ] d ν ,
= - B ( ν ) e - i φ ( ν ) e - 2 π i ν t d ν ,
B ( ν ) e - i φ ( ν ) = m ( ν ) = - M ( t ) e 2 π i v t d t , = m r ( ν ) + i m i ( ν ) ,
B ( ν ) = m ( ν ) = [ m r 2 ( ν ) + m i 2 ( ν ) ] 1 2 ,
φ ( ν ) = - arg m ( ν ) , = - arctan [ m i ( ν ) / m r ( ν ) ] .
B ( ν ) = m ( ν ) e i φ ( ν ) , = m r ( ν ) cos φ ( ν ) - m i ( ν ) sin φ ( ν ) .
F ( t ) = - + e i φ ( ν ) e - 2 π i ν t d ν ,
F ( t ) = 2 0 cos φ ( ν ) cos 2 π ν t d ν + 2 0 sin φ ( ν ) sin 2 π ν t d ν .
b ( t ) = - + M ( t ) F ( t - t ) d t , = M ( t ) F ( t ) .
φ ( ν ) = 2 π ν .
F ( t ) = 1 τ sin π [ ( t - ) / τ ] π [ ( t - ) / τ ] = 1 τ sinc t - τ .
M ( m τ ) = 1 τ n = m - p m + p M ( + n τ ) sinc [ ( m - n ) t τ - τ ]