Abstract

An analysis is presented of the intensity of ghostlines, caused by a periodic nonlinearity in the travel of the movable mirror in a two-beam Fourier spectrometer, used in the step-record mode. The ghostlines are studied for two cases: (1) for a modulus spectrum calculated after a complex Fourier transform; (2) for a spectrum calculated by a cosine Fourier transform after symmetrizing the measured interferogram. In the latter case, the intensity of the ghostlines is also dependent on the position of the center of the interferogram. This dependence has been examined theoretically and verified experimentally for the case of a monochromatic source. It is shown that an appropriate choice of the position of the center of the interferogram and the use of a cosine Fourier transform can reduce the intensity of the ghostlines drastically in practice.

© 1983 Optical Society of America

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References

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  1. J. Connes, Rev. Opt. Theor. Instrum. 40, 45 (1961).
  2. A. S. Zachor, Appl. Opt. 16, 1412 (1977).
    [CrossRef] [PubMed]
  3. M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
    [CrossRef]
  4. T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).
  5. A. S. Zachor, S. M. Aaronson, Appl. Opt. 18, 68 (1979).
    [CrossRef] [PubMed]
  6. A. S. Zachor, I. Coleman, W. G. Mankin, Spectrometric Techniques (Academic, New York, 1981), Chap. 3.
  7. G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
    [CrossRef]
  8. H. Sakai, G. A. Vanasse, M. L. Forman, J. Opt. Soc. Am. 58, 84 (1968).
    [CrossRef]
  9. For a review, see Sh. M. Kogan, T. M. Lifshits, Phys. Status Solidi A 39, 11 (1977).
    [CrossRef]
  10. H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
    [CrossRef]

1980 (1)

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

1979 (2)

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

A. S. Zachor, S. M. Aaronson, Appl. Opt. 18, 68 (1979).
[CrossRef] [PubMed]

1977 (2)

A. S. Zachor, Appl. Opt. 16, 1412 (1977).
[CrossRef] [PubMed]

For a review, see Sh. M. Kogan, T. M. Lifshits, Phys. Status Solidi A 39, 11 (1977).
[CrossRef]

1975 (1)

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

1969 (1)

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

1968 (1)

1961 (1)

J. Connes, Rev. Opt. Theor. Instrum. 40, 45 (1961).

Aaronson, S. M.

Chamberlain, J.

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

Chantry, G. W.

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

Coleman, I.

A. S. Zachor, I. Coleman, W. G. Mankin, Spectrometric Techniques (Academic, New York, 1981), Chap. 3.

Connes, J.

J. Connes, Rev. Opt. Theor. Instrum. 40, 45 (1961).

Evans, H. M.

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

Forman, M. L.

Gebbie, H. A.

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

Jongbloets, H. W. H. M.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

Kogan, Sh. M.

For a review, see Sh. M. Kogan, T. M. Lifshits, Phys. Status Solidi A 39, 11 (1977).
[CrossRef]

Lifshits, T. M.

For a review, see Sh. M. Kogan, T. M. Lifshits, Phys. Status Solidi A 39, 11 (1977).
[CrossRef]

Mankin, W. G.

A. S. Zachor, I. Coleman, W. G. Mankin, Spectrometric Techniques (Academic, New York, 1981), Chap. 3.

Masutani, K.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Morii, M.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Nishiyama, T.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Ohno, M.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Sakai, H.

Stoelinga, J. H. M.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

Ura, N.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

van de Steeg, M. J. H.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

van der Heijden, R. W.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

van Vucht, R. J. M.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

Vanasse, G. A.

Wyder, P.

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

Yamauchi, T.

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Zachor, A. S.

A. S. Zachor, S. M. Aaronson, Appl. Opt. 18, 68 (1979).
[CrossRef] [PubMed]

A. S. Zachor, Appl. Opt. 16, 1412 (1977).
[CrossRef] [PubMed]

A. S. Zachor, I. Coleman, W. G. Mankin, Spectrometric Techniques (Academic, New York, 1981), Chap. 3.

Appl. Opt. (2)

Infrared Phys. (2)

M. J. H. van de Steeg, H. W. H. M. Jongbloets, J. H. M. Stoelinga, R. W. van der Heijden, R. J. M. van Vucht, P. Wyder, Infrared Phys. 20, 121 (1980).
[CrossRef]

G. W. Chantry, H. M. Evans, J. Chamberlain, H. A. Gebbie, Infrared Phys. 9, 85 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

T. Nishiyama, T. Yamauchi, M. Ohno, M. Morii, N. Ura, K. Masutani, Jpn. J. Appl. Phys. 14, Suppl. 14-1, 67 (1975).

Phys. Rev. B (1)

H. W. H. M. Jongbloets, J. H. M. Stoelinga, M. J. H. van de Steeg, P. Wyder, Phys. Rev. B 20, 3328 (1979).
[CrossRef]

Phys. Status Solidi A (1)

For a review, see Sh. M. Kogan, T. M. Lifshits, Phys. Status Solidi A 39, 11 (1977).
[CrossRef]

Rev. Opt. Theor. Instrum. (1)

J. Connes, Rev. Opt. Theor. Instrum. 40, 45 (1961).

Other (1)

A. S. Zachor, I. Coleman, W. G. Mankin, Spectrometric Techniques (Academic, New York, 1981), Chap. 3.

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Figures (5)

Fig. 1
Fig. 1

Deviation from a linear translation as a function of the position of the movable mirror: continuous curve, measured deviation; dashed curve, description of the measured deviation by the first two terms of a Fourier analysis.

Fig. 2
Fig. 2

Measured modulus spectrum at PCI = 0 μm using a monochromatic source.

Fig. 3
Fig. 3

Measured real spectra for different PCIs within one revolution period of the micrometer using a monochromatic source.

Fig. 4
Fig. 4

Intensities of ghostlines R1, R2, and R3 as a function of the PCI taken from the real spectra and normalized to the intensity of the monochromatic line.

Fig. 5
Fig. 5

Photoconductivity spectra for a high-purity germanium sample originating from one interferogram: (a) real spectrum, (b) modulus spectrum. The expected line positions for boron, aluminium, gallium, and indium shallow acceptor impurities and the spectral resolution are indicated in the upper part of this figure. The structure indicated by the arrows is ascribed to ghostlines.

Tables (1)

Tables Icon

Table I Values for the Parameters [Defined in Eq. (6)] of the First Three Terms of the Fourier Expansion of the Periodic Nonlinearity in the Travel of the Movable Mirrora

Equations (8)

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x = x + ε · sin [ 2 π ( x x 0 ) / L ] .
I ( x ) = S · cos ( 4 π σ 0 { ( x x c ) + ε · sin [ 2 π ( x x 0 ) / L ] } ) ,
I ( x ) = S · n = J n ( 4 π σ 0 ε ) · cos [ 2 π n ( x 0 x c ) / L ] · cos [ 4 π ( σ 0 + n 2 L ) · ( x x c ) ] + S · n = J n ( 4 π σ 0 ε ) · sin [ 2 π n ( x 0 x c ) / L ] · sin [ 4 π ( σ 0 + n 2 L ) · ( x x c ) ] .
P ( σ n ) = S · | J n ( 4 π σ 0 ε ) |
S ( σ n ) = S · J n ( 4 π σ 0 ε ) · cos [ 2 π n ( x 0 x c ) / L ]
x x = m = 1 ε m · sin [ 2 π m ( x x 0 , m ) / L ] .
P ( σ m , 1 ) = S · | J 1 ( 4 π σ 0 ε m ) | ,
S ( σ m , 1 ) = S · J 1 ( 4 π σ 0 ε m ) · cos [ 2 π m ( x 0 , m x c ) / L ] .

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