Abstract

A new class of apodizing functions suitable for Fourier spectrometry (and similar applications) is introduced. From this class, three specific functions are discussed in detail, and the resulting instrumental line shapes are compared to numerous others proposed for the same purpose.

© 1976 Optical Society of America

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Corrections

R. H. Norton and R. Beer, "Errata: New Apodizing Functions For Fourier Spectrometry," J. Opt. Soc. Am. 67, 419-419 (1977)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-67-3-419

References

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  1. J. Connes, AFCRL-71-0019, pp. 83–115 (1971). .
  2. A. H. Filler, J. Opt. Soc. Am. 54, 762 (1964).
    [Crossref]
  3. A. E. Siegman, Appl. Opt. 13, 705 (1974).
    [Crossref] [PubMed]
  4. P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).
  5. J. Connes (private communication).
  6. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1959), p. 98.
  7. Perfect sampling implies that the occupied spectral interval exactly fills the alias.

1974 (1)

1967 (1)

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

1964 (1)

Beer, R.

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1959), p. 98.

Cayford, A. H.

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

Connes, J.

J. Connes (private communication).

J. Connes, AFCRL-71-0019, pp. 83–115 (1971). .

Fellgett, P.

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

Filler, A. H.

Siegman, A. E.

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1959), p. 98.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Phys. (Paris) (1)

P. Fellgett in printed comments on R. Beer and A. H. Cayford, J. Phys. (Paris) 28, C2–33 (1967).

Other (4)

J. Connes (private communication).

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover, New York, 1959), p. 98.

Perfect sampling implies that the occupied spectral interval exactly fills the alias.

J. Connes, AFCRL-71-0019, pp. 83–115 (1971). .

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Figures (6)

FIG. 1
FIG. 1

Filler diagram for about 1150 apodizing functions. The V-shaped patterns are from various families of functions, unidentified for clarity. Attention is drawn to the concentration of the plotted points into the upper right half of the diagram.

FIG. 2
FIG. 2

The preferred apodizing functions.

FIG. 3
FIG. 3

Instrumental line shape resulting from function 1 compared to sinc (function 0).

FIG. 4
FIG. 4

Instrumental line shape resulting from function 2 compared to sinc (function 0).

FIG. 5
FIG. 5

Instrumental line shape resulting from function 3 compared to sinc (function 0).

FIG. 6
FIG. 6

Filler diagram for the instrumental line shapes resulting from the preferred apodizations. The line represents the boundary seen in Fig. 1.

Tables (2)

Tables Icon

TABLE I Coefficients of the preferred apodizing functions.

Tables Icon

TABLE II Half-width, height, and position of the first 10 secondary maxima of the instrumental line shapes resulting from the preferred apodizations.a

Equations (8)

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log 10 h / h 0 1.939 - 1.401 ( W / W 0 ) - 0.597 ( W / W 0 ) 2 .
D α ( U ) = cos ( π U / 2 ) + α cos ( 3 π U / 2 )             0 α 1
E α ( U ) = 1 + ( 1 + α ) cos ( π U ) + α cos ( 2 π U )             0 α 1.
P α ( U ) = 1 + p + ( 1 + α ) cos ( π U ) + α cos ( 2 π U ) ,             - 1 α 1 ,             0 p 1
F N ( U ) = i = 0 n C i ( 1 - U 2 ) i ;             i = 0 n C i 1 , N = 0 , 1 , 2 , 3.
C 0 = 0.23977 , C 1 = 0.45806 , C 2 = 0.22498 , C 3 = 0.07719 ,
I N ( σ ) = i = 0 n C i Q i ,             N = 0 , 1 , 2 , 3.
Q 0 = 1 - a 2 6 + a 4 120 - a 6 5040 + a 8 362 880 - , Q 1 = 1 - a 2 10 + a 4 280 - a 6 15 120 + a 8 1 330 560 - , Q 2 = 1 - a 2 14 + a 4 504 - a 6 33 264 + a 8 3 459 456 - , Q 3 = 1 - a 2 18 + a 4 792 - a 6 61 776 + a 8 7 413 120 - , Q 4 = 1 - a 2 22 + a 4 1144 - a 6 102 960 + a 8 14 002 560 - ,