Abstract

Apodization is a mathematical tool used in Fourier transform spectrometry to reduce the spurious oscillation in the output spectrum. We investigate Norton–Beer apodizing functions and take advantage of the main series to introduce a family of new functions. They weigh the interferogram to zero continuously within the same optical path difference and, accordingly, improve the convergence property of the instrumental line shape (ILS) for the apodized spectrum. In the meantime, the range of spectral smearing is well reduced. Compared with the Norton–Beer functions, the new functions are more flexible in practice and are more applicable with regard to distinguishing the spectral lines, especially the weak lines, which are not too close to the center of a strong line but are still susceptible to the ringing of ILS.

© 2012 Optical Society of America

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References

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  1. H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
    [CrossRef]
  2. U. Amato, D. De Canditiis, and C. Serio, “Effect of apodization on the retival of geophysical parameters form Fourier-transform spectrometers,” Appl. Opt. 37, 6537–6543 (1998).
    [CrossRef]
  3. S. Ceccherini, C. Belotti, B. Carli, and P. Raspollini, “Use of apodization in quantitative spectrometer,” Opt. Lett. 32, 1329–1331 (2007).
    [CrossRef]
  4. A. S. Filler, “Apodization and interpolation in Fourier transform spectrometer,” J. Opt. Soc. Am. 54, 762–767 (1964).
    [CrossRef]
  5. R. H. Norton and R. Beer, “New apodizing functions for Fourier spectrometry,” J. Opt. Soc. Am. 66, 259–264(1976).
    [CrossRef]
  6. R. H. Norton and R. Beer, “New apodizing functions for Fourier spectrometry: errata,” J. Opt. Soc. Am. 67, 419(1977).
    [CrossRef]
  7. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
    [CrossRef]
  8. A. H. Nuttal, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-29, 84–91 (1981).
    [CrossRef]
  9. P. A. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometer, 2nd ed. (Wiley, 2007).
  10. J. H. Park, “Effect of interferogram smearing on atmospheric limb sounding by Fourier transform spectrometer,” Appl. Opt. 21, 1356–1366 (1982).
    [CrossRef]
  11. C. D. Boone, S. D. Mcleod, and P. Bernath, “Apodization effect in the retrieval of volume mixing ratio profiles,” Appl. Opt. 41, 1029–1034 (2002).
    [CrossRef]
  12. D. A. Naylor and M. K. Tahic, “Apodizing functions for Fourier transform spectroscopy,” J. Opt. Soc. Am. A 24, 3644–3648 (2007).
    [CrossRef]

2007 (2)

2003 (1)

H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
[CrossRef]

2002 (1)

1998 (1)

1982 (1)

1981 (1)

A. H. Nuttal, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-29, 84–91 (1981).
[CrossRef]

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

1977 (1)

1976 (1)

1964 (1)

Amato, U.

Beer, R.

Belotti, C.

Bernath, P.

Boone, C. D.

Carli, B.

Ceccherini, S.

De Canditiis, D.

de Haseth, J. A.

P. A. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometer, 2nd ed. (Wiley, 2007).

Filler, A. S.

Griffiths, P. A.

P. A. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometer, 2nd ed. (Wiley, 2007).

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Jianwen, H.

H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
[CrossRef]

Mcleod, S. D.

Naylor, D. A.

Norton, R. H.

Nuttal, A. H.

A. H. Nuttal, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-29, 84–91 (1981).
[CrossRef]

Park, J. H.

Raspollini, P.

Serio, C.

Tahic, M. K.

Wang, M.

H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
[CrossRef]

Wang, P.

H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
[CrossRef]

Appl. Opt. (3)

IEEE Trans. Acoust. Speech Signal Proc. (1)

A. H. Nuttal, “Some windows with very good sidelobe behavior,” IEEE Trans. Acoust. Speech Signal Proc. ASSP-29, 84–91 (1981).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Proc. IEEE (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Proc. SPIE (1)

H. Jianwen, P. Wang, and M. Wang, “Fourier interferometry for space-borne atmospheric sounding,” Proc. SPIE 4891, 169–179 (2003).
[CrossRef]

Other (1)

P. A. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometer, 2nd ed. (Wiley, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Weak, medium, and strong Norton–Beer apodizing functions.

Fig. 2.
Fig. 2.

Profiles of q0(u) functions. As the m value increases from 1 to 16, q0(u) approaches the boxcar function.

Fig. 3.
Fig. 3.

(a1) Weak window functions (dashed line is the original function, and solid line is the new function); (a2) Comparison of ILSs corresponding to the weak functions; (a3) Sidelobe details corresponding to the ILSs; (b1–b3) Figure series corresponding to the medium functions; (c1–c3) Figure series corresponding to the strong functions.

Tables (2)

Tables Icon

Table 1. Coefficients of the Norton–Beer Weak, Medium, and Strong Apodizing Functions [6]

Tables Icon

Table 2. FWHM, Height, and Position of the First Five Minima of the DL Functions Compared With Those of the Norton–Beer Functions

Equations (11)

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I(δ)=+B(σ)exp(j2πσδ)dσ=FT1{B(σ)},B(σ)=+I(δ)exp(j2πσδ)dδ=FT{I(δ)},
B(σ)=L+LI(δ)exp(j2πσδ)dδ.
IL(δ)=Π(δ)I(δ),BL(σ)=W(σ)*B(σ),
FN(δL)=i=0nCi(1(δL)2)i,i=0nCi=1,n=0,1,2,3.
log10|h/h0|1.9391.401(W/W0)0.597(W/W0)2,
q0(u)=12[1+cos(π·um)]u=δL,mN.
{q0(0)=1q0(±1)=0,
{q0(u)=mπ2um1sin(πum)limu1+q0(u)=0,limu+1q0(u)=0.
DL(u)=C012[1+cos(πum)]+i=1nCi(1u2)i;n=1,2,3,
{DL(0)=i=0nCi=1DL(±1)=0.
DL(u)=C112[1+cos(πum)]+i=2nCi(1u2)i;n=2,3,4.

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