Abstract

The effective position of a strong line partially blended with a weaker one is found as a function of their separation for three different line profiles and two line-position criteria. Some practical examples illustrate the use of the results.

© 1978 Optical Society of America

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References

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  1. J. Hartmann, “Ueber die Ausmessung und Reduction der photographischen Aufnahmen von Sternspektren,” Astron. Machr. 155, 81–118 (1901).
    [Crossref]
  2. We may regard noise in the spectrum as equivalent to many random weak blending lines; hence, the peak is less affected by noise than the other criteria, if the noise is filtered to the same spectral resolution as the signal.
  3. L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
    [Crossref]
  4. L. D. Gray, “Relative intensity calculation for carbon dioxide-III. Relative line intensities of transition from the vibrational ground state for temperatures from 160 ° to 280 °K,” J. Quant. Spectrosc. Radiat. Transfer 7, 795–803 (1967).
    [Crossref]
  5. L. D. Gray, R. A. Schorn, and E. S. Barker, “High dispersion spectroscopic observations of Venus IV. The weak carbon dioxide band at 7883 Å,” Appl. Opt. 8, 2087–2093 (1969).
    [Crossref] [PubMed]
  6. L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).
  7. L. D. G. Young, “High resolution spectra of Venus—A Review,” Icarus 17, 632–658 (1972).
    [Crossref]
  8. But note that a reduction in the HWHM to 0.08 cm−1 would give practically the same result for a Gaussian profile as 0.09 cm−1 gives for a Lorentzian.
  9. R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).
  10. C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).
  11. “The half-width of the slit image” corresponds to 14.8 μ m on the plate, but the full projected width of the slit is given9 as 15 μ m. This must be degraded considerably by the photographic line-spread function. A HWHM near 15 μ m is typical of fast spectroscopic plates in the blue (unsensitized) region.
  12. C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).
  13. P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
    [Crossref]
  14. An exact solution for two-component blends of unequal widths was published by J. B. Tatum15 ten years ago, but it is so unwieldy that it has never been used in practical cases.
  15. J. B. Tatum, “The blending effect in the measurement of spectroscopic binary spectra,” Mon. Not. R. Astron. Soc. 141, 43–55 (1968).

1977 (1)

P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
[Crossref]

1972 (1)

L. D. G. Young, “High resolution spectra of Venus—A Review,” Icarus 17, 632–658 (1972).
[Crossref]

1971 (1)

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

1970 (1)

L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
[Crossref]

1969 (1)

1968 (1)

J. B. Tatum, “The blending effect in the measurement of spectroscopic binary spectra,” Mon. Not. R. Astron. Soc. 141, 43–55 (1968).

1967 (1)

L. D. Gray, “Relative intensity calculation for carbon dioxide-III. Relative line intensities of transition from the vibrational ground state for temperatures from 160 ° to 280 °K,” J. Quant. Spectrosc. Radiat. Transfer 7, 795–803 (1967).
[Crossref]

1966 (1)

C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).

1958 (1)

R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).

1901 (1)

J. Hartmann, “Ueber die Ausmessung und Reduction der photographischen Aufnahmen von Sternspektren,” Astron. Machr. 155, 81–118 (1901).
[Crossref]

Adams, E. F.

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

Andrews, D. H.

R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).

Babcock, H. D.

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

Barker, E. S.

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

L. D. Gray, R. A. Schorn, and E. S. Barker, “High dispersion spectroscopic observations of Venus IV. The weak carbon dioxide band at 7883 Å,” Appl. Opt. 8, 2087–2093 (1969).
[Crossref] [PubMed]

Conti, P. S.

P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
[Crossref]

Gray, L. D.

L. D. Gray, R. A. Schorn, and E. S. Barker, “High dispersion spectroscopic observations of Venus IV. The weak carbon dioxide band at 7883 Å,” Appl. Opt. 8, 2087–2093 (1969).
[Crossref] [PubMed]

L. D. Gray, “Relative intensity calculation for carbon dioxide-III. Relative line intensities of transition from the vibrational ground state for temperatures from 160 ° to 280 °K,” J. Quant. Spectrosc. Radiat. Transfer 7, 795–803 (1967).
[Crossref]

Gray Young, L. D.

L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
[Crossref]

Hartmann, J.

J. Hartmann, “Ueber die Ausmessung und Reduction der photographischen Aufnahmen von Sternspektren,” Astron. Machr. 155, 81–118 (1901).
[Crossref]

Houtgast, J.

C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).

John, C. E. St.

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

Leep, E. M.

P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
[Crossref]

Lorre, J. J.

P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
[Crossref]

McDonald, J. K.

R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).

Minnaert, M. G. J.

C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).

Moore, C. E.

C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

Petrie, R. M.

R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).

Schorn, R. A.

L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
[Crossref]

L. D. Gray, R. A. Schorn, and E. S. Barker, “High dispersion spectroscopic observations of Venus IV. The weak carbon dioxide band at 7883 Å,” Appl. Opt. 8, 2087–2093 (1969).
[Crossref] [PubMed]

Schorn, R. A. J.

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

Tatum, J. B.

J. B. Tatum, “The blending effect in the measurement of spectroscopic binary spectra,” Mon. Not. R. Astron. Soc. 141, 43–55 (1968).

Ware, L. M.

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

Woszczyk, A.

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

Young, A. T.

L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
[Crossref]

Young, L. D. G.

L. D. G. Young, “High resolution spectra of Venus—A Review,” Icarus 17, 632–658 (1972).
[Crossref]

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

Acta Astron. (1)

L. D. G. Young, R. A. J. Schorn, E. S. Barker, and A. Woszczyk, “High dispersion spectroscopic observations of Venus during 1968 and 1969. I. The carbon dioxide bands at 7820 Å and 7883 Å,” Acta Astron. 21, 329–363 (1971).

Appl. Opt. (1)

Astron. Machr. (1)

J. Hartmann, “Ueber die Ausmessung und Reduction der photographischen Aufnahmen von Sternspektren,” Astron. Machr. 155, 81–118 (1901).
[Crossref]

Astrophys. J. (1)

P. S. Conti, E. M. Leep, and J. J. Lorre, “Spectroscopic studies of O-type stars. VIII. Radial velocities and the K-term,” Astrophys. J. 214, 759–772 (1977).
[Crossref]

Icarus (1)

L. D. G. Young, “High resolution spectra of Venus—A Review,” Icarus 17, 632–658 (1972).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (2)

L. D. Gray Young, A. T. Young, and R. A. Schorn, “Improved Constants for the 7820 Å and 7883 Å bands of CO2,” J. Quant. Spectrosc. Radiat. Transfer 10, 1291–1300 (1970).
[Crossref]

L. D. Gray, “Relative intensity calculation for carbon dioxide-III. Relative line intensities of transition from the vibrational ground state for temperatures from 160 ° to 280 °K,” J. Quant. Spectrosc. Radiat. Transfer 7, 795–803 (1967).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

J. B. Tatum, “The blending effect in the measurement of spectroscopic binary spectra,” Mon. Not. R. Astron. Soc. 141, 43–55 (1968).

Natl. Bur. Stand. (U.S.) Monog. 61 (1)

C. E. Moore, M. G. J. Minnaert, and J. Houtgast, “The solar spectrum 2935 Å to 8770 Å, Natl. Bur. Stand. (U.S.) Monog. 61 (1966).

Publ. Dom. Astrophys. Obs., Victoria, B. C. (1)

R. M. Petrie, D. H. Andrews, and J. K. McDonald, “Wave-length standards for radial-velocity determinations. Spectral types A3-K8 with low dispersion,” Publ. Dom. Astrophys. Obs., Victoria, B. C. 10, 415–423 (1958).

Other (5)

C. E. St. John, C. E. Moore, L. M. Ware, E. F. Adams, and H. D. Babcock, Revision of Rowland’s Preliminary Table of Solar Spectrum Wave-Lengths, Carnegie Inst. Wash. Publ. 396; Pap. Mt. Wilson Obs.3(1928).

“The half-width of the slit image” corresponds to 14.8 μ m on the plate, but the full projected width of the slit is given9 as 15 μ m. This must be degraded considerably by the photographic line-spread function. A HWHM near 15 μ m is typical of fast spectroscopic plates in the blue (unsensitized) region.

But note that a reduction in the HWHM to 0.08 cm−1 would give practically the same result for a Gaussian profile as 0.09 cm−1 gives for a Lorentzian.

We may regard noise in the spectrum as equivalent to many random weak blending lines; hence, the peak is less affected by noise than the other criteria, if the noise is filtered to the same spectral resolution as the signal.

An exact solution for two-component blends of unequal widths was published by J. B. Tatum15 ten years ago, but it is so unwieldy that it has never been used in practical cases.

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Figures (5)

FIG. 1
FIG. 1

Blending shifts of a Lorentzian line due to a weak neighbor of relative strength f at separation Δ. The abscissa is in units of the half-width at half-maximum. Top panel: shift of mid-half peak, δm. Bottom: shift of blended peak, δp. Dashed lines: shift of centroid, δc. The profile of the stronger line is shown for comparison in the upper panel. Each curve is marked with the corresponding value of f.

FIG. 2
FIG. 2

Same as Fig. 1, but for a Gaussian line profile. The abscissa is in units of the Doppler half-width.

FIG. 3
FIG. 3

Shift of the mid-half-peak of blended lines having a triangular profile. The curves of δm follow δc up to Δ = 1 + 0.5f, and fall to zero at Δ = 3. The abscissa is in units of the HWHM. The peak position of a triangular line is unaffected by blending.

FIG. 4
FIG. 4

Blended line positions in the R branch of the 7883 Å CO2 band. The ordinate shows the displacements of the blends from the positions of their main component; the abscissa is component separation, in units of the HWHM. A HWHM of 25 μm on the original plates, corresponding to 0.009 cm−1, is assumed (see Tables I and II). The lower panel shows the relative strength of the weaker line in each blend.

FIG. 5
FIG. 5

Observed minus computed positions of multicomponent blends, as functions of the HWHM used in the computation. Observed positions are from Petrie et al.9; the method of computing expected positions for a given HWHM is described in the text. The wavelengths of the more discordant lines are indicated in the figure; these are discussed in the text.

Tables (2)

Tables Icon

TABLE I Blends in the R branch of the 7883 Å CO2 band.

Tables Icon

TABLE II Sam le calculation of blend position, showing iterations, assuming a Gaussian profile of 0.09 cm−1 HWHM.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

δ c = Δ f / ( 1 + f ) ,
P ( x ) = exp ( - x 2 ) + f exp [ - ( x - Δ ) 2 ] ,
f ( Δ - δ ) exp [ - ( Δ - δ ) 2 ] = δ ,
δ G = Δ f exp ( - Δ 2 ) .
δ L = Δ f ( 1 + Δ 2 ) - 2 .
δ = i ( Δ i w i ) / i ( w i ) .
δ = Δ w ( f , Δ ) / [ 1 + w ( f , Δ ) ] ,
w ( f , Δ ) = δ / ( Δ - δ ) δ / Δ
w G = δ G / Δ = f exp ( - Δ 2 )
w L = δ L / Δ = f ( 1 + Δ 2 ) - 2 .