Abstract

This calibration method, developed for a Perkin-Elmer Model 12 spectrometer, covers the regions 5 to 15μ (NaCl) and 2 to 5μ (LiF). Standardized techniques lowered the standard deviation of the spectrometer itself to 0.10 cm−1 at 1000 cm−1. The formula Ti=T0+(a/νi2ν02) is shown to be analogous in form and method of solution to the Hartmann dispersion formula, λi0+(c/d0di). Thus Hartmann formula techniques have been applied to the calibration equation. Solutions are readily handled on a calculating machine; graphical interpolations are obviated. The results have standard deviation of 0.28 cm−1 at 1000 cm−1.

© 1951 Optical Society of America

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References

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  1. D. S. McKinney and R. A. Friedel, J. Opt. Soc. Am. 38, 222 (1948).
    [Crossref] [PubMed]
  2. A. E. Martin, J. Opt. Soc. Am. 41, 56 (L) (1951).
    [Crossref]
  3. P. Torkington, J. Opt. Soc. Am. 40, 481 (L) (1950).
    [Crossref]
  4. G. W. King, Phys. Rev. 76, 473 (1949).
  5. Perkin-Elmer Letter re wave drive worm-Littrow mirror mechanism to UBC, 1949.
  6. R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 230.
  7. Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
    [Crossref]
  8. C. D. Hodgman (editor), Handbook of Chemistry and Physics (Rubber Publishing Company, Cleveland, 1947), thirtieth edition, p. 2114.
  9. W. W. Sleator, Astrophys. J. 48, 125 (1918).
    [Crossref]
  10. Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
    [Crossref]
  11. J. G. Moorhead, Phys. Rev. 39, 83 (1932).
    [Crossref]
  12. G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).
  13. E. F. Barker, Phys. Rev. 44, 984 (1933).
    [Crossref]
  14. E. F. Barker, Astrophys. J. 55, 391 (1922).
    [Crossref]
  15. A. H. Nielsen and H. H. Nielsen, Phys. Rev. 48, 864 (1935).
    [Crossref]
  16. G. A. Stinchcomb and E. F. Barker, Phys. Rev. 33, 305 (1929).
    [Crossref]
  17. E. K. Plyler and C. W. Peters, J. Research Natl. Bur. Standards 45, 462 (1950).
    [Crossref]

1951 (1)

A. E. Martin, J. Opt. Soc. Am. 41, 56 (L) (1951).
[Crossref]

1950 (2)

P. Torkington, J. Opt. Soc. Am. 40, 481 (L) (1950).
[Crossref]

E. K. Plyler and C. W. Peters, J. Research Natl. Bur. Standards 45, 462 (1950).
[Crossref]

1949 (1)

G. W. King, Phys. Rev. 76, 473 (1949).

1948 (1)

1947 (1)

Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
[Crossref]

1942 (1)

Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
[Crossref]

1935 (1)

A. H. Nielsen and H. H. Nielsen, Phys. Rev. 48, 864 (1935).
[Crossref]

1933 (1)

E. F. Barker, Phys. Rev. 44, 984 (1933).
[Crossref]

1932 (1)

J. G. Moorhead, Phys. Rev. 39, 83 (1932).
[Crossref]

1929 (1)

G. A. Stinchcomb and E. F. Barker, Phys. Rev. 33, 305 (1929).
[Crossref]

1922 (1)

E. F. Barker, Astrophys. J. 55, 391 (1922).
[Crossref]

1918 (1)

W. W. Sleator, Astrophys. J. 48, 125 (1918).
[Crossref]

Barker, E. F.

E. F. Barker, Phys. Rev. 44, 984 (1933).
[Crossref]

G. A. Stinchcomb and E. F. Barker, Phys. Rev. 33, 305 (1929).
[Crossref]

E. F. Barker, Astrophys. J. 55, 391 (1922).
[Crossref]

Dickens,

Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
[Crossref]

Friedel, R. A.

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).

Kao,

Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
[Crossref]

King, G. W.

G. W. King, Phys. Rev. 76, 473 (1949).

Lagemann,

Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
[Crossref]

Martin, A. E.

A. E. Martin, J. Opt. Soc. Am. 41, 56 (L) (1951).
[Crossref]

McKinney, D. S.

Moorhead, J. G.

J. G. Moorhead, Phys. Rev. 39, 83 (1932).
[Crossref]

Nielsen,

Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
[Crossref]

Nielsen, A. H.

A. H. Nielsen and H. H. Nielsen, Phys. Rev. 48, 864 (1935).
[Crossref]

Nielsen, H. H.

A. H. Nielsen and H. H. Nielsen, Phys. Rev. 48, 864 (1935).
[Crossref]

Oetjen,

Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
[Crossref]

Peters, C. W.

E. K. Plyler and C. W. Peters, J. Research Natl. Bur. Standards 45, 462 (1950).
[Crossref]

Plyler, E. K.

E. K. Plyler and C. W. Peters, J. Research Natl. Bur. Standards 45, 462 (1950).
[Crossref]

Randall,

Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
[Crossref]

Sawyer, R. A.

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 230.

Sleator, W. W.

W. W. Sleator, Astrophys. J. 48, 125 (1918).
[Crossref]

Stinchcomb, G. A.

G. A. Stinchcomb and E. F. Barker, Phys. Rev. 33, 305 (1929).
[Crossref]

Torkington, P.

P. Torkington, J. Opt. Soc. Am. 40, 481 (L) (1950).
[Crossref]

Astrophys. J. (2)

W. W. Sleator, Astrophys. J. 48, 125 (1918).
[Crossref]

E. F. Barker, Astrophys. J. 55, 391 (1922).
[Crossref]

J. Opt. Soc. Am. (3)

D. S. McKinney and R. A. Friedel, J. Opt. Soc. Am. 38, 222 (1948).
[Crossref] [PubMed]

A. E. Martin, J. Opt. Soc. Am. 41, 56 (L) (1951).
[Crossref]

P. Torkington, J. Opt. Soc. Am. 40, 481 (L) (1950).
[Crossref]

J. Research Natl. Bur. Standards (1)

E. K. Plyler and C. W. Peters, J. Research Natl. Bur. Standards 45, 462 (1950).
[Crossref]

Phys. Rev. (6)

E. F. Barker, Phys. Rev. 44, 984 (1933).
[Crossref]

A. H. Nielsen and H. H. Nielsen, Phys. Rev. 48, 864 (1935).
[Crossref]

G. A. Stinchcomb and E. F. Barker, Phys. Rev. 33, 305 (1929).
[Crossref]

G. W. King, Phys. Rev. 76, 473 (1949).

Lagemann, Nielsen, and Dickens, Phys. Rev. 72, 284 (1947).
[Crossref]

J. G. Moorhead, Phys. Rev. 39, 83 (1932).
[Crossref]

Rev. Sci. Instr. (1)

Oetjen, Kao, and Randall, Rev. Sci. Instr. 13, 515 (1942).
[Crossref]

Other (4)

C. D. Hodgman (editor), Handbook of Chemistry and Physics (Rubber Publishing Company, Cleveland, 1947), thirtieth edition, p. 2114.

G. Herzberg, Infrared and Raman Spectra (D. Van Nostrand Company, Inc., New York, 1945).

Perkin-Elmer Letter re wave drive worm-Littrow mirror mechanism to UBC, 1949.

R. A. Sawyer, Experimental Spectroscopy (Prentice-Hall, Inc., New York, 1944), p. 230.

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Figures (1)

Fig. 1
Fig. 1

Diagram of wave drive worm and Littrow mirror mechanism. M is Littrow mirror; R, radius arm; N, rearmost position of radius arm; N′, foremost position of radius arm; and S, worm screw.

Tables (5)

Tables Icon

Table I Spectrometer reproducibility.

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Table II Constants for formula (4).

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Table IIIa Calibration: NaCl region.

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Table IIIb Calibration: LiF region.

Tables Icon

Table IV Calibration errors.

Equations (29)

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tan θ = ( T - T 0 / 9.80 × 13 ) ,
φ = α + tan - 1 ( T - T 0 / 9.80 × 13 ) .
Δ α = ( a Δ T / 1 + a 2 ( T - T 0 ) 2 ) ,             where             a = 1 / 9.80 × 13.
Δ α = 0.1 / 9.80 × 13 = 0.000785 radians.
0.000785 = 0.00785 Δ T 1 + ( 25 - 10 / 9.80 × 13 ) 2 .
T + T 0 = A ν 2 + ( B / ν 2 2 - ν 2 ) ,
T = T 0 + ( a / ν 2 - ν 0 2 )
λ = λ 0 + ( c / d 0 - d )
ν 2 = ν 0 2 + ( a / T - T 0 ) .
c = ( λ 1 - λ 0 ) ( d 0 - d 1 )
c = ( λ 2 - λ 0 ) ( d 0 - d 2 )
c = ( λ 3 - λ 0 ) ( d 0 - d 3 )
λ i = λ i - λ 1 ;             d i = d i - d 1 ;             α i = d i / λ i             where             i = 2 , 3.
λ 2 = c ( d 2 - d 1 ) / ( d 0 - d 1 ) ( d 0 - d 2 )
λ 3 = c ( d 3 - d 1 ) / ( d 0 - d 1 ) ( d 0 - d 3 ) .
X = ( c / d 0 - d 1 ) ,
α 3 = ( d 0 - d 3 ) / X ;
X 1 = ( d 3 - d 2 ) / ( α 2 - α 3 ) .
λ 0 = λ 1 - X 1 .
λ 1 d 1 - λ 0 d 1 - λ 1 d 0 = λ 2 d 2 - λ 0 d 2 - λ 2 d 0 .
( d 0 - d 1 ) = d 2 - d 1 λ 2 - λ 1 ( λ 2 - λ 0 ) = α 2 ( λ 2 - λ 0 ) .
ν i 2 = ν i 2 - ν 1 2 ;             T i = T i - T 1 ;             α i = T i / ν i 2             where             i = 2 , 3.
X 1 = ( T 3 - T 2 ) / α 2 - α 3 = ( a / T 1 - T 0 )
ν 0 2 = ν 1 2 - X 1
T 0 - T 1 = α 2 ( ν 2 2 - ν 0 2 ) .
T i = T 0 + α β i             where             i = 1 , 2 , 3.
a = ( T 1 - T 2 ) / ( β 1 - β 2 )
T 0 = ( β 1 T 2 - β 2 T 1 ) / ( β 1 - β 2 ) .
ν 0 2 = ν 1 2 - k 2 ν 3 2 1 - k 2             where             k 2 = ν 1 2 - ν 2 2 ν 2 2 - ν 3 2 / T 1 - T 2 T 2 - T 3 .