Abstract

A technique is suggested which allows an estimate to be made of the errors introduced into spectrophotometric measurements by the use of slits of finite width. The technique depends upon approximate analytic expressions for the slit function, the variation of the instrument sensitivity with wave-length, and the variation of the absorption coefficient with wave-length. A slit function is suggested for use with spectrophotometers with entrance and exit slits of equal width but with optics of varying dispersion. Expressions are derived for two convenient approximations for the absorption coefficient in the neighborhood of a maximum: a parabolic form, and two intersecting straight lines of opposite slope. Application of these expressions is made to experimental data on solutions of benzene, oxyhemoglobin, and neodymium chloride.

© 1950 Optical Society of America

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References

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  1. A. C. Hardy and F. M. Young, J. Opt. Soc. Am. 39, 265 (1949).
    [Crossref]
  2. Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
    [Crossref]
  3. B. L. Horecker, J. Biol. Chem. 148, 173 (1943).
  4. W. T. Ziegler, Georgia Institute of Technology, Atlanta, Georgia (private communication).

1949 (1)

1943 (1)

B. L. Horecker, J. Biol. Chem. 148, 173 (1943).

1937 (1)

Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
[Crossref]

Hardy, A. C.

Hogness,

Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
[Crossref]

Horecker, B. L.

B. L. Horecker, J. Biol. Chem. 148, 173 (1943).

Sidwell,

Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
[Crossref]

Young, F. M.

Ziegler, W. T.

W. T. Ziegler, Georgia Institute of Technology, Atlanta, Georgia (private communication).

Zscheile,

Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
[Crossref]

J. Biol. Chem. (1)

B. L. Horecker, J. Biol. Chem. 148, 173 (1943).

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

Hogness, Zscheile, and Sidwell, J. Phys. Chem. 41, 379 (1937).
[Crossref]

Other (1)

W. T. Ziegler, Georgia Institute of Technology, Atlanta, Georgia (private communication).

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Figures (3)

Fig. 1
Fig. 1

Slit function for Beckman Model DU quartz spectrophotometer. Dashed curve: simple slit function calculated for constant dispersion. Solid curve: slit function corrected for varying dispersion.

Fig. 2
Fig. 2

Extinction coefficient of oxyhemoglobin. Dashed curve: parabolic form assumed for calculations.

Fig. 3
Fig. 3

Variation of optical density with concentration of NdCl3 measured at λ794 mμ with fixed slit-width. Dashed curve: calculated for zero slit-width. Solid curve: calculated for slit-width used in measurements, 2.25 mμ.

Tables (7)

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Table I Slit functions for Beckman Model DU quartz spectrophotometer as determined by monochromatic radiation from Hg λ546.0 mμ.

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Table II Dependence on slit-width of the extinction coefficient of benzene in isooctane solution for the mean wave-length λ2540A.

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Table III Extinction coefficient of benzene at λ2540A corrected for slit-width effects.

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Table IV Dependence on slit-width of optical density of oxyhemoglobin solution measured at λ576.5 mμ. Concentration of HbO2=3.50×10−8 mole/cm3.

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Table V Variation of optical density with concentration of oxyhemoglobin solutions measured at λ567.5 mμ with fixed slit-width Δs=0.22 mm or 6.7 mμ.

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Table VI Dependence on slit-width of optical density of neodymium chloride solution. Concentration NdCl3=0.042F.

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Table VII Variation of optical density with concentration of NdCl3 measured at λ794.0 mμ with fixed slit-width, Δs=0.036 mm or 2.25 mμ.

Equations (13)

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D ( λ ) = - log E ( λ ) / E 0 ( λ ) = - log t s ( λ ) = ( λ ) c l / 2.303 ,
R 0 = 0 H ( λ ) S ( λ ) M ( λ ) t 0 ( λ ) d λ ,
R = 0 H ( λ ) S ( λ ) M ( λ ) t ( λ ) d λ ,
r 0 ( λ ) = r 0 ( λ 0 ) [ 1 + μ ( λ - λ 0 ) ] .
T s = exp ( - 0 c l ) { 1 + γ c l z 3 ( α 2 - β 2 ) + γ 2 c 2 l 2 z 2 12 ( α 3 + β 3 ) ( 1 - 2 μ γ c l - 2 δ γ 2 c l ) + γ 3 c 3 l 3 z 3 60 ( α 4 - β 4 ) ( 1 - 3 μ γ c l - 6 δ γ 2 c l - 24 μ δ γ 3 c 2 l 2 ) ( α + β ) - ( μ z / 3 ) ( α 2 - β 2 ) } ,
T s = exp ( - 0 c l ) × { 1 + c l z 3 ( α 2 γ 1 - β 2 γ 2 ) + c 2 l 2 z 2 12 [ ( α 3 γ 1 2 + β 2 γ 2 2 ) - 2 μ ( α 3 γ 1 + β 3 γ 2 ) ] + c 3 l 3 z 3 60 [ ( α 4 γ 1 3 - β 4 γ 2 3 ) - 3 μ ( α 4 γ 1 2 - β 4 γ 2 2 ) ] ( α + β ) - ( μ z / 3 ) ( α 2 - β 2 ) } .
T s = exp ( - 0 c l ) { 1 + γ 2 c 2 l 2 z 2 12 ( 1 - 2 δ γ 2 c l ) }
T s = exp ( - 0 c l ) { 1 + c l z 6 ( γ 1 - γ 2 ) + c 2 l 2 z 2 24 ( γ 1 2 + γ 2 2 ) + c 3 l 3 z 3 120 ( γ 1 3 - γ 2 3 ) } ,
T s = exp ( - 519 c l ) { 1 + 9.1 c l z + 74 c 2 l 2 z 2 + 470 c 3 l 3 z 3 } ,
( λ ) = 36.9 × 10 6 - 2.88 × 10 5 ( λ - 576.5 ) 2 .
T s = exp ( - 0 c l ) { 1 + 4.80 × 10 4 c l z 2 } .
T s , 574 = exp ( - 16.0 c l ) { 1 + 0.41 c l z + 0.13 c 2 l 2 z 2 + 0.03 c 3 l 3 z 3 }
T s , 794 = exp ( - 23.0 c l ) { 1 + 1.4 c l z + 2.4 c 2 l 2 z 2 + 0.36 c 3 l 3 z 3 } .