Abstract

This paper describes the application of the integrating sphere or cavity to the measurement of the absorption coefficient (cm−1) of a material introduced into the cavity. The absorption coefficient is determined by measuring the decrease in the radiation density within the integrating cavity caused by insertion of the sample. This method has the virtue of being independent of the scattering within the material sample, the reflectivity of the material surface, and the geometry of the sample. The method is particularly attractive for materials with small absorption coefficients. Experimental verification of the method is described showing agreement with direct transmittance measurements to within ±10%.

© 1970 Optical Society of America

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References

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  1. J. W. T. Walsh, Photometry (Constable, London, 1953), pp. 141, 259.
  2. F. A. Benford, General Electric Rev., 23, 72 (1920).
  3. J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 58–60.
  4. See Ref. 1, pp. 278–280.
  5. F. Grum, G. W. Luckey, Appl. Opt. 7, 2289 (1968).
    [CrossRef] [PubMed]

1968 (1)

1920 (1)

F. A. Benford, General Electric Rev., 23, 72 (1920).

Benford, F. A.

F. A. Benford, General Electric Rev., 23, 72 (1920).

Grum, F.

Luckey, G. W.

Strong, J.

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 58–60.

Walsh, J. W. T.

J. W. T. Walsh, Photometry (Constable, London, 1953), pp. 141, 259.

Appl. Opt. (1)

General Electric Rev. (1)

F. A. Benford, General Electric Rev., 23, 72 (1920).

Other (3)

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958), pp. 58–60.

See Ref. 1, pp. 278–280.

J. W. T. Walsh, Photometry (Constable, London, 1953), pp. 141, 259.

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Figures (4)

Fig. 1
Fig. 1

Apparatus used for measuring the reflectivity of the integrating cavity surface. Diffuser is included to make the detector insensitive to the angular distribution of emerging radiation. Auxiliary aperture not shown.

Fig. 2
Fig. 2

Geometry of air–sample interface. The irradiance incident on the interface from the air side is Hs and that incident on the interface from the sample side is Hs.

Fig. 3
Fig. 3

Integrating cube measurement of absorption coefficient. The radiation source consists of a mercury lamp and filter providing 5460-Å radiation. Note that the sample is not directly irradiated by the entering beam. The auxiliary aperture is not shown.

Fig. 4
Fig. 4

Direct transmittance measurement of absorption coefficient. The integrating cube is used to insure that the detector is insensitive to beam deflection caused by insertion of the sample.

Tables (1)

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Table I Comparison of Direct Transmittance and Integrating Cavity Measurements

Equations (17)

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P 0 = P 0 ( 1 ρ ) + H A ( 1 ρ ) .
P 0 = P 0 ( 1 ρ ) + H a ( 1 ρ ) ( A a ) + H a a .
1 ρ = a / [ A ( H / H a 1 ) + a ] .
d U = k U d x .
d U / d t = U k c / n ,
P s = u V k c / n .
d H s = N s cos θ 2 π sin θ d θ .
d H s = N s cos θ 2 π sin θ d θ .
N s sin θ d θ cos θ = N s sin θ d θ cos θ .
N s n d θ cos θ = N s d θ cos θ .
N s n 2 = N s .
H s = u c / 4 n .
H s n 2 = u c / 4 n .
P s = 4 n 2 H s V k .
P 0 = P 0 ( 1 ρ ) + A H s ( 1 ρ ) + 4 n 2 H s V k .
H A ( 1 ρ ) = A H s ( 1 ρ ) + 4 n 2 H s V k ,
k = A ( 1 ρ ) ( H / H s 1 ) / 4 n 2 V .

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