Abstract

The general theory of the integrating sphere as used in the measurement of total spectral reflectance is formulated as an integral equation and solved for five special cases. Two methods of measuring reflectance are considered. In the substitution method, sample and standard are placed in turn at the sample aperture and the ratio of the respective photocell readings determined. In the comparison method, both sample and standard are in place at all times at their respective apertures. The beam is switched from sample to standard and the ratio of the respective photocell readings determined. The efficiency and error, and their interdependence are discussed for both methods and for different geometries of the sphere. The design of a comparison type sphere with maximum efficiency and low error is considered.

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  1. 1 J. W. T. Walsh, Photometry (Constable & Co. Ltd., London, 1953), second edition.
  2. E. Karrer, Sci. Papers Bur. Standards. No. 415, pp. 203–225 (1921).
  3. H. J. McNicholas, Bur. Standards J. Research 1, 29 (1928).
  4. E. B. Rosa and A. H. Taylor, Sci. Papers Bur. Standards No. 447, pp. 281–325 (1922).
  5. A. H. Taylor, Sci. Papers Bur. Standards, No. 391, pp. 421–436 (1920).
  6. A. C. Hardy and O. W. Pineo, J. Opt. Soc. Am. 21, 502 (1931).
  7. J. S. Preston, Trans. Opt. Soc. (London) 31, 15 (1929–30).
  8. P. Moon, J. Opt. Soc. Am. 30, 195 (1940).
  9. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, New York, 1950), fourth edition.
  10. W. V. Lovitt, Linear Integral Equations (Dover Publications Inc., New York, 1950), first edition.
  11. K. S. Gibson, Natl. Bur. Standards, Circular No. 484, (1949).

Gibson, K. S.

K. S. Gibson, Natl. Bur. Standards, Circular No. 484, (1949).

Hardy, A. C.

A. C. Hardy and O. W. Pineo, J. Opt. Soc. Am. 21, 502 (1931).

Karrer, E.

E. Karrer, Sci. Papers Bur. Standards. No. 415, pp. 203–225 (1921).

Lovitt, W. V.

W. V. Lovitt, Linear Integral Equations (Dover Publications Inc., New York, 1950), first edition.

McNicholas, H. J.

H. J. McNicholas, Bur. Standards J. Research 1, 29 (1928).

Moon, P.

P. Moon, J. Opt. Soc. Am. 30, 195 (1940).

Pineo, O. W.

A. C. Hardy and O. W. Pineo, J. Opt. Soc. Am. 21, 502 (1931).

Preston, J. S.

J. S. Preston, Trans. Opt. Soc. (London) 31, 15 (1929–30).

Rosa, E. B.

E. B. Rosa and A. H. Taylor, Sci. Papers Bur. Standards No. 447, pp. 281–325 (1922).

Taylor, A. H.

E. B. Rosa and A. H. Taylor, Sci. Papers Bur. Standards No. 447, pp. 281–325 (1922).

A. H. Taylor, Sci. Papers Bur. Standards, No. 391, pp. 421–436 (1920).

Walsh, J. W. T.

1 J. W. T. Walsh, Photometry (Constable & Co. Ltd., London, 1953), second edition.

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, New York, 1950), fourth edition.

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, New York, 1950), fourth edition.

Other

1 J. W. T. Walsh, Photometry (Constable & Co. Ltd., London, 1953), second edition.

E. Karrer, Sci. Papers Bur. Standards. No. 415, pp. 203–225 (1921).

H. J. McNicholas, Bur. Standards J. Research 1, 29 (1928).

E. B. Rosa and A. H. Taylor, Sci. Papers Bur. Standards No. 447, pp. 281–325 (1922).

A. H. Taylor, Sci. Papers Bur. Standards, No. 391, pp. 421–436 (1920).

A. C. Hardy and O. W. Pineo, J. Opt. Soc. Am. 21, 502 (1931).

J. S. Preston, Trans. Opt. Soc. (London) 31, 15 (1929–30).

P. Moon, J. Opt. Soc. Am. 30, 195 (1940).

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, New York, 1950), fourth edition.

W. V. Lovitt, Linear Integral Equations (Dover Publications Inc., New York, 1950), first edition.

K. S. Gibson, Natl. Bur. Standards, Circular No. 484, (1949).

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