Abstract

The term “visual efficiency” is used here to represent interchangeably the concepts of visual transmission factors of filters and of visual reflection factors of reflecting surfaces. Fluorescent substances are excluded from consideration. A material exhibits hue because visible radiation in some wavelength bands is more or less completely absorbed. This partial absorption of incident energy, necessary for the appearance of hue, obviously decreases the visual efficiency below the unit efficiency characteristic of a nonabsorbing, hueless, white material. Of all the conceivable spectrophotometric curves of materials exhibiting a given chromaticity when illuminated with light of a specified quality, there must be at least one which yields a maximum value for the visual efficiency. This paper describes the general type of spectrophotometric curve which is known to have this unique property. A new proof of the validity and uniqueness of this type of curve is presented. This proof takes advantage of the simplifications made available by the adoption of the I. C. I. 1931 coordinate system for colorimetry.

© 1935 Optical Society of America

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References

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  1. W. Ostwald, Königle Sächs. Ges. d. Wiss. Abh. d Math. Phys. 34, 471 (1917);Physik. Zeits. 17, 328 (1916).
  2. Erwin Schrödinger, Theorie der Pigmente von grösster Leuchtkraft, Ann. d. Physik 62, 603 (1920).
  3. Luther, Zeits. f. tech. Physik 8, 540 (1927).
  4. Nyberg, Zeits. f. Physik 52, 407 (1928).
  5. S. Rösch, Fortshritte der Mineral., Krist. & Petr. 13, 143 (1929).
  6. H. P. Gage, J. O. S. A. and R. S. I. 18, 167 (1930).
  7. D. B. Judd, The I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933).

1933 (1)

D. B. Judd, The I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933).

1930 (1)

H. P. Gage, J. O. S. A. and R. S. I. 18, 167 (1930).

1929 (1)

S. Rösch, Fortshritte der Mineral., Krist. & Petr. 13, 143 (1929).

1928 (1)

Nyberg, Zeits. f. Physik 52, 407 (1928).

1927 (1)

Luther, Zeits. f. tech. Physik 8, 540 (1927).

1920 (1)

Erwin Schrödinger, Theorie der Pigmente von grösster Leuchtkraft, Ann. d. Physik 62, 603 (1920).

1917 (1)

W. Ostwald, Königle Sächs. Ges. d. Wiss. Abh. d Math. Phys. 34, 471 (1917);Physik. Zeits. 17, 328 (1916).

Gage, H. P.

H. P. Gage, J. O. S. A. and R. S. I. 18, 167 (1930).

Judd, D. B.

D. B. Judd, The I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933).

Luther,

Luther, Zeits. f. tech. Physik 8, 540 (1927).

Nyberg,

Nyberg, Zeits. f. Physik 52, 407 (1928).

Ostwald, W.

W. Ostwald, Königle Sächs. Ges. d. Wiss. Abh. d Math. Phys. 34, 471 (1917);Physik. Zeits. 17, 328 (1916).

Rösch, S.

S. Rösch, Fortshritte der Mineral., Krist. & Petr. 13, 143 (1929).

Schrödinger, Erwin

Erwin Schrödinger, Theorie der Pigmente von grösster Leuchtkraft, Ann. d. Physik 62, 603 (1920).

Fortshritte der Mineral., Krist. & Petr. (1)

S. Rösch, Fortshritte der Mineral., Krist. & Petr. 13, 143 (1929).

J. O. S. A. and R. S. I. (1)

H. P. Gage, J. O. S. A. and R. S. I. 18, 167 (1930).

Königle Sächs. Ges. d. Wiss. Abh. d Math. Phys. (1)

W. Ostwald, Königle Sächs. Ges. d. Wiss. Abh. d Math. Phys. 34, 471 (1917);Physik. Zeits. 17, 328 (1916).

The I. C. I. Standard Observer and Coordinate System for Colorimetry (1)

D. B. Judd, The I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933).

Theorie der Pigmente von grösster Leuchtkraft (1)

Erwin Schrödinger, Theorie der Pigmente von grösster Leuchtkraft, Ann. d. Physik 62, 603 (1920).

Zeits. f. Physik (1)

Nyberg, Zeits. f. Physik 52, 407 (1928).

Zeits. f. tech. Physik (1)

Luther, Zeits. f. tech. Physik 8, 540 (1927).

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Figures (3)

F. 1a
F. 1a

Spectrophotometric curves for two green samples having dominant wavelength about 525 mμ and visual efficiency about 0.50. Box shaped curve, full line, has maximum attainable purity.

F. 1b
F. 1b

Spectrophotometric curves for two purple samples complementary to 505 mμ and having visual efficiency about 0.50.

F. 2
F. 2

Color mixture diagram according to I.C.I. standardization, with construction used in proof that box shaped spectrophotometric curve results in maximum purity for every specified dominant wavelength and visual efficiency.

Equations (8)

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X = 0 x ¯ λ E λ r λ d λ , Y = 0 y ¯ λ E λ r λ d λ , Z = 0 z ¯ λ E λ r λ d λ .
x λ = x ¯ λ / ( x ¯ λ + y ¯ λ + z ¯ λ ) , y λ = y ¯ λ / ( x ¯ λ + y ¯ λ + z ¯ λ ) .
x = X / ( X + Y + Z ) , y = Y / ( X + Y + Z ) .
( X + Y + Z ) = 0 ( x ¯ + y ¯ + z ¯ ) λ E λ r λ d λ = 0 m λ d λ .
x ¯ λ E λ r λ = x λ m λ , y ¯ λ E λ r λ = y λ m λ .
X = 0 x λ m λ d λ and Y = 0 y λ m λ d λ ,
x = 0 x λ m λ d λ / 0 m λ d λ , y = 0 y λ m λ d λ / 0 m λ d λ .
m λ = ( x ¯ + y ¯ + z ¯ ) λ E λ r λ .