Abstract

Surface appearance, apart from texture, is defined by the goniophotometric curve giving the angular distribution of the reflected light. A summary of current goniophotometric techniques shows that essential parts of these fundamental data have been neglected. This paper applies an established method of statistics to the problem of goniophotometric-curve analysis and interpretation whereby such data are reduced to dispersion, skewness, and kurtosis indexes. The kurtosis index is shown to correlate better with subjective estimates of the distinctness of the reflected images than the conventional measure, 60° specular gloss. The kurtosis index is applied to one problem in the selection of optimum glossmeter geometry.

© 1952 Optical Society of America

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References

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  1. F. Thaler, Ann. Physik 11, 996 (1903).
    [Crossref]
  2. V. G. W. Harrison, Definition and Measurement of Gloss (Patra, London, 1945), p. 106.
  3. W. W. Barkas, Proc. Phys. Soc. (London) 51, 274 (1939).
    [Crossref]
  4. G. I. Pokrowski, “Zur Theorie der diffusen Lichtreflexion,” Pt. I, Z. physik 30 (1924); Pt. II,  35 (1925); Pt. III,  35 (1925); Pt. IV,  36 (1926).
  5. A. Fresnel, Ann. chim. et phys. 17, 194, 312 (1821).
  6. T. K. Chinmayanandam, Phys. Rev. 13, (2), 96 (1919).
    [Crossref]
  7. H. L. Reitz, Mathematical Statistics (The Open Court Publishing Company, La Salle, Illinois, 1927).
  8. F. E. Croxton and D. J. Cowden, Applied General Statistics, (Prentice-Hall, Inc., New York, 1946).
  9. M. P. Pelton, Trans. Opt. Soc. Ltd. 31, 184 (1930).
    [Crossref]
  10. R. S. Hunter, “Gloss investigations using reflected images of a target pattern,” J. Research Natl. Bur. Standards, RP879,  16, 357 (1936).
  11. “ASTM method of test for 60° specular gloss of paint finishes” Am. Soc. Testing Materials designation D523, Book of Am. Soc. Testing Materials Standards, Part 4 (1949).
  12. I. Nimeroff, J. Research Natl. Bur. Standards RP2336,  48, (1952).

1952 (1)

I. Nimeroff, J. Research Natl. Bur. Standards RP2336,  48, (1952).

1939 (1)

W. W. Barkas, Proc. Phys. Soc. (London) 51, 274 (1939).
[Crossref]

1936 (1)

R. S. Hunter, “Gloss investigations using reflected images of a target pattern,” J. Research Natl. Bur. Standards, RP879,  16, 357 (1936).

1930 (1)

M. P. Pelton, Trans. Opt. Soc. Ltd. 31, 184 (1930).
[Crossref]

1924 (1)

G. I. Pokrowski, “Zur Theorie der diffusen Lichtreflexion,” Pt. I, Z. physik 30 (1924); Pt. II,  35 (1925); Pt. III,  35 (1925); Pt. IV,  36 (1926).

1919 (1)

T. K. Chinmayanandam, Phys. Rev. 13, (2), 96 (1919).
[Crossref]

1903 (1)

F. Thaler, Ann. Physik 11, 996 (1903).
[Crossref]

1821 (1)

A. Fresnel, Ann. chim. et phys. 17, 194, 312 (1821).

Barkas, W. W.

W. W. Barkas, Proc. Phys. Soc. (London) 51, 274 (1939).
[Crossref]

Chinmayanandam, T. K.

T. K. Chinmayanandam, Phys. Rev. 13, (2), 96 (1919).
[Crossref]

Cowden, D. J.

F. E. Croxton and D. J. Cowden, Applied General Statistics, (Prentice-Hall, Inc., New York, 1946).

Croxton, F. E.

F. E. Croxton and D. J. Cowden, Applied General Statistics, (Prentice-Hall, Inc., New York, 1946).

Fresnel, A.

A. Fresnel, Ann. chim. et phys. 17, 194, 312 (1821).

Harrison, V. G. W.

V. G. W. Harrison, Definition and Measurement of Gloss (Patra, London, 1945), p. 106.

Hunter, R. S.

R. S. Hunter, “Gloss investigations using reflected images of a target pattern,” J. Research Natl. Bur. Standards, RP879,  16, 357 (1936).

Nimeroff, I.

I. Nimeroff, J. Research Natl. Bur. Standards RP2336,  48, (1952).

Pelton, M. P.

M. P. Pelton, Trans. Opt. Soc. Ltd. 31, 184 (1930).
[Crossref]

Pokrowski, G. I.

G. I. Pokrowski, “Zur Theorie der diffusen Lichtreflexion,” Pt. I, Z. physik 30 (1924); Pt. II,  35 (1925); Pt. III,  35 (1925); Pt. IV,  36 (1926).

Reitz, H. L.

H. L. Reitz, Mathematical Statistics (The Open Court Publishing Company, La Salle, Illinois, 1927).

Thaler, F.

F. Thaler, Ann. Physik 11, 996 (1903).
[Crossref]

Ann. chim. et phys. (1)

A. Fresnel, Ann. chim. et phys. 17, 194, 312 (1821).

Ann. Physik (1)

F. Thaler, Ann. Physik 11, 996 (1903).
[Crossref]

J. Research Natl. Bur. Standards (1)

R. S. Hunter, “Gloss investigations using reflected images of a target pattern,” J. Research Natl. Bur. Standards, RP879,  16, 357 (1936).

J. Research Natl. Bur. Standards RP2336 (1)

I. Nimeroff, J. Research Natl. Bur. Standards RP2336,  48, (1952).

Phys. Rev. (1)

T. K. Chinmayanandam, Phys. Rev. 13, (2), 96 (1919).
[Crossref]

Proc. Phys. Soc. (London) (1)

W. W. Barkas, Proc. Phys. Soc. (London) 51, 274 (1939).
[Crossref]

Pt. I, Z. physik (1)

G. I. Pokrowski, “Zur Theorie der diffusen Lichtreflexion,” Pt. I, Z. physik 30 (1924); Pt. II,  35 (1925); Pt. III,  35 (1925); Pt. IV,  36 (1926).

Trans. Opt. Soc. Ltd. (1)

M. P. Pelton, Trans. Opt. Soc. Ltd. 31, 184 (1930).
[Crossref]

Other (4)

“ASTM method of test for 60° specular gloss of paint finishes” Am. Soc. Testing Materials designation D523, Book of Am. Soc. Testing Materials Standards, Part 4 (1949).

V. G. W. Harrison, Definition and Measurement of Gloss (Patra, London, 1945), p. 106.

H. L. Reitz, Mathematical Statistics (The Open Court Publishing Company, La Salle, Illinois, 1927).

F. E. Croxton and D. J. Cowden, Applied General Statistics, (Prentice-Hall, Inc., New York, 1946).

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Figures (3)

Fig. 1
Fig. 1

Typical goniophotometric curves on log-linear coordinates.

Fig. 2
Fig. 2

Kurtosis index, α4, plotted against 60° specular gloss. Note the division of the specimens into two groups: specimens forming sharp images, ●; specimens forming no sharp images, ○.

Fig. 3
Fig. 3

Comparison of 60° with 20° incidence angles. 60° incidence on left; 20° incidence on right; sand-blasted black glass, S; acid-etched black glass, A.

Tables (3)

Tables Icon

Table I Moments about the mean in terms of moments about an assumed mean.

Tables Icon

Table II Illustrative computation of indexes, σ, α3, and α4.

Tables Icon

Table III Summary of correlation coefficients.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

σ = [ i 1 n f i d i 2 / i 1 n f i ] 1 2 ,
α 3 = [ i 1 n f i d i 3 / i 1 n f i ] / σ 3 ,
α 4 = [ i 1 n f i d i 4 / i 1 n f i ] / σ 4 ,
σ θ = ( B θ Θ 2 / B θ ) 1 2 ,
ν k = [ i 1 n f i d i k / i 1 n f i ,
π k = t 0 k [ ( k ! t ! ( k - t ) ! ) ( - ν 1 ) t ( ν k - t ) ] ,
ρ = 1 - [ 6 D 2 / N ( N 2 - 1 ) ] ,
- a a F 1 δ d - - a a F 2 δ d = K ,
- a a F 1 δ d = K - a a F 2 δ d ,