Abstract

An optical method for measuring marble and limestone surface finish is described. This method is capable of ordering the different varieties of rocks subjected to the same industrial finishing process consistent with an arrangement made by an average human observer. The measure of finish is defined as the ratio between the specularly reflected luminous flux from a sample and the total diffused light.

© 1986 Optical Society of America

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References

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  1. L. Asuni, G. Rossi, I. Uras, “Analisi…Lucidat,” paper presented at First Convegno Internationale Sulla Cultivacione di Pietre e Minerali Litoidi, Torino (1974), p. 13.
  2. J. S. Christie, “An Instrument for the Geometric Attributes of Metallic Appearance,” Appl. Opt. 8, 1777 (1969).
    [CrossRef] [PubMed]
  3. F. Gascón, M. Balbás, “Optical Measurement of Granite Surface Polish,” J. Test. Eval. 13, 367 (1985).
    [CrossRef]
  4. J. F. Marcotorchino, P. Michand, Optimisation en analyse ordinate des donnees (Masson, Paris, 1979), p. 160.
  5. J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, CA, 1982), pp. 180–185.
  6. E. Chacon, F. Miguez, Estadistica Aplicada (Rugarte S.L., Madrid, 1980), pp. 444 and 445.

1985 (1)

F. Gascón, M. Balbás, “Optical Measurement of Granite Surface Polish,” J. Test. Eval. 13, 367 (1985).
[CrossRef]

1969 (1)

Asuni, L.

L. Asuni, G. Rossi, I. Uras, “Analisi…Lucidat,” paper presented at First Convegno Internationale Sulla Cultivacione di Pietre e Minerali Litoidi, Torino (1974), p. 13.

Balbás, M.

F. Gascón, M. Balbás, “Optical Measurement of Granite Surface Polish,” J. Test. Eval. 13, 367 (1985).
[CrossRef]

Chacon, E.

E. Chacon, F. Miguez, Estadistica Aplicada (Rugarte S.L., Madrid, 1980), pp. 444 and 445.

Christie, J. S.

Gascón, F.

F. Gascón, M. Balbás, “Optical Measurement of Granite Surface Polish,” J. Test. Eval. 13, 367 (1985).
[CrossRef]

Marcotorchino, J. F.

J. F. Marcotorchino, P. Michand, Optimisation en analyse ordinate des donnees (Masson, Paris, 1979), p. 160.

Michand, P.

J. F. Marcotorchino, P. Michand, Optimisation en analyse ordinate des donnees (Masson, Paris, 1979), p. 160.

Miguez, F.

E. Chacon, F. Miguez, Estadistica Aplicada (Rugarte S.L., Madrid, 1980), pp. 444 and 445.

Rossi, G.

L. Asuni, G. Rossi, I. Uras, “Analisi…Lucidat,” paper presented at First Convegno Internationale Sulla Cultivacione di Pietre e Minerali Litoidi, Torino (1974), p. 13.

Taylor, J. R.

J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, CA, 1982), pp. 180–185.

Uras, I.

L. Asuni, G. Rossi, I. Uras, “Analisi…Lucidat,” paper presented at First Convegno Internationale Sulla Cultivacione di Pietre e Minerali Litoidi, Torino (1974), p. 13.

Appl. Opt. (1)

J. Test. Eval. (1)

F. Gascón, M. Balbás, “Optical Measurement of Granite Surface Polish,” J. Test. Eval. 13, 367 (1985).
[CrossRef]

Other (4)

J. F. Marcotorchino, P. Michand, Optimisation en analyse ordinate des donnees (Masson, Paris, 1979), p. 160.

J. R. Taylor, An Introduction to Error Analysis (University Science Books, Mill Valley, CA, 1982), pp. 180–185.

E. Chacon, F. Miguez, Estadistica Aplicada (Rugarte S.L., Madrid, 1980), pp. 444 and 445.

L. Asuni, G. Rossi, I. Uras, “Analisi…Lucidat,” paper presented at First Convegno Internationale Sulla Cultivacione di Pietre e Minerali Litoidi, Torino (1974), p. 13.

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Figures (6)

Fig. 1
Fig. 1

Pattern, sample, and observer.

Fig. 2
Fig. 2

Incident beam and emerging light.

Fig. 3
Fig. 3

Illuminated ellipse and detector.

Fig. 4
Fig. 4

Variables in the geometric factor.

Fig. 5
Fig. 5

Experimental arrangement.

Fig. 6
Fig. 6

Points of measurement.

Tables (6)

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Table I Subjective Matrix aij

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Table II Subjective Superclassification

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Table III Mean Subjective Ranks

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Table IV Geometric Factor

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Table V Objective Results

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Table VI Corrected Objective Results

Equations (38)

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a i j a j i > 1 ;             a i j - a j i 30 1 3 ;             30 - ( a i j + a j i ) a i j 1 2 .
A i = - j = 1 30 a i j ,
r i = - A i / 30.
d 2 F = d I · d Ω = L · d A · cos σ · d Ω ,
F T D = A d A h s L cos σ d Ω = π L A .
F D = A A L cos σ cos σ d A d A r 2 = π L A 1 A ' A A cos σ cos σ d A d A π r 2 .
ϕ = 1 A A A cos σ cos σ d A d A π r 2 ,
F D L = π L A ϕ L .
F D S = π L A ϕ S ,
F T D = F D L ϕ L ,
F D S = F D L ϕ L / ϕ S .
p = F S P F S P + F T D .
F L = F S P + F D L ,
F S = F S P + F D S .
F S = F S P + F D L ϕ L / ϕ S ,
F S P = ϕ L F S - ϕ S F L ϕ L - ϕ S ,
F D L = ϕ L ϕ L - ϕ S ( F L - F S ) .
F T D = F D L ϕ L = 1 ϕ L - ϕ S ( F L - F S ) .
p = ϕ L F S - ϕ S F L ϕ L F S - ϕ S F L + F L - F S .
d A = l · d β · d l , d A = 2 l · d β · d l , cos σ = D - l sin β 2 r , cos σ = D - l sin β r , r = D [ ( tan γ cos β - tan α cos β ) 2 + ( tan γ sin β - tan α sin β ) 2 + ( 1 - tan γ sin β ) 2 ] 1 / 2 .
ϕ = 2 A / A π 2 tan 2 δ - π 2 π / 2 d β 0 2 π d β 0 δ d α 0 arctan ( tan δ / A / A ) × d γ { tan α tan γ ( 1 - tan γ sin β ) · ( 1 - tan α sin β ) · cos - 2 α cos - 2 γ · [ ( tan γ cos β - tan α cos β ) 2 + ( tan γ sin β - tan α sin β ) 2 + ( 1 - tan γ sin β ) 2 ] - 2 } .
p = Σ F S P i Σ F S P i + Σ F T D i = ϕ L ϕ S Σ F S i - Σ F L i ϕ L ϕ S Σ F S i - Σ F L i + 1 ϕ L ϕ L ϕ S Σ F L i - 1 ϕ L ϕ L ϕ S Σ F S i = ϕ L F S - ϕ S F L ϕ L F S - ϕ S F L + F L - F S ,
E = F A F = E · A { F L = E L · A , F S = E S · A ,
p = ϕ L E S - ϕ S E L ϕ L E S - ϕ S E L + E L - E S .
d ( A A ) = 2 R R 2 d r + 2 R 2 R 3 d R .
d ( A A ) = 0.048.
δ = arctan ( R D ) d δ = 1 1 + ( R + D ) 2 ( 1 D d R + R D 2 d D ) .
d ϕ = ϕ δ d δ + ϕ ( A / A ) d ( A / A ) [ ( ϕ ( δ + d δ ) - ϕ ( δ ) ] A / A + [ ϕ [ A / A + d ( A / A ) ] - ϕ ( A / A ) } δ .
A / A = 2 { ϕ ( 34 ) = 0.22423 , ϕ ( 35 ) = 0.2356 , ϕ ( 2 ) = 0.00086 , ϕ ( 2 , 10 ) = 0.00095 , A / A = 2 , 048 { ϕ ( 34 ) = 0.22423 , ϕ ( 2 ) = 0.00086 ,
{ d ϕ L = 0.011 , d ϕ S = 0.000009.
d E = E V d V ,
N = ϕ L E S - ϕ S E L , D = N + E L - E S
d p = | ( D - N ) E s D 2 | d ϕ L + | - ( D - N ) E L D 2 | d ϕ s + | ( D - N ) ϕ L + N D 2 | ( E V ) V s d V + | - ( D - N ) ϕ S - N D 2 | ( E V ) V L d V .
R U ( E S ) = t Σ ( E S i - E S ) 2 n ( n - 1 )
R U ( p ) = [ ( D - N ) ϕ L + N D 2 R U ( E S ) ] 2 + [ ( D - N ) ϕ S + N D 2 R U ( E L ) ] 2 ,
tan Δ 2 = 12 2 - 2.83 2 3400 Δ 2 = 0.1 ° .
p 9 = 0.1079 ± 0.0391 = { 0.1470 , 0.0688 , p 5 = 0.1112 ± 0.0478 = { 0.1590 , 0.0634.
S = 1 - 6 ( i = 1 10 d i 2 ) / [ 10 ( 10 2 - 1 ) ] ;

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