Abstract

In order to determine the relation between the visual impression of graininess and the objectively determined granularity of a wide range of granularity types, a series of samples was prepared containing uniformly exposed black-and-white materials and prints (transparencies) containing varying degrees of mottle. These samples were judged by the method of paired comparisons at different magnifications and scanned to obtain the standard deviation σ(D) for a wide range of scanning apertures. The psychophysical relationship between the two functions, (1) graininess versus magnification and (2) granularity σ(D) versus the square root of the scanning area, depends on the character of the scanning operation performed by the eye. An estimate of the size of the effective scanning spot of the eye can be obtained from these data.

© 1959 Optical Society of America

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References

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  1. L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 35, 435 (1945).
    [Crossref]
  2. Jones, Higgins, and Stultz, J. Opt. Soc. Am. 45, 107 (1955).
    [Crossref]
  3. H. J. Zweig, J. Opt. Soc. Am. 46, 805, 812 (1956).
    [Crossref]
  4. H. J. Zweig, J. Opt. Soc. Am. 49, 238 (1959).
    [Crossref]
  5. E. W. H. Selwyn, Phot. J. 75, 571 (1935).
  6. Jones, Higgins, Stultz, and Hoesterey, J. Opt. Soc. Am. 47, 312 (1957).
    [Crossref]
  7. F. Flamant, Rev. opt. 34, 433 (1955).
  8. K. F. Stultz and D. A. Koch, J. Opt. Soc. Am. 46, 832 (1956).
    [Crossref]
  9. R. C. Jones, J. Opt. Soc. Am. 45, 799 (1955).
    [Crossref]
  10. A. Marriage and E. Pitts, J. Opt. Soc. Am. 46, 1019 (1956).
    [Crossref]

1959 (1)

1957 (1)

1956 (3)

1955 (3)

1945 (1)

1935 (1)

E. W. H. Selwyn, Phot. J. 75, 571 (1935).

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Figures (14)

F. 1
F. 1

Photomicrographs showing two types of graininess: (A) sharp, clearly defined granularity pattern; (B) mottled pattern.

F. 2
F. 2

Photomicrograph of print showing mottle superimposed on primary grain.

F. 3
F. 3

Autocorrelation function of sample similar to Fig. 2. The curves are identified by the diameter d of the scanning aperture. The component attributable to the mottle is indicated by the broken curve.

F. 4
F. 4

Typical granularity spectra of primary grain and print mottle.

F. 5
F. 5

Typical curve of standard deviation for primary grain and mottle as a function of the diameter d of the scanning aperture.

F. 6
F. 6

Relative graininess of numbered samples compared with control samples A to G. The rating G+ means “higher than G.”

F. 7
F. 7

Optical system of microphotometer used to measure rms fluctuations of samples. Elements indicated by the same letter are at conjugate points.

F. 8
F. 8

Relation between standard deviation in density σ(D) and diameter d of scanning aperture for Kodak Tri-X, Kodak Panatomic-X, and Eastman Fine Grain Release Positive Films (solid lines) and prints of the former two on the last (broken lines).

F. 9
F. 9

Relation between σ(D) and d for two negative materials (broken lines), four prints made with specular illumination (solid lines), and four prints made with diffuse illumination (dotted lines). The numbers on the curves correspond to the sample numbers in Table I.

F. 10
F. 10

Relation between σ(D) and d for the seven control samples.

F. 11
F. 11

Average coefficient of variation between granularity and graininess for the 10 samples in Table I as a function of the diameter of the scanning aperture.

F. 12
F. 12

Estimated spread-function of the human eye on the assumptions that f(x)∼epx and p = 0.125.

F. 13
F. 13

Sine-wave response of the human eye on the basis of the spread-function shown in Fig. 12.

F. 14
F. 14

Comparison between granularity A and graininess B for the 10 samples of Table I at the three apertures giving the best average correlation for the viewing magnifications used. Granularity was measured in terms of σ(D); graininess by comparison with the control samples listed in Table III.

Tables (3)

Tables Icon

Table I Characteristics of samples used in study.

Tables Icon

Table II Results of direct paired comparisons. Entries for each magnification show percentage of observers preferring sample A over sample B.

Tables Icon

Table III Graininess values, σ(D), assigned to control samples.

Equations (28)

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σ 2 print = σ 2 primary + σ 2 mottle .
d · σ = constant ,
σ 2 primary · d 2 = c 1 ( c 1 = constant ) ,
σ 2 mottle = c 2 .
σ 2 mottle σ 2 print = c 2 c 1 / d 2 + c 2 ,
σ ( V ) C σ ( T ) / T .
σ ( T ) / T = σ ( D ) / 0.4343 ,
σ ( D ) σ ( V ) / C .
k i j = graininess granularity
C . V . = σ ( k ) / k ¯ ,
k ¯ = k . j = 1 10 i = 1 10 k i j j = 1 , 2 , 3
σ ( k ) = σ j ( k ) = [ 1 10 i = 1 10 ( k i j k . j ) 2 ] 1 2 . j = 1 , 2 , 3 .
f ( r ) = f [ ( x 2 + y 2 ) 1 2 ] = ( p 2 / 2 π ) exp [ p ( x 2 + y 2 ) 1 2 ] = ( 1 / 2 π ) p 2 e p r ,
f # # ( ν 1 , ν 2 ) = f ( x , y ) exp [ 2 π i ( ν 1 x + ν 2 y ) ] dx dy ,
f # # ( ν r ) = 0 2 π 0 r f ( r ) exp [ 2 π i ν r r ( cos θ + sin θ ) ] dr d θ , = 0 r f ( r ) J 0 ( 2 π ν r r ) d r .
f # # ( ν r ) = 0.125 2 π 0 r e 0.125 r J 0 ( 2 π ν r r ) d r = [ 1 + ( 0.05 ν r ) 2 ] 3 2 .
I = e k x ,
d 2 d w 2 [ w 2 σ w 2 ( D ) ] 2 ϕ 0 ( w )
w 2 d 2 d w 2 [ σ w 2 ( D ) ] + 4 w d d w [ σ w 2 ( D ) ] + 2 σ w 2 ( D ) = 2 ϕ 0 ( w ) ,
y + P ( x ) y + Q ( x ) y = R ( x ) .
Φ ( ν 1 , ν 2 ) = ϕ 0 # # = ϕ 0 ( x 1 , x 2 ) × exp [ 2 π i ( ν 1 x 1 + ν 2 x 2 ) ] d x 1 d x 2 .
ν = ( ν 1 2 + ν 2 2 ) 1 2 , r = ( x 1 2 + x 2 2 ) 1 2 ,
Φ 0 ( ν ) = 0 0 2 π ϕ 0 ( r ) exp [ 2 π i ν r cos ( θ ϕ ) ] r dr d θ = 2 π 0 r ϕ 0 ( r ) J 0 ( 2 π ν r ) d r .
σ 2 ( d ) = 8 π d 2 0 J 1 2 ( π ν d ) ν Φ 0 ( ν ) d ν .
w 2 d 2 d w 2 [ w 1 ] + 4 w d d w [ w 1 ] + 2 w ϕ 0 ( w ) .
ϕ 0 ( w ) w 1 ,
w 2 x ( x 1 ) w x 2 + 4 w x w x 1 + 2 w x ϕ 0 ( w )
w x [ x 2 + 3 x + 2 ] ϕ 0 ( w ) .