Abstract

We compare the measured Wiener spectra of practical film graininess of radiographic granularity with theoretical results of the conventional random dot model and the extended random dot model which has been proposed previously. Comparing theoretical Wiener spectra and computer-generated random dot patterns with measured results, we found that whereas the extended random dot model can reproduce the experimental results in low frequency regions by using proper values of parameters of the model, the conventional random dot model cannot.

© 1989 Optical Society of America

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References

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  1. K. Rossmann, “Modulation Transfer Function of Radiographic Systems Using Fluorescent Screens,” J. Opt. Soc. Am. 52, 774–777 (1962).
    [CrossRef]
  2. B. Picinbono, “Statistical Model for the Distribution of Silver Grains in Photographic Negatives,” Compt. Rend. 240, 2206–2208 (1955).
  3. M. Savelli, “Study of a Model for Representing the Statistical Properties of Transmittance of Photographic Emulsions,” Compt. Rend. 244, 1710–1712 (1957).
  4. B. E. Bayer, “Relation Between Granularity and Density for a Random-Dot Model,” J. Opt. Soc. Am. 54, 1485–2490 (1964).
    [CrossRef]
  5. S. A. Benton, R. E. Kronauer, “Properties of Granularity Wiener Spectra,” J. Opt. Soc. Am. 61, 524–529 (1971).
    [CrossRef]
  6. L. Berwart, “Wiener Spectrum of Experimental Emulsions with Cubic Homogeneous Grains, Comparison of the Spectra with the Wiener Spectra of Commercial Emulsions,” J. Photogr. Sci. 17, 41–47 (1969).
  7. J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), pp. 299–302.
  8. M. Takano, “Size of Silver Halide Grain and Wiener Spectrum,” Oyo-Butsuri (in Japanese), 37, 1120–1127 (1988).
  9. H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).
  10. K. Tanaka, S. Uchida, “Extended Random-Dot Model,” J. Opt. Soc. Am. 73, 1312–1319 (1983).
    [CrossRef]
  11. K. Tanaka, S. Uchida, “Random-Dot Model for Grain Aggregations Having Size Distribution,” J. Opt. Soc. Am. A 2, 1883–1884 (1985).
    [CrossRef]
  12. J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), p. 307.

1988 (1)

M. Takano, “Size of Silver Halide Grain and Wiener Spectrum,” Oyo-Butsuri (in Japanese), 37, 1120–1127 (1988).

1985 (1)

1983 (1)

1981 (1)

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

1971 (1)

1969 (1)

L. Berwart, “Wiener Spectrum of Experimental Emulsions with Cubic Homogeneous Grains, Comparison of the Spectra with the Wiener Spectra of Commercial Emulsions,” J. Photogr. Sci. 17, 41–47 (1969).

1964 (1)

1962 (1)

1957 (1)

M. Savelli, “Study of a Model for Representing the Statistical Properties of Transmittance of Photographic Emulsions,” Compt. Rend. 244, 1710–1712 (1957).

1955 (1)

B. Picinbono, “Statistical Model for the Distribution of Silver Grains in Photographic Negatives,” Compt. Rend. 240, 2206–2208 (1955).

Bayer, B. E.

Benton, S. A.

Berwart, L.

L. Berwart, “Wiener Spectrum of Experimental Emulsions with Cubic Homogeneous Grains, Comparison of the Spectra with the Wiener Spectra of Commercial Emulsions,” J. Photogr. Sci. 17, 41–47 (1969).

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), pp. 299–302.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), p. 307.

Kanamori, H.

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

Kronauer, R. E.

Miyake, Y.

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

Nakamori, N.

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

Picinbono, B.

B. Picinbono, “Statistical Model for the Distribution of Silver Grains in Photographic Negatives,” Compt. Rend. 240, 2206–2208 (1955).

Rossmann, K.

Savelli, M.

M. Savelli, “Study of a Model for Representing the Statistical Properties of Transmittance of Photographic Emulsions,” Compt. Rend. 244, 1710–1712 (1957).

Shaw, R.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), pp. 299–302.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), p. 307.

Takano, M.

M. Takano, “Size of Silver Halide Grain and Wiener Spectrum,” Oyo-Butsuri (in Japanese), 37, 1120–1127 (1988).

Tanaka, K.

Uchida, S.

Yamauchi, Y.

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

Compt. Rend. (2)

B. Picinbono, “Statistical Model for the Distribution of Silver Grains in Photographic Negatives,” Compt. Rend. 240, 2206–2208 (1955).

M. Savelli, “Study of a Model for Representing the Statistical Properties of Transmittance of Photographic Emulsions,” Compt. Rend. 244, 1710–1712 (1957).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

J. Photogr. Sci. (1)

L. Berwart, “Wiener Spectrum of Experimental Emulsions with Cubic Homogeneous Grains, Comparison of the Spectra with the Wiener Spectra of Commercial Emulsions,” J. Photogr. Sci. 17, 41–47 (1969).

J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese) (1)

H. Kanamori, N. Nakamori, Y. Miyake, Y. Yamauchi, “Simulation of Granularity of Radiographs Exposed with Screen Film Systems,” J. Soc. Photogr. Sci. Tech. Jpn. (in Japanese), 44, 472–476 (1981).

Oyo-Butsuri (in Japanese) (1)

M. Takano, “Size of Silver Halide Grain and Wiener Spectrum,” Oyo-Butsuri (in Japanese), 37, 1120–1127 (1988).

Other (2)

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), p. 307.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974), pp. 299–302.

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Figures (8)

Fig. 1
Fig. 1

Numerical examples of the average transmittance T ¯ of the ERDM.

Fig. 2
Fig. 2

Numerical examples of the normalized Wiener spectrum of transmittance fluctuations Wt(ω)/a of the ERDM for T ¯ = 0.5 and MS = 10. The abscissa is the spatial frequency normalized by the radius of the grain r.

Fig. 3
Fig. 3

Measured Wiener spectrum (circles) of type A film. Solid curves show three theoretical Wiener spectra of the ERDM [(A) r = 1.8 μm, MC = 0.5, MS = 7, (B) r = 1.8 μm, MC = 0.1, MS = 7, (C) r = 1.8 μm, MC = 0.1, MS = 10]. Broken curve shows the theoretical Wiener spectrum of the RDM which has same grain density with the curve (B) of the ERDM.

Fig. 4
Fig. 4

Computer-generated random dot patterns. The upper half corresponds to the solid curve (B) of the ERDM in Fig. 3 and the lower half corresponds to the broken curve of the RDM.

Fig. 5
Fig. 5

Microphotograph of the type A film.

Fig. 6
Fig. 6

Measured Wiener spectrum (circles) of type B film. Solid curves show three theoretical Wiener spectra of the ERDM [(A) r = 1.5 μm, MC = 0.5, MS = 8, (B) r = 1.5 μm, MC = 0.1, MS = 8, (C) r = 1.5 μm, MC = 0.1, MS = 10]. Broken curve shows the theoretical Wiener spectrum of the RDM which has same grain density with the curve (B) of the ERDM.

Fig. 7
Fig. 7

Computer-generated random dot patterns. The upper half corresponds to the solid curve (B) of the ERDM in Fig. 6 and the lower half corresponds to the broken curve of the RDM.

Fig. 8
Fig. 8

Microphotograph of the type B film.

Equations (9)

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T ¯ = exp [ ( 1 t ) υ a ] , for RDM
T ¯ = exp ( Q A { 1 exp [ ( 1 t ) q a ] } ) , for ERDM
Φ ( Δ ) = T ¯ 2 exp { ( 1 t ) 2 υ a α [ Δ / ( 2 r ) ] } , for RDM
Φ ( Δ ) = exp [ 2 Q A { 1 α [ Δ / ( 2 R ) ] } × ( 1 exp { ( 1 t ) q a t ( 1 t ) q a α [ Δ / ( 2 r ) ] } ) Q A α [ Δ / ( 2 R ) ] ( 1 exp { 2 ( 1 t ) q a + ( 1 t ) 2 × q a α [ Δ / ( 2 r ) ] } ) ] , for EDRM ,
α ( x ) = ( 2 / π [ cos 1 ( x ) x ( 1 x 2 ) 1 / 2 ] x 1 0 x > 1
M C = q / Q , M S = R / r .
W t ( ω ) 2 π 0 [ Φ ( Δ ) T ¯ 2 ] J 0 ( 2 π ω Δ ) Δ d Δ ,
ϕ ( Δ ) = ( log 10 e ) 2 [ Φ ( Δ ) T ¯ 2 ] / T ¯ 2 .
W ( ω = ) 2 π 0 ϕ ( Δ ) J 0 ( 2 π ω Δ ) Δ d Δ .

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