Abstract

An optical method for grey level pseudocolor encoding in real time based on the scattering properties of film grain noise is proposed. The light scattered by the film is studied by means of a lognormal model applied to the wave front emerging from the object. Three beams, each with a primary color, are used to illuminate the original black-and-white picture, giving a pseudocolored image.

© 1983 Optical Society of America

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References

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  1. J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
    [CrossRef]
  2. H. K. Lin, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
    [CrossRef]
  3. G. Indebetouw, J. Opt. 9, 1 (1978).
    [CrossRef]
  4. A. Tai, F. T. S. Yu, H. Chen, Opt. Lett. 3, 190 (1978).
    [CrossRef] [PubMed]
  5. G. Indebetouw, Appl. Opt. 18, 4206 (1979).
    [CrossRef] [PubMed]
  6. J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
    [CrossRef]
  7. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  8. H. Stark, W. R. Bennett, M. Arm, Appl. Opt. 8, 2165 (1969).
    [CrossRef] [PubMed]
  9. D. H. R. Vilkomerson, Appl. Opt. 9, 2080 (1970).
    [CrossRef] [PubMed]
  10. H. M. Smith, Appl. Opt. 11, 26 (1972).
    [CrossRef] [PubMed]
  11. J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.
  12. R. C. Jones, J. Opt. Soc. Am. 45, 799 (1955).
    [CrossRef]
  13. E. N. Leith, Photogr. Sci. Eng. 6, 75 (1962).
  14. C. W. Helstrom, J. Opt. Soc. Am. 56, 433 (1966).
    [CrossRef]
  15. J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).
    [CrossRef] [PubMed]
  16. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  17. J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Chap. 7.
  18. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.
  19. B. Picinbono, C. R. Acad. Sci. 240, 2206 (1955).
  20. M. A. Kriss, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 21.
  21. G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, in Inverse Scattering Problems in Optics, H. P. Baltes, Ed. (Springer, Berlin, 1980), Chap. 2.
  22. E. Wolf, J. Opt. Soc. Am. 68, 1597 (1978).
    [CrossRef]
  23. E. W. H. Selwyn, Photogr. J. 75, 571 (1935).
  24. E. Parzen, Modern Probability Theory and Its Applications (Wiley, New York, 1960), p. 538.
  25. J. H. Altman, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 17.
  26. J. Gasper, J. J. de Palma, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 20, Sec. D.2.
  27. R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
    [CrossRef]

1982 (1)

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

1979 (2)

J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
[CrossRef]

G. Indebetouw, Appl. Opt. 18, 4206 (1979).
[CrossRef] [PubMed]

1978 (3)

1976 (1)

H. K. Lin, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

1972 (1)

1970 (1)

1969 (2)

J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
[CrossRef]

H. Stark, W. R. Bennett, M. Arm, Appl. Opt. 8, 2165 (1969).
[CrossRef] [PubMed]

1967 (1)

1966 (2)

1962 (1)

E. N. Leith, Photogr. Sci. Eng. 6, 75 (1962).

1955 (2)

B. Picinbono, C. R. Acad. Sci. 240, 2206 (1955).

R. C. Jones, J. Opt. Soc. Am. 45, 799 (1955).
[CrossRef]

1935 (1)

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

Altman, J. H.

J. H. Altman, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 17.

Arizaga, R.

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Arm, M.

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Bennett, W. R.

Bescós, J.

J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
[CrossRef]

Bolognini, N.

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Chen, H.

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Chap. 7.

de Palma, J. J.

J. Gasper, J. J. de Palma, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 20, Sec. D.2.

Fiddy, M. A.

G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, in Inverse Scattering Problems in Optics, H. P. Baltes, Ed. (Springer, Berlin, 1980), Chap. 2.

Fried, D. L.

Garavaglia, M.

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Gasper, J.

J. Gasper, J. J. de Palma, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 20, Sec. D.2.

Gazley, C.

J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
[CrossRef]

Gea, M.

J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
[CrossRef]

Goodman, J. W.

H. K. Lin, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).
[CrossRef] [PubMed]

Helstrom, C. W.

Indebetouw, G.

Jones, R. C.

Kriss, M. A.

M. A. Kriss, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 21.

Leith, E. N.

E. N. Leith, Photogr. Sci. Eng. 6, 75 (1962).

Lin, H. K.

H. K. Lin, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

Nieto-Vesperinas, M.

G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, in Inverse Scattering Problems in Optics, H. P. Baltes, Ed. (Springer, Berlin, 1980), Chap. 2.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.

Parzen, E.

E. Parzen, Modern Probability Theory and Its Applications (Wiley, New York, 1960), p. 538.

Picinbono, B.

B. Picinbono, C. R. Acad. Sci. 240, 2206 (1955).

Rabal, H. J.

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Ross, G.

G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, in Inverse Scattering Problems in Optics, H. P. Baltes, Ed. (Springer, Berlin, 1980), Chap. 2.

Santamaria, J.

J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
[CrossRef]

Selwyn, E. W. H.

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

Shaw, R.

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

Sheppard, J. J.

J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
[CrossRef]

Sicre, E. E.

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Smith, H. M.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Stark, H.

Stratton, R. H.

J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
[CrossRef]

Tai, A.

Vilkomerson, D. H. R.

Wolf, E.

Yu, F. T. S.

Am. J. Optom. (1)

J. J. Sheppard, R. H. Stratton, C. Gazley, Am. J. Optom. 46, 735 (1969).
[CrossRef]

Appl. Opt. (4)

C. R. Acad. Sci. (1)

B. Picinbono, C. R. Acad. Sci. 240, 2206 (1955).

J. Opt. (2)

G. Indebetouw, J. Opt. 9, 1 (1978).
[CrossRef]

J. Santamaria, M. Gea, J. Bescós, J. Opt. 10, 151 (1979).
[CrossRef]

J. Opt. Soc. Am. (5)

Nouv. Rev. Opt. (1)

H. K. Lin, J. W. Goodman, Nouv. Rev. Opt. 7, 285 (1976).
[CrossRef]

Opt. Commun. (1)

R. Arizaga, N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia, Opt. Commun. 43, 12 (1982).
[CrossRef]

Opt. Lett. (1)

Photogr. J. (1)

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

Photogr. Sci. Eng. (1)

E. N. Leith, Photogr. Sci. Eng. 6, 75 (1962).

Other (9)

J. C. Dainty, in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), Chap. 7.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), p. 113.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

J. C. Dainty, R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

E. Parzen, Modern Probability Theory and Its Applications (Wiley, New York, 1960), p. 538.

J. H. Altman, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 17.

J. Gasper, J. J. de Palma, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 20, Sec. D.2.

M. A. Kriss, in The Theory of the Photographic Process, T. H. James, Ed. (Macmillan, New York, 1977), Chap. 21.

G. Ross, M. A. Fiddy, M. Nieto-Vesperinas, in Inverse Scattering Problems in Optics, H. P. Baltes, Ed. (Springer, Berlin, 1980), Chap. 2.

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Figures (11)

Fig. 1
Fig. 1

Photographs and intensity diagrams of a densitometric wedge: (a) original picture; (b) reflection image.

Fig. 2
Fig. 2

Diffuse transmission image.

Fig. 3
Fig. 3

Scattering geometry.

Fig. 4
Fig. 4

Experimental setup for measuring scattered intensities.

Fig. 5
Fig. 5

Power spectra of film grain noise.

Fig. 6
Fig. 6

Power spectra of film grain noise.

Fig. 7
Fig. 7

Scattered intensity as a function of amplitude transmittance at 18°, 30°, and 40°.

Fig. 8
Fig. 8

Plot of the film density variance σD vs the statistical mean density D ¯.

Fig. 9
Fig. 9

Optical pseudocolor system.

Fig. 10
Fig. 10

Intensity diagrams of the images obtained with each color for a continuous densitometric wedge.

Fig. 11
Fig. 11

Thermographic images for different primary colors: (a) original straight-through image (red); (b) reflection image (blue); (c) diffuse transmission image (green).

Tables (3)

Tables Icon

Table I Scattered Intensities for Ten Different Film Densities; Values for θ ⩾ 5° are Multiplied by 10−4

Tables Icon

Table II Scattered Intensities for Ten Different Densities of Film immersed in a Liquid Gate; Values for θ ⩾ 5° are Multiplied by 10−4

Tables Icon

Table III Statistical Parameters

Equations (21)

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U ( x , y ) = U 0 exp [ - l ( x , y ) ] exp [ i ϕ ( x , y ) ] ,
D ( x , y ) = - log 10 T ( x , y ) ,
I ( x , y ) = I 0 exp [ - 2 α D ( x , y ) ] ,
l ( x , y ) = α D ( x , y ) ,
U 0 = I 0 .
I ( u , v ) = 4 π 2 k 2 cos 2 θ | A d x d y exp [ - i k ( u x + v y ) ] × U 0 exp [ - α D ( x , y ) ] exp [ i ϕ ( x , y ) ] | 2 ,
exp [ - α D ( x , y ) ] exp [ - α D ( x , y ) ] exp [ i ϕ ( x , y ) ] exp [ - i ϕ ( x , y ) ] = exp [ - α D ( x , y ) ] exp [ - α D ( x , y ) ] × exp [ i ϕ ( x , y ) ] exp [ - i ϕ ( x , y ) ] .
ψ = exp [ - α d ( x , y ) ] exp [ - α D ( x , y ) ] = exp ( - 2 α D ¯ ) exp [ α 2 σ D 2 [ 1 + C D ( τ ) ] ] ,
τ = ( x - x ) 2 + ( y - y ) 2 .
Φ = exp [ i ϕ ( x , y ) ] exp [ - i ϕ ( x , y ) ] = exp { - σ ϕ 2 [ 1 - C ϕ ( τ ) ] } ,
I ( s ) = 0 exp [ - 2 α [ D ¯ - α σ D 2 ) ] exp ( - α 2 σ D 2 ) exp ( - σ ϕ 2 ) × ( 1 - s 2 ) 0 d τ τ J 0 ( k s τ ) × exp [ α 2 σ D 2 C D ( τ ) ] exp σ ϕ 2 C ϕ ( τ ) ,
0 = ( 2 π ) 3 k 2 A U 0 2
J = A U 0 2 exp [ - 2 α [ D ¯ - α σ D 2 ]
D d = D ¯ - α σ D 2
D s = [ D ¯ - α σ D 2 ] + α σ D 2 2 + σ ϕ 2 2 = D ¯ - α σ D 2 2 + σ ϕ 2 2
I ( s ) = 0 exp [ - 2 α [ D ¯ - α σ D 2 ) ] exp ( - α σ D 2 ) exp ( - σ ϕ 2 ) ( 1 - s 2 ) × [ δ ( s ) s + α 2 σ D 2 W D ( s ) + σ ϕ 2 W ϕ ( s ) ] ;
W D ( s ) = 0 d τ τ J 0 ( k s τ ) C D ( τ ) ,
W ϕ ( s ) = 0 d τ τ J 0 ( k s τ ) C ϕ ( τ ) .
C D ( τ ) = exp ( - τ ) / T ,
I ( s ) = F 0 exp [ - 2 α ( D ¯ - α σ D 2 ) exp ( - α 2 σ D 2 ) ] ( 1 - s 2 ) × [ δ ( s ) s + α 2 σ D 2 T 2 ` ( 1 + k 2 T 2 s 2 ) 3 / 2 ] .
T a = exp ( - α D d ) .

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