Abstract

Since the multirecording telecine system includes the negative photographic film as a component, it is a nonlinear system. In this paper, the distortions of the three electrical primary color signals generated by the film nonlinearity are analyzed and represented as the function of the film gamma γ and recording level. The chromaticity errors of the reproduced image are calculated for various values of γ and recording level k. The condition where the color differences of all colors are less than 7.5 is defined as the linear recording condition. The regions of γ and k to satisfy this linear recording condition are calculated.

© 1974 Optical Society of America

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References

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  1. Masahide Yoneyama, Appl. Opt. 12, 2721 (1973).
    [Crossref] [PubMed]
  2. P. F. Mueller, Appl. Opt. 8, 267 (1969).
    [Crossref] [PubMed]
  3. A. Macovski, IEEE Trans. BC-16, 75 (1970).
  4. Singo Ohue, J. Jap. Soc. Appl. Phys. 29, 717 (1960).
  5. David G. Falconer, Opt. Act. 17, 639 (1970).
    [Crossref]
  6. Masahide Yoneyama, J. Inst. of the Telev. Eng. Jap. 27. 689 (1973).
  7. C. E. Kenneth Mees, T. H. James, The Theory of the Photographic Process (Macmillan Company, New York, 1971).
  8. M. Morita, T. Sato, J. Inst. Telev. Eng. Jap. 23, 44 (1969).
  9. Charles J. Hirsh, RCA Broadcast News No. 133, 30 (1967).

1973 (2)

Masahide Yoneyama, Appl. Opt. 12, 2721 (1973).
[Crossref] [PubMed]

Masahide Yoneyama, J. Inst. of the Telev. Eng. Jap. 27. 689 (1973).

1970 (2)

David G. Falconer, Opt. Act. 17, 639 (1970).
[Crossref]

A. Macovski, IEEE Trans. BC-16, 75 (1970).

1969 (2)

P. F. Mueller, Appl. Opt. 8, 267 (1969).
[Crossref] [PubMed]

M. Morita, T. Sato, J. Inst. Telev. Eng. Jap. 23, 44 (1969).

1960 (1)

Singo Ohue, J. Jap. Soc. Appl. Phys. 29, 717 (1960).

Falconer, David G.

David G. Falconer, Opt. Act. 17, 639 (1970).
[Crossref]

Hirsh, Charles J.

Charles J. Hirsh, RCA Broadcast News No. 133, 30 (1967).

James, T. H.

C. E. Kenneth Mees, T. H. James, The Theory of the Photographic Process (Macmillan Company, New York, 1971).

Kenneth Mees, C. E.

C. E. Kenneth Mees, T. H. James, The Theory of the Photographic Process (Macmillan Company, New York, 1971).

Macovski, A.

A. Macovski, IEEE Trans. BC-16, 75 (1970).

Morita, M.

M. Morita, T. Sato, J. Inst. Telev. Eng. Jap. 23, 44 (1969).

Mueller, P. F.

Ohue, Singo

Singo Ohue, J. Jap. Soc. Appl. Phys. 29, 717 (1960).

Sato, T.

M. Morita, T. Sato, J. Inst. Telev. Eng. Jap. 23, 44 (1969).

Yoneyama, Masahide

Masahide Yoneyama, J. Inst. of the Telev. Eng. Jap. 27. 689 (1973).

Masahide Yoneyama, Appl. Opt. 12, 2721 (1973).
[Crossref] [PubMed]

Appl. Opt. (2)

IEEE Trans. (1)

A. Macovski, IEEE Trans. BC-16, 75 (1970).

J. Inst. of the Telev. Eng. Jap. (1)

Masahide Yoneyama, J. Inst. of the Telev. Eng. Jap. 27. 689 (1973).

J. Inst. Telev. Eng. Jap. (1)

M. Morita, T. Sato, J. Inst. Telev. Eng. Jap. 23, 44 (1969).

J. Jap. Soc. Appl. Phys. (1)

Singo Ohue, J. Jap. Soc. Appl. Phys. 29, 717 (1960).

Opt. Act. (1)

David G. Falconer, Opt. Act. 17, 639 (1970).
[Crossref]

Other (2)

Charles J. Hirsh, RCA Broadcast News No. 133, 30 (1967).

C. E. Kenneth Mees, T. H. James, The Theory of the Photographic Process (Macmillan Company, New York, 1971).

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Figures (8)

Fig. 1
Fig. 1

TE characteristic taken from the D–logE characteristic.

Fig. 2
Fig. 2

Chromaticity errors generated from the film nonlinearity (γ = 0.6, k = 1).

Fig. 3
Fig. 3

Chromaticity errors generated from the film nonlinearity (γ = 0.6, k = 0.3).

Fig. 4
Fig. 4

Chromaticity shifting of the white for γ variation.

Fig. 5
Fig. 5

Chromaticity shifting of the white for k variation.

Fig. 6
Fig. 6

Relations between the color difference Δs and recording level k for the various high chroma colors.

Fig. 7
Fig. 7

Relations between the color difference of red and recording level k for the various chroma level ζ.

Fig. 8
Fig. 8

Regions of γ and k to satisfy the linear recording condition for all colors (Δs ≤ 7.5).

Tables (1)

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Table I Values of q1 and q2 Used for the Numerical Calculations

Equations (31)

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f ( x , y ) = g g ( x , y ) + ( 1 / 2 ) g r ( x , y ) + ( 1 / 2 ) g b ( x , y ) + g r ( x , y ) n = 1 ( 2 / N π ) sin 2 π N ( u r x + υ r y ) + g b ( x , y ) n = 1 ( 2 / N π ) sin 2 π N ( u b x υ b y ) .
g g ( x , y ) = A g g r ( x , y ) = A r g b ( x , y ) = A b } ,
E ( x , y ) = τ · [ A g + ( 1 / 2 ) A r + ( 1 / 2 ) A b ] + τ · A r n = 1 ( 2 / N π ) sin 2 π N ( u r x + υ r y ) + τ · A b n = 1 ( 2 / N π ) sin 2 π N ( u b x υ b y ) ,
E ( x , y ) = E ( ξ , η ) h ( x ξ , y η ) d ξ d η .
E ( x , y ) = τ · [ A g + ( 1 / 2 ) A r + ( 1 / 2 ) A b ] · H ( O , O ) + ( 2 / π ) τ A r · H ( u r , υ r ) sin 2 π ( u r x + υ r y ) + ( 2 / π ) τ A b H ( u b , υ b ) sin 2 π ( u b x υ b y ) ,
H ( O , O ) = 1 ; ( 2 / π ) H ( u r , υ r ) = q 1 ; ( 2 / π ) H ( u b , υ b ) = q 2 . }
E ( x , y ) = τ · [ A g + ( 1 / 2 ) A r + ( 1 / 2 ) A b ] + q 1 A r τ sin 2 π ( u r x + υ r y ) + q 2 A b τ sin 2 π ( u b x υ b y ) .
D = γ log ( E / E 0 ) ,
T = ( E / E 0 ) γ .
T = T d ( 1 + E / E d ) γ ,
T d = ( E d / E 0 ) γ .
T = T d { 1 γ · ( E / E d ) + ( 1 / 2 ) γ ( γ + 1 ) ( E / E d ) 2 ( 1 / 6 ) γ ( γ + 1 ) ( γ + 2 ) ( E / E d ) 2 + } .
T ( x , y ) = T d { 1 γ ( τ / E d ) A gg + ( 1 / 2 ) γ ( γ + 1 ) ( τ / E d ) 2 [ A gg 2 + ( 1 / 2 ) ( q 1 2 A r 2 + q 2 2 A b 2 ) ] + ( 1 / 6 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 [ A gg 3 + ( 3 / 2 ) A gg ( q 1 2 A r 2 + q 2 2 A b 2 ) ] q 1 A r [ ( τ / E d ) γ γ ( γ + 1 ) ( τ / E d ) 2 A gg + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 ( q 1 2 A r 2 / 4 + q 2 2 A b 2 / 2 + A gg 2 ) ] × sin 2 π ( u r x + υ r y ) q 2 A b [ ( τ / E d ) γ γ ( γ + 1 ) ( τ / E d ) 2 A gg + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 × ( q 2 2 A b 2 / 4 + q 1 2 A r 2 / 2 + A gg 2 ) ] sin 2 π ( u b x υ b y ) } ,
A gg = A g + ( 1 / 2 ) A r + ( 1 / 2 ) A b .
Δ T ( x , y ) = T d T ( x , y ) = T d { γ ( τ / E d ) A gg ( 1 / 2 ) γ ( γ + 1 ) ( τ / E d ) 2 [ A gg 2 + ( 1 / 2 ) ( q 1 2 A r 2 + q 2 2 A b 2 ) ] ( 1 / 6 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 [ A gg 3 + ( 3 / 2 ) A gg ( q 1 2 A r 2 + q 2 2 A b 2 ) ] + q 1 A r [ γ ( τ / E d ) γ ( γ + 1 ) ( τ / E d ) 2 A gg + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 ( q 1 2 A r 2 / 4 + q 2 2 A b 2 / 2 + A gg 2 ) ] × sin 2 π ( u r x + υ r y ) + q 2 A b [ γ ( τ / E d ) γ ( γ + 1 ) ( τ / E d ) 2 A gg + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) ( τ / E d ) 3 × ( q 2 2 A b 2 / 4 + q 1 2 A r 2 / 2 + A gg 2 ) · sin 2 π ( u b x υ b y ) } .
[ A r A g A b ] = a · [ R G B ] .
a · τ = k · E d .
Δ T ( x , y ) = T d { γ k G g ( 1 / 2 ) γ ( γ + 1 ) k 2 [ G g 2 + ( 1 / 2 ) ( q 1 2 R 2 + q 2 2 B 2 ) ] + ( 1 / 6 ) γ ( γ + 1 ) ( γ + 2 ) k 3 [ G g 3 + ( 3 / 2 ) G g ( q 1 2 R 2 + q 2 2 B 2 ) ] + q 1 k R [ γ γ ( γ + 1 ) k G g + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) k 2 ( q 1 2 R 2 / 4 + q 2 2 B 2 / 2 + G g 2 ) ] sin 2 π ( u r x + υ r y ) + q 2 k B [ γ γ ( γ + 1 ) k G g + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) k 2 ( q 2 2 B 2 / 4 + q 1 2 R 2 / 2 + G g 2 ) ] sin 2 π ( u b x υ b y ) } .
G g = G + ( 1 / 2 ) ( R + B ) .
V g g = γ k T d G g + g g V r = γ k T d R + r V b = γ k T a B + b } ,
g g = ( 1 / 2 ) γ ( γ + 1 ) k 2 T d [ G g 2 + ( 1 / 2 ) ( q 1 2 R 2 + q 2 2 B 2 ) ] + ( 1 / 6 ) γ ( γ + 1 ) ( γ + 2 ) k 3 T d [ G g 3 + ( 3 / 2 ) G g ( q 1 2 R + q 2 2 B 2 ) ] .
r = γ ( γ + 1 ) k 2 T d G g R + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) k 3 T d R ( q 1 2 R 2 / 4 + q 2 2 B 2 / 2 + G g 2 ) .
b = γ ( γ + 1 ) k 2 T d G g B + ( 1 / 2 ) γ ( γ + 1 ) ( γ + 2 ) k 3 T d B ( q 2 2 B 2 / 4 + q 1 2 R 2 / 2 + G g 2 ) .
V g = γ k T d G + g V r = γ k T d R + r V b = γ k T d B + b } ,
g = g g ( 1 / 2 ) ( r + b ) .
( U V W ) = ( 0.405 0.116 0.133 0.299 0.587 0.114 0.145 0.827 0.627 ) · ( V r V g V b ) ;
u = U / ( U + V + W ) υ = V / ( U + V + W ) } .
( U V W ) = ( 0.405 0.116 0.133 0.299 0.587 0.114 0.145 0.827 0.627 ) · ( R G B ) ;
u = U / ( U + V + W ) υ = V / ( U + V + W ) } .
blue ; [ R G B ] = [ ζ ζ 1 ] cyan ; [ R G B ] = [ ζ 1 1 ] green : [ R G B ] = [ ζ 1 ζ ] yellow : [ R G B ] = [ 1 1 ζ ] red : [ R G B ] = [ 1 ζ ζ ] purple : [ R G B ] = [ 1 ζ 1 ]
Δ s = 280 [ ( u u ) 2 + ( υ υ ) 2 ] 1 / 2

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