Abstract

In the study of the human vision system based on the temporal-modulation transfer-function curve, Kelly [J. Opt. Soc. Am. 59, 1665 (1969); 61, 537 (1971)] proposed two different diffusion models. In Kelly’s second model the theoretical results fitted well with his experimental data in a wide range of adaptation levels. However, from a mathematical point of view, this model was based on formal assumptions without reasonable justifications. The purpose here is to derive a new transfer function utilizing a more rigorous mathematical development and to show that it is compatible with Kelly’s two models.

© 1989 Optical Society of America

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References

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  1. H. E. Ives, J. Opt. Soc. Am. 6, 343 (1922).
    [CrossRef]
  2. F. Veringa, “Enige natuurkundige aspecten van het zien van gemoduleerd licht,” Ph.D. dissertation (University of Amsterdam, Amsterdam, 1961).
  3. D. H. Kelly, J. Opt. Soc. Am. 59, 1665 (1969).
    [CrossRef] [PubMed]
  4. D. H. Kelly, J. Opt. Soc. Am. 61, 537 (1971).
    [CrossRef] [PubMed]
  5. C. M. Close, D. K. Frederick, Modeling and Analysis of Dynamics Systems (Houghton Mifflin, Boston, Mass., 1978).
  6. W. J. Palm, Control System Engineering (Wiley, New York, 1986).

1971

1969

1922

Close, C. M.

C. M. Close, D. K. Frederick, Modeling and Analysis of Dynamics Systems (Houghton Mifflin, Boston, Mass., 1978).

Frederick, D. K.

C. M. Close, D. K. Frederick, Modeling and Analysis of Dynamics Systems (Houghton Mifflin, Boston, Mass., 1978).

Ives, H. E.

Kelly, D. H.

Palm, W. J.

W. J. Palm, Control System Engineering (Wiley, New York, 1986).

Veringa, F.

F. Veringa, “Enige natuurkundige aspecten van het zien van gemoduleerd licht,” Ph.D. dissertation (University of Amsterdam, Amsterdam, 1961).

J. Opt. Soc. Am.

Other

F. Veringa, “Enige natuurkundige aspecten van het zien van gemoduleerd licht,” Ph.D. dissertation (University of Amsterdam, Amsterdam, 1961).

C. M. Close, D. K. Frederick, Modeling and Analysis of Dynamics Systems (Houghton Mifflin, Boston, Mass., 1978).

W. J. Palm, Control System Engineering (Wiley, New York, 1986).

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Equations (37)

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G ( ω ) = f ( x + 1 , t ) / f ( x , t ) ,
2 f / x 2 = 2 τ ( f / t ) ,
f ( 0 , t ) = exp ( jωt ) ,
f ( , t ) = 0 .
f ( x , t ) = exp  [ ( 2 jωτ ) 1 / 2 x + jωt ]
G ( ω ) = exp  ( α ) = exp  [ ( 2 τjω ) 1 / 2 ] .
K ( 2 f / x 2 ) = ( f / t ) + ρf ,
f ( x , 0 ) = 0 .
K x F ( x , s ) = ( s + ρ ) F ( x , s ) ,
F ( x 0 , s ) = 0 .
( s + ρ ) / K = a 2 ,
p 2 F ¯ ( p , s ) pF ( 0 , s ) x F ( 0 , s ) = a 2 F ¯ ( p , s ) ,
F ¯ ( p , s ) = [ pF ( 0 , s ) + x F ( 0 , s ) ] / ( p 2 a 2 ) .
F ( x , s ) = F ( 0 , s ) cosh ax + ( 1 / a ) [ x F ( 0 , s ) ] sinh ax .
( 1 / a ) x F ( 0 , s ) = F ( 0 , s ) coth a x 0 .
F ( x , s ) / F ( 0 , s ) = cosh ax coth a x 0 sinh ax .
G ( x , x 0 , s ) = [ x F ( x , s ) ] / [ x F ( 0 , s ) ] .
G ( x , x 0 , s ) = cosh ax tanh a x 0 sinh ax .
x 0 ,
x = 1 ,
1 / K = 2 τ .
G ( 1 , , s ) = exp  { [ 2 τ ( s + ρ ) ] 1 / 2 } ,
G ( 1 , 1 , s ) = sech [ 2 τ ( s + ρ ) 1 / 2 ] ,
H ( s ) = F ( x + 1 , s ) / F ( x , s ) ,
F ( x + 1 , s ) / F ( 0 , s ) = cosh a ( x + 1 ) coth a x 0 sinh a ( x + 1 ) .
H ( s ) =  cosh a ( x + 1 ) coth a x 0 sinh a ( x + 1 )  cosh ax coth a x 0 sinh ax .
F ( , s ) = 0 .
H ( s ) = [ cosh a ( x + 1 ) sinh a ( x + 1 ) ] / × [ cosh ax sinh ax ] = exp  [ a ( x + 1 ) ] / exp  ( ax ) = exp  ( a ) ,
( 1 / 2 τ ) ( 2 f / x 2 ) = f / t , K ( 2 F / x 2 ) = ( s + ρ ) F ,
f F ,
1 / 2 τ K ,
f / t ( s + ρ ) F .
H ( s ) = exp ( a ) = exp  { [ 2 τ ( s + ρ ) ] 1 / 2 } ,
ρ = 0 .
f / t = jωf .
s + ρ = .
H ( s ) = H ( ) = exp  [ ( 2 τj ω ) 1 / 2 ] .

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