Abstract

Many electro-optical systems exhibit a performance which is governed by both temporal and spatial response characteristics. The analysis of such systems may be facilitated by the use of the spatiotemporal transfer function introduced earlier. Here we formulate the conditions when this is necessary, present some experimental results, and apply the theory to the display of a moving object.

© 1983 Optical Society of America

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References

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  1. L. Levi, Opt. Acta 17, 869 (1970).
    [CrossRef]
  2. M. Assous, “Influence of Time on the Spread Function,” student project at Jerusalem College of Technology (1980), in Hebrew.
  3. JEDEC Publ. No. 16, “Optical Characteristics of CRT Screens,” JEDEC Electron Tube Council, Newark, N.J. (1960).
  4. H. W. Leverenz, An Introduction to Luminescence of Solids (Dover, New York, 1968), pp. 255 and 269.

1970 (1)

L. Levi, Opt. Acta 17, 869 (1970).
[CrossRef]

Assous, M.

M. Assous, “Influence of Time on the Spread Function,” student project at Jerusalem College of Technology (1980), in Hebrew.

Leverenz, H. W.

H. W. Leverenz, An Introduction to Luminescence of Solids (Dover, New York, 1968), pp. 255 and 269.

Levi, L.

L. Levi, Opt. Acta 17, 869 (1970).
[CrossRef]

Opt. Acta (1)

L. Levi, Opt. Acta 17, 869 (1970).
[CrossRef]

Other (3)

M. Assous, “Influence of Time on the Spread Function,” student project at Jerusalem College of Technology (1980), in Hebrew.

JEDEC Publ. No. 16, “Optical Characteristics of CRT Screens,” JEDEC Electron Tube Council, Newark, N.J. (1960).

H. W. Leverenz, An Introduction to Luminescence of Solids (Dover, New York, 1968), pp. 255 and 269.

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Figures (2)

Fig. 1
Fig. 1

Line-impulse response. The luminance L is viewed as the product of the impulse response I(t) and the line-spread function P(x).

Fig. 2
Fig. 2

Experimental arrangement. Light source (S) imaged, via lens (L), on slit in plane P1. P1 is imaged via lens (L2) on plane (P2) on photocathode of image tube (T). The tube's phosphor screen in plane P3 is imaged via lens (L3) and rotable mirror (M) on plane P4, containing slit, attached to micrometer driven detector (D). The output signal is displayed on CRT via amplifier (A).

Equations (34)

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T ̂ ( ν , ν t ) = P ̂ ( x , t ) exp [ i 2 π ( ν x + ν t t ) ] d x d t ,
P ̂ ( x , t ) P ( x ) I ( t ) ,
L ( x , t ) = j ( t ) L ( x , 0 ) ,
P ( x ) = L ( x , t ) / L ( x , t ) d x ,
= L ( x , 0 ) / L ( x , 0 ) d x ,
I ( t ) = L ( x , t ) / L ( x ; t ) d t ,
= j ( t ) / j ( t ) d t ,
d L d t = a ( L ) .
t = L 0 L t d L a ( L ) = A ( L t ) A ( L 0 ) ,
A ( L ) = d L / a ( L ) ,
A ( L t ) = A ( L c ) + t ,
L t = L t ( t , L c ) .
I ( t ) = L t / L t d t .
P ̂ ( x , t ) = L t [ t , L ( x , 0 ) ] / L t [ t , L ( x , 0 ) ] d x d t ,
P ( x ) = L t [ t , L ( x , 0 ) ] / L t [ t , L ( x , 0 ) ] d x .
d L d t = c , t < L 0 / c , = 0 , t L 0 / c .
A ( L ) = L / c , A ( L t ) = L t / c = L 0 / c + t , L t = L 0 c t , t < L 0 / c .
I ( t ) = ( L 0 c t ) / 0 L 0 / c ( L 0 c t ) d t = 2 c ( L 0 c t ) / L 0 2 .
d L d t = b L .
L t = L 0 exp ( b t ) ,
I ( t ) = b exp ( b t ) ,
L = p d n d t = q 2 n 2 ,
n = p n 0 / ( p + n 0 q 2 t ) ,
n 0 = L 0 / q .
L = L 0 / ( 1 + q L 0 t / p ) 2 .
I ( t ) = p q L 0 / ( p + q L 0 t ) 2 .
f ̂ ( x , t ) = f ̂ ( x υ d t ) = f ̂ ( x υ t ) , υ constant ,
f ̂ ( x , t ) = f ̂ ( x υ t ) P ̂ ( x x , t t ) d x d t .
F ̂ ( ν , ν t ) = exp [ i 2 π ( ν x + ν t t ) ] f ̂ ( x , t ) d x d t .
F ̂ ( ν , ν t ) = exp [ i 2 π ( ν x + ν t t ) ] × { I ( t t ) f ̂ ( x υ t ) P ( x x ) d x d t } d x d t .
F ( ν , ν t ) = f ̂ ( x υ t ) [ I ( t t ) exp ( i 2 π ν t t ) d t P ( x x ) exp ( i 2 π ν x ) d x ] d x d t , = f ̂ ( x υ t ) S ( ν t ) exp ( i 2 π ν t t ) T ( ν ) exp ( i 2 π ν x ) d x d t , = S ( ν t ) T ( ν ) exp ( i 2 π ν t t ) f ̂ ( x υ t ) exp ( i 2 π ν x ) d x d t , = S ( ν t ) T ( ν ) F ( ν ) exp ( i 2 π ν t t ) exp ( i 2 π υ ν t ) d t , = S ( ν t ) T ( ν ) F ( ν ) δ ( ν t υ ν ) .
ν t υ / | υ | 2
S ( ν t ) = F [ exp ( t / t ) ] = ( 1 + i 2 π τ ν t ) / [ 1 + ( 2 π τ ν t ) 2 ] .
F ( ν ) = F ( ν ) T ( ν ) ( 1 + i 2 π τ υ ν ) / [ 1 + ( 2 π τ υ ν ) 2 ] ,

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