Abstract

An analysis of input–output characteristics of scanned systems is presented from the input camera to the output reproducer. The system characteristics are developed in terms of both spatial coordinates and spatial frequency responses in both dimensions. These include the effects of the scanning apertures of both the camera and the reproducer, in addition to the electrical filter on the resultant signal. The effects of time varying input patterns are also considered in terms of the temporal responses of the camera and the phosphor characteristic of the reproducer.

© 1970 Optical Society of America

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References

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  1. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2.
  3. G. E. Anner, Elements of Television Systems (Prentice-Hall, New York, 1951).
  4. G. M. Glasford, Fundamentals of Television Engineering (McGraw-Hill, New York, 1955), pp. 108–109.

Anner, G. E.

G. E. Anner, Elements of Television Systems (Prentice-Hall, New York, 1951).

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Glasford, G. M.

G. M. Glasford, Fundamentals of Television Engineering (McGraw-Hill, New York, 1955), pp. 108–109.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2.

Other (4)

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2.

G. E. Anner, Elements of Television Systems (Prentice-Hall, New York, 1951).

G. M. Glasford, Fundamentals of Television Engineering (McGraw-Hill, New York, 1955), pp. 108–109.

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Figures (2)

Fig. 1
Fig. 1

Basic scanned system.

Fig. 2
Fig. 2

Output spatial frequency response in fy dimension.

Equations (42)

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f ( t ) = m I ( x , y ) s [ x υ ( t m T ) , y m Y ] d x d y .
f 1 ( t ) = f ( t ) * h ( t ) = f ( t t ) h ( t ) d t = m I ( x , y ) s [ x υ ( t t m T ) , y m Y ] h ( t ) d x d y d t .
I 1 ( x 1 , y 1 ) = m f 1 ( t ) r [ x 1 υ ( t m T ) , y 1 m Y ] d t = m I ( x , y ) s [ x υ ( t t m T ) , y m Y ] × h ( t ) r [ x 1 υ ( t m T ) , y 1 m Y ] d x d y d t .
m = g ( m Y ) = 1 Y g ( z ) comb ( z Y ) d z ,
comb ( z Y ) = Y m = δ ( z m Y ) .
I 1 ( x 1 , y 1 ) = 1 Y I ( x , y ) s [ x υ ( t t z T Y ) , y z ] × h ( t ) r [ x 1 υ ( t z T Y ) , y 1 z ] comb ( z Y ) d x d y d t d t d z .
I 1 ( x 1 , y 1 ) = 1 Y I [ υ ( t t z T Y ) , z ] * s [ υ ( t t z T Y ) , z ] × h ( t ) r [ x 1 υ ( t z T Y ) , y 1 z ] comb ( z Y ) d t d t d z .
I 1 ( f x , f y ) = I 1 ( x 1 , y 1 ) exp { j [ ω x x 1 + ω y y 1 ] } d x 1 d y 1 = 1 Y I [ υ ( t t z T Y ) , z ] * s [ υ ( t t z T Y ) , z ] × comb ( z Y ) h ( t ) r [ x 1 υ ( t z T Y ) , y 1 z ] × exp { j [ ω x x 1 + ω y y 1 ] } d t d t d z d x 1 d y 1 .
I 1 ( f x , f y ) = R ( f x , f y ) Y I [ υ ( t t z T Y ) , z ] * s [ υ ( t t z T Y ) , z ] comb z Y h ( t ) × exp { j [ ω x υ ( t z T Y ) + ω y z ] } d t d t d z .
I 1 ( f x , f y ) = R ( f x , f y ) υ Y I ( α υ t , z ) * s ( α + υ t , z ) × comb ( z Y ) ( h t ) exp [ j ( ω x α + ω y z ) ] d t d α d z .
I 1 ( f x , f y ) = ( 1 / υ Y ) R ( f x , f y ) [ I ( f x , f y ) S ( f x , f y ) * Y comb ( Y f y ) δ ( f x ) ] × h ( t ) exp ( j ω x υ t ) d t = ( 1 / υ ) R ( f x , f y ) [ I ( f x , f y ) S ( f x , f y ) * comb ( Y f y ) δ ( f x ) ] H ( υ f x ) .
I 1 ( f x , f y ) = 1 υ R ( f x , f y ) H ( υ f x ) m = I ( f x , f y m Y ) × S ( f x , f y + m Y ) .
I 1 ( f x , f y ) m = 0 = ( 1 / υ ) R ( f x , f y ) S ( f x , f y ) H ( υ f x ) I ( f x , f y ) = A ( f x , f y ) I ( f x , f y ) ,
I 1 ( x 1 , y 1 ) = ( 1 / υ 2 Y ) r ( x 1 , y 1 ) * h ( x 1 / υ ) δ ( y 1 ) * { [ I ( x 1 , y 1 ) * s ( x 1 , y 1 ) ] comb ( y 1 / Y ) } .
I 1 ( x 1 , y 1 ) = r ( x 1 , y 1 ) * h ( x 1 / υ ) δ ( y 1 ) * s ( x 1 , y 1 ) * I ( x 1 , y 1 ) .
f ( t ) = m I ( x , y ) s [ x υ ( t m T ) , y Y 2 m Y ] d x d y .
I 1 ( x 1 , y 1 ) = m f 1 ( t ) r [ x 1 υ ( t m T ) , y 1 Y 2 m Y ] d t .
I 1 ( x 1 , y 1 ) = m f 1 ( t ) r [ x 1 υ ( t m T ) , y 1 Y 2 m Y ] d t .
I ˆ 1 ( x 1 , y 1 ) = I 1 ( x 1 , y 1 ) + I 1 ( x 1 , y 1 ) = m I ( x , y ) s [ x υ ( t t m T ) , y m Y 2 ] × h ( t ) r [ x 1 υ ( t m T ) , y 1 m Y 2 ] d x d y d t d t ,
I ˆ 1 ( x 1 , y 1 ) = 1 Y I [ υ ( t t z T Y ) , z 2 ] * s [ υ ( t t z T Y ) , z 2 ] x h ( t ) r [ x 1 υ ( t z T Y ) , y 1 z 2 ] comb ( z Y ) d t d t d z .
I 1 ( f x , f y ) = 1 υ R ( f x , f y ) [ I ( f x , f y ) S ( f x , f y ) * comb ( Y 2 f y ) ] H ( υ f x ) = 1 υ R ( f x , f y ) H ( υ f x ) m = I ( f x , f y 2 m Y ) × S ( f x , f y + 2 m Y ) .
f ( t ) = n m [ I ( x , y , t ) * c ( t ) ] s [ x υ ( t m T n τ ) , y m Y ] d x d y ,
I ( x , y , t ) * c ( t ) = 1 τ t τ t I ( x , y , u ) d u .
c ( t ) = rect . ( t τ / 2 τ ) .
c ( t ) = σ ( t ) * rect . ( t τ / 2 τ ) .
f 1 ( t ) = h ( t ) * t n m [ I ( υ t , m Y , t ) * s ( υ t , m Y ) c ( t ) ] .
[ I ( t ) * c ( t ) ] * h ( t ) I ( t ) * c ( t ) .
p ( t 1 ) = u ( t 1 ) exp ( t 1 / τ p ) ,
I 1 ( x 1 , y 1 , t 1 ) = n m p ( t 1 m T n τ x 1 υ ) f 1 ( t ) × r [ x 1 υ ( t m T n τ ) , y 1 m Y ] d t .
comb ( q τ ) = τ n = δ ( q n τ ) .
I 1 ( x 1 y 1 t 1 ) = 1 τ Y { I [ υ ( t t - z T Y q ) , z , t ] × * s [ υ ( t t z T Y q ) , z ] c ( t ) } h ( t ) × p ( t 1 z T Y q x 1 υ ) r [ x 1 υ ( t z T Y q ) , y 1 z ] × comb ( z y ) comb ( q τ ) d z d q d t d t .
I 1 = 1 υ τ Y [ I ( γ υ t , z , t ) * s ( γ + υ t , z ) c ( t ) ] h ( t ) × comb ( z Y ) comb ( t ( z T / Y ) ( γ / υ ) τ ) p ( t 1 + γ υ t x 1 υ ) × r ( x 1 γ , y 1 z ) d z d t d γ d t .
I 1 = 1 υ τ Y r ( x 1 , y 1 ) * xy [ I ( x 1 υ t , y 1 , t ) * s ( x 1 + υ t , y 1 ) c ( t ) ] × comb ( y 1 Y ) comb ( [ t ( y 1 T / Y ) ( x 1 / υ ) ] τ ) × n ( t ) p ( t 1 t ) d t d t .
I 1 = ( 1 / υ 2 τ Y ) h ( x 1 / υ ) * x r ( x 1 , y 1 ) p ( t 1 ) * { [ I ( x 1 , y 1 , t 1 ) * s ( x 1 , y 1 ) c ( t 1 ) ] × comb ( y 1 Y ) ( comb t 1 y 1 ( T / Y ) ( x 1 / υ ) τ ) } .
I 1 ( x 1 , y 1 , t 1 ) = 1 υ 2 τ Y n m [ p ( t 1 m T x 1 υ n τ ) ] [ I ( x 1 , m Y , t 1 ) * c ( t 1 ) ] .
I ( x , y , t ) = cos 2 π β ( x υ 1 t ) .
I ( x , y , t ) * c ( t ) = 1 τ t τ t cos 2 π β ( x υ 1 u ) d u = sinc ( τ β υ 1 ) cos 2 π β ( x υ 1 t + υ 1 τ 2 ) ,
I 1 ( x 1 , y 1 , t 1 ) = 1 υ 2 τ Y n m [ p ( t 1 m T x 1 υ n τ ) ] sinc ( τ β υ 1 ) × cos 2 π β ( x 1 υ 1 t 1 + υ 1 τ 2 ) δ ( y 1 m Y ) .
I 1 ( x 1 , y 1 , f ) = 1 υ 2 τ Y n m P ( f ) × exp { j ω [ m T + ( x 1 / υ ) + n τ ] } * [ I ( x 1 , m Y , f ) C ( f ) ] .
I ( x , y , f ) = 1 2 [ δ ( f β υ 1 ) + δ ( f + β υ 1 ) ] exp [ j ( ω x / υ 1 ) .
C ( f ) = τ sinc ( τ f ) exp [ j ( ω τ / 2 ) ] .
I 1 ( x 1 , y 1 , f ) = 1 2 υ 2 Y n m P ( f ) sinc ( r β υ 1 ) [ δ ( f β 1 υ 1 ) + δ ( f + β 1 υ 1 ) ] × exp { j ω [ m T + ( x 1 / υ ) + n τ + ( τ / 2 ) ] } δ ( y 1 m T ) .

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