Abstract

Transparent luminescing screens can be used as image transducers in radiographic and image-intensifier systems. The modulation transfer function (MTF) and efficiency of these screens when used in conjunction with a receiver or recording medium are obtained from the derivation of the point spread function of the screen–receiver system. The derivation accounts for all optical paths and attenuations of the luminescent energy producing the spread function. Both the theoretical MTF’s and energy-transducing efficiencies of several screen–receiver systems are presented for various system parameters. The MTF of an actual (ZnS) screen–film system, computed from this derivation, was found to be in excellent agreement with the MTF of the system determined by photographic photometry.

© 1973 Optical Society of America

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References

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  1. A. R. Spowart, J. Photogr. Sci. 19, 1 (1971).
  2. F. J. Studer and D. A. Cusano, J. Opt. Soc. Am. 45, 493 (1955).
    [Crossref]
  3. C. Feldman and M. O’Hara, J. Opt. Soc. Am. 47, 300 (1957).
    [Crossref]
  4. C. Feldman, J. Opt. Soc. Am. 47, 790 (1957).
    [Crossref] [PubMed]
  5. C. Feldman, Natl. Acad. Sci. - Natl. Res. Counc. Publ. 595, 169 (1958).
  6. C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).
  7. F. K. Davey, U.S. patent No.2 851 612.
  8. For convenience, the word “light” will be used when discussing the luminescent energy, although its spectral distribution could fall outside the visible region.
  9. R. N. Wolfe, E. W. Marchand, and J. J. DePalma, J. Opt. Soc. Am. 58, 1245 (1968).
    [Crossref]

1971 (1)

A. R. Spowart, J. Photogr. Sci. 19, 1 (1971).

1968 (1)

1959 (1)

C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).

1958 (1)

C. Feldman, Natl. Acad. Sci. - Natl. Res. Counc. Publ. 595, 169 (1958).

1957 (2)

1955 (1)

Albrecht, C.

C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).

Cusano, D. A.

Davey, F. K.

F. K. Davey, U.S. patent No.2 851 612.

DePalma, J. J.

Feldman, C.

Marchand, E. W.

O’Hara, M.

Oosterkamp, W. J.

C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).

Spowart, A. R.

A. R. Spowart, J. Photogr. Sci. 19, 1 (1971).

Studer, F. J.

van Osenbruggen, C.

C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).

Wolfe, R. N.

J. Opt. Soc. Am. (4)

J. Photogr. Sci. (1)

A. R. Spowart, J. Photogr. Sci. 19, 1 (1971).

Medica Mundi (1)

C. Albrecht, W. J. Oosterkamp, and C. van Osenbruggen, Medica Mundi 5, 80 (1959).

Natl. Acad. Sci. - Natl. Res. Counc. Publ. (1)

C. Feldman, Natl. Acad. Sci. - Natl. Res. Counc. Publ. 595, 169 (1958).

Other (2)

F. K. Davey, U.S. patent No.2 851 612.

For convenience, the word “light” will be used when discussing the luminescent energy, although its spectral distribution could fall outside the visible region.

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Figures (9)

Fig. 1
Fig. 1

Cross-sectional view of a transparent luminescing screen showing the geometrical parameters used in the derivation of the point spread function of the screen–receiver system.

Fig. 2
Fig. 2

Reference transparent luminescent screen–receiver system. The screen absorbs 50% of the x-ray energy, has a luminescence efficiency (∊) of 5%, and does not absorb any luminescent energy. The refractive index of the screen at the luminescent wavelength is 1.7.

Fig. 3
Fig. 3

MTF of the reference screen–receiver system. The overall energy-transducing efficiency of this system is 0.24%.

Fig. 4
Fig. 4

Change of the MTF and efficiency of the reference (R) system due to a change of absorption of the exciting energy; – – – receiver 0.01 mm below screen that absorbs 90% of the x-ray energy.

Fig. 5
Fig. 5

Change of the MTF and efficiency of the reference system when the screen absorbs 30 or 70% of the luminescent energy over a path length of 0.5 mm.

Fig. 6
Fig. 6

Change of the MTF and efficiency of the reference system when the thickness of the screen is varied.

Fig. 7
Fig. 7

Change of the MTF of the reference system when the receiver separation distance is altered.

Fig. 8
Fig. 8

Dependence of the MTF and efficiency of the reference system on the reflectance of the back surface of the screen.

Fig. 9
Fig. 9

Comparison of the predicted and measured MTF’s for a hot-pressed ZnS transparent fluorescent screen: – – – closed-form solution, ○ photographic photometry.

Equations (24)

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U τ = τ 13 U i = τ 13 E a ,
d U ( z ) = τ 13 K 1 U 1 e K 1 z d z
d U ( z ) = τ 13 K E 1 e K 1 z a d z ,
= total luminesent energy radiated from d V total exciting energy absorbed by d V ,
d 2 U ( z , α ) = τ 13 K 1 U i e K 1 z sin α d α d z / 2 .
ρ P ( α ) 12 e K 1 l 0 d 2 U / 2 ,
ρ N ( α ) 12 e K 1 l 0 d 2 U / 2 .
d 2 U P ( z , α ; m ) = ρ P m / 2 ( α ) 12 ρ P m / 2 ( α ) 13 τ P ( α ) 12 × e K 1 L ( z , α ; m ) d 2 U ( z , α ) / 2 ,
d 2 U N ( z , α ; m ) = ρ N m / 2 ( α ) 12 ρ N m / 2 ( α ) 13 τ N ( α ) 12 × e K 1 L ( z , α ; m ) d 2 U ( z , α ) / 2 .
L ( z , α ; m ) = l 0 + l 1 + .. . + l m = [ ( m + 1 ) T z ] sec α ,
r out = L sin α ,
r = r out + S sin α [ ( n 2 / n 1 ) 2 sin 2 α ] 1 2 ,
d 2 U P ( z , α ; m ) = ρ P ( m 1 ) / 2 ( α ) 12 ρ P ( m + 1 ) / 2 ( α ) 13 τ P ( α ) 12 × e K 1 L ( z , α ; m ) d 2 U ( z , α ) / 2 ,
d 2 U N ( z , α ; m ) = ρ N ( m 1 ) / 2 ( α ) 12 ρ N ( m + 1 ) / 2 ( α ) 13 τ N ( α ) 12 × e K 1 L ( z , α ; m ) d 2 U ( z , α ) / 2 ,
L ( z , α ; m ) = ( m T + z ) sec α ,
r out = L sin α ,
r = r out + S sin α [ ( n 2 / n 1 ) 2 sin 2 α ] 1 2 ,
d 2 U ( z , α ) = d 2 U ( z , r ) = m = 0 [ d 2 U P ( z , α ; m ) + d 2 U N ( z , α ; m ) ] .
d E ( z , r ) = d 2 U ( z , r ) / d A ;
E ( r ) = 1 2 π r d r z = 0 z = T d 2 U ( z , r ) .
E ( r ) = ( τ 13 K 1 U i / 8 π d r ) 0 T { j = 0 [ ρ P m / 2 ( α ) 12 ρ P m / 2 ( α ) 13 τ P ( α ) 12 + ρ N m / 2 ( α ) 12 ρ N m / 2 ( α ) 13 τ N ( α ) 12 ] e K 1 L ( z , α ; m ) sin α d α + k = 1 [ ρ P ( m 1 ) / 2 ( α ) 12 ρ P ( m + 1 ) / 2 ( α ) 13 τ P ( α ) 12 + ρ N ( m 1 ) / 2 ( α ) 12 ρ N ( m + 1 ) / 2 ( α ) 13 τ N ( α ) 12 ] e K 1 L ( z , α ; m ) sin α d α } e K 1 z d z ,
d r / d α = [ ( m + 1 ) T z ] sec 2 α + ( n 2 / n 1 ) 2 S cos α [ ( n 2 / n 1 ) 2 sin 2 α ] 3 2 ;
sin α d α / r d r = r 1 sin α cos 2 α { ( m + 1 ) T z + ( n 2 / n 1 ) 2 S cos 3 α [ ( n 2 / n 1 ) 2 sin 2 α ] 3 2 } 1 ;
Efficency = total luminscenst energy reaching the receiver total exciting energy incident on the screen .