Abstract

The complete Fourier analysis in space and time is performed for a three-dimensional model of thin-film thermal-imaging systems. The model includes heat losses by thermal radiation and by heat conduction within the film as well as into the adjacent medium. Dirac δ functions are used for the description of the specific heat and the thermal conductivity. The exact solutions of the basic heat equation are applied for a comparison of different types of the Panicon, a passive thermal imaging device. The relevant temperature response is illustrated in the Fourier space. The inclusion of the adjacent medium implies an occasional maximum of the response function in k space.

© 1974 Optical Society of America

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References

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  1. R. W. Astheimer, E. M. Wormser, J. Opt. Soc. Am. 49, 179 (1959).
    [CrossRef]
  2. C. Hilsum, W. R. Harding, Infrared Phys. 1, 67 (1961).
    [CrossRef]
  3. F. Urbach, N. R. Nail, D. Pearlman, J. Opt. Soc. Am. 39, 1011 (1949).
    [CrossRef]
  4. J. L. Fergason, T. P. Vogl, M. Garbuny, U.S. Patent3,114,836 (1963).
  5. G. W. McDaniel, D. Z. Robinson, Appl. Opt. 1, 311 (1962).
    [CrossRef]
  6. A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
    [CrossRef]
  7. E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
    [CrossRef]
  8. J. Gaynor, in Proc. Internat. Congress on Photographic Science, Moscow (1970), p. 1–44.
  9. J. G. Hirschberg, Appl. Opt. 9, 761 (1970).
    [CrossRef] [PubMed]
  10. F. Mast, U. La Roche, Proc. Int. Electro-Optical Design Conf., Brighton (1971).
  11. A. I. Carlson, Appl. Opt. 8, 243 (1969).
    [CrossRef] [PubMed]
  12. F. Pointeau, Infrared Phys. 12, 137 (1972).
    [CrossRef]
  13. R. M. Logan, T. P. McLean, Infrared Phys. 13, 15 (1973).
    [CrossRef]
  14. R. M. Logan, K. Moore, Infrared Phys. 13, 37 (1973).
    [CrossRef]
  15. R. M. Logan, Infrared Phys. 13, 91 (1973).
    [CrossRef]
  16. Gretag AG, CH-8105 Regensdorf, Switzerland.
  17. F. Mast, U. La Roche, Private Communications.

1973

R. M. Logan, T. P. McLean, Infrared Phys. 13, 15 (1973).
[CrossRef]

R. M. Logan, K. Moore, Infrared Phys. 13, 37 (1973).
[CrossRef]

R. M. Logan, Infrared Phys. 13, 91 (1973).
[CrossRef]

1972

F. Pointeau, Infrared Phys. 12, 137 (1972).
[CrossRef]

1970

J. Gaynor, in Proc. Internat. Congress on Photographic Science, Moscow (1970), p. 1–44.

J. G. Hirschberg, Appl. Opt. 9, 761 (1970).
[CrossRef] [PubMed]

1969

1965

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

1962

1961

C. Hilsum, W. R. Harding, Infrared Phys. 1, 67 (1961).
[CrossRef]

1959

1949

Astheimer, R. W.

Carlson, A. I.

Fergason, J. L.

J. L. Fergason, T. P. Vogl, M. Garbuny, U.S. Patent3,114,836 (1963).

Garbuny, M.

J. L. Fergason, T. P. Vogl, M. Garbuny, U.S. Patent3,114,836 (1963).

Gaynor, J.

J. Gaynor, in Proc. Internat. Congress on Photographic Science, Moscow (1970), p. 1–44.

Hadni, A.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Harding, W. R.

C. Hilsum, W. R. Harding, Infrared Phys. 1, 67 (1961).
[CrossRef]

Henninger, Y.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Hilsum, C.

C. Hilsum, W. R. Harding, Infrared Phys. 1, 67 (1961).
[CrossRef]

Hirschberg, J. G.

La Roche, U.

F. Mast, U. La Roche, Private Communications.

F. Mast, U. La Roche, Proc. Int. Electro-Optical Design Conf., Brighton (1971).

Logan, R. M.

R. M. Logan, T. P. McLean, Infrared Phys. 13, 15 (1973).
[CrossRef]

R. M. Logan, K. Moore, Infrared Phys. 13, 37 (1973).
[CrossRef]

R. M. Logan, Infrared Phys. 13, 91 (1973).
[CrossRef]

Mast, F.

F. Mast, U. La Roche, Private Communications.

F. Mast, U. La Roche, Proc. Int. Electro-Optical Design Conf., Brighton (1971).

McDaniel, G. W.

McLean, T. P.

R. M. Logan, T. P. McLean, Infrared Phys. 13, 15 (1973).
[CrossRef]

Moore, K.

R. M. Logan, K. Moore, Infrared Phys. 13, 37 (1973).
[CrossRef]

Nail, N. R.

Pearlman, D.

Pointeau, F.

F. Pointeau, Infrared Phys. 12, 137 (1972).
[CrossRef]

Putley, E. H.

E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
[CrossRef]

Robinson, D. Z.

Savage, S. D.

E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
[CrossRef]

Thomas, R.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Urbach, F.

Vergnat, P.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Vogl, T. P.

J. L. Fergason, T. P. Vogl, M. Garbuny, U.S. Patent3,114,836 (1963).

Watton, R.

E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
[CrossRef]

Wormser, E. M.

Wreathall, W. M.

E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
[CrossRef]

Wyncke, B.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Appl. Opt.

Infrared Phys.

C. Hilsum, W. R. Harding, Infrared Phys. 1, 67 (1961).
[CrossRef]

F. Pointeau, Infrared Phys. 12, 137 (1972).
[CrossRef]

R. M. Logan, T. P. McLean, Infrared Phys. 13, 15 (1973).
[CrossRef]

R. M. Logan, K. Moore, Infrared Phys. 13, 37 (1973).
[CrossRef]

R. M. Logan, Infrared Phys. 13, 91 (1973).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.

A. Hadni, Y. Henninger, R. Thomas, P. Vergnat, B. Wyncke, J. Phys. 26, 345 (1965).
[CrossRef]

Proc. Internat. Congress on Photographic Science, Moscow

J. Gaynor, in Proc. Internat. Congress on Photographic Science, Moscow (1970), p. 1–44.

Other

E. H. Putley, R. Watton, W. M. Wreathall, S. D. Savage, in Proc. Fifth Symp. Photoelectronic Image Devices (Imperial College, London, 1971); B. R. Holeman, W. M. Wreathall, J. Phys. D 4, 1898 (1971).
[CrossRef]

J. L. Fergason, T. P. Vogl, M. Garbuny, U.S. Patent3,114,836 (1963).

Gretag AG, CH-8105 Regensdorf, Switzerland.

F. Mast, U. La Roche, Private Communications.

F. Mast, U. La Roche, Proc. Int. Electro-Optical Design Conf., Brighton (1971).

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Figures (4)

Fig. 1
Fig. 1

Model of the thin film imager.

Fig. 2
Fig. 2

Temperature response of the Panicon: normalized amplitude and phase as functions of ω and k.

Fig. 3
Fig. 3

Temperature response of the prototype Membrane Panicon with Xe: normalized amplitude and phase as functions of ω and k.

Fig. 4
Fig. 4

Temperature response of the hypothetical Membrane Panicon with a vacuum chamber: normalized amplitude and phase as functions of ω and k.

Tables (1)

Tables Icon

Table I Characteristic Data of 3 Image Converters

Equations (30)

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θ ( x , y , z , t ) = T ( x , y , z , t ) - T 0 ,
θ [ x , y , z ( b / 2 ) , t ]
ρ c = ρ m · c m + δ ( z ) · b · ρ f · c f ; λ = [ λ m + δ ( z ) b λ f 0 0 0 λ m + δ ( z ) b λ f 0 0 0 λ m ] .
α I ( x , y , t )
α · δ ( z ) I ( x , y , t )
4 σ T 3 { θ [ x , y , + ( b / 2 ) , t ] + θ [ x , y , - ( b / 2 ) , t ] }
8 σ T 3 δ ( z ) θ ( x , y , z , t ) .
ρ c θ t ( x , y , z , t ) = + div [ λ grad θ ( x , y , z , t ) ] - 8 σ T 3 δ ( z ) θ ( x , y , z , t ) + α δ ( z ) I ( x , y , t ) ,
j = - λ grad θ ( x , y , z , t ) .
ρ m c m ( θ / t ) = λ m 2 x y z θ
0 = ( θ / t ) - a m 2 θ ,
a m = λ m / ρ m c m .
θ ( x , y , - z , t ) = θ ( x , y , z , t ) ,
lim ζ 0 S 0 1 S S d x d y - ζ + ζ d z ρ c θ t = lim ζ 0 S 0 1 S S d x d y ( 2 ζ ρ m c m + b ρ f c f ) θ t = b ρ f c f θ 0 t = b · λ f · 2 x y θ 0 + 2 λ m θ z | 0 - 8 σ T 3 θ 0 + α I ,
I = A θ 0 - B 2 x y θ 0 + C θ 0 t - D θ z | 0 ,
θ 0 = θ ( x , y , 0 , t ) , θ z | 0 = θ z ( x , y , + 0 , t ) ,
A = ( / α ) · 8 σ T 3 , B = ( λ f / α ) · b , C = ( ρ f c f / α ) · b , D = 2 ( λ m / α ) .
I ( x , y , t ) = I c .
θ ( x , y , z , t ) = θ c · ( 1 - z / w ) , θ c / I c = [ A ( 1 + w 0 / w ) ] - 1 ,
w 0 = D / A = λ m / 4 σ T 3 .
I ( x , y , t ) = I ( k ) cos k x ,
θ ( x , y , z , t ) = θ ( k ) · cos k x · exp ( - k z )
θ c ( k ) / I c ( k ) = ( 1 / A ) [ 1 + w 0 k + ( k / k 0 ) ] - 2
k 0 = ( A / B ) 1 / 2 = ( 8 σ T 3 / λ f b ) 1 / 2 .
I ( x , y , t ) = I ( k , w ) cos k x cos ω t .
θ ( x , y , z , t ) = θ ( k , w ) cos k x cos [ ω t - ψ ( k , ω ) - K ( k , ω ) z ] · exp [ - q ( k , ω ) · z ] .
q ( k , ω ) K ( k , ω ) = k ( 2 ) 1 / 2 [ ( 1 + ω 2 a m 2 k 4 ) 1 / 2 ± 1 ] 1 / 2 .
θ ( k , ω ) / I ( k , ω ) = 1 A { [ 1 + ( k k 0 ) 2 + w 0 q ] 2 + [ ( ω ω 0 ) + w 0 K ] 2 } - 1 / 2 ,
tan ψ ( k , ω ) = ( ω / ω 0 ) + ω 0 K 1 + ( k / k ) 2 + w 0 q ,
ω 0 = A / C = ( 8 σ T 3 ) / ( b ρ f c f ) .

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