Abstract

Recent work on the ultimate sensitivity of radiation detectors is reviewed and discussed. It is shown that the validity of Clark Jones’ treatment is more restricted than was supposed. By an extension of his argument a general method is obtained giving the ultimate sensitivity throughout the region of the electromagnetic spectrum in which the limit is set by temperature radiation. It is found that Clark Jones’ method, suitably interpreted, is a useful approximation in most practical cases. The method is applied to a number of detectors. The well-known result for the noise level in a radio antenna is confirmed. The performance of certain photo-multipliers and photo-conductive infra-red cells is assessed. It is found that the sensitivities of recent lead telluride cells closely approach the ultimate limit corresponding to room temperature. Consequently, improvements to these cells cannot give rise to substantially increased sensitivity unless the cells are used in cooled enclosures.

© 1949 Optical Society of America

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References

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  1. J. M. W. Milatz and H. A. Van der Velden, Physica 10, 369 (1943).
    [Crossref]
  2. J. G. Daunt—unpublished report circulated by Admiralty.
  3. M. Golay, Rev. Sci. Inst. 18, 347 (1947).
    [Crossref]
  4. R. Clark Jones, J. Opt. Soc. Am. 37, No. 11, 879 (1947).
  5. R. H. Fowler, Statistical Mechanics (Cambridge University Press, London, 1929), Eq. 1435.
  6. P. B. Fellgett, Proc. Phys. Soc. 62B, 351 (1949).
    [Crossref]
  7. H. Nyquist, Phys. Rev. 32, 110 (1928).
    [Crossref]
  8. W. B. Lewis, Proc. Phys. Soc. 59, 34 (1947).
    [Crossref]
  9. W. Schottky, Ann. d. Physik 57, 541 (1918).
    [Crossref]
  10. International Critical Tables, first edition, Vol. 1, p. 92.
  11. R. Engstrom, J. Opt. Soc. Am. 37, No. 6, 421 (1947).
    [Crossref]
  12. S. Dushman, Rev. Mod. Phys. 2, 382 (1930).
    [Crossref]
  13. A. S. Baxter, private communication.
  14. Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
    [Crossref]
  15. Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
    [Crossref]
  16. O. Simpson, Proc. Phys. Soc. 61, 486 (1948).
    [Crossref]
  17. M. S. Neiman, Proc. I.R.E.667 (December, 1943).
  18. O. Rice, Bell Sys. Tech. J. 24, 46 (1945).
    [Crossref]
  19. E. T. Whittaker and G. Robinson, Calculus of Observations (Blackie and Son Limited, London, 1924) page 182.
  20. R. E. Burgess, Proc. Phys. Soc. 53, 293 (1941).
    [Crossref]
  21. E. F. Daly, private communication.

1949 (1)

P. B. Fellgett, Proc. Phys. Soc. 62B, 351 (1949).
[Crossref]

1948 (2)

Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
[Crossref]

O. Simpson, Proc. Phys. Soc. 61, 486 (1948).
[Crossref]

1947 (4)

M. Golay, Rev. Sci. Inst. 18, 347 (1947).
[Crossref]

R. Clark Jones, J. Opt. Soc. Am. 37, No. 11, 879 (1947).

W. B. Lewis, Proc. Phys. Soc. 59, 34 (1947).
[Crossref]

R. Engstrom, J. Opt. Soc. Am. 37, No. 6, 421 (1947).
[Crossref]

1946 (1)

Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
[Crossref]

1945 (1)

O. Rice, Bell Sys. Tech. J. 24, 46 (1945).
[Crossref]

1943 (2)

J. M. W. Milatz and H. A. Van der Velden, Physica 10, 369 (1943).
[Crossref]

M. S. Neiman, Proc. I.R.E.667 (December, 1943).

1941 (1)

R. E. Burgess, Proc. Phys. Soc. 53, 293 (1941).
[Crossref]

1930 (1)

S. Dushman, Rev. Mod. Phys. 2, 382 (1930).
[Crossref]

1928 (1)

H. Nyquist, Phys. Rev. 32, 110 (1928).
[Crossref]

1918 (1)

W. Schottky, Ann. d. Physik 57, 541 (1918).
[Crossref]

Baxter, A. S.

A. S. Baxter, private communication.

Blackwell,

Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
[Crossref]

Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
[Crossref]

Burgess, R. E.

R. E. Burgess, Proc. Phys. Soc. 53, 293 (1941).
[Crossref]

Clark Jones, R.

Daly, E. F.

E. F. Daly, private communication.

Daunt, J. G.

J. G. Daunt—unpublished report circulated by Admiralty.

Dushman, S.

S. Dushman, Rev. Mod. Phys. 2, 382 (1930).
[Crossref]

Engstrom, R.

R. Engstrom, J. Opt. Soc. Am. 37, No. 6, 421 (1947).
[Crossref]

Fellgett,

Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
[Crossref]

Fellgett, P. B.

P. B. Fellgett, Proc. Phys. Soc. 62B, 351 (1949).
[Crossref]

Fowler, R. H.

R. H. Fowler, Statistical Mechanics (Cambridge University Press, London, 1929), Eq. 1435.

Golay, M.

M. Golay, Rev. Sci. Inst. 18, 347 (1947).
[Crossref]

Lewis, W. B.

W. B. Lewis, Proc. Phys. Soc. 59, 34 (1947).
[Crossref]

Milatz, J. M. W.

J. M. W. Milatz and H. A. Van der Velden, Physica 10, 369 (1943).
[Crossref]

Neiman, M. S.

M. S. Neiman, Proc. I.R.E.667 (December, 1943).

Nyquist, H.

H. Nyquist, Phys. Rev. 32, 110 (1928).
[Crossref]

Rice, O.

O. Rice, Bell Sys. Tech. J. 24, 46 (1945).
[Crossref]

Robinson, G.

E. T. Whittaker and G. Robinson, Calculus of Observations (Blackie and Son Limited, London, 1924) page 182.

Schottky, W.

W. Schottky, Ann. d. Physik 57, 541 (1918).
[Crossref]

Simpson,

Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
[Crossref]

Simpson, O.

O. Simpson, Proc. Phys. Soc. 61, 486 (1948).
[Crossref]

Sutherland,

Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
[Crossref]

Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
[Crossref]

Van der Velden, H. A.

J. M. W. Milatz and H. A. Van der Velden, Physica 10, 369 (1943).
[Crossref]

Whittaker, E. T.

E. T. Whittaker and G. Robinson, Calculus of Observations (Blackie and Son Limited, London, 1924) page 182.

Ann. d. Physik (1)

W. Schottky, Ann. d. Physik 57, 541 (1918).
[Crossref]

Bell Sys. Tech. J. (1)

O. Rice, Bell Sys. Tech. J. 24, 46 (1945).
[Crossref]

J. Opt. Soc. Am. (2)

R. Engstrom, J. Opt. Soc. Am. 37, No. 6, 421 (1947).
[Crossref]

R. Clark Jones, J. Opt. Soc. Am. 37, No. 11, 879 (1947).

Nature (2)

Sutherland, Blackwell, and Fellgett, Nature 158, 873 (1946).
[Crossref]

Simpson, Sutherland, and Blackwell, Nature 161, 281 (1948).
[Crossref]

Phys. Rev. (1)

H. Nyquist, Phys. Rev. 32, 110 (1928).
[Crossref]

Physica (1)

J. M. W. Milatz and H. A. Van der Velden, Physica 10, 369 (1943).
[Crossref]

Proc. I.R.E. (1)

M. S. Neiman, Proc. I.R.E.667 (December, 1943).

Proc. Phys. Soc. (4)

R. E. Burgess, Proc. Phys. Soc. 53, 293 (1941).
[Crossref]

W. B. Lewis, Proc. Phys. Soc. 59, 34 (1947).
[Crossref]

P. B. Fellgett, Proc. Phys. Soc. 62B, 351 (1949).
[Crossref]

O. Simpson, Proc. Phys. Soc. 61, 486 (1948).
[Crossref]

Rev. Mod. Phys. (1)

S. Dushman, Rev. Mod. Phys. 2, 382 (1930).
[Crossref]

Rev. Sci. Inst. (1)

M. Golay, Rev. Sci. Inst. 18, 347 (1947).
[Crossref]

Other (6)

J. G. Daunt—unpublished report circulated by Admiralty.

R. H. Fowler, Statistical Mechanics (Cambridge University Press, London, 1929), Eq. 1435.

A. S. Baxter, private communication.

International Critical Tables, first edition, Vol. 1, p. 92.

E. T. Whittaker and G. Robinson, Calculus of Observations (Blackie and Son Limited, London, 1924) page 182.

E. F. Daly, private communication.

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Figures (2)

F. 1
F. 1

Noise power spectrum for black detector, f(ν), T = 288°K.

F. 2
F. 2

A—Lead sulfide cell. Solid CO2 cooled, exposed to radiation from 288 °K. B—Lead telluride cell. Liquid air cooled, exposed to radiation from 288°K. (a) Energy spectral response of cell, (ν). (b) Noise power spectrum for black receiver, f(ν). (c) Noise power spectrum for cell, f(ν)(ν), to same scale as f(ν). Curves (b) and (c) touch at the peak of the cell response.

Tables (1)

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Table I

Equations (37)

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Δ E 2 Av = k T 2 E T = k T 2 c ,
Δ T N 2 Av = k T 2 / c .
Δ T N 2 Av = k T 2 c = 4 k T 2 r 4 c r = 4 k T 2 B r .
W = 1 s ( 4 k T 2 B r ) 1 2 .
R D = T S 2 r
Δ T N 2 Av = 4 k T 2 B r ,
1 / r = d d T ( σ A T 4 ) = 4 σ A 1 T 3 ( where 1 = + T 4 d d T , and σ is Stefan’s constant ) .
W = 4 [ k T 5 B σ A 1 s 2 ] 1 2 .
0 x s 1 e x 1 d x = Γ ( s ) ζ ( s ) = ( s 1 ) ! n = 1 1 n s .
m ( ν ) d ν = ncA 4 d ν = c A 4 · 8 π ν 2 d ν c 3 ( e h ν / k T 1 )
1 r r = d d T ( E ( ν ) d ν ) = h ν · d m d T = 2 π A c 2 · h 2 ν 4 e h ν / k T d ν k T 2 ( e h ν / k T 1 ) 2 .
Δ E 2 Av d ν = 2 π A c 2 · h 2 ν 4 e h ν / k T d ν ( e h ν / k T 1 ) 2 .
Δ m 2 Av = Δ E 2 Av / h 2 ν 2 = m [ 1 + 1 ( e h ν / k T 1 ) ] = m [ 1 + n / N ]
Δ E 2 Av = 2 π A c 2 0 ( ν ) e h ν / k T h 2 ν 4 ( e h ν / k T 1 ) 2 d ν = 2 π A ( k T ) 5 c 2 h 3 0 ( ν ) e x x 4 ( e x 1 ) 2 d x .
Δ E 2 Av = 2 π A ( k T ) 5 c 2 h 3 0 4 x 3 ( e x 1 ) d x = 8 π A ( k T ) 5 c 2 h 3 · Γ ( 4 ) ζ ( 4 ) = 8 π 5 A ( k T ) 5 15 c 2 h 3 .
Δ m 2 Av = 2 π A c 2 0 ( ν ) e h ν / k T ν 2 d ν ( e h ν / k T 1 ) 2 .
Δ m 2 Av = 2 π A ( k T ) 3 c 2 h 3 0 2 x ( e x 1 ) d x = 2 π A ( k T ) 3 c 2 h 3 2 ζ ( 2 ) .
m = 1 4 c A 0 n d ν = 2 π A c 2 0 ν 2 d ν ( e h ν / k T 1 ) = 2 π A ( k T ) 3 c 2 h 3 x 2 d x ( e x 1 ) = 2 π A ( k T ) 3 c 2 h 3 Γ ( 3 ) ζ ( 3 ) .
Δ m 2 Av = ζ ( 2 ) ζ ( 3 ) m = 1.37 m .
E = 2 π A ( k T ) 4 c 2 h 3 0 { x 3 / ( e x 1 ) } d x = 2 π A ( k T ) 3 c 2 h 3 Γ ( 4 ) ζ ( 4 ) .
h ν ¯ E = 3 k T ζ ( 4 ) ζ ( 3 ) = 2.70 k T .
h ν ¯ Δ = k T { 12 ζ ( 4 ) / ζ ( 2 ) } 1 2 = ( 4 3 ) 1 2 π k T = 2.8 k T .
m = 2 π 0 A c 2 ν 0 ν 2 d ν ( e h ν / k T 1 ) .
m 2 π 0 k T c 2 h ν 0 2 e h ν 0 / k T .
m = 0.018 quanta per second .
I = 120.4 ( 1 r ) T 2 e h ν 0 / k T amp . / cm 2
Δ E 2 Av = 2 π A h 2 c 2 0 ( ν ) ν 4 e h ν / k T d ν = 2 π A h 2 c 2 0 ( ν ) f ( ν ) d ν .
( ν ) = sensitivity at ν sensitivity at peak of spectral response .
ν 0 f ( ν ) d ν = 7.7 × 10 12 erg 2 / cm 2 sec .
Δ E Av 2 = 1.42 × 7.7 + 10 12 erg 2 / cm 2 sec . , W s = 4.7 × 10 13 watt , W = 2.1 × 10 13 watt .
Δ E Av 2 = 8.5 × 7.7 × 10 12 erg 2 / cm 2 sec . W s = 11.4 × 10 13 watt , W = 2.3 × 10 13 watt .
Δ E 2 d ν = 2 π A c 2 ( k T ) 2 ν 2 d ν .
F / λ 2 = D cos 2 x 4 π
Δ E 2 Av = 2 π k 2 T 2 d ν λ 2 · λ 2 2 π k 2 T 2 d ν .
2 k 2 T 2 B 2 = 1 R 2 { V 2 V ¯ 2 } 2 Av = 1 R 2 { V ¯ 4 2 V ¯ 2 · V ¯ 2 + ( V ¯ 2 ) 2 } = 2 R 2 ( V ¯ 2 ) 2 = 2 ( Ē N ) 2 .
Ē N = kTB .
P ¯ N = 4 Ē N = 4 kTB .