Abstract

New theoretical results for noise in cryogenic bolometers are derived. Johnson noise is reduced by as much as 60% by electrothermal feedback from the bias supply. Phonon noise in the thermal link is reduced by as much as 30% relative to the usual equilibrium formula. Photon noise in the Rayleigh-Jeans limit is computed with attention to the attenuation of the photon correlations in the light beam. Basic results on bolometer responsivity, time constant, and thermal properties are presented in a new and convenient form. Excess 1/f and contact shot noise are also discussed.

© 1982 Optical Society of America

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References

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  1. F. R. Arams, Ed., Infrared-to-Millimeter Wavelength Detectors (Artech House, Dedham, Mass., 1973).
  2. E. H. Putley, Phys. Status Solidi 6, 571 (1964).
    [CrossRef]
  3. F. J. Low, A. R. Hoffman, Appl. Opt. 2, 649 (1963).
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  4. R. C. Jones, J. Opt. Soc. Am. 43, 1 (1953).
    [CrossRef]
  5. W. S. Boyle, K. F. Rogers, J. Opt. Soc. Am. 49, 66 (1959).
    [CrossRef]
  6. F. J. Low, J. Opt. Soc. Am. 51, 1300 (1961).
    [CrossRef]
  7. S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
    [CrossRef]
  8. K. M. van Vliet, Appl. Opt. 6, 1145 (1967).
    [CrossRef] [PubMed]
  9. M. G. Hauser, “Calculation of Expected Infrared Signals and Background-Induced Noise Limitations,” available from the author, NASA/GSFC, Greenbelt, Md. 20771.
  10. A. Van der Ziel, Noise (Prentice-Hall, Englewood Cliffs, N.J., 1970), p. 109.

1968 (1)

S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
[CrossRef]

1967 (1)

1964 (1)

E. H. Putley, Phys. Status Solidi 6, 571 (1964).
[CrossRef]

1963 (1)

1961 (1)

1959 (1)

1953 (1)

Boyle, W. S.

Hauser, M. G.

M. G. Hauser, “Calculation of Expected Infrared Signals and Background-Induced Noise Limitations,” available from the author, NASA/GSFC, Greenbelt, Md. 20771.

Hoffman, A. R.

Jones, R. C.

Low, F. J.

Putley, E. H.

E. H. Putley, Phys. Status Solidi 6, 571 (1964).
[CrossRef]

Rogers, K. F.

Smith, R. A.

S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
[CrossRef]

Theriault, J. P.

S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
[CrossRef]

Van der Ziel, A.

A. Van der Ziel, Noise (Prentice-Hall, Englewood Cliffs, N.J., 1970), p. 109.

van Vliet, K. M.

Zwerdling, S.

S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
[CrossRef]

Appl. Opt. (2)

Infrared Phys. (1)

S. Zwerdling, R. A. Smith, J. P. Theriault, Infrared Phys. 8, 271 (1968).
[CrossRef]

J. Opt. Soc. Am. (3)

Phys. Status Solidi (1)

E. H. Putley, Phys. Status Solidi 6, 571 (1964).
[CrossRef]

Other (3)

F. R. Arams, Ed., Infrared-to-Millimeter Wavelength Detectors (Artech House, Dedham, Mass., 1973).

M. G. Hauser, “Calculation of Expected Infrared Signals and Background-Induced Noise Limitations,” available from the author, NASA/GSFC, Greenbelt, Md. 20771.

A. Van der Ziel, Noise (Prentice-Hall, Englewood Cliffs, N.J., 1970), p. 109.

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Figures (4)

Fig. 1
Fig. 1

Bolometer definitions: (a) bias circuit; (b) thermal design; (c) sample current–voltage plot; (d) equivalent small signal circuit; (e) complex impedance as a function of frequency.

Fig. 2
Fig. 2

(a) Johnson noise of a resistor or bolometer with thermal feedback neglected; (b) equivalent circuit including feedback; (c) Thevenin equivalent of (b).

Fig. 3
Fig. 3

Elements of thermal noise analysis. Terms are defined in text.

Fig. 4
Fig. 4

Equivalent noise circuit of bolometer and amplifier. Terms are defined in text.

Equations (39)

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S ( ω ) = 1 2 I ( Z / R ) - 1 ( Z / Z L ) + 1 1 1 + j ω τ e .
τ = C G = τ e · 2 R Z + R Z + Z L R + Z L .
Z ( ω ) = Z · 1 + j ω τ Z + R 2 Z 1 + j ω τ Z + R 2 R .
Z ( ω ) = Z + R 2 + Z - R 2 1 - j ω τ Z + R 2 R 1 + j ω τ Z + R 2 R ,
e g = - Q / 2 I ,
R N = R Z / ( R - Z ) ,
L = τ 2 R R + Z R - Z .
G = I 2 d R d T Z + R Z - R .
NEP 2 = NEP Johnson 2 + NEP thermal 2 + NEP photon 2 + NEP load 2 + NEP amplifier 2 + NEP excess 2 ,
NEP Johnson 2 = 4 k B T P | Z + R Z - R | 2 ( 1 + ω 2 τ 2 ) ,
NEP thermal 2 = 4 k B G T 2 T c T [ t k ( t ) T k ( T ) ] 2 d t T c T [ k ( t ) k ( T ) ] d t ,
NEP photon 2 = 4 A Ω c 2 ( k B T s ) 5 h 3 x 4 d x e x - 1 ( 1 + α f e x - 1 ) ( α f ) ,
x = h ν / k B T s ,
NEP load 2 = 4 k B T L Z L | 2 Z I Z R - 1 | 2 [ 1 + ω 2 τ 2 ( Z + R 2 Z ) 2 ] ,
NEP amp 2 = i A 2 | 2 Z I Z R - 1 | 2 [ 1 + ω 2 τ 2 ( Z + R 2 Z ) 2 ] + e A 2 S 2 ( ω ) .
e J ( ω ) = [ S D ( e J ) ω ] 1 / 2 ,
e J ( ω ) = e J ( ω ) j ω τ + 1 j ω τ + 2 R R + Z .
e J ( ω ) = e J ( ω ) Z L R + Z L ω + 1 j τ ω + 1 j τ e .
S D ( e J ) = 4 k B T R .
NEP = e J ( ω ) / S ( ω ) = 4 k B T P Z + R Z - R 1 + j ω τ ,
S D ( P n ) = 4 k B T 2 G ,
P n ( ω ) = [ S D ( P n ) ω ] 1 / 2 .
W ( T , T c ) = k ( t ) A ( x ) d t d x ,
W ( T , T c ) = T c T k ( t ) d t ÷ 0 X [ A ( x ) ] - 1 d x ,
G = d W / d T = k ( T ) ÷ 0 X [ A ( x ) ] - 1 d x .
q = G j b Δ t j ,
p i j = ( G j b + G j i ) Δ t j - G i j Δ t i ,
- p i j = ( G i s + G i j ) Δ t i - G j i Δ t j .
q = p i j · [ ( G j b + G j i ) ( R j b ) + G i j R i s ] - 1 .
q p i j R i j / ( R i s + R i b ) .
R i s + R i b = 1 k ( t i ) [ 0 x i 1 A ( x ) d x + x i x s 1 A ( x ) d x ] = 1 k ( t i ) 0 x d x A ( x ) = k ( t b ) k ( t i ) R b s .
R i j = ( x j - x i ) k ( t i ) A ( x i ) .
S D ( q ) = elements ( R i j R i s + R i b ) 2 4 k B t i 2 G i j .
S D ( q ) = 4 k B G T 2 T c T [ t k ( t ) T k ( T ) ] 2 d t T c T k ( t ) k ( T ) d t .
S D ( q ) = 4 k B G T 2 [ 1 - ( β 2 + 1 ) Δ + ( β + 2 ) ( 3 β + 2 ) 12 Δ 2 ] .
S D ( Q ) = 2 d ν Q ν h ν [ 1 + η ( ν ) ] ,
η ( ν ) = α f / ( e x - 1 ) ,
Q ν = 2 ( α f ) A Ω h ν 3 c 2 2 e x - 1 .
e n 2 ( ω ) = ( 4 k B T L Z L + i A 2 ( ω ) ) ( Z Z L Z + Z L ) 2 | 1 + j ω τ Z + R 2 Z 1 + j ω τ e | 2 + e A 2 ( ω ) .

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