Abstract

Theoretical expressions for Johnson noise and thermal noise in bolometers are considered, and optimization with respect to thermal conductivity and bias power is performed. Numerical approximations are given for the ultimate NEP of bolometers as a function of material parameters and compared with photon noise including photon correlations. A resonating capacitor is shown to improve the coupling to an amplifier, so that the amplifier need not limit performance even for very low temperature bolometers.

© 1984 Optical Society of America

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References

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  1. F. J. Low, J. Opt. Soc. Am. 51, 1300 (1961).
    [Crossref]
  2. J. C. Mather, Appl. Opt. 21, 1125 (1982).
    [Crossref] [PubMed]
  3. P. M. Downey, “The low-temperature conductivity of ion-implanted silicon and its application in a cryogenic far IR monolithic bolometer,” Ph.D. Thesis, Massachusetts Institute of Téchnology, 1980.

1982 (1)

1961 (1)

Downey, P. M.

P. M. Downey, “The low-temperature conductivity of ion-implanted silicon and its application in a cryogenic far IR monolithic bolometer,” Ph.D. Thesis, Massachusetts Institute of Téchnology, 1980.

Low, F. J.

Mather, J. C.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Other (1)

P. M. Downey, “The low-temperature conductivity of ion-implanted silicon and its application in a cryogenic far IR monolithic bolometer,” Ph.D. Thesis, Massachusetts Institute of Téchnology, 1980.

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Figures (3)

Fig. 1
Fig. 1

Optimum bolometer parameters at zero radiant background, as a function of the resistance exponent A. Symbols are defined in text.

Fig. 2
Fig. 2

Parameters of optimum bolometers as a function of background power. Symbols are defined in text.

Fig. 3
Fig. 3

Resonant signal enhancement for a bolometer with Z = 106j Ω at 10 Hz, a 2 × 107-Ω load resistor, and a shunt capacitance of 0.0159 μF.

Equations (17)

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NEP Johnson 2 = 4 k B T P ( 1 + ω 2 τ 2 ) ( Z + R ) 2 / ( Z - R ) 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 .
P + Q = G ( T β + 1 - T c β + 1 ) / ( β + 1 ) T β ,
NEP 2 = 4 k B T c 2 ω C 0 { t 3 ( g 2 + t 2 γ ) / A 2 - q + g ( t - t - β ) / ( β + 1 ) + g ( β + 1 ) ( t 2 β + 3 - 1 ) ( 2 β + 3 ) t β ( t β + 1 - 1 ) } .
g = m + [ ( t 2 γ + m 2 ) / { 1 + A 2 [ 1 - t - ( 2 β + 3 ) ] / ( 2 β + 3 ) } ] 1 / 2 .
4 k B T N R e ( Z ) = e noise 2 .
T N T c = R R e Z ( ω ) ( NE P ) 2 p [ 1 + ω 2 τ 2 ( Z + R 2 R ) 2 ] - 1 ( g t p A + 1 ) - 2 .
NEP = [ 4 k B T c ( ω C 0 T c ) ( 9 A + 25 A 2 ) ] 1 / 2 .
NEP = [ 4 k B T C ( ω C 0 T c ) ( 9 A + 25 A 2 ) + 4 k B T C ( 36 Q / A ) ] 1 / 2 ,
NEP photon [ 2 Q ( h ν ¯ + α ɛ f k B T S ) ] 1 / 2 ,
k B T c A 36 ( h ν ¯ + α ɛ f k B T S ) .
Z opt = ( Z L - 2 + i n 2 / e A 2 ) - 1 / 2 ,
4 k B T A L [ Re Z ( ω ) ] = e A 2 | 1 + Z ( ω ) Z L | 2 + ( i A 2 ) Z L 2 ( 1 + i n 2 e A 2 Z L 2 ) - 1 .
ω 2 τ 2 = ( Z - R Z + R ) 2 - 1.
g = β + 1 A t γ { [ 1 - t - ( β + 1 ) ] 2 - ( β - 1 ) 2 / A 2 } - 1 / 2 .
NEP 2 = ( 4 k B ω C 0 T c 2 ) { ( t β + 1 - 1 ) t β - 1 ( β + 1 ) + β + 1 2 β + 3 t 2 β + 3 - 1 t β ( t β + 1 - 1 ) } g .
( 1 + i n 2 Z L 2 / e A 2 ) 1 / 2 / { [ Z L / Z ( ω ) ] + 1 2 + i n 2 Z L 2 / e A 2 } 1 / 2 .

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