Abstract

In Part I, a classification system for radiation detectors is proposed. The system is based upon the manner in which the noise equivalent power depends upon the time constant and the sensitive area, when the sensitivity is limited either by radiation fluctuations or by internally generated noise.

The major part of Part I is devoted to establishing the reference condition for the measuring of the noise equivalent power. In establishing the reference condition of measurement (Section 6), the output of the detector in the absence of a signal is first equalized so that the noise power per unit frequency band width is constant. The reference time constant is then defined in terms of the relative response as a function of signal modulation frequency (Section 7). The equalization is then modified by the addition of an RC low pass filter with a time constant equal to the reference time constant, and the noise equivalent power is measured. The power so obtained is termed the noise equivalent power in reference condition A, denoted by Pm. This procedure has the property that the noise equivalent power of the detector is measured in the presence of noise whose band width is equal to the band width of the detector.

In order to establish the reference condition of measurement it is necessary to consider the various sources of noise which are involved in detectors (Section 2), and the various types of time constants (Section 3). The important concept of responsivity-to-noise ratio is defined in Section 4. A general theorem involving the sensitive area and the responsivity-to-noise ratio is established in Section 5.

After the question of detectors with non-uniform spectral sensitivity is discussed in Section 8, the classification system is defined in Section 9: A detector is a Type I detector if its noise equivalent power depends upon its sensitive area A and its reference time constant τ in accordance with

Pm=A12/k1τ12,
where k1 is independent of A and τ. A Type II detector is defined by
Pm=A12/k2τ,
and more generally, a Type n detector is defined by
Pm=A12/knτ12n.

The usefulness of the proposed classification is illustrated in Section 10 by its application to sequential scanning systems.

In Part II the classification system proposed in Part I is used to determine the type number of each of eight different kinds of detectors. By a detailed analysis of each kind of detector, it is found that all of the detectors studied are either Type I or Type II detectors. The results of the analysis are summarized in Table I.

The detectors studied include bolometers (Section 2), thermocouples and thermopiles (Section 3), the Golay detector (Section 4), photographic plates and films (Section 5), vacuum and gas photo-tubes and photo-multiplier tubes (Section 6), and dipole antennas (Section 7). In the case of the dipole antenna it is shown that Johnson noise becomes equivalent to the noise produced by radiation fluctuations.

© 1949 Optical Society of America

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References

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  1. C. J. Christensen and G. L. Pearson, Bell Sys. Tech. J. 15, 197–223 (1936).
    [CrossRef]
  2. B. Davydov and B. Gurevich, “Voltage fluctuations in semi-conductors,” J. Phys., USSR,  7, 138–140 (1943). In Russian.
  3. Albert Rose, J. Opt. Soc. Am. 38, 196–208 (1948);J. Soc. Mot. Pict. Eng. 47, 273–294 (1946).
    [CrossRef] [PubMed]
  4. In order that this specification be unique, it is. necessary to require that the complex gain versus frequency function of the amplifier be of the minimum-theta type. See Hendrik W. Bode, Network Analysis and Feedback Amplifier Design (D. Van Nostrand Company, Inc., New York, 1945).
  5. Liouville’s Theorem. See E. T. Whittaker and G. N. Watson, Modern Analysis, fourth edition (Cambridge University Press, London, 1927), p. 105.
  6. Harald H. Nielsen, Comparative Testing of Thermal Detectors, , Contract OEMsr-1168 (October31, 1945).
  7. Marcel J. E. Golay, Rev. Sci. Inst. 18, 347–362 (1947).
    [CrossRef]
  8. For a summary of the experimental information, See L. A. Jones and G. C. Higgins, J. Opt. Soc. Am. 36, 203–227 (1946).
  9. Private communication from David L. MacAdam dated January4, 1949.
  10. Photographic Plates for Scientific and Technical Use, sixth edition (Eastman Kodak Company, Rochester, 1948), p. 11.
  11. Ralph W. Engstrom, J. Opt. Soc. Am. 37, 420–431 (1947).
    [CrossRef]
  12. E. B. Moullin, Spontaneous fluctuations of voltage (Clarendon Press, Oxford, 1938), Chapter 2.
  13. Ralph Engstrom in a private communication dated January3, 1949, suggests that the cathode dark current of the very best 1P21 is about 10−15ampere, and that the average cathode dark current for this tube is about 10−14ampere. The HB-3 RCA Tube Manual states that the maximum anode dark current of the 1P21 is 10−7ampere when the gain is 2×106; this corresponds to a maximum cathode dark current of 5×10−14ampere.
  14. R. D. Sard, J. App. Phys. 17, 768–777 (1946).
    [CrossRef]
  15. J. A. Rajchman and R. L. Snyder, Electronics 13, 20–23, 58, 60, December (1940);W. Shockley and J. R. Pierce, Proc. Inst. Rad. Eng. 26, 321–332 (1938);private communication dated August17, 1948, from Hartland S. Snyder (Brook-haven National Laboratory).

1948 (1)

1947 (2)

Ralph W. Engstrom, J. Opt. Soc. Am. 37, 420–431 (1947).
[CrossRef]

Marcel J. E. Golay, Rev. Sci. Inst. 18, 347–362 (1947).
[CrossRef]

1946 (2)

1943 (1)

B. Davydov and B. Gurevich, “Voltage fluctuations in semi-conductors,” J. Phys., USSR,  7, 138–140 (1943). In Russian.

1940 (1)

J. A. Rajchman and R. L. Snyder, Electronics 13, 20–23, 58, 60, December (1940);W. Shockley and J. R. Pierce, Proc. Inst. Rad. Eng. 26, 321–332 (1938);private communication dated August17, 1948, from Hartland S. Snyder (Brook-haven National Laboratory).

1936 (1)

C. J. Christensen and G. L. Pearson, Bell Sys. Tech. J. 15, 197–223 (1936).
[CrossRef]

Bode, Hendrik W.

In order that this specification be unique, it is. necessary to require that the complex gain versus frequency function of the amplifier be of the minimum-theta type. See Hendrik W. Bode, Network Analysis and Feedback Amplifier Design (D. Van Nostrand Company, Inc., New York, 1945).

Christensen, C. J.

C. J. Christensen and G. L. Pearson, Bell Sys. Tech. J. 15, 197–223 (1936).
[CrossRef]

Davydov, B.

B. Davydov and B. Gurevich, “Voltage fluctuations in semi-conductors,” J. Phys., USSR,  7, 138–140 (1943). In Russian.

Engstrom, Ralph

Ralph Engstrom in a private communication dated January3, 1949, suggests that the cathode dark current of the very best 1P21 is about 10−15ampere, and that the average cathode dark current for this tube is about 10−14ampere. The HB-3 RCA Tube Manual states that the maximum anode dark current of the 1P21 is 10−7ampere when the gain is 2×106; this corresponds to a maximum cathode dark current of 5×10−14ampere.

Engstrom, Ralph W.

Golay, Marcel J. E.

Marcel J. E. Golay, Rev. Sci. Inst. 18, 347–362 (1947).
[CrossRef]

Gurevich, B.

B. Davydov and B. Gurevich, “Voltage fluctuations in semi-conductors,” J. Phys., USSR,  7, 138–140 (1943). In Russian.

Higgins, G. C.

Jones, L. A.

MacAdam, David L.

Private communication from David L. MacAdam dated January4, 1949.

Moullin, E. B.

E. B. Moullin, Spontaneous fluctuations of voltage (Clarendon Press, Oxford, 1938), Chapter 2.

Nielsen, Harald H.

Harald H. Nielsen, Comparative Testing of Thermal Detectors, , Contract OEMsr-1168 (October31, 1945).

Pearson, G. L.

C. J. Christensen and G. L. Pearson, Bell Sys. Tech. J. 15, 197–223 (1936).
[CrossRef]

Rajchman, J. A.

J. A. Rajchman and R. L. Snyder, Electronics 13, 20–23, 58, 60, December (1940);W. Shockley and J. R. Pierce, Proc. Inst. Rad. Eng. 26, 321–332 (1938);private communication dated August17, 1948, from Hartland S. Snyder (Brook-haven National Laboratory).

Rose, Albert

Sard, R. D.

R. D. Sard, J. App. Phys. 17, 768–777 (1946).
[CrossRef]

Snyder, R. L.

J. A. Rajchman and R. L. Snyder, Electronics 13, 20–23, 58, 60, December (1940);W. Shockley and J. R. Pierce, Proc. Inst. Rad. Eng. 26, 321–332 (1938);private communication dated August17, 1948, from Hartland S. Snyder (Brook-haven National Laboratory).

Watson, G. N.

Liouville’s Theorem. See E. T. Whittaker and G. N. Watson, Modern Analysis, fourth edition (Cambridge University Press, London, 1927), p. 105.

Whittaker, E. T.

Liouville’s Theorem. See E. T. Whittaker and G. N. Watson, Modern Analysis, fourth edition (Cambridge University Press, London, 1927), p. 105.

Bell Sys. Tech. J. (1)

C. J. Christensen and G. L. Pearson, Bell Sys. Tech. J. 15, 197–223 (1936).
[CrossRef]

Electronics (1)

J. A. Rajchman and R. L. Snyder, Electronics 13, 20–23, 58, 60, December (1940);W. Shockley and J. R. Pierce, Proc. Inst. Rad. Eng. 26, 321–332 (1938);private communication dated August17, 1948, from Hartland S. Snyder (Brook-haven National Laboratory).

J. App. Phys. (1)

R. D. Sard, J. App. Phys. 17, 768–777 (1946).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys., USSR (1)

B. Davydov and B. Gurevich, “Voltage fluctuations in semi-conductors,” J. Phys., USSR,  7, 138–140 (1943). In Russian.

Rev. Sci. Inst. (1)

Marcel J. E. Golay, Rev. Sci. Inst. 18, 347–362 (1947).
[CrossRef]

Other (7)

E. B. Moullin, Spontaneous fluctuations of voltage (Clarendon Press, Oxford, 1938), Chapter 2.

Ralph Engstrom in a private communication dated January3, 1949, suggests that the cathode dark current of the very best 1P21 is about 10−15ampere, and that the average cathode dark current for this tube is about 10−14ampere. The HB-3 RCA Tube Manual states that the maximum anode dark current of the 1P21 is 10−7ampere when the gain is 2×106; this corresponds to a maximum cathode dark current of 5×10−14ampere.

Private communication from David L. MacAdam dated January4, 1949.

Photographic Plates for Scientific and Technical Use, sixth edition (Eastman Kodak Company, Rochester, 1948), p. 11.

In order that this specification be unique, it is. necessary to require that the complex gain versus frequency function of the amplifier be of the minimum-theta type. See Hendrik W. Bode, Network Analysis and Feedback Amplifier Design (D. Van Nostrand Company, Inc., New York, 1945).

Liouville’s Theorem. See E. T. Whittaker and G. N. Watson, Modern Analysis, fourth edition (Cambridge University Press, London, 1927), p. 105.

Harald H. Nielsen, Comparative Testing of Thermal Detectors, , Contract OEMsr-1168 (October31, 1945).

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Figures (6)

F. 1
F. 1

Responsivity as a function of the frequency for the Schwarz thermopile, as measured by Nielsen. Since the noise is assumed to be Johnson noise only, the curve representing the reponsivity-to-noise ratio has the same shape. The curve slopes off more gradually at high frequencies than it does in the case of a detector with a single time constant. This characteristic defines a curve as a Class I curve.

F. 2
F. 2

Responsivity as a function of the frequency for the Strong bolometer, as measured by Nielsen. Since the noise is assumed to be Johnson noise only, the curve representing the responsivity-to-noise ratio has the same shape. The curve falls off more rapidly at high frequencies than it does in the case of a single time constant. This characteristic defines the curve as a Class II curve.

F. 3
F. 3

Responsivity as a function of the frequency for the Golay pneumatic heat detector, as measured by Nielsen. Since the noise is assumed to be Johnson noise only, the curve representing the responsivity-to-noise ratio has the same shape. The defining characteristic of the Class III type of curve is that the responsivity-to-noise ratio falls off at low frequencies.

F. 4
F. 4

Showing on logarithmic coordinate scales the relation between the responsivity-to-noise ratio R and the frequency f for a Type I detector with a single time constant. The separate curves correspond to different values of the reference time constant. The curves all approach asymptotically the same horizontal line at low frequencies, in accordance with the fact that the zero-frequency responsivity-to-noise ratio is independent of the time constant for Type I detectors.

F. 5
F. 5

Showing on logarithmic coordinate scales the relation between the responsivity-to-noise ratio R and the frequency f for a Type II detector with a single time constant. The separate curves correspond to different values of the reference time constant. A straight line drawn tangent to the knees of the separate curves has a negative slope of 3 decibels per octave. These curves make very clear the fact that in order to maximize the responsivity-to-noise ratio for a sinusoidal signal with angular frequency ω, the time constant of a Type II detector should be set equal to 1/ω.

F. 6
F. 6

Showing on logarithmic coordinate scales the relation betweer. the responsivity-to-noise ratio R and the frequency f for a Type I detector with a single time constant. The separate curves correspond to different values of the reference time constant. The curves all approach asymptotically the same straight line at high frequencies. This line has a negative slope of 6 decibels per octave.

Tables (1)

Tables Icon

Table I Summary of the classification of the eight kinds of detectors studied in Part II. The range of attainable reference time constants for each of the detectors is also shown, as well as the section in which the detector is studied.

Equations (81)

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P m = A 1 2 / k 1 τ 1 2 ,
P m = A 1 2 / k 2 τ ,
P m = A 1 2 / k n τ 1 2 n .
R S / N 1 2 .
P m = E N / S 0 .
N ( f ) = N 0 1 + ( 2 π f τ ) 2 ,
E N 2 = 0 N ( f ) d f = N 0 / 4 τ .
S 0 = N 0 1 2 R 0 .
P m = 1 / ( 2 τ 1 2 R 0 ) .
H m P m / A 1 2 ,
Δ f = 0 N ( f ) d f N max .
P m = P · R s R 0 · ( 1 / 4 τ Δ f ) 1 2 · ( N ( f s ) N max ) 1 2 ,
R ( f ) = R 0 ( 1 + ( 2 π f τ ) 2 ) 1 2 ,
τ = 1 4 R max 2 0 R 2 d f ,
R 0 = k n τ 1 2 ( n 1 ) 2 A 1 2 ,
P m = ( A 1 2 / k n τ 1 2 n ) .
R ( f ) = k n τ 1 2 ( n 1 ) 2 A 1 2 ( 1 + ( 2 π f τ ) 2 ) 1 2 .
P = 1 4 π D 2 T S ,
ω = A / f 2 ,
N D / 2 f .
P = 1 2 π NDT ( A / ω ) 1 2 S .
P m = 1 2 π NDT ( A / ω ) 1 2 S m ,
P m = ( A / τ n ) 1 2 / k n ,
1 / S m = 1 2 π k n NDT ( τ n / ω ) 1 2 .
Ω ˙ = ω / τ .
1 / S m = 1 4 π k n NDT ( ω n 1 / Ω ˙ n ) 1 2 .
( ω n 1 / Ω ˙ n ) 1 2
1 / Ω 1 2 .
ω 1 2 / Ω ˙ .
N 0 = 4 kTR ,
R 0 = S 0 / ( 4 kTR ) 1 2 .
S 0 = α R I Δ T / P ,
Δ T = P / κ A ,
τ = C / κ ,
S 0 = α R I τ / C A .
I 2 R = θ κ A = θ C A / τ .
S 0 = α ( θ R τ / C A ) 1 2
R 0 = α 2 · ( θ kTC ) 1 2 · τ 1 2 A 1 2 .
R 0 = α 2 · ( θ k T κ ) 1 2 · 1 A 1 2
P m = ( k T 2 C A ) 1 2 τ · ( 1 α 2 θ T ) 1 2 .
Δ T r . m . s . = ( k T 2 / C A ) 1 2 .
P m = ( k T 2 C A ) 1 2 τ .
P m = ( k T 2 C A ) 1 2 τ ( 1 + 1 α 2 θ T ) 1 2 .
S 0 = n Q Δ T / P ,
Δ T = P κ A + n ( σ 1 + σ 2 ) ,
τ = C A κ A + n ( σ 1 + σ 2 ) ,
σ 1 = k 1 a 1 / l 1 ,
σ 2 = k 2 a 2 / l 2 ,
S 0 = n Q τ / C A .
R = n ( l 1 ρ 1 / a 1 + l 2 ρ 2 / a 2 ) .
R = n ( k 1 ρ 1 / σ 1 + k 2 ρ 2 / σ 2 ) .
σ 1 σ 2 = ( k 1 ρ 1 k 2 ρ 2 ) 1 2 ,
a 1 l 2 a 2 l 1 = ( k 2 ρ 1 k 2 ρ 1 ) 1 2 .
R = n σ 1 + σ 2 ( ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 ) 2 ,
R = n 2 τ C A ( ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 ) 2 ( 1 + κ A n ( σ 1 + σ 2 ) ) .
S 0 = Q ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 · ( 1 + κ A n ( σ 1 + σ 2 ) ) 1 2 ( R τ C A ) 1 2 .
R 0 = Q ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 · 1 ( kTC ) 1 2 · ( 1 + κ A n ( σ 1 + σ 2 ) ) 1 2 · τ 1 2 A 1 2 .
κ A n ( σ 1 + σ 2 ) .
P m = ( k T 2 C A ) 1 2 τ · ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 2 Q T 1 2 ( 1 + κ A n ( σ 1 + σ 2 ) ) 1 2 .
P m = ( k T 2 C A ) 1 2 τ · { 1 + [ ( k 1 ρ 1 ) 1 2 + ( k 2 ρ 2 ) 1 2 ] 2 4 Q 2 T ( 1 + κ A n ( σ 1 + σ 2 ) ) } 1 2 .
Δ D = k P τ / A ,
P m = A Δ D r . m . s . / k τ
Δ D r . m . s . = κ A 1 2 ,
P m = ( κ / k ) ( A 1 2 / τ ) .
i 2 = 2 e I c Δ f ,
i 2 = ( 4 k T / R ) Δ f .
i 2 = ( 2 e I c + 4 k T / R ) Δ f .
I c R ( 2 k T / e ) = 0.0518 volt at T = 300 ° K .
τ = R 0 C ( R e q / R 0 ) 1 2 , τ = ( R 0 R e q ) 1 2 C ,
i m = ( 2 e I c Δ f ) 1 2 = ( e I c / 2 τ ) 1 2 .
i 2 = 2 e I c F G 2 Δ f = 2 e I a F G Δ f ,
F n n 2 p n ( n n p n ) 2 .
I c R 2 k T / e G 2 .
V f = α V ν 2 ,
N f = α 2 Δ ν N ν 2 ,
N ν = 4 kTZ ,
N f 1 2 = 4 α kTZ ( Δ ν ) 1 2 .
V ν 2 = Z P ,
V f = α Z P
S V f / P = α Z .
R 0 = S N f 1 2 = 1 4 k T ( Δ ν ) 1 2 .