Abstract

Temperature discrimination in optical and radiation pyrometers using photoelectric detectors is discussed and analyzed for the two cases where the discrimination is limited by noise in the detector and by the fundamental fluctuations in the radiation stream reaching the detector, respectively. The design of amplifiers consistent with these limits and the limits imposed by reference source instability is also discussed briefly. Graphical data are given for the calculation of detection limits for each of the two cases for both broad-spectral-bandwidth pyrometers with various long-wavelength cutoffs and for narrow-bandwidth pyrometers at various wavelengths.

The data are especially relevant to pyrometer design when the measurement of transients, small sources, or low temperatures is involved, and also in the design of narrow-spectral-bandwidth pyrometers for realizing temperature scales. For this last case an analysis is given for estimating the optimum spectral bandwidth required to obtain the maximum scale accuracy. It is shown that it should be possible to realize the International Practical Temperature Scale (IPTS) with an accuracy of about 0.01°C near 1063°C and 0.1°C near 1769°C by using a special trialkali photosurface photomultiplier or a silicon photodiode at a 1.0-μ wavelength. The accuracy of realization of a radiation scale of temperature below 1063°C is also discussed.

© 1962 Optical Society of America

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References

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  1. E. H. MacLaren, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).
  2. H. Wagenbreth, Comité Intern. Poids et Mesures Procès-Verbaux T123 (1959).
  3. V. A. Kovalevski, Soviet Instr. Exptl. Techniques 444(1959).
  4. R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infra-Red Radiation (Oxford University Press, New York, 1957).
  5. G. K. T. Conn and D. G. Avery, Infrared Methods (Academic Press Inc., New York1960).
  6. F. H. R. Almer and G. P. van Zanten, Philips Tech. Rev. 20, 89 (1958–59).
  7. J. Middlehurst and T. P. Jones, J. Sci. Instr. 38, 202 (1961).
    [Crossref]
  8. L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).
  9. G. D. Nutter, Fourth Symposium on Temperature. Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).
  10. R. D. Lee, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).
  11. J. S. Lord, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published, 1962).
  12. P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, Inc., New York, 1962).
  13. M. M. Fulk, M. M. Reynolds, and R. M. Burley, in American Institute of Physics Handbook (McGraw-Hill Book Company, New York, 1957).
  14. D. R. Lovejoy, Can. J. Phys. 36, 1397 (1958).
    [Crossref]
  15. J. A. Dobrowolski, J. Opt. Soc. Am. 49, 794 (1959).
    [Crossref]
  16. I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).
  17. L. H. Treiman, Fourth Symposium on Temperature. Columbus, Ohio, March 1961.Reinhold Publishing Corporation, New York, (to be published 1962).
  18. H. Moser, Fourth Symposium on Temperature, Columbus, Ohio, March 1961. Reinhold Publishing Corporation, New York, (to be published, 1962).

1961 (1)

J. Middlehurst and T. P. Jones, J. Sci. Instr. 38, 202 (1961).
[Crossref]

1960 (1)

I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).

1959 (4)

J. A. Dobrowolski, J. Opt. Soc. Am. 49, 794 (1959).
[Crossref]

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

H. Wagenbreth, Comité Intern. Poids et Mesures Procès-Verbaux T123 (1959).

V. A. Kovalevski, Soviet Instr. Exptl. Techniques 444(1959).

1958 (1)

D. R. Lovejoy, Can. J. Phys. 36, 1397 (1958).
[Crossref]

Almer, F. H. R.

F. H. R. Almer and G. P. van Zanten, Philips Tech. Rev. 20, 89 (1958–59).

Avery, D. G.

G. K. T. Conn and D. G. Avery, Infrared Methods (Academic Press Inc., New York1960).

Bojarski, L. A.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Burley, R. M.

M. M. Fulk, M. M. Reynolds, and R. M. Burley, in American Institute of Physics Handbook (McGraw-Hill Book Company, New York, 1957).

Chasmar, R. P.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infra-Red Radiation (Oxford University Press, New York, 1957).

Conn, G. K. T.

G. K. T. Conn and D. G. Avery, Infrared Methods (Academic Press Inc., New York1960).

Dobrowolski, J. A.

Fulk, M. M.

M. M. Fulk, M. M. Reynolds, and R. M. Burley, in American Institute of Physics Handbook (McGraw-Hill Book Company, New York, 1957).

Gordov, A. N.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Ioselson, G. L.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Jones, F. E.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infra-Red Radiation (Oxford University Press, New York, 1957).

Jones, T. P.

J. Middlehurst and T. P. Jones, J. Sci. Instr. 38, 202 (1961).
[Crossref]

Kandiba, V. V.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Kirenkov, I. I.

I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Kovalevski, V. A.

I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

V. A. Kovalevski, Soviet Instr. Exptl. Techniques 444(1959).

Krakhmalnikova, G. A.

I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Kruse, P. W.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, Inc., New York, 1962).

Lapina, E. A.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Lee, R. D.

R. D. Lee, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

Lord, J. S.

J. S. Lord, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published, 1962).

Lovejoy, D. R.

D. R. Lovejoy, Can. J. Phys. 36, 1397 (1958).
[Crossref]

MacLaren, E. H.

E. H. MacLaren, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

McGlauchlin, L. D.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, Inc., New York, 1962).

McQuistan, R. B.

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, Inc., New York, 1962).

Middlehurst, J.

J. Middlehurst and T. P. Jones, J. Sci. Instr. 38, 202 (1961).
[Crossref]

Moser, H.

H. Moser, Fourth Symposium on Temperature, Columbus, Ohio, March 1961. Reinhold Publishing Corporation, New York, (to be published, 1962).

Nutter, G. D.

G. D. Nutter, Fourth Symposium on Temperature. Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

Reynolds, M. M.

M. M. Fulk, M. M. Reynolds, and R. M. Burley, in American Institute of Physics Handbook (McGraw-Hill Book Company, New York, 1957).

Smith, R. A.

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infra-Red Radiation (Oxford University Press, New York, 1957).

Tarajanz, K. G.

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

Treiman, L. H.

L. H. Treiman, Fourth Symposium on Temperature. Columbus, Ohio, March 1961.Reinhold Publishing Corporation, New York, (to be published 1962).

van Zanten, G. P.

F. H. R. Almer and G. P. van Zanten, Philips Tech. Rev. 20, 89 (1958–59).

Wagenbreth, H.

H. Wagenbreth, Comité Intern. Poids et Mesures Procès-Verbaux T123 (1959).

Can. J. Phys. (1)

D. R. Lovejoy, Can. J. Phys. 36, 1397 (1958).
[Crossref]

Comité Intern. Poids et Mesures Procès-Verbaux (2)

H. Wagenbreth, Comité Intern. Poids et Mesures Procès-Verbaux T123 (1959).

L. A. Bojarski, A. N. Gordov, G. L. Ioselson, V. V. Kandiba, I. I. Kirenkov, V. A. Kovalevski, G. A. Krakhmalnikova, E. A. Lapina, and K. G. Tarajanz. Comité Intern. Poids et Mesures Procès-Verbaux T151 (1959).

J. Opt. Soc. Am. (1)

J. Sci. Instr. (1)

J. Middlehurst and T. P. Jones, J. Sci. Instr. 38, 202 (1961).
[Crossref]

Philips Tech. Rev. (1)

F. H. R. Almer and G. P. van Zanten, Philips Tech. Rev. 20, 89 (1958–59).

Soviet Instr. Exptl. Techniques (1)

V. A. Kovalevski, Soviet Instr. Exptl. Techniques 444(1959).

Soviet Measurement Techniques (1)

I. I. Kirenkov, V. A. Kovalevski, and G. A. Krakhmalnikova, Soviet Measurement Techniques 112(1960).

Other (10)

L. H. Treiman, Fourth Symposium on Temperature. Columbus, Ohio, March 1961.Reinhold Publishing Corporation, New York, (to be published 1962).

H. Moser, Fourth Symposium on Temperature, Columbus, Ohio, March 1961. Reinhold Publishing Corporation, New York, (to be published, 1962).

E. H. MacLaren, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

R. A. Smith, F. E. Jones, and R. P. Chasmar, The Detection and Measurement of Infra-Red Radiation (Oxford University Press, New York, 1957).

G. K. T. Conn and D. G. Avery, Infrared Methods (Academic Press Inc., New York1960).

G. D. Nutter, Fourth Symposium on Temperature. Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

R. D. Lee, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published 1962).

J. S. Lord, Fourth Symposium on Temperature, Columbus, Ohio, March 1961Reinhold Publishing Corporation, New York, (to be published, 1962).

P. W. Kruse, L. D. McGlauchlin, and R. B. McQuistan, Elements of Infrared Technology (John Wiley & Sons, Inc., New York, 1962).

M. M. Fulk, M. M. Reynolds, and R. M. Burley, in American Institute of Physics Handbook (McGraw-Hill Book Company, New York, 1957).

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Figures (5)

Fig. 1
Fig. 1

Detector-noise-limited temperature discrimination ΔT°K as a function of source temperature T°K for radiation pyrometers with various long-wavelength cutoffs. =10−4 cm2; Wm=10−10 W; Δf=1 cps.

Fig. 2
Fig. 2

Radiation-noise-limited temperature discrimination ΔT°K as a function of source temperature T°K for radiation pyrometers with various long-wavelength cutoffs. =10−4 cm2; Δf=1 cps.

Fig. 3
Fig. 3

Detector-noise-limited temperature discrimination ΔT°K as a function of source temperature T°K for monochromatic pyrometers at various wavelengths. Δλ=10−10 cm3; Wm=10−12 W; Δf=1 cps.

Fig. 4
Fig. 4

Radiation-noise-limited temperature discrimination ΔT°K as a function of source temperature T°K for monochromatic pyrometers at various wavelengths. Δλq=10−10 cm3; Δf=1 cps.

Fig. 5
Fig. 5

Number of photoelectrons ne emitted from an S1 and an S20 photosurface, respectively, in 1 sec, when a source of 1-mm2 area is imaged on the surface with an optical efficiency η of 0.01. Log ne is plotted as a function of reciprocal source temperature.

Tables (2)

Tables Icon

Table I Minimum detectable power, Wm in W for 1 cps, and long-wavelength cutoffs λc. λc is the wavelength for which the detector sensitivity has fallen to 10% of its peak value.

Tables Icon

Table II Amplifier bandwidth required by various monochromatic pyrometer systems to give a temperature discrimination of 0.01°C at 1063°C. 5-cm diameter optics at f/4 and 10% transmittance. A wavelength of 0.65 μ (except for column 8) and a spectral bandwidth of 1 mμ is assumed. A dispersion system with /dλ=103 rad cm−1 is assumed in columns 1 and 5 and with /dλ=104 rad cm−1 in columns 2 and 6. An interference filter is assumed in the other cases with column 4 applying to a photon-counting pyrometer and column 8 to a silicon detector with λ=1.0 μ. For the prism or grating the slit length is 10 mm while for the interference filter the source area is 1 mm2.

Equations (51)

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S = s ( Δ f i / Δ f 0 ) 1 / 2
S = 2 - 1 / 2 s 2 ( Δ f i / Δ f 0 ) 1 / 2 .
Δ f = 1 / 4 R C .
Δ f = 1 / 2 t .
E = A η σ T 4 ,
d E / d T = 4 A η σ T 3 .
Δ T d = 0.25 W m Δ f 1 / 2 A - 1 η - 1 σ - 1 T - 3
Δ T d = 4.4 × 10 10 ( A η ) - 1 Δ f 1 / 2 W m T - 3 ,
15 π - 4 ( x 0 3 + 3 x 0 2 + 6 x 0 + 6 ) exp ( - x 0 )
Δ T d = 1.15 × 10 12 ( A η ) - 1 Δ f 1 / 2 W m T - 3 ( exp x 0 ) ( x 0 4 + 4 x 0 3 + 12 x 0 2 + 24 x 0 + 24 ) - 1 .
E = c 1 A η Δ λ λ - 5 exp ( - c 2 / λ T ) ,
E / T = c 1 c 2 A η Δ λ λ - 6 T - 2 exp ( - c 2 / λ T ) ,
Δ T d = ( c 1 c 2 A η Δ λ ) - 1 Δ f 1 / 2 W m T 2 λ 6 exp ( c 2 / λ T ) ,
Δ T d = 1.86 × 10 11 ( A η Δ λ ) - 1 × Δ f 1 / 2 W m T 2 λ 6 exp ( 1.438 / λ T ) .
λ m = c 2 / 5 T
λ = c 2 / 6 T .
N = σ T 4 / 2.75 k T ,
n = 7.6 × 10 10 A η Δ f - 1 T 3 ,
d n / d T = 2.28 × 10 11 A η Δ f - 1 T 2 .
Δ n = n 1 / 2 = 2.76 × 10 5 ( A η ) 1 / 2 Δ f - 1 / 2 T 3 / 2
Δ T r = 1.21 × 10 - 6 ( A η ) - 1 / 2 Δ f 1 / 2 T - 1 / 2 ,
0.417 ( x 0 2 + 2 x 0 + 2 ) exp ( - x 0 ) .
Δ T r = 5.61 × 10 - 6 ( A η ) - 1 / 2 Δ f 1 / 2 T - 1 / 2 × [ ( x 0 - 2 + 2 x 0 - 3 + 2 x 0 - 4 ) exp ( x 0 ) ] 1 / 2 × ( x 0 + 3 + 6 x 0 - 1 + 6 x 0 - 2 ) - 1 .
n = E q λ / 2 Δ f h c ,
n = ( 2 Δ f h c ) - 1 A η Δ λ q c 1 λ - 4 exp ( - c 2 / λ T ) ,
n / T = ( 2 h c Δ f ) - 1 A η Δ λ q c 1 c 2 λ - 5 T - 2 exp ( - c 2 / λ T ) .
Δ T r = 2 ( h c Δ f ) 1 / 2 × ( A η Δ λ c 1 q ) - 1 / 2 c 2 - 1 λ 3 T 2 exp ( c 2 / 2 λ T )
Δ T r = 3.2 × 10 - 6 × ( A η Δ λ q Δ f - 1 ) - 1 / 2 λ 3 T 2 exp ( 1.438 / 2 λ T ) .
λ = c 2 / 6 T .
A η A Ω t / π A A t / π d 2 A Ω t / π ,
Δ T 2 2 = Δ T λ , 2 2 + Δ T 1 , 2 2 .
- ln r = c 2 λ ( 1 T 1 - 1 T 2 ) ,
Δ T λ , 2 = p ( T 2 - T 1 ) λ - 1 T 2 T 1 - 1 Δ λ ,
Δ T 1 , 2 = ( T 2 / T 1 ) 2 Δ T 1 .
Δ x = F D ( d θ / d λ ) Δ λ ,
A = l Δ x = l F D ( d θ / d λ ) Δ λ ,
A η Δ λ = l t D ( d θ / d λ ) Δ λ 2 / 4 F .
Δ T 1 , 2 = 400 W m Δ f 1 / 2 F Δ T d , 1 T 2 2 l t D ( d θ / d λ ) Δ λ 2 T 1 2 ,
Δ λ = ( 5.70 W m Δ f 1 / 2 F λ Δ T d , 1 T 2 p l t D ( d θ / d λ ) ( T 2 - T 1 ) T 1 ) 1 / 3 ,
Δ T 2 = 1.5 1 / 2 Δ T λ , 2 .
Δ T 1 , 2 = 2 × 10 - 5 Δ f 1 / 2 F 1 / 2 Δ T r , 1 T 2 2 [ l t D ( d θ / d λ ) ] 1 / 2 Δ λ T 1 2 ,
Δ λ = { 2 × 10 - 5 Δ f 1 / 2 F 1 / 2 λ Δ T r , 1 T 2 p [ l t D ( d θ / d λ ) ] 1 / 2 ( T 2 - T 1 ) T 1 } 1 / 2 ,
Δ T 2 = 2 1 / 2 Δ T λ , 2 .
A η Δ λ = A t Δ λ / 4 F 2
Δ T 1 , 2 = 400 W m Δ f 1 / 2 F 2 Δ T d , 1 T 2 2 A t Δ λ T 1 2 ,
Δ λ = [ 400 W m Δ f 1 / 2 F 2 λ Δ T d , 1 T 2 p A t ( T 2 - T 1 ) T 1 ] 1 / 2
Δ T 2 = 2 1 / 2 Δ T λ , 2 .
Δ T 1 , 2 = 2 × 10 - 5 Δ f 1 / 2 F Δ T r , 1 T 2 2 ( A t q Δ λ ) 1 / 2 T 1 2 ,
Δ λ = [ 2 × 10 - 10 Δ f F 2 λ 2 Δ T r , 1 2 T 2 2 p 2 A t q ( T 2 - T 1 ) 2 T 1 2 ] 1 / 3
Δ T 2 = 3 1 / 2 Δ T λ , 2 .
F = 4 ; D = 5 cm ; 1 = 1 cm ; p = 0.02 ; Δ f = 1 cps .