Abstract

The extent to which the thermal capacitance and resistance of a black coating on a pyroelectric detector offset the gain in optical absorptance is investigated. A black paint is shown to be of little value, but a coating of gold–black may increase the detector responsivity for modulation frequencies up to at least several kilohertz. When a coated pyroelectric detector is calibrated electrically, a correction is necessary for the thermal impedance of the black. For gold–blacks of superficial density 2 g m−2, this correction is shown to be less than 2% for frequencies within the 0–100-Hz range.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Smith, F. E. Jones, R. P. Chasmar, The Detection and Measurement of Infra-red Radiation (Clarendon Press, Oxford, 1958).
  2. L. Harris, “The Optical Properties of Metal Blacks and Carbon Blacks,” (Monograph Series No. 1, Massachusetts Institute of Technology and The Eppley Foundation for Research, 1967).
  3. E. H. Putley, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic Press, New York, 1970), Vol. 5.
    [CrossRef]
  4. B. R. Holeman, Infrared Phys. 12, 125 (1972).
    [CrossRef]
  5. R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
    [CrossRef]
  6. Certain commercial materials are identified in this paper in order to specify the experimental procedure adequately. This identification does not imply that the materials are necessarily the best available for the purpose.
  7. W. R. Blevin, Appl. Opt. 12, 2802 (1973).
    [CrossRef] [PubMed]
  8. W. R. Blevin, W. J. Brown, Metrologia 2, 139 (1966).
    [CrossRef]
  9. W. R. Blevin, W. J. Brown, J. Sci. Instrum. 42, 385 (1965).
    [CrossRef]
  10. R. J. Phelan, A. R. Cook, Appl. Opt. 12, 2494 (1973).
    [CrossRef] [PubMed]
  11. E. J. Gillham, Proc. Roy. Soc. (London) A269, 249 (1962).

1973

1972

B. R. Holeman, Infrared Phys. 12, 125 (1972).
[CrossRef]

1971

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
[CrossRef]

1966

W. R. Blevin, W. J. Brown, Metrologia 2, 139 (1966).
[CrossRef]

1965

W. R. Blevin, W. J. Brown, J. Sci. Instrum. 42, 385 (1965).
[CrossRef]

1962

E. J. Gillham, Proc. Roy. Soc. (London) A269, 249 (1962).

Blevin, W. R.

W. R. Blevin, Appl. Opt. 12, 2802 (1973).
[CrossRef] [PubMed]

W. R. Blevin, W. J. Brown, Metrologia 2, 139 (1966).
[CrossRef]

W. R. Blevin, W. J. Brown, J. Sci. Instrum. 42, 385 (1965).
[CrossRef]

Brown, W. J.

W. R. Blevin, W. J. Brown, Metrologia 2, 139 (1966).
[CrossRef]

W. R. Blevin, W. J. Brown, J. Sci. Instrum. 42, 385 (1965).
[CrossRef]

Chasmar, R. P.

R. A. Smith, F. E. Jones, R. P. Chasmar, The Detection and Measurement of Infra-red Radiation (Clarendon Press, Oxford, 1958).

Cook, A. R.

R. J. Phelan, A. R. Cook, Appl. Opt. 12, 2494 (1973).
[CrossRef] [PubMed]

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
[CrossRef]

Gillham, E. J.

E. J. Gillham, Proc. Roy. Soc. (London) A269, 249 (1962).

Harris, L.

L. Harris, “The Optical Properties of Metal Blacks and Carbon Blacks,” (Monograph Series No. 1, Massachusetts Institute of Technology and The Eppley Foundation for Research, 1967).

Holeman, B. R.

B. R. Holeman, Infrared Phys. 12, 125 (1972).
[CrossRef]

Jones, F. E.

R. A. Smith, F. E. Jones, R. P. Chasmar, The Detection and Measurement of Infra-red Radiation (Clarendon Press, Oxford, 1958).

Mahler, R. J.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
[CrossRef]

Phelan, R. J.

R. J. Phelan, A. R. Cook, Appl. Opt. 12, 2494 (1973).
[CrossRef] [PubMed]

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
[CrossRef]

Putley, E. H.

E. H. Putley, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic Press, New York, 1970), Vol. 5.
[CrossRef]

Smith, R. A.

R. A. Smith, F. E. Jones, R. P. Chasmar, The Detection and Measurement of Infra-red Radiation (Clarendon Press, Oxford, 1958).

Appl. Opt.

Appl. Phys. Lett.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971).
[CrossRef]

Infrared Phys.

B. R. Holeman, Infrared Phys. 12, 125 (1972).
[CrossRef]

J. Sci. Instrum.

W. R. Blevin, W. J. Brown, J. Sci. Instrum. 42, 385 (1965).
[CrossRef]

Metrologia

W. R. Blevin, W. J. Brown, Metrologia 2, 139 (1966).
[CrossRef]

Proc. Roy. Soc. (London)

E. J. Gillham, Proc. Roy. Soc. (London) A269, 249 (1962).

Other

Certain commercial materials are identified in this paper in order to specify the experimental procedure adequately. This identification does not imply that the materials are necessarily the best available for the purpose.

R. A. Smith, F. E. Jones, R. P. Chasmar, The Detection and Measurement of Infra-red Radiation (Clarendon Press, Oxford, 1958).

L. Harris, “The Optical Properties of Metal Blacks and Carbon Blacks,” (Monograph Series No. 1, Massachusetts Institute of Technology and The Eppley Foundation for Research, 1967).

E. H. Putley, in Semiconductors and Semimetals, R. K. Willardson, A. C. Beer, Eds. (Academic Press, New York, 1970), Vol. 5.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Model for applying linear heat conduction theory to a pyroelectric detector having a black coating on its front surface.

Fig. 2
Fig. 2

Theoretical curves for a hypothetical pyroelectric detector coated with a black of thickness Xb and heated by radiation modulated sinusoidally at frequency f. Plotted against f for seven values of Xb are (top) the ratio |ir/i0| of the pyroelectric current to the value that it would have when Xb = 0 if heat losses from the detector were negligible, and (bottom) the phase ϕr of the pyroelectric current with respect to the incident radiation. The absorptance of the detector is assumed to be independent of Xb.

Fig. 3
Fig. 3

Experimental curves for pyroelectric detectors of 13-μm-thick PVF film in air, coated with (1) 3M black paint, (2) 6 g m−2 gold–black, and (3) 2 g m−2 gold–black and heated by radiation modulated sinusoidally at frequency f. Plotted against f are (top) the ratio of the pyroelectric current, after applying the black coating, to its original value, and (bottom) the lag caused by the black coating in the phase of the pyroelectric current.

Fig. 4
Fig. 4

Theoretical curves for the detector of Fig. 2, now heated sinusoidally at frequency f by an electrical element beneath the black coating. Plotted against f for several values of Xb are (top) the ratio |ie/i0| of the pyroelectric current to the value it would have when Xb = 0 if heat losses from the detector were negligible, and (bottom) the phase ϕe of the pyroelectric current with respect to the applied electrical power.

Fig. 5
Fig. 5

Experimental curves for the pyroelectric detectors of Fig. 3, now heated sinusoidally at frequency f by an electrical element beneath the black coating. Plotted against f are (top) the ratio of the pyroelectric current, after applying the black coating, to its original value, and (bottom) the change caused by the black coating in the phase of the pyroelectric current.

Tables (2)

Tables Icon

Table I Principal Symbols

Tables Icon

Table II Measurements on Three Gold-Black Coatings Deposited, in a Nitrogen Atmosphere, on Pyroelectric Detectors Distant 7 cm from Filament

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

R = X / K             and             C = X ρ c .
i r = p t             [ 0 X p T ( x p ) d x p / X p ] ,
T ( x ) = A cosh μ x + B sinh μ x
T ( x a ) = 0.
T ( x a ) = T ( x b ) ,
Φ exp ( j ω t ) = K a [ T ( x a ) / x a ] - K b [ T ( x b ) / x b ] + H a T ( x a ) .
T ( x b ) = T ( x p ) ,
K b [ T ( x b ) / x b ] = K p [ T ( x p ) / x p ] .
T ( x p ) = T ( x s ) ,
- K p [ T ( x p ) / x p ] = - K s [ T ( x s ) / x s ] + H s T ( x s ) .
T ( x s ) = 0.
i r = i o [ ( K p μ p ) N - ( H s + K s μ s coth μ s X s ) ] / [ ( K b μ b ) U + ( H a + K a μ a coth μ a X a ) V ]
i 0 = ( p Φ / C p ) exp ( j ω t ) ,
U = M sinh μ b X b + N ( K p μ p / K b μ b ) cosh μ b X b ,
V = M cosh μ b X b + N ( K p μ p / K b μ b ) sinh μ b X b ,
M = cosh μ p X p + [ ( H s + K s μ s coth μ s X s ) / K p μ p ] sinh μ p X p ,
N = sinh μ p X p + [ ( H s + K s μ s coth μ s X s ) / K p μ p ] cosh μ p X p .
i r = i 0 / [ cosh μ b X b + ( K b α b sinh μ b X b ) / K p α p tanh μ p X p ] ,
i r / i 0 [ C p / ( C p + C b ) ] cos ϕ r ,
tan ϕ r π f C p C b ( R b + 2 R p / 3 + R b C b / 3 C p ) / ( C p + C b ) .
i r / i 0 2 [ 1 + ( C b R p / C p R b ) 1 / 2 ] - 1 exp [ - ( π f R b C b ) 1 / 2 ] ,
ϕ r ( π f R b C b ) 1 / 2 .
At x a = X a , x b = 0 , K b [ T ( x b ) / x b ] = K a [ T ( x a ) / x a ] + H a T ( x a ) .
At x b = X b , x p = 0 , Φ exp ( j ω t ) = K b [ T ( x b ) / x b ] - K p [ T ( x p ) / x p ] .
i e = { cosh μ b X b + [ ( H a + K a μ a coth μ a X a ) / K b μ b ] × sinh μ b X b } i r ,
i e = i 0 / [ 1 + ( K b μ b tanh μ b X b ) / ( K p μ p tanh μ p X p ) ] .
i e / i 0 [ C p / ( C p + C b ) ] cos ϕ e ,
tan ϕ e 2 π f C b ( R p C p - R b C b ) / 3 ( C p + C b ) .
i e / i 0 [ 1 + ( C b R p / C p R b ) 1 / 2 ] - 1
ϕ e 0.
i e / i r [ 1 + R b ( H a + K a α a ) ] sec ( ϕ r - ϕ e ) ,
tan ( ϕ r - ϕ e ) R b ( π f C b + K a α a ) / [ 1 + R b ( H a + K a α a ) ] .
i e / i r = 1 + R b ( H a + K a / X a ) .

Metrics