Abstract

Superposition and calibrated attenuator methods are often used to determine the nonlinearity of photodetectors. A variation of these methods is described and applied to the calibration of optical pyrometers. This scheme allows a considerable reduction in the time needed for the measurement because only three independent sets of measurements are required, without any need to realize an accurate radiance scale on the sources.

© 1980 Optical Society of America

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References

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  1. C. L. Sanders, J. Res. Natl. Bur. Stand. Sec. A: 76, 437 (1972).
    [CrossRef]
  2. L. N. Aksyutov, G. K. Kholopov, Sov. J. Opt. Technol. 40, 634 (1973).
  3. G. Ruffino, F. Righini, A. Rosso, in Temperature. Its Measurement and Control in Science and Industry, H. H. Plumb, Ed. (Instrument Society of America, Pittsburgh, Pa., 1972), p. 531.
  4. L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).
  5. L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
    [CrossRef]
  6. G. Golub, Numer. Math. 7, 206 (1965).
    [CrossRef]

1979 (1)

L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
[CrossRef]

1975 (1)

L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).

1973 (1)

L. N. Aksyutov, G. K. Kholopov, Sov. J. Opt. Technol. 40, 634 (1973).

1972 (1)

C. L. Sanders, J. Res. Natl. Bur. Stand. Sec. A: 76, 437 (1972).
[CrossRef]

1965 (1)

G. Golub, Numer. Math. 7, 206 (1965).
[CrossRef]

Aksyutov, L. N.

L. N. Aksyutov, G. K. Kholopov, Sov. J. Opt. Technol. 40, 634 (1973).

Coslovi, L.

L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
[CrossRef]

L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).

Golub, G.

G. Golub, Numer. Math. 7, 206 (1965).
[CrossRef]

Kholopov, G. K.

L. N. Aksyutov, G. K. Kholopov, Sov. J. Opt. Technol. 40, 634 (1973).

Righini, F.

L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
[CrossRef]

L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).

G. Ruffino, F. Righini, A. Rosso, in Temperature. Its Measurement and Control in Science and Industry, H. H. Plumb, Ed. (Instrument Society of America, Pittsburgh, Pa., 1972), p. 531.

Rosso, A.

L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
[CrossRef]

L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).

G. Ruffino, F. Righini, A. Rosso, in Temperature. Its Measurement and Control in Science and Industry, H. H. Plumb, Ed. (Instrument Society of America, Pittsburgh, Pa., 1972), p. 531.

Ruffino, G.

G. Ruffino, F. Righini, A. Rosso, in Temperature. Its Measurement and Control in Science and Industry, H. H. Plumb, Ed. (Instrument Society of America, Pittsburgh, Pa., 1972), p. 531.

Sanders, C. L.

C. L. Sanders, J. Res. Natl. Bur. Stand. Sec. A: 76, 437 (1972).
[CrossRef]

Alta Freq. (1)

L. Coslovi, F. Righini, A. Rosso, Alta Freq. 44, 592 (1975).

J. Phys E (1)

L. Coslovi, F. Righini, A. Rosso, J. Phys E: 12, 216 (1979).
[CrossRef]

J. Res. Natl. Bur. Stand. Sec. A (1)

C. L. Sanders, J. Res. Natl. Bur. Stand. Sec. A: 76, 437 (1972).
[CrossRef]

Numer. Math. (1)

G. Golub, Numer. Math. 7, 206 (1965).
[CrossRef]

Sov. J. Opt. Technol. (1)

L. N. Aksyutov, G. K. Kholopov, Sov. J. Opt. Technol. 40, 634 (1973).

Other (1)

G. Ruffino, F. Righini, A. Rosso, in Temperature. Its Measurement and Control in Science and Industry, H. H. Plumb, Ed. (Instrument Society of America, Pittsburgh, Pa., 1972), p. 531.

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Figures (3)

Fig. 1
Fig. 1

Determination of the nonlinearity of photodetectors using the superposition method.

Fig. 2
Fig. 2

Experimental points P1, P2, and Ps belong to curve φ = g(υ) with the local constraint expressed by Eq. (8).

Fig. 3
Fig. 3

Determination of the nonlinearity of photodetectors using the calibrated attenuator method.

Equations (22)

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V = f ( Φ ) ,
φ = f 1 ( υ ) = g ( υ ) ,
φ = a 0 + a 1 υ + a 2 υ 2 + + a n υ n + E ( υ ) .
i = 1 m [ E ( υ i ) ] 2 .
φ s = φ 1 + φ 2 ,
i = 0 n a i υ s i + E ( υ s ) = i = 0 n a i υ 1 i + E ( υ 1 ) + i = 0 n a i υ 2 i + E ( υ 2 ) .
i = 0 n a i ( υ 1 i + υ 2 i υ s i ) = E ( υ s ) E ( υ 1 ) E ( υ 2 ) .
υ 1 i + υ 2 i υ s i = s i , E ( υ s ) E ( υ 1 ) E ( υ 2 ) = r ,
i = 0 n a i s i = r .
i = 0 n a i s i j = r j , j = 1,2 , m .
i = 0 n a i = 1 ,
a 0 = 1 a 1 a 2 a n
{ 1 + a 1 ( s 11 1 ) + + a n ( s 1 n 1 ) = r 1 , 1 + a 1 ( s m 1 1 ) + + a n ( s m n 1 ) = r m .
S a b = r ,
S = [ s 11 1 s 12 1 s 1 n 1 s m 1 1 s m 2 1 s m n 1 ] , a = [ a 1 a 2 a n ] , b = [ 1 1 1 ] , r = [ r 1 r 2 r m ] .
S a b = min r = ( j = 1 m r j 2 ) 1 / 2 .
b j = 1 υ s j , d i j = s i j 1 υ s j .
φ τ = τ φ .
i = 0 n a i υ τ i + E ( υ τ ) = [ i = 0 n a i υ i + E ( υ ) ] τ .
i = 0 n a i ( υ τ i υ i τ ) = τ E ( υ ) E ( υ τ ) .
s i = υ τ i τ υ i , τ E ( υ ) E ( υ τ ) = r ,
i = 0 n a i s i = r ,

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