Abstract

Narcissus, a composite of self-images of a cryogenically cooled detector array, is an effect peculiar to scanning thermal imaging systems. It occurs when the detectors sense variations in the amount of background radiation reaching them via reflections from lens surfaces. Paraxial surface-contribution formulas derived from Lagrange invariants, coupled with the system spectral response, determine narcissus in terms of its equivalent scene temperature difference (NARCΔT). The equations give the intensity and size of the narcissus ghost in terms of paraxial ray data at the contributing surfaces and the system f/No. This Gaussian formulation has sufficient radiometric accuracy to make extensive ray tracing unnecessary.

© 1982 Optical Society of America

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References

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  1. I. R. Abel, Opt. Eng. 16241 (1977).
    [CrossRef]
  2. A. S. Lau, Proc. Soc. Photo-Opt. Instrum. Eng. 107, 57 (1977).

1977

I. R. Abel, Opt. Eng. 16241 (1977).
[CrossRef]

A. S. Lau, Proc. Soc. Photo-Opt. Instrum. Eng. 107, 57 (1977).

Abel, I. R.

I. R. Abel, Opt. Eng. 16241 (1977).
[CrossRef]

Lau, A. S.

A. S. Lau, Proc. Soc. Photo-Opt. Instrum. Eng. 107, 57 (1977).

Opt. Eng.

I. R. Abel, Opt. Eng. 16241 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

A. S. Lau, Proc. Soc. Photo-Opt. Instrum. Eng. 107, 57 (1977).

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Figures (9)

Fig. 1
Fig. 1

Narcissus induced artificially in a thermal imaging system appears as a small dark area in the center of the display. The brightness level has been turned up to accentuate the narcissus at the expense of image detail.

Fig. 2
Fig. 2

Thermal imaging optical system consists of an afocal telescope, scanner, and detector lens.

Fig. 3
Fig. 3

Narcissus occurs when the detector sees itself on-axis and the warm instrument housing off-axis.

Fig. 4
Fig. 4

Lagrange invariant is formed from forward and reflected ray data.

Fig. 5
Fig. 5

Lagrange invariant is related to the narcissus ghost size.

Fig. 6
Fig. 6

Cold return is the ratio of the detector area times its emissivity to the narcissus ghost area.

Fig. 7
Fig. 7

Two Lagrange invariants, I1 and I2, are formed to determine the size of the narcissus image on the display.

Fig. 8
Fig. 8

Narcissus ghost moves in the image plan as the system scans.

Fig. 9
Fig. 9

Spectral distribution of narcissus and scene signals provide a basis for discrimination.

Equations (15)

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I = y r n u - y n u r ,
I = - 2 y n i ,
I = y r n u = y r 2 f # ,
- 2 y n i = y r 2 f # ,             y r = - 4 y n i f # ,
C = M π ( 4 y n i f # ) 2 ,
V s = Δ T K 0 L ( λ , T s ) T A ( λ ) τ s ( λ ) ξ ( λ ) d λ ,
V n j = C j K 0 L ( λ , T h ) τ j 2 ( λ ) R j ( λ ) ξ ( λ ) d λ ,
NARC Δ T = all lens SURFACES IN FRONT OF THE SCANNER [ C j 0 L ( λ , T h ) τ j 2 ( λ ) R j ( λ ) ξ ( λ ) d λ 0 L ( λ , T s ) T A ( λ ) τ s ( λ ) ξ ( λ ) d λ ] .
I 1 = y ¯ r n u - y n u ¯ r ,
I 1 = ( y ¯ n u - y n u ¯ ) - 2 y n i ¯ .
I 1 = y ¯ r n u ,
I 2 = y ¯ n u - y n u ¯ ,
I 2 = y ¯ n u .
y ¯ n u = y ¯ n u - 2 y n i ¯ . y ¯ r = y ¯ - 4 y n i ¯ f #
y ¯ r = - 4 y n i ¯ f # .

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