Abstract

A very simple model of thermal radiation sources and detectors is used to examine the resultant response of the combination. The desired output of this combination is the characteristic of the source. Through this simple model it is demonstrated that the detector output may be very misleading if the entrance aperture of the detector is large or the spatial variation of the source varies wildly. Only if the source spatial variation is very large compared to the area seen by the detector is there any hope of obtaining the desired information.

© 1984 Optical Society of America

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References

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  1. G. C. Mönch, “Lichtmodulation Durch Öffnungen in Parallel Bewegten Blenden,” Optik 10, 350 (1953).
  2. G. C. Mönch, “Lichtmodulation Durch Öffnungen in Rotierenden Scheiben,” Optik 10, 365 (1953).
  3. W. G. Tam, A. Zardecki, “Multiple Scattering Corrections to the Beer-Lambert Law. 1: Open Detector,” Appl. Opt. 21, 2405 (1982).
    [Crossref] [PubMed]
  4. A. Zardecki, W. G. Tam, “Multiple Scattering Corrections to the Beer-Lambert Law. 2: Detector with a Variable Field of View,” Appl. Opt. 21, 2413 (1982).
    [Crossref] [PubMed]

1982 (2)

1953 (2)

G. C. Mönch, “Lichtmodulation Durch Öffnungen in Parallel Bewegten Blenden,” Optik 10, 350 (1953).

G. C. Mönch, “Lichtmodulation Durch Öffnungen in Rotierenden Scheiben,” Optik 10, 365 (1953).

Appl. Opt. (2)

Optik (2)

G. C. Mönch, “Lichtmodulation Durch Öffnungen in Parallel Bewegten Blenden,” Optik 10, 350 (1953).

G. C. Mönch, “Lichtmodulation Durch Öffnungen in Rotierenden Scheiben,” Optik 10, 365 (1953).

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Figures (9)

Fig. 1
Fig. 1

(a) Ideal and (b) actual light rays or field of view from a source and/or detector.

Fig. 2
Fig. 2

Generalized source–detector pair.

Fig. 3
Fig. 3

Base view of source–detector interaction.

Fig. 4
Fig. 4

Geometry for a uniform source and uniform detector.

Fig. 5
Fig. 5

Base view of source–detector interaction where the base areas are different sizes: (a) 0 < η < π/2 and (b) π/2 < η < π.

Fig. 6
Fig. 6

Geometry for a nonuniform source (or detector) and a uniform detector (or source).

Fig. 7
Fig. 7

Normalized response for various source–detector combinations.

Fig. 8
Fig. 8

View of a very large source and a very small detector, each with spatially nonuniform responses.

Fig. 9
Fig. 9

Comparison of the response of the system represented as Fig. 8: I1m → ∞, I2m = 2, and 2I2.

Equations (22)

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- ξ ξ b b r d r d θ = 2 - ξ ξ b ' b r d r d θ ,
R = - ξ ξ b b h 1 ( r , θ ) h 2 ( r , θ ) r d r d θ ,
R 1 = - ξ ξ b b h 1 ( r , θ ) h 2 ( r , θ ) r d r d θ ,
R 2 = - ξ ξ b b h 1 ( r , θ ) h 2 ( r , θ ) r d r d θ ,
h 1 ( r , θ ) = a 1 ( 1 - r m b m ) ,             m 0 ,
h 2 ( r , θ ) = a 2 { 1 - [ ( r b ) 2 + ( D b ) 2 - 2 ( D r b 2 ) cos θ ] n / 2 } ,             n 0 ,
R = a 1 a 2 - ξ ξ b b [ ( 1 - r m b m ) { 1 - [ ( r b ) 2 + ( D b ) 2 - 2 ( D r b 2 ) cos θ ] n / 2 } × r d r d θ
R 1 = R 2 = a 1 a 2 - ξ ξ b b r d r d θ .
R ( x ) = 2 a 1 a 2 b 2 [ tan - 1 ( b 2 - x 2 b 2 ) - x b 2 b 2 - x 2 ] .
R ( ξ ) = 2 a 1 a 2 b 2 ( ξ - sin ξ cos ξ ) .
F n = R ( ξ ) R ( ξ = π 2 ) = 2 π ( ξ - sin ξ cos ξ ) .
R ( ξ ) a 1 a 2 π c 2 = 1 π c 2 [ b 2 c 2 ξ + η - b 2 c 2 sin ξ cos ξ - sin η cos η ] , 0 η π 0 ξ sin - 1 ( c b ) ,
lim c 0 R a 1 a 2 π c 2 = 0 ( η = 0 ) 1 ( η = π ) .
R 1 = a 1 a 2 - ξ ξ b b ( 1 - r m b m ) r d r d θ = a 1 a 2 b 2 [ m ξ m + 2 - sin ξ cos ξ + cos m + 2 ξ m + 2 × - ξ ξ sec m + 2 θ d θ ] ,
R 2 = a 1 a 2 - ξ ξ b b ( 1 - r m b m ) r d r d θ
R = a 1 a 2 b 2 [ ξ ( 1 - 4 cos 2 ξ ) + cos ξ sin ξ ( 1 + 2 cos 2 ξ ) .
F c p = R ( ξ ) R ( ξ = π / 2 = F n + 4 π sin ξ cos ξ ( 1 + cos 2 ξ ) - 8 ξ π cos 2 ξ .
R ( ξ ) = 2 a 1 a 2 b 2 [ ξ ( 1 3 - 2 cos 2 ξ ) + sin ξ cos ξ ( 1 3 + 16 9 cos 2 ξ - 4 9 cos 4 ξ ) ] ,
F p p = R ( ξ ) R ( ξ = π / 2 ) = F n + 4 π [ 1 3 sin ξ cos ξ ( 3 + 8 cos 2 ξ - 2 cos 4 ξ ) - 3 ξ cos 2 ξ ] .
R ( ξ ) = 2 3 a 1 b 3 tan α [ 2 sin ξ + sin ξ cos 2 ξ - 3 ξ cos ξ ] - 4 a 1 b 3 tan α { sin ξ m + 3 - ξ cos ξ m + 2 ] - cos m + 3 ξ 2 [ 1 ( m + 3 ) ( m + 2 ) 0 ξ sec m + 2 θ d θ ] } .
R ( m ) = a 1 b 3 3 tan α [ sin ξ ( 2 + cos 2 ξ ) - 3 ξ cos ξ ]
R ( m = 2 ) = a 1 b 3 3 tan α [ 4 5 sin ξ + 9 10 sin ξ cos ξ - 3 2 ξ cos ξ - 1 5 sin ξ cos 4 ξ ] .

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