Abstract

General expressions are derived for the radiance of a nonisothermal gas in terms of the equivalent width of the relevant spectral lines. Any appropriate expression for the equivalent width may be used in these equations taken either from the theory of band models or from exact calculations which use molecular constants. A general expression for the radiance is derived which is based on the Curtis-Godson approximation; this is compared with exact calculations. Radiance calculations for four different temperature distributions are given in order to illustrate the method.

© 1967 Optical Society of America

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References

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  1. F. S. Simmons, Appl. Opt. 5, 1801 (1966).
    [CrossRef] [PubMed]
  2. G. N. Plass, Appl. Opt. 2, 515 (1963).
    [CrossRef]
  3. G. N. Plass, Appl. Opt. 4, 69 (1965).
    [CrossRef]
  4. J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.
  5. G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
    [CrossRef]
  6. G. N. Plass, J. Opt. Soc. Am. 50, 868 (1960).
    [CrossRef]
  7. B. Krakow, H. J. Babrov, G. J. Maclay, A. L. Shabott, Appl. Opt. 5, 1791 (1966).
    [CrossRef] [PubMed]

1966 (2)

1965 (1)

1963 (1)

1960 (1)

1958 (1)

Babrov, H. J.

Grube, R. H.

J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.

Jamieson, J. A.

J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.

Krakow, B.

Maclay, G. J.

McFee, R. H.

J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.

Plass, G. N.

G. N. Plass, Appl. Opt. 4, 69 (1965).
[CrossRef]

G. N. Plass, Appl. Opt. 2, 515 (1963).
[CrossRef]

G. N. Plass, J. Opt. Soc. Am. 50, 868 (1960).
[CrossRef]

G. N. Plass, J. Opt. Soc. Am. 48, 690 (1958).
[CrossRef]

J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.

Richards, R. G.

J. A. Jamieson, R. H. McFee, G. N. Plass, R. H. Grube, R. G. Richards, Infrared Physics and Engineering (McGraw-Hill Book Co., Inc., New York, 1963), pp. 12–101.

Shabott, A. L.

Simmons, F. S.

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Figures (3)

Fig. 1
Fig. 1

Assumed blackbody radiance in arbitrary units as a function of fractional optical depth (u/u0) to boundary of flame for four different temperature distributions.

Fig. 2
Fig. 2

Radiance in arbitrary units as a function of x0 for a single spectral line and the temperature distribution shown in Fig. 1.

Fig. 3
Fig. 3

Radiance in arbitrary units as a function of x0 for the statistical band and the temperature distributions shown in Fig. 1.

Tables (1)

Tables Icon

Table I Radiance for x0 = 1

Equations (27)

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u = 0 l ρ a d l ,
I = Δ ν d ν 0 u 0 I b ( ν , u ) k ( ν , u ) exp [ - 0 u k ( ν , u ) d u ] d u ,
I = - Δ ν d ν 0 u 0 I b ( ν , u ) ( / u ) × { exp [ - 0 u k ( ν , u ) d u ] } d u .
I = 0 u 0 I b ( u ) d u ( d / d u ) × Δ ν { 1 - exp [ - 0 u k ( ν , u ) d u ] } d ν .
W ( u ) = Δ ν { 1 - exp [ - 0 u k ( v , u ) d u ] } d ν .
I = 0 u 0 I ¯ b ( u ) ( d W / d u ) d u
I = 0 W 0 I ¯ b ( W ) d W .
I = I ¯ b ( u 0 ) W ( u 0 ) - 0 u 0 W ( u ) ( d I b / d u ) d u .
W S L = 2 π α x e - x [ I 0 ( x ) + I 1 ( x ) ] = 2 π α f ( x ) ,
W E / d = 1 - ( 2 π ) - 1 × - π π exp [ - β x sinh β / ( cosh β - cos z ) ] d z ,
W E / d = ϕ [ ( 1 2 β 2 x ) 1 2 ] = ϕ [ ( π S α u / d 2 ) 1 2 ] ,
W S / d = 1 - exp ( W ¯ S L / d ) .
W ¯ S L = 0 W S L ( S ) P ( S ) d S
W = Σ i 0 u 0 S i ( u ) d u ,
W = 2 Σ i [ 0 u 0 S i ( u ) α i ( u ) d u ] 1 2 .
W E / d = ϕ { [ ( π / d 2 ) 0 u 0 S ( u ) α ( u ) u d u ] 1 2 } .
I = I ¯ b W ( u 0 ) .
I ¯ b ( u ) = [ I ¯ b ( u 0 ) - I ¯ b ( 0 ) ] ( u / u 0 ) + I ¯ b ( 0 ) .
I = 1 2 Σ i S i u 0 [ I ¯ b ( 0 ) + I ¯ b ( u 0 ) ] .
I = 0 u 0 I ¯ b ( u ) [ Σ i S i ( u ) α i ( u ) ] [ Σ j 0 u S j ( u ) α j ( u ) d u ] - 1 2 d u .
x h = F 0 2 F 1 - 2
β h = F 1 2 F 0 - 1 ,
F 0 = I ¯ b h - 1 0 u 0 I ¯ b d ( β x ) ,
F 1 = I ¯ b h - 1 0 u 0 I ¯ b d ( β x 1 2 ) ,
I = I ¯ b h d F 1 2 F 0 - 1 f ( F 0 2 F 1 - 2 ) ,
I ¯ b ( u ) = I ¯ b ( 0 ) [ 1 + ( u / u 0 ) + 4 ( u / u 0 ) 2 ] .
I ¯ b ( u ) = I ¯ b ( 0 ) [ 6 - 10 ( u / u 0 ) + 10 ( u / u 0 ) 2 ] .

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