Abstract

An exact, closed-form expression is derived for the apparent local emissivity of a point at the vertex of a diffuse conical or V-groove cavity. This expression is obtained by a substitution into an approximate equation for the apparent local emissivity of a point within a cavity of any shape. The exact expression depends only on the emissivity of the cavity wall material and the angle factor between the point at the cavity vertex and the cavity opening. The values predicted by this expression agree well with those obtained from a numerical solution of the integral equation characteristic of a diffuse conical cavity.

© 1966 Optical Society of America

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References

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  1. H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).
  2. Z. Yamauti, Comité International des Poids et Mesures, Procès-Verbaux 16, 243 (1933).
  3. A. Gouffé, Rev. Opt. 24, 1 (1945).
  4. E. W. Treuenfels, J. Opt. Soc. Am. 53, 1162 (1963).
    [CrossRef]
  5. F. J. Kelly, J. Res. Natl. Bur. Std. 69B, 165 (1965).
  6. E. M. Sparrow, V. K. Jonsson, J. Opt. Soc. Am. 53, 816 (1963).
    [CrossRef]
  7. C. H. Page, Natl. Bur. Std. Rept.1673 (15May1952), Natl. Bur. Std. Project 1002–43–1030.

1965 (1)

F. J. Kelly, J. Res. Natl. Bur. Std. 69B, 165 (1965).

1963 (2)

1952 (1)

C. H. Page, Natl. Bur. Std. Rept.1673 (15May1952), Natl. Bur. Std. Project 1002–43–1030.

1945 (1)

A. Gouffé, Rev. Opt. 24, 1 (1945).

1933 (1)

Z. Yamauti, Comité International des Poids et Mesures, Procès-Verbaux 16, 243 (1933).

1927 (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Buckley, H.

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Gouffé, A.

A. Gouffé, Rev. Opt. 24, 1 (1945).

Jonsson, V. K.

Kelly, F. J.

F. J. Kelly, J. Res. Natl. Bur. Std. 69B, 165 (1965).

Page, C. H.

C. H. Page, Natl. Bur. Std. Rept.1673 (15May1952), Natl. Bur. Std. Project 1002–43–1030.

Sparrow, E. M.

Treuenfels, E. W.

Yamauti, Z.

Z. Yamauti, Comité International des Poids et Mesures, Procès-Verbaux 16, 243 (1933).

Comité International des Poids et Mesures, Procès-Verbaux (1)

Z. Yamauti, Comité International des Poids et Mesures, Procès-Verbaux 16, 243 (1933).

J. Opt. Soc. Am. (2)

J. Res. Natl. Bur. Std. (1)

F. J. Kelly, J. Res. Natl. Bur. Std. 69B, 165 (1965).

Natl. Bur. Std. Rept. (1)

C. H. Page, Natl. Bur. Std. Rept.1673 (15May1952), Natl. Bur. Std. Project 1002–43–1030.

Phil. Mag. (1)

H. Buckley, Phil. Mag. 4, 753 (1927); Phil. Mag. 6, 447 (1928); Phil. Mag. 17, 576 (1934).

Rev. Opt. (1)

A. Gouffé, Rev. Opt. 24, 1 (1945).

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Tables (1)

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Table I Computed Apparent Emissivities of Cone Tip

Equations (7)

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ρ a ( x ) = ρ F x - o + ρ 2 ( s / S ) ( 1 - F x - o ) [ 1 + ρ ( 1 - s / S ) + ρ 2 ( 1 - s / S ) 2 + ] = ρ F x - o + { ρ 2 ( s / S ) ( 1 - F x - o ) / [ 1 - ρ ( 1 - s / S ) ] } .
= α = 1 - ρ ,
a ( x ) = α a ( x ) = 1 - ρ a ( x ) .
a ( x ) = [ 1 + ( 1 - ) ( s / S - F x - o ) ] ( 1 - s / S ) + s / S .
a ( t ) = / [ + ( 1 - ) F t - o ]
F t - o = lim x 0 ξ 1 F r - d ( x , ξ ) = lim x 0 ξ 1 [ ξ 2 sin ( θ / 2 ) / 2 x ] × ( F d - d / x ) = sin 3 ( θ / 2 ) ,
F d - d ( ξ , x ) = x 2 + ξ 2 - 2 x ξ cos 2 ( θ / 2 ) - ξ - x [ ( x + ξ ) 2 - 4 x ξ cos 2 ( θ / 2 ) ] 1 2 2 ξ 2 sin 2 ( θ / 2 ) .

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