Abstract

The specification of the transfer function for luminous flux in an enclosure is a necessary component of the lighting design process. Daylight and lamplight excitations are coupled to the luminance and illuminance distributions in space by the luminous reflectances of the surfaces and the geometrical parameters. An idealized representation of this luminous transfer utilizes a postulate of uniform excitation and response over discrete spatial regions. This leads to a matrix equation and an equivalent circuit or network representation of the light distributions. The discrete formulation is particularly adapted to numerical specification of the transfer function for luminous flux and thus to the lighting design process.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Harrison, E. A. Anderson, Trans. Illum. Eng. Soc. 11, 67 (1916).
  2. W. M. Potter, A. H. Russell, Illum. Engr. 46, 619 (1951).
  3. J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).
  4. P. Moon, D. E. Spencer, Lighting Design (Addison-Wesley Publ. Co., Cambridge1948).
  5. P. F. O’Brien, J. A. Howard, Illum. Engr. 54, 209 (1959).
  6. P. F. O’Brien, R. P. Bobco, Illum. Engr. 59, 337 (1964).
  7. P. F. O’Brien, Illum. Engr. 61, 198 (1966).
  8. P. F. O’Brien, E. F. Sowell, J. Opt. Soc. Am. 57, 28 (1967).
    [CrossRef]

1967

1966

P. F. O’Brien, Illum. Engr. 61, 198 (1966).

1964

P. F. O’Brien, R. P. Bobco, Illum. Engr. 59, 337 (1964).

1959

P. F. O’Brien, J. A. Howard, Illum. Engr. 54, 209 (1959).

1955

J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).

1951

W. M. Potter, A. H. Russell, Illum. Engr. 46, 619 (1951).

1916

W. Harrison, E. A. Anderson, Trans. Illum. Eng. Soc. 11, 67 (1916).

Anderson, E. A.

W. Harrison, E. A. Anderson, Trans. Illum. Eng. Soc. 11, 67 (1916).

Arner, W. J.

J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).

Bobco, R. P.

P. F. O’Brien, R. P. Bobco, Illum. Engr. 59, 337 (1964).

Conover, W. E.

J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).

Griffith, J. W.

J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).

Harrison, W.

W. Harrison, E. A. Anderson, Trans. Illum. Eng. Soc. 11, 67 (1916).

Howard, J. A.

P. F. O’Brien, J. A. Howard, Illum. Engr. 54, 209 (1959).

Moon, P.

P. Moon, D. E. Spencer, Lighting Design (Addison-Wesley Publ. Co., Cambridge1948).

O’Brien, P. F.

P. F. O’Brien, E. F. Sowell, J. Opt. Soc. Am. 57, 28 (1967).
[CrossRef]

P. F. O’Brien, Illum. Engr. 61, 198 (1966).

P. F. O’Brien, R. P. Bobco, Illum. Engr. 59, 337 (1964).

P. F. O’Brien, J. A. Howard, Illum. Engr. 54, 209 (1959).

Potter, W. M.

W. M. Potter, A. H. Russell, Illum. Engr. 46, 619 (1951).

Russell, A. H.

W. M. Potter, A. H. Russell, Illum. Engr. 46, 619 (1951).

Sowell, E. F.

Spencer, D. E.

P. Moon, D. E. Spencer, Lighting Design (Addison-Wesley Publ. Co., Cambridge1948).

Illum. Engr.

P. F. O’Brien, J. A. Howard, Illum. Engr. 54, 209 (1959).

P. F. O’Brien, R. P. Bobco, Illum. Engr. 59, 337 (1964).

P. F. O’Brien, Illum. Engr. 61, 198 (1966).

W. M. Potter, A. H. Russell, Illum. Engr. 46, 619 (1951).

J. W. Griffith, W. J. Arner, W. E. Conover, Illum. Engr. 50, 103 (1955).

J. Opt. Soc. Am.

Trans. Illum. Eng. Soc.

W. Harrison, E. A. Anderson, Trans. Illum. Eng. Soc. 11, 67 (1916).

Other

P. Moon, D. E. Spencer, Lighting Design (Addison-Wesley Publ. Co., Cambridge1948).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Flow diagram.

Fig. 2
Fig. 2

The network representation of luminous emittance and flux flow in an infinite room whose surfaces display a specular and a diffuse component.

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

L d A n = L O d A n + space ρ ϕ ( d A n , d A s ) L d A s d A s .
L 1 = L O 1 + ρ D 1 [ ϕ ( 1 , 1 ) L 1 + ϕ ( 1 , 2 ) L 2 + + ϕ ( 1 , n ) L n ] ,
E ( 2 , 1 ) = ϕ ( 1 , 2 ) L 2 ,
ϕ ( 1 , 2 ) = F ( 1 , 2 ) + F [ 1 , 2 ( 1 + 2 + 3 + ) ] ρ S 1 ρ S 2 ρ S 3 .
A n ϕ ( n , m ) = A m ϕ ( m , n ) .
( 1 - ρ S 1 ) ϕ ( 1 , 1 ) + ( 1 - ρ S 2 ) ϕ ( 1 , 2 ) + + ( 1 - ρ S n ) ϕ ( 1 , n ) = 1.
| + 1 [ ( 1 / ρ D 1 ) - ϕ ( 1 , 1 ) ] - ϕ ( 1 , 2 ) - ϕ ( 1 , 3 ) - - ϕ ( 2 , 1 ) + [ ( 1 / ρ D 2 ) - ϕ ( 2 , 2 ) ] - ϕ ( 2 , 3 ) - - ϕ ( 3 , 1 ) - ϕ ( 3 , 2 ) + [ ( 1 / ρ D 3 ) - ϕ ( 3 , 3 ) ] + | Transfer Matrix × | L 1 L 2 L 3 | Response Vector = | L O 1 / ρ D 1 L O 2 / ρ D 2 L O 3 / ρ D 3 | Excitation Vector .
| + ρ D 1 ( L 1 , 1 L O 1 ) + ρ D 2 ( L 1 , 2 L O 2 ) + ρ D 3 ( L 1 , 3 L O 3 ) + + ρ D 1 ( L 2,1 L O 1 ) + ρ D 2 ( L 2 , 2 L O 2 ) + ρ D 3 ( L 2 , 3 L O 3 ) + + ρ D 1 ( L 3 , 1 L O 1 ) + ρ D 2 ( L 3 , 2 L O 2 ) + ρ D 3 ( L 3 , 3 L O 3 ) + | · | L O 1 ρ D 1 L O 2 ρ D 2 L O 3 ρ D 3 | = | L 1 L 2 L 3 | .
L 1 = ( L 1 , 1 L O 1 ) × L O 1 + ( L 1 , 2 L O 2 ) × L O 2 + ( L 1 , 3 L O 3 ) × L O 3 + .
A n ρ D n ( L n , m L O m ) = A m ρ D m ( L m , n L O n ) .
( 1 - ρ S 1 - ρ D 1 ) ( L 1 , 1 / L O 1 ) + ( 1 - ρ S 2 - ρ D 2 ) ( L 1 , 2 / L O 2 ) + = 1 - ρ S 1 ,
( 1 - ρ S 1 - ρ D 1 ) ρ D 1 [ ( L 1 , 1 L O 1 ) - 1 ] + ( 1 - ρ S 2 - ρ D 2 ) ρ D 1 ( L 1 , 2 L O 2 ) + ( 1 - ρ S 3 - ρ D 3 ) ρ D 1 ( L 1 , 3 L O 3 ) + = 1 ,
( 1 - ρ S 1 - ρ D 1 ) [ ϕ ( 1 , 1 ) L 1 , 1 L O 1 + ϕ ( 1 , 2 ) L 2 , 1 L O 1 + ] + ( 1 - ρ S 2 - ρ D 2 ) [ ϕ ( 1 , 1 ) L 1 , 2 L O 2 + ϕ ( 1 , 2 ) L 2 , 2 L O 2 + ] + = 1.
( 1 - ρ S 1 - ρ D 1 ) 2 A 1 ρ D 1 ( L 1 , 1 L O 1 ) + ( 1 - ρ S 2 - ρ D 2 ) 2 A 2 ρ D 2 ( L 2 , 2 L O 2 ) + = A 1 ( 1 - ρ S 1 ) ( 1 - ρ S 1 - ρ D 1 ) ρ D 1 + A 2 ( 1 - ρ S 2 ) ( 1 - ρ S 2 - ρ D 2 ) ρ D 2 + .
L 1 = L O 1 + ρ D 1 [ ϕ ( 1 , 1 ) L 1 + ϕ ( 1 , 2 ) L 2 ] .
ϕ ( 1 , 2 ) = F ( 1 , 2 ) + F [ 1 , 2 ( 1 , 2 ) ] ρ S 1 ρ S 2 + F [ 1 , 2 ( 1 , 2 , 1 , 2 ) ] ρ S 1 2 ρ S 2 2 +
ϕ ( 1 , 2 ) = 1 / ( 1 - ρ S 1 ρ S 2 ) .
ϕ ( 1 , 2 ) = ϕ ( 2 , 1 ) = 1 / ( 1 - ρ S 1 ρ S 2 ) .
ϕ ( 1 , 1 ) = 1 - ( 1 - ρ S 2 ) ϕ ( 1 , 2 ) ( 1 - ρ S 1 ) = ρ S 2 1 - ρ S 1 ρ S 2 .
ϕ ( 1 , 1 ) = ρ S 2 ϕ ( 1 , 2 ) = ρ S 2 ϕ ( 2 , 1 ) ,
ϕ ( 1 , 2 ) - ρ S 1 ϕ ( 1 , 1 ) = ϕ ( 1 , 2 ) [ 1 - ρ S 1 ρ S 2 ] = 1.
L 1 ( 1 - ρ S 1 ) ( 1 - ρ S 1 ) = L O 1 ( 1 - ρ S 1 - ρ D 1 ) ( 1 - ρ S 1 - ρ D 1 ) + ρ D 1 ρ S 2 ϕ ( 1 , 2 ) L 1 + ρ D 1 ϕ ( 1 , 2 ) L 2 .
[ L O 1 ( 1 - ρ S 1 - ρ D 1 ) - L 1 ( 1 - ρ S 1 ) ρ D 1 / A 1 ( 1 - ρ S 1 ) ( 1 - ρ S 1 - ρ D 1 ) ] = [ L 1 ( 1 - ρ S 1 ) - L 2 ( 1 - ρ S 2 ) 1 / A 1 ( 1 - ρ S 1 ) ( 1 - ρ S 2 ) ϕ ( 1 , 2 ) ] .
[ L O 1 / ( 1 - ρ S 1 - ρ D 1 ) ] - [ L O 2 / ( 1 - ρ S 2 - ρ D 2 ) ] R O 1 + R 12 + R O 2 = [ L 1 / ( 1 - ρ S 1 ) ] - [ L 2 / ( 1 - ρ S 2 ) ] R 12 .
( L 1 , 1 / L O 1 ) = [ 1 - ρ D 2 ϕ ( 2 , 2 ) / Z ] ,
( L 2 , 1 / L O 1 ) = [ ρ D 2 ϕ ( 2 , 1 ) / Z ] ,
Z = 1 - ρ D 1 ϕ ( 1 , 1 ) - ρ D 2 ϕ ( 2 , 2 ) + ρ D 1 ρ D 2 × [ ϕ ( 1 , 1 ) ϕ ( 2 , 2 ) - ϕ ( 2 , 1 ) ϕ ( 1 , 2 ) ] .
( L 2 , 2 / L O 2 ) = [ 1 - ρ D 1 ϕ ( 1 , 1 ) / Z ] ,
( L 1 , 2 / L O 2 ) = [ ρ D 1 ϕ ( 1 , 2 ) / Z ] .
φ ( 1 , 1 ) = ρ S 2 / ( 1 - ρ S 1 ρ S 2 ) ,
ϕ ( 1 , 2 ) = 1 / ( 1 - ρ S 1 ρ S 2 ) ,
ϕ ( 2 , 1 ) = [ ( A 1 / A 2 ) / ( 1 - ρ S 1 ρ S 2 ) ] ,
ϕ ( 2 , 2 ) = [ 1 - ρ S 1 ρ S 2 - ( 1 - ρ S 1 ) ( A 1 / A 2 ) ] / [ ( 1 - ρ S 2 ) ( 1 - ρ S 1 ρ S 2 ) ] .

Metrics