Abstract

This report describes the fabrication of an integrating hemiellipsoid and the associated analytical and empirical evaluation of it. The focusing properties of the instrument are seen to be of high quality, and quantitative information is presented regarding the selection of the size of a detector to be used.

© 1970 Optical Society of America

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References

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  1. Von F. Paschen, Gesammtsitzung 27, 405 (1899).
  2. W. W. Coblentz, Nat. Bur. Stand. Bull. 9, 283 (1913).
    [CrossRef]
  3. R. C. Birkebak, J. P. Hartnett, Trans. ASME 80, 373 (1958).
  4. R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
    [CrossRef]
  5. B. P. Kozyrev, O. E. Vershinin, Opt. Spektrosk. 6, 542 (1959) [Opt. Spectrosc. 6, 345 (1959)].
  6. J. E. Janssen, R. H. Torborg, in “Measurement of Thermal Radiation Properties of Solids,” J. C. Richmond, Ed., NASA SP-31, 1963.
  7. J. T. Neu, “Design, Fabrication, and Performance of an Ellipsoidal Spectroreflectometer,” NASA CR-73193, March1968.
  8. S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).
  9. W. M. Brandenberg, J. Opt. Soc. Amer. 54, 1235 (1964).
    [CrossRef]

1966

S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).

1964

W. M. Brandenberg, J. Opt. Soc. Amer. 54, 1235 (1964).
[CrossRef]

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

1959

B. P. Kozyrev, O. E. Vershinin, Opt. Spektrosk. 6, 542 (1959) [Opt. Spectrosc. 6, 345 (1959)].

1958

R. C. Birkebak, J. P. Hartnett, Trans. ASME 80, 373 (1958).

1913

W. W. Coblentz, Nat. Bur. Stand. Bull. 9, 283 (1913).
[CrossRef]

1899

Von F. Paschen, Gesammtsitzung 27, 405 (1899).

Birkebak, R. C.

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

R. C. Birkebak, J. P. Hartnett, Trans. ASME 80, 373 (1958).

Brandenberg, W. M.

W. M. Brandenberg, J. Opt. Soc. Amer. 54, 1235 (1964).
[CrossRef]

Coblentz, W. W.

W. W. Coblentz, Nat. Bur. Stand. Bull. 9, 283 (1913).
[CrossRef]

Dunn, S. T.

S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).

Eckert, E. R. G.

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

Hartnett, J. P.

R. C. Birkebak, J. P. Hartnett, Trans. ASME 80, 373 (1958).

Janssen, J. E.

J. E. Janssen, R. H. Torborg, in “Measurement of Thermal Radiation Properties of Solids,” J. C. Richmond, Ed., NASA SP-31, 1963.

Kozyrev, B. P.

B. P. Kozyrev, O. E. Vershinin, Opt. Spektrosk. 6, 542 (1959) [Opt. Spectrosc. 6, 345 (1959)].

Neu, J. T.

J. T. Neu, “Design, Fabrication, and Performance of an Ellipsoidal Spectroreflectometer,” NASA CR-73193, March1968.

Paschen, Von F.

Von F. Paschen, Gesammtsitzung 27, 405 (1899).

Ramsey, J. W.

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

Richmond, J. C.

S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).

Sparrow, E. M.

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

Torborg, R. H.

J. E. Janssen, R. H. Torborg, in “Measurement of Thermal Radiation Properties of Solids,” J. C. Richmond, Ed., NASA SP-31, 1963.

Vershinin, O. E.

B. P. Kozyrev, O. E. Vershinin, Opt. Spektrosk. 6, 542 (1959) [Opt. Spectrosc. 6, 345 (1959)].

Wiebelt, J. A.

S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).

Gesammtsitzung

Von F. Paschen, Gesammtsitzung 27, 405 (1899).

J. Heat Transfer

R. C. Birkebak, E. M. Sparrow, E. R. G. Eckert, J. W. Ramsey, J. Heat Transfer 86C, 193 (1964).
[CrossRef]

J. Opt. Soc. Amer.

W. M. Brandenberg, J. Opt. Soc. Amer. 54, 1235 (1964).
[CrossRef]

J. Res. Nat. Bur. Stand.

S. T. Dunn, J. C. Richmond, J. A. Wiebelt, J. Res. Nat. Bur. Stand. 70C, 75 (1966).

Nat. Bur. Stand. Bull.

W. W. Coblentz, Nat. Bur. Stand. Bull. 9, 283 (1913).
[CrossRef]

Opt. Spektrosk.

B. P. Kozyrev, O. E. Vershinin, Opt. Spektrosk. 6, 542 (1959) [Opt. Spectrosc. 6, 345 (1959)].

Trans. ASME

R. C. Birkebak, J. P. Hartnett, Trans. ASME 80, 373 (1958).

Other

J. E. Janssen, R. H. Torborg, in “Measurement of Thermal Radiation Properties of Solids,” J. C. Richmond, Ed., NASA SP-31, 1963.

J. T. Neu, “Design, Fabrication, and Performance of an Ellipsoidal Spectroreflectometer,” NASA CR-73193, March1968.

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Figures (10)

Fig. 1
Fig. 1

Ellipsoid male mold.

Fig. 2
Fig. 2

Hemiellipsoid.

Fig. 3
Fig. 3

Image quality determination fixture mounted on hemiellipsoidal reflector.

Fig. 4
Fig. 4

Experimental determination of ellipsoidal reflector quality.

Fig. 5
Fig. 5

Reflection of aluminized epoxy specimens.

Fig. 6
Fig. 6

General coordinate system for ellipsoid.

Fig. 7
Fig. 7

Two-dimensional coordinate system.

Fig. 8
Fig. 8

Image of source boundary for rays emitting from a 45° cone about the surface normal of the source.

Fig. 9
Fig. 9

Image of entire source emitting from a 10° vertical cone about the surface normal.

Fig. 10
Fig. 10

Image of the entire source emitting in all directions.

Equations (8)

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( x 2 / a 2 ) + [ ( y 2 + z 2 ) / b 2 ] = 1 ,
x 3 = 0 ,
y 3 = y 2 ( 1 a 2 / b 2 ) .
g = a 2 / b 2
h = r 23 2 / ( r 12 2 r 13 2 ) = r 34 / r 13 .
x 4 = x 1 h ,
y 4 = y 2 ( 1 g ) ( 1 + h ) h y 1 ,
r 12 2 = r 1 2 + r 2 2 2 r 1 × r 2 = x 1 2 + y 1 2 + x 2 2 + y 2 2 + z 2 2 2 x 1 x 2 2 y 1 y 2 , r 13 2 = y 2 2 ( 1 g ) 2 + x 1 2 + y 1 2 2 y 1 y 2 ( 1 g ) , r 12 2 r 13 2 = x 2 ( x 2 2 x 1 ) + z 2 2 + g y 2 [ y 2 ( 2 g ) 2 y 1 ] , r 23 2 = x 2 2 + z 2 2 + g 2 y 2 2 .

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