Comparison of four analytic methods for the calculation of irradiance in integrating spheres
JOSA A, Vol. 15, Issue 12, pp. 3086-3096 (1998)
http://dx.doi.org/10.1364/JOSAA.15.003086
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Abstract
The relative merits of four methods—energy balance, summation of reflections, inversion of the irradiance-transfer matrix, and solution of the integral equation—are compared by using each to determine irradiance in a multizone true sphere and in a sphere with a flat port; in the process several new solutions are presented. Although limited in applicability, the energy-balance method is by far the most direct. For the flat-port configuration the relationships among various published expressions are established; furthermore, the curved-surface interreflection irradiance is shown to be nonuniform when the initial irradiance is restricted to a part of the curved surface.
© 1998 Optical Society of America
OCIS Codes
(120.3150) Instrumentation, measurement, and metrology : Integrating spheres
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.5700) Instrumentation, measurement, and metrology : Reflection
Citation
John F. Clare, "Comparison of four analytic methods for the calculation of irradiance in integrating spheres," J. Opt. Soc. Am. A 15, 3086-3096 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-12-3086
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References
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- This is known in illumination engineering as McAllister’s equilux theorem; see Ref. 6, p. 301. It can also be derived by using the contour integration theorem to replace the flat F with the cap K. The latter theorem states that the flux from a surface of uniform radiance L bounded by a contour C^{′} is the same as that from any other surface of uniform radiance L that is also bounded by C^{′} (Ref. 6, p. 312).
- M. W. Finkel, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970). Finkel omits all but the first two groups of terms in Eq. (55) of the present paper.
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