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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 26 — Sep. 10, 2008
  • pp: 4714–4722

Determining the irradiance signal from an asymmetric source with directional detectors: application to calibrations of radiometers with diffusers

Pasi Manninen, Petri Kärhä, and Erkki Ikonen  »View Author Affiliations

Applied Optics, Vol. 47, Issue 26, pp. 4714-4722 (2008)

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The energy transfer integral between radiating rectangular and detecting circular parallel plates having nonideal angular characteristics is solved for modeling the distance dependence of the irradiance signal. The equation derived for the irradiance signal, which is called the modified inverse-square law, depends on the position, shape, size, and angular characteristics of the light source and the detector. We apply the new model equation to the calibration of a spectroradiometer to determine accurately the distance offsets, which fix the positions of the effective receiving apertures of diffusers used in the entrance optics of spectroradiometers. Earlier measurement results, e.g., for solar UV irradiance, may include uncorrected effects and can be corrected reliably as diffuser offsets and other correction factors are determined with the modified inverse-square law. Simplifications of the modified inverse-square law for analyzing the distance offsets and the correction factors are studied. Simplified equations for the diffuser offset analysis may be used without losing the accuracy when the cosine response of the diffuser is reasonably good. However, for diffusers whose angular responsivities deviate much from the cosinusoidal angular responsivity, large approximation errors in the diffuser offset values may appear if the angular effects are not properly taken into account.

© 2008 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(080.0080) Geometric optics : Geometric optics
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(230.1980) Optical devices : Diffusers

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: May 14, 2008
Manuscript Accepted: July 24, 2008
Published: September 9, 2008

Pasi Manninen, Petri Kärhä, and Erkki Ikonen, "Determining the irradiance signal from an asymmetric source with directional detectors: application to calibrations of radiometers with diffusers," Appl. Opt. 47, 4714-4722 (2008)

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