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Updated: Jul 12, 2026

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Quantitative spectrophotometry of scattering media via frequency-domain and constant-intensity measurements
John Crowe1, David Morris, Malcolm Woolfson
1Applied Optics Group, School of Electrical and Electronic Engineering, University of Nottingham, UK. john.crowe@nottingham.ac.uk
Abstract:
The attenuation of light by scattering and absorbing media is nonlinearly dependent upon the absorption coefficient, since detected light has experienced many different flight times. The frequency response of such a sample to modulated light is also nonlinear. We derive an expression for the attenuation that includes both the absorption coefficient and the modulation frequency. Its form is a power series whose coefficients are the cumulants of the temporal point-spread function (TPSF). Recasting this expression in terms of intensity leads to a similar expression with the cumulants replaced by the moments of the TPSF. A means of exploiting this relationship to produce estimates of the absolute concentration of the absorbing species is suggested.
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