Soleillet&#x2019;s formalism of coherence and partial polarization in 2D and 3D: application to fluorescence polarimetry

Oriol Arteaga; Shane Nichols

doi:10.1364/JOSAA.35.001254

Journal of the Optical Society of America A
Vol. 35,
Issue 8,
pp. 1254-1260
(2018)
•https://doi.org/10.1364/JOSAA.35.001254

Soleillet’s formalism of coherence and partial polarization in 2D and 3D: application to fluorescence polarimetry

Oriol Arteaga and Shane Nichols

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Oriol Arteaga and Shane Nichols, "Soleillet’s formalism of coherence and partial polarization in 2D and 3D: application to fluorescence polarimetry," J. Opt. Soc. Am. A 35, 1254-1260 (2018)

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Abstract

We review here the pioneering research conducted by Paul Soleillet on the statistical properties of light in his doctoral thesis from 1929 [Ann. Phys. 10, 23 (1929)]. Soleillet’s wide-reaching work on polarization, coherence, fluorescence scattering, and three-dimensional fields has remained largely unrecognized; yet, his original contributions rival the modern rediscoveries in both generality and form. Only now, 89 years after Soleillet’s original publication and stimulated by our current research on fluorescence polarimetry, have we been able to fully understand and recognize the significance of his results.

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Equations (38)

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	Linear Oscillators	Circular Oscillators	Elliptical Oscillators
$t_{i}$	$t_{1} = 1 t_{2} = 1 t_{3} = 1$	$t_{1} = 4 t_{2} = 4 t_{3} = 0$	$t_{1} = 4 - 4 ϵ^{2} + ϵ^{4} t_{2} = 4 - 4 ϵ^{2} + ϵ^{4} t_{3} = ϵ^{4}$
$a_{i}^{j}$	$a_{1}^{1} = \frac{3}{15}$	$a_{1}^{1} = \frac{8}{15}$	$a_{1}^{1} = \frac{8 - 8 ϵ^{2} + 3 ϵ^{4}}{15}$
	$a_{6}^{6} = \frac{2}{15}$	$a_{6}^{6} = \frac{2}{15}$	$a_{6}^{6} = \frac{2 (1 - ϵ^{2} + ϵ^{4})}{15}$
	$a_{9}^{9} = 0$	$a_{9}^{9} = \frac{10}{15}$	$a_{9}^{9} = \frac{10 (1 - ϵ^{2})}{15}$
$a$ , $b$ , $c$	$a = \frac{4}{15}$	$a = \frac{14}{15}$	$a = \frac{8 - 8 ϵ^{2} + 3 ϵ^{4}}{15}$
	$b = \frac{1}{15}$	$b = \frac{1}{15}$	$b = \frac{1 - ϵ^{2} + ϵ^{4}}{15}$
	$c = 0$	$c = \frac{5}{15}$	$c = \frac{5 (1 - ϵ^{2})}{15}$

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Journal of the Optical Society of America A