Radiant Flux from a Cylindrical Distributed Source*

W. R. Anderson; I. B. Berlman

doi:10.1364/JOSA.51.001229

Journal of the Optical Society of America
Vol. 51,
Issue 11,
pp. 1229-1234
(1961)
•https://doi.org/10.1364/JOSA.51.001229

Radiant Flux from a Cylindrical Distributed Source

W. R. Anderson and I. B. Berlman

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W. R. Anderson and I. B. Berlman, "Radiant Flux from a Cylindrical Distributed Source*," J. Opt. Soc. Am. 51, 1229-1234 (1961)

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Abstract

Of the total radiant flux produced in a right-circular cylindrical cell containing a uniformly distributed isotropic source of radiant energy, the fraction emanating from the end window is computed both for a cell with ideal, perfectly reflecting mirror surfaces and for a cell with ideal, totally absorbing surfaces. Graphs are presented of the calculated radiant-flux fractions from the cylinder as a function of the absorbance of the contents. Also presented are results of measurements of the radiant flux emitted from a cylindrical cell containing an externally excited scintillating solution when the inner reflecting surfaces of the cell are (1) polished aluminum, (2) aluminum evaporated on glass, (3) aluminum oxide, and (4) Teflon. These results are expressed relative to the radiant flux emitted by the same cell-solution combination with blackened inner cell surfaces. The actual radiant-flux fractions emitted by the cells are estimated by using the calculation for a cell possessing ideal, totally absorbing surfaces.

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(1)	(2)	(3)	(4)	(5)	(6)

2aH	$\int_{1}^{\infty} e^{- 2 a H x} x^{- 3} d x$	$\frac{1}{2 a H}$	$\frac{1}{2 a H} \int_{1}^{\infty} e^{- 2 a H x} x^{- 3} d x$	$\frac{1}{4 a H}$	F
0	0.5000				1.00
0.01	0.4903	100	49.03	50	0.97
0.05	0.4549	20	9.098	10	0.902
0.1	0.4163	10	4.163	5	0.837
0.25	0.3247	4	1.299	2	0.701
0.5	0.2216	2	0.4432	1	0.5568
1.0	0.1097	1	0.1097	0.5000	0.3903
1.5	0.0567	$\frac{2}{3}$	0.0378	0.3333	0.2955
2.0	0.0301	$\frac{1}{2}$	0.0150	0.2500	0.2350
2.5	0.0163	$\frac{2}{5}$	0.0065	0.2000	0.1935
3.0	0.0089	$\frac{1}{3}$	0.0030	0.1667	0.1637
4.0	0.0028	$\frac{1}{4}$	0.0007	0.1250	0.1243
5.0	0.0009	$\frac{1}{5}$	0.0002	0.1000	0.0998
6.0	0.0003	$\frac{1}{6}$	0.00005	0.08333	0.08328

A₁(cm⁻¹)	F
0	0.154
0.1	0.118
0.3	0.078
0.6	0.049
2.0	0.017
(∞)	(0)

	(1)	(2)	(3)	(4)
	Solution I		Solution II
Surface	Output ratio to black	Indicated % emerging	Output ratio to black	Indicated % emerging
Black reference (See Table II)	1	15.4	1	15.4
Aluminum	1.7±0.05	26±1	1.9±0.05	29±1
Aluminum on glass	3.2±0.05	49±1	3.6±0.05	55±1
Aluminum oxide	4.0±0.05	62±1	4.1±0.05	63±1
Teflon I	4.8±0.05	74±1	4.8±0.05	74±1
Teflon II	5.2±0.05	80±1	5.2±0.05	80±1

(1)	(2)	(3)	(4)	(5)	(6)

2aH	$\int_{1}^{\infty} e^{- 2 a H x} x^{- 3} d x$	$\frac{1}{2 a H}$	$\frac{1}{2 a H} \int_{1}^{\infty} e^{- 2 a H x} x^{- 3} d x$	$\frac{1}{4 a H}$	F
0	0.5000				1.00
0.01	0.4903	100	49.03	50	0.97
0.05	0.4549	20	9.098	10	0.902
0.1	0.4163	10	4.163	5	0.837
0.25	0.3247	4	1.299	2	0.701
0.5	0.2216	2	0.4432	1	0.5568
1.0	0.1097	1	0.1097	0.5000	0.3903
1.5	0.0567	$\frac{2}{3}$	0.0378	0.3333	0.2955
2.0	0.0301	$\frac{1}{2}$	0.0150	0.2500	0.2350
2.5	0.0163	$\frac{2}{5}$	0.0065	0.2000	0.1935
3.0	0.0089	$\frac{1}{3}$	0.0030	0.1667	0.1637
4.0	0.0028	$\frac{1}{4}$	0.0007	0.1250	0.1243
5.0	0.0009	$\frac{1}{5}$	0.0002	0.1000	0.0998
6.0	0.0003	$\frac{1}{6}$	0.00005	0.08333	0.08328

A₁(cm⁻¹)	F
0	0.154
0.1	0.118
0.3	0.078
0.6	0.049
2.0	0.017
(∞)	(0)

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Equations (14)

Journal of the Optical Society of America