## Abstract

We correct an equation, calculating the radiating power from a selective solar absorber, which is missing an extra factor of π. We also correct the results of the affected figures.

In section 3 of article [1] we showed two equations for calculating the power being absorbed and emitted from a selective solar absorber. The Pin term was missing a factor of π for integrating over all solid angles. The following equations should replace Eqs. (4) and (5) in the original article.

$Pout=∫02π∫0π2(∫0λsαuλdevice(Tdevice)dλ+∫λs∞εuλdevice(Tdevice)dλ)sin(θ)cos(θ)dθdφPout=π(∫0λsαuλdevice(Tdevice)dλ+∫λs∞εuλdevice(Tdevice)dλ)$
$Pin=πC(∫0λsαuλsolar(Tsun)dλ+∫λs∞εuλsolar(Tsun)dλ)$

The missing factor of π also causes the exact peaks of Figs. 3 , 4 , and 5 to shift to slightly lesser wavelengths and higher temperatures. Because of this shift our claim in the abstract should read “With an emissivity of 5%, solar concentration of 10 times the AM1.5 spectrum the optimum transition wavelength is found to be 1.08µm and have a 1230K equilibrium temperature.” The following figures should replace Figs. 3, 4, and 5 in the original article. We would also like to thank Jacob Jonsson, at Lawrence Berkeley National Lab for pointing out our error.

Fig. 3 (a) The ideal thermal equilibrium temperature between a selective absorber and the sun with no concentration (C=1) as a function of transition wavelength. As the emissivity increases notice that the optimum transition wavelength for a certain operating temperature is shifted to shorter wavelengths. AM0 will have a very similar result to this case.

Fig. 4 Thermal equilibrium temperature as a function of transition wavelength and emissivity for the AM1.5 solar spectrum with no concentration (C=1)

Fig. 5 Thermal equilibrium temperature as a function of transition wavelength for a selective absorber with an emissivity of 5% under AM1.5 illumination at different concentrations. The optimal transition wavelength is highly dependent on the concentration of incoming radiation.

1. K. D. Olson and J. J. Talghader, “Absorption to reflection transition in selective solar coatings,” Opt. Express 20(S4Suppl 4), A554–A559 (2012). [CrossRef]   [PubMed]

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### Figures (3)

Fig. 3

(a) The ideal thermal equilibrium temperature between a selective absorber and the sun with no concentration (C=1) as a function of transition wavelength. As the emissivity increases notice that the optimum transition wavelength for a certain operating temperature is shifted to shorter wavelengths. AM0 will have a very similar result to this case.

Fig. 4

Thermal equilibrium temperature as a function of transition wavelength and emissivity for the AM1.5 solar spectrum with no concentration (C=1)

Fig. 5

Thermal equilibrium temperature as a function of transition wavelength for a selective absorber with an emissivity of 5% under AM1.5 illumination at different concentrations. The optimal transition wavelength is highly dependent on the concentration of incoming radiation.

### Equations (2)

$P o u t = ∫ 0 2 π ∫ 0 π 2 ( ∫ 0 λ s α u λ d e v i c e ( T d e v i c e ) d λ + ∫ λ s ∞ ε u λ d e v i c e ( T d e v i c e ) d λ ) sin ( θ ) cos ( θ ) d θ d φ P o u t = π ( ∫ 0 λ s α u λ d e v i c e ( T d e v i c e ) d λ + ∫ λ s ∞ ε u λ d e v i c e ( T d e v i c e ) d λ )$
$P i n = π C ( ∫ 0 λ s α u λ s o l a r ( T s u n ) d λ + ∫ λ s ∞ ε u λ s o l a r ( T s u n ) d λ )$