Corrigendum: Modeling Circadian Phototransduction: Quantitative Predictions of Psychophysical Data

In the original article, there was an error. One of the inherent mathematical assumptions for Equation 3 as published, should be explicitly added to the mathematical formulation. The published terms “V_λ” and “S_λ” therefore have been replaced by “V_cλ” and “S_cλ” respectively, to convey the implicit normalizations in the corrected equation. The term k has also been defined.

A correction has been made to Equation 3.

$$C{L}_{A}2.0=1548\{\begin{array}{l}\left({\displaystyle \int M{c}_{\lambda }{E}_{\lambda }d\lambda }-a_{rod1}\left(\frac{{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{{\displaystyle \int V_{c\lambda }{E}_{\lambda }d\lambda }+g_1{\displaystyle \int S_{c\lambda }{E}_{\lambda }d\lambda }}\right)\left(1-e^{\frac{-{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{RodSat}}\right)\right)\\ +\left(a_{b-y}({\displaystyle \int S_{c\lambda }{E}_{\lambda }d\lambda }-k{\displaystyle \int V_{c\lambda }{E}_{\lambda }d\lambda }\right)-a_{rod2}\left(\frac{{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{{\displaystyle \int V_{c\lambda }{E}_{\lambda }d\lambda }+g_2{\displaystyle \int S_{c\lambda }{E}_{\lambda }d\lambda }}\right)\\ \left(1-e^{\frac{-{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{RodSat}}\right)),b-y>0\\ \left({\displaystyle \int M{c}_{\lambda }{E}_{\lambda }d\lambda }-a_{rod1}\left(\frac{{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{{\displaystyle \int V_{c\lambda }{E}_{\lambda }d\lambda }+g_1{\displaystyle \int S_{c\lambda }{E}_{\lambda }d\lambda }}\right)\left(1-e^{\frac{-{\displaystyle \int V_{\lambda }^{\prime }{E}_{\lambda }d\lambda }}{RodSat}}\right)\right),b-y\le 0\end{array}$$

where,

$$b-y=\int S_{c\lambda }{E}_{\lambda }d\lambda -k\int V_{c\lambda }{E}_{\lambda }d\lambda$$

k = 0.2616	Eλ: light source spectral irradiance.
ab−y = 0.21	Mcλ: melanopsin sensitivity (corrected for crystalline lens spectral transmittance) (Wyszecki and Stiles, 1982)
arod1 = 2.30	Sλ: S-cone fundamental (Smith and Pokorny, 1975).
arod2 = 1.60	mpλ: macular pigment spectral transmittance (Snodderly et al., 1984).
g1 = 1.00	Vλ: photopic luminous efficiency function (Commission Internationale de l'Éclairage, 1994).
g2 = 0.16	${V^{\prime }}_{\lambda }$: scotopic luminous efficiency function (Commission Internationale de l'Éclairage, 1994).

RodSat = 6.50 W m⁻²

$$\begin{array}{l}{V}_{c\lambda }=\frac{(\frac{V_{\lambda }}{m{p}_{\lambda }})}{max(\frac{V_{\lambda }}{m{p}_{\lambda }})}{S}_{c\lambda }=\frac{(\frac{S_{\lambda }}{m{p}_{\lambda }})}{max(\frac{S_{\lambda }}{m{p}_{\lambda }})}\end{array}$$

The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

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