The circadian variation of indices of natural irradiance of the terrestrial surface produced by solar radiation is the main physical factor that controls the circadian activities of the entire human body [1]. This variation is also affected by the clear 11-year solar activity cycle, which is also known as the Schwabe cycle [2–4]. The cyclic variation in solar activity, associated with the number of sunspots (Wolf number W [2]) on the apparent surface of the photosphere of the Sun, causes cyclic changes in the effective absolute temperature Teff of solar radiation, the absolute indices of the spectral density of photosphere luminance, and photosphere luminance itself. The maximum amplitudes of photosphere luminance indices within one solar activity cycle can reach approximately 35%. Obviously, these changes affect the control and indices of human circadian activities in any phase of the solar cycle.

Studies and models of processes that control human circadian activities have not considered the combined action of circadian and 11-year cyclic variations of irradiance thus far.

This work presents a description of spectrally selective transformations performed by receivers of optical radiation in the pathway controlling circadian activities under the combined effect of circadian and 11-year variations in spectral and energetic indices of solar irradiance. This description is important for biology, chronobiology, and light engineering.

Solar radiation acts on the analog receivers of optical radiation, which are a system of blue-sensitive cones (S cones) and rods that are located in peripheral areas of the retina [5]. Rods and S cones are the initial step in the pathway that controls human circadian activity [1]. At this step, the circadian activity control pathway receives solar radiation and performs its spectrally selective processing. This processing includes the isolation of the circadian component of the solar radiation spectrum and supports the control of human circadian activity proper.

This processing generates neuron signals formed by retinal ganglion (output) cells. They bear binary information on the spectral density of irradiance (SDI), which has been received and processed by the analog receivers of optical radiation [5].

The output signals formed by retinal ganglion cells are transduced to the suprachiasmatic nuclei of the hypothalamus, where signals that control the circadian activity of the pineal gland, which secretes melatonin to blood plasma, are formed. The circadian changes in the blood plasma melatonin level ultimately control human circadian activities.

The binary retinal outputs signals form a bijective and bicontinuous homeomorphic map of the SDI acting on the retina. Therefore, for clarity and convenience, the transformations of signals in the circadian activities controlling pathway are described below via analog representations of binary signals with appropriate terms and concepts.

The \({{m}_{{eS}}}(\lambda ,T)\) function of the spectral density of the luminance of the photosphere of the Sun is described by Planck’s law for a black body [6, 7]:

$${{m}_{{eS}}}(\lambda ,T) = {{C}_{1}}{{\lambda }^{{ - 5}}}{{\left( {\exp \frac{{{{C}_{2}}}}{{\lambda T}} - 1} \right)}^{{ - 1}}},$$
(1)

where λ is the radiation wavelength; T, the absolute temperature of the equilibrium black body radiation; C1 ≈ 3.742 × 10–16 W m2; and C2 ≈ 1.439 × 10–2 m K.

The SDI at the normal incidence of solar radiation on an area at the upper boundary of the terrestrial atmosphere is

$$\begin{gathered} {{e}_{{eS}}}(\lambda ,{{T}_{{{\text{eff}}}}}) = {{\left( {\frac{r}{R}} \right)}^{2}}{{m}_{{eS}}}(\lambda ,{{T}_{{{\text{eff}}}}}) \\ = {{\left( {\frac{r}{R}} \right)}^{2}}{{C}_{1}}{{\lambda }^{{ - 5}}}{{\left( {\exp \frac{{{{C}_{2}}}}{{\lambda {{T}_{{{\text{eff}}}}}}} - 1} \right)}^{{ - 1}}}, \\ \end{gathered} $$
(2)

where Teff is the effective (averaged over the photosphere) absolute temperature of the solar radiation, r = 6.96 × 105 km is the Sun’s equatorial radius, and R = 1.496 × 1012 km is the radius of the Earth’s circular orbit [8, 9].

According to the recommendations of the International Radiation Commission [10], Teff is taken to be constant; this does not allow the dependence of eeS(λ, Teff) on the year number within a solar cycle to be constructed.

Obviously, in Eq. (2)Teff = Teff(n). To determine the Teff(n) function, we applied the solar constant SC (Eq. (3)), which is the irradiance of an area at the upper boundary of the terrestrial atmosphere at the normal incidence of solar radiation [11].

$$\begin{gathered} {{E}_{{{\text{SC}}}}}({{T}_{{{\text{eff}}}}}) = \int\limits_0^\infty {{{e}_{{eS}}}(\lambda ,{{T}_{{{\text{eff}}}}})d\lambda } \\ = {{\left( {\frac{r}{R}} \right)}^{2}}\int\limits_0^\infty {{{m}_{{eS}}}(\lambda ,{{T}_{{{\text{eff}}}}})d\lambda } . \\ \end{gathered} $$
(3)

Satellite solar radiometrical measurements of the maximum values of the 20th and 21st solar activity cycles [2–4] indicate that the most probable ESC(Teff) value is within 1368–1377 W/m2, with the time variation of this index being irregular. Therefore, the term solar constant is used. The standard solar constant value, which corresponds to the maximum solar activity, is taken to be ESC, max(Teff) ≈ 1370 W/m2, in accordance with the International Pyrheliometric Scale [9, 10]. As follows from Eqs. (2) and (3), this ESC, max(Teff) value corresponds to Teff, max = 5780 K.

The Teff, min and ESC_min values were calculated by invoking the so-called light solar constant ELSC, min(Teff) within the wavelength range 350 × 10–9 ≤ λ ≤ 770 × 10–9 m:

$$\begin{gathered} {{E}_{{{\text{LSC}}}}}({{T}_{{{\text{eff}}}}}) = 683\int\limits_{350 \times {{{10}}^{{ - 9}}}}^{770 \times {{{10}}^{{ - 9}}}} {{{e}_{{eS}}}[\lambda ,{{T}_{{{\text{eff}}}}}V(\lambda )]d\lambda } \\ = {{\left( {\frac{r}{R}} \right)}^{2}} \times 683\int\limits_{350 \times {{{10}}^{{ - 9}}}}^{770 \times {{{10}}^{{ - 9}}}} {{{m}_{{eS}}}[\lambda ,{{T}_{{{\text{eff}}}}}]V(\lambda )d\lambda } , \\ \end{gathered} $$
(4)

which is the illuminance of an area at the upper boundary of the terrestrial atmosphere at the normal incidence of the solar radiation at the minimum solar activity. At the minimum solar activity, ELSC, min = 135 110 lx [12]. It follows from Eqs. (2) and (4) that this ELSC, min value corresponds to ESC, min = 1106 W/m2 and Teff, min = 5480 K.

The above indices for the maximum solar activity (ESC, max(Teff) ≈ 1370 W/m2 and Teff, max = 5780 K correspond to the light solar constant value ELSC = 173 600 lx.

The variation of the effective absolute temperature of the Sun’s photosphere radiation Teff(n) at the above Teff, min and Teff, max values within an arbitrary solar cycle, whose temporal indices are obtained by averaging of the 25 known solar activity cycles [2–4], is described as

$${{T}_{{{\text{eff}}}}}(n) = {{T}_{{{\text{eff}}{\text{,}}\,\,{\text{avg}}}}}\left[ {1 + 0.027\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right],$$
(5)

where Teff, avg = 0.5(Teff, min + Teff, max).

Equation (5) is plotted in Fig. 1.

Fig. 1.
figure 1

The variation of the effective absolute temperature of the radiation of the Sun’s photosphere within an 11-year solar cycle.

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The minimum and maximum values of the so-called solar and light solar constants in various wavelength ranges are shown in Table 1.

Table 1. The values of the solar constant ESC in various spectral ranges and light solar constant ELSC values in the visible spectral range at the maximum and minimum solar activities.
Full size table

The ESC dependences deduced from Eq. (3) at ESC, min and ESC, max) values calculated for the wavelength range 0 ≤ λ ≤ ∝ nm, the atmospheric spectral window 300 ≤ λ ≤ 1200 nm, and the circadian spectral range 350 ≤ λ ≤ 570 nm are:

$${{E}_{{{\text{SC}}}}}(n) = {{E}_{{{\text{SC}}{\text{,}}\,\,{\text{avg}}}}}\left[ {1 + 0.1062\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right],$$
(6)

at 0 ≤ λ ≤ ∞ nm,

$${{E}_{{{\text{SC}}}}}(n) = {{E}_{{{\text{SC}}{\text{,}}\,\,{\text{avg}}}}}\left[ {1 + 0.1153\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right],$$
(7)

at 300 ≤ λ ≤ 1200 nm, and

$${{E}_{{{\text{SC}}}}}(n) = {{E}_{{{\text{SC}}{\text{,}}\,\,{\text{avg}}}}}\left[ {1 + 0.1485\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right],$$
(8)

at 350 ≤ λ ≤ 570 nm.

The ESC, avg values for each spectral range are shown in the bottom row of Table 1. The plots of Eqs. (6)–(8) are shown in Fig. 2.

Fig. 2.
figure 2

The variation of the solar constant in various spectral ranges (nm) of solar radiation in an arbitrary solar cycle: (1) 0 ≤ λ ≤ ∝; (2) 300 ≤ λ ≤ 1200; (3) 350 ≤ λ ≤ 770.

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Solar radiation that has passed through the atmosphere has direct and diffuse components. The direct eDir_eS(λ, h) and diffuse eDif_eS(λ, h) components of SDI after the propagation in the atmospheric spectral window are described as

$$\begin{gathered} {{e}_{{{\text{Dir}}{\text{,}}\,eS}}}\left[ {\lambda ,{{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dir}}}}}(h)} \right] \\ = {{\left( {\frac{r}{R}} \right)}^{2}}{{m}_{{eS}}}\left[ {\lambda ,{{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dir}}}}}(h)} \right]{{\tau }_{{{\text{Dir}}}}}(h), \\ \end{gathered} $$
(9)
$$\begin{gathered} {{e}_{{{\text{Dif}}{\text{,}}\,eS}}}\left[ {\lambda ,{{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dif}}}}}(h)} \right] \\ = {{\left( {\frac{r}{R}} \right)}^{2}}{{m}_{{eS}}}\left[ {\lambda ,{{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dif}}}}}(h)} \right]{{\tau }_{{{\text{Dif}}}}}(h), \\ \end{gathered} $$
(10)

where τDir(h) and τDif(h) are the dependences of the integral atmospheric transmission coefficients for the direct and diffuse components of solar radiation on the Sun’s elevation in the spectral window of the Earth’s atmosphere of 300 ≤ λ ≤ 1200 nm.

Obviously, the types of the τDir(h) and τDif(h) functions depend significantly on the current state of the atmosphere and are determined by the presence or absence of clouds and by their quantity.

The τDir(h) and τDif(h) functions used below were deduced from experimental data [12]. The data presented by Sharonov [12] are the most complete corpus of knowledge that permit one to construct the dependences of illuminance and irradiation of the Earth’s surface on the Sun’s elevation.

We consider the case of a cloudless sky as an example. In this case, the τDir(h) and τDif(h) functions are described as follows:

$${{\tau }_{{{\text{Dir}}}}}(h) = {{\tau }_{{{\text{Dir}}}}}(90^\circ ) \times 0.5[1 + \sin (0.035h - 1.47)],$$
(11)
$${{\tau }_{{{\text{Dif}}}}}(h) = {{\tau }_{{{\text{Dif}}}}}(90^\circ ) \times 0.5[1 + \sin (0.029h - 1.09)].$$
(12)

In Eqs. (11) and (12), the values τDir(90°) and τDif(90°) are the integral coefficients of atmospheric light transmission with a cloudless sky at the equator with the normal incidence of solar radiation on the Earth’s surface on the days of the March or September equinox.

The circadian dependences of the direct TDir(h) and diffuse TDif(h) components of the absolute temperature of solar radiation on the Earth’s surface with regard to the 11-year solar cycle are:

$${{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dir}}}}}(h,n) = [ - 3780\exp ( - 0.2444h) + {{T}_{{{\text{eff}}}}}(n)],$$
(13)
$${{T}_{{{\text{eff}}{\text{,}}\,\,{\text{Dif}}}}}(h,n) = [8950\exp ( - 0.2084h) + {{T}_{{{\text{eff}}}}}(n)].$$
(14)

The first terms in Eqs. (13) and (14) are the dependences of the absolute temperatures of the direct and diffuse components of solar radiation on the Earth’s surface in the daytime of an arbitrary day of the year as determined from independent experimental data. The second terms are described by Eq. (5).

By substituting expressions (13) and (14) and numerical values of τDir(90°) and τDif(90°) to Eqs. (9) and (10), we obtain the formulas for the dependences of SDI of the direct eDir_eS(λ, h, n) and diffuse eDif_eS(λ, h, n) components of solar radiation on wavelength l in the atmospheric spectral window and on the Sun’s elevation at any point of the Earth’s surface at a certain n in the solar cycle:

$$\begin{gathered} {{e}_{{{\text{Dir}},\,\,eS}}}(\lambda ,h,n) = {{\left( {\frac{r}{R}} \right)}^{2}}{{C}_{1}}{{\lambda }^{{ - 5}}}{{\left\{ {\exp \frac{{{{C}_{2}}}}{\begin{gathered} \lambda \left[ { - 3780\exp ( - 0.2444h) + 5630\left[ {1 + 0.027\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right]} \right] \hfill \\ \hfill \\ \end{gathered} } - 1} \right\}}^{{ - 1}}} \\ \times 0.729 \times 0.5[1 + \sin (0.035h - 1.47)], \\ \end{gathered} $$
(15)
$$\begin{gathered} {{e}_{{{\text{Dif}},\,\,eS}}}(\lambda ,h,n) = {{\left( {\frac{r}{R}} \right)}^{2}}{{C}_{1}}{{\lambda }^{{ - 5}}}{{\left\{ {\exp \frac{{{{C}_{2}}}}{{\lambda \left[ {8950\exp ( - 0.2084h) + 5630\left[ {1 + 0.027\sin \left( {\frac{{2\pi n}}{{11}} - \frac{\pi }{2}} \right)} \right]} \right]}} - 1} \right\}}^{{ - 1}}} \\ \times 0.205 \times 0.5[1 + \sin (0.029h - 1.09)]. \\ \end{gathered} $$
(16)

The values n = 0 and n = 5.5 in Eqs. (15) and (16) refer to the minimum and maximum solar activities, respectively. The differences between values of (15) at n = 0 and n = 5.5 and between values of (16) at n = 0 and n = 5.5 describe the maximum variations of SDI eDir_eS(λ, h) and eDif_eS(λ, h) on the Earth’s surface within a single solar cycle.

The solar radiation that reaches the Earth’s surface and is described by the SDIs of the direct and diffuse components (Eqs. (15) and (16)) or their sum acts on the S cones and rods of the retina. These light receivers process the radiation in a spectrally selective manner by the relative spectral circadian efficiency function c(λ) [5], which has been deduced from results of independent experiments [15–17]. The c(λ) function can be presented as the normalized sum of weighted functions of relative spectral sensitivity of S cones (c1(λ)) and rods (c2(λ)) [5]:

$$\begin{gathered} c(\lambda ) = {{c}_{1}}(\lambda ) + {{c}_{2}}(\lambda ) = \frac{{{{\alpha }_{1}}}}{{{{\sigma }_{1}}\sqrt {2\pi } }}\exp \left[ { - \frac{{{{{(\lambda - {{\lambda }_{{1\max }}})}}^{2}}}}{{2\sigma _{1}^{2}}}} \right] \\ + \,\,\frac{{{{\alpha }_{2}}}}{{{{\sigma }_{2}}\sqrt {2\pi } }}\exp \left[ { - \frac{{{{{(\lambda - {{\lambda }_{{2\max }}})}}^{2}}}}{{2\sigma _{2}^{2}}}} \right], \\ \end{gathered} $$
(17)

where α1 = 72.56 nm, σ1 = 28.99 nm, λ1, max = 445 nm, α2 = 25.89 nm, σ2 = 21.21 nm, λ2, max = 505 nm.

This function is plotted in Fig. 3.

Fig. 3.
figure 3

Plots of the relative spectral circadian efficiency: c1(λ); c2(λ); c(λ).

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The analog representations of binary signals formed by retinal ganglion cells depend on the Sun’s elevation. They are expressed as a product in which the multiplicand is the direct eDir, eS(λ, h, n), or diffuse eDif, eS(λ, h, n) component of solar radiation, or their sum, and the multiplier is the relative spectral circadian efficiency factor c(λ). The c(λ) function, as well as its terms c1(λ) and c2(λ), can be treated as characteristics of light filters that isolate narrow bands in the spectral ranges of their domains from the broadband solar radiation (within the atmospheric spectral window). These functions thus perform the narrow-band spectral selection of solar radiation [18].

Obviously, in the actual control of human circadian activities by solar radiation retinal S cones and rods are most exposed to the sum of the direct eDir, eS(λ, h, n) and diffuse eDif, eS(λ, h, n) components. Normally, without catastrophic injuries of the fiber tracts from S cones and rods to hypothalamic suprachiasmatic nuclei, the direct and diffuse components undergo spectral selection by the sum of functions c1(λ) and c2(λ).

The variants of separate processing of the direct eDir, eS(λ, h, n) and diffuse eDif, eS(λ, h, n) SDI components by the functions c1(λ) and c2(λ) or their combinations are also of theoretical and practical interest.

In this case, we can compose the products ei, eS(λ, h, n) × cj(λ) (the index i = 1, 2 denotes the direct or diffuse SDI component, and j = 1, 2 denotes c1(λ) or c2(λ)), elucidate features of the separate processing of the direct eDir, eS(λ, h, n) and diffuse eDif, eS(λ, h, n) SDI components by the functions c1(λ) and c2(λ) or their sum, and describe various paths of spectral selection of solar radiation in the control of human circadian activities.

The domains of the functions c1(λ) and c2(λ) are within 350 ≤ λ ≤ 550 nm and 435 ≤ λ ≤ 570 nm, respectively, and the domain of their sum is in the spectral range 350 ≤ λ ≤ 570 nm [5].

The spectral functions c1(λ) and c2(λ) form two overlapping spectral channels of solar radiation processing: short-wave and long-wave, respectively.

The variants of solar radiation processing with just one of the functions c1(λ) or c2(λ) describe the cases of catastrophic damage of the neuronal paths from rods and S cones, respectively, to hypothalamic suprachiasmatic nuclei.

The weighting factors α1 and α2 in Eq. (17) do not vary with the Sun’s elevation in the daytime [19]. It is obvious that the spectral characteristics of the functions c1(λ) and c2(λ), as well as the spectral characteristics of the products ei, eS(λ, h, n) × cj(λ) also remain constant, regardless of the α1 and α2 values. The absolute values of ei, eS(λ, h, n) × cj(λ) still depend on the Sun’s elevation.

In the most frequent case, when the sum of the direct and diffuse solar radiation components simultaneously act on the short- and long-wave spectral channels (Eqs. (15)–(17)), the equation for SDI formed by spectrally selective processing of solar radiation with the function c(λ) = c1(λ) + c2(λ) takes the form

$$\begin{gathered} {{e}_{{{\text{Dir + Dif}}{\text{,}}\,\,{\text{SW + LW}}}}}(\lambda ,h,n) = [{{e}_{{{\text{Dir}},\,eS}}}(\lambda ,h,n) + {{e}_{{{\text{Dif}},\,eS}}}(\lambda ,h,n)][{{c}_{1}}(\lambda ) + {{c}_{2}}(\lambda )] \\ = {{\left( {\frac{r}{R}} \right)}^{2}}{{C}_{1}}{{\lambda }^{{ - 5}}}\left[ {\left\{ {{{{\left[ {\exp \frac{{{{C}_{2}}}}{{\lambda [ - 3780\exp ( - 0.2444h) + {{T}_{{{\text{eff}}}}}(n)]}} - 1} \right]}}^{{ - 1}}} \times 0.729 \times 0.5[1 + \sin (0.035h - 1.47)]} \right\}} \right. \\ \left. { + \,\,\left\{ {{{{\left[ {\exp \frac{{{{C}_{2}}}}{{\lambda [8950\exp ( - 0.2084h) + {{T}_{{{\text{eff}}}}}(n)]}} - 1} \right]}}^{{ - 1}}} \times 0.205 \times 0.5[1 + \sin (0.029h - 1.09)]} \right\}} \right] \\ \times \left\{ {\frac{{{{\alpha }_{1}}}}{{{{\sigma }_{1}}\sqrt {2\pi } }}\exp \left[ { - \frac{{{{{(\lambda - {{\lambda }_{{1\max }}})}}^{2}}}}{{2\sigma _{1}^{2}}}} \right] + \frac{{{{\alpha }_{2}}}}{{{{\sigma }_{2}}\sqrt {2\pi } }}\exp \left[ { - \frac{{{{{(\lambda - {{\lambda }_{{2\max }}})}}^{2}}}}{{2\sigma _{2}^{2}}}} \right]} \right\}, \\ \end{gathered} $$
(18)

where the function Teff(n) is described by Eq. (5).

Various combinations of eDir, eS(λ, h, n), eDif, eS(λ, h, n), c1(λ), and c2(λ) can be constructed by using Eq. (18). The equation also allows the description and analysis of features of spectrally selective solar radiation processing with various combinations of functions (14)–(16).

Figure 4 presents plots of Eq. (18) in the circadian range of solar radiation at the maximum and minimum solar activities (n = 5.5, Teff = 5780 K and n = 0, Teff = 5480 K, respectively) and a plot showing the dif-ferences between the absolute values of eDir + Dif, SW + LW(λ, h, n) at the maximum and minimum solar activities obtained by spectrally selective processing of solar radiation by retinal rods and cones.

Fig. 4.
figure 4

The dependence of the spectral density of illuminance on the Sun’s angular elevation and radiation wavelength, formed by the sum of the direct and diffuse solar radiation components at the simultaneous action on the short- and long-wave spectral channels: (a) at the maximum solar activity (n = 5.5; Teff = 5780 K); (b) at the minimum solar activity (n = 0, Teff = 5480 K). (c) The difference between the SDIs at the maximum and minimum solar activity.

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It immediately follows from Figs. 4a, 4b that the spectral characteristics of the functions eDir, eS(λ, h, n) and eDif, eS(λ, h, n) retain their shapes regardless of the Sun’s elevation. In contrast, their energetic characteristics depend considerably on the wavelength of solar radiation in the circadian spectral range and on the current elevation of the Sun.

Figure 5 presents plots of the difference between SDI values at the maximum and minimum solar activities ΔeDir + Dif, SW + LW(λ, h, n) at the wavelength λ = 445 nm and of the difference between SDI values taken relative to SDI at the minimum solar activity \(\frac{{\Delta {{e}_{{{\text{Dir + Dif}}{\text{,}}\,\,{\text{SW + LW}}}}}{\text{(}}\lambda ,h,n{\text{)}}}}{{{{e}_{{{\text{Dir + Dif}}{\text{,}}\,\,{\text{SW + LW}}}}}{{{{\text{(}}\lambda ,h,n{\text{)}}}}_{{\min }}}}}\) with the Sun’s elevation h varying from 0° to 90°.

Fig. 5.
figure 5

(a) The variation of the SDI difference at λ = 445 nm with the Sun’s elevation h from 0° to 90°. (b) Variation of the SDI difference taken relative to SDI at the minimum solar activity.

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The maximum value of the SDI difference in the circadian range of the solar emission spectrum at the maximum and minimum solar activities at λ = 445 nm, h = 90° is 4.302 × 108 W/m3.

It follows from Fig. 5b that the relative SDI differences at the maximum and minimum solar activities occur at small elevations of the Sun and range from 5 to 36%. This value reaches the plateau of 36% at the elevations of the Sun of h > 25°.

By using this method, explicit expressions that describe the integral transmission coefficients of the Earth’s atmosphere and the spectrally selective processing of solar radiation that controls human circadian activities with various types and percentages of the cloud canopy can be obtained in a similar way from the data reported in [12].

This analysis indicates that the circadian activity component in the spectrum of any broad-band source of optical radiation is determined solely by the spectral-selective properties of rods and S cones. However, in this case the use factor of broad-band radiation is too low. This factor can be improved by utilizing specialized lighting systems designed for the prevention and/or mitigation of disturbances of human circadian activities. Such systems should employ narrow-band sources of optical radiation with overall radiation spectra corresponding to the spectral range of human circadian activity 350 ≤ λ ≤ 570 nm.

These results indicate that biological, chronobiological, and light-engineering studies of diurnal variations should take the 11-year solar optical activity cycle into consideration. In particular, experimental and theoretical studies of circadian activities and the modeling of control of human circadian activities by solar radiation would allow correct interpretation of the results and proper inferences.