Solar radiation - Introduction

The spectrum of solar radiation at the surface of the earth extends from about 300 nm to about 2500 nm. Its maximum occurs at about 550 nm. Absorptions in the atmosphere remove all radiant energy outside of this band. The concentration of ozone affects the amount of absorption at the shorter wavelengths of the ultraviolet band (300 nm to 400 nm). Absorption by water vapor and carbon dioxide occur at several wavelengths of the near-infrared band (780 nm to 2500 nm). Because the actinicity of this longer wavelength region is very small, the focus of this report is on ultraviolet and visible radiation (300 nm to 780 nm).

Many measurements of the spectral composition (radiant power as a function of wavelength) at ground level (various altitudes) and above the atmosphere have provided excellent information on solar spectra. Complex computer calculations that incorporate several of the physical parameters that affect the transmission of radiation through the atmosphere provide reliable tables of spectral irradiances that can be used to calculate ocular irradiances for defined exposure experiences. This report uses solar spectra from Publ. No CIE 85 [1].

Except for occasions of the sun low in the sky, direct viewing of the solar disc and its very bright aureole should be, and usually is, avoided, and even the low sun should be viewed only briefly. Therefore, we derive the solar spectrum of the horizon sky under an overhead (air mass 1) sun and a clear sky. Except for a brightly lit snowfield (diffuse reflectance about 80%), the horizon sky is the brightest source ordinarily seen in terrestrial experience. In the blue-light region of the spectrum (380 nm to 500 nm), it is about three times as bright as the surface of the ground having a typical diffuse reflectance of 20% (at every wavelength).

Calculating ocular exposures to solar radiation

The diffuse solar irradiance from the whole sky on a horizontal surface at ground level is equal to the global irradiance minus the direct irradiance [1, 2]. From this, the average radiance of the sky is π-1 (= o.3168) times that total diffuse irradiance. Kondratyev [2] says that the radiance of the clear sky increases from the zenith to the horizon. An increase by a factor of two has been found experimentally.

He also states that, although limited clouds in a particular configuration slightly increase the global irradiance, a long-term average of varied cloudiness shows that clouds should generally be assumed always to decrease global irradiance (hence, too, average sky radiance). Clear-sky conditions should be assumed when calculating retinal irradiance, thereby avoiding under-estimation.

The average radiance of the ground is π^-1 (0.3168) times the diffuse reflectance of the ground times the global irradiance.

The spectral irradiance of the retina, E_retina (λ), from a source with spectral radiance, N(λ) is [3]:

E_retina (λ) = N_source (λ) x A_pupil x τ_eye(λ)/ (f_eye)2

where:

A_pupil is the area of the pupil
f_eye is the focal length of the eye, nominally 17 mm, and
τ_eye(λ) is the transmittance of the elements of the eye anterior to the retina; it is mainly determined by absorption in the crystalline lens. Other absorptions are small enough to be ignored.

The area of the pupil is determined by calculating the luminance of the source using spectral radiances of the source from 380 nm to 780 nm.

To calculate the irradiance of the cornea, an average radiance for the scene viewed, part horizon sky, and part ground surface, is estimated. The solid angle subtense of the scene is estimated.

Transmittances of the elements of the eye

The cornea, aqueous, and vitreous

The cornea is about 78% water [4]; therefore it is a strong absorber of infrared radiation. Similar absorption in the aqueous ensures that almost no infrared radiation reaches the crystalline lens, but any that penetrates to the vitreous will be completely absorbed therein.

The reflectance of the tear film on the cornea is about 2%. It is too slowly varying with wavelength for the effect to be considered. Reflectances at interior interfaces are negligibly small.

The spectral transmittances of these three elements are high; this author does not have numerical values. The transmittance of the cornea (and probably the aqueous and vitreous, as well) rolls off below 380 nm to approach zero near 300 nm. (Fig. 1)

Fig. 1: Spectral transmittances in the ultraviolet range of lenses from very young eyes

1 - Lens of a newborn, one specimen.
2 - Average transmittances of 9 lenses, birth to 2 yrs.
3 - Average of 17 lenses, 2 to 9 yrs.
4 - Average of 27 lenses, 10 to 19 years.
5 - Average of 36 lenses, 20 to 29 years.

The crystalline lens

The crystalline lens is the strongest absorber of ultraviolet and visible radiation. Barker and Brainard [5] measured direct (visual axis) transmittances of excised eyes. Their report details spectral transmittances from 200 nm to 2500 nm and reports averaged spectral values by age groups: birth to 2 yrs; 2-9 yrs; 10-19 yrs; 20- 29 yrs; and by decades to 90-99 yrs. Above 20 years of age, ultraviolet transmittances below 380 nm are less than 1%. There is a “window” around 320 nm in younger eyes. Figure 1 shows five spectra of the average transmittances, 300 nm to 400 nm. A peak transmittance of 21% at 320 nm, for one of the eyes, at birth, is listed.

Figure 2 shows average transmittances, 380 nm to 700 nm, for four decades of age: 2 – 9 yrs; 20 – 29 yrs; 40 – 49 yrs; and 70-79 yrs. (Fig. 2).

Fig. 2: Average spectral transmittances, 378 nm to 700 nm, of lenses from four decades of age

1 – 2 to 9 yrs.
2 – 20 to 29 yrs.
3 – 40 to 49 yrs.
4 – 70 to 79 yrs.

Infrared transmittances are about 70%, 700 nm to 1350 nm; there is a very strong absorption band (water), 1350 nm to 1500 nm, after which transmittances range over 5% to 20%, and are essentially zero beyond 1900 nm. Average infrared transmittances do not vary appreciably with age.

Solar spectral irradiances and radiances

Global and direct solar spectral irradiances on a horizontal surface at sea level for an Am-1 sun and clear sky were used to calculate, in accordance with the procedures described in Clause 2, the diffuse irradiance from the whole sky, the average radiance of the sky, and the radiance of the horizon sky. Using the stated diffuse reflectance of the ground surface (20 %), which affects the global irradiance, the spectral radiances of the ground were calculated. These results are displayed in Figure 3. From n analysis not shown in this report, a multiplier was determined for converting irradiances and radiances at sea level to their corresponding values at 3 km altitude. Curve 7 of figure 3 represents the radiance of the horizon sky at 3 km; it corresponds closely with curve 3 of figure 3.

Fig. 3: Solar spectral irradiances (μW cm^-2 nm^-1) and radiances (μW cm^-2 nm^-1 sr^-1), 375 nm to 700 nm, for an AM^-1 sun, clear sky, diffuse ground reflectance of 20 %, at sea level.

1 – Direct irradiance on horizontal surface.
2 – Global irradiance.
3 – Irradiance from whole sky diffuse radiation.
4 – Average radiance of sky.
5 – Radiance of horizon sky.
6 – Radiance of ground
7 – Radiance of horizon sky at 3 km altitude.

Irradiance of the retina by radiation from the horizon sky at sea level

The spectral irradiances (μW cm^-2) of the retina over the wavelength range 380 nm to 700 nm are shown in figure 4. The diameter of the pupil, 1.74 mm, was determined by calculating the luminance of the horizon sky at sea level. The spectral transmittances of the lens were the averages for the age-group, 10 – 19 years, from [5]. Because of the very small spectral transmittances of teen-age and adult lenses, ultraviolet irradiances of the retina are usually negligibly small for solar radiation when direct viewing of the solar disc is excluded.

Fig. 4: Spectral irradiances (μW cm^-2) 300 to 700 nm, of the retina by radiation from the horizon sky, 1.74mm pupillary diameter, using the average spectral transmittances of lenses in the age group 10 to 19