Distributions of Direct, Reflected, and Diffuse Irradiance for Ocular UV Exposure at Different Solar Elevation Angles

To analyze intensities of ocular exposure to direct (Eo,dir), reflected (Eo,refl), and diffuse (Eo,diff) ultraviolet (UV) irradiance at different solar elevation angles (SEAs), a rotating manikin and dual-detector spectrometer were used to monitor the intensity of ocular exposure to UV irradiation (Eo) and ambient UV radiation (UVR) under clear skies in Sanya, China. Eo,dir was derived as the difference between maximum and minimum measured Eo values. Eo,refl was converted from the value measured at a height of 160 cm. Eo,diff was calculated as the minimum measured Eo value minus Eo,refl. Regression curves were fitted to determine distributions of intensities and growth rates at different wavelengths and SEAs. Eo,dir differed from ambient UVR exposure. Linear, quadratic, and linear Eo,dir distributions were obtained in SEA ranges of 14°–30°, 30°–50°, and 50°–90°, respectively, with maximum Eo,dir at 32°–38° SEA. Growth rates of Eo,dir with increasing wavelength were fitted with quadratic functions in all SEA ranges. Distributions and growth rate of Eo,refl values were fitted with quadratic functions. Maximum Eo,diff was achieved at the same SEA for all fitted quadratic functions. Growth rate of Eo,diff with increasing wavelength was fitted with a linear function. Eo,dir distributions were fitted with linear or quadratic functions in different SEA ranges. All Eo,refl and Eo,diff distributions were fitted with quadratic functions. As SEA increased, the Eo,dir portion of Eo increased and then decreased; the Eo,refl portion increased from an initial minimum; and the Eo,diff portion first decreased and then increased. The findings may provide data supporting on construction of a mathematical model of ocular UV exposure.


Introduction
Ultraviolet (UV) radiation (UVR) has harmful effects on humans, causing damage to the ocular lens, cornea, and retina [1][2][3]. Any estimation of the risk of ocular UV damage should include an evaluation of the intensity of ocular exposure to UV irradiation (E o ). Effects of UVR exposure have been studied in animals, provided important preliminary data [4][5][6], as well as in human subjects wearing UVR dose detectors [7]. For instance, UVR exposure across the corneal surface was measured in subjects wearing polysulfone contact lenses while walking on a grass field on a cloudy day [8]. In another study, UVR-sensitive films were placed on subjects' hats, glasses, and chins to evaluate ocular exposure to UV irradiation [9]. Field-based UVR sensors placed on the human body have been used to measure ocular exposure to UV irradiation for a range of solar elevation angles (SEAs), ambient conditions, and head orientations [10]. Manikins have also been used to simulate ocular UV exposure for humans [11,12].
Ultraviolet (UV) radiation dose has been estimated by using mathematical models, based on data from environmental monitoring, ozone layer thickness, aerosol, cloud thickness, and other parameters. Models have been used to calculate intensities of direct, diffuse, and reflected solar UV irradiance on the horizontal, vertical, and inclined planes [13][14][15][16][17][18][19][20][21][22] or in the environment [23,24]. Researchers have utilized three-dimensional digital models or different body position models to simulate UV exposure [16,25,26]. However, because of the complexity of ocular anatomy, monitoring instruments cannot be used to measure directly the intensities of ocular exposure to direct (E o,dir ), reflected (E o,refl ) or diffuse (E o,diff ) UV irradiance.
Previous studies of ocular exposure to UV irradiance have concentrated on monitoring the ocular UV exposure state. To the best of our knowledge, no study has described splitting ocular exposure to UV irradiation into components of direct, reflected, and diffuse UV irradiance. We previously analyzed ocular exposure to UVR at different wavelengths, azimuths, orientations, and reflected backgrounds [10,11,27,28]. We determined that ocular exposure to direct, reflected, and diffuse UV irradiance can be regarded as basic parameters for constructing a mathematical model of ocular UV exposure, which could be used to calculate and compare ocular UV exposure in different regions.
The present study was conducted to monitor the direct, reflected, and diffuse components of ocular exposure to UV irradiation using our self-made ocular UV exposure model. Distributions of ocular exposure to direct, reflected, and diffuse UV irradiance on a rotating manikin were analyzed for different UVR wavelengths and solar elevation angles during the daytime under fine weather in Sanya, China. The goal was to determine the times of maximum ocular exposure to UV irradiation, enabling the prevention of ocular injury from solar UV. Moreover, the findings will provide important data supporting the construction of a mathematical model of ocular UV exposure.

Experimental apparatus
The experimental apparatus was a rotating manikin, which comprised a turntable base, shelf, and anthropomorphic model with realistic facial features (Fig 1). The eye level was at a height of approximately 160 cm. The chosen solar UV sensor, a dual-channel miniature fiber optic spectrometer (AvaSpec-2048x14-2-USB2, Netherlands) with two detectors, was placed on the shelf. One detector was mounted on a plane tangent to the position of the right cornea at the most anterior point on the manikin to record ocular UV exposure ( Fig 1A). The other was placed at the vertex of the head of the manikin to record ambient UV irradiance. The visual line was approximately 10˚below the horizontal (Fig 1B). The field of view of the manikin was approximately 139˚, due to the forehead and malar (Fig 1B). Ground reflection data were obtained with the monitoring instrument at a height of 160 cm and facing the ground. Spectrometer and other equipment were calibrated by the National Physical Laboratory GB before the experiment, as described previously [11].

Study location
The study site was located in the town of Hai Tang Wan in Sanya city (8.4˚N, 109.7˚E, altitude 18 m) in the province of Hainan, China. Sanya is the southernmost city in Hainan Island, which has a maximum SEA of nearly 90˚in July. The experimental apparatus was located on the asphalt-covered concrete roof of a five-story hotel surrounded by grass with an unobstructed view. The owner of this hotel called ''Dingjun Xu" permitted us to carry out measurements on the roof of his hotel.

Meteorological conditions
Measurements of UV irradiance exposure were conducted on July 11, 2010 from 08:00 to 19:00 China Standard Time (CST) (solar noon at about 12:55 CST). This day was a sunny day and clear sky.

UV irradiance measurements
The manikin was rotated clockwise at a constant speed during data collection, beginning with the position of facing the sun. UV irradiance can be monitored (unit μW cm -2 nm -1 ) was calculated in 1-s intervals from the integration of the UVA band (320-400 nm) and UVB band (300-320 nm). Duration of each measurement progression was 1 min, and the measurement interval was 5 min. There were 60 groups of irradiance data per manikin revolution. The maximum E o at different wavelengths of each revolution was calculated to simulate the actual maximum UVR exposure under clear skies. The same procedure was used simultaneously to obtain data from the ambient detector.
Definitions E o,dir referred to UV irradiation received by the probe placed at the eye position of monitoring model, which consisted of direct solar UV irradiation going straight into the eyes at a certain range of SEAs and/or refraction from direct solar UV hitting the facial structure. E o,dir was measured as the difference between the maximum and minimum values of E o measured from the instrument. Intensity of UV irradiance measured by the equipment at a height of 160 cm was converted to E o,refl , according to the structure of the human eye, using the formula [29]: where S(λ) is the measured spectral irradiance. E o,diff was calculated as the difference between the minimum value of measured ocular UV exposure and E o,refl .

Data calculation
Data from the spectrometer were processed with AvaSoft 7.4 USB2.0. Ocular UV exposure and ambient UV data were processed separately. Maximum and minimum integrated E o values of each revolution were calculated from the actual maximum and minimum UV exposures under clear skies. Ocular UV exposure data obtained from the position of the model facing the sun were used to simulate the maximum E o value. When the manikin had its back towards the sun, E o had only reflected and diffuse irradiance dimensions. Data obtained in this position were used as the minimum E o values.

Monitoring time and SEA
Monitoring time was from 08:00 CST (25˚SEA) to 18:00 CST (14˚SEA). Range of SEAs was from 14˚to 90˚, with maximum SEA occurring at about 12:40 CST. According to the relationship between monitoring time and SEA, E o was measured in three ranges of SEA: 14˚< SEA 30˚(low), 30˚< SEA 50˚(middle) and 50˚< SEA 90˚(high). Maximum UV irradiance at each SEA was used as the intensity of ambient UV irradiance (E amb ). Total E o was determined at nine representative wavelengths of the 300-400 nm UV spectral range, including five wavelengths in the 300-320 nm range (300, 305, 310, 315, and 320 nm) and four wavelengths in the 325-400 nm range (325, 350, 375, and 399 nm). E amb increased with increasing SEA, with maximum E amb being measured at the highest SEA (Fig 2A). Maximum E o with different wavelengths was achieved in the 30˚-40˚SEA range ( Fig 2B).

Ambient and ocular UV irradiance at different SEAs
Distributions and growth rates of E o,dir at selected wavelengths and different SEAs E o,dir distributions at different SEAs differed markedly from the E amb distribution (Fig 3). In the low range (14˚-30˚SEA), E o,dir values at different wavelengths increased with increasing SEA, and the distributions were fitted with linear functions (Fig 3D). In the middle range (30˚-50˚SEA), E o,dir showed binomial distributions, first increasing and then decreasing with SEA, peaking at about 32-38˚SEA ( Fig 3E). These distributions were fitted with quadratic functions. As wavelength increased in the middle SEA range, the opening of the curve of the quadratic function gradually decreased. In the high range (50˚-90˚SEA), E o,dir distributions were largely parallel to the x-axis and constant with increasing SEA from 300 to 310 nm, but decreased with increasing SEA from 310 to 400 nm. E o,dir distributions were fitted with linear functions (Fig 3F). For a given SEA, E o,dir increased with increasing wavelength. Equations for regression curves fitted to the E o,dir distributions with increasing SEA are given in Table 1.
To describe the growth rates of E o,dir values with increasing wavelength, coefficients of each fitted equation in Table 1 were used to fit curves with different wavelengths (Fig 4). In the low coefficients of the fitted equations increased with increasing wavelength. The growth rate of the absolute values of the binomial coefficients was fitted with a quadratic function (y = -0.0007x 2 + 0.390x -57.123; R 2 = 0.999). In the high SEA range (Fig 4C), the curve slope of each linear equation increased with increasing wavelength. The growth rate of the absolute values of the curve slopes was fitted with a quadratic function (y = -0.001x 2 + 0.5227x -69.305; R 2 = 0.9997).

Distributions and growth rates of E o,refl at selected wavelengths and different SEAs
Distributions of E o,refl values at different SEAs differed from the distributions of E o,dir values ( Fig 5). Distributions of E o,refl of selected wavelengths increased with increasing SEA and were fitted with quadratic functions ( Table 2). The maximum value of each quadratic function increased with increasing SEA or increasing UV wavelength. Absolute values of the binomial coefficients of the fitted equations increased with increasing wavelength (Fig 6). The growth rate of these changes was fitted with a quadratic function (y = -3E-06x 2 + 0.001x -0.183; R 2 = 0.9989). E o,refl increased quickly with increasing SEA or increasing wavelength. The opening of the curve of the quadratic function gradually decreased and the binomial curve become steeper with increasing SEA (Fig 5).

Distributions and growth rates of E o,diff at selected wavelengths and different SEAs
Distributions of E o,diff at different SEAs differed from E o,dir but were similar to E o,refl distributions (Fig 7). At the selected wavelengths, E o,diff first increased and then decreased with increasing SEA. All distributions were fitted with quadratic functions (Table 3). In contrast to E o,refl , the maximum E o,diff of each fitted quadratic function with increasing wavelength was achieved at the same SEA of about 62˚. Absolute values of the binomial coefficients of each fitted equation increased with increasing wavelength (Fig 8). The growth rate with increasing wavelength was fitted with a linear function (y = -0.0012x + 0.362; R 2 = 0.999). As wavelength increased, the opening of the curve of the quadratic function decreased at a constant speed. As SEA increased, the rate of change of E o,diff was faster at larger wavelengths (Fig 7).  9A) and 399 nm ( Fig 9B). As SEA increased, the relative percentages of the three components significantly differed from each other. The percentage due to E o,dir first increased and then  decreased with increasing SEA. The percentage due to E o,refl gradually increased from an initial minimum. The percentage due to E o,diff first decreased and then increased.

Discussion
As we all known, the diurnal distribution of environmental UV exposure is a bell shaped curve, the highest ambient UV irradiances were measured at the highest solar elevation angle, the direction is the dominant in ambient UV irradiances. However, for the ocular UV irradiance, the findings in our previous studies showed the ocular UV irradiances diurnal variations exhibited a bimodal distribution [11,27,30], in which the ocular exposure to reflected and diffuse UV irradiance contribute to the bimodal distribution of ocular UV exposure. Therefore, it is necessary to study the distributions of direct, reflected, and diffuse irradiance for ocular UV exposure at different solar elevation angles.
In this study, we found that the distributions of ocular exposure to direct UV irradiance values were different from the distributions of ambient UV irradiance values (which were linear in the entire range of solar elevation angles), but the same as distributions of total ocular  exposure to UV irradiation values. Ocular exposure to direct UV irradiance accounted for a large proportion of total ocular exposure to UV irradiation when solar elevation angle was below 50˚. In the high solar elevation angle range (50˚-90˚), ocular exposure to direct UV irradiance decreased with increasing solar elevation angle, but the decreasing trend was significantly faster than that of the total ocular exposure to UV irradiation. One possible reason for this finding is that total ocular exposure to UV irradiation was compensated by the increased impact of ocular exposure to diffuse and reflected UV irradiance. Distributions of ocular exposure to reflected and diffuse UV irradiance values fit quadratic functions in the entire range of solar elevation angles. The ocular exposure to reflected UV irradiance distribution increased along the entire curve of increasing solar elevation angle, whereas the quadratic curve of ocular exposure to diffuse UV irradiance showed a maximum at about 60s olar elevation angle. The increase of ocular exposure to reflected UV irradiance and the magnitude of changes with increasing solar elevation angle were related to the increased ocular exposure to direct UV irradiance and gradual reduction of the incident angle of reflected light. The ocular exposure to diffuse UV irradiance distribution had a quadratic shape, unlike the largely constant intensity of diffuse UV irradiation. Ocular exposure to diffuse UV irradiance first increased and then decreased with increasing solar elevation angle. One reason for this finding may be that the scattering background causes a deviation of the light scattering angle along with the change of solar elevation angle. Another reason may be that diffusion was affected by changes in ambient UV exposure, which would alter the intensity of diffuse UV irradiation to the eyes.
The percentage of ocular exposure to direct UV irradiance in the total ocular exposure to UV irradiation first increased and then decreased with increasing solar elevation angle. For solar elevation angle below 30˚, ocular exposure to direct UV irradiance increased with increasing solar elevation angle, but ocular exposure to reflected and diffuse UV irradiance were less affected. For solar elevation angle above 30˚, ocular exposure to reflected and diffuse UV irradiance increased the amount of UV irradiation incoming to the eyes, whereas the proportion of ocular exposure to direct UV irradiance was lower. This result reaffirms the need to prevent excessive ocular exposure to reflected and diffuse UV irradiation in the higher solar elevation angle range.
This study was performed on a clear, fine day in Sanya city. The measurement site has a relatively unpolluted atmosphere (air pollution index < 50 year round), such that the impact of air pollution was negligible. However, the reflection background was an asphalt surface. Distribution characteristics of ocular exposure to UV irradiation components will be different in snow, water, sand, or other backgrounds. In addition, the meaning of "direct" ocular UV exposure was not the same as the physical concept, but was related to our model monitoring conditions. Overall, the results of this study confirm that eye protection should be used at different times throughout the day because of the different proportions of direct, diffuse, and reflected ocular UV irradiation. The findings also support the construction of mathematical models of ocular UV exposure.

Conclusions
E o,dir distributions were fitted with linear or quadratic functions in different SEA ranges. All E o,refl and E o,diff distributions were fitted with quadratic functions. As SEA increased, the E o,dir portion of E o increased and then decreased; the E o,refl portion increased from an initial minimum; and the E o,diff portion first decreased and then increased.