= Code Structure =

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[[NoteBox(note,This page is part of the **UV Exposure Model** (UVEM) documentation. \\ It contains a documentation about the realization of the program code of the exposure model. \\ For an overview of all UVEM-related pages\, see the **[wiki:doc/tec/uvem UV Exposure Model main page]**.)]]
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[[Image(integration_equation.png, 900px)]] 
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== Code realization of exposure model ==
To calculate the human exposure the 3 main exposure model parameters (biologically weighted radiance, human geometry and obstructions) and an array of integration factors are used. The latter one is important for the integration over all solid angles e.g. over all directions of the upper hemisphere. This spatial integration can then easily be done by summation of all final weighted radiance values.

The calculation can be illustrated by using the polar plots of the exposure model parameters (see sections basic model and obstacles) and arrange them as an exploded view (see Fig. 2.4). The process of weighting the radiance of each solid angle with the human geometry and the existing obstructions can be easily envisioned by multiplying each value of the top polar plot with the corresponding values below. This is indicated in Figure 2.4 by the red asterisks and the black arrows.

Visualization of the exposure model parameters and the calculation of the final weighted radiance. The red asterisks mark values of exemplary directions and the black arrows indicate the multiplication of these values. The polar plots are shown as function of azimuth and incident angle 
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[[Image(exploded_view.png, 600px)]] 
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== Integration factors ==

For the calculation of the exposure, the weighted radiances (see polar plot in Figure ??) are integrated over all solid angles (directions). For this, the area of each solid angle d on a unit sphere must be calculated. These dimensionless areas have the unit [sr] and can be understood as weighting factors since not all considered solid angles from the different directions have the same size (see also Fig. 2.5).

The summation of the radiances, multiplied with the areas of the solid angles of the corresponding directions, yields the final integral. 

Figure 2.5: Schematic diagram of an exemplary segmented upper hemisphere, that visualizes the different segments. The numbers and proportions of the segments in the schematic diagram are for demonstration purposes only and do not exactly match the solid
angles used in the exposure model.
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[[Image(segments.png, 600px)]] 
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== References: ==
* [=#Seckmeyer2013] '''Seckmeyer, G., Schrempf, M.Wieczorek, A., Riechelmann, S., Graw, K., Seckmeyer, S., and Zankl, M.''' 2013. A Novel Method to Calculate Solar UV Exposure Relevant to Vitamin D Production in Humans, Photochem. Photobiol., 89(4), 974-983, DOI: 10.1111/php.12074.
* [=#Schrempf2017a] '''Schrempf, M., Thuns, N., Lange, K., and Seckmeyer, G.''' 2017a. Einuss der Verschattung auf die Vitamin-D-gewichtete UV-Exposition eines Menschen, Aktuelle Derm, DOI: 10.1055/s-0043-105258.
* [=#Schrempf2017b] '''Schrempf, M., Thuns, N., Lange, K., and Seckmeyer, G.''' 2017b. Impact of Orientation on the Vitamin D Weighted Exposure of a Human in an Urban Environment, Int. J. Environ. Res. Public Health, 14(8), 920, DOI: 10.3390/ijerph14080920.\\