Changes between Version 9 and Version 10 of doc/tec/biomet/uv_basic_model
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- Jul 25, 2019 1:20:05 PM (5 years ago)
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doc/tec/biomet/uv_basic_model
v9 v10 23 23 \end{equation*} 24 24 }}} 25 which depends on the wavelength ''λ'', the time t and the incident angle which is defined as the angle between incident light beam and horizontal plane. In addition, dQ represents the radiant energy, dA the area element and d''Ω'' the solid angle. For a receiver that is not orientated normal to the source, the area element dA must be weighted with the cosine of the angle between the direction of the beam and the normal to the area dA (WMO, 2008; CIE, 2011). The radiance can be a source or a receiver based quantity. However, in this model the radiance is used as a receiver based quantity only. This can be best visualized by a reversed cone with the given solid angle d''Ω'' as its base and the vertex on the area dA. See schematic diagram in Figure 1. 1.25 which depends on the wavelength ''λ'', the time t and the incident angle which is defined as the angle between incident light beam and horizontal plane. In addition, dQ represents the radiant energy, dA the area element and d''Ω'' the solid angle. For a receiver that is not orientated normal to the source, the area element dA must be weighted with the cosine of the angle between the direction of the beam and the normal to the area dA (WMO, 2008; CIE, 2011). The radiance can be a source or a receiver based quantity. However, in this model the radiance is used as a receiver based quantity only. This can be best visualized by a reversed cone with the given solid angle d''Ω'' as its base and the vertex on the area dA. See schematic diagram in Figure 1. 26 26 In comparison the spectral irradiance E_lambda is defined as the radiant energy dQ arriving per time interval dt, per wavelength ''λ'' and per area dA from any origin incident onto a horizontally oriented area element (Seckmeyer et al., 2010) The quantity irradiance is sometimes also referred to as radiative flux. 27 27 28 28 29 29 [[Image(expo_quantities.png, 800px)]]\\ 30 Figure 1 .1: Schematic diagram of the quantities radiance (a) and (b) and irradiance (c). In (a) the receiving area dA is oriented normal to the source, while in (b) the angle between the normal of the area and the incident beam is 45°. The diagram (c) visualizes the irradiance, where radiation of any origin is received by the area element dA.\\\\30 Figure 1: Schematic diagram of the quantities radiance (a) and (b) and irradiance (c). In (a) the receiving area dA is oriented normal to the source, while in (b) the angle between the normal of the area and the incident beam is 45°. The diagram (c) visualizes the irradiance, where radiation of any origin is received by the area element dA.\\\\ 31 31 \\\\ 32 32 … … 36 36 To calculate the biologically-weighted UV exposure the spectral radiance L is weighted with a biological action spectrum. In this model, the action spectra for erythema, defined by the CIE (1998),and the action spectra for the vitamin D3 synthesis is used. 37 37 38 In Figure 2 .1, the simulated (diffuse) sky radiance weighted with the vitamin D,,3,, action spectrum is shown for Hannover on 21 March at solar noon. The radiance in Figure 2.1is visualized as a polar plot, where the zenith is located in the center and the azimuth angles are marked around the plot. It should be noted, that similar to an astronomical map, the directions of east and west are inverted.\\\\38 In Figure 2, the simulated (diffuse) sky radiance weighted with the vitamin D,,3,, action spectrum is shown for Hannover on 21 March at solar noon. The radiance in Figure 2 is visualized as a polar plot, where the zenith is located in the center and the azimuth angles are marked around the plot. It should be noted, that similar to an astronomical map, the directions of east and west are inverted.\\\\ 39 39 40 40 Distribution of vitamin D,,3,,-weighted sky radiance in Hannover on 21 March at … … 51 51 == Human Geometry == 52 52 For the calculation of the exposure, the human geometry is taken into account. This is done by using projection areas of all uncovered surface areas of the human. For the calculation of the projection areas a, 3D voxel (volumetric pixel) model, segmented from data of a whole-body computed tomography scan of a patient, is used. The person was 38 years old, 176 cm of height and had a weight of 68.9 kg, thus approximately representing an average male adult (Valentin, 2002). 53 In the Figure 2.2(on the right), a two-dimensional projection of the voxel model is shown for three different viewpoints. Additionally, the projection areas of a human with no clothing, summer clothing and winter clothing are visualized as function of the azimuth and zenith angle in form of polar plots.\\\\53 In the Figure 3 (on the right), a two-dimensional projection of the voxel model is shown for three different viewpoints. Additionally, the projection areas of a human with no clothing, summer clothing and winter clothing are visualized as function of the azimuth and zenith angle in form of polar plots.\\\\ 54 54 55 Figure 2.2: (a) Projection of the 3D voxel model with winter clothing, visualized for incident angles 30°, 60° and 85°, with the front turned by 30° in azimuth direction. Only hands and face are exposed to UV radiation, which is shown in light gray color and clothing shown in dark gray. (b)-(d) projection areas of the 3D voxel model oriented towards 180° (south), as a function of incident and azimuth angles. The minimal projection area in each plot is located in the middle of each picture, representing a view from the zenith at an incident angle of 90°. (b) Projection area of a human with winter clothing. The three asterisks mark the projections shown in (a). (c) Projection area of a human without any clothing, which results in nearly identical projection areas between the front and back of the human. (d) Projection area of a human with summer clothing, where face, hands, neck and arms are exposed.\\55 Figure 3: (a) Projection of the 3D voxel model with winter clothing, visualized for incident angles 30°, 60° and 85°, with the front turned by 30° in azimuth direction. Only hands and face are exposed to UV radiation, which is shown in light gray color and clothing shown in dark gray. (b)-(d) projection areas of the 3D voxel model oriented towards 180° (south), as a function of incident and azimuth angles. The minimal projection area in each plot is located in the middle of each picture, representing a view from the zenith at an incident angle of 90°. (b) Projection area of a human with winter clothing. The three asterisks mark the projections shown in (a). (c) Projection area of a human without any clothing, which results in nearly identical projection areas between the front and back of the human. (d) Projection area of a human with summer clothing, where face, hands, neck and arms are exposed.\\ 56 56 }}} 57 57 {{{#!td style="text-align:left;style=width: 50px"
