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TracePro_User_Manual_5.0.pdf
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Interpretation of Polar Iso-Candela Plots

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z

[0.5 ( -1 + 3z2 )] [0.5 ( -3z + 5z3 )]

[0.125 ( 3 – 30z2 + 35z4 )] [0.125 ( 15z – 70z3 + 63z5 )] 1

z

[0.5 ( -1 + 3z2 )] [0.5 ( -3z + 5z3 )]

[0.125 ( 3 – 30z2 + 35z4 )] [0.125 ( 15z – 70z3 + 63z5 )] 1

z

[0.5 ( -1 + 3z2 )] [0.5 ( -3z + 5z3 )]

[0.125 ( 3 – 30z2 + 35z4 )] [0.125 ( 15z – 70z3 + 63z5 )] 1

z

[0.5 ( -1 + 3z2 )] [0.5 ( -3z + 5z3 )]

[0.125 ( 3 – 30z2 + 35z4 )] [0.125 ( 15z – 70z3 + 63z5 )]

cos4θ

cos4θ

cos4θ

cos4θ

cos4θ

sin4θ

sin4θ

sin4θ

sin4θ

sin4θ

sin4θ

cos5θ

cos5θ

cos5θ

cos5θ

cos5θ

cos5θ

sin5θ

sin5θ

sin5θ

sin5θ

sin5θ

sin5θ

Interpretation of Polar Iso-Candela Plots

Iso-candela intensity plots (i.e., W/sr or cd depending on the units) can cause confusion to users. This section addresses such potential confusion by providing an example that illustrates what happens when you project a hemispherical distribution onto a plane. Figure 7.20 shows the sphere over which the intensity distribution should be viewed, and then how it is projected to the base plane of this hemisphere. For this simple illustration the projected solid angle is given by

dΩ = dωcosθ

(7.45)

where is the angle with respect to the normal axis, is the solid angle, and

is the

projected solid angle. In TracePro the angle is the one with respect to the

 

Normal (as defined in Analysis|Candela Plot Options). Each of the rays is binned within constant solid angle bins (i.e., they span the same surface are on the unit hemisphere). Additionally, for Polar Iso-Candela plots, individually each

TracePro 5.0 User’s Manual

7.81

Technical Reference

ray is corrected for the nonlinear projection from this hemisphere to the plane. This nonlinear projection is due to the constant angular spacing in the radial direction on polar iso-candela plots, as shown in Figure 7.21 and Figure 7.22 (i.e., the annular pie slices do not have constant areas as function of the radiant angle). Thus, two rays at different angles that are in the same bin with the same flux will contribute different amounts of intensity (cd or W/sr) to this bin. If you save the Polar Iso-candela data (File|Save As… of type *.txt), the nonlinear projection is also saved.

θ

FIGURE 7.20 - Depiction of solid angle projection from a hemisphere to the base plane of the hemisphere.

To illustrate this, consider the case shown in Figure 7.21, there are grid sources comprised each of single rays. Grid 1 has a ray in the x-z plane at an angle of 63.426º to the z axis. Grid 2 has a ray in the x-z plane at an angle of 64.537º to the z axis. Figure 7.22 shows the iso-candela plots (Analysis|Candela Plots|Polar Iso-Candela) for (a) Grid 1 and (b) Grid 2. Note the difference in the maximum candela values, which arises due to the nonlinear projection. Polar iso-candela plots in direction cosine values do not suffer from this projection effect since the cos(q) value in See Equation 7.45 on page 7.81 is simply the axial plot dimension. However such plots are currently not available in TracePro.

Finally, one can rotate the plot normal, by, for example, placing the Grid 1 ray at the pole. This is done by changing Analysis|Candela Plot Options > Orientation and Rays tab X to 0.8944 and Z to 0.4472. Figure 36 shows the results for (a) Grid 1 and (b) Grid 2.

7.82

TracePro 5.0 User’s Manual

Interpretation of Polar Iso-Candela Plots

FIGURE 7.21 - Polar Iso-Candela Plots for Grids (a) 1 and (b) 2, Normal = (0, 0, 1).

FIGURE 7.22 - Polar Iso-Candela Plots for Grids (a) 1 and (b) 2, Normal = (0.8944, 0, 0.4472).

TracePro 5.0 User’s Manual

7.83

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