Integration and Assessment

Solid-Angle Weighting

In Type-C coordinates, with angles in radians:

dOmega = sin(gamma) dgamma dC

For a constant intensity over a cell bounded by C1, C2, gamma1 and gamma2:

DeltaOmega = (C2 - C1) * (cos(gamma1) - cos(gamma2))
DeltaPhi = I_cell * DeltaOmega

This illustrates the weighting principle, not a promise that every report uses constant-cell quadrature. Implementations can interpolate or integrate data differently. Equal angle increments do not represent equal solid angles, particularly near the poles.

Zones and Normalization

Zonal lumens integrate a specified directional region. Ratios need a stated denominator: for example, integrated luminaire flux or total lamp flux. A missing, non-finite or zero flux is not a valid normalization basis. Forward and backward utilization curves describe different regions.

See Zonal Lumen Table and Luminaire Classification System.

Calculation Context

A distribution alone does not determine every lighting result. Indoor glare assessments also require emitting geometry, observer arrangements and room assumptions. Roadway assessments require road and luminaire arrangements and the chosen calculation settings:

• UGR Table
• Utilization Factor Table
• IES Roadway Report
• Roadway Calculator

Before comparing results, match units, normalization, geometry, orientation, sampling and calculation mode. Retain original files and record modifications for reproducibility.