In brief
Two quantities are determined for each reflection: the luminance (cd/m²), i.e. how bright the reflecting surface appears, and the illuminance at the eye (lx), which also takes into account how large the surface appears from the observer's position. Both depend on the module type, the sun position and the angle of incidence.
Two quantities are calculated for every hit cell:
| Quantity | Unit | Describes |
|---|---|---|
| Luminance | cd/m² | how bright the reflecting surface appears, independent of its size |
| Illuminance at the eye | lx | how much light of the glare source arrives at the eye; additionally depends on the apparent size of the source |
V.5.1 Luminance
The luminance follows from the reflection profile of the decisive zone (Ch. V.3) at the current angle of incidence. Because the profile applies to 100,000 lx on the module surface, it is scaled with the actual illuminance of the module surface: the direct irradiance at that moment (Ch. V.1), the cosine of the angle of incidence and the luminous efficacy of solar radiation. A low or obliquely incident sun therefore produces a lower luminance than the strong midday sun.
The luminous efficacy converts radiant power (W) into luminous flux (lm). It depends on the solar elevation, because at low sun the atmosphere filters out more short-wave light, and it is applied according to Littlefair (1988).
For the perfect mirror no curve applies: the luminance of the reflection is the luminance of the solar disc, that is, the illuminance of the direct radiation divided by the solid angle of the sun, without cosine factor and with complete reflection.
V.5.2 Illuminance at the eye
Luminance alone does not say how much light arrives: a small bright area at a great distance brings less light to the eye than the same area close up. What also matters is the solid angle subtended by the luminous area. It follows from the point grid (Ch. V.2): each calculation point contributes the angular area it represents. The illuminance of a cell is the product of luminance and solid angle.
Over the cells and PV areas of a time step, the illuminance is added up: more luminous area brings more light to the eye. Luminance is not added up; it is a property of the surface, and the highest value is reported.
Deep dive: formulas and constants
1. Illuminance on the module surface:
E_v [lx] = DNI [W/m²] · cos θ · K(γ) [lm/W]
2. Luminance of the reflection:
L [cd/m²] = L_profile(θ) · E_v / 100,000 lx
3. Perfect mirror:
L_sun [cd/m²] = DNI · K(γ) / Ω_sun, Ω_sun = π · (0.53° / 2 in rad)² ≈ 6.7 · 10⁻⁵ sr
4. Solid angle of a cell:
Ω [sr] = Σ g_i · cos(el_i) · Δaz · Δel
summed over the counted calculation points i of the cell; Δaz and Δel are the step sizes of the area's point grid in radians, el_i the elevation of the point, g_i its area share: 1 inside the area, at the edge the share of its grid cell on the module surface (Ch. V.2). The cosine compensates for the distortion of the azimuth-elevation grid towards the zenith.
5. Illuminance at the eye:
E [lx] = L · Ω
per cell; per time step, E is summed over the cells and L is reported as the maximum.
| Symbol | Meaning |
|---|---|
| θ | angle of incidence of the sun to the surface normal |
| γ | solar elevation in degrees |
| DNI | direct normal irradiance under clear sky (Ineichen and Perez) |
| K(γ) | luminous efficacy of direct sunlight according to Littlefair (1988): K = 51.8 + 1.646·γ − 0.01513·γ² lm/W, with γ limited to 0° to 54.4°; about 67 lm/W at 10°, at most 96.6 lm/W from 54.4° |
| L_profile(θ) | reflection profile of the decisive zone, referred to 100,000 lx |
Why 100,000 lx is applied separately. The profile values apply to a fixed illuminance on the module surface, independent of the angle of incidence. The incident light decreasing with cos θ is contained in E_v; if it were also contained in the profile, the decrease would be counted twice.
Partially blocked cells. For a visible cell, only its unblocked points count. If the lobe covers a hit cell only partly, each visible point counts with the share of its area that lies in the lobe; in the point-by-point check only the points hit count, at the lobe edge likewise with their share (Ch. V.2).
Merged sub-areas. With differentiated cross-tilt, a cell hit by several sub-areas receives the solid-angle-weighted mean of their luminances; the illuminance remains the sum of the individual contributions.
V.5.3 Putting the quantities into context
The luminance of the sun reaches up to 1.5 · 10⁹ cd/m² (LAI, Annex 2 No. 2, pp. 21–22; EnergieSchweiz/Swissolar guide 2023, p. 38). Absolute glare, at which the eye can no longer adapt, occurs according to the LAI guidance at about 10⁵ cd/m² (Annex 2 No. 2.1, p. 21) and according to OVE R 11-3 from about 10⁴ cd/m² (section 4.1, p. 8); the key points paper of the Federal Highway Authority states more than 30,000 to 100,000 cd/m² for a direct look (ch. 3, p. 5).
Some guidelines use a luminance threshold as a criterion:
| Source | Threshold | Reference |
|---|---|---|
| EnergieSchweiz/Swissolar guide 2023 | luminance of the reflecting surface above 50,000 cd/m² counts as glare; the value is under review | Annex 1, p. 38 |
| Key points paper of the Federal Highway Authority | reflections of at most 30,000 cd/m² count as not significantly impairing | ch. 3, p. 6 |
| EASA CS-ADR-DSN | at most 20,000 cd/m² as acceptable luminance of solar installations at aerodromes (guidance material) | GM1 ADR-DSN.M.615 (k), Issue 6, p. 162 |
| Toggweiler et al. (2024), report for EnergieSchweiz | below 30,000 cd/m² "low-glare", above 50,000 cd/m² may disturb | pp. 3, 25, 28 |
The LAI guidance and the OVE guideline assess duration, not luminance. None of the PV guidelines named gives a threshold for the illuminance at the eye; the key points paper requires the intensity to be determined, for example as illuminance near the eye or as luminance (ch. 4, p. 7). RVS 05.06.11 limits the glare illuminance of information carriers at roads to 1 lx within a 30° visual cone (section 5.1, p. 13); it contains no criteria for PV installations.
The irradiance on the retina and the hazard levels derived from it (after-image, retinal damage), as reported by the method of Ho, Ghanbari and Diver (2011) and the former FAA tool SGHAT (78 FR 63278), are not calculated.