3D view of the geometry
Irradiance on the target surface
Key figures (evaluated on target/model only)
Cross-section profiles through the centre
Profile along u (v = 0)
Profile along v (u = 0)
Data export
Model description
Show explanation of the simulation model
Basic principle
Each LED is modelled as a compact source of 5 sub-sources across the ~3.5 mm die in the LED plane (z = h above the pivot/origin), emitting vertically downwards. The irradiance E at a point on the target is the incoherent sum of the contributions of all sources (UV LEDs are mutually incoherent, powers simply add). In the far field the model is equivalent to a point source; the sub-sources reproduce the real smoothing of the distribution in the near field.
LED emission characteristic
The angular distribution of the radiant intensity follows the generalised Lambertian model:
I(θ) = I₀ · cosᵐ(θ) with m = ln 0.5 / ln cos θ½θ is the angle to the optical axis. The half angle θ½ is interpreted as the angle at which the radiant intensity has dropped to 50 %. θ½ = 60° gives m = 1 (ideal Lambertian emitter, unlensed chip); θ½ = 20° gives m ≈ 11 (strongly collimating lens). Normalising over the hemisphere ensures the total emitted power equals the set radiant flux Φ:
I₀ = Φ · (m + 1) / (2π) [mW/sr]By default (and always for the predefined luminaires) the OPSY1 LED model is used instead of the pure Lambertian model — the effective emission characteristic of the built-in high-power LED: a super-Gaussian profile I(θ) = exp(−(θ/36.2°)³) with half angle θ½ = ±32°, smoothly terminated to zero between 42° and ±52°. The profile follows the measured emission curve of the LED up to about 30° and has been validated against Monte-Carlo ray tracing of a 3×3 array at 10 mm distance. In addition, each LED is modelled as 5 sub-sources across the ~3.5 mm die — together this reproduces the real near-field distribution without artificial peaks between adjacent LEDs. It is likewise energy-normalised over the hemisphere (I₀ = Φ / [2π·∫ I(θ)·sin θ dθ]), so the total emitted power equals Φ exactly. In custom mode the curve can additionally be compressed along the angle axis by up to −5° ("beam narrowing" slider); energy normalisation remains exact. Emission characteristic models and the per-wavelength assignment (radiant flux, model) can be adjusted via the password-protected LED parameterisation; OPSY1 is the default parameterisation.
Irradiance calculation
For every target point P and every LED, the photometric distance law with cosine correction of the angle of incidence is applied:
E(P) = Σ over all LEDs: I(θ_LED) · cos(θ_inc) / r²Here I(θ) is the radiant intensity of the selected emission model — the OPSY1 LED model by default, or I₀·cosᵐθ in Lambertian mode. 1/r² describes the geometric dilution with distance, cos(θ_inc) the projection onto the (possibly tilted) receiving surface. Points above the LED plane or on faces turned away from an LED receive no contribution.
Geometry
- Flat target (rectangle/circle): an N×N grid of local coordinates (u, v) is mapped into 3D via the tilt basis (rotation about X and Y around the centre at distance h); for the circle, points outside the diameter are masked.
- CAD model (STEP/STL): the model is triangulated (STEP via OpenCascade, STL directly), centred at the origin and transformed (scale, translation, rotation R = Rz·Ry·Rx). E is evaluated per triangle at its centroid; the normal follows from the vertices, back faces receive E = 0.
- Overall area: an independent flat reference plane at z = 0 shown as a grid in the 3D view.
Numerics
Flat targets use a fixed 251 × 251 grid; the incident power is integrated with the trapezoidal rule (area-weighted over triangles for CAD models). Key figures such as uniformity (min/max) and mean refer exclusively to the target surface or the irradiated outer faces of the model.
What is taken into account
- Emission characteristic: OPSY1 LED model (θ½ = ±32°, narrowable by up to −5° in custom mode) or selectable Lambertian model (θ½ ±20°…±60°)
- Inverse-square distance law (1/r²)
- Angle of incidence on tilted or arbitrarily oriented surfaces (cos θ_inc)
- Superposition of all LEDs of the array (positions from rows/columns/pitch)
- Energy conservation: I₀ normalised to the set radiant flux
What is not taken into account
- Reflections from surroundings, overall area or housing (the blue housing is purely visual)
- Fresnel losses at the target surface (E is the incident, not the absorbed irradiance)
- Self-shadowing of concave CAD models — occluding geometry between LED and face is not checked
- Near-field effects are only approximated (soft effective profile, die area as 5 sub-sources); wave-optical effects are not considered
- Spectral effects, absorption in air, LED binning and temperature dependence of the flux
Validation
Checked against analytical limiting cases: in Lambertian mode, directly below a single LED E = Φ·(m+1)/(2π·h²) holds exactly; at lateral offset h·tan θ½ the radiant intensity drops to exactly 50 %; on a very large receiver the integrated power converges to the total flux (>99.9 % at 4 × 4 m, both emission models); tilting reduces E at the centre exactly by cos(αx)·cos(αy). The OPSY1 LED model is additionally validated against Monte-Carlo ray tracing (see emission characteristic).
Units
Inputs in mm and %, internal calculation in cm, result in mW/cm² (switchable to W/m²: 1 mW/cm² = 10 W/m²). The radiant flux per LED is stored for each wavelength and corresponds to the 100 % setting; the "LED power" slider scales it down linearly.