Luminous Intensity Distribution Tool

Interactive tool for visualizing LED illuminance distributions on a 2D target panel. Helps engineers design uniform lighting arrays by simulating Lambertian (cos) emitters in a grid, adjustable height, spacing, panel dimensions, and reflective side panels.

What it does

1. Polar plot — shows the single-emitter radiation pattern (cos theta Lambertian)
2. Top-down heatmap — 2D view looking down at the target panel, showing illuminance as a white-to-green color gradient with LED positions and reflector outlines
3. Cross-section chart — line plot of illuminance along y=0 through the center of the panel
4. Reflective panels — optional rectangular reflector enclosure around the LED array with configurable reflectivity
5. Power & energy calculator — computes total power, efficiency (% of emitted light hitting the target), energy density (J/cm²), and time-to-target calculations
6. Interactive hover — hover the heatmap or cross-section for exact position and intensity values

Parameters

Each parameter has a direct-entry number field (type any value), a slider, and configurable min/max/step.

Reflector presets

Reflectors form a rectangular enclosure around the LED array at x = +/-(colsd/2) and y = +/-(rowsd/2). They redirect sideways-emitted light back onto the target panel, improving both efficiency and edge uniformity. Light outside the reflectors is attenuated by (1-R).

Power & energy calculations

• Total power: cols x rows x power-per-LED
• Efficiency: fraction of total emitted power that lands on the target panel (direct + reflected, properly integrated using Lambertian irradiance model)
• Target receives: total power x efficiency
• Energy density: (target power / panel area in cm²) x time = J/cm²
• Time calculator: enter target J/cm², get time needed (or enter time, get J/cm²)

The irradiance integration accounts for:

• Lambertian cos(theta) emission pattern
• Inverse-square distance falloff
• Angle of incidence on reflector walls
• First-order reflections from all 4 walls
• Proper energy conservation (efficiency capped at 100%)

How to use

The tool is a single self-contained HTML file served via a local HTTP server:

cd /home/adom/project
python3 -m http.server 8123 &>/dev/null &

Open in a Hydrogen webview:

PROXY_URL="${VSCODE_PROXY_URI/\{\{port\}\}/8123}luminous-intensity.html"
adom-cli hydrogen webview open-or-refresh \
  --name "Luminous Intensity" \
  --url "$PROXY_URL"

URL parameters can preset values: ?h=100&d=30&cols=12&rows=14&l=300&w=340&r=88

Physics model

• Single source: Lambertian emitter with intensity I(theta) = I0 * cos(theta)
• Illuminance on plane: E(x,y) = sum of cos^3(theta_i) / h^2, where theta_i = atan(sqrt((x-xi)^2 + (y-yi)^2) / h)
• Reflectors: Mirror sources placed symmetrically across each wall, with gain = reflectivity. Light outside reflectors attenuated by (1-R).
• Wall irradiance: cos(theta_source) * cos(theta_wall) / (pi * r^2), properly integrated over wall height and width
• Color mapping: Linear interpolation from white (0%) to green #2e7d32 (100%)

Source file

The tool lives at /home/adom/project/luminous-intensity.html.