Calculator Input
Example Data Table
Use these sample cases to understand how aperture area, angular acceptance, refractive media, and efficiency affect optical throughput.
| Case | Aperture | Angular Input | n | Channels | Efficiency | Effective Etendue |
|---|---|---|---|---|---|---|
| Bench collimator | Circular, 10 mm diameter | Half-angle 20° | 1.00 | 1 | 95% | 28.30 mm²·sr |
| Imaging relay | Rectangular, 20 × 10 mm | NA 0.30 | 1.00 | 2 | 90% | 104.04 mm²·sr |
| Glass-coupled sensor | Circular, 50 mm diameter | Half-angle 5° | 1.50 | 1 | 92% | 97.58 mm²·sr |
| Multi-channel collector | Direct area, 500 mm² | Solid angle 0.80 sr | 1.33 | 4 | 85% | 2,404.31 mm²·sr |
Formula Used
This implementation accepts area in mm² and reports etendue in both mm²·sr and m²·sr. When numerical aperture is used, the refractive index converts NA into a cone half-angle before computing solid angle.
How to Use This Calculator
- Select how you want to define the aperture: circular, rectangular, or direct area.
- Enter the matching geometric dimensions in millimeters or enter area directly in mm².
- Choose the angular method: half-angle, numerical aperture, or direct solid angle.
- Provide refractive index, tilt angle, channel count, and overall efficiency.
- Press Calculate Etendue to display results above the form.
- Review the projected area, solid angle, per-channel etendue, and effective system etendue.
- Use the CSV and PDF buttons to export the current result set.
- Inspect the Plotly graph to see sensitivity against angular acceptance.
Frequently Asked Questions
1) What is etendue in optical engineering?
Etendue measures how much light an optical system can accept or transport. It combines aperture area, angular spread, and refractive medium effects into one throughput quantity.
2) Why does refractive index appear as n²?
Optical throughput in a medium scales with the square of refractive index. Including n² keeps the etendue definition consistent when light propagates inside materials instead of air.
3) Why is tilt included in the calculation?
Tilt reduces the effective projected area normal to the incoming ray bundle. That smaller projected area lowers etendue, even when the physical aperture size stays unchanged.
4) When should I use numerical aperture instead of half-angle?
Use numerical aperture when your component specifications are given as NA, such as fibers, sensors, and couplers. Use half-angle when the acceptance cone is specified directly in degrees.
5) What does effective etendue mean?
Effective etendue applies your system efficiency to the theoretical throughput. It is useful when coatings, absorption, alignment loss, or other transmission penalties reduce practical performance.
6) Can etendue decrease through passive optics?
In ideal passive optical systems, etendue cannot be reduced without losing light. This is a core brightness-conservation principle used in illumination, imaging, and fiber-coupling design.
7) Why are results shown in both mm²·sr and m²·sr?
Small laboratory systems are often easier to interpret in mm²·sr, while larger engineering models and publications frequently use m²·sr. Showing both units supports quick comparison.
8) What is a realistic efficiency input?
A realistic efficiency depends on your losses. Clean, aligned systems may exceed 90%, while complex or misaligned systems can be much lower. Use measured transmission when available.