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Etendue calculator
Compare the etendue of a flat source with a fiber or an aperture. The coupling ratio is a geometric ceiling, not a ray-trace result. A smaller core or a lower NA drops that ceiling.
Result
Etendue is the room a beam takes up in area and angle together. Passive optics can reshape that room. They cannot make it smaller. If the source etendue is larger than the receiver, some of the light cannot enter.
Source etendue
3.14159 mm² sr
Area 1 mm². Half-angle 90°.
A = width × height. G = π n² A sin²(θ), with θ the half-angle from the normal.
Flat area into a circular cone. This is the etendue of a Lambertian source limited to that cone.
Receiver etendue
0.61685 mm² sr
Area 0.785398 mm². Half-angle 30°.
A = π (diameter / 2)². G = π A NA², with NA the external numerical aperture in air.
The core is circular and the NA is the external NA. Fresnel loss is not included.
Maximum geometric coupling
19.63%
At most 19.63% of the source etendue can pass into this receiver. Passive optics cannot close that gap.
Coupling = receiver etendue / source etendue, capped at 100%.
Passive optics cannot reduce etendue, so this ratio is a ceiling before reflection loss and misalignment.
The LED-to-fiber coupling feasibility study started from an etendue budget, then compared added optics with direct contact. Spot size and throw are on the LED beam angle calculator.