Passive IR detection — irradiance at the sensor vs range

Stern — plume + hot parts Beam — skin (J≈50) NEI noise floor Rmax crossing
Source & atmosphere
Intensity J1000 W/sr
Extinction α0.15 /km
NEI floor1.0e-10
Rmax stern
—
J = 1000 W/sr
Rmax beam
—
J = 50 W/sr
Vacuum √(J) rule
—
promised ratio
Actual ratio
—
atmosphere allows
—
IR rule: Rmax ~ √(J·τ/NEI), with τ(R)=e-αR. In vacuum (τ=1) intensity enters as √J. Radar's monostatic range scales only as σ1/4 (four-way spreading). Either way the exponent is small — brute-force signature growth buys little range once the exponential atmosphere takes its cut.
Every doubling of J buys less range than the last — to hide you must attack J by orders of magnitude, component by component (L24).