Demo — IR Detection Range

Demo — IR Detection Range#

A passive IR sensor detects a target the instant the radiated heat arriving at its aperture clears its own noise floor. This demo puts that condition on a single axis so you can watch two things at once: how far a sensor sees a bright source versus a dim one, and how the exponential atmosphere quietly steals most of the advantage that raw intensity seems to promise.

The concept#

Source intensity \(J\) (watts per steradian) spreads over the inverse square of range and is attenuated by atmospheric transmittance \(\tau(R)=\exp(-\alpha R)\). The irradiance reaching the sensor is therefore

\[ E(R) \;=\; \frac{J\,\exp(-\alpha R)}{R^{2}}, \]

and detection occurs wherever \(E(R)\) stays at or above the noise-equivalent irradiance (NEI). Watch the units: with \(J\) in W/sr and NEI in W/m², the \(R^2\) in the denominator is in meters while \(\alpha R\) uses kilometers (the source script converts via \(R_m = 10^3\,R_{km}\)). The crossover defines the maximum range, which scales as

\[ R_{\max} \;\propto\; \sqrt{\dfrac{J\,\tau}{\text{NEI}}}. \]

Contrast the square-root-of-\(J\) dependence with radar’s \(R_{\max}\propto\sigma^{1/4}\): cutting radar cross-section starves the radar, but it leaves \(J\) — and therefore IR range — untouched.

Interactive demo#

Open in full screen

Walkthrough#

  1. Read the curve. The falling curve is \(E(R)=J\exp(-\alpha R)/R^2\) on a log-irradiance axis; the horizontal dashed line is the sensor’s NEI. Where the curve crosses NEI is \(R_{\max}\), marked with a dot.

  2. Slide \(J\). Push source intensity up and the whole curve lifts, moving the crossing outward — but notice how little the crossing moves once the exponential term dominates.

  3. Slide \(\alpha\). Raise the extinction coefficient (haze, humidity) and the curve bends down faster; a clear day (\(\alpha\approx 0.15\) /km) and a hazy one give very different reach.

  4. Slide NEI. Lowering the noise floor (better cooling, better detector) drops the dashed line and pushes \(R_{\max}\) out.

  5. Load the two-target preset. Stern (\(J=1000\) W/sr, plume plus hot parts) versus beam (\(J=50\) W/sr, skin only). The vacuum rule promises \(\sqrt{20}\approx 4.5\times\) more range for the stern; the atmosphere delivers only about \(1.4\times\).

Key observations#

  • The atmosphere is the referee. In vacuum, range would scale as \(\sqrt{J}\) and the stern would out-reach the beam by \(4.5\times\). With \(\tau(R)=\exp(-\alpha R)\) in play, stern reaches about 54 km and beam about 39 km — only \(1.4\times\).

  • Diminishing returns on intensity. Because the crushing term is exponential, every doubling of \(J\) buys less added range than the last. Modest signature trimming buys modest range.

  • This is the counter-LO argument, and the setup for L24. Radar range dies with \(\sigma^{1/4}\); IR range lives on \(J\), which stealth does not touch. To hide from IR you must attack \(J\) by orders of magnitude, component by component — plume, hot parts, skin — which is exactly the signature-suppression fight the next lesson opens.

Source#

MATLAB bundle · L23_IRDetectionRange.m↓

The companion script sweeps range from 0.5 to 80 km, computes \(E(R)=J\exp(-\alpha R)/R^2\) for the stern (\(J=1000\) W/sr) and beam (\(J=50\) W/sr) sources against a clear-air \(\alpha=0.15\) /km and NEI \(=10^{-10}\) W/m², plots both on a log-irradiance axis with the NEI floor, and prints the two crossing ranges so the class can compare the \(4.5\times\) vacuum promise with the \(1.4\times\) the atmosphere actually delivers.

Contents