Demo — Blackbody Explorer

Demo — Blackbody Explorer#

Two temperature facts define an IR signature: how much a source radiates and where that energy peaks. This demo puts Planck’s curve on a log axis so you can slide the source temperature, watch the peak march between the MWIR and LWIR windows, and read off how much of the emission actually lands in each band.

The curve and the two rules#

Planck’s law gives the spectral radiant exitance of a blackbody — the power radiated per unit area per unit wavelength:

\[ M(\lambda, T) = \frac{2\pi h c^2}{\lambda^5 \left( e^{\,hc/(\lambda k_B T)} - 1 \right)}. \]

Two rules of thumb read the operationally useful parts off that curve. Wien’s law locates the peak, and Stefan-Boltzmann sets the area under it:

\[ \lambda_{\text{peak}} \; [\mu\text{m}] \approx \frac{2898}{T \; [\text{K}]}, \qquad M_{\text{total}} \propto T^4. \]

The dynamic range across temperatures is enormous, which is why the exitance axis is logarithmic — a 5800 K Sun outshines a 290 K background by many orders of magnitude at every wavelength.

Interactive demo#

Open in full screen

Walkthrough#

  1. Read the curve. The plotted line is Planck’s law, \(M(\lambda, T)\), on a log exitance axis. The two shaded bands are the MWIR (3–5 µm) and LWIR (8–12 µm) atmospheric windows.

  2. Slide the temperature. As you raise \(T\), the whole curve lifts (Stefan-Boltzmann, \(T^4\)) and its peak slides left toward shorter wavelengths (Wien). The dashed marker tracks \(\lambda_{\text{peak}}\).

  3. Try the presets. Sun (5800 K) peaks near 0.5 µm in the visible; a plume (1000 K) peaks near 2.9 µm at the MWIR edge; a tailpipe (800 K) peaks near 3.6 µm in the MWIR; aero skin (325 K) peaks near 8.9 µm in the LWIR; a 290 K background peaks near 10 µm, right on top of it.

  4. Watch the in-band fractions. The readout integrates Planck over each window and divides by the total emission. As the peak enters a window, that window’s fraction climbs — a direct measure of how much signal a sensor in that band actually collects.

Key observations#

  • Hot hunts short, cool hunts long. The plume’s peak falls in the MWIR; the skin’s peak falls in the LWIR. Pick the window where your target’s peak lives.

  • Height and location move together. Raising temperature both lifts the curve and shifts the peak bluer — the two rules are two readouts of the same Planck curve.

  • A cool skin sits on top of its background. At 325 K the airframe and a 290 K background nearly overlap in the LWIR, which is why long-wave detection is a contrast problem, not a brightness problem.

  • The in-band fraction is the point of a window. A source can be intensely bright yet deliver little into your band; integrating over the window tells you what the sensor really sees.

Source#

MATLAB bundle · L21_PlanckBlackbody.m↓

The companion script evaluates Planck’s law over 0.3–15 µm for a jet plume, aero-heated skin, and the Sun, plots all three on a log axis with the MWIR and LWIR windows shaded, marks each Wien peak, and prints where each source lands. The book demo extends it with the temperature presets and the MWIR/LWIR in-band-fraction readout.

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