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:
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:
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#
Walkthrough#
Read the curve. The plotted line is Planck’s law, \(M(\lambda, T)\), on a log exitance axis. The blue and red bands are the MWIR (3–5 µm) and LWIR (8–12 µm) atmospheric windows; the grey ones are what the atmosphere closes — the water-vapor wall from 5 to 8 µm, and the narrow CO₂ notch near 4.3 µm sitting inside the MWIR.
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 \(\lambda_{\text{peak}}\).
Try the presets. The demo opens on the plume. 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.
Watch the in-band fractions. The readout integrates Planck over each window and divides by the total emission. It is pure blackbody physics: the shaded absorption features mark where the atmosphere bites, but they are not subtracted from these numbers. As the peak approaches 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 at the MWIR edge; the skin’s peak falls in the LWIR. Pick the window where your target’s peak lives.
The peak need not be inside the window. At the 1000 K plume preset the peak sits at 2.9 µm, just short of the band — yet the MWIR still collects about 36% of the total emission, four times what the LWIR gets. Drive the slider and the MWIR share tops out near 36% around 925 K; the LWIR share tops out near 29% around 370 K, a source whose peak sits inside the closed 5–8 µm wall. The peak points you at a window; the in-band fraction tells you what you actually collect.
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. Flip between the aero-skin and background presets: the peak moves only 8.92 → 9.99 µm and the total exitance 6.3e2 → 4.0e2 W/m², so on a log axis the curve barely moves. That 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 along with its Stefan-Boltzmann total \(\sigma T^4\) and the plume-to-skin power ratio. The book demo extends it with the temperature presets and the MWIR/LWIR in-band-fraction readout.