The Thermoptic Camouflage Bench: The Physics Bill for Invisibility · Signals from the Periphery

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THE SUIT

Passive band

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Display seam

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Heat budget

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THE THERMOPTIC CAMOUFLAGE BENCH · THE PHYSICS BILL FOR INVISIBILITY
Ghost in the Shell (Oshii, 1995): a suit that hides a body from eyes and from thermal imagers
It shimmers when she moves; water finds it at once; the film never shows the heat
the light's linewidths, the imager's noise, the rain's drop spectrum are the record's
the band, the seam, the lag, the splashes and the minutes are arithmetic on them
the alley, the mannequin and the suit's tiles are drawn, and say so
put the suit on · calibrate to your eye · step aside · switch the lamp · switch the camera

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Evidence

fact ⇄ what kind of claim · live

The film: a suit called thermoptic camouflage that shows its background, ripples when the Major moves, and is found out by water in the canal fight; no numbers given, only behaviour

Oshii 1995, quoted as premise; the site's signed review is linked from the intro

REPORTED

Detour (π/2 − 1)·D; delay ≥ detour/c; slip φ = 2 asin(√f/2); Δλ = φλ₀²/(π·detour); seam d·B/R; lag v·τ; drop flux R/V(D₀); heat m·c·ΔT and m_ice·L; contact temperature by effusivity

closed-form arithmetic on declared inputs; the display's projection in the 3D view is exact geometry

EXACT

Craeye & Bhattacharya 2012 and Monticone & Alù 2016 (the bound); Sohl et al. 2007 (the sum rule); Tachi 2003 (one-viewpoint optical camouflage); Marshall & Palmer 1948; NETD 50 / 20 mK; body 3,470 J/kg/K, 100 / 300 / 700 W; ADAPTIV's 14 cm tiles (BAE 2011); ice 334 kJ/kg

the published physics and the published devices the bench is priced against

MEASURED

The tolerance (10 dB), the body's width and top area, the wall's distance, one frame of latency, 3 mm pixels, a 30 ms splash, 10 mm of aerogel, COP 2.5, 2 kg of ice, +2 K of core, a flux-pulse footprint on dry concrete; the alley and the mannequin

choices, shown as dials; every finding is quoted across their range

MODELLED

Whether a device that works for one eye, one wavelength or one ice pack at a time is 'the film getting it right' or 'a prop with an honest shimmer'

the one question this bench refuses to close for you

READING

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The suit

The light

Thermal imagerwhite-hot; the suit's outer skin in tiles

Imager window · black to white25 K

Tile error±0.10 K

How far each hexagon sits from the set-point. The imager's noise is 0.05 or 0.02 K.

RainMarshall & Palmer drops; splashes at the model's rate

Rain rate10 mm/h

Cameras

Show the calibrated eye

Bare soles leave printsthermal view; off = soles held at background

Labels

The passive cloak

Width light must go round45 cm

The Major at the shoulders is 0.45 m. A hand is 0.1, a coin 0.024, a tank 3.5.

Design wavelength550 nm

Suppression required10 dB · 10 % residual

The residual scattering the cloak may leave before it counts as seen. Tighter is narrower.

The display suit

Wall behind the body · B1.5 m

Moves the façade in the 3D view too. The seam grows with it.

Range to the body · R (seam view)8.0 m

Second eye's offset · d (seam view)1.00 m

In the 3D view the offset is wherever your camera stands from the calibrated eye.

Latency16.7 ms · one video frame

Pixel pitch3.0 mm

The eye resolves one arcminute: 2.3 mm at 8 m.

The heat

Metabolic heat100 W

Body mass70 kg

Core rise allowed+2.0 K

Ice carried2.0 kg

334 kJ a kilogram. Two kilograms is a small vest.

Night temperature20 °C

Insulation · aerogel10 mm

Tiles' COP2.5

Peltier coefficient of performance at a small temperature difference.

Readout · live

passive band · of λ₀

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largest hidden · daylight · laser

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light inside the band

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display seam

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display lag

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rain on the body

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heat budget

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What is exact vs modelled here

Exact: the detour, the delay and the band at a stated tolerance; the seam, the lag and the pitch geometry; the drop flux from the Marshall & Palmer spectrum; the heat capacity, the latent heat, the leak and the budget; the contact temperature. Measured: the bound (Craeye & Bhattacharya 2012; Monticone & Alù 2016), the sum rule (Sohl et al. 2007), Tachi's device (2003), the imagers' NETD, ADAPTIV's tiles, the body's constants. Reported: the film's behaviour, as premise. Modelled: the tolerance, the widths and areas, the wall, the latency, the pitch, the splash life, the insulation, the COP, the ice, the footprint model; the alley and the mannequin.

The model, in full

Band: detour = (π/2 − 1)·D; delay = detour/c; φ = 2 asin(√f/2) for residual f; Δω = 2φ/delay; Δλ = φλ₀²/(π·detour); transmission = share × min(1, Δλ/W). Sum rule: ∫σ_ext dλ = π²γ, γ the orientation-averaged polarisability of a conducting prolate spheroid of the body's volume and height. Seam: jump = d·B/R; angle = d·B/(R(R+B)); lag = v·τ; pitch = θ_eye·R. Rain: Λ = 4.1R^−0.21, D₀ = 3.67/Λ, flux = R/V(D₀), hits = flux × 0.12 m². Heat: dT/dt = P/(m·c); leak = kAΔT/th; elec = leak/COP; budget = (m_ice·L + m·c·ΔT)/(P + elec). Breath: 6 L/min at 34 °C saturated, sensible + latent. Footprint: T_c by effusivities; ΔT(t) = ΔT_c(√t − √(t − t_c))/√t_c. All pinned by scripts/thermoptic-tune.mjs.

Where this instrument takes liberties

The tolerance that turns 'cloaked' into a number is a dial, and the detour is the least a cylinder allows: real cloak shells add to it, so the bound is generous. The transmission is a top-hat band against a top-hat line, a coarse share. The display suit is drawn as a perfect Lambertian screen with one reference eye; a real one would also fail on brightness, on colour and on the wearer's own shadow. The body is human-sized and human-warm; a cyborg's actuators would raise the heat bill. The footprint model is a flux pulse into dry concrete with no wind. The alley, the façade, the mannequin and the splash sprites are drawn. Nothing is fitted to make a point; the film's behaviour comes out of the physics first.

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