Thermal detector

A thermal detector measures light by the heat it deposits. An absorber warms, and a temperature-sensitive transducer turns the rise into a voltage or current. Three transducers dominate: the thermopile, a chain of thermocouples read through the Seebeck voltage; the bolometer, whose resistance changes with temperature; and the pyroelectric detector, whose polarization changes with temperature and which therefore responds only to changing light. Because the signal depends only on absorbed energy, the response per watt is flat across any band in which the absorber is black, from the ultraviolet to the far infrared. The cost is speed and sensitivity: time constants are typically 10 ms for micromachined elements and a second or more for large power meter heads, and the noise floor at room temperature lies far above that of a cooled photon detector.

Thermal and photon detectors

A photodiode or other photon detector produces one carrier per absorbed photon, so at a fixed quantum efficiency its current responsivity rises in proportion to wavelength and drops to zero beyond the bandgap cutoff. A thermal detector has no cutoff and no wavelength dependence other than that of its absorber coating. This suits broadband radiometry, power measurements across many laser lines, and the 8–14 µm long-wave infrared, where photon detectors need cryogenic cooling to suppress dark current.

Time constant and responsivity

An absorber of heat capacity $C_{th}$, tied to a heat sink through a link of conductance $G_{th}$, obeys $C_{th}\,d(\Delta T)/dt = \eta P - G_{th}\,\Delta T$, where $\eta$ is the absorptance. Its step response is exponential with

$$\tau = \frac{C_{th}}{G_{th}},$$

and for sinusoidally modulated light the temperature response rolls off above $f_c = 1/(2\pi\tau)$. A pixel with $C_{th} = 10^{-9}$ J/K and $G_{th} = 10^{-7}$ W/K has $\tau$ = 10 ms and $f_c$ = 15.9 Hz. In steady state $\Delta T = \eta P/G_{th}$, so 10 nW absorbed by that pixel warms it by 0.1 K.

Responsivity is quoted in V/W (or A/W for pyroelectric elements in current mode):

$$\mathcal{R}_V(f) = \frac{\eta\,(dV/dT)}{G_{th}\sqrt{1 + (2\pi f\tau)^2}}.$$

For a resistive bolometer read out at a constant bias current $I_b$, $dV/dT = \alpha I_b R = \alpha V_b$, where $V_b$ is the bias voltage across it, where $\alpha$ is the temperature coefficient of resistance. With $|\alpha|$ = 0.02 K⁻¹, $V_b$ = 1 V, $\eta$ = 1 and the conductance above, the low-frequency responsivity is $2 \times 10^5$ V/W, ignoring electrothermal feedback. The trade-off is fixed by the formula: lowering $G_{th}$ raises the responsivity and lengthens $\tau$ in equal proportion, so a faster detector at the same sensitivity requires a smaller heat capacity, hence thin membranes suspended on narrow legs.

Noise limits

Even with a perfect readout, the energy in the absorber fluctuates because heat crosses the thermal link in discrete exchanges. This temperature-fluctuation noise gives a noise-equivalent power of

$$\mathrm{NEP}_{th} = \sqrt{4 k_B T^2 G_{th}}.$$

At 300 K with $G_{th} = 10^{-7}$ W/K it is 7.1 × 10⁻¹³ W/√Hz. Johnson noise in a bolometer resistor, 1/f noise in the sensing film and amplifier noise add to it, and in uncooled arrays the readout terms usually dominate. The lowest possible conductance is the radiative one: a detector at 300 K exchanging blackbody radiation with a 300 K hemisphere, with no other heat path, reaches a specific detectivity of about 1.8 × 10¹⁰ Jones. That figure is the background limit for any room-temperature thermal detector, independent of wavelength; photon detectors limited by background photons can exceed it within their band. Cryogenic bolometers reach far smaller NEPs by lowering $T$ and, with suitable materials, $G_{th}$.

Where thermal detectors are used

Thermopile heads are the standard sensors in broadband optical power meters for watt-level and kilowatt-level beams, with photodiode heads taking over at low power. Pyroelectric heads measure pulse energy, and DTGS pyroelectric elements are the standard room-temperature detectors in FTIR spectrometers, where the interferometer scan supplies the modulation. Uncooled microbolometer arrays form the focal planes of most thermal cameras, and single thermopiles sit in non-contact infrared thermometers and gas sensors.

Pitfalls

Anything that changes the absorber's temperature reads as signal: air currents, a hand near the head, a drift in ambient temperature, or heating of the housing by scattered light. Power meter heads need time to reach equilibrium and a zero taken with the beam blocked. Absorber coatings are never perfectly black, so calibration keeps a small wavelength dependence. Chopped or modulated signals above $f_c$ are attenuated, and pyroelectric detectors give no output at all for steady light.

Common questions

What is the difference between a thermal detector and a photon detector?

A photon detector converts each absorbed photon into a carrier, so its response depends on photon energy and stops at a cutoff wavelength. A thermal detector responds to absorbed power, nearly equally at all wavelengths, at the cost of speed and noise.

Why are thermal detectors slow?

The element must heat up and cool down through its thermal link, which takes $\tau = C_{th}/G_{th}$. Reducing $G_{th}$ for sensitivity lengthens $\tau$, so practical elements settle at milliseconds to seconds.

References: E. L. Dereniak and G. D. Boreman, Infrared Detectors and Systems (Wiley, 1996); P. W. Kruse, Uncooled Thermal Imaging: Arrays, Systems, and Applications (SPIE Press, 2001); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); P. L. Richards, "Bolometers for infrared and millimeter waves," Journal of Applied Physics 76, 1 (1994).