Thermal Dynamic Sensing Scheme

• Thermal dynamic sensing is a methodology that probes temperature and heat flow using physical interactions such as thermal diffuse scattering and Raman photon ratios.
• It employs algorithmic workflows including Fourier analysis, cross-correlation fitting, and machine learning regression to extract transient thermal signals with high accuracy.
• Various platforms like SEM-based nanothermometry, fiber-optic distributed sensing, and quantum probes demonstrate significant improvements in spatial and temporal resolution.

A thermal dynamic sensing scheme is a methodology or device architecture that dynamically probes temperature, heat flow, or related thermodynamic quantities with high temporal, spatial, or sensitivity performance. Such schemes span a wide range of platforms, from ultrafast nanothermometry in electron microscopes and fiber-based distributed temperature sensing, to on-chip photonic microresonators, quantum probe protocols, and algorithmically adaptive materials-based sensors. The following discussion synthesizes key classes, mechanisms, algorithmic workflows, and performance boundaries of contemporary thermal dynamic sensing schemes as established in leading research.

1. Physical and Theoretical Principles of Dynamic Thermal Sensing

Thermal dynamic sensing exploits the interaction of thermal excitations with physical, electronic, or optical degrees of freedom, enabling quantitative reconstruction of temperature and its evolution from observables that are sensitive to heat-driven dynamics.

In scattering-based electron microscopy approaches, such as EBSD-based nanothermometry, temperature information is encoded via thermal diffuse scattering (TDS) of backscattered electrons, which manifests as increased smearing or softening of electron diffraction (Kikuchi) bands. The Debye–Waller relation describes the reduction in coherent intensity:

$\frac{I}{I_0} = \exp(-2Bs^2)$

where $B(T)$ is the Debye–Waller factor increasing with temperature, and $s$ is the diffraction vector (Gnabasik et al., 7 Jul 2025).

In fiber-optic schemes, the anti-Stokes to Stokes intensity ratio of Raman backscattered photons encodes the temperature via the Bose–Einstein phonon occupancy, which is locally mapped along the fiber length by precise time-of-flight (OTDR) methods:

$$T(x)=\frac{\Delta E}{k_B \ln(C \cdot I_S(x)/I_{AS}(x))}$$

where $I_S$ and $I_{AS}$ are Stokes and anti-Stokes intensities (Cochet et al., 14 Nov 2025).

Quantum dynamic sensing analyzes the quantum Fisher information (QFI) for thermal probe states subject to unitary encoding, showing that the attainable sensitivity bounds depend on the non-commutativity of the encoding generator and the probe Hamiltonian, with the QFI scaling as $(\beta t)^2 \|[G,H]\|^2$ for inverse temperature $\beta$ and evolution time $t$ (Zhang et al., 2 Dec 2025).

Thermal dynamic sensors frequently exploit time-dependent changes (e.g., fast heat-induced lattice expansion, time-resolved electron transport, modulation of radiative properties) to distinguish the dynamical thermal signature from static backgrounds, enhance signal-to-noise, or resolve transient events.

2. Algorithmic and Analytical Methods

Thermal dynamic schemes implement diverse signal extraction and data analysis pipelines optimized for the underlying measurement physics.

• Fourier analysis of electron diffraction patterns: In EBSD-based nanothermometry, the 2D Fourier transform of the whole EBSD image is radially integrated to extract a 1D spectrum $A(k;T)$. The normalized amplitude at the spatial frequency where temperature-induced change is maximized ($k_0$) is used as the thermometer signal; the temperature coefficient $\alpha$ links $\Delta A/A$ to $\Delta T$ (Gnabasik et al., 7 Jul 2025).
• Raman S/AS ratio calibration: Distributed fiber sensors utilize calibration procedures to map photon-timing bins to spatial positions, and fit the measured ratio signal to invert the local temperature, incorporating compensation for instrument response and photon statistics (Cochet et al., 14 Nov 2025).
• Full-pattern cross-correlation fitting: In transmission Kikuchi diffraction thermometry (KDTh), each acquired Kikuchi pattern is matched with simulated patterns (varying lattice parameter), and best-fit shifts are converted into temperature using the material coefficient of thermal expansion (Chen et al., 16 Oct 2025).
• Phase-sensitive detection and harmonic discrimination: AC-driven schemes, such as the 2$\omega$ Thomson method, spectrally decompose the voltage response of a current-carrying wire under an imposed temperature gradient, isolating the second-harmonic voltage proportional to the Thomson coefficient and thus to the spatial temperature gradient (Dunn et al., 2018).
• Machine learning regression: For high-accuracy junction temperature inference, neural network models are trained to map transient electrothermal features (e.g., TSEP signals, circuit parameters) to corrected temperature, incorporating compensation for self-heating, parameter coupling, and distributional noise (Zhang et al., 9 Jan 2025).

3. Platform-Specific Implementations and Representative Devices

Thermal dynamic sensing is realized across a variety of technological platforms, each leveraging distinctive physics and optimized readout.

• SEM-based Nanothermometry: Using a high-performance direct electron detector in a 10 keV SEM, EBSD patterns are acquired, normalized, Fourier-transformed, and analyzed to yield nanometric spatial temperature maps with $\sim$0.15%/K simulated and 0.14%/K measured sensitivity; pixel-level temperature uncertainty is $\sim$13–14 K with 10 s acquisition and $\sim$40 nm spatial precision (Gnabasik et al., 7 Jul 2025).
• Fiber-based Distributed Temperature Sensing: In Raman OTDR sensors applied to PCB thermography, a single-mode fiber is routed with cm-scale pitch, with sub-ns laser pulses and SNSPD photon counting enabling $\sim$3 cm spatial and 2 °C temperature resolution (5 min integration). Cryogenic operation maintains $<1$ K precision at 77 K (Cochet et al., 14 Nov 2025).
• Resonant Photonic Microdevices: PDMS-coated silica microtoroid sensors achieve $S_\mathrm{max}=0.151$ nm/K sensitivity (order-of-magnitude over bare SiO2), with temperature resolution $10^{-4}$ K and ms-scale dynamic response (Li et al., 2010).
• Proximity Josephson Junctions: In ABS-engineered graphene JJs, both threshold (switching) and inductive (resonator) readout schemes are employed. Critical current sensitivity up to $|dI_c/dT|\cdot I_c^{-1}=0.6$ K$^{-1}$ is observed at $T \sim$50 mK in Ti-based devices, supporting GHz-bandwidth calorimetry (Jung et al., 10 Mar 2025).
• Cryogenic Transition Edge Sensors: Broadband radiometric thermometry via impedance-matched superconducting microstrip links and TES detection yields sub-mK resolution and ms-scale time constants, with differential calibration eliminating wiring and systematic drift (Goldie et al., 2011).
• Dynamic thermal emission modulation: Mid-IR thermal emission is dynamically modulated (by phase-change, optical, or carrier-injection mechanisms), demodulated by lock-in detection—enabling sub-mK detection with lock-in-limited bandwidths determined by the modulation mechanism (Picardi et al., 2022).

4. Performance, Resolution, and Sensitivity Limits

The performance of a thermal dynamic sensing scheme is encapsulated by metrics such as spatial/temporal resolution, thermal sensitivity, uncertainty, and mapping throughput.

Platform/Method	Resolution	Sensitivity/Limit	Mapping Speed/Remark
EBSD-Fourier (SEM) (Gnabasik et al., 7 Jul 2025)	~40 nm	0.14%/K; 14 K/pixel uncertainty (10 s)	$\sim$10 s/pixel
Fiber Raman OTDR (Cochet et al., 14 Nov 2025)	3 cm	2 °C (5 min, RT); 1 K (77 K)	Temporal resolution $\sim$1 min
KDTh-TKD (SEM) (Chen et al., 16 Oct 2025)	$\leq$10 nm	2.2 K$/\sqrt{\mathrm{Hz}}$	24–49 ms/pixel
PDMS microtoroid (Li et al., 2010)	N/A	0.15 nm/K; $10^{-4}$ K resolution	ms timescales
TES radiometry (Goldie et al., 2011)	$\mu$m	0.5 mK measured	3 s/measurement, ms response
JJs (threshold/inductor) (Jung et al., 10 Mar 2025)	N/A	$0.6\,\,\mathrm{K}^{-1}$ responsivity	GHz dynamic response
Dynamic emission (Picardi et al., 2022)	N/A	sub-mK (modulated), ppm gas detection	Bandwidth set by actuator

Spatial resolution is fundamentally limited by probe size/interaction volume (SEM), photon mean-free path (fiber optic), or device dimensions. Temporal resolution often trades off with signal-to-noise (integration time) or detector bandwidth.

Sensitivity is set by the slope of the thermal response, random noise (detector, photon statistics), and, in quantum schemes, by the commutator norm between the probe Hamiltonian and the parameter-encoding generator (Zhang et al., 2 Dec 2025).

5. Advantages, Challenges, and Limitations

Advantages:

• Non-contact and non-invasive operation (electron/photonic/fiber schemes).
• Sub-diffraction-scale mapping (SEM, KDTh).
• Broad temperature range, including cryogenic (TES, fiber OTDR).
• Integration with existing device metrologies (SEM, PCB, photonics).
• Compatibility with dynamic or real-time monitoring.

Challenges and Limitations:

• Speed: SEM-based and some photonic schemes have limited per-point readout due to integration/statistics.
• Sample requirements: Crystallinity and pattern contrast (KDTh, EBSD); fiber routing and index matching (OTDR).
• Thermal gradients can introduce stress/strain artifacts in diffraction/band geometry (Gnabasik et al., 7 Jul 2025).
• Instrumentation complexity (SNSPDs, direct electron detectors).
• For dynamic emission, limitations arise from actuator modulation rates and long-term material cyclability (Picardi et al., 2022).
• In distributed approaches, spatial resolution constrained by pulse width and detector jitter (Cochet et al., 14 Nov 2025).

6. Emerging Strategies and Outlook

Optimizations across schemes are advancing rapidly:

• Machine learning is anticipated to further exploit full-pattern data in diffraction-based thermometry, potentially reducing exposure times and extracting higher-order correlations (Gnabasik et al., 7 Jul 2025).
• Hardware developments such as faster electron detectors, sub-100 ps Raman pulses, and improved sensor integration are pushing dynamic range and spatial/temporal resolution boundaries (Cochet et al., 14 Nov 2025).
• Quantum dynamic sensing is approaching fundamental bounds derived from commutator norm scaling of quantum Fisher information, providing a theoretical limit for all thermal dynamic quantum protocols (Zhang et al., 2 Dec 2025).
• Methods integrating reconfigurability or adaptivity in material thermal conductivity offer universal matching to unknown or varying backgrounds, critical for robust deployment in heterogeneous systems (Tan et al., 7 Jan 2024).
• New application domains involve privacy-preserving human sensing with thermal arrays, contactless occupancy or health monitoring, and non-invasive device diagnostics at both nano- and macro-scales (Zhang et al., 26 Sep 2024).

Thermal dynamic sensing thus encompasses a suite of methodologies unifying advanced physical insight, sophisticated analysis, and hardware innovations to address the metrological demands of next-generation device engineering and fundamental thermal science.