Scan-Free Nanometre Depth Sensing

• Scan-free nanometre resolution depth sensing is a method that uses optical wavefront manipulation, nonlinear effects, and computational techniques to capture depth in a single shot.
• Techniques such as spectral encoding, coherent interference, and metasurface engineering achieve resolutions from sub-nanometre to a few nanometres with high precision.
• Applications span semiconductor metrology, biophysics, and medical diagnostics, offering non-destructive 3D imaging with chemical specificity and high-speed measurement.

Scan-free nanometre resolution depth sensing encompasses a class of optical, computational, and tactile techniques capable of resolving depth at nanometre or near-nanometre scales without mechanical scanning of the sample or sensor. These methods leverage tailored physical phenomena—such as wavefront manipulation, nonlinear optics, spectral encoding, coherent interference, and deep computational architectures—to encode depth information into a single-shot measurement or a parallel acquisition. Advances in scan-free depth sensing have enabled high-speed, high-precision, non-contact, and chemically specific 3D imaging across condensed-matter physics, semiconductor manufacturing, biophysics, and medical diagnostics.

1. Physical Principles Underlying Scan-Free Depth Sensing

At the core of scan-free nanometre resolution depth sensing are approaches that encode spatial (including depth) information into optical or tactile signals that can be acquired in parallel or at high speed. Techniques include:

• Wave Front Shaping & Speckle Interferometry: A spatial light modulator (SLM) alters the phase of incident light to generate an “optical fingerprint” focused through a complex scattering medium. The overlap between the fingerprint and the medium’s instantaneous configuration is quantified by changes in detected focal intensity, given by $$I_0(\Delta r) = \eta I_{\text{bg}} [\gamma(\Delta r)]^2$$ where $$\gamma(\Delta r)^2 = [2 J_1(k_{\text{max}} \Delta r)/(k_{\text{max}}\Delta r)]^2$$ for displacement $\Delta r$ (Putten et al., 2011).
• Nonlinear Optical Correlation: In rapid nanometre-precision autocorrelation, two ultrashort pulses are overlapped in a nonlinear crystal (e.g., BBO) and the intensity change in sum-frequency generated light is recorded on a camera. The intensity dependence on delay yields depth with sub-nanometre standard error after statistical estimation (Morland et al., 2022).
• Extreme Ultraviolet (EUV) Phase-Sensitive Reflectometry: Coherent EUV light, shaped by high-harmonic generation, impinges on a layered nanostructure at controlled angles. Phase shifts in reflectometry encode depth and chemical specificity, reconstructed via variable-angle ptychographic imaging and genetic algorithm fitting (Tanksalvala et al., 28 Mar 2024).
• Metasurface and PSF Engineering: Custom-patterned metasurfaces (TiO₂, Si₃N₄) manipulate incident wavefronts to impart depth-dependent phase rotations or double-helix PSFs, which can be decoded via neural networks or software to recover depth metrics with fractional errors of order $1.7\%$ (Colburn et al., 2019, Li et al., 20 Mar 2025).
• Chromatic Confocal Profilometry: Diffractive optical elements introduce wavelength-dependent focus depths; spectral decomposition at each pixel reconstructs surface profiles with repeatability of 120 nm (Nguyen et al., 2018).
• Frequency-Resolved Two-Photon Interference: In quantum-limited delay sensing, frequency-resolved Hong-Ou-Mandel interferometry extracts delay (thus depth) information from oscillatory spectral interference: $$P_{\text{FR}}(\Delta t, \Delta \omega) = \frac{1}{2}\mathcal{C}(\Delta \omega)[1 + \delta\eta^2\cos(\Delta \omega \Delta t)]$$ extending dynamic range by more than an order of magnitude (Brooks et al., 26 Sep 2025).

2. Optical and Algorithmic Architectures

A diverse set of architectures enable scan-free nanometre depth sensing:

• Non-Imaging Photodiodes and Superposition Fingerprinting: Optical fingerprints are spatially programmed and superposed so that differential intensity changes (measured by GHz bandwidth photodiodes) directly encode position changes at nanometre resolution. Sensitivity is set by $$S_{\text{opt}} = (5.8 \text{NA} \eta / \lambda) I_{\text{bg}}$$ (Putten et al., 2011).
• Ptychographic Phase Retrieval and Regularization: Overlapping diffraction patterns, corrected for experimental tilt and processed via total variation regularization and genetic algorithms, reconstruct chemically specific 3D profiles with axial precision of 2 Å (Tanksalvala et al., 28 Mar 2024).
• Software Decoding of Engineered PSFs: Metasurface depth cameras and polarization-multiplexed systems generate depth-dependent point spread functions. Scene reconstruction applies total-variation regularized deconvolution, and PSF orientation analysis (using Gouy phase or neural correlators) yields a transverse depth map (Colburn et al., 2019, Li et al., 20 Mar 2025).
• Learning-Based Tactile Reconstruction: High-resolution GelSight sensors with custom gels encode fine topographic details into images. A convolutional neural network predicts surface normals, which are then Poisson-integrated and processed to yield wrinkle depth estimates at $\sim$12 µm MAE (Padmanabha et al., 14 Sep 2025).
• Transformer and CNN-Based Super-Resolution: Depth map super-resolution models, e.g., Swin-DMSR and NAF-DMSR, exploit transformer attention mechanisms or simplified convolutional blocks to fuse RGB guidance and sparse depth priors, facilitating scan-free upscaling to near-nanometre resolution (Peterson et al., 2023).
• Event-Driven Adaptive Sensing: Event-guided depth sensors modulate illumination density according to detected activity, focusing sensing power on moving objects to achieve near-nanometre resolution (especially valuable in dynamic or sparse scenes) (Muglikar et al., 2021).

3. Performance Metrics and State-of-the-Art Achievements

Nanometre and sub-nanometre depth resolution have been empirically validated across multiple platforms:

Technique	Achieved Depth Resolution	Acquisition Mode	Reference
Non-imaging speckle interferometry	2.1 nm	High-speed, scan-free	(Putten et al., 2011)
Rapid autocorrelator (sCMOS+BBO)	<1 nm (SE, 30 s, 1024 px)	Parallel, scan-free	(Morland et al., 2022)
EUV ptychographic imaging reflectometry	2 Å	Multiframe, scan-free	(Tanksalvala et al., 28 Mar 2024)
Chromatic confocal profilometer	120 nm	Full-field, one-shot	(Nguyen et al., 2018)
Frequency-resolved HOM microscopy	~nm over mm dynamic range	Quantum, scan-free	(Brooks et al., 26 Sep 2025)
GelSight tactile imaging probe	12.55 µm (MAE)	Contact, scan-free	(Padmanabha et al., 14 Sep 2025)
Metasurface neural depth camera	Metric resolution, $<2\%$ fractional error	Single-shot	(Colburn et al., 2019, Li et al., 20 Mar 2025)

Notably, scan-free methodologies are often bounded by photon budgets, sensor noise (e.g., Fano factor), and calibration stability but generally achieve better speed, form factor, or parallelization than raster-scanned or mechanical methods.

4. Comparative Advantages and Domain-Specific Impact

Scan-free nanometre resolution techniques offer several advantages over traditional scanned depth imaging:

• Non-contact and Non-destructive: EUV imaging reflectometry, coherent pop-out metrology, and metasurface depth cameras avoid mechanical stress or sample alteration, enabling sensitive inspection of fragile or dynamic specimens (Tanksalvala et al., 28 Mar 2024, Balakrishnan et al., 2022, Colburn et al., 2019).
• High Speed and Wide Dynamic Range: Methods utilizing parallel spectral correlation (Nguyen et al., 2018), event-guided adaptive sensing (Muglikar et al., 2021), and frequency-resolved quantum protocols (Brooks et al., 26 Sep 2025) provide rapid depth extraction, adaptability, and dynamic range unattainable with conventional raster scanning.
• Chemical and Modal Specificity: Phase-sensitive reflectometry is uniquely capable of resolving chemical composition (dopant profiles) concurrent with geometric features (Tanksalvala et al., 28 Mar 2024).
• Miniaturization and CMOS Compatibility: Metasurface-based cameras and neural decoders showcase form factors suited for mobile, embedded, or consumer platforms (Colburn et al., 2019, Li et al., 20 Mar 2025).

Applications include wafer and device metrology, dynamic cellular imaging, autonomous navigation (AR/VR, robotics), in-vivo skin diagnostics, and quantum material characterization.

5. Measurement and Calibration Strategies

Precise scan-free depth sensing typically requires:

• Direct quantitative mapping from optical signals (intensity, phase, spectral shifts, PSF orientation, neural features) to metric depth. For instance, $$z = (1/2) \cdot (\phi(\Lambda) \cdot \Lambda / 2\pi)$$ for synthetic-wavelength interferometry (Ballester et al., 2022), or $h = \phi/(2k \sin\theta)$ for phase-to-height conversion in EUV reflectometry (Tanksalvala et al., 28 Mar 2024).
• Statistical estimation theory for error reduction, as in averaging pixelwise autocorrelation measurements (Morland et al., 2022).
• Algorithmic phase unwrapping, regularization, and optimization—including total variation denoising, genetic algorithm fitting, and PSF analysis—underpin robust and artefact-free reconstructions (Tanksalvala et al., 28 Mar 2024, Colburn et al., 2019, Peterson et al., 2023).
• Calibration protocols leveraging reference objects (spherical indenters for tactile sensors, spectral calibration for profilometers, ground truth for neural models) to ensure real-world depth correspondence (Padmanabha et al., 14 Sep 2025, Nguyen et al., 2018).

A plausible implication is that with further improvements in calibration and noise suppression, these systems may approach shot-noise or quantum limits in real-time operation.

6. Limitations, Controversies, and Future Directions

Current limitations include:

• Material and field-of-view constraints: Some optical methods are limited by NA, sample roughness, or localized field of view—though metasurface and chip-based approaches are progressing toward scalable wide-field coverage (Liu et al., 2019, Li et al., 20 Mar 2025).
• Computational overhead and data management: Deep neural architectures, spectral analysis, and phase retrieval can be resource-intensive, but advances in hardware and algorithmic efficiency are mitigating bottlenecks (Peterson et al., 2023).
• Environmental sensitivity: Calibration drift, temperature changes, and mechanical vibrations affect measurement reliability, necessitating environmental controls or real-time recalibration (Nguyen et al., 2018, Tanksalvala et al., 28 Mar 2024).
• Generalization and sensor bias: Sensor-agnostic depth estimation via depth prompting modules demonstrates that systematic biases (density, pattern, range) can impair generalization but can be suppressed by explicit disentanglement of depth and image features (Park et al., 20 May 2024).

Future research directions include integration with larger pre-trained foundation models, further miniaturization for consumer deployment, enhanced chemical specificity down to atomic layers, and adaptation for new quantum and biological applications. Emerging modalities such as quantum-limited delay sensing and fusion of tactile and optical signals suggest that depth sensing will continue to expand in precision, speed, and versatility.