Sensing Plane: Fundamentals and Innovations

Updated 2 July 2026

Sensing plane is the interface where observables (e.g., light, charge) are converted into measurable signals, defining key performance metrics.
They are implemented in diverse systems such as focal-plane sensors in adaptive optics, pupil-plane wavefront sensors, and direct charge-collection in TPCs.
Engineered architectures and algorithmic inversion methods enable real-time adaptability and high-resolution recovery crucial for multi-domain sensing applications.

A sensing plane is defined as the physical or effective plane within an experimental apparatus, instrument, or optical system at which physical information (e.g., electromagnetic field, thermal gradient, charge, or other observable) is directly quantified, transduced, or otherwise mapped to a measurable output. In contemporary research, the realization and engineering of specialized sensing planes—whether in the context of photonic, electronic, or multi-physical sensing—are central to achieving performance targets such as sensitivity, background-rejection, dynamic range, and environmental adaptability. The sensing plane’s physical, functional, or information-theoretic definition is dictated by the measurement modality, sensor technology, and application domain.

1. Fundamentals and Physical Realizations of Sensing Planes

A sensing plane is instantiated wherever the observable of interest is transduced into a form suitable for measurement with the requisite spatial, temporal, and spectral fidelity.

Focal-Plane Sensing The focal plane is the canonical sensing plane in optical systems where the intensity distribution encodes phase aberrations, speckles, or scene structure. In adaptive optics, the focal-plane wavefront sensor (FPWFS) defines its sensing plane at the science or calibrated image plane, into which the modulated pupil field is Fourier-transformed. This configuration ensures direct measurement of phase-induced speckle structures—critical for non-common-path aberration (NCPA) correction and high-contrast imaging (Vievard et al., 2020, Bos et al., 2021, Dou et al., 2015).
Pupil-Plane Sensing The reimaged telescope pupil serves as the sensing plane for devices such as Shack–Hartmann, pyramid, and INGOT wavefront sensors. Here, the spatial intensity pattern encodes derivatives (slopes) of the phase (Ragazzoni et al., 2020).
Direct Charge-Sensing Plane In ton-scale time projection chamber (TPC) experiments, the sensing plane is a tiled, segmented plane of CMOS charge-collection nodes that directly record drifted ionization tracks, eschewing gain amplification. The physical plane is defined by the array of electrodes (e.g., Topmetal pixels) at the end of a gaseous or liquid drift volume (Mei et al., 2020).
Meta- and Expanded-Plane Architectures Reconfigurable expanded-plane structures in thermal sensing realize the sensing plane by extending the field sampling into stacked, high-conductivity “planes” or “rings,” allowing adjustable in-plane conductivity and thus dynamic field-matching across various backgrounds (Tan et al., 2024).
Plasmonic Sensing Planes Surface plasmon resonance (SPR) sensors employing graphene mono/bilayers engineer the active sensing plane as the atomically thin 2D material at which plasmon-exciton interaction—and analyte adsorption—directly perturbs the evanescent field (Kumar et al., 2022).

2. Optical Sensing Planes: Design and Performance Implications

In high-contrast astronomical imaging, the focal-plane or an engineered intermediate plane downstream of the coronagraph is used for wavefront control.

Chromatic Invariance via Dispersive Optics The Wyne corrector utilizes a composite lens system located between a Lyot stop and focal plane to maintain the point-spread function (PSF) size across Δλ/λ₀ ≈ 50%, exploiting the dependence of each triplet's net optical power on wavelength to counteract speckle magnification, thereby extending the usable bandwidth of focal-plane sensors and boosting closed-loop operation rates by ×50 for the same photon flux (Sanchez et al., 2024).
Interaction with Coronagraphs and Apodizers The spatially-clipped self-coherent camera (SCSCC), introduced for high-contrast coronagraphy, splits the sensing plane into two parallel measurement channels (interferometric and non-interferometric) via a knife-edge downstream of a Lyot stop. This configuration enables single-frame recovery of the speckle electric field, crucial for deep, time-resolved contrast optimization (to ~4×10⁻¹⁰ at 5–20 λ/D) (Liberman et al., 4 Sep 2025).
Multimodal and Photonic Integration MMF-based and lantern-based FPWFS define the sensing plane at the fiber input facet, converting the 2D focal-plane field into modal intensities that encode phase aberrations. Neural networks or analytical inversion methods then reconstruct the low-order (Zernike) coefficients rapidly and without NCPA (Padrón-Brito et al., 3 Oct 2025, Lin et al., 2022).

3. Mathematical Models Linking Sensing Plane Measurements to Physical Quantities

Measurement at the sensing plane generally entails physical and algorithmic mappings of observable distributions (voltage, charge, light intensity) to spatially resolved variables of interest.

Optical FPWFS The connection between measured focal-plane intensity and pupil-plane phase is given, for example, by

$I(x,y) = \left|\mathcal{F}\{A(\rho,\theta)e^{i\varphi(\rho,\theta)}\}(x,y)\right|^2,$

where the challenge lies in the nonlinear, non-bijective mapping between the low-order coefficients $\{a_j\}$ and measured $I(x,y)$ (Taheri et al., 2024, Dou et al., 2015).

Photonic Lantern Sensing Intensity outputs at N single-mode ports ( $p_{\rm out}$ ) relate linearly (for small aberrations) to modal phase coefficients:

$p_{\rm out} \approx p_0 + B' a,$

where $B'$ is the Jacobian matrix, and $a$ are the phase mode amplitudes. The nonlinear regime is treated by higher-order tensor expansions for improved fidelity (Lin et al., 2022).

Direct Charge Sensing in TPCs The energy resolution in charge-collecting planes is dictated by collective noise properties as

${\rm FWHM} = 2.355 \cdot \sigma_E / Q_{\rm total},$

with $\sigma_E = \sigma_n \sqrt{N}$ , $\sigma_n$ being per-pixel noise, and $\{a_j\}$ 0 the number of hit pixels (Mei et al., 2020).

4. Reconfigurability, Universal Matching, and Environmental Adaptation

Modern sensing plane architectures increasingly incorporate reconfigurable or universal-match features to address the demands for robustness and adaptability.

Expanded-Plane Dynamic Thermal Sensing The expanded-plane sensor allows real-time mechanical tuning of effective in-plane conductivity $\{a_j\}$ 1 by varying the stack height $\{a_j\}$ 2 of copper rings, thereby matching the sensor's perceived conductivity to the background medium and minimizing field distortion:

$\{a_j\}$ 3

achieving sub-0.5% error and dynamic operation over $\{a_j\}$ 4 spanning 338–380 W/mK (Tan et al., 2024).

Charge Sensing Planes with Gas Modality Swapping CMOS-based charge-sensing planes in TPCs enable rapid hardware-free swapping between Xe and highly electronegative SeF₆ operation, simply by adjusting bias and sample timing, allowing cross-checks of candidate signals and backgrounds (Mei et al., 2020).

5. Information Processing and Algorithmic Inversion at the Sensing Plane

The computational framework applied to the raw data from the sensing plane determines achievable spatial, temporal, and modal resolution.

Machine Learning Inversion in FPWFS Architectures such as ResNet-18 or custom convolutional neural networks are trained to invert nonlinear mappings between PSFs and Zernike phases, enabling robust recovery of low-order aberrations directly from focal-plane images under realistic noise and sampling conditions. Practically, RMSE <60 nm and $\{a_j\}$ 5 0.9 are attained on telescope data (Taheri et al., 2024, Padrón-Brito et al., 3 Oct 2025).
Interaction Matrix and Regularization Interaction matrices (e.g., $\{a_j\}$ 6 or $\{a_j\}$ 7 above) facilitate control and reconstruction via Tikhonov or SVD-regularized pseudo-inverses, with regularization parameters set empirically or by minimizing cross-talk and noise sensitivity (Liberman et al., 4 Sep 2025, Gerard et al., 2023).
Single-Exposure and Sequential Algorithms Algorithms such as Fast & Furious provide sequential, non-iterative phase recovery linked to focal-plane DM diversity, or single-shot field recovery via spatially multiplexed fringe sensing (Bos et al., 2021, Liberman et al., 4 Sep 2025).

6. Performance Metrics, Constraints, and Application Domains

Performance at the sensing plane is quantified by metrics such as energy or phase resolution, linearity range, contrast, and recovery rate.

Sensing Plane Type	Metric	Value/Range
Focal-plane (Wyne corrector)	Spot dispersion (Δd)	<1.8 µm over 36% Δλ/λ₀
CMOS direct charge plane	FWHM energy resolution	<1% at Qββ
Expanded-plane thermal	Temp. dist. error	<0.5 K on 20 K grad.
FPWFS, deep-contrast (SCSCC)	Dark-hole contrast	~4×10⁻¹⁰ at 5–20 λ/D
FPWFS (AI, IR)	Zernike RMSE	30–60 nm
PLWFS (lantern)	Lin. range (Zernike RMS)	<0.35–0.45 rad

Performance is contingent on spectral bandwidth, NCPA suppression, calibration stability, and environmental compatibility, with implications from laboratory to astroparticle and biomedical sensing (Sanchez et al., 2024, Mei et al., 2020, Tan et al., 2024, Liberman et al., 4 Sep 2025).

7. Sensing Planes in Emerging and Hybrid Systems

Recent expansions include metasurface reflection planes for NLOS (non-line-of-sight) imaging, where the sensing plane—realized as periodic passive electromagnetic skins—enables stroboscopic, multi-angle synthetic aperture imaging in previously inaccessible regions by coordinated beam and angular sweeps (Bellini et al., 2024).

In integrated sensing and communication systems, a two-dimensional pilot matrix generated in the delay–Doppler plane serves as an information-theoretic sensing plane, with physical instantiation through resource allocations in time–frequency space. This enables high-resolution parametric estimation coexistent with data communication under orthogonality and minimal resource overhead (Yuan, 2024).

The sensing plane unifies physical, engineering, and computational dimensions of measurement, directly controlling the ultimate performance, adaptability, and interpretability of sensors across modern scientific and technological domains.