DeCAL: Diverse Systems Across Domains

• DeCAL is a multifaceted label representing distinct systems in radio astronomy, optical calibration, neutron detector design, and clinical active learning.
• In radio interferometry, DDECAL uses a directional-solving algorithm with spectral smoothness constraints to enhance 21-cm foreground subtraction.
• Other implementations, such as DECal for DECam calibration and DECAL for patient-aware active learning, provide precision and efficiency in their respective fields.

Across the arXiv literature, DeCAL and closely related capitalizations denote several domain-specific systems rather than a single standardized method. The label appears most prominently as DDECAL, a LOFAR direction-dependent calibration algorithm for 21-cm Epoch of Reionisation analysis (Gan et al., 2022); DECal, a spectrophotometric calibration system for DECam on the CTIO Blanco 4 m telescope (Marshall et al., 2013); DECal, the Detector Efficiency Calculator for thin-film thermal-neutron detectors (Basañez et al., 2018); and DECAL, DEployable Clinical Active Learning, a patient-aware active-learning framework for medical imaging (Logan et al., 2022). Additional exact and near-homographic usages include a DECAL Digital Electromagnetic Calorimeter sensor prototype (Aslanis et al., 2 Sep 2025), DA-Cal for cross-domain calibration in semantic segmentation (Li et al., 24 Feb 2026), DEC for deep equilibrium canonicalization (Rahman et al., 19 Aug 2025), DECaLS as the Dark Energy Camera Legacy Survey (Yao et al., 2023), and graphics usages of decal in surface-conforming visualization and texture painting (Mota et al., 14 Sep 2025, Lim et al., 2024).

1. Major expansions and domain separation

The supplied literature uses closely related labels for distinct technical objects. The intended referent is therefore domain-specific.

Label	Expansion or meaning	Domain
DDECAL	Direction-Dependent Calibration	LOFAR 21-cm calibration
DECal	spectrophotometric calibration system for DECam	optical astronomy instrumentation
DECal	Detector Efficiency Calculator	thermal-neutron detector design
DECAL	DEployable Clinical Active Learning	medical machine learning
DECAL	Digital Electromagnetic Calorimeter sensor prototype	detector electronics / TRNG study

This distribution of meanings is not merely orthographic. Each usage attaches the label to a different technical stack: radio interferometric gain solving, telescope-throughput metrology, analytical neutron-detector efficiency optimization, clinically constrained sample acquisition, or sensor-noise characterization. Closely related names such as DECaLS, DA-Cal, and DEC are separate labels with their own expansions and should be distinguished on first use in technical writing (Yao et al., 2023, Li et al., 24 Feb 2026, Rahman et al., 19 Aug 2025).

2. DDECAL in LOFAR Epoch of Reionisation calibration

In low-frequency radio interferometry, DDECAL is explicitly expanded as Direction-Dependent Calibration and is implemented inside DP3 as a LOFAR calibration algorithm for solving direction-dependent complex gains in wide-field 21-cm observations (Gan et al., 2022). Its motivation is the standard EoR calibration problem: the foreground sky is many orders of magnitude brighter than the 21-cm signal, while LOFAR station-beam and ionospheric effects vary across the field of view. The paper frames the problem through the radio interferometric measurement equation,

$$V_{ij\nu t} = J_{i\nu t}\: C_{ij\nu t} \: J^\mathrm{H}_{j\nu t} + N_{ij\nu t},$$

and, for a clustered sky with $K$ solved directions,

$$V_{ij\nu t} = \sum_{k=1}^{K} J_{ik\nu t}\: C_{ijk\nu t} \: J^\mathrm{H}_{jk\nu t} + N_{ij\nu t}.$$

Within this formulation, DDECAL uses a directional-solving algorithm that solves for all directions for one element at a time, unlike SAGECAL, which solves for all elements in one direction at a time.

The study emphasizes two technical features. First, DDECAL regularizes gains through a spectral smoothness constraint implemented by Gaussian smoothing during each iteration; 4 MHz smoothing performed better for sky subtraction than 1 MHz. Second, DDECAL was run with the LOFAR HBA station beam model applied (usebeammodel in DP3), so calibration used an intrinsic sky model rather than an apparent one. This beam-model inclusion is the paper’s main practical explanation for DDECAL’s improved subtraction in the primary-beam region. The solver can use normal equations, QR, or SVD, and the implementation reports QR decomposition as a good speed/accuracy compromise.

The empirical comparison was performed on LOFAR HBA observation L612832 from 2017-10-02/03, covering 113.8657–127.1469 MHz for about 11.6 h, with analysis of the NCP and the RA 18h flanking field. In the flanking-field setup, the sky model was clustered into 20 directions, with Cassiopeia A and Cygnus A added as separate directions, giving either a 1-step or 2-step subtraction workflow. The clearest result was asymmetric: DDECAL performed better in the primary beam region, while SAGECAL performed better on the bright far sidelobe sources Cas A and Cyg A. The paper attributes the former mainly to beam modeling and notes that time- and frequency-smearing corrections were applied only for SAGECAL, which likely helped the latter. After Gaussian Process Regression foreground removal, however, the final post-GPR power spectra became comparable, and the authors conclude that the current LOFAR-EoR 21-cm power-spectrum limits are not likely to depend strongly on whether DDECAL or SAGECAL is used (Gan et al., 2022).

3. DECal as the DECam spectrophotometric calibration system

In optical instrumentation, DECal is the calibration system built for the CTIO Blanco 4 m telescope to support DECam and the photometric requirements of the Dark Energy Survey (Marshall et al., 2013). Its stated purpose is twofold: daily broadband flat-field calibration to correct pixel-to-pixel detector sensitivity variations, and regular narrowband spectrophotometric calibration to measure the wavelength-dependent response of the entire telescope+instrument system. The system was developed because DES required about 1% photometric accuracy (0.01 mag) over the survey, and standard photometric calibration alone was not sufficient to track throughput changes from filter transmission, coating degradation, detector response, and related wavelength-dependent effects.

The architecture consists of three main parts sharing a common projection target: a Lambertian flat-field screen, a broadband LED flat-field subsystem, and a monochromator-based spectrophotometric subsystem. The screen is a 2×4 grid of 4 ft × 8 ft aluminum honeycomb panels coated with Labsphere Duraflect, with a 4.64 m white circular active region and a surrounding black ring to suppress dome stray light. The broadband subsystem uses LEDs chosen for the DES grizy bands, plus a planned u-band LED, with selected wavelengths 365 nm, broad warm white, 650 nm, 780 nm, 905 nm, 970 nm, and 1030 nm, mounted at four locations around the top of the telescope ring. The narrowband subsystem uses a Horiba iHR-320 monochromator, a custom 75 m 87-fiber line-to-spot bundle, four projection units, a custom RPC Photonics engineered diffuser producing a 20° half-angle cone with >80% of the light within the full 40° cone, Hamamatsu S2281 calibrated photodiodes, and a monitor spectrometer.

Operationally, the DECam implementation is designed for

$300 < \lambda < 1100~\mathrm{nm},$

with approximately ~1 nm bandwidth in the abstract and 1–10 nm bandwidth in the spectrophotometric section, controlled by slit width. The monitor spectrometer measures central wavelength and FWHM to 0.1 nm precision. The paper stresses that DECal measures the relative instrumental response, not absolute throughput in physical units. Broadband flats are intended daily, while spectrophotometric scans are intended roughly once per month. Because the monochromator is relatively faint, the paper estimates peak output power = 2 mW, corresponding to about 800 photons s$^{-1}$ pixel$^{-1}$ at DECam and about 1 minute per exposure, and expects the spectrophotometric measurements to be best taken on a cloudy night. Prototype systems on the Swope 1 m and du Pont 2.5 m telescopes achieved about 1% accuracy, which is the principal quantitative performance result supporting the DECal design (Marshall et al., 2013).

4. DECal as Detector Efficiency Calculator

In neutron instrumentation, DECal is the Detector Efficiency Calculator, an open-source Python tool for the analytical calculation, visualization, and optimization of thermal neutron detector efficiency for detectors using thin-film solid converters, with the implementation in the paper focused on $^{10}$B-based detectors and especially $^{10}$B$_4$C coatings (Basañez et al., 2018). The tool addresses the standard design problem that a single thin $^{10}$B$K$0C layer has only modest efficiency, so practical detector design depends on converter thickness, back-scattering versus transmission geometry, double-coated blade configuration, number of blades, incidence angle $K$1, neutron wavelength $K$2, and energy threshold.

The implemented model supports single layer, single blade, and multi-blade / multi-layer stack configurations. A blade is a substrate coated on one or both sides with converter material, and the paper distinguishes back-scattering layer, transmission layer, and double-coated blade geometries. DECal packages the earlier analytical theory into both a Python library and a GUI application. The software is built around the functions efficiency4boron and efficiency2particles, with main classes Detector, Blade, and B10. High-level functions include calculate_eff_multiblade(...), calculate_eff_json(path), plot_eff_vs_thick(path), plot_eff_vs_wave(path), optimize_config_same_thick(originPath, destinyPath), and optimize_config_diff_thick(originPath, destinyPath). The code can be run through a GUI or from the command line, and the core library is installable via pip install neutron_detector_eff_functions.

The tool’s outputs include total detector efficiency, separate back-scattering and transmission efficiencies for single-layer configurations, per-blade efficiencies in depth order, and efficiency plots as functions of converter thickness, wavelength, and blade number. It also supports optimization for a single wavelength or a wavelength distribution. For polychromatic optimization, the paper notes an important approximation from the underlying theory: optimizing using the barycenter of the wavelength distribution is a sufficient approximation to the full optimum. A significant stated limitation is that the material and thickness of the substrate are not considered in the calculations presented here and will be the topic of a future improvement. DECal is therefore best understood as an analytical design-and-optimization environment rather than a full transport simulation (Basañez et al., 2018).

5. DECAL as DEployable Clinical Active Learning

In medical machine learning, DECAL expands to DEployable Clinical Active Learning and is proposed as a clinical active-learning framework intended to make standard image-based active-learning methods more realistic for medical deployment (Logan et al., 2022). Its central premise is that clinical decisions use bi-modal information—diagnostic images together with electronic medical record (EMR) context—whereas conventional active-learning methods for natural images assume the relevant attributes are contained within the image alone. In the implementation studied, the only EMR-derived variable actually used is patient identity, and DECAL injects this information as a plug-in constraint so that queried samples come from unique patient IDs.

DECAL is presented as a wrapper around standard pool-based active learning rather than a new acquisition function. The framework leaves the underlying image model and scoring method intact, but modifies initialization and batch construction so that queried samples better reflect intra-class, inter-patient diversity. The paper evaluates DECAL with random, entropy, margin, least confidence, and BADGE acquisition strategies, and emphasizes that it does not introduce a joint image-EMR neural fusion architecture. The combination of image and EMR happens at the active-learning control layer: image modality drives model predictions and acquisition scores, while EMR imposes a patient-aware constraint.

Experiments are reported on two medical-image datasets: retinal OCT scans with classes CNV, DME, and Drusen, and chest X-Ray images with classes healthy, viral pneumonia, and bacterial pneumonia. The evaluation uses ResNet-18, ResNet-50, and DenseNet-121, with no pretrained models, across 20 rounds of active learning. The abstract reports that DECAL increases generalization across 20 rounds by approximately 4.81%. As an initialization strategy, it yields a 5.59% increase in average accuracy for OCT and 7.02% for X-Ray. The active-learning results were achieved using 3000 (5%) samples of OCT data and 2000 (38%) samples of X-Ray data. The paper is explicit about its scope: the framework is bi-modal in the workflow/interface sense, not as a learned multimodal encoder, and the experiments use only patient identity from the EMR side (Logan et al., 2022).

6. Additional exact and near-homographic usages

A further exact usage appears in detector electronics, where DECAL denotes a Digital Electromagnetic Calorimeter sensor prototype studied as a possible entropy source for true random number generation (Aslanis et al., 2 Sep 2025). The device is a DMAPS prototype with a $K$3 pixel matrix, $K$4 pixel pitch, and a $K$5 epitaxial layer. In the reported TRNG pipeline, repeated threshold scans are fitted by Gaussian distributions, the sequence of fitted means is modeled by ARIMA(3,1,5), the estimated residuals are thresholded at zero to form bits, and the resulting bitstreams pass the reported NIST tests. The principal limitation is throughput: 100000 scans require about 310 minutes, yielding about $K$6 bps, which the paper identifies as too low for practical real-time TRNG use under the current configuration.

Several near-homographic labels also generate confusion. DECaLS is the Dark Energy Camera Legacy Survey, not a calibration acronym. In one paper it is the weak-lensing shear catalog used for DESI galaxy-galaxy lensing, with a footprint overlap of about $K$7 and an average source density of about $K$8 (Yao et al., 2023). In another, Galaxy Zoo DECaLS 5 provides morphology labels for 253,287 DECaLS galaxies that are transferred to BASS/MzLS through unsupervised domain adaptation (Ye et al., 2024). Both are survey-data usages of DECaLS, not instances of DECal/DECAL.

Machine-learning literature contains additional related acronyms with distinct expansions. DA-Cal is Domain-Adaptation Calibration for unsupervised domain adaptation in semantic segmentation; it reformulates target-domain calibration as soft pseudo-label optimization with a Meta Temperature Network and bi-level optimization (Li et al., 24 Feb 2026). DEC is Deep Equilibrium Canonicalizer, a method for improving local scale equivariance and invariance in pretrained backbones such as ViT, DeiT, Swin, and BEiT (Rahman et al., 19 Aug 2025). These works are orthographically close to DeCAL but technically separate.

Graphics literature uses decal in a different sense again. The 3De lens paper builds on a Decal lens specialized for surface-area selection, defining the surface patch as

$K$9

and fusing this surface-following component with a volumetric 3D lens for multi-geometry visualization in virtual reality (Mota et al., 14 Sep 2025). The Reverse Projection paper presents a real-time local-space texture-mapping method for painting a decal directly into an object’s texture, emphasizing persistent texture-space stamping rather than a calibration system (Lim et al., 2024). These graphics usages belong to surface-conforming visualization and texture painting, not to the calibration, detector-design, or active-learning meanings summarized above.