MetaCalibration in Weak Lensing

• MetaCalibration is a self-calibration technique for weak-lensing shear measurement that estimates shear-response directly from artificially sheared images.
• It integrates both measurement and selection responses to correct multiplicative and additive shear biases without heavy dependence on external simulations.
• Recent developments extend the framework to deep-field calibration, metadetection, harmonic-space analyses, and even machine-learning calibration strategies.

Searching arXiv for relevant papers on MetaCalibration in weak lensing and related usages. arxiv_search.query({"search_query":"all:metacalibration weak lensing", "start":0, "max_results":10}) arxiv_search.query({"search_query":"all:\"Meta-Calibration\" calibration neural networks", "start":0, "max_results":10}) MetaCalibration is primarily a self-calibration technique for weak-lensing shear measurement in which the response of a shape estimator is measured directly from imaging data by artificially shearing the images, remeasuring galaxy shapes, and inferring the shear-response matrix from finite differences. In this usage, it replaces or sharply reduces the dependence on external image simulations for calibrating multiplicative and additive shear biases, while also allowing selection effects to be propagated through the same response formalism (Huff et al., 2017). A separate machine-learning literature uses the near-homonymous term “Meta-Calibration” for a bilevel optimization framework that learns model calibration by minimizing a differentiable surrogate of expected calibration error on validation data (Bohdal et al., 2021).

1. Historical emergence and conceptual scope

The foundational weak-lensing formulation was given by Huff & Mandelbaum, who described MetaCalibration as “Direct Self-Calibration of Biases in Shear Measurement” and emphasized that the method infers multiplicative shear calibration parameters by modifying the actual survey data to simulate the effects of a known shear (Huff et al., 2017). In that formulation, the central motivation is that real images already contain the true morphology distribution, PSF structure, and noise properties of the survey, so the response of the estimator can be measured on the data themselves rather than transferred from an external simulation suite.

Sheldon & Huff then provided the practical formalism that made the method survey-grade. They introduced the treatment of shear response and selection response in a unified framework, and identified correlated noise produced by the deconvolution–shear–reconvolution cycle as a major low-$S/N$ issue, for which they developed an empirical correction. In their image simulations, including parametric models, real COSMOS galaxies, realistic PSFs, selection cuts, stellar contamination, and missing data, the recovered input shear was accurate to better than a part in a thousand in all tested cases (Sheldon et al., 2017).

Within survey pipelines, MetaCalibration became a fiducial shear-calibration strategy rather than a purely methodological proposal. In DES Year 1 it was one of two independent shear pipelines, and the resulting metacalibration catalogue was adopted as the fiducial source sample for cosmology because it combined self-calibration of selection and noise biases with higher effective number density than the alternative IM3SHAPE catalogue (Zuntz et al., 2017).

2. Core formalism and estimator structure

The starting point is a small-shear expansion of a two-component ellipticity or shape estimator. In the notation used across DES, SuperBIT, and related work, one writes

$$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$

The per-object shear-response matrix is then estimated by finite differences on artificially sheared images,

$$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$

with $\gamma_j=0.01$ in several practical implementations (Sheldon et al., 2017).

After averaging over a sample with random intrinsic orientations, the ensemble mean ellipticity is proportional to the ensemble response, and the mean shear is estimated from the response-corrected average ellipticity,

$$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$

DES Year 1 also wrote the calibrated per-bin shear estimate in the compact form

$$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$

with a bin-averaged response matrix used in practice for each tomographic bin (Camacho et al., 2021).

The full response includes not only the measurement response but also a selection response. In the DES and SuperBIT conventions,

$$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$

where $\langle \boldsymbol{R}^{S}\rangle$ is obtained by reapplying the sample selection on sheared images and finite-differencing the resulting mean ellipticity of the unsheared measurements. DES Y3 galaxy–galaxy lensing used this decomposition explicitly and reported bin-averaged total responses of $0.7682$, $0.7266$, $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$0, and $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$1 across its four source bins, with the response matrix essentially diagonal and isotropic (Prat et al., 2021).

Some implementations also track additive terms explicitly. In the SuperBIT pipeline, where reconvolution is performed with a slightly dilated rather than perfectly round PSF, the metacalibrated shear estimator includes additive corrections from galaxy shear and PSF shear,

$$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$2

with $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$3 (Saha et al., 19 Mar 2026).

3. Selection, noise, detection, and two-point propagation

A central advance of the practical formalism was the explicit inclusion of selection response. In DES Y1 and Y3, selections on $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$4, size, and tomographic bin assignment are shear-dependent and therefore enter the total response through $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$5. In DES Y1, selection response from source binning and related cuts was a percent-level correction, and in DES Y3 the response-factor approximation based on a single bin-averaged $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$6 per source bin produced negligible scale dependence, with differences between exact scale-dependent and bin-averaged estimators corresponding to $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$7 (Prat et al., 2017, Prat et al., 2021).

Noise is another defining issue. The deconvolution–shear–reconvolution sequence induces anisotropic correlated noise in the sheared images, and Sheldon & Huff introduced an empirical correction that adds an independent noise realization with the opposite shear, at the cost of doubling the noise variance in the metacalibrated images (Sheldon et al., 2017). “Deep-field metacalibration” was introduced to reduce that precision penalty by measuring the response on a deeper calibration survey while retaining the wide-field ellipticity measurements; it conservatively reduces the degradation in precision from $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$8 for standard metacalibration to $$\boldsymbol{e}(\boldsymbol{\gamma}) = \left.\boldsymbol{e}\right|_{\gamma=0} + \left. \frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\gamma}} \right|_{\gamma=0} \boldsymbol{\gamma} +\cdots \equiv \left.\boldsymbol{e}\right|_{\gamma=0} + \boldsymbol{R}^\gamma \boldsymbol{\gamma} +\cdots.$$9 or less and yields an equivalent calibration error of $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$0 from sample variance in LSST-like deep drilling fields (Zhang et al., 2022).

Blending exposed a distinct failure mode. Standard metacalibration applied to a fixed detection catalogue exhibits a few percent shear measurement bias for galaxy densities relevant for current surveys, and that bias increases with galaxy number density. Sheldon et al. showed that the dominant effect is not blending itself but shear-dependent object detection, and introduced “metadetection,” in which artificial shear is applied to larger image regions and detection is rerun on each sheared realization. In their realistic DES-like and LSST-like simulations, metadetection removed the detection bias, while an extreme scenario in which the space between objects was completely unsheared produced at most a few tenths of a percent bias for future surveys (Sheldon et al., 2019).

For harmonic-space analyses, response corrections do not propagate as a single global scalar. A full-sky treatment decomposes the spatially varying response into spin-0 and spin-4 fields $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$1 and $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$2, so that the observed ellipticity field obeys

$$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$3

This induces $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$4-mixing and $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$5 mixing in the power spectra. The “2-sphere pixel correction” approach requires local inversion of noisy response matrices and introduces a condition-number trade-off between area loss and noise amplification, whereas forward-modelling the power spectrum via response-field mixing matrices avoids that tuning parameter and the associated shot-noise amplification (Kitching et al., 2023).

A related analytical development concerns the renoising step. Li & Mandelbaum showed that within the AnaCal framework the Metacalibration renoising idea can recover shear to second order, $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$6, and in LSST-like simulations the resulting multiplicative bias is less than a few tenths of a percent without requiring external image-simulation-based calibration of shear (Li et al., 2024).

4. DES as the canonical large-survey implementation

DES Year 1 established MetaCalibration as a survey-scale production pipeline. The DES Y1 weak-lensing shape-catalogue paper described a metacalibration catalogue built from $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$7-band data with a Gaussian model and an internal calibration scheme, yielding $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$8 million objects over about $$R^\gamma_{ij} = \frac{e_i^{+}-e_i^{-}}{\Delta\gamma_j}, \qquad \Delta\gamma_j = 2\gamma_j,$$9 square degrees and a $\gamma_j=0.01$0 multiplicative-shear-calibration uncertainty of $\gamma_j=0.01$1 (Zuntz et al., 2017). In the companion galaxy–galaxy lensing analysis, after area and redshift cuts the fiducial metacalibration source sample used $\gamma_j=0.01$2 million galaxies in four tomographic bins over $\gamma_j=0.01$3, and the same catalogue underpinned the DES Y1 3$\gamma_j=0.01$42pt cosmological analysis (Prat et al., 2017).

The DES Y1 harmonic-space cosmic-shear analysis later reused the same metacalibration source catalogue in a pseudo-$\gamma_j=0.01$5 pipeline. That analysis covered a contiguous area of $\gamma_j=0.01$6, contained $\gamma_j=0.01$7 million galaxies, had $\gamma_j=0.01$8, used BPZ photo-$\gamma_j=0.01$9 to define four tomographic bins in $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$0, and treated the shear response as a $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$1 matrix $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$2 for each object while converting to calibrated shears with a bin-averaged response. Residual multiplicative uncertainties were encoded as nuisance parameters $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$3 for the four bins (Camacho et al., 2021).

DES Year 3 extended the same logic to higher-precision galaxy–galaxy lensing. The source catalogue consisted of $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$4 million galaxies in four tomographic bins, and the tangential-shear estimator used a single tomographic-bin-averaged response $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$5 per source bin. A direct test of scale-dependent response corrections found $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$6 for redMaGiC and $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$7 for MagLim over the full data vector, and even smaller differences after the $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$8 scale cuts, showing that scale dependence of the effective response was negligible for DES Y3 galaxy–galaxy lensing at that precision (Prat et al., 2021).

The DES validation program also established standard null tests for metacalibrated catalogues: cross-component $$\langle \boldsymbol{\gamma} \rangle \approx \langle \boldsymbol{R} \rangle^{-1} \langle \boldsymbol{e} \rangle.$$9 around lenses, PSF residual correlations, survey-property splits, and B-mode tests. In DES Y1, Metacalibration and IM3SHAPE were consistent in all such tests, and in the harmonic-space cosmic-shear analysis $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$0 and $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$1 were consistent with zero while shear–PSF cross-spectra and survey-property cross-correlations showed no significant residual contamination once scale cuts were applied (Prat et al., 2017, Camacho et al., 2021).

5. Extensions beyond DES: Roman, SuperBIT, UNIONS, and KiDS

Roman HLIS simulations tested MetaCalibration in an undersampled space-based regime with extremely stringent requirements. In simplified Roman-like simulations, the method calibrated shapes to $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$2. In the most realistic six-square-degree simulation suite, the constraints were much looser, with $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$3 for joint multi-band single-epoch measurements and $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$4 for multi-band coadd measurements; all were consistent with zero within $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$5–$$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$6, but the results were far from the Roman requirement of about $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$7, and blending was explicitly neglected (Yamamoto et al., 2022).

SuperBIT provided a distinct high-resolution application. Its weak-lensing catalogue for $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$8 merging clusters used metacalibration wrapped around ngmix, with selections in $$\hat{\vec{\gamma}}_i = \langle R_i\rangle^{-1}\,\vec e_i,$$9 and $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$0, a gridded shear response in $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$1–$$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$2 space, and realistic simulation-based validation. The fiducial gridded-response calibration yielded

$$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$3

This was the main quantification of residual multiplicative systematics for the current SuperBIT pipeline (Saha et al., 19 Mar 2026).

UNIONS/CFIS used metacalibrated shears for weak-lensing peak counts and emphasized spatially varying calibration. The survey adopted a local rather than purely global metacalibration scheme by tiling the field into non-overlapping square patches and computing local ensemble responses and additive terms in each patch; $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$4 patches were chosen as the fiducial compromise between locality and noise in the selection response. A residual multiplicative bias from simulations of isolated galaxies, $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$5, was then added as a conservative worst-case correction. Relative to a global calibration baseline, the combination of $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$6 local calibration and $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$7 shifted $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$8 by $$\langle \boldsymbol{R} \rangle = \langle \boldsymbol{R}^{\gamma}\rangle + \langle \boldsymbol{R}^{S}\rangle,$$9, corresponding to $\langle \boldsymbol{R}^{S}\rangle$0 (Ayçoberry et al., 2022).

KiDS-1000 later implemented MetaCalibration as an alternative to lensfit for cosmic shear. In that reanalysis, the final multiplicative biases satisfied $\langle \boldsymbol{R}^{S}\rangle$1 in all cosmology bins with negligible additive bias, the effective source density increased to $\langle \boldsymbol{R}^{S}\rangle$2, and the cosmological constraint became

$\langle \boldsymbol{R}^{S}\rangle$3

The resulting constraining power improved by about $\langle \boldsymbol{R}^{S}\rangle$4 relative to the KiDS-1000 lensfit analysis, while the remaining mild tension with Planck stayed at a similar level, implying that it was not caused by the shear measurements (Yoon et al., 1 Oct 2025).

6. Limitations, active developments, and secondary usage of the term

Across these applications, the main limitations recur with notable regularity. Detection bias is not automatically cured unless detection is itself included in the metacalibration process, motivating metadetection (Sheldon et al., 2019). High-shear regions violate the linear approximation: SuperBIT explicitly excluded the innermost radii where $\langle \boldsymbol{R}^{S}\rangle$5 in its shear-bias validation, and Roman analyses emphasized that current tests are confined to the weak-shear regime and isolated objects (Saha et al., 19 Mar 2026, Yamamoto et al., 2022). Residual multiplicative uncertainty is often prior-dominated rather than data-constrained, as in DES Y1, and PSF modeling remains an external requirement rather than something metacalibration eliminates (Camacho et al., 2021).

Methodological development has therefore focused on reducing the noise penalty, incorporating detection, and generalizing response propagation to map-level inference. Deep-field metacalibration addresses the variance cost of the standard renoising strategy (Zhang et al., 2022); the spherical forward-modelling framework treats response as a field rather than a constant and is especially relevant for power-spectrum analyses (Kitching et al., 2023); analytical renoising within AnaCal shows that Metacalibration-style response correction can be embedded in faster estimators without external calibration from image simulations for shear itself (Li et al., 2024).

The term also has a distinct, non-lensing usage in machine learning. There, “Meta-Calibration” denotes a framework with two components: a differentiable surrogate for expected calibration error, DECE, and a bilevel meta-learning scheme that optimizes validation-set calibration with respect to model hyper-parameters such as expressive label-smoothing parameters. In that literature the objective is not weak-lensing shear estimation but probabilistic calibration of neural-network confidence scores (Bohdal et al., 2021).

In the weak-lensing sense, MetaCalibration now denotes a family of response-based calibration methods centered on artificial image shearing, finite-difference response estimation, and explicit treatment of shear-dependent selection. Its modern extensions—metadetection, deep-field calibration, harmonic-space response propagation, and analytical renoising—show that the original self-calibration idea has evolved from a catalogue-level correction into a broader framework for response-aware inference across survey modalities and summary statistics (Huff et al., 2017).