Initial commit: he11lib mode-purity reconstruction library
Full implementation of Laguerre-Gauss modal reconstruction for gyrotron beam diagnostics, per the approved design spec, plus tests, docs, and a runnable end-to-end example. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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Martino Ferrari
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# he11lib API Reference
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`he11lib` reconstructs the Laguerre-Gauss (LG) modal content ("mode purity")
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of a free-space-propagating gyrotron RF beam from a set of thermal (flux)
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images taken at different distances from the output window.
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See `examples/full_pipeline_example.py` for a runnable end-to-end
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demonstration, and
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`docs/superpowers/specs/2026-07-02-gyrotron-mode-purity-design.md` for the
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full design rationale.
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Every class/function below is exported from the top-level `he11lib` package
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(e.g. `from he11lib import BeamReconstructor`), except where noted.
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## Quick start
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```python
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from he11lib import BeamReconstructor, MeasurementPlane
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# planes: a list of >=3 MeasurementPlane objects built from your own
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# flux arrays (see MeasurementPlane below).
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reconstructor = BeamReconstructor(w0=5e-3, z0=0.5, wavelength=1.76e-3)
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result = reconstructor.reconstruct(planes)
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for mode, (power_fraction, phase_rad) in result.purity.items():
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print(mode, power_fraction, phase_rad)
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```
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## `data` — `MeasurementPlane`, `ReconstructionResult`
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### `MeasurementPlane(flux, z, pixel_scale=None, viewing_angle_deg=None, label=None)`
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One measurement: a 2D flux array plus its acquisition metadata.
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- `flux` — 2D `np.ndarray` of flux values. Dead-pixel correction, background
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subtraction, and saturation clipping are assumed already handled upstream.
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- `z` — nominal distance from the output window, in meters. Must be `> 0`.
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- `pixel_scale` — known meters/pixel, or `None` if unknown (then jointly
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fit by `ModalFitter`/`BeamReconstructor`).
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- `viewing_angle_deg` — known camera viewing angle relative to the beam
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axis, in degrees, or `None` if unknown (also jointly fit).
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- `label` — optional human-readable identifier.
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### `validate_planes(planes)`
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Raises `ValueError` if there are fewer than 3 planes, planes have
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mismatched flux shapes, or `z` values are not all distinct. Called
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internally by `ModalFitter.fit`/`fit_auto`, `PhaseRetriever.retrieve`, and
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`BeamReconstructor.reconstruct` — you generally don't need to call it
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yourself. Not exported from the top-level package; import via
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`from he11lib.data import validate_planes` if needed.
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### `ReconstructionResult`
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Output of a full reconstruction (returned by `ModalFitter.fit`/`fit_auto`
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and `BeamReconstructor.reconstruct`):
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- `purity: dict[(p, l), (power_fraction, phase_rad)]`
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- `reconstructed_field: np.ndarray` — reconstructed complex field.
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- `centers: list[(x, y)]` — fitted beam transverse center per plane, meters.
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- `pointing_angle_deg: float` — fitted shared beam pointing angle (tilt).
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- `geometry: dict[str, float]` — geometry parameters used or fitted (keys
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`pixel_scale_{i}`, `viewing_angle_deg_{i}` per plane index `i`).
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- `residuals: list[np.ndarray]` — per-plane (measured − modeled) flux maps.
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Empty when `used_phase_retrieval` is `True`.
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- `coefficient_uncertainty: dict[(p, l), float]` — 1-sigma uncertainty on
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each mode's fitted power fraction. `NaN` per mode when
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`used_phase_retrieval` is `True`.
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- `used_phase_retrieval: bool` — whether the phase-retrieval fallback (not
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the modal fit) produced this result.
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## `modes` — `LGBasis`
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`LGBasis(w0, z0, wavelength)` — the LG mode basis referenced to a known
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waist radius `w0` (m), waist location `z0` (m), and radiation `wavelength`
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(m).
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- `beam_radius(z)` — `w(z)`.
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- `inverse_radius_of_curvature(z)` — `1/R(z)` (well-defined, `0`, at the
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waist).
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- `gouy_phase(z, p, l)` — Gouy phase of mode `(p, l)` at `z`.
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- `field(x, y, z, p, l)` — complex `LG_{p,l}` field sampled on the `(x, y)`
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grid at distance `z`.
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- `field_superposition(x, y, z, coefficients)` — complex field for
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`coefficients: dict[(p, l), complex]`.
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- `project(complex_field, x, y, dx, z, modes)` — projects `complex_field`
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onto each `(p, l)` in `modes`, returning `dict[(p, l), complex]`
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coefficients (Riemann-sum inner product; `dx` is the grid spacing).
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## `geometry` — `GeometryCalibration`
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`GeometryCalibration(plane)` wraps a single `MeasurementPlane` and resolves
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its pixel-to-physical-coordinate mapping.
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- `pixel_scale_known` / `viewing_angle_known` — `bool` properties.
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- `physical_coordinates(pixel_scale=None, viewing_angle_deg=None)` —
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returns `(x, y)` physical coordinate grids matching the plane's flux
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shape. Values known on the `MeasurementPlane` take precedence over the
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`override` arguments; raises `ValueError` if a value is neither known nor
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overridden.
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## `noise` — `NoiseEstimator`
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`NoiseEstimator()` — automatic per-image noise estimation (no
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user-supplied noise parameter needed).
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- `estimate_std(image)` — fast Laplacian-based (Immerkær 1996) noise
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standard-deviation estimate.
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- `weights(image)` — per-pixel weights (`1/sigma**2`) for noise-weighted
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least squares.
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## `deconvolution` — `DiffusionDeconvolver`
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`DiffusionDeconvolver(thermal_diffusivity, dwell_time)` — optional
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correction for lateral thermal-diffusion blur in the absorbing target
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(`thermal_diffusivity` in m²/s, `dwell_time` in s). Disabled unless you
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pass a `deconvolver` to `BeamReconstructor`.
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- `blur_sigma_m()` — Gaussian blur standard deviation, in meters.
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- `blur(image, pixel_scale)` — forward blur (for synthetic testing).
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- `deconvolve(image, pixel_scale, noise_to_signal_ratio=1e-3)` — regularized
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(Wiener) removal of the blur.
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Note: the blur/deconvolution kernel is isotropic in pixel space. If a
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plane has a nonzero `viewing_angle_deg`, its `x` and `y` pixel axes have
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different physical scales (see `SyntheticBeamGenerator` below), so
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deconvolution is only exact for `viewing_angle_deg == 0`; at oblique
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angles it is an approximation.
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## `synthetic` — `SyntheticBeamGenerator`
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`SyntheticBeamGenerator(basis, image_shape, pixel_scale)` — forward model
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used to validate the pipeline against known ground truth, and to evaluate
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experimental design (e.g. "would these distances separate my modes?").
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`pixel_scale` is the physical pixel size, in meters, along the non-tilted
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`y` axis; the `x` axis is compressed by `1/cos(viewing_angle_deg)` to model
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an oblique camera view.
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- `generate(coefficients, z_list, *, center=(0, 0), pointing_angle_deg=0.0, viewing_angle_deg=0.0, noise_std=0.0, seed=None)`
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— returns one `MeasurementPlane` per `z` in `z_list`. The beam's
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transverse center drifts linearly with `z` according to
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`pointing_angle_deg`, starting from `center` at `z0`.
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## `fitting` — `ModalFitter`, `generate_mode_shells`
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### `generate_mode_shells(max_order)`
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Groups candidate `LG_{p,l}` modes into shells of increasing order
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`2p + |l|`, up to and including `max_order`. Returns
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`list[list[(p, l)]]`, one list of modes per order.
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### `ModalFitter(basis, noise_estimator=None)`
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Core reconstruction path: a joint nonlinear least-squares fit of complex LG
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coefficients, beam center/pointing, and (if unknown) geometry.
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- `fit(planes, modes, initial_coefficients=None, initial_center=(0.0, 0.0), initial_tilt_deg=(0.0, 0.0), initial_pixel_scale=None, initial_viewing_angle_deg=0.0) -> ReconstructionResult`
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— fits exactly the given candidate `modes`.
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- `fit_auto(planes, max_order=4, bic_improvement_threshold=10.0) -> ReconstructionResult`
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— starts from `LG_00` and grows the candidate mode set shell-by-shell
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(via `generate_mode_shells`), stopping once BIC no longer improves by
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more than `bic_improvement_threshold`, capped at `max_order`. Emits a
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`UserWarning` (does not raise) if the cap is reached while the fit is
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still improving.
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## `phase_retrieval` — `PhaseRetriever`, `propagate_angular_spectrum`
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Fallback reconstruction path for when the modal fit's residual stays high,
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or when the mode content isn't well described by a small finite mode set.
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### `propagate_angular_spectrum(field, dx, dz, wavelength)`
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Free-space-propagates a complex `field` (pixel spacing `dx`) by distance
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`dz` via the (paraxial) angular-spectrum method — the same propagation
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model implicitly assumed by `LGBasis`'s closed-form paraxial modes.
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### `PhaseRetriever(wavelength)`
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- `retrieve(planes, pixel_scale=None, viewing_angle_deg=None, max_iterations=200) -> PhaseRetrievalResult`
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— multi-plane Gerchberg-Saxton phase retrieval: propagates a trial
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complex field back and forth between planes, enforcing the measured
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amplitude (`sqrt(flux)`) at each plane, without assuming a finite mode
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basis.
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### `PhaseRetrievalResult`
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`field, x, y, z, center, residual` — the recovered complex field (at the
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smallest-`z` plane) on its `(x, y)` grid, the estimated beam center
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(intensity centroid), and the final RMS amplitude-mismatch residual.
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Project `field` onto `LGBasis` (via `LGBasis.project`) to get a purity
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table, as `BeamReconstructor` does internally for its fallback path.
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## `reconstruct` — `BeamReconstructor`
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`BeamReconstructor(w0, z0, wavelength, max_order=4, noise_estimator=None, deconvolver=None, force_phase_retrieval=False, phase_retrieval_residual_threshold=None)`
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High-level orchestrator wiring together the full pipeline: optional
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diffusion deblurring → `ModalFitter.fit_auto` → optional
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`PhaseRetriever` fallback.
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- `reconstruct(planes) -> ReconstructionResult`
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1. Validates `planes` (see `validate_planes`).
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2. If `deconvolver` is set, deblurs each plane (raises `ValueError` if a
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plane's `pixel_scale` isn't known).
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3. Runs `ModalFitter(basis, noise_estimator).fit_auto(planes, max_order)`.
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4. Runs the `PhaseRetriever` fallback instead, projecting its recovered
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field onto all modes up to `max_order`, if `force_phase_retrieval` is
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`True`, or if `phase_retrieval_residual_threshold` is set and the
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modal fit's noise-weighted RMS residual exceeds it. In that case
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`result.residuals` is empty and `coefficient_uncertainty` is `NaN`
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per mode (phase retrieval doesn't produce a fit covariance).
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## `plotting` — diagnostic visualizations
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Each function returns a `matplotlib.figure.Figure` for the caller to
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display (`fig.show()`) or save (`fig.savefig(...)`); none of them call
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`plt.show()` themselves.
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- `plot_mode_purity(result)` — bar chart of power fraction per mode.
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- `plot_center_trace(planes, result)` — fitted beam center `(x, y)` vs. `z`.
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- `plot_residuals(planes, result)` — per-plane residual maps. Raises
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`ValueError` if `result.residuals` is empty (e.g. after the
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phase-retrieval fallback).
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