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Initial commit: he11lib mode-purity reconstruction library

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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>
This commit is contained in:
Martino Ferrari
2026-07-02 21:47:40 +02:00
commit 03b63ba03a
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# Python
__pycache__/
*.py[cod]
*.egg-info/
.eggs/
build/
dist/
# Virtual environments
.venv/
venv/
# Test / tool caches
.pytest_cache/
.mypy_cache/
.ruff_cache/
# Editors
.vscode/
.idea/
# Claude Code local settings (machine-specific, not project config)
.claude/settings.local.json
CLAUDE.md
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# CLAUDE.md
This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
## What this is
`he11lib` reconstructs the Laguerre-Gauss (LG) modal content ("mode purity") of a
free-space-propagating gyrotron RF beam from a set of thermal (flux) images taken at
different distances from the output window. It accounts for camera geometry (unknown
pixel scale / oblique viewing angle), sensor noise, target thermal-diffusion blur, and
unknown beam center/pointing.
The full design rationale lives in
`docs/superpowers/specs/2026-07-02-gyrotron-mode-purity-design.md` — read it before
making architectural changes. `docs/api.md` is the API reference for the implemented
public interface; keep it in sync when changing public signatures.
## Commands
```bash
pip install -e ".[dev]" # editable install with test dependencies (numpy, scipy, matplotlib, pytest)
pytest # run the full test suite (discovers tests/, per pyproject.toml)
pytest tests/test_modes.py # run one test file
pytest tests/test_modes.py::test_field_at_waist # run one test
python examples/full_pipeline_example.py # runnable end-to-end demo
```
There is a project `.venv`; activate it or otherwise ensure the editable install's
dependencies are available before running tests.
`tests/conftest.py` forces the `Agg` matplotlib backend so plotting tests run headless.
This project is not (yet) a git repository.
## Architecture
Data flows through the pipeline as a list of `MeasurementPlane` (one per imaging
distance `z`), each holding a raw 2D `flux` array plus optionally-known
`pixel_scale`/`viewing_angle_deg`. Everything downstream is keyed off `LGBasis`, which
defines the mode basis relative to a known waist `w0`/`z0`/`wavelength`.
Module responsibilities (`he11lib/`):
- **`data.py`** — `MeasurementPlane`, `ReconstructionResult` (the shared input/output
types) and `validate_planes` (>=3 planes, matching shapes, distinct `z`).
- **`modes.py`** — `LGBasis`: closed-form paraxial LG fields, beam radius `w(z)`,
Gouy phase, inverse radius of curvature, and projection of a measured field onto a
candidate mode set. This is the analytic ground truth all fitting is checked against.
- **`geometry.py`** — `GeometryCalibration`: resolves a plane's pixel-to-physical
coordinate grid, deferring to known `pixel_scale`/`viewing_angle_deg` on the plane
over any override passed in.
- **`noise.py`** — `NoiseEstimator`: automatic per-image noise-std estimation
(Laplacian method) and per-pixel weights for noise-weighted least squares.
- **`deconvolution.py`** — `DiffusionDeconvolver`: optional forward blur / Wiener
deconvolution for thermal-diffusion blur in the absorbing target. The blur kernel is
isotropic in pixel space, so it's only exact when `viewing_angle_deg == 0` (an
oblique view makes x/y pixel scales differ) — an accepted approximation, not a bug.
- **`synthetic.py`** — `SyntheticBeamGenerator`: forward model that produces
`MeasurementPlane`s from known ground-truth coefficients/center/pointing/geometry.
Used throughout the test suite and examples to validate the pipeline end-to-end.
- **`fitting.py`** — `ModalFitter` (`fit`, `fit_auto`) and `generate_mode_shells`: the
core joint nonlinear least-squares fit (complex LG coefficients + beam
center/pointing + unknown geometry) via `scipy.optimize.least_squares`. `fit_auto`
grows the candidate mode set shell-by-shell (by order `2p + |l|`), stopping via a BIC
improvement threshold, capped at `max_order` (emits `UserWarning`, doesn't raise, if
still improving at the cap).
- **`phase_retrieval.py`** — `propagate_angular_spectrum` (FFT-based paraxial
free-space propagation) and `PhaseRetriever` (multi-plane Gerchberg-Saxton), the
fallback reconstruction path for when a finite mode basis doesn't fit well.
- **`reconstruct.py`** — `BeamReconstructor`: the orchestrator. Pipeline order:
validate planes → optional deconvolution (requires known `pixel_scale` per plane) →
`ModalFitter.fit_auto` → optional `PhaseRetriever` fallback (forced via
`force_phase_retrieval`, or triggered automatically when the noise-weighted RMS
residual exceeds `phase_retrieval_residual_threshold`). The fallback path projects
the recovered field onto all modes up to `max_order` and produces a
`ReconstructionResult` with `used_phase_retrieval=True`, empty `residuals`, and NaN
`coefficient_uncertainty` (no fit covariance available from phase retrieval).
- **`plotting.py`** — diagnostic figures (`plot_mode_purity`, `plot_center_trace`,
`plot_residuals`); each returns a `Figure` rather than calling `plt.show()`.
Everything above is re-exported from the top-level `he11lib` package (see
`he11lib/__init__.py`); import from there rather than submodules.
## Known physics/fitting pitfalls (read before writing new tests or examples)
These aren't library bugs — they're consequences of realistic optics parameters and of
automatic order-selection being genuinely data-driven — but they've caused most of the
debugging time in this project's history:
1. **Rayleigh-range / frame clipping.** `w(z)` grows with `|z - z0|` relative to
`zR = pi*w0**2/wavelength`. With typical test parameters (`w0=5e-3`,
`wavelength=1.76e-3`), `zR` is only ~4.46 cm, so z-distances spanning tens of cm put
the beam many Rayleigh ranges out, where `w(z)` can exceed a small test frame —
clipping the beam and corrupting fits, or introducing FFT wraparound artifacts in
`propagate_angular_spectrum`. Keep z-distances within roughly ±1-2 Rayleigh ranges of
`z0`, or enlarge the frame/pixel_scale accordingly.
2. **Automatic mode-set growth can overfit deconvolution artifacts.** Wiener-deconvolved
data always has some residual imperfection; `fit_auto`'s BIC-driven growth will try
to "explain" it with spurious higher-order modes, degrading fitted beam
center/pointing via parameter degeneracy (observed: pointing angle off by 4-6x at
`max_order=3` vs. matching ground truth almost exactly at `max_order=1`, for the same
2-mode ground truth). When demonstrating growth with deconvolution or noise, set
`max_order` close to the true expected mode content rather than generously high,
unless the test specifically targets growth behavior itself.
LICENSE
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README.md
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# he11lib
Mode purity reconstruction of a free-space-propagating gyrotron RF beam from a
set of thermal (flux) images taken at different distances from the output
window.
Decomposes the beam into Laguerre-Gauss (LG) modes referenced to a known
waist size/location/wavelength, accounting for camera geometry, sensor noise,
target thermal-diffusion blur, and unknown beam centering/pointing.
See `docs/api.md` for the full API reference and
`examples/full_pipeline_example.py` for a runnable end-to-end
demonstration, and
`docs/superpowers/specs/2026-07-02-gyrotron-mode-purity-design.md` for the
full design.
## Install (editable, for development)
```bash
pip install -e ".[dev]"
```
## Run tests
```bash
pytest
```
## License
GPL-3.0-or-later. See `LICENSE`.
## AI-assisted development disclosure
The initial implementation of this library (design, code, tests, and
documentation) was produced with AI assistance:
- **Model:** Claude Sonnet 5 (`claude-sonnet-5`)
- **Agent/harness:** Claude Code CLI, version 2.1.92
All output was reviewed and directed by a human collaborator throughout
development.
docs/api.md
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# he11lib API Reference
`he11lib` reconstructs the Laguerre-Gauss (LG) modal content ("mode purity")
of a free-space-propagating gyrotron RF beam from a set of thermal (flux)
images taken at different distances from the output window.
See `examples/full_pipeline_example.py` for a runnable end-to-end
demonstration, and
`docs/superpowers/specs/2026-07-02-gyrotron-mode-purity-design.md` for the
full design rationale.
Every class/function below is exported from the top-level `he11lib` package
(e.g. `from he11lib import BeamReconstructor`), except where noted.
## Quick start
```python
from he11lib import BeamReconstructor, MeasurementPlane
# planes: a list of >=3 MeasurementPlane objects built from your own
# flux arrays (see MeasurementPlane below).
reconstructor = BeamReconstructor(w0=5e-3, z0=0.5, wavelength=1.76e-3)
result = reconstructor.reconstruct(planes)
for mode, (power_fraction, phase_rad) in result.purity.items():
print(mode, power_fraction, phase_rad)
```
## `data` — `MeasurementPlane`, `ReconstructionResult`
### `MeasurementPlane(flux, z, pixel_scale=None, viewing_angle_deg=None, label=None)`
One measurement: a 2D flux array plus its acquisition metadata.
- `flux` — 2D `np.ndarray` of flux values. Dead-pixel correction, background
subtraction, and saturation clipping are assumed already handled upstream.
- `z` — nominal distance from the output window, in meters. Must be `> 0`.
- `pixel_scale` — known meters/pixel, or `None` if unknown (then jointly
fit by `ModalFitter`/`BeamReconstructor`).
- `viewing_angle_deg` — known camera viewing angle relative to the beam
axis, in degrees, or `None` if unknown (also jointly fit).
- `label` — optional human-readable identifier.
### `validate_planes(planes)`
Raises `ValueError` if there are fewer than 3 planes, planes have
mismatched flux shapes, or `z` values are not all distinct. Called
internally by `ModalFitter.fit`/`fit_auto`, `PhaseRetriever.retrieve`, and
`BeamReconstructor.reconstruct` — you generally don't need to call it
yourself. Not exported from the top-level package; import via
`from he11lib.data import validate_planes` if needed.
### `ReconstructionResult`
Output of a full reconstruction (returned by `ModalFitter.fit`/`fit_auto`
and `BeamReconstructor.reconstruct`):
- `purity: dict[(p, l), (power_fraction, phase_rad)]`
- `reconstructed_field: np.ndarray` — reconstructed complex field.
- `centers: list[(x, y)]` — fitted beam transverse center per plane, meters.
- `pointing_angle_deg: float` — fitted shared beam pointing angle (tilt).
- `geometry: dict[str, float]` — geometry parameters used or fitted (keys
`pixel_scale_{i}`, `viewing_angle_deg_{i}` per plane index `i`).
- `residuals: list[np.ndarray]` — per-plane (measured − modeled) flux maps.
Empty when `used_phase_retrieval` is `True`.
- `coefficient_uncertainty: dict[(p, l), float]` — 1-sigma uncertainty on
each mode's fitted power fraction. `NaN` per mode when
`used_phase_retrieval` is `True`.
- `used_phase_retrieval: bool` — whether the phase-retrieval fallback (not
the modal fit) produced this result.
## `modes` — `LGBasis`
`LGBasis(w0, z0, wavelength)` — the LG mode basis referenced to a known
waist radius `w0` (m), waist location `z0` (m), and radiation `wavelength`
(m).
- `beam_radius(z)` — `w(z)`.
- `inverse_radius_of_curvature(z)` — `1/R(z)` (well-defined, `0`, at the
waist).
- `gouy_phase(z, p, l)` — Gouy phase of mode `(p, l)` at `z`.
- `field(x, y, z, p, l)` — complex `LG_{p,l}` field sampled on the `(x, y)`
grid at distance `z`.
- `field_superposition(x, y, z, coefficients)` — complex field for
`coefficients: dict[(p, l), complex]`.
- `project(complex_field, x, y, dx, z, modes)` — projects `complex_field`
onto each `(p, l)` in `modes`, returning `dict[(p, l), complex]`
coefficients (Riemann-sum inner product; `dx` is the grid spacing).
## `geometry` — `GeometryCalibration`
`GeometryCalibration(plane)` wraps a single `MeasurementPlane` and resolves
its pixel-to-physical-coordinate mapping.
- `pixel_scale_known` / `viewing_angle_known` — `bool` properties.
- `physical_coordinates(pixel_scale=None, viewing_angle_deg=None)` —
returns `(x, y)` physical coordinate grids matching the plane's flux
shape. Values known on the `MeasurementPlane` take precedence over the
`override` arguments; raises `ValueError` if a value is neither known nor
overridden.
## `noise` — `NoiseEstimator`
`NoiseEstimator()` — automatic per-image noise estimation (no
user-supplied noise parameter needed).
- `estimate_std(image)` — fast Laplacian-based (Immerkær 1996) noise
standard-deviation estimate.
- `weights(image)` — per-pixel weights (`1/sigma**2`) for noise-weighted
least squares.
## `deconvolution` — `DiffusionDeconvolver`
`DiffusionDeconvolver(thermal_diffusivity, dwell_time)` — optional
correction for lateral thermal-diffusion blur in the absorbing target
(`thermal_diffusivity` in m²/s, `dwell_time` in s). Disabled unless you
pass a `deconvolver` to `BeamReconstructor`.
- `blur_sigma_m()` — Gaussian blur standard deviation, in meters.
- `blur(image, pixel_scale)` — forward blur (for synthetic testing).
- `deconvolve(image, pixel_scale, noise_to_signal_ratio=1e-3)` — regularized
(Wiener) removal of the blur.
Note: the blur/deconvolution kernel is isotropic in pixel space. If a
plane has a nonzero `viewing_angle_deg`, its `x` and `y` pixel axes have
different physical scales (see `SyntheticBeamGenerator` below), so
deconvolution is only exact for `viewing_angle_deg == 0`; at oblique
angles it is an approximation.
## `synthetic` — `SyntheticBeamGenerator`
`SyntheticBeamGenerator(basis, image_shape, pixel_scale)` — forward model
used to validate the pipeline against known ground truth, and to evaluate
experimental design (e.g. "would these distances separate my modes?").
`pixel_scale` is the physical pixel size, in meters, along the non-tilted
`y` axis; the `x` axis is compressed by `1/cos(viewing_angle_deg)` to model
an oblique camera view.
- `generate(coefficients, z_list, *, center=(0, 0), pointing_angle_deg=0.0, viewing_angle_deg=0.0, noise_std=0.0, seed=None)`
— returns one `MeasurementPlane` per `z` in `z_list`. The beam's
transverse center drifts linearly with `z` according to
`pointing_angle_deg`, starting from `center` at `z0`.
## `fitting` — `ModalFitter`, `generate_mode_shells`
### `generate_mode_shells(max_order)`
Groups candidate `LG_{p,l}` modes into shells of increasing order
`2p + |l|`, up to and including `max_order`. Returns
`list[list[(p, l)]]`, one list of modes per order.
### `ModalFitter(basis, noise_estimator=None)`
Core reconstruction path: a joint nonlinear least-squares fit of complex LG
coefficients, beam center/pointing, and (if unknown) geometry.
- `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`
— fits exactly the given candidate `modes`.
- `fit_auto(planes, max_order=4, bic_improvement_threshold=10.0) -> ReconstructionResult`
— starts from `LG_00` and grows the candidate mode set shell-by-shell
(via `generate_mode_shells`), stopping once BIC no longer improves by
more than `bic_improvement_threshold`, capped at `max_order`. Emits a
`UserWarning` (does not raise) if the cap is reached while the fit is
still improving.
## `phase_retrieval` — `PhaseRetriever`, `propagate_angular_spectrum`
Fallback reconstruction path for when the modal fit's residual stays high,
or when the mode content isn't well described by a small finite mode set.
### `propagate_angular_spectrum(field, dx, dz, wavelength)`
Free-space-propagates a complex `field` (pixel spacing `dx`) by distance
`dz` via the (paraxial) angular-spectrum method — the same propagation
model implicitly assumed by `LGBasis`'s closed-form paraxial modes.
### `PhaseRetriever(wavelength)`
- `retrieve(planes, pixel_scale=None, viewing_angle_deg=None, max_iterations=200) -> PhaseRetrievalResult`
— multi-plane Gerchberg-Saxton phase retrieval: propagates a trial
complex field back and forth between planes, enforcing the measured
amplitude (`sqrt(flux)`) at each plane, without assuming a finite mode
basis.
### `PhaseRetrievalResult`
`field, x, y, z, center, residual` — the recovered complex field (at the
smallest-`z` plane) on its `(x, y)` grid, the estimated beam center
(intensity centroid), and the final RMS amplitude-mismatch residual.
Project `field` onto `LGBasis` (via `LGBasis.project`) to get a purity
table, as `BeamReconstructor` does internally for its fallback path.
## `reconstruct` — `BeamReconstructor`
`BeamReconstructor(w0, z0, wavelength, max_order=4, noise_estimator=None, deconvolver=None, force_phase_retrieval=False, phase_retrieval_residual_threshold=None)`
High-level orchestrator wiring together the full pipeline: optional
diffusion deblurring → `ModalFitter.fit_auto` → optional
`PhaseRetriever` fallback.
- `reconstruct(planes) -> ReconstructionResult`
1. Validates `planes` (see `validate_planes`).
2. If `deconvolver` is set, deblurs each plane (raises `ValueError` if a
plane's `pixel_scale` isn't known).
3. Runs `ModalFitter(basis, noise_estimator).fit_auto(planes, max_order)`.
4. Runs the `PhaseRetriever` fallback instead, projecting its recovered
field onto all modes up to `max_order`, if `force_phase_retrieval` is
`True`, or if `phase_retrieval_residual_threshold` is set and the
modal fit's noise-weighted RMS residual exceeds it. In that case
`result.residuals` is empty and `coefficient_uncertainty` is `NaN`
per mode (phase retrieval doesn't produce a fit covariance).
## `plotting` — diagnostic visualizations
Each function returns a `matplotlib.figure.Figure` for the caller to
display (`fig.show()`) or save (`fig.savefig(...)`); none of them call
`plt.show()` themselves.
- `plot_mode_purity(result)` — bar chart of power fraction per mode.
- `plot_center_trace(planes, result)` — fitted beam center `(x, y)` vs. `z`.
- `plot_residuals(planes, result)` — per-plane residual maps. Raises
`ValueError` if `result.residuals` is empty (e.g. after the
phase-retrieval fallback).
docs/superpowers/specs/2026-07-02-gyrotron-mode-purity-design.md
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# he11lib — Gyrotron Beam Mode Purity Reconstruction
**Date:** 2026-07-02
**Status:** Approved for planning
## Purpose
A general-purpose, reusable Python library for reconstructing the Laguerre-Gauss
(LG) modal content ("mode purity") of a free-space-propagating gyrotron RF beam,
from a set of thermal (flux) images captured at different distances from the
gyrotron output window. The library must account for real-world measurement
issues: unknown/partial camera geometry, sensor noise, target thermal-diffusion
blur, and unknown beam pointing/centering — not just an idealized intensity fit.
This is a from-scratch library (empty project directory), intended to be used by
others beyond the initial author.
## Scope
- Beam regime: **free-space quasi-optical propagation** (post mode-converter /
output window), not waveguide-confined hybrid modes.
- Mode basis: **Laguerre-Gauss modes** `LG_{p,l}`, referenced to a **known**
waist size `w0` and waist location `z0` supplied by the user (design values
from the gyrotron/mode-converter specs) — these are inputs, not fit
parameters.
- Input data: **pre-processed NumPy flux arrays** (already extracted from raw
NVF radiometric camera files by the user's own pipeline). Dead-pixel
correction, background/ambient subtraction, and saturation-clipping detection
are already handled upstream and out of scope for this library. Because the
data is flux (not temperature), there is no temperature-to-power nonlinearity
to correct.
- Number of measurement planes: **3 to 10**, at distances spanning roughly
0–100 cm from the output window (e.g. 30/40/50/60 cm), known to a nominal
precision (set by a translation stage or tape measure).
- Camera geometry (pixel-to-length scale, viewing angle relative to beam axis):
may be **known from a prior calibration** (supplied as input) **or unknown**
(estimated jointly with everything else).
- Beam **transverse center and pointing angle** are always unknown and must be
estimated from the images.
- Residual sensor noise (NETD-type, after upstream preprocessing) is
**auto-estimated per image**; no user-supplied noise parameter required for
the default path.
- Target thermal-diffusion blur correction (deconvolution) is **optional**,
parametrized by target thermal diffusivity + exposure/dwell time.
- Deliverables include full API docs and an end-to-end example
script/notebook demonstrating the complete pipeline.
## Architecture
Modular/composable design: each concern is an independent, testable component
with a clear interface, wired together by a high-level orchestrator. This
supports both simple end-to-end use and power-user access to individual
stages (e.g., using `LGBasis` standalone, or swapping in a custom noise
model).
### Components
- **`data.py` — `MeasurementPlane`, `ReconstructionResult`**
`MeasurementPlane`: container for one measurement — flux array, nominal `z`
distance, optional known pixel scale (mm/px) and viewing angle (deg),
optional metadata (timestamp, label). `ReconstructionResult`: container for
all pipeline outputs (see below).
- **`geometry.py` — `GeometryCalibration`**
Applies projective/perspective correction to compensate for oblique camera
viewing angle, and converts pixel coordinates to physical length units. If
pixel scale and/or viewing angle are supplied on a `MeasurementPlane`, uses
them directly; if not supplied, exposes them as free parameters to be
solved jointly by the `ModalFitter`.
- **`noise.py` — `NoiseEstimator`**
Estimates residual per-image noise standard deviation automatically (e.g.
from low-signal/background regions or high-frequency residual content).
Produces per-pixel or per-image weights used by the `ModalFitter`'s
noise-weighted least squares.
- **`deconvolution.py` — `DiffusionDeconvolver`**
Optional step. Given target material thermal diffusivity and
exposure/dwell time, builds a blur kernel modeling lateral heat spreading
in the absorbing target and deconvolves it from each plane before fitting.
Disabled by default.
- **`modes.py` — `LGBasis`**
Given reference `w0`, `z0`, generates complex LG mode fields `LG_{p,l}(x,
y, z)` at arbitrary transverse coordinates and axial distance `z`,
including correct Gouy phase and beam-radius evolution. Supports
evaluating a finite candidate set of `(p, l)` indices and projecting an
arbitrary complex field onto the basis (used both by the modal fit and by
the phase-retrieval fallback).
- **`fitting.py` — `ModalFitter`**
Core reconstruction path. Parameters: complex LG coefficients
(amplitude + phase) for each candidate mode, beam transverse center `(x,
y)` per plane, a shared beam pointing angle (tilt), and any uncalibrated
geometry parameters (pixel scale / viewing angle) not supplied on the
`MeasurementPlane`s. Objective: noise-weighted nonlinear least-squares
residual between modeled `|Σ c_j · LG_j(x, y, z)|²` and measured flux,
summed over all planes.
**Automatic mode-set growth**: starts from `LG_00`, incrementally adds
candidate modes in shells of increasing order, and stops growing once an
information-criterion (e.g. BIC) / residual-reduction test shows no
meaningful improvement, subject to a configurable maximum order cap (for
tractability and as a safety bound). Warns (does not error) if the cap is
hit while still improving, or if final residuals remain large.
- **`phase_retrieval.py` — `PhaseRetriever`**
Optional/fallback path. Gerchberg-Saxton-style iterative multi-plane phase
retrieval: propagates a trial complex field back and forth between
measurement planes (via free-space propagation, e.g. angular spectrum),
enforcing the measured amplitude (sqrt of flux) at each plane, without
assuming a finite mode basis. Used when explicitly requested, or
automatically as a fallback when `ModalFitter`'s residual stays high after
mode-set growth completes. The recovered field is then projected onto
`LGBasis` to produce a purity table.
- **`synthetic.py` — `SyntheticBeamGenerator`**
Forward model: given known mode coefficients, `w0`/`z0`, geometry
(center, tilt, viewing angle, pixel scale), noise level, and optional
diffusion blur, generates synthetic multi-plane flux images. Used for
library validation (recover known ground truth) and for users to test
experimental design (e.g., "would these 4 distances separate my modes?").
- **`reconstruct.py` — `BeamReconstructor`**
High-level orchestrator: given a list of `MeasurementPlane`s and
configuration (known `w0`/`z0`, optional deconvolution params, optional
mode-set cap, optional forced phase-retrieval mode), runs geometry
correction → noise estimation → optional deconvolution → modal fit (with
automatic growth) → optional phase-retrieval fallback → produces a
`ReconstructionResult`. Each stage remains independently accessible for
power users.
- **`plotting.py`**
Diagnostic visualizations: measured vs. reconstructed intensity per plane,
residual maps, mode purity bar chart, beam center/pointing trace across
planes.
### Data flow
1. Build a list of `MeasurementPlane` objects (flux array + nominal z +
optional known geometry per plane).
2. `GeometryCalibration` applies projective correction using supplied
pixel-scale/viewing-angle, or flags them as unknowns.
3. `NoiseEstimator` computes per-plane noise weights.
4. `DiffusionDeconvolver` optionally deblurs each plane.
5. `ModalFitter` runs the joint noise-weighted nonlinear least-squares fit
over LG coefficients + center + pointing + any uncalibrated geometry
params, growing the mode set automatically.
6. If requested, or if fit residual remains high, `PhaseRetriever` runs as a
fallback and its result is projected onto `LGBasis`.
7. `BeamReconstructor` assembles a `ReconstructionResult` containing: mode
purity table (power fraction + phase per mode), reconstructed complex
field, fitted beam center/pointing per plane, geometry parameters used or
fitted, per-plane residual maps, and coefficient uncertainties (from the
fit's covariance).
## Testing strategy
`SyntheticBeamGenerator` is the backbone of validation: generate synthetic
multi-plane data from known ground-truth mode content, geometry, and noise,
run it through the full pipeline (and through individual components in
isolation), and assert recovered parameters match ground truth within
tolerance. Individual components also get targeted unit tests against known
analytic cases (e.g. `LGBasis` orthogonality and known Gouy phase values,
single-pure-mode recovery, geometry correction on synthetic projective
distortions).
## Error handling
Validate only at boundaries: reject malformed `MeasurementPlane` inputs
(mismatched array shapes, non-positive `z`, fewer than 3 planes). Warn
(rather than raise) when automatic mode-set growth hits its configured cap
while still improving, or when final fit residuals remain large — the caller
gets the result plus a diagnostic flag, not a crash.
## Dependencies
NumPy, SciPy (`optimize` for the nonlinear least-squares fit, `ndimage` for
projective transforms and deconvolution), Matplotlib for diagnostic
plotting. No GPU requirement.
## Package layout
```
he11lib/
data.py # MeasurementPlane, ReconstructionResult
geometry.py # GeometryCalibration
noise.py # NoiseEstimator
deconvolution.py # DiffusionDeconvolver
modes.py # LGBasis
fitting.py # ModalFitter (+ automatic mode-set growth)
phase_retrieval.py # PhaseRetriever
synthetic.py # SyntheticBeamGenerator
reconstruct.py # BeamReconstructor (orchestrator)
plotting.py # diagnostic visualizations
docs/
... # API docs
examples/
full_pipeline_example.py # end-to-end demo of the whole pipeline
tests/
...
```
## Deliverables
- Full implementation of all components above.
- API documentation for the public interface of every module.
- An end-to-end example (script or notebook) exercising the complete
pipeline on synthetic data, from `SyntheticBeamGenerator` through
`BeamReconstructor` to `plotting.py` diagnostics.
- Test suite covering synthetic ground-truth recovery and per-component unit
tests.
examples/full_pipeline_example.py
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"""End-to-end demonstration of the he11lib reconstruction pipeline.
Simulates a gyrotron beam that is mostly the LG_00 fundamental mode with a
small admixture of LG_01, viewed by a thermal camera at four distances from
the output window. The camera has an unknown transverse offset/pointing and
adds sensor noise; the target also has some thermal-diffusion blur that we
correct for. We then reconstruct the mode purity, beam center/pointing, and
plot the diagnostics.
Run with:
python examples/full_pipeline_example.py
"""
from __future__ import annotations
import matplotlib.pyplot as plt
from he11lib import (
BeamReconstructor,
DiffusionDeconvolver,
LGBasis,
SyntheticBeamGenerator,
plot_center_trace,
plot_mode_purity,
plot_residuals,
)
# --- Known reference beam parameters (from the gyrotron/mode-converter design) ---
W0 = 5e-3 # reference waist radius, meters
Z0 = 0.5 # reference waist location, meters from the output window
WAVELENGTH = 1.76e-3 # radiation wavelength, meters (e.g. a 170 GHz gyrotron)
# --- Ground truth for the synthetic beam (unknown to the reconstructor) ---
TRUE_COEFFICIENTS = {(0, 0): 0.95 + 0j, (0, 1): 0.25 + 0.05j}
TRUE_CENTER = (0.4e-3, -0.3e-3) # beam offset from the camera's optical axis
TRUE_POINTING_DEG = 0.15 # beam pointing (tilt) angle
CAMERA_VIEWING_ANGLE_DEG = 5.0 # oblique camera viewing angle (known)
CAMERA_PIXEL_SCALE = 4e-4 # meters/pixel (known calibration)
IMAGE_SHAPE = (81, 81)
# Measurement plane distances, meters. Kept within roughly +/-2 Rayleigh
# ranges of z0 so the (widening) beam stays well within the camera frame --
# planes much farther out would be clipped by the finite frame, which
# degrades the fit.
Z_LIST = [0.4, 0.45, 0.55, 0.6]
# --- Target thermal-diffusion blur (known target material properties) ---
THERMAL_DIFFUSIVITY = 1e-6 # m^2/s
DWELL_TIME = 0.2 # s
def main() -> None:
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
generator = SyntheticBeamGenerator(
basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=CAMERA_PIXEL_SCALE
)
planes = generator.generate(
coefficients=TRUE_COEFFICIENTS,
z_list=Z_LIST,
center=TRUE_CENTER,
pointing_angle_deg=TRUE_POINTING_DEG,
viewing_angle_deg=CAMERA_VIEWING_ANGLE_DEG,
noise_std=2e-4,
seed=42,
)
# Apply the same thermal-diffusion blur a real target would exhibit.
blur_deconvolver = DiffusionDeconvolver(
thermal_diffusivity=THERMAL_DIFFUSIVITY, dwell_time=DWELL_TIME
)
for plane in planes:
plane.flux = blur_deconvolver.blur(plane.flux, plane.pixel_scale)
# The ground truth only has order-0 and order-1 content, so a max_order
# of 1 is enough for automatic mode-set growth to find it; growing much
# further would start fitting deconvolution/noise artifacts as spurious
# higher-order modes.
reconstructor = BeamReconstructor(
w0=W0,
z0=Z0,
wavelength=WAVELENGTH,
max_order=1,
deconvolver=blur_deconvolver,
)
result = reconstructor.reconstruct(planes)
print("Mode purity table (power fraction, phase [rad]):")
for mode, (fraction, phase) in sorted(
result.purity.items(), key=lambda item: -item[1][0]
):
print(f" LG_{mode[0]},{mode[1]}: {fraction:6.3%} (phase {phase:+.3f} rad)")
print(f"\nFitted pointing angle: {result.pointing_angle_deg:.4f} deg")
print("Fitted beam center per plane (m):")
for plane, (cx, cy) in zip(planes, result.centers):
print(f" z={plane.z:.2f} m -> ({cx:.3e}, {cy:.3e})")
print(f"\nUsed phase-retrieval fallback: {result.used_phase_retrieval}")
plot_mode_purity(result)
plot_center_trace(planes, result)
plot_residuals(planes, result)
plt.show()
if __name__ == "__main__":
main()
he11lib/__init__.py
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"""he11lib: mode purity reconstruction of free-space gyrotron beams.
See docs/ for the full API and design documentation.
"""
from .data import MeasurementPlane, ReconstructionResult
from .deconvolution import DiffusionDeconvolver
from .fitting import ModalFitter, generate_mode_shells
from .geometry import GeometryCalibration
from .modes import LGBasis
from .noise import NoiseEstimator
from .phase_retrieval import PhaseRetrievalResult, PhaseRetriever, propagate_angular_spectrum
from .plotting import plot_center_trace, plot_mode_purity, plot_residuals
from .reconstruct import BeamReconstructor
from .synthetic import SyntheticBeamGenerator
__all__ = [
"MeasurementPlane",
"ReconstructionResult",
"BeamReconstructor",
"DiffusionDeconvolver",
"ModalFitter",
"generate_mode_shells",
"GeometryCalibration",
"LGBasis",
"NoiseEstimator",
"PhaseRetrievalResult",
"PhaseRetriever",
"propagate_angular_spectrum",
"plot_center_trace",
"plot_mode_purity",
"plot_residuals",
"SyntheticBeamGenerator",
]
__version__ = "0.1.0"
he11lib/data.py
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"""Data containers for he11lib: measurement inputs and reconstruction outputs."""
from __future__ import annotations
from dataclasses import dataclass, field
import numpy as np
@dataclass
class MeasurementPlane:
"""A single thermal (flux) image at a known distance from the output window.
Parameters
----------
flux : 2D array of flux values (already dead-pixel/background/saturation
corrected upstream).
z : distance from the output window, in meters. Must be positive.
pixel_scale : known mm/pixel scale, if calibrated. If None, treated as an
unknown to be estimated jointly during reconstruction.
viewing_angle_deg : known camera viewing angle relative to the beam axis,
in degrees, if calibrated. If None, treated as an unknown.
label : optional human-readable label (e.g. "plane_40cm").
"""
flux: np.ndarray
z: float
pixel_scale: float | None = None
viewing_angle_deg: float | None = None
label: str | None = None
def __post_init__(self) -> None:
if self.flux.ndim != 2:
raise ValueError(
f"MeasurementPlane.flux must be a 2D array, got shape {self.flux.shape}"
)
if self.z <= 0:
raise ValueError(f"MeasurementPlane.z must be positive, got {self.z}")
def validate_planes(planes: list[MeasurementPlane]) -> None:
"""Validate a list of MeasurementPlanes for use in reconstruction.
Raises ValueError if there are fewer than 3 planes, shapes mismatch
across planes, or z distances are not distinct.
"""
if len(planes) < 3:
raise ValueError(
f"At least 3 measurement planes are required, got {len(planes)}"
)
shapes = {p.flux.shape for p in planes}
if len(shapes) > 1:
raise ValueError(f"All MeasurementPlanes must have the same shape, got {shapes}")
z_values = [p.z for p in planes]
if len(set(z_values)) != len(z_values):
raise ValueError(f"MeasurementPlane z distances must be distinct, got {z_values}")
@dataclass
class ReconstructionResult:
"""Output of a full mode-purity reconstruction.
Parameters
----------
purity : mapping from (p, l) mode index to (power_fraction, phase_rad).
reconstructed_field : reconstructed complex field (at the reference
waist, or as configured).
centers : fitted beam transverse center (x, y) in meters, per plane.
pointing_angle_deg : fitted shared beam pointing angle (tilt), in degrees.
geometry : geometry parameters used or fitted (e.g. pixel_scale,
viewing_angle_deg), keyed by name.
residuals : per-plane residual maps (measured - modeled flux).
coefficient_uncertainty : mapping from (p, l) mode index to the
1-sigma uncertainty on its fitted power fraction.
used_phase_retrieval : whether the phase-retrieval fallback was used
instead of (or to seed) the modal fit.
"""
purity: dict[tuple[int, int], tuple[float, float]]
reconstructed_field: np.ndarray
centers: list[tuple[float, float]]
pointing_angle_deg: float
geometry: dict[str, float] = field(default_factory=dict)
residuals: list[np.ndarray] = field(default_factory=list)
coefficient_uncertainty: dict[tuple[int, int], float] = field(default_factory=dict)
used_phase_retrieval: bool = False
he11lib/deconvolution.py
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"""Optional correction for lateral thermal-diffusion blur in the target.
The absorbing target spreads heat laterally during the camera's exposure /
dwell time, blurring the true beam profile by a Gaussian kernel whose width
follows from the target's thermal diffusivity. This module provides both
the forward blur (for synthetic testing) and a regularized (Wiener)
deconvolution to remove it.
"""
from __future__ import annotations
import numpy as np
from scipy.ndimage import gaussian_filter
class DiffusionDeconvolver:
"""Models and removes lateral thermal-diffusion blur in a target.
Parameters
----------
thermal_diffusivity : target material thermal diffusivity, in m^2/s.
dwell_time : camera exposure/integration time, in s.
"""
def __init__(self, thermal_diffusivity: float, dwell_time: float):
self.thermal_diffusivity = thermal_diffusivity
self.dwell_time = dwell_time
def blur_sigma_m(self) -> float:
"""Gaussian blur standard deviation, in meters, from 2D heat diffusion."""
return np.sqrt(2 * self.thermal_diffusivity * self.dwell_time)
def blur(self, image: np.ndarray, pixel_scale: float) -> np.ndarray:
"""Apply the forward diffusion blur to `image` (for synthetic testing)."""
sigma_px = self.blur_sigma_m() / pixel_scale
return gaussian_filter(image, sigma=sigma_px)
def deconvolve(
self, image: np.ndarray, pixel_scale: float, noise_to_signal_ratio: float = 1e-3
) -> np.ndarray:
"""Remove the diffusion blur via regularized (Wiener) deconvolution."""
sigma_px = self.blur_sigma_m() / pixel_scale
psf = self._gaussian_psf(image.shape, sigma_px)
otf = np.fft.fft2(np.fft.ifftshift(psf))
image_ft = np.fft.fft2(image)
wiener_filter = np.conj(otf) / (np.abs(otf) ** 2 + noise_to_signal_ratio)
deconvolved = np.fft.ifft2(image_ft * wiener_filter).real
return deconvolved
@staticmethod
def _gaussian_psf(shape: tuple[int, int], sigma_px: float) -> np.ndarray:
rows, cols = shape
row_idx = np.arange(rows) - rows // 2
col_idx = np.arange(cols) - cols // 2
col_grid, row_grid = np.meshgrid(col_idx, row_idx)
psf = np.exp(-(row_grid**2 + col_grid**2) / (2 * sigma_px**2))
return psf / psf.sum()
he11lib/fitting.py
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"""Joint nonlinear least-squares modal fit with automatic mode-set growth."""
from __future__ import annotations
import warnings
import numpy as np
from scipy.optimize import least_squares
from .data import MeasurementPlane, ReconstructionResult, validate_planes
from .geometry import GeometryCalibration
from .modes import LGBasis
from .noise import NoiseEstimator
def generate_mode_shells(max_order: int) -> list[list[tuple[int, int]]]:
"""Group candidate LG_{p,l} modes into shells of increasing order 2p+|l|."""
shells: list[list[tuple[int, int]]] = [[] for _ in range(max_order + 1)]
for p in range(0, max_order + 1):
for l in range(-max_order, max_order + 1):
order = 2 * p + abs(l)
if order <= max_order:
shells[order].append((p, l))
return shells
class ModalFitter:
"""Fits LG mode coefficients, beam center/pointing, and geometry to measured planes."""
def __init__(self, basis: LGBasis, noise_estimator: NoiseEstimator | None = None):
self.basis = basis
self.noise_estimator = noise_estimator or NoiseEstimator()
def fit(
self,
planes: list[MeasurementPlane],
modes: list[tuple[int, int]],
initial_coefficients: dict[tuple[int, int], complex] | None = None,
initial_center: tuple[float, float] = (0.0, 0.0),
initial_tilt_deg: tuple[float, float] = (0.0, 0.0),
initial_pixel_scale: float | None = None,
initial_viewing_angle_deg: float = 0.0,
) -> ReconstructionResult:
"""Jointly fit complex coefficients for `modes` plus center/tilt/geometry."""
validate_planes(planes)
unknown_scale_idx = [i for i, p in enumerate(planes) if p.pixel_scale is None]
unknown_angle_idx = [i for i, p in enumerate(planes) if p.viewing_angle_deg is None]
weights = [np.sqrt(self.noise_estimator.weights(p.flux)) for p in planes]
def pack_initial() -> np.ndarray:
x: list[float] = []
for i, mode in enumerate(modes):
c = (initial_coefficients or {}).get(mode)
if c is None:
# Nonzero seed for every mode: starting a coefficient at
# exactly 0+0j sits at a flat/degenerate point for the
# optimizer and can prevent it from ever leaving zero.
c = 1.0 + 0j if i == 0 else 0.1 + 0.05j
x += [c.real, c.imag]
x += [initial_center[0], initial_center[1], initial_tilt_deg[0], initial_tilt_deg[1]]
for _ in unknown_scale_idx:
x.append(initial_pixel_scale if initial_pixel_scale is not None else 1e-4)
for _ in unknown_angle_idx:
x.append(initial_viewing_angle_deg)
return np.array(x, dtype=float)
n_modes = len(modes)
def unpack(x: np.ndarray):
coeffs = {mode: complex(x[2 * i], x[2 * i + 1]) for i, mode in enumerate(modes)}
offset = 2 * n_modes
x0, y0, tilt_x_deg, tilt_y_deg = x[offset : offset + 4]
offset += 4
scales = {}
for idx in unknown_scale_idx:
scales[idx] = x[offset]
offset += 1
angles = {}
for idx in unknown_angle_idx:
angles[idx] = x[offset]
offset += 1
return coeffs, (x0, y0), (tilt_x_deg, tilt_y_deg), scales, angles
def plane_center(x0: float, y0: float, tilt_deg: tuple[float, float], z: float):
drift_x = (z - self.basis.z0) * np.tan(np.deg2rad(tilt_deg[0]))
drift_y = (z - self.basis.z0) * np.tan(np.deg2rad(tilt_deg[1]))
return x0 + drift_x, y0 + drift_y
def model_flux_for_plane(i: int, plane: MeasurementPlane, coeffs, center0, tilt_deg, scales, angles):
scale = plane.pixel_scale if plane.pixel_scale is not None else scales[i]
angle = plane.viewing_angle_deg if plane.viewing_angle_deg is not None else angles[i]
calib = GeometryCalibration(plane)
x_grid, y_grid = calib.physical_coordinates(pixel_scale=scale, viewing_angle_deg=angle)
cx, cy = plane_center(center0[0], center0[1], tilt_deg, plane.z)
field = self.basis.field_superposition(x_grid - cx, y_grid - cy, plane.z, coeffs)
return np.abs(field) ** 2
def residuals(x: np.ndarray) -> np.ndarray:
coeffs, center0, tilt_deg, scales, angles = unpack(x)
parts = []
for i, plane in enumerate(planes):
model_flux = model_flux_for_plane(i, plane, coeffs, center0, tilt_deg, scales, angles)
parts.append(((plane.flux - model_flux) * weights[i]).ravel())
return np.concatenate(parts)
x0_vec = pack_initial()
# 'trf' + x_scale='jac' handles the very different natural magnitudes
# of these parameters (coefficients ~O(1), pixel_scale ~O(1e-3),
# angles ~O(1-90)); plain 'lm' can terminate prematurely on 'xtol'
# because its unscaled step-size test is dominated by the largest
# parameters.
opt_result = least_squares(
residuals, x0_vec, method="trf", x_scale="jac", max_nfev=5000
)
coeffs, center0, tilt_deg, scales, angles = unpack(opt_result.x)
total_power = sum(abs(c) ** 2 for c in coeffs.values())
if total_power == 0:
total_power = 1.0
purity = {mode: (abs(c) ** 2 / total_power, float(np.angle(c))) for mode, c in coeffs.items()}
centers = [plane_center(center0[0], center0[1], tilt_deg, p.z) for p in planes]
pointing_angle_deg = float(np.hypot(tilt_deg[0], tilt_deg[1]))
geometry: dict[str, float] = {}
for i in range(len(planes)):
geometry[f"pixel_scale_{i}"] = (
planes[i].pixel_scale if planes[i].pixel_scale is not None else scales[i]
)
geometry[f"viewing_angle_deg_{i}"] = (
planes[i].viewing_angle_deg if planes[i].viewing_angle_deg is not None else angles[i]
)
residual_maps = []
for i, plane in enumerate(planes):
model_flux = model_flux_for_plane(i, plane, coeffs, center0, tilt_deg, scales, angles)
residual_maps.append(plane.flux - model_flux)
coefficient_uncertainty = self._estimate_uncertainty(opt_result, modes, coeffs, total_power)
reference_z = min(planes, key=lambda p: abs(p.z - self.basis.z0)).z
field_at_reference = self._field_on_default_grid(coeffs, reference_z)
return ReconstructionResult(
purity=purity,
reconstructed_field=field_at_reference,
centers=centers,
pointing_angle_deg=pointing_angle_deg,
geometry=geometry,
residuals=residual_maps,
coefficient_uncertainty=coefficient_uncertainty,
used_phase_retrieval=False,
)
def fit_auto(
self,
planes: list[MeasurementPlane],
max_order: int = 4,
bic_improvement_threshold: float = 10.0,
) -> ReconstructionResult:
"""Fit with automatic mode-set growth, capped at `max_order`."""
validate_planes(planes)
shells = generate_mode_shells(max_order)
current_modes = list(shells[0])
best_result = self.fit(planes, current_modes)
best_bic = self._bic(planes, best_result, current_modes)
grew_until_cap = True
for shell in shells[1:]:
trial_modes = current_modes + shell
warm_start = self._warm_start_coefficients(best_result, current_modes)
trial_result = self.fit(planes, trial_modes, initial_coefficients=warm_start)
trial_bic = self._bic(planes, trial_result, trial_modes)
if trial_bic < best_bic - bic_improvement_threshold:
current_modes = trial_modes
best_result = trial_result
best_bic = trial_bic
else:
grew_until_cap = False
break
if grew_until_cap and len(shells) > 1:
warnings.warn(
"Automatic mode-set growth hit the configured max_order cap "
f"({max_order}) while still improving the fit; consider raising max_order.",
stacklevel=2,
)
return best_result
def _warm_start_coefficients(
self, previous_result: ReconstructionResult, previous_modes: list[tuple[int, int]]
) -> dict[tuple[int, int], complex]:
"""Reconstruct approximate complex coefficients from a previous fit's purity."""
coeffs = {}
for mode in previous_modes:
fraction, phase = previous_result.purity[mode]
amplitude = np.sqrt(max(fraction, 0.0))
coeffs[mode] = amplitude * np.exp(1j * phase)
return coeffs
def _bic(self, planes: list[MeasurementPlane], result: ReconstructionResult, modes: list[tuple[int, int]]) -> float:
chi2 = sum(np.sum((r * np.sqrt(self.noise_estimator.weights(p.flux))) ** 2) for r, p in zip(result.residuals, planes))
n_data = sum(p.flux.size for p in planes)
n_params = 2 * len(modes) + 4
return float(chi2 + n_params * np.log(n_data))
def _estimate_uncertainty(self, opt_result, modes, coeffs, total_power):
try:
jac = opt_result.jac
cov = np.linalg.pinv(jac.T @ jac)
except np.linalg.LinAlgError:
return {mode: float("nan") for mode in modes}
uncertainty = {}
for i, mode in enumerate(modes):
var_re = cov[2 * i, 2 * i]
var_im = cov[2 * i + 1, 2 * i + 1]
c = coeffs[mode]
sigma_c = np.sqrt(max(var_re, 0) + max(var_im, 0))
uncertainty[mode] = float(2 * abs(c) * sigma_c / total_power)
return uncertainty
def _field_on_default_grid(self, coeffs, z: float, n: int = 128, half_width_in_w: float = 6.0):
w_z = self.basis.beam_radius(z)
extent = half_width_in_w * w_z
coords = np.linspace(-extent, extent, n)
x, y = np.meshgrid(coords, coords)
return self.basis.field_superposition(x, y, z, coeffs)
he11lib/geometry.py
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"""Camera geometry correction: pixel-to-physical scale and viewing angle.
Converts a MeasurementPlane's pixel grid into physical (x, y) coordinates in
the beam's transverse plane, compensating for an oblique camera viewing
angle (which compresses the image along the tilt axis by cos(angle)).
Known calibration values (on the MeasurementPlane) are used directly; when a
value is unknown, an override must be supplied (e.g. by ModalFitter while
exploring it as a free parameter).
"""
from __future__ import annotations
import numpy as np
from .data import MeasurementPlane
class GeometryCalibration:
"""Resolves pixel scale / viewing angle and builds a physical coordinate grid."""
def __init__(self, plane: MeasurementPlane):
self.plane = plane
@property
def pixel_scale_known(self) -> bool:
return self.plane.pixel_scale is not None
@property
def viewing_angle_known(self) -> bool:
return self.plane.viewing_angle_deg is not None
def physical_coordinates(
self,
pixel_scale: float | None = None,
viewing_angle_deg: float | None = None,
) -> tuple[np.ndarray, np.ndarray]:
"""Physical (x, y) grid matching the plane's flux array shape.
Known values on the MeasurementPlane take precedence; overrides are
only used to fill in values that are not known/calibrated.
"""
scale = self.plane.pixel_scale if self.pixel_scale_known else pixel_scale
angle_deg = (
self.plane.viewing_angle_deg if self.viewing_angle_known else viewing_angle_deg
)
if scale is None:
raise ValueError(
"pixel_scale is not known for this MeasurementPlane and no override was given"
)
if angle_deg is None:
raise ValueError(
"viewing_angle_deg is not known for this MeasurementPlane and no override was given"
)
rows, cols = self.plane.flux.shape
row_idx = np.arange(rows) - rows // 2
col_idx = np.arange(cols) - cols // 2
col_grid, row_grid = np.meshgrid(col_idx, row_idx)
cos_angle = np.cos(np.deg2rad(angle_deg))
x = col_grid * scale / cos_angle
y = row_grid * scale
return x, y
he11lib/modes.py
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"""Laguerre-Gauss mode basis for free-space gyrotron beam propagation."""
from __future__ import annotations
import math
import numpy as np
from scipy.special import eval_genlaguerre
class LGBasis:
"""Laguerre-Gauss mode basis referenced to a known waist size/location.
Parameters
----------
w0 : reference waist radius, in meters.
z0 : reference waist location, in meters.
wavelength : radiation wavelength, in meters (e.g. ~1.76 mm for a
170 GHz gyrotron).
"""
def __init__(self, w0: float, z0: float, wavelength: float):
self.w0 = w0
self.z0 = z0
self.wavelength = wavelength
self.k = 2 * np.pi / wavelength
self.zR = np.pi * w0**2 / wavelength
def beam_radius(self, z: float) -> float:
"""Beam radius w(z)."""
return self.w0 * math.sqrt(1.0 + ((z - self.z0) / self.zR) ** 2)
def inverse_radius_of_curvature(self, z: float) -> float:
"""1/R(z), well-defined (=0) at the waist."""
dz = z - self.z0
return dz / (dz**2 + self.zR**2)
def gouy_phase(self, z: float, p: int, l: int) -> float:
"""Gouy phase for mode (p, l) at distance z."""
order = 2 * p + abs(l) + 1
return order * math.atan((z - self.z0) / self.zR)
def field(self, x: np.ndarray, y: np.ndarray, z: float, p: int, l: int) -> np.ndarray:
"""Complex LG_{p,l} field sampled on the given (x, y) grid at distance z."""
w_z = self.beam_radius(z)
r2 = x**2 + y**2
r = np.sqrt(r2)
phi = np.arctan2(y, x)
abs_l = abs(l)
c_pl = math.sqrt(2 * math.factorial(p) / (math.pi * math.factorial(p + abs_l)))
radial = (
c_pl
/ w_z
* (r * math.sqrt(2) / w_z) ** abs_l
* eval_genlaguerre(p, abs_l, 2 * r2 / w_z**2)
* np.exp(-r2 / w_z**2)
)
curvature_phase = self.k * r2 * self.inverse_radius_of_curvature(z) / 2
gouy = self.gouy_phase(z, p, l)
phase = np.exp(1j * (curvature_phase + gouy - l * phi))
return radial * phase
def field_superposition(
self,
x: np.ndarray,
y: np.ndarray,
z: float,
coefficients: dict[tuple[int, int], complex],
) -> np.ndarray:
"""Complex field for a superposition of modes with given complex coefficients."""
total = np.zeros_like(x, dtype=complex)
for (p, l), coeff in coefficients.items():
total = total + coeff * self.field(x, y, z, p, l)
return total
def project(
self,
complex_field: np.ndarray,
x: np.ndarray,
y: np.ndarray,
dx: float,
z: float,
modes: list[tuple[int, int]],
) -> dict[tuple[int, int], complex]:
"""Project a complex field onto the given candidate modes at distance z.
Returns the complex coefficient of each mode via the inner product
<LG_mode | field>, using a Riemann-sum approximation of the integral
over the (x, y) grid (spacing dx, assumed square/uniform).
"""
coefficients: dict[tuple[int, int], complex] = {}
for p, l in modes:
mode_field = self.field(x, y, z, p, l)
coefficients[(p, l)] = np.sum(np.conj(mode_field) * complex_field) * dx**2
return coefficients
he11lib/noise.py
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"""Automatic residual sensor noise estimation.
Uses the Immerkaer (1996) fast noise-variance estimator: convolving the
image with a Laplacian-of-Gaussian-like kernel suppresses smooth signal
content (the beam profile) while passing high-frequency noise, giving a
closed-form estimate of the noise standard deviation without needing a
dedicated background region.
"""
from __future__ import annotations
import numpy as np
from scipy.signal import convolve2d
_LAPLACIAN_KERNEL = np.array(
[
[1, -2, 1],
[-2, 4, -2],
[1, -2, 1],
],
dtype=float,
)
class NoiseEstimator:
"""Estimates residual per-image noise and produces least-squares weights."""
def estimate_std(self, image: np.ndarray) -> float:
"""Estimate the additive Gaussian noise standard deviation in `image`."""
rows, cols = image.shape
convolved = convolve2d(image, _LAPLACIAN_KERNEL, mode="valid")
sigma = np.sqrt(np.pi / 2) * np.sum(np.abs(convolved)) / (
6 * (cols - 2) * (rows - 2)
)
return float(sigma)
def weights(self, image: np.ndarray) -> np.ndarray:
"""Per-pixel weights (1/sigma^2) for noise-weighted least squares."""
sigma = self.estimate_std(image)
return np.full(image.shape, 1.0 / sigma**2)
he11lib/phase_retrieval.py
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"""Gerchberg-Saxton-style multi-plane phase retrieval (fallback reconstruction path).
Used when the finite-mode-basis fit (ModalFitter) leaves a high residual, or
when explicitly requested. Iteratively propagates a trial complex field
between measurement planes via free-space (angular-spectrum) propagation,
enforcing the measured amplitude at each plane without assuming a finite
mode basis. The recovered field can then be projected onto an LGBasis for a
purity table.
"""
from __future__ import annotations
from dataclasses import dataclass
import numpy as np
from .data import MeasurementPlane, validate_planes
from .geometry import GeometryCalibration
def propagate_angular_spectrum(
field: np.ndarray, dx: float, dz: float, wavelength: float
) -> np.ndarray:
"""Free-space-propagate a complex field by distance dz via the angular spectrum method.
`dx` is the (square) pixel spacing of `field`. Evanescent components
(where the transverse spatial frequency exceeds 1/wavelength) are
dropped, which is an excellent approximation for paraxial beams.
"""
ny, nx = field.shape
fx = np.fft.fftfreq(nx, d=dx)
fy = np.fft.fftfreq(ny, d=dx)
fx_grid, fy_grid = np.meshgrid(fx, fy)
k = 2 * np.pi / wavelength
kz_squared = k**2 - (2 * np.pi * fx_grid) ** 2 - (2 * np.pi * fy_grid) ** 2
kz = np.sqrt(np.maximum(kz_squared, 0.0))
propagating = kz_squared >= 0
transfer_function = np.where(propagating, np.exp(1j * kz * dz), 0.0)
field_ft = np.fft.fft2(field)
return np.fft.ifft2(field_ft * transfer_function)
@dataclass
class PhaseRetrievalResult:
"""Result of multi-plane phase retrieval.
field : recovered complex field at distance `z` (the smallest-z plane),
on the (x, y) physical grid.
x, y : physical coordinate grids matching `field`'s shape.
z : distance at which `field` is defined.
center : estimated beam transverse center (intensity centroid), in
meters, on the same grid.
residual : final RMS mismatch between enforced and propagated amplitude
across all planes (diagnostic of convergence quality).
"""
field: np.ndarray
x: np.ndarray
y: np.ndarray
z: float
center: tuple[float, float]
residual: float
class PhaseRetriever:
"""Multi-plane Gerchberg-Saxton phase retrieval.
Parameters
----------
wavelength : radiation wavelength, in meters.
"""
def __init__(self, wavelength: float):
self.wavelength = wavelength
def retrieve(
self,
planes: list[MeasurementPlane],
pixel_scale: float | None = None,
viewing_angle_deg: float | None = None,
max_iterations: int = 200,
) -> PhaseRetrievalResult:
"""Run Gerchberg-Saxton phase retrieval across the given planes.
Planes must share the same known (or overridden) pixel_scale and
viewing_angle_deg, since all planes are propagated on one common
physical grid.
"""
validate_planes(planes)
ordered = sorted(planes, key=lambda p: p.z)
x, y = GeometryCalibration(ordered[0]).physical_coordinates(
pixel_scale=pixel_scale, viewing_angle_deg=viewing_angle_deg
)
dx = float(x[0, 1] - x[0, 0])
amplitudes = [np.sqrt(np.clip(p.flux, 0, None)) for p in ordered]
z_values = [p.z for p in ordered]
field = amplitudes[0].astype(complex).copy()
residual = float("inf")
for _ in range(max_iterations):
residual = 0.0
# forward sweep
for i in range(len(ordered) - 1):
dz = z_values[i + 1] - z_values[i]
field = propagate_angular_spectrum(field, dx, dz, self.wavelength)
mismatch = np.abs(field) - amplitudes[i + 1]
residual += float(np.sum(mismatch**2))
phase = np.angle(field)
field = amplitudes[i + 1] * np.exp(1j * phase)
# backward sweep
for i in range(len(ordered) - 1, 0, -1):
dz = z_values[i - 1] - z_values[i]
field = propagate_angular_spectrum(field, dx, dz, self.wavelength)
mismatch = np.abs(field) - amplitudes[i - 1]
residual += float(np.sum(mismatch**2))
phase = np.angle(field)
field = amplitudes[i - 1] * np.exp(1j * phase)
n_pixels = sum(a.size for a in amplitudes)
rms_residual = float(np.sqrt(residual / n_pixels)) if n_pixels else 0.0
intensity = np.abs(field) ** 2
total_intensity = np.sum(intensity)
cx = float(np.sum(x * intensity) / total_intensity)
cy = float(np.sum(y * intensity) / total_intensity)
return PhaseRetrievalResult(
field=field, x=x, y=y, z=z_values[0], center=(cx, cy), residual=rms_residual
)
he11lib/plotting.py
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"""Diagnostic visualizations for reconstruction results.
Each function returns a `matplotlib.figure.Figure` for the caller to display
(`fig.show()` / inline in a notebook) or save (`fig.savefig(...)`).
"""
from __future__ import annotations
import matplotlib.figure
import matplotlib.pyplot as plt
from .data import MeasurementPlane, ReconstructionResult
def plot_mode_purity(result: ReconstructionResult) -> matplotlib.figure.Figure:
"""Bar chart of power fraction per candidate LG mode."""
modes = list(result.purity.keys())
fractions = [result.purity[mode][0] for mode in modes]
labels = [f"LG_{p},{l}" for p, l in modes]
fig, ax = plt.subplots()
ax.bar(labels, fractions)
ax.set_ylabel("Power fraction")
ax.set_xlabel("Mode")
ax.set_title("Mode purity")
return fig
def plot_center_trace(
planes: list[MeasurementPlane], result: ReconstructionResult
) -> matplotlib.figure.Figure:
"""Fitted beam transverse center (x, y) as a function of z across planes."""
z_values = [p.z for p in planes]
x_values = [c[0] for c in result.centers]
y_values = [c[1] for c in result.centers]
fig, (ax_x, ax_y) = plt.subplots(1, 2, sharex=True)
ax_x.plot(z_values, x_values, marker="o")
ax_x.set_xlabel("z (m)")
ax_x.set_ylabel("center x (m)")
ax_y.plot(z_values, y_values, marker="o")
ax_y.set_xlabel("z (m)")
ax_y.set_ylabel("center y (m)")
fig.suptitle(f"Beam center (pointing angle {result.pointing_angle_deg:.3g} deg)")
return fig
def plot_residuals(
planes: list[MeasurementPlane], result: ReconstructionResult
) -> matplotlib.figure.Figure:
"""Per-plane residual maps (measured - modeled flux)."""
if not result.residuals:
raise ValueError(
"No per-plane residuals are available on this ReconstructionResult "
"(e.g. the phase-retrieval fallback was used, which does not produce them)."
)
n = len(planes)
fig, axes = plt.subplots(1, n, squeeze=False)
axes = axes[0]
for ax, plane, residual in zip(axes, planes, result.residuals):
im = ax.imshow(residual)
ax.set_title(f"z={plane.z:g} m")
fig.colorbar(im, ax=ax)
return fig
he11lib/reconstruct.py
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"""High-level orchestrator wiring together the full reconstruction pipeline."""
from __future__ import annotations
from dataclasses import replace
import numpy as np
from .data import MeasurementPlane, ReconstructionResult, validate_planes
from .deconvolution import DiffusionDeconvolver
from .fitting import ModalFitter, generate_mode_shells
from .modes import LGBasis
from .noise import NoiseEstimator
from .phase_retrieval import PhaseRetriever
class BeamReconstructor:
"""Runs the complete mode-purity reconstruction pipeline.
Given a list of `MeasurementPlane`s, this orchestrates (optional)
diffusion deblurring, the joint modal least-squares fit with automatic
mode-set growth, and an optional Gerchberg-Saxton phase-retrieval
fallback -- producing a single `ReconstructionResult`.
Parameters
----------
w0, z0, wavelength : known reference beam parameters (see `LGBasis`).
max_order : cap on automatic candidate-mode-set growth (see
`ModalFitter.fit_auto`), and also the mode set used to project the
phase-retrieval fallback's recovered field onto the LG basis.
noise_estimator : shared noise model; defaults to `NoiseEstimator()`.
deconvolver : if given, each plane's flux is deblurred (its
`pixel_scale` must be known) before fitting.
force_phase_retrieval : if True, always run the phase-retrieval fallback
instead of the modal fit.
phase_retrieval_residual_threshold : if set (and `force_phase_retrieval`
is False), the phase-retrieval fallback runs automatically whenever
the modal fit's noise-weighted RMS residual exceeds this value.
"""
def __init__(
self,
w0: float,
z0: float,
wavelength: float,
max_order: int = 4,
noise_estimator: NoiseEstimator | None = None,
deconvolver: DiffusionDeconvolver | None = None,
force_phase_retrieval: bool = False,
phase_retrieval_residual_threshold: float | None = None,
):
self.basis = LGBasis(w0=w0, z0=z0, wavelength=wavelength)
self.wavelength = wavelength
self.max_order = max_order
self.noise_estimator = noise_estimator or NoiseEstimator()
self.deconvolver = deconvolver
self.force_phase_retrieval = force_phase_retrieval
self.phase_retrieval_residual_threshold = phase_retrieval_residual_threshold
def reconstruct(self, planes: list[MeasurementPlane]) -> ReconstructionResult:
"""Run the full pipeline and return a `ReconstructionResult`."""
validate_planes(planes)
planes = self._deconvolve(planes)
fitter = ModalFitter(self.basis, self.noise_estimator)
result = fitter.fit_auto(planes, max_order=self.max_order)
if self.force_phase_retrieval or self._residual_too_high(result, planes):
result = self._phase_retrieval_fallback(planes)
return result
def _deconvolve(self, planes: list[MeasurementPlane]) -> list[MeasurementPlane]:
if self.deconvolver is None:
return planes
deblurred = []
for plane in planes:
if plane.pixel_scale is None:
raise ValueError(
"Deconvolution requires a known pixel_scale on every MeasurementPlane."
)
flux = self.deconvolver.deconvolve(plane.flux, plane.pixel_scale)
deblurred.append(replace(plane, flux=flux))
return deblurred
def _residual_too_high(
self, result: ReconstructionResult, planes: list[MeasurementPlane]
) -> bool:
if self.phase_retrieval_residual_threshold is None:
return False
total = 0.0
n_pixels = 0
for residual_map, plane in zip(result.residuals, planes):
weights = self.noise_estimator.weights(plane.flux)
total += float(np.sum((residual_map**2) * weights))
n_pixels += residual_map.size
rms = np.sqrt(total / n_pixels) if n_pixels else 0.0
return rms > self.phase_retrieval_residual_threshold
def _phase_retrieval_fallback(
self, planes: list[MeasurementPlane]
) -> ReconstructionResult:
retriever = PhaseRetriever(self.wavelength)
pr_result = retriever.retrieve(planes)
modes = [mode for shell in generate_mode_shells(self.max_order) for mode in shell]
dx = float(pr_result.x[0, 1] - pr_result.x[0, 0])
coeffs = self.basis.project(pr_result.field, pr_result.x, pr_result.y, dx, pr_result.z, modes)
total_power = sum(abs(c) ** 2 for c in coeffs.values())
if total_power == 0:
total_power = 1.0
purity = {mode: (abs(c) ** 2 / total_power, float(np.angle(c))) for mode, c in coeffs.items()}
return ReconstructionResult(
purity=purity,
reconstructed_field=pr_result.field,
centers=[pr_result.center for _ in planes],
pointing_angle_deg=float("nan"),
geometry={},
residuals=[],
coefficient_uncertainty={mode: float("nan") for mode in modes},
used_phase_retrieval=True,
)
he11lib/synthetic.py
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"""Forward model: synthetic thermal (flux) images from known ground truth.
Used to validate the reconstruction pipeline (recover known mode content)
and to help users evaluate experimental design (e.g. whether a given set of
measurement distances will separate candidate modes).
"""
from __future__ import annotations
import numpy as np
from .data import MeasurementPlane
from .modes import LGBasis
class SyntheticBeamGenerator:
"""Generates synthetic multi-plane flux images for a known ground-truth beam.
Parameters
----------
basis : LGBasis defining the reference w0, z0, wavelength.
image_shape : (rows, cols) pixel shape of generated images.
pixel_scale : physical size of one pixel, in meters, along the
non-tilted (y) axis. The tilt/projection axis is assumed to be x.
"""
def __init__(self, basis: LGBasis, image_shape: tuple[int, int], pixel_scale: float):
self.basis = basis
self.image_shape = image_shape
self.pixel_scale = pixel_scale
def _pixel_grid(self, center: tuple[float, float], viewing_angle_deg: float):
rows, cols = self.image_shape
row_idx = np.arange(rows) - rows // 2
col_idx = np.arange(cols) - cols // 2
col_grid, row_grid = np.meshgrid(col_idx, row_idx)
cos_angle = np.cos(np.deg2rad(viewing_angle_deg))
x = col_grid * self.pixel_scale / cos_angle - center[0]
y = row_grid * self.pixel_scale - center[1]
return x, y
def generate(
self,
coefficients: dict[tuple[int, int], complex],
z_list: list[float],
*,
center: tuple[float, float] = (0.0, 0.0),
pointing_angle_deg: float = 0.0,
viewing_angle_deg: float = 0.0,
noise_std: float = 0.0,
seed: int | None = None,
) -> list[MeasurementPlane]:
"""Generate one MeasurementPlane per requested z distance.
The beam transverse center drifts linearly with z according to
pointing_angle_deg (tilt of the beam axis along x), starting from
`center` at the basis's reference z0.
"""
rng = np.random.default_rng(seed)
tilt_rad = np.deg2rad(pointing_angle_deg)
planes = []
for z in z_list:
drift_x = (z - self.basis.z0) * np.tan(tilt_rad)
plane_center = (center[0] + drift_x, center[1])
x, y = self._pixel_grid(plane_center, viewing_angle_deg)
field = self.basis.field_superposition(x, y, z, coefficients)
flux = np.abs(field) ** 2
if noise_std > 0:
flux = flux + rng.normal(0.0, noise_std, size=flux.shape)
planes.append(
MeasurementPlane(
flux=flux,
z=z,
pixel_scale=self.pixel_scale,
viewing_angle_deg=viewing_angle_deg,
)
)
return planes
pyproject.toml
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[build-system]
requires = ["setuptools>=68", "wheel"]
build-backend = "setuptools.build_meta"
[project]
name = "he11lib"
version = "0.1.0"
description = "Mode purity reconstruction of free-space gyrotron beams from multi-plane thermal (flux) images."
readme = "README.md"
requires-python = ">=3.10"
license = { text = "GPL-3.0-or-later" }
dependencies = [
"numpy>=1.24",
"scipy>=1.10",
"matplotlib>=3.7",
]
[project.optional-dependencies]
dev = [
"pytest>=7.4",
]
[tool.setuptools.packages.find]
include = ["he11lib*"]
[tool.pytest.ini_options]
testpaths = ["tests"]
tests/__init__.py
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tests/conftest.py
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import matplotlib
matplotlib.use("Agg")
tests/test_data.py
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import numpy as np
import pytest
from he11lib.data import MeasurementPlane, ReconstructionResult, validate_planes
def test_measurement_plane_stores_fields():
flux = np.ones((4, 4))
plane = MeasurementPlane(flux=flux, z=0.3)
assert plane.z == 0.3
assert np.array_equal(plane.flux, flux)
assert plane.pixel_scale is None
assert plane.viewing_angle_deg is None
assert plane.label is None
def test_measurement_plane_stores_optional_fields():
flux = np.ones((4, 4))
plane = MeasurementPlane(
flux=flux, z=0.4, pixel_scale=0.1, viewing_angle_deg=5.0, label="plane_40cm"
)
assert plane.pixel_scale == 0.1
assert plane.viewing_angle_deg == 5.0
assert plane.label == "plane_40cm"
def test_measurement_plane_rejects_non_2d_flux():
with pytest.raises(ValueError, match="2D"):
MeasurementPlane(flux=np.ones((4, 4, 3)), z=0.3)
def test_measurement_plane_rejects_non_positive_z():
with pytest.raises(ValueError, match="positive"):
MeasurementPlane(flux=np.ones((4, 4)), z=0.0)
with pytest.raises(ValueError, match="positive"):
MeasurementPlane(flux=np.ones((4, 4)), z=-0.1)
def test_validate_planes_rejects_fewer_than_three():
planes = [
MeasurementPlane(flux=np.ones((4, 4)), z=0.3),
MeasurementPlane(flux=np.ones((4, 4)), z=0.4),
]
with pytest.raises(ValueError, match="[Aa]t least 3"):
validate_planes(planes)
def test_validate_planes_rejects_mismatched_shapes():
planes = [
MeasurementPlane(flux=np.ones((4, 4)), z=0.3),
MeasurementPlane(flux=np.ones((5, 5)), z=0.4),
MeasurementPlane(flux=np.ones((4, 4)), z=0.5),
]
with pytest.raises(ValueError, match="same shape"):
validate_planes(planes)
def test_validate_planes_rejects_duplicate_z():
planes = [
MeasurementPlane(flux=np.ones((4, 4)), z=0.3),
MeasurementPlane(flux=np.ones((4, 4)), z=0.3),
MeasurementPlane(flux=np.ones((4, 4)), z=0.5),
]
with pytest.raises(ValueError, match="distinct"):
validate_planes(planes)
def test_validate_planes_accepts_valid_list():
planes = [
MeasurementPlane(flux=np.ones((4, 4)), z=0.3),
MeasurementPlane(flux=np.ones((4, 4)), z=0.4),
MeasurementPlane(flux=np.ones((4, 4)), z=0.5),
]
validate_planes(planes) # should not raise
def test_reconstruction_result_stores_fields():
result = ReconstructionResult(
purity={(0, 0): (1.0, 0.0)},
reconstructed_field=np.ones((4, 4), dtype=complex),
centers=[(0.0, 0.0)],
pointing_angle_deg=0.0,
geometry={"pixel_scale": 0.1, "viewing_angle_deg": 2.0},
residuals=[np.zeros((4, 4))],
coefficient_uncertainty={(0, 0): 0.01},
used_phase_retrieval=False,
)
assert result.purity[(0, 0)] == (1.0, 0.0)
assert result.used_phase_retrieval is False
tests/test_deconvolution.py
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import numpy as np
import pytest
from he11lib.deconvolution import DiffusionDeconvolver
def gaussian_bump(n, sigma_px):
coords = np.arange(n) - n // 2
xx, yy = np.meshgrid(coords, coords)
return np.exp(-(xx**2 + yy**2) / (2 * sigma_px**2))
def profile_std(image):
n = image.shape[0]
coords = np.arange(n) - n // 2
weights = image[n // 2, :]
weights = np.clip(weights, 0, None)
mean = np.sum(coords * weights) / np.sum(weights)
var = np.sum(weights * (coords - mean) ** 2) / np.sum(weights)
return np.sqrt(var)
def test_blur_sigma_m_from_diffusivity_and_dwell_time():
diffusivity = 1e-6 # m^2/s
dwell_time = 0.5 # s
deconvolver = DiffusionDeconvolver(thermal_diffusivity=diffusivity, dwell_time=dwell_time)
expected_sigma = np.sqrt(2 * diffusivity * dwell_time)
assert deconvolver.blur_sigma_m() == pytest.approx(expected_sigma)
def test_blur_widens_a_sharp_peak():
deconvolver = DiffusionDeconvolver(thermal_diffusivity=1e-6, dwell_time=0.5)
pixel_scale = 2e-4
sharp = gaussian_bump(101, sigma_px=3)
blurred = deconvolver.blur(sharp, pixel_scale=pixel_scale)
assert profile_std(blurred) > profile_std(sharp)
def test_deconvolve_reduces_error_relative_to_blurred():
deconvolver = DiffusionDeconvolver(thermal_diffusivity=1e-6, dwell_time=0.3)
pixel_scale = 2e-4
sharp = gaussian_bump(101, sigma_px=4)
blurred = deconvolver.blur(sharp, pixel_scale=pixel_scale)
deconvolved = deconvolver.deconvolve(blurred, pixel_scale=pixel_scale)
error_blurred = np.sum((blurred - sharp) ** 2)
error_deconvolved = np.sum((deconvolved - sharp) ** 2)
assert error_deconvolved < error_blurred
def test_deconvolve_narrows_width_back_toward_original():
deconvolver = DiffusionDeconvolver(thermal_diffusivity=1e-6, dwell_time=0.3)
pixel_scale = 2e-4
sharp = gaussian_bump(101, sigma_px=4)
blurred = deconvolver.blur(sharp, pixel_scale=pixel_scale)
deconvolved = deconvolver.deconvolve(blurred, pixel_scale=pixel_scale)
std_sharp = profile_std(sharp)
std_blurred = profile_std(blurred)
std_deconvolved = profile_std(deconvolved)
assert std_sharp < std_deconvolved < std_blurred
tests/test_fitting.py
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import numpy as np
import pytest
from he11lib.data import validate_planes
from he11lib.fitting import ModalFitter, generate_mode_shells
from he11lib.modes import LGBasis
from he11lib.synthetic import SyntheticBeamGenerator
W0 = 5e-3
Z0 = 0.5
WAVELENGTH = 1.76e-3
PIXEL_SCALE = 4e-4
IMAGE_SHAPE = (61, 61)
Z_LIST = [0.35, 0.5, 0.65, 0.8]
def make_basis():
return LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
def make_generator(basis):
return SyntheticBeamGenerator(basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=PIXEL_SCALE)
def test_generate_mode_shells_orders_by_2p_plus_abs_l():
shells = generate_mode_shells(max_order=2)
assert shells[0] == [(0, 0)]
assert set(shells[1]) == {(0, 1), (0, -1)}
assert set(shells[2]) == {(0, 2), (0, -2), (1, 0)}
def test_fit_recovers_pure_fundamental_mode():
basis = make_basis()
gen = make_generator(basis)
planes = gen.generate(
coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, noise_std=1e-4, seed=0
)
fitter = ModalFitter(basis)
result = fitter.fit(planes, modes=[(0, 0)])
power_fraction, _ = result.purity[(0, 0)]
assert power_fraction == pytest.approx(1.0, abs=1e-6)
for cx, cy in result.centers:
assert cx == pytest.approx(0.0, abs=2 * PIXEL_SCALE)
assert cy == pytest.approx(0.0, abs=2 * PIXEL_SCALE)
def test_fit_recovers_two_mode_purity_ratio():
basis = make_basis()
gen = make_generator(basis)
true_coeffs = {(0, 0): 0.9 + 0j, (1, 0): 0.3 + 0.1j}
planes = gen.generate(coefficients=true_coeffs, z_list=Z_LIST, noise_std=1e-4, seed=1)
fitter = ModalFitter(basis)
result = fitter.fit(planes, modes=list(true_coeffs.keys()))
true_total = sum(abs(c) ** 2 for c in true_coeffs.values())
for mode, c in true_coeffs.items():
expected_fraction = abs(c) ** 2 / true_total
recovered_fraction, _ = result.purity[mode]
assert recovered_fraction == pytest.approx(expected_fraction, abs=0.03)
def test_fit_recovers_center_offset():
basis = make_basis()
gen = make_generator(basis)
true_center = (10 * PIXEL_SCALE, -5 * PIXEL_SCALE)
planes = gen.generate(
coefficients={(0, 0): 1.0 + 0j},
z_list=Z_LIST,
center=true_center,
noise_std=1e-4,
seed=2,
)
fitter = ModalFitter(basis)
result = fitter.fit(planes, modes=[(0, 0)], initial_center=true_center)
for cx, cy in result.centers:
assert cx == pytest.approx(true_center[0], abs=2 * PIXEL_SCALE)
assert cy == pytest.approx(true_center[1], abs=2 * PIXEL_SCALE)
def test_fit_recovers_unknown_pixel_scale():
# Use a coarser pixel scale so the (much wider, far-field) beam at the
# outer z distances still fits within the frame -- otherwise pixel scale
# becomes unobservable from clipped images.
basis = make_basis()
local_pixel_scale = 1.5e-3
gen = SyntheticBeamGenerator(basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=local_pixel_scale)
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, noise_std=1e-4, seed=3)
# hide the known calibration to force the fitter to solve for it
for plane in planes:
plane.pixel_scale = None
plane.viewing_angle_deg = None
fitter = ModalFitter(basis)
result = fitter.fit(
planes,
modes=[(0, 0)],
initial_pixel_scale=local_pixel_scale * 1.1,
initial_viewing_angle_deg=0.0,
)
fitted_scales = [result.geometry[f"pixel_scale_{i}"] for i in range(len(planes))]
for scale in fitted_scales:
assert scale == pytest.approx(local_pixel_scale, rel=0.05)
def test_fit_auto_does_not_add_modes_for_pure_fundamental():
basis = make_basis()
gen = make_generator(basis)
planes = gen.generate(
coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, noise_std=1e-4, seed=4
)
fitter = ModalFitter(basis)
result = fitter.fit_auto(planes, max_order=2)
assert set(result.purity.keys()) == {(0, 0)}
def test_fit_auto_grows_to_include_second_mode():
basis = make_basis()
gen = make_generator(basis)
true_coeffs = {(0, 0): 0.9 + 0j, (0, 1): 0.4 + 0j}
planes = gen.generate(coefficients=true_coeffs, z_list=Z_LIST, noise_std=1e-4, seed=5)
fitter = ModalFitter(basis)
result = fitter.fit_auto(planes, max_order=2)
assert (0, 1) in result.purity or (0, -1) in result.purity
tests/test_geometry.py
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import numpy as np
import pytest
from he11lib.data import MeasurementPlane
from he11lib.geometry import GeometryCalibration
def test_pixel_scale_known_reflects_plane():
plane_known = MeasurementPlane(flux=np.ones((5, 5)), z=0.3, pixel_scale=1e-4)
plane_unknown = MeasurementPlane(flux=np.ones((5, 5)), z=0.3)
assert GeometryCalibration(plane_known).pixel_scale_known is True
assert GeometryCalibration(plane_unknown).pixel_scale_known is False
def test_viewing_angle_known_reflects_plane():
plane_known = MeasurementPlane(flux=np.ones((5, 5)), z=0.3, viewing_angle_deg=10.0)
plane_unknown = MeasurementPlane(flux=np.ones((5, 5)), z=0.3)
assert GeometryCalibration(plane_known).viewing_angle_known is True
assert GeometryCalibration(plane_unknown).viewing_angle_known is False
def test_physical_coordinates_uses_known_calibration():
plane = MeasurementPlane(
flux=np.ones((5, 5)), z=0.3, pixel_scale=2e-4, viewing_angle_deg=0.0
)
calib = GeometryCalibration(plane)
x, y = calib.physical_coordinates()
row_idx = np.arange(5) - 2
col_idx = np.arange(5) - 2
expected_x = col_idx * 2e-4
expected_y = row_idx * 2e-4
np.testing.assert_allclose(x[2, :], expected_x)
np.testing.assert_allclose(y[:, 2], expected_y)
def test_physical_coordinates_compresses_x_for_viewing_angle():
plane = MeasurementPlane(
flux=np.ones((5, 5)), z=0.3, pixel_scale=2e-4, viewing_angle_deg=60.0
)
calib = GeometryCalibration(plane)
x, y = calib.physical_coordinates()
col_idx = np.arange(5) - 2
expected_x = col_idx * 2e-4 / np.cos(np.deg2rad(60.0))
np.testing.assert_allclose(x[2, :], expected_x)
def test_physical_coordinates_raises_without_calibration_or_override():
plane = MeasurementPlane(flux=np.ones((5, 5)), z=0.3)
calib = GeometryCalibration(plane)
with pytest.raises(ValueError, match="pixel_scale"):
calib.physical_coordinates()
def test_physical_coordinates_accepts_override_for_unknown_values():
plane = MeasurementPlane(flux=np.ones((5, 5)), z=0.3)
calib = GeometryCalibration(plane)
x, y = calib.physical_coordinates(pixel_scale=1e-4, viewing_angle_deg=0.0)
col_idx = np.arange(5) - 2
np.testing.assert_allclose(x[2, :], col_idx * 1e-4)
def test_known_calibration_takes_precedence_over_override():
plane = MeasurementPlane(
flux=np.ones((5, 5)), z=0.3, pixel_scale=2e-4, viewing_angle_deg=0.0
)
calib = GeometryCalibration(plane)
# override should be ignored since plane already specifies calibration
x, _ = calib.physical_coordinates(pixel_scale=999.0, viewing_angle_deg=45.0)
col_idx = np.arange(5) - 2
np.testing.assert_allclose(x[2, :], col_idx * 2e-4)
tests/test_modes.py
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import numpy as np
import pytest
from he11lib.modes import LGBasis
W0 = 5e-3 # 5 mm waist
Z0 = 0.5 # waist at 0.5 m
WAVELENGTH = 1.76e-3 # ~170 GHz gyrotron
def make_grid(w, half_widths_in_w=6.0, n=300):
extent = half_widths_in_w * w
coords = np.linspace(-extent, extent, n)
dx = coords[1] - coords[0]
x, y = np.meshgrid(coords, coords)
return x, y, dx
def test_beam_radius_at_waist_equals_w0():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
assert basis.beam_radius(Z0) == pytest.approx(W0)
def test_beam_radius_at_one_rayleigh_range():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
zR = np.pi * W0**2 / WAVELENGTH
assert basis.beam_radius(Z0 + zR) == pytest.approx(W0 * np.sqrt(2))
def test_gouy_phase_zero_at_waist():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
assert basis.gouy_phase(Z0, p=0, l=0) == pytest.approx(0.0)
assert basis.gouy_phase(Z0, p=1, l=2) == pytest.approx(0.0)
def test_gouy_phase_at_one_rayleigh_range_for_fundamental():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
zR = np.pi * W0**2 / WAVELENGTH
# order (2p+|l|+1) = 1 for p=0,l=0; atan(1) = pi/4
assert basis.gouy_phase(Z0 + zR, p=0, l=0) == pytest.approx(np.pi / 4)
def test_fundamental_mode_matches_analytic_gaussian_at_waist():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
x, y, _ = make_grid(W0, n=50)
r2 = x**2 + y**2
field = basis.field(x, y, Z0, p=0, l=0)
expected_intensity_shape = np.exp(-2 * r2 / W0**2)
intensity = np.abs(field) ** 2
# shapes should match up to a constant normalization factor
ratio = intensity / expected_intensity_shape
ratio_center = ratio[len(ratio) // 2, len(ratio) // 2]
np.testing.assert_allclose(ratio / ratio_center, 1.0, atol=1e-6)
def test_mode_is_normalized_at_waist():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
x, y, dx = make_grid(W0, n=400)
field = basis.field(x, y, Z0, p=0, l=0)
total_power = np.sum(np.abs(field) ** 2) * dx**2
assert total_power == pytest.approx(1.0, rel=2e-3)
def test_mode_is_normalized_away_from_waist():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
z = Z0 + 0.2
w_z = basis.beam_radius(z)
x, y, dx = make_grid(w_z, n=400)
field = basis.field(x, y, z, p=1, l=2)
total_power = np.sum(np.abs(field) ** 2) * dx**2
assert total_power == pytest.approx(1.0, rel=2e-3)
def test_modes_are_orthogonal():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
z = Z0 + 0.1
w_z = basis.beam_radius(z)
x, y, dx = make_grid(w_z, n=400)
field_a = basis.field(x, y, z, p=0, l=0)
field_b = basis.field(x, y, z, p=1, l=0)
inner_product = np.sum(field_a * np.conj(field_b)) * dx**2
assert abs(inner_product) < 1e-3
def test_project_recovers_known_coefficients():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
z = Z0 + 0.15
w_z = basis.beam_radius(z)
x, y, dx = make_grid(w_z, n=400)
true_coeffs = {(0, 0): 0.8 + 0.1j, (1, 0): 0.2 - 0.3j}
field = basis.field_superposition(x, y, z, true_coeffs)
recovered = basis.project(field, x, y, dx, z, modes=list(true_coeffs.keys()))
for mode, coeff in true_coeffs.items():
assert recovered[mode] == pytest.approx(coeff, abs=5e-3)
tests/test_noise.py
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import numpy as np
import pytest
from he11lib.noise import NoiseEstimator
def test_estimate_std_recovers_known_noise_on_flat_image():
rng = np.random.default_rng(0)
true_std = 0.05
image = np.ones((200, 200)) * 10.0 + rng.normal(0, true_std, size=(200, 200))
estimated = NoiseEstimator().estimate_std(image)
assert estimated == pytest.approx(true_std, rel=0.15)
def test_estimate_std_recovers_known_noise_on_smooth_bump():
rng = np.random.default_rng(1)
x = np.linspace(-3, 3, 200)
xx, yy = np.meshgrid(x, x)
smooth = np.exp(-(xx**2 + yy**2))
true_std = 0.01
image = smooth + rng.normal(0, true_std, size=smooth.shape)
estimated = NoiseEstimator().estimate_std(image)
assert estimated == pytest.approx(true_std, rel=0.35)
def test_estimate_std_near_zero_for_noise_free_image():
x = np.linspace(-3, 3, 100)
xx, yy = np.meshgrid(x, x)
smooth = np.exp(-(xx**2 + yy**2))
estimated = NoiseEstimator().estimate_std(smooth)
assert estimated < 1e-6
def test_weights_are_uniform_and_match_shape():
rng = np.random.default_rng(2)
image = np.ones((50, 50)) * 5.0 + rng.normal(0, 0.1, size=(50, 50))
weights = NoiseEstimator().weights(image)
assert weights.shape == image.shape
assert np.allclose(weights, weights.flat[0])
expected_std = NoiseEstimator().estimate_std(image)
assert weights.flat[0] == pytest.approx(1.0 / expected_std**2, rel=1e-6)
tests/test_phase_retrieval.py
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import numpy as np
import pytest
from he11lib.modes import LGBasis
from he11lib.phase_retrieval import PhaseRetriever, propagate_angular_spectrum
from he11lib.synthetic import SyntheticBeamGenerator
W0 = 5e-3
Z0 = 0.5
WAVELENGTH = 1.76e-3
PIXEL_SCALE = 3e-4
IMAGE_SHAPE = (121, 121)
def make_basis():
return LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
def make_grid():
coords = (np.arange(IMAGE_SHAPE[0]) - IMAGE_SHAPE[0] // 2) * PIXEL_SCALE
x, y = np.meshgrid(coords, coords)
return x, y
def test_propagate_round_trip_recovers_original_field():
basis = make_basis()
x, y = make_grid()
field = basis.field(x, y, Z0, p=0, l=0)
forward = propagate_angular_spectrum(field, PIXEL_SCALE, dz=0.05, wavelength=WAVELENGTH)
back = propagate_angular_spectrum(forward, PIXEL_SCALE, dz=-0.05, wavelength=WAVELENGTH)
np.testing.assert_allclose(back, field, atol=1e-3 * np.max(np.abs(field)))
def test_propagate_matches_lgbasis_analytic_evolution():
basis = make_basis()
x, y = make_grid()
field_at_waist = basis.field(x, y, Z0, p=0, l=0)
dz = 0.05
propagated = propagate_angular_spectrum(field_at_waist, PIXEL_SCALE, dz=dz, wavelength=WAVELENGTH)
analytic = basis.field(x, y, Z0 + dz, p=0, l=0)
# compare intensity profiles (phase reference/global constant may differ)
np.testing.assert_allclose(
np.abs(propagated) ** 2, np.abs(analytic) ** 2, atol=1e-2 * np.max(np.abs(analytic) ** 2)
)
def test_retrieve_recovers_pure_mode_purity():
# Keep z distances close to the waist so the (widening) beam stays well
# within the frame -- otherwise FFT wraparound/clipping at the edges
# degrades angular-spectrum propagation accuracy.
basis = make_basis()
gen = SyntheticBeamGenerator(basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=PIXEL_SCALE)
z_list = [0.47, 0.5, 0.53]
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=z_list, noise_std=1e-5, seed=0)
retriever = PhaseRetriever(wavelength=WAVELENGTH)
result = retriever.retrieve(planes, viewing_angle_deg=0.0, max_iterations=100)
coeffs = basis.project(
result.field, result.x, result.y, PIXEL_SCALE, result.z, modes=[(0, 0), (1, 0), (0, 1)]
)
total_power = sum(abs(c) ** 2 for c in coeffs.values())
purity_00 = abs(coeffs[(0, 0)]) ** 2 / total_power
assert purity_00 > 0.9
def test_retrieve_estimates_beam_center():
basis = make_basis()
gen = SyntheticBeamGenerator(basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=PIXEL_SCALE)
z_list = [0.47, 0.5, 0.53]
true_center = (15 * PIXEL_SCALE, -8 * PIXEL_SCALE)
planes = gen.generate(
coefficients={(0, 0): 1.0 + 0j}, z_list=z_list, center=true_center, noise_std=1e-5, seed=1
)
retriever = PhaseRetriever(wavelength=WAVELENGTH)
result = retriever.retrieve(planes, viewing_angle_deg=0.0, max_iterations=100)
assert result.center[0] == pytest.approx(true_center[0], abs=3 * PIXEL_SCALE)
assert result.center[1] == pytest.approx(true_center[1], abs=3 * PIXEL_SCALE)
tests/test_plotting.py
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import matplotlib.figure
import numpy as np
import pytest
from he11lib.data import MeasurementPlane, ReconstructionResult
from he11lib.plotting import plot_center_trace, plot_mode_purity, plot_residuals
def make_result(**overrides):
defaults = dict(
purity={(0, 0): (0.9, 0.1), (1, 0): (0.1, -0.2)},
reconstructed_field=np.zeros((5, 5), dtype=complex),
centers=[(0.0, 0.0), (1e-4, -1e-4), (2e-4, -2e-4)],
pointing_angle_deg=0.5,
residuals=[np.ones((5, 5)), np.ones((5, 5)) * 2, np.ones((5, 5)) * 3],
)
defaults.update(overrides)
return ReconstructionResult(**defaults)
def make_planes():
return [
MeasurementPlane(flux=np.zeros((5, 5)), z=0.3),
MeasurementPlane(flux=np.zeros((5, 5)), z=0.5),
MeasurementPlane(flux=np.zeros((5, 5)), z=0.7),
]
def test_plot_mode_purity_draws_one_bar_per_mode():
result = make_result()
fig = plot_mode_purity(result)
assert isinstance(fig, matplotlib.figure.Figure)
ax = fig.axes[0]
assert len(ax.patches) == len(result.purity)
def test_plot_center_trace_plots_one_point_per_plane():
planes = make_planes()
result = make_result()
fig = plot_center_trace(planes, result)
assert isinstance(fig, matplotlib.figure.Figure)
ax = fig.axes[0]
line = ax.lines[0]
assert len(line.get_xdata()) == len(planes)
def test_plot_residuals_draws_one_axes_per_plane():
planes = make_planes()
result = make_result()
fig = plot_residuals(planes, result)
assert isinstance(fig, matplotlib.figure.Figure)
image_axes = [ax for ax in fig.axes if ax.images]
assert len(image_axes) == len(planes)
def test_plot_residuals_raises_when_phase_retrieval_used_without_residuals():
planes = make_planes()
result = make_result(residuals=[], used_phase_retrieval=True)
with pytest.raises(ValueError, match="residuals"):
plot_residuals(planes, result)
tests/test_reconstruct.py
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from dataclasses import replace
import pytest
from he11lib.deconvolution import DiffusionDeconvolver
from he11lib.fitting import ModalFitter
from he11lib.modes import LGBasis
from he11lib.reconstruct import BeamReconstructor
from he11lib.synthetic import SyntheticBeamGenerator
W0 = 5e-3
Z0 = 0.5
WAVELENGTH = 1.76e-3
PIXEL_SCALE = 4e-4
IMAGE_SHAPE = (61, 61)
Z_LIST = [0.35, 0.5, 0.65, 0.8]
def make_basis():
return LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
def make_generator(basis):
return SyntheticBeamGenerator(basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=PIXEL_SCALE)
def test_reconstruct_recovers_pure_mode_purity():
basis = make_basis()
gen = make_generator(basis)
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, noise_std=1e-4, seed=0)
reconstructor = BeamReconstructor(w0=W0, z0=Z0, wavelength=WAVELENGTH, max_order=2)
result = reconstructor.reconstruct(planes)
power_fraction, _ = result.purity[(0, 0)]
assert power_fraction == pytest.approx(1.0, abs=1e-3)
assert result.used_phase_retrieval is False
def test_reconstruct_recovers_center_offset():
basis = make_basis()
gen = make_generator(basis)
true_center = (10 * PIXEL_SCALE, -5 * PIXEL_SCALE)
planes = gen.generate(
coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, center=true_center, noise_std=1e-4, seed=1
)
reconstructor = BeamReconstructor(w0=W0, z0=Z0, wavelength=WAVELENGTH, max_order=2)
result = reconstructor.reconstruct(planes)
for cx, cy in result.centers:
assert cx == pytest.approx(true_center[0], abs=2 * PIXEL_SCALE)
assert cy == pytest.approx(true_center[1], abs=2 * PIXEL_SCALE)
def test_reconstruct_with_deconvolution_corrects_blur():
basis = make_basis()
gen = make_generator(basis)
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=Z_LIST, noise_std=1e-4, seed=2)
deconvolver = DiffusionDeconvolver(thermal_diffusivity=1e-6, dwell_time=30.0)
blurred_planes = [
replace(p, flux=deconvolver.blur(p.flux, p.pixel_scale)) for p in planes
]
# Without deconvolution, blur should measurably hurt purity recovery.
fitter = ModalFitter(basis)
result_no_deconv = fitter.fit(blurred_planes, modes=[(0, 0), (1, 0), (0, 1)])
purity_no_deconv, _ = result_no_deconv.purity[(0, 0)]
reconstructor = BeamReconstructor(
w0=W0, z0=Z0, wavelength=WAVELENGTH, max_order=2, deconvolver=deconvolver
)
result = reconstructor.reconstruct(blurred_planes)
purity_with_deconv, _ = result.purity[(0, 0)]
assert purity_with_deconv > purity_no_deconv
assert purity_with_deconv > 0.9
def test_reconstruct_forces_phase_retrieval_fallback():
basis = make_basis()
gen = SyntheticBeamGenerator(basis=basis, image_shape=(121, 121), pixel_scale=3e-4)
z_list = [0.47, 0.5, 0.53]
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=z_list, noise_std=1e-5, seed=3)
reconstructor = BeamReconstructor(
w0=W0, z0=Z0, wavelength=WAVELENGTH, max_order=2, force_phase_retrieval=True
)
result = reconstructor.reconstruct(planes)
assert result.used_phase_retrieval is True
power_fraction, _ = result.purity[(0, 0)]
assert power_fraction > 0.9
def test_reconstruct_falls_back_automatically_on_high_residual():
basis = make_basis()
gen = SyntheticBeamGenerator(basis=basis, image_shape=(121, 121), pixel_scale=3e-4)
z_list = [0.47, 0.5, 0.53]
planes = gen.generate(coefficients={(0, 0): 1.0 + 0j}, z_list=z_list, noise_std=1e-5, seed=4)
reconstructor = BeamReconstructor(
w0=W0,
z0=Z0,
wavelength=WAVELENGTH,
max_order=2,
phase_retrieval_residual_threshold=1e-8,
)
result = reconstructor.reconstruct(planes)
assert result.used_phase_retrieval is True
tests/test_synthetic.py
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import numpy as np
import pytest
from he11lib.modes import LGBasis
from he11lib.synthetic import SyntheticBeamGenerator
W0 = 5e-3
Z0 = 0.5
WAVELENGTH = 1.76e-3
PIXEL_SCALE = 2e-4 # 0.2 mm/px
IMAGE_SHAPE = (161, 161) # odd so there's a well-defined center pixel
def make_generator():
basis = LGBasis(w0=W0, z0=Z0, wavelength=WAVELENGTH)
return SyntheticBeamGenerator(
basis=basis, image_shape=IMAGE_SHAPE, pixel_scale=PIXEL_SCALE
)
def test_generate_returns_planes_with_requested_z():
gen = make_generator()
z_list = [0.3, 0.4, 0.5]
planes = gen.generate(coefficients={(0, 0): 1 + 0j}, z_list=z_list)
assert [p.z for p in planes] == z_list
assert all(p.flux.shape == IMAGE_SHAPE for p in planes)
def test_generate_pure_mode_peak_at_image_center_when_centered():
gen = make_generator()
planes = gen.generate(coefficients={(0, 0): 1 + 0j}, z_list=[Z0], center=(0.0, 0.0))
flux = planes[0].flux
peak_idx = np.unravel_index(np.argmax(flux), flux.shape)
center_idx = (IMAGE_SHAPE[0] // 2, IMAGE_SHAPE[1] // 2)
assert peak_idx == center_idx
def test_generate_applies_center_offset():
gen = make_generator()
offset_m = 20 * PIXEL_SCALE # 20 pixels
planes = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], center=(offset_m, 0.0)
)
flux = planes[0].flux
peak_idx = np.unravel_index(np.argmax(flux), flux.shape)
center_row = IMAGE_SHAPE[0] // 2
center_col = IMAGE_SHAPE[1] // 2
assert peak_idx[0] == center_row
assert peak_idx[1] == pytest.approx(center_col + 20, abs=1)
def test_generate_applies_pointing_angle_as_linear_drift():
gen = make_generator()
pointing_angle_deg = 1.0 # small tilt
z_list = [Z0, Z0 + 0.2]
planes = gen.generate(
coefficients={(0, 0): 1 + 0j},
z_list=z_list,
center=(0.0, 0.0),
pointing_angle_deg=pointing_angle_deg,
)
peaks_col = []
for plane in planes:
peak_idx = np.unravel_index(np.argmax(plane.flux), plane.flux.shape)
peaks_col.append(peak_idx[1])
expected_shift_m = 0.2 * np.tan(np.deg2rad(pointing_angle_deg))
expected_shift_px = expected_shift_m / PIXEL_SCALE
actual_shift_px = peaks_col[1] - peaks_col[0]
assert actual_shift_px == pytest.approx(expected_shift_px, abs=1)
def test_generate_noise_is_reproducible_with_seed():
gen = make_generator()
planes_a = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], noise_std=0.01, seed=42
)
planes_b = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], noise_std=0.01, seed=42
)
np.testing.assert_array_equal(planes_a[0].flux, planes_b[0].flux)
def test_generate_noise_std_matches_requested_level():
gen = make_generator()
noise_std = 0.02
planes_noisy = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], noise_std=noise_std, seed=1
)
planes_clean = gen.generate(coefficients={(0, 0): 1 + 0j}, z_list=[Z0], noise_std=0.0)
diff = planes_noisy[0].flux - planes_clean[0].flux
assert np.std(diff) == pytest.approx(noise_std, rel=0.15)
def test_generate_viewing_angle_compresses_tilt_axis():
gen = make_generator()
planes_straight = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], viewing_angle_deg=0.0
)
planes_tilted = gen.generate(
coefficients={(0, 0): 1 + 0j}, z_list=[Z0], viewing_angle_deg=60.0
)
def width_along_axis(flux, axis):
profile = flux[flux.shape[0] // 2, :] if axis == 1 else flux[:, flux.shape[1] // 2]
half_max = profile.max() / 2
above = np.where(profile >= half_max)[0]
return above[-1] - above[0]
width_straight_x = width_along_axis(planes_straight[0].flux, axis=1)
width_tilted_x = width_along_axis(planes_tilted[0].flux, axis=1)
width_straight_y = width_along_axis(planes_straight[0].flux, axis=0)
width_tilted_y = width_along_axis(planes_tilted[0].flux, axis=0)
# tilt compresses the viewed beam along the tilt (x) axis, y unaffected
assert width_tilted_x < width_straight_x
assert width_tilted_y == pytest.approx(width_straight_y, abs=1)