Add charge diffusion to optika.sensors.vmr_signal

[roytsmart]

Summary

optika.sensors.vmr_signal previously ignored charge diffusion, so it disagreed with the Monte Carlo signal() function for sensors with a field-free region (it overestimated the VMR by ~50% for EUV wavelengths on a device like the e2v CCD97).

This PR generalizes the analytic VMR to include charge diffusion. The existing expression is rewritten compactly as

$$F(N_e'') = 1 + \left( \overline{n} + \mathcal{F} - 1 \right) \frac{\langle \eta^2(z) \rangle}{\langle \eta(z) \rangle},$$

where the constant term is the uncorrelated (Poisson) component and the second term is the photon-correlated component, arising because the $\sim \overline{n}$ electrons produced by a single photon are measured together in the same pixel. Charge diffusion weakens exactly this correlation: weighting the correlated component by the probability $D(z)$ that two electrons from the same photon land in the same pixel gives

$$F(N_e'') = 1 + \left( \overline{n} + \mathcal{F} - 1 \right) \frac{\langle D(z) , \eta^2(z) \rangle}{\langle \eta(z) \rangle}.$$

For the Gaussian diffusion kernel used by electrons_measured, $D(z)$ has a closed form per axis (averaged over the photon's uniform sub-pixel position); only the depth average requires numerical quadrature, performed in CDF space of the truncated-exponential absorption-depth distribution.

Changes

• vmr_signal gains thickness_depletion, thickness_substrate, and width_pixel parameters (defaults mirror signal, so no diffusion and no behavior change by default) plus a diffusion toggle alongside shot/fano/pcc. The derivation is documented in the Notes section, with a new example comparing against a diffused Monte Carlo.
• New private helper _probability_same_pixel implementing the per-axis pair-coincidence probability.
• The correction is threaded up the uncertainty stack: AbstractSensorMaterial.uncertainty (and implementations) gain a width_pixel parameter, and AbstractImagingSensor.uncertainty passes width_pixel=self.width_pixel, mirroring what expose() already does for the signal itself. expose(uncertainty=True) therefore now attaches a width consistent with its own diffused signal realization.

Validation

• Against signal() with thickness_depletion=2 μm, wrap=True, 100–1000 Å: agreement within Monte Carlo noise (~0.5%) at every wavelength (e.g. 9.37 vs 9.37 electron at 100 Å, where the no-diffusion formula gives 14.3).
• A standalone Monte Carlo replicating the diffusion model (shared depth and sub-pixel position per photon, binomial CCE, Fano noise) confirms the formula to ~0.1%, including the coupled PCC + diffusion case.
• The 1001-point quadrature is converged to ~4e-5 relative error in the worst case (absorption length ≪ field-free thickness).
• New test_vmr_signal_diffusion compares the analytic result against signal() to 10%, and the shared test_uncertainty now exercises width_pixel across every material fixture.

The analytic result assumes uniform illumination and a periodic pixel grid (wrap=True); it remains a good approximation away from the edges of a sensor with wrap=False.

🤖 Generated with Claude Code

https://claude.ai/code/session_0192abyvBf2Zw5rq5CQ62JFb

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.58%. Comparing base (43f7e49) to head (2ecd0d3).

Additional details and impacted files

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  Coverage   99.57%   99.58%           
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  Files         118      118           
  Lines        6880     6933   +53     
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+ Hits         6851     6904   +53     
  Misses         29       29           

Flag	Coverage Δ
unittests	99.58% <100.00%> (+<0.01%)	⬆️

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