torch/autograd support for the Mie scatterer and backend

[edudc]

Summary

This makes torch MieSphere rendering differentiable through both geometric and hybrid modes, including propagation and optical field assembly. The Mie backend now uses DeepTrack's array API namespace where possible, using the existing SciPy based NumPy path for special functions.

Prerequisites

This PR depends on two active prerequisite fixes from other PRs:

• optics.py: al/bf-mie-fix #478
• aberrations.py: fix z-coeffs skip when 0 for torch #479

Please merge them first.

Changes

• Refactor deeptrack.backend.mie to support torch tensors and autograd.
• Add Riccati-Bessel polynomial recurrences for non NumPy backends using array API.
• Preserve existing NumPy/SciPy behavior for the NumPy path.
• Add torch parity and autodiff coverage for:
  • homogeneous Mie coefficients
  • stratified Mie coefficients
  • Mie harmonics
• Refactor MieScatterer field construction to use Python array API operations for:
  • coordinate grids and masks
  • polarization coefficients
  • geometric and hybrid field assembly
  • FFT / inverse FFT paths
  • propagation matrix application
• Make get_propagation_matrix backend-aware so torch inputs remain differentiable.
• Preserve torch tensors through MieSphere coefficients so gradients flow to radius and
  refractive index.
• Keep MieStratifiedSphere tensor safe where it shares the same conversion path.
• Add a tensor-safe unit conversion path in ConversionTable so torch tensors, including tensor-valued tuples like position=(x, y), do not get routed through Pint conversions that can trigger NumPy/scalar conversion.
• Keep tensor-valued voxel_size flowing through the microscope, Mie field setup, and torch pupil path so resolution and magnification remain differentiable.
• Update _pupil_torch to keep NA, wavelength, refractive_index_medium, voxel_size, and defocus on the torch path/device.
• Replace the nan_to_num cleanup in the pupil phase calculation with a pre-sqrt clamp that is compatible with torch autograd.
• Add torch regression tests for:
  • MieSphere.resolve() autodiff in geometric and hybrid modes
  • multiple torch Mie fields summed through brightfield optics
  • torch autodiff through get_propagation_matrix
  • zero-valued learnable Zernike coefficients staying in the graph
  • learnable x, y, resolution, NA, magnification, wavelength, and
    refractive_index_medium.

Notes

polynomials.py currently depends on SciPy’s arbitrary order cylindrical Bessel/Hankel functions. torch.special does have Bessel functions, but does not cover arbitrary order jv/yv or h1vp. Also PyTorch's implementation does not work with autograd. In 2.11.0 this fails:

x = torch.tensor(1.0, requires_grad=True)
y = torch.special.bessel_j0(x)
y.backward()

because y has no grad_fn. (PyTorch forum discussion about this: https://discuss.pytorch.org/t/a-problem-about-autograd-and-special-bessel-j0/192062).

For integer-order Riccati-Bessel functions used by Mie, we can compute them from sin, cos and the recurrence relations, which makes it autograd friendly (and works on GPU).

[cmanzo]

The PR currently breaks several tests and appears to break the upscale property for Brightfield.

It also introduces substantial changes to optics and scatterers, which I was not expecting to be necessary. These changes should be carefully reviewed, as they may introduce unintended regressions.

In addition, I tried using backpropagation to optimize the position of a single scatterer, but the optimization does not appear to converge.