At upstream commit 2201ab0d7ac6f88d529dc7ec8444448e674d9a9c, both RayOperand.AOI and the batched evaluator's _extract_aoi convert the computed angle to a Python float with .item(). An AOI-only objective therefore loses its connection to optical variables on the Torch backend.

For a Cooke triplet, tracing the on-axis field at pupil (0, 0.5) to surface 1 gives an AOI of about 6.520933 degrees. Varying its radius gives a finite-difference derivative of about -0.297509 degrees per lens unit, but the optimization residual and merit have requires_grad=False with batching either enabled or disabled.

Minimal reproduction (repeat with batching=False for the standard path):

import optiland.backend as be
import torch
from optiland.optimization import OptimizationProblem
from optiland.samples import CookeTriplet

be.set_backend("torch")
be.set_precision("float64")
lens = CookeTriplet()
problem = OptimizationProblem(batching=True)
problem.add_variable(lens, "radius", surface_number=1)
variable = problem.variables[0].variable
radius = torch.tensor(variable.get_value().item(), dtype=torch.float64,
                      requires_grad=True)
variable.update_value(radius)
problem.update_optics()
problem.add_operand("AOI", target=5.0, input_data=dict(
    optic=lens, surface_number=1, Hx=0.0, Hy=0.0, Px=0.0, Py=0.5,
    wavelength=lens.primary_wavelength,
))
print(problem.residual_vector().requires_grad)  # False before the fix
print(problem.sum_squared().requires_grad)     # False before the fix

Preserving the tensor alone also reveals a NaN derivative from acos(1) for a normal-incidence zero-target merit.

I have prepared a focused fix that keeps a scalar backend value, uses a shared equivalent unsigned atan2 angle calculation for both evaluation paths, and covers the scalar-stacking regression from #352. Local NumPy/Torch tests check ordinary incidence against finite differences and normal-incidence zero-target merit gradients. No new operand or optical convention is introduced.