diff --git a/scripts/jax_grad/interferometer.py b/scripts/jax_grad/interferometer.py
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+"""
+Tests JAX gradients of the interferometer log-likelihood, in two stages
+(finiteness, then autodiff-vs-central-finite-difference correctness — see
+``util.py``), for the two configurations used in practice:
+
+**Variant A — parametric light profiles** (``lp.Sersic`` standard +
+``lp_linear.Sersic``): the visibility-space analogue of
+``imaging_lp.py``. The source is the only light in interferometer data, so
+the model has no lens light component and the evaluation point is anchored
+near the simulator truth so the positive-only NNLS keeps the linear source
+live.
+
+**Variant B — ``RectangularAdaptDensity`` via the sparse linear-algebra
+path**: mirrors ``jax_likelihood_functions/interferometer/rectangular_sparse.py``
+exactly — ``TransformerDFT`` + ``apply_sparse_operator(use_jax=True)`` (the
+sparse NUFFT response-matrix formalism; the operator is aux state built once
+outside the JIT trace), ``RectangularAdaptDensity`` mesh + ``reg.Adapt()`` +
+``al.AdaptImages``. **Measured verdict (2026-07-09): the imaging os_pix=1
+staircase applies** — interferometer pixelization has no over-sampling, so the
+mesh's rank-transform queries coincide with its knots and the likelihood is
+invariant to smooth mass perturbations: every mass/shear autodiff gradient is
+exactly zero (correct — FD shows only ~1e-7-scale micro-jumps from rank
+re-orderings, no smooth slope). With the model having no lens light, that means
+**no usable gradients at all** in this configuration. The assertions document
+this staircase so a change in mesh differentiability fails loudly.
+
+**Variant C — ``RectangularUniform`` via the same sparse path**: the working
+alternative for gradient-based inference — no adaptive transform, so mass/shear
+gradients are live and strictly FD-matched.
+
+See the audit README
+(`autolens_workspace_developer/jax_profiling/gradient/README.md`).
+"""
+
+import numpy as np
+import jax
+import jax.numpy as jnp
+from os import path
+
+import autofit as af
+import autolens as al
+
+import util
+
+"""
+__Mask + Dataset__
+"""
+real_space_mask = al.Mask2D.circular(
+    shape_native=(256, 256),
+    pixel_scales=0.1,
+    radius=3.0,
+)
+
+dataset_name = "simple"
+dataset_path = path.join("dataset", "interferometer", dataset_name)
+
+"""
+__Dataset Auto-Simulation__
+"""
+if al.util.dataset.should_simulate(dataset_path):
+    import subprocess
+    import sys
+
+    subprocess.run(
+        [sys.executable, "scripts/jax_likelihood_functions/interferometer/simulator.py"],
+        check=True,
+    )
+
+dataset = al.Interferometer.from_fits(
+    data_path=path.join(dataset_path, "data.fits"),
+    noise_map_path=path.join(dataset_path, "noise_map.fits"),
+    uv_wavelengths_path=path.join(dataset_path, "uv_wavelengths.fits"),
+    real_space_mask=real_space_mask,
+    transformer_class=al.TransformerDFT,
+)
+
+from autofit.non_linear.fitness import Fitness
+
+
+def mass_and_shear():
+    """
+    Truth-centred lens mass model (simulator: Isothermal ER=1.6, shear 0.05).
+    """
+    mass = af.Model(al.mp.Isothermal)
+    mass.centre.centre_0 = af.GaussianPrior(mean=0.0, sigma=0.005)
+    mass.centre.centre_1 = af.GaussianPrior(mean=0.0, sigma=0.005)
+    mass.einstein_radius = af.GaussianPrior(mean=1.6, sigma=0.05)
+    mass.ell_comps.ell_comps_0 = af.GaussianPrior(mean=0.05, sigma=0.01)
+    mass.ell_comps.ell_comps_1 = af.GaussianPrior(mean=0.05, sigma=0.01)
+    shear = af.Model(al.mp.ExternalShear)
+    shear.gamma_1 = af.GaussianPrior(mean=0.05, sigma=0.005)
+    shear.gamma_2 = af.GaussianPrior(mean=0.05, sigma=0.005)
+    return mass, shear
+
+
+def param_vector_from(model):
+    param_vector = jnp.array(model.physical_values_from_prior_medians)
+    key = jax.random.PRNGKey(42)
+    perturbation = jax.random.uniform(
+        key, shape=param_vector.shape, minval=0.001, maxval=0.005
+    )
+    return param_vector + perturbation
+
+
+def finiteness_checks(fitness, param_vector, n_params):
+    value, grad = jax.value_and_grad(fitness.call)(param_vector)
+    print(f"Log likelihood = {float(value):.6f}")
+    assert np.isfinite(float(value)), "Log likelihood is not finite"
+    assert grad.shape == (n_params,), f"Gradient shape mismatch: {grad.shape}"
+    assert np.all(
+        np.isfinite(np.array(grad))
+    ), f"Gradient contains non-finite values: {np.array(grad)}"
+    assert not np.all(np.array(grad) == 0.0), "Gradient is all zeros"
+    return grad
+
+
+"""
+__Variant A: parametric light profiles (standard + linear Sersic source)__
+"""
+for variant, bulge_cls in [
+    ("lp.Sersic (standard)", al.lp.Sersic),
+    ("lp_linear.Sersic (linear)", al.lp_linear.Sersic),
+]:
+    print(f"\n=== interferometer {variant} ===")
+
+    source_bulge = af.Model(bulge_cls)
+    source_bulge.centre.centre_0 = af.GaussianPrior(mean=0.0, sigma=0.005)
+    source_bulge.centre.centre_1 = af.GaussianPrior(mean=0.0, sigma=0.005)
+    source_bulge.ell_comps.ell_comps_0 = af.GaussianPrior(mean=0.05, sigma=0.01)
+    source_bulge.ell_comps.ell_comps_1 = af.GaussianPrior(mean=0.05, sigma=0.01)
+    source_bulge.effective_radius = af.GaussianPrior(mean=1.0, sigma=0.05)
+    source_bulge.sersic_index = af.GaussianPrior(mean=1.0, sigma=0.2)
+
+    mass, shear = mass_and_shear()
+    lens = af.Model(al.Galaxy, redshift=0.5, mass=mass, shear=shear)
+    source = af.Model(al.Galaxy, redshift=1.0, bulge=source_bulge)
+    model = af.Collection(galaxies=af.Collection(lens=lens, source=source))
+
+    analysis = al.AnalysisInterferometer(dataset=dataset)
+
+    fitness = Fitness(
+        model=model,
+        analysis=analysis,
+        fom_is_log_likelihood=True,
+        resample_figure_of_merit=-1.0e99,
+    )
+
+    param_vector = param_vector_from(model)
+    param_names = util.parameter_names_from(model)
+
+    finiteness_checks(fitness, param_vector, n_params=len(param_names))
+
+    f_jit = jax.jit(fitness.call)
+
+    util.assert_eager_jit_consistent(fitness.call, f_jit, param_vector)
+
+    comparison = util.compare_gradients(
+        fitness.call,
+        param_vector,
+        param_names=param_names,
+        f_fd=f_jit,
+    )
+
+    util.assert_gradients_match(comparison)
+
+    print(f"interferometer {variant}: autodiff matches finite differences.")
+
+"""
+__Variants B + C: rectangular pixelized source via the sparse-operator path__
+
+The sparse NUFFT operator is aux state and must be built once, outside any JIT
+trace (mirrors ``rectangular_sparse.py``).
+"""
+dataset_sparse = dataset.apply_sparse_operator(use_jax=True, show_progress=True)
+
+mesh_shape = (8, 8)
+
+
+def sparse_fitness(mesh, regularization):
+    mass, shear = mass_and_shear()
+    lens = af.Model(al.Galaxy, redshift=0.5, mass=mass, shear=shear)
+
+    pixelization = al.Pixelization(mesh=mesh, regularization=regularization)
+    source = af.Model(al.Galaxy, redshift=1.0, pixelization=pixelization)
+    model = af.Collection(galaxies=af.Collection(lens=lens, source=source))
+
+    bulge = al.lp.Sersic()
+    adapt_image = bulge.image_2d_from(grid=dataset_sparse.grid)
+    adapt_images = al.AdaptImages(
+        galaxy_name_image_dict={
+            "('galaxies', 'lens')": adapt_image,
+            "('galaxies', 'source')": adapt_image,
+        }
+    )
+
+    analysis = al.AnalysisInterferometer(
+        dataset=dataset_sparse,
+        adapt_images=adapt_images,
+        raise_inversion_positions_likelihood_exception=False,
+    )
+
+    fitness = Fitness(
+        model=model,
+        analysis=analysis,
+        fom_is_log_likelihood=True,
+        resample_figure_of_merit=-1.0e99,
+    )
+    return fitness, param_vector_from(model), util.parameter_names_from(model)
+
+
+"""
+__Variant B: RectangularAdaptDensity — the documented staircase__
+"""
+print("\n=== interferometer RectangularAdaptDensity + reg.Adapt, sparse operator ===")
+
+fitness, param_vector, param_names = sparse_fitness(
+    mesh=al.mesh.RectangularAdaptDensity(shape=mesh_shape),
+    regularization=al.reg.Adapt(),
+)
+
+value, grad = jax.value_and_grad(fitness.call)(param_vector)
+print(f"Log likelihood = {float(value):.6f}")
+assert np.isfinite(float(value)), "Log likelihood is not finite"
+assert np.all(
+    np.isfinite(np.array(grad))
+), f"Gradient contains non-finite values: {np.array(grad)}"
+
+f_jit = jax.jit(fitness.call)
+
+util.assert_eager_jit_consistent(fitness.call, f_jit, param_vector)
+
+# The staircase: with no over-sampling the adaptive mesh's rank transform makes
+# the likelihood invariant to smooth mass/shear perturbations, and *every* model
+# parameter here is mass/shear (interferometer data has no lens light). The
+# correct autodiff gradient is therefore ~zero across the board. If this
+# assertion ever fails the mesh has become differentiable — rerun the full FD
+# audit and update this script + the audit README.
+assert np.all(np.abs(np.array(grad)) < 1e-6), (
+    "Autodiff mass/shear gradients are no longer ~zero on the sparse "
+    f"RectangularAdaptDensity path: {np.array(grad)}"
+)
+
+print(
+    "interferometer sparse RectangularAdaptDensity: staircase confirmed — "
+    "all autodiff gradients ~zero (correct; no smooth mass information)."
+)
+
+"""
+__Variant C: RectangularUniform — the gradient-capable alternative__
+"""
+print("\n=== interferometer RectangularUniform + reg.Constant, sparse operator ===")
+
+fitness, param_vector, param_names = sparse_fitness(
+    mesh=al.mesh.RectangularUniform(shape=mesh_shape),
+    regularization=al.reg.Constant(coefficient=1.0),
+)
+
+grad = finiteness_checks(fitness, param_vector, n_params=len(param_names))
+
+f_jit = jax.jit(fitness.call)
+
+util.assert_eager_jit_consistent(fitness.call, f_jit, param_vector)
+
+comparison = util.compare_gradients(
+    fitness.call,
+    param_vector,
+    param_names=param_names,
+    f_fd=f_jit,
+)
+
+util.assert_gradients_match(comparison)
+
+assert np.all(np.abs(comparison["ad"]) > 0.0), (
+    "A parameter gradient is exactly zero on the sparse RectangularUniform "
+    f"path: {[(n, a) for n, a in zip(param_names, comparison['ad']) if a == 0.0]}"
+)
+
+print(
+    "interferometer sparse RectangularUniform: all gradients live and "
+    "FD-matched."
+)
+
+print("\ninterferometer.py JAX gradient checks passed.")