tip modelling and deconvolution

tests/node_tests/tip_model.py

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+import numpy as np
+import pytest
+from tests.node_tests._shared import make_field
+
+
+def make_tip(shape="parabola", radius=10e-9, half_angle=20.0, n_pixels=65, field=None):
+    from backend.nodes.tip_model import TipModel
+    if field is None:
+        # 1 nm/pixel reference field
+        field = make_field(shape=(128, 128), xreal=128e-9, yreal=128e-9)
+    node = TipModel()
+    result, = node.process(field=field, shape=shape, radius=radius,
+                           half_angle=half_angle, n_pixels=n_pixels)
+    return result
+
+
+# ── Shape and dimensionality ────────────────────────────────────────────────
+
+def test_tip_output_is_data_field():
+    from backend.data_types import DataField
+    tip = make_tip()
+    assert isinstance(tip, DataField)
+
+
+def test_tip_shape_matches_n_pixels():
+    """Output grid must be (n_pixels, n_pixels)."""
+    for n in (5, 9, 33, 65):
+        tip = make_tip(n_pixels=n)
+        assert tip.data.shape == (n, n)
+
+
+def test_tip_n_pixels_even_forced_odd():
+    """Even n_pixels should be silently bumped to n+1."""
+    tip = make_tip(n_pixels=64)
+    assert tip.data.shape[0] % 2 == 1
+    assert tip.data.shape[0] == 65
+
+
+def test_tip_xreal_equals_n_times_pixel_size():
+    """xreal must equal n_pixels * pixel_size of the reference field."""
+    pixel_size = 1e-9
+    field = make_field(shape=(128, 128), xreal=128 * pixel_size, yreal=128 * pixel_size)
+    tip = make_tip(n_pixels=65, field=field)
+    assert abs(tip.xreal - 65 * pixel_size) < 1e-25
+
+
+def test_tip_units_inherited_from_field():
+    field = make_field()
+    field.si_unit_xy = "nm"
+    field.si_unit_z = "V"
+    tip = make_tip(field=field)
+    assert tip.si_unit_xy == "nm"
+    assert tip.si_unit_z == "V"
+
+
+# ── Apex and minimum conventions ────────────────────────────────────────────
+
+@pytest.mark.parametrize("shape", ["parabola", "cone", "sphere"])
+def test_tip_min_is_zero(shape):
+    """All shapes must shift the data so the minimum is 0."""
+    tip = make_tip(shape=shape)
+    assert tip.data.min() >= -1e-15
+
+
+@pytest.mark.parametrize("shape", ["parabola", "cone", "sphere"])
+def test_tip_apex_at_centre(shape):
+    """Centre pixel must equal the maximum for all shapes."""
+    tip = make_tip(shape=shape)
+    n = tip.data.shape[0]
+    ci = n // 2
+    assert tip.data[ci, ci] == pytest.approx(tip.data.max(), abs=1e-20)
+
+
+@pytest.mark.parametrize("shape", ["parabola", "cone", "sphere"])
+def test_tip_radial_symmetry(shape):
+    """All shapes must be left-right and up-down symmetric."""
+    tip = make_tip(shape=shape)
+    data = tip.data
+    assert np.allclose(data, np.flipud(data), atol=1e-12)
+    assert np.allclose(data, np.fliplr(data), atol=1e-12)
+
+
+# ── Parabola formula verification ────────────────────────────────────────────
+
+def test_parabola_apex_formula():
+    """Parabola apex height = (half_width)² / R (Gwyddion: z0 = 2a·x_half²)."""
+    radius = 20e-9
+    n = 65
+    pixel_size = 1e-9
+    field = make_field(shape=(256, 256), xreal=256 * pixel_size, yreal=256 * pixel_size)
+    tip = make_tip(shape="parabola", radius=radius, n_pixels=n, field=field)
+
+    x_half = (n // 2) * pixel_size    # = 32 nm
+    expected_apex = x_half**2 / radius # = 1024e-18 / 20e-9 = 51.2 nm
+    assert abs(tip.data[n // 2, n // 2] - expected_apex) < 1e-12 * expected_apex
+
+
+def test_parabola_decreases_monotonically_from_centre():
+    """Parabola row profile must be monotonically decreasing from centre outward."""
+    tip = make_tip(shape="parabola", n_pixels=33)
+    ci = 16
+    row = tip.data[ci, :]
+    assert np.all(np.diff(row[:ci + 1]) >= 0)   # left half increases toward centre
+    assert np.all(np.diff(row[ci:]) <= 0)        # right half decreases from centre
+
+
+def test_parabola_corner_value_is_zero():
+    """Gwyddion constructs z0 so that z at (±half, ±half) = 0 exactly."""
+    n = 33
+    tip = make_tip(shape="parabola", n_pixels=n)
+    corner = tip.data[0, 0]
+    # The corner is by construction the minimum; after the min-shift it should be ~0
+    assert abs(corner) < 1e-15 * tip.data[n // 2, n // 2]
+
+
+# ── Cone shape ──────────────────────────────────────────────────────────────
+
+def test_cone_apex_greater_than_edges():
+    tip = make_tip(shape="cone", half_angle=20.0, n_pixels=33)
+    ci = 16
+    assert tip.data[ci, ci] > tip.data[0, 0]
+    assert tip.data[0, 0] >= -1e-15   # edges should be ~0
+
+
+def test_cone_decreases_away_from_centre():
+    """Cone must be monotonically decreasing along any radial line from centre."""
+    tip = make_tip(shape="cone", half_angle=20.0, n_pixels=33)
+    ci = 16
+    row = tip.data[ci, :]
+    assert np.all(np.diff(row[ci:]) <= 0)
+
+
+def test_cone_different_half_angles_differ():
+    """Tips with different half-angles must produce different shapes."""
+    tip_wide = make_tip(shape="cone", half_angle=40.0, n_pixels=33)
+    tip_narrow = make_tip(shape="cone", half_angle=10.0, n_pixels=33)
+    assert not np.allclose(tip_wide.data, tip_narrow.data)
+
+
+# ── Sphere shape ─────────────────────────────────────────────────────────────
+
+def test_sphere_curvature_near_apex():
+    """Near the apex the sphere cap gives z ≈ sqrt(R²-r²), so
+    z[ci,ci] - z[ci, ci+1] ≈ pixel_size² / (2R) for r << R."""
+    radius = 100e-9
+    pixel_size = 1e-9
+    field = make_field(shape=(256, 256), xreal=256 * pixel_size, yreal=256 * pixel_size)
+    tip = make_tip(shape="sphere", radius=radius, n_pixels=33, field=field)
+    ci = 16
+    delta_z = tip.data[ci, ci] - tip.data[ci, ci + 1]
+    expected = pixel_size**2 / (2 * radius)
+    # relative tolerance 0.1% (small-angle approximation holds well for r << R)
+    assert abs(delta_z - expected) / expected < 1e-3