BUG: fix error in parallel_beam_geometry overestimating number of points

odl/test/tomo/geometry/geometry_test.py

@@ -123,14 +123,14 @@ def test_parallel_3d_single_axis_geometry():
     assert repr(geom)
 
 
-def test_parallel_beam_helper():
+def test_parallel_beam_geometry_helper():
     """Test that parallel_beam_geometry satisfies the sampling conditions."""
     # --- 2d case ---
     space = odl.uniform_discr([-1, -1], [1, 1], [20, 20])
     geometry = odl.tomo.parallel_beam_geometry(space)
 
     rho = np.sqrt(2)
-    omega = 2 * np.pi * 10.0
+    omega = np.pi * 10.0
 
     # Validate angles
     assert geometry.motion_partition.is_uniform
@@ -168,7 +168,7 @@ def test_parallel_beam_helper():
     geometry = odl.tomo.parallel_beam_geometry(space)
 
     rho = np.sqrt(2) * 2
-    omega = 2 * np.pi * 10.0
+    omega = np.pi * 10.0
 
     # Validate angles
     assert geometry.motion_partition.is_uniform

odl/tomo/geometry/parallel.py

@@ -434,7 +434,7 @@ def parallel_beam_geometry(space, angles=None, det_shape=None):
     flexibility of the geometries, but simply want a geometry that works.
 
     This default geometry gives a fully sampled sinogram according to the
-    nyquist criterion, which in general results in a very large number of
+    Nyquist criterion, which in general results in a very large number of
     samples.
 
     Parameters
@@ -462,9 +462,9 @@ def parallel_beam_geometry(space, angles=None, det_shape=None):
     >>> space = odl.uniform_discr([-1, -1], [1, 1], [20, 20])
     >>> geometry = parallel_beam_geometry(space)
     >>> geometry.angles.size
-    89
+    45
     >>> geometry.detector.size
-    57
+    29
 
     Notes
     -----
@@ -507,9 +507,13 @@ def parallel_beam_geometry(space, angles=None, det_shape=None):
     corners = space.domain.corners()[:, :2]
     rho = np.max(np.linalg.norm(corners, axis=1))
 
-    # Find default values according to Nyquist criterion
+    # Find default values according to Nyquist criterion.
+
+    # We assume that the function is bandlimited by a wave along the x or y
+    # axis. The highest frequency we can measure is then a standing wave with
+    # period of twice the inter-node distance.
     min_side = min(space.partition.cell_sides[:2])
-    omega = 2 * np.pi / min_side
+    omega = np.pi / min_side
 
     if det_shape is None:
         if space.ndim == 2: