SphericalDetector

class odl.tomo.geometry.detector.SphericalDetector(partition, axes, radius, check_bounds=True)

Bases: Detector

A 2D detector on a spherical surface in 3D space.

The spherical surface that corresponds to the partition is rotated to be aligned with given axes and shifted to cross the origin. Note, the partition angles increase in the direction of -y (clockwise) and z axis, by analogy to flat detectors.

Attributes:

axes

Fixed array of unit vectors with which the detector is aligned.

check_bounds

If True, methods computing vectors check input arguments.

grid

Sampling grid of the parameters.

ndim

Number of dimensions of the parameters (= surface dimension).

params

Surface parameter set of this detector.

partition

Partition of the detector parameter set into subsets.

radius

Curvature radius of the detector.

rotation_matrix

Rotation matrix that is used to align the detector with a given axis.

shape

Number of subsets (pixels) of the detector per axis.

size

Total number of pixels.

space_ndim

Number of dimensions of the embedding space.

translation

A vector used to shift the detector towards the origin.

Methods

surface(param)	Return the detector surface point corresponding to param.
surface_deriv(param)	Return the surface derivative at param.
surface_measure(param)	Density function of the surface measure.
surface_normal(param)	Unit vector perpendicular to the detector surface at param.

__init__(partition, axes, radius, check_bounds=True)

Initialize a new instance.

Parameters:

partition2-dim. RectPartition

Partition of the parameter interval, corresponding to the angular partition in two directions.

axessequence of array-like's

Fixed pair of of unit vectors with which the detector is aligned. The vectors must have shape (3,) and be perpendicular.

radiusnonnegative float

Radius of the sphere.

check_boundsbool, optional

If True, methods computing vectors check input arguments. Checks are vectorized and add only a small overhead.

Examples

Initialize a detector with radius 2 extending to 90 degrees in both directions along the equator and 45 degrees in both directions towards the poles.

>>> part = odl.uniform_partition([-np.pi / 2, -np.pi / 3],
...                              [ np.pi / 2,  np.pi / 3], [20, 10])
>>> det = SphericalDetector(
...     part, axes=[(1, 0, 0), (0, 0, 1)], radius = 2)
>>> det.axes
array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])
>>> det.radius
2.0
>>> np.allclose(det.surface_normal([0, 0]), [0, -1, 0])
True