FanBeamGeometry¶

class odl.tomo.geometry.conebeam.FanBeamGeometry(apart, dpart, src_radius, det_radius, det_curvature_radius=None, src_to_det_init=(0, 1), src_shift_func=None, det_shift_func=None, **kwargs)[source]¶

Bases: DivergentBeamGeometry

Fan beam (2d cone beam) geometry.

The source moves on a circle with radius src_radius, and the detector reference point is opposite to the source, i.e. at maximum distance, on a circle with radius det_radius. One of the two radii can be chosen as 0, which corresponds to a stationary source or detector, respectively.

The motion parameter is the 1d rotation angle parameterizing source and detector positions simultaneously.

In the standard configuration, the detector is perpendicular to the ray direction, its reference point is initially at (0, 1), and the initial detector axis is (1, 0).

For details, check the online docs.

Attributes:

angles: Discrete angles given in this geometry.
check_bounds: If True, methods computing vectors check input arguments.
det_axis_init: Detector axis at angle 0.
det_curvature_radius: Detector curve radius of this geometry.
det_grid: Sampling grid of det_params.
det_params: Continuous detector parameter range, an IntervalProd.
det_partition: Partition of the detector parameter set into subsets.
det_radius: Detector circle radius of this geometry.
det_shift_func: Detector shifts in the geometry.
detector: Detector representation of this geometry.
grid: Joined sampling grid for motion and detector.
implementation_cache: Dictionary acting as a cache for this geometry.
motion_grid: Sampling grid of motion_params.
motion_params: Continuous motion parameter range, an IntervalProd.
motion_partition: Partition of the motion parameter set into subsets.
ndim: Number of dimensions of the geometry.
params: Joined parameter set for motion and detector.
partition: Joined parameter set partition for motion and detector.
src_radius: Source circle radius of this geometry.
src_shift_func: Source shifts in the geometry.
src_to_det_init: Initial source-to-detector unit vector.
translation: Shift of the origin of this geometry.

Methods

`det_axis`(angle)	Return the detector axis at `angle`.
`det_point_position`(mparam, dparam)	Return the detector point at `(mparam, dparam)`.
`det_refpoint`(angle)	Return the detector reference point position at `angle`.
`det_to_src`(angle, dparam[, normalized])	Vector or direction from a detector location to the source.
`frommatrix`(apart, dpart, src_radius, ...[, ...])	Create an instance of `FanBeamGeometry` using a matrix.
`rotation_matrix`(angle)	Return the rotation matrix for `angle`.
`src_position`(angle)	Return the source position at `angle`.

__init__(apart, dpart, src_radius, det_radius, det_curvature_radius=None, src_to_det_init=(0, 1), src_shift_func=None, det_shift_func=None, **kwargs)[source]¶

Initialize a new instance.

Parameters:

apart1-dim. RectPartition: Partition of the angle interval.
dpart1-dim. RectPartition: Partition of the detector parameter interval.
src_radiusnonnegative float: Radius of the source circle.
det_radiusnonnegative float: Radius of the detector circle. Must be nonzero if src_radius is zero.
det_curvature_radiusnonnegative float, optional: Radius of the detector curvature. If None, a flat detector is used, otherwise must be positive.
src_to_det_initarray-like (shape (2,)), optional: Initial state of the vector pointing from source to detector reference point. The zero vector is not allowed.
src_shift_funccallable, optional: Function with signature src_shift_func(angle) -> shift returning a source shift for a given angle. Each shift is interpreted as a vector [shift_d, shift_t], where "d" and "t" denote shifts in the detector-to-source and tangent directions, respectively.
det_shift_funccallable, optional: Function with signature det_shift_func(angle) -> shift returning a detector shift for a given angle. Each shift is interpreted as a vector [shift_d, shift_t], where "d" and "t" denote shifts in the source-to-detector and tangent directions, respectively.

Other Parameters:

det_axis_initarray-like (shape (2,)), optional: Initial axis defining the detector orientation. The default depends on src_to_det_init, see Notes.
translationarray-like, shape (2,), optional: Global translation of the geometry. This is added last in any method that computes an absolute vector, e.g., det_refpoint, and also shifts the center of rotation.
check_boundsbool, optional: If True, methods computing vectors check input arguments. Checks are vectorized and add only a small overhead. Default: True

Notes

In the default configuration, the initial source-to-detector vector is (0, 1), and the initial detector axis is (1, 0). If a different src_to_det_init is chosen, the new default axis is given as a rotation of the original one by a matrix that transforms (0, 1) to the new (normalized) src_to_det_init. This matrix is calculated with the rotation_matrix_from_to function. Expressed in code, we have

init_rot = rotation_matrix_from_to((0, 1), src_to_det_init)
det_axis_init = init_rot.dot((1, 0))

Examples

Initialization with default parameters and some radii:

>>> apart = odl.uniform_partition(0, 2 * np.pi, 10)
>>> dpart = odl.uniform_partition(-1, 1, 20)
>>> geom = FanBeamGeometry(apart, dpart, src_radius=1, det_radius=5)
>>> geom.src_position(0)
array([ 0., -1.])
>>> geom.det_refpoint(0)
array([ 0.,  5.])
>>> geom.det_point_position(0, 1)  # (0, 5) + 1 * (1, 0)
array([ 1.,  5.])

Checking the default orientation:

>>> geom.src_to_det_init
array([ 0.,  1.])
>>> geom.det_axis_init
array([ 1.,  0.])

Specifying curvature of the detector:

>>> apart = odl.uniform_partition(0, 2 * np.pi, 10)
>>> dpart = odl.uniform_partition(-np.pi / 2, np.pi / 2, 10)
>>> geom = FanBeamGeometry(apart, dpart, src_radius=1, det_radius=5,
...                        det_curvature_radius=10)
>>> geom.src_position(0)
array([ 0., -1.])
>>> geom.det_refpoint(0)
array([ 0.,  5.])
>>> # (0, 5) + 10 * (sin(pi/6), cos(pi/6) - 1)
>>> np.round(geom.det_point_position(0, np.pi / 6), 2)
array([ 5.  ,  3.66])

Specifying an initial detector position by default rotates the standard configuration to this position:

>>> e_x, e_y = np.eye(2)  # standard unit vectors
>>> geom = FanBeamGeometry(apart, dpart, src_radius=1, det_radius=5,
...                        src_to_det_init=(1, 0))
>>> np.allclose(geom.src_to_det_init, e_x)
True
>>> np.allclose(geom.det_axis_init, -e_y)
True
>>> geom = FanBeamGeometry(apart, dpart, src_radius=1, det_radius=5,
...                        src_to_det_init=(0, -1))
>>> np.allclose(geom.src_to_det_init, -e_y)
True
>>> np.allclose(geom.det_axis_init, -e_x)
True

The initial detector axis can also be set explicitly:

>>> geom = FanBeamGeometry(
...     apart, dpart, src_radius=1, det_radius=5,
...     src_to_det_init=(1, 0), det_axis_init=(0, 1))
>>> np.allclose(geom.src_to_det_init, e_x)
True
>>> np.allclose(geom.det_axis_init, e_y)
True

Specifying a flying focal spot and detector offset:

>>> apart = odl.uniform_partition(0, 2 * np.pi, 4)
>>> geom = FanBeamGeometry(
...     apart, dpart,
...     src_radius=1, det_radius=5,
...     src_shift_func=lambda angle: odl.tomo.flying_focal_spot(
...             angle, apart=apart, shifts=[(0.1, 0), (0, 0.1)]),
...     det_shift_func=lambda angle: [0.0, 0.05])
>>> geom.src_shift_func(geom.angles)
array([[ 0.1, 0. ],
       [ 0. , 0.1],
       [ 0.1, 0. ],
       [ 0. , 0.1]])
>>> geom.det_shift_func(geom.angles)
[0.0, 0.05]