def calculate_speeds(IM, origin=None, Jacobian=False, dr=1, dt=None):
""" Angular integration of the image.
Returning the one-dimentional intensity profile as a function of the
radial coordinate.
Parameters
----------
IM: rows x cols 2D np.array
The data image.
origin: tuple
Image center coordinate relative to *bottom-left* corner
defaults to (rows//2+rows%2,cols//2+cols%2).
Jacobian: boolean
Include r*sinθ in the angular sum (integration).
dr: float
Radial coordinate grid spacing, in pixels (default 1).
dt: float
Theta coordinate grid spacing in degrees, defaults to rows//2.
Returns
-------
1D np.array
Integrated intensity array (vs radius).
1D np.array
Corresponding radial coordinates
"""
polarIM, r_grid, theta_grid = reproject_image_into_polar(IM,
origin,
Jacobian=Jacobian,
dr=dr,
dt=dt)
theta = theta_grid[0, :] # theta coordinates
r = r_grid[:, 0] # radial coordinates
if Jacobian: # x r sinθ
sintheta = np.abs(np.sin(theta))
polarIM = polarIM * sintheta[np.newaxis, :]
polarIM = polarIM * r[:, np.newaxis]
speeds = np.sum(polarIM, axis=1)
n = speeds.shape[0]
return speeds, r[:n] # limit radial coordinates range to match speed
def calculate_speeds(IM, origin=None, Jacobian=False, dr=1, dt=None):
""" Angular integration of the image.
Returning the one-dimentional intensity profile as a function of the
radial coordinate.
Parameters
----------
IM: rows x cols 2D np.array
The data image.
origin: tuple
Image center coordinate relative to *bottom-left* corner
defaults to (rows//2+rows%2,cols//2+cols%2).
Jacobian: boolean
Include r*sinθ in the angular sum (integration).
dr: float
Radial coordinate grid spacing, in pixels (default 1).
dt: float
Theta coordinate grid spacing in degrees, defaults to rows//2.
Returns
-------
1D np.array
Integrated intensity array (vs radius).
1D np.array
Corresponding radial coordinates
"""
polarIM, r_grid, theta_grid = reproject_image_into_polar(IM, origin,
Jacobian=Jacobian, dr=dr, dt=dt)
theta = theta_grid[0, :] # theta coordinates
r = r_grid[:, 0] # radial coordinates
if Jacobian: # x r sinθ
sintheta = np.abs(np.sin(theta))
polarIM = polarIM*sintheta[np.newaxis, :]
polarIM = polarIM*r[:, np.newaxis]
speeds = np.sum(polarIM, axis=1)
n = speeds.shape[0]
return speeds, r[:n] # limit radial coordinates range to match speed
def calculate_angular_distributions(IM, radial_ranges=None):
""" Intensity variation in the angular coordinate, theta.
This function is the theta-coordinate complement to 'calculate_speeds(IM)'
(optionally and more useful) returning intensity vs angle for defined
radial ranges.
Parameters
----------
IM: 2D np.array
Image data
radial_ranges: list of tuples
[(r0, r1), (r2, r3), ...]
Evaluate the intensity vs angle for the radial ranges
r0_r1, r2_r3, etc.
Returns
--------
2D np.array
Intensity vs angle distribution for each selected radial range.
1D np.array
Angle coordinates, referenced to vertical direction.
"""
polarIM, r_grid, theta_grid = reproject_image_into_polar(IM)
theta = theta_grid[0, :] # theta coordinates
r = r_grid[:, 0] # radial coordinates
if radial_ranges is None:
radial_ranges = [
(0, r[-1]),
]
intensity_vs_theta_at_R = []
for rr in radial_ranges:
subr = np.logical_and(r >= rr[0], r <= rr[1])
# sum intensity across radius of spectral feature
intensity_vs_theta_at_R.append(np.sum(polarIM[subr], axis=0))
return intensity_vs_theta_at_R, theta
def calculate_angular_distributions(IM, radial_ranges=None):
""" Intensity variation in the angular coordinate, theta.
This function is the theta-coordinate complement to 'calculate_speeds(IM)'
(optionally and more useful) returning intensity vs angle for defined
radial ranges.
Parameters
----------
IM: 2D np.array
Image data
radial_ranges: list of tuples
[(r0, r1), (r2, r3), ...]
Evaluate the intensity vs angle for the radial ranges
r0_r1, r2_r3, etc.
Returns
--------
2D np.array
Intensity vs angle distribution for each selected radial range.
1D np.array
Angle coordinates, referenced to vertical direction.
"""
polarIM, r_grid, theta_grid = reproject_image_into_polar(IM)
theta = theta_grid[0, :] # theta coordinates
r = r_grid[:, 0] # radial coordinates
if radial_ranges is None:
radial_ranges = [(0, r[-1]), ]
intensity_vs_theta_at_R = []
for rr in radial_ranges:
subr = np.logical_and(r >= rr[0], r <= rr[1])
# sum intensity across radius of spectral feature
intensity_vs_theta_at_R.append(np.sum(polarIM[subr], axis=0))
return intensity_vs_theta_at_R, theta