AberrationsFit#
- class pyrost.AberrationsFit(parent, defocus, distance, pixels, pixel_aberrations, pixel_size, wavelength, phase=None, roi=None)#
Least squares optimizer for the lens aberrations’ profiles.
AberrationsFitis capable of fitting lens’ pixel aberrations, deviation angles, and phase profile with polynomial function. Based onscipy.optimise.least_squares().- Parameters
parent (
ReferenceType) – The Speckle tracking data container, from which the object is derived.kwargs – Necessary and optional attributes specified in the notes section.
- Raises
ValueError – If any of the necessary attributes has not been provided.
Notes
Necessary attributes:
defocus : Defocus distance [m].
distance : Sample-to-detector distance [m].
pixels : Pixel coordinates [pixels].
pixel_aberrations : Pixel aberrations profile [pixels].
pixel_size : Pixel’s size [m].
wavelength : Incoming beam’s wavelength [m].
Optional attributes:
roi : Region of interest.
thetas : Scattering angles [rad].
theta_ab : angular displacement profile [rad].
phase : aberrations phase profile [rad].
See also
scipy.optimize.least_squares(): Full nonlinear least-squares algorithm description.- contents()#
Return a list of the attributes stored in the container that are initialised.
- crop_data(roi)#
Return a new
AberrationsFitobject with the updated roi.- Parameters
roi (
Iterable) – Region of interest in the detector plane.- Return type
- Returns
New
AberrationsFitobject with the updated roi.
- fit(max_order=2, xtol=1e-14, ftol=1e-14, loss='cauchy')#
Fit lens’ pixel aberrations with polynomial function using
scipy.optimise.least_squares().- Parameters
max_order (
int) – Maximum order of the polynomial model function.xtol (
float) – Tolerance for termination by the change of the independent variables.ftol (
float) – Tolerance for termination by the change of the cost function.loss (
str) –Determines the loss function. The following keyword values are allowed:
linear :
rho(z) = z. Gives a standard least-squares problem.soft_l1 :
rho(z) = 2 * ((1 + z)**0.5 - 1). The smooth approximation of l1 (absolute value) loss. Usually a good choice for robust least squares.huber :
rho(z) = z if z <= 1 else 2*z**0.5 - 1. Works similarly to ‘soft_l1’.cauchy (default) :
rho(z) = ln(1 + z). Severely weakens outliers influence, but may cause difficulties in optimization process.arctan :
rho(z) = arctan(z). Limits a maximum loss on a single residual, has properties similar to ‘cauchy’.
- Return type
- Returns
A dictionary with the fitting information. The following elements are defined inside:
c_3 : Third order aberrations coefficient [rad / mrad^3].
c_4 : Fourth order aberrations coefficient [rad / mrad^4].
fit : Array of the polynomial function coefficients of the pixel aberrations fit.
ph_fit : Array of the polynomial function coefficients of the phase aberrations fit.
rel_err : Vector of relative errors of the fit coefficients.
r_sq :
R**2goodness of fit.
See also
scipy.optimize.least_squares(): Full nonlinear least-squares algorithm description.
- fit_phase(max_order=3, xtol=1e-14, ftol=1e-14, loss='linear')#
Fit lens’ phase aberrations with polynomial function using
scipy.optimise.least_squares().- Parameters
max_order (
int) – Maximum order of the polynomial model function.xtol (
float) – Tolerance for termination by the change of the independent variables.ftol (
float) – Tolerance for termination by the change of the cost function.loss (
str) –Determines the loss function. The following keyword values are allowed:
linear :
rho(z) = z. Gives a standard least-squares problem.soft_l1 :
rho(z) = 2 * ((1 + z)**0.5 - 1). The smooth approximation of l1 (absolute value) loss. Usually a good choice for robust least squares.huber :
rho(z) = z if z <= 1 else 2*z**0.5 - 1. Works similarly to ‘soft_l1’.cauchy (default) :
rho(z) = ln(1 + z). Severely weakens outliers influence, but may cause difficulties in optimization process.arctan :
rho(z) = arctan(z). Limits a maximum loss on a single residual, has properties similar to ‘cauchy’.
- Return type
- Returns
A dictionary with the fitting information. The following elements are defined inside:
c_3 : Third order aberrations coefficient [rad / mrad^3].
c_4 : Fourth order aberrations coefficient [rad / mrad^4].
fit : Array of the polynomial function coefficients of the pixel aberrations fit.
ph_fit : Array of the polynomial function coefficients of the phase aberrations fit.
rel_err : Vector of relative errors of the fit coefficients.
r_sq :
R**2goodness of fit.
See also
scipy.optimize.least_squares(): Full nonlinear least-squares algorithm description.
- get(attr, value=None)#
Retrieve a dataset, return
valueif the attribute is not found.
- items()#
Return (key, value) pairs of the datasets stored in the container.
- Return type
- Returns
(key, value) pairs of the datasets stored in the container.
- keys()#
Return a list of the attributes available in the container.
- model(fit)#
Return the polynomial function values of lens’ deviation angles fit.
- phase_to_pix(ph_fit)#
Convert fit coefficients from pixel aberrations fit to aberrations phase fit.
- pix_to_phase(fit)#
Convert fit coefficients from pixel aberrations fit to aberrations phase fit.
- remove_linear_term(fit=None, xtol=1e-14, ftol=1e-14, loss='cauchy')#
Return a new
AberrationsFitobject with the linear term removed from pixel_aberrations profile.- Parameters
fit (
Optional[ndarray]) – Fit coefficients of a first order polynomial. Inferred from pixel_aberrations by fitting a line if None.xtol (
float) – Tolerance for termination by the change of the independent variables.ftol (
float) – Tolerance for termination by the change of the cost function.loss (
str) –Determines the loss function. The following keyword values are allowed:
linear :
rho(z) = z. Gives a standard least-squares problem.soft_l1 :
rho(z) = 2 * ((1 + z)**0.5 - 1). The smooth approximation of l1 (absolute value) loss. Usually a good choice for robust least squares.huber :
rho(z) = z if z <= 1 else 2*z**0.5 - 1. Works similarly to ‘soft_l1’.cauchy (default) :
rho(z) = ln(1 + z). Severely weakens outliers influence, but may cause difficulties in optimization process.arctan :
rho(z) = arctan(z). Limits a maximum loss on a single residual, has properties similar to ‘cauchy’.
- Return type
- Returns
New
AberrationsFitobject with the updated pixel_aberrations and phase.
- replace(**kwargs)#
Return a new container object with a set of attributes replaced.
- update_center(center)#
Return a new
AberrationsFitobject with the pixels centered around center.- Parameters
center (
float) – Index of the zerro scattering angle or direct beam pixel.- Return type
- Returns
New
AberrationsFitobject with the updated pixels, phase, and pixel_aberrations.
- update_phase()#
Return a new
AberrationsFitobject with the updated phase.- Return type
- Returns
New
AberrationsFitobject with the updated phase.
- values()#
Return the attributes’ data stored in the container.
- Return type
- Returns
List of data stored in the container.