psfsim.basis

Basis functions for decomposition of the figure errors.

Attributes

basis_set

Classes

`_FigureBasis`	Base class for basis functions for figures.
`ZernikeBasis`	Zernike basis set.
`LegendreBasis`	Legendre basis set.
`LegendreBasisMaxOrder`	Legendre basis set with maximum order.
`RomanBasisSet`	Class to build a table of basis sets from a dictionary.

Module Contents

class _FigureBasis[source]

Base class for basis functions for figures.

Parameters:: None

N[source]

The number of basis modes.

Type:: int

basis()[source]: Function to take an array: valid(x,y), where x and y are numpy arrays, and return an array with one extra axis (at the end) giving the basis mode index. Should be replaced when you inherit.

valid()[source]: Function to take an array: valid(x,y), where x and y are numpy arrays, and return a Boolean numpy array of whether it is valid. Should be replaced when you inherit.

N = 1[source]

basis(x, y)[source]

Dummy basis function (all 1’s).

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

Basis function array at these points; shape is np.shape(x) + (N,), where N is the number of basis functions.

Return type:

np.ndarray of float

valid(x, y)[source]

Dummy valid function (all True).

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

True if valid, False if not; shape is the same as x.

Return type:

np.ndarray of bool

class ZernikeBasis(radius, nmax, skip=0)[source]

Bases: _FigureBasis

Zernike basis set.

Parameters:

radius (float) – The maximum radius.
nmax (int) – The maximum Zernike order.
skip (int, optional) – If specified, skip orders below this value (e.g., skip=1 to not use piston).

radius[source]

nmax[source]

skip = 0[source]

N[source]

basis(x, y)[source]

Zernike basis functions.

These are normalized in a circle of radius self.radius.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

Basis function array at these points; shape is np.shape(x) + (N,), where N is the number of basis functions.

Return type:

np.ndarray of float

valid(x, y)[source]

Valid function.

This is True for points in a circle of radius self.radius.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

True if valid, False if not; shape is the same as x.

Return type:

np.ndarray of bool

class LegendreBasis(bbox, nmax_x, nmax_y, skip=0)[source]

Bases: _FigureBasis

Legendre basis set.

Parameters:

bbox (array-like of float) – The bounding box, in the form [xmin, xmax, ymin, ymax].
nmax_x (int) – The maximum Legendre order on each axis.
nmax_y (int) – The maximum Legendre order on each axis.
skip (int, optional) – Skip modes below this order.

xmin[source]

xmax[source]

ymin[source]

ymax[source]

nmax_x[source]

nmax_y[source]

skip = 0[source]

N[source]

basis(x, y)[source]

The Legendre basis functions.

These are organized by order in x (outer loop) and y (inner loop), and are normalized to rms=1.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

Basis function array at these points; shape is np.shape(x) + (N,), where N is the number of basis functions.

Return type:

np.ndarray of float

valid(x, y)[source]

Valid function.

This is True for points in a circle of radius self.radius.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

True if valid, False if not; shape is the same as x.

Return type:

np.ndarray of bool

class LegendreBasisMaxOrder(bbox, nmax, skip=0)[source]

Bases: _FigureBasis

Legendre basis set with maximum order.

Parameters:

bbox (array-like of float) – The bounding box, in the form [xmin, xmax, ymin, ymax].
nmax (int) – The maximum Legendre order (total).
skip (int, optional) – Skip modes below this order.

xmin[source]

xmax[source]

ymin[source]

ymax[source]

nmax[source]

skip = 0[source]

N[source]

basis(x, y)[source]

The Legendre basis functions.

These are organized by order in x (outer loop) and y (inner loop), and are normalized to rms=1.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns:

Basis function array at these points; shape is np.shape(x) + (N,), where N is the number of basis functions.

Return type:

np.ndarray of float

valid(x, y)[source]

Valid function.

This is True for points in a circle of radius self.radius.

Parameters:

x (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.
y (np.ndarray of float) – The x and y coordinates of the points to evaluate. These should be the same shape.

Returns: