prysm.zernike¶

Zernike functions.

prysm.zernike.piston(rho, phi)¶: Zernike Piston.

prysm.zernike.tip(rho, phi)¶: Zernike Tilt-Y.

prysm.zernike.tilt(rho, phi)¶: Zernike Tilt-X.

prysm.zernike.defocus(rho, phi)¶: Zernike defocus.

prysm.zernike.primary_astigmatism_00(rho, phi)¶: Zernike primary astigmatism 0°.

prysm.zernike.primary_astigmatism_45(rho, phi)¶: Zernike primary astigmatism 45°.

prysm.zernike.primary_coma_y(rho, phi)¶: Zernike primary coma Y.

prysm.zernike.primary_coma_x(rho, phi)¶: Zernike primary coma X.

prysm.zernike.primary_spherical(rho, phi)¶: Zernike primary Spherical.

prysm.zernike.primary_trefoil_y(rho, phi)¶: Zernike primary trefoil Y.

prysm.zernike.primary_trefoil_x(rho, phi)¶: Zernike primary trefoil X.

prysm.zernike.zernikes_to_magnitude_angle_nmkey(coefs)¶

Convert Zernike polynomial set to a magnitude and phase representation.

Parameters: coefs (list of tuples) – a list looking like[(1,2,3),] where (1,2) are the n, m indices and 3 the coefficient
Returns: dict keyed by tuples of (n, |m|) with values of (rho, phi) where rho is the magnitudes, and phi the phase
Return type: dict

prysm.zernike.zernikes_to_magnitude_angle(coefs)¶

Convert Zernike polynomial set to a magnitude and phase representation.

This function is identical to zernikes_to_magnitude_angle_nmkey, except its keys are strings instead of (n, |m|)

Parameters: coefs (list of tuples) – a list looking like[(1,2,3),] where (1,2) are the n, m indices and 3 the coefficient
Returns: dict keyed by friendly name strings with values of (rho, phi) where rho is the magnitudes, and phi the phase
Return type: dict

prysm.zernike.zernike_norm(n, m)¶: Norm of a Zernike polynomial with n, m indexing.

prysm.zernike.n_m_to_fringe(n, m)¶: Convert (n,m) two term index to Fringe index.

prysm.zernike.n_m_to_ansi_j(n, m)¶: Convert (n,m) two term index to ANSI single term index.

prysm.zernike.ansi_j_to_n_m(idx)¶: Convert ANSI single term to (n,m) two-term index.

prysm.zernike.noll_to_n_m(idx)¶: Convert Noll Z to (n, m) two-term index.

prysm.zernike.fringe_to_n_m(idx)¶: Convert Fringe Z to (n, m) two-term index.

prysm.zernike.zero_separation(n)¶: Zero separation in normalized r based on radial order n.

prysm.zernike.n_m_to_name(n, m)¶

Convert an (n,m) index into a human readable name.

Parameters

n (int) – radial polynomial order
m (int) – azimuthal polynomial order

Returns

a name, e.g. Piston or Primary Spherical

Return type

str

class prysm.zernike.ZCacheMN(gridcache=<prysm.coordinates.GridCache object>)¶

Bases: object

Cache of Zernike terms evaluated over the unit circle, based on (n, m) indices.

get_zernike(n, m, samples, norm)¶: Get an array of phase values for a given radial order n, azimuthal order m, number of samples, and orthonormalization.

grid_bypass(n, m, norm, r, p)¶

Bypass the grid computation, providing radial coordinates directly.

Notes

To avoid memory leaks, you should use grid_bypass_cleanup after you are finished with this function for a given pair of r, p arrays

Parameters

n (int) – radial order
m (int) – azimuthal order
norm (bool) – whether to orthonormalize the polynomials
r (numpy.ndarray) – radial coordinates. Unnormalized in the sense of the coordinate perturbation of the jacobi polynomials. Notionally on a regular grid spanning [0,1]
p (numpy.ndarray) – azimuthal coordinates matching r

Returns

zernike polynomial n or m at this coordinate.

Return type

numpy.ndarray

grid_bypass_cleanup(r, p)¶

Remove data related to r, p from the cache.

Parameters

r (numpy.ndarray) – radial coordinates
p (numpy.ndarray) – azimuthal coordinates

clear(*args)¶: Empty the cache.

nbytes()¶: Total size in memory of the cache in bytes.

class prysm.zernike.BaseZernike(*args, **kwargs)¶

Bases: prysm.pupil.Pupil

Basic class implementing Zernike features.

build()¶

Use the wavefront coefficients stored in this class instance to build a wavefront model.

Returns: self – this Zernike instance
Return type: BaseZernike

top_n(n=5)¶

Identify the top n terms in the wavefront.

Parameters: n (int, optional) – identify the top n terms.
Returns: list of tuples (magnitude, index, term)
Return type: list

magnitudes¶: Return the magnitude and angles of the zernike components in this wavefront.

names¶: Names of the terms in self.

barplot(orientation='h', buffer=1, zorder=3, number=True, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of coefficients and their names.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
number (bool, optional) – if True, plot numbers along the y=0 line showing indices
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_magnitudes(orientation='h', sort=False, buffer=1, zorder=3, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of magnitudes of coefficient pairs and their names.

E.g., astigmatism will get one bar.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
sort (bool, optional) – whether to sort the zernikes in descending order
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_topn(n=5, orientation='h', buffer=1, zorder=3, fig=None, ax=None)¶

Plot the top n terms in the wavefront.

Parameters

n (int, optional) – plot the top n terms.
orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

truncate(n)¶

Truncate the wavefront to the first n terms.

Parameters: n (int) – number of terms to keep.
Returns: modified FringeZernike instance.
Return type: self

truncate_topn(n)¶

Truncate the pupil to only the top n terms.

Parameters: n (int) – number of parameters to keep
Returns: modified FringeZernike instance.
Return type: self

Sa¶: Sa phase error. DIN/ISO Sa.

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_xy_unit(to, inplace=True)¶

Change the x/y unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray, numpy.ndarray – x, y from self, if inplace=False

change_z_unit(to, inplace=True)¶

Change the z unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray – data from self, if inplace=False

copy()¶: Return a (deep) copy of this instance.

diameter¶: Greater of (self.diameter_x, self.diameter_y).

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

exact_polar(rho, phi=None)¶

Retrieve data at the specified radial coordinates pairs.

Parameters

r (iterable) – radial coordinate(s) to sample
phi (iterable) – azimuthal coordinate(s) to sample

Returns

data at the given points

Return type

numpy.ndarray

exact_x(x)¶

Return data at an exact x coordinate along the y=0 axis.

Parameters: x (number or numpy.ndarray) – x coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

exact_xy(x, y=None)¶

Retrieve data at the specified X-Y frequency pairs.

Parameters

x (iterable) – X coordinate(s) to retrieve
y (iterable) – Y coordinate(s) to retrieve

Returns

data at the given points

Return type

numpy.ndarray

exact_y(y)¶

Return data at an exact y coordinate along the x=0 axis.

Parameters: y (number or numpy.ndarray) – y coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None, mask_phase=True)¶

Create a new Pupil instance from an interferogram.

Parameters

interferogram (Interferogram) – an interferogram object
wvl (float, optional) – wavelength of light, in micrometers, if not present in interferogram.meta

Returns

new Pupil instance

Return type

Pupil

Raises

ValueError – wavelength not present

interferogram(visibility=1, passes=2, interpolation='lanczos', fig=None, ax=None)¶

Create an interferogram of the Pupil.

Parameters

visibility (float) – Visibility of the interferogram
passes (float) – Number of passes (double-pass, quadra-pass, etc.)
interp_method (str, optional) – interpolation method, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional) – Figure to draw plot in
ax (matplotlib.axes.Axis) – Axis to draw plot in

Returns

fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

phase¶: phase is the Z (“height” or “opd”) data.

phase_unit¶: Unit used to describe the optical phase.

plot2d(xlim=None, ylim=None, clim=None, cmap=None, log=False, power=1, interpolation=None, show_colorbar=True, show_axlabels=True, fig=None, ax=None)¶

Plot the data in 2D.

Parameters

xlim (float or iterable, optional) – x axis limits. If not iterable, symmetric version of the single value
ylim (float or iterable, optional) – y axis limits. If None and xlim is not None, copied from xlim. If not iterable, symmetric version of the single value.
clim (iterable, optional) – clim passed directly to matplotlib. If None, looked up on self._default_clim.
cmap (str, optional) – colormap to use, passed directly to matplotlib if not None. If None, looks up the default cmap for self._data_type on config
log (bool, optional) – if True, plot on a log color scale
power (float, optional) – if not 1, plot on a power stretched color scale
interpolation (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – if True, draws the colorbar
show_axlabels (bool, optional) – if True, draws the axis labels
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

pv¶: Peak-to-Valley phase error. DIN/ISO St.

rms¶: RMS phase error. DIN/ISO Sq.

sample_spacing¶: center-to-center sample spacing.

samples_x¶: Number of samples in the x dimension.

samples_y¶: Number of samples in the y dimension.

semidiameter¶: Half of self.diameter.

shape¶: Proxy to phase or data shape.

size¶: Proxy to phase or data size.

slices(twosided=None)¶

Create a Slices instance from this instance.

Parameters: twosided (bool, optional) – if None, copied from self._default_twosided
Returns: a Slices object
Return type: Slices

spatial_unit¶: Unit used to describe the spatial phase.

std¶: Standard deviation of phase error.

strehl¶: Strehl ratio of the pupil.

class prysm.zernike.FringeZernike(*args, **kwargs)¶

Bases: prysm.zernike.BaseZernike

Fringe Zernike description of an optical pupil.

Sa¶: Sa phase error. DIN/ISO Sa.

barplot(orientation='h', buffer=1, zorder=3, number=True, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of coefficients and their names.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
number (bool, optional) – if True, plot numbers along the y=0 line showing indices
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_magnitudes(orientation='h', sort=False, buffer=1, zorder=3, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of magnitudes of coefficient pairs and their names.

E.g., astigmatism will get one bar.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
sort (bool, optional) – whether to sort the zernikes in descending order
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_topn(n=5, orientation='h', buffer=1, zorder=3, fig=None, ax=None)¶

Plot the top n terms in the wavefront.

Parameters

n (int, optional) – plot the top n terms.
orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

build()¶

Use the wavefront coefficients stored in this class instance to build a wavefront model.

Returns: self – this Zernike instance
Return type: BaseZernike

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_xy_unit(to, inplace=True)¶

Change the x/y unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray, numpy.ndarray – x, y from self, if inplace=False

change_z_unit(to, inplace=True)¶

Change the z unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray – data from self, if inplace=False

copy()¶: Return a (deep) copy of this instance.

diameter¶: Greater of (self.diameter_x, self.diameter_y).

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

exact_polar(rho, phi=None)¶

Retrieve data at the specified radial coordinates pairs.

Parameters

r (iterable) – radial coordinate(s) to sample
phi (iterable) – azimuthal coordinate(s) to sample

Returns

data at the given points

Return type

numpy.ndarray

exact_x(x)¶

Return data at an exact x coordinate along the y=0 axis.

Parameters: x (number or numpy.ndarray) – x coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

exact_xy(x, y=None)¶

Retrieve data at the specified X-Y frequency pairs.

Parameters

x (iterable) – X coordinate(s) to retrieve
y (iterable) – Y coordinate(s) to retrieve

Returns

data at the given points

Return type

numpy.ndarray

exact_y(y)¶

Return data at an exact y coordinate along the x=0 axis.

Parameters: y (number or numpy.ndarray) – y coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None, mask_phase=True)¶

Create a new Pupil instance from an interferogram.

Parameters

interferogram (Interferogram) – an interferogram object
wvl (float, optional) – wavelength of light, in micrometers, if not present in interferogram.meta

Returns

new Pupil instance

Return type

Pupil

Raises

ValueError – wavelength not present

interferogram(visibility=1, passes=2, interpolation='lanczos', fig=None, ax=None)¶

Create an interferogram of the Pupil.

Parameters

visibility (float) – Visibility of the interferogram
passes (float) – Number of passes (double-pass, quadra-pass, etc.)
interp_method (str, optional) – interpolation method, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional) – Figure to draw plot in
ax (matplotlib.axes.Axis) – Axis to draw plot in

Returns

fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

magnitudes¶: Return the magnitude and angles of the zernike components in this wavefront.

names¶: Names of the terms in self.

phase¶: phase is the Z (“height” or “opd”) data.

phase_unit¶: Unit used to describe the optical phase.

plot2d(xlim=None, ylim=None, clim=None, cmap=None, log=False, power=1, interpolation=None, show_colorbar=True, show_axlabels=True, fig=None, ax=None)¶

Plot the data in 2D.

Parameters

xlim (float or iterable, optional) – x axis limits. If not iterable, symmetric version of the single value
ylim (float or iterable, optional) – y axis limits. If None and xlim is not None, copied from xlim. If not iterable, symmetric version of the single value.
clim (iterable, optional) – clim passed directly to matplotlib. If None, looked up on self._default_clim.
cmap (str, optional) – colormap to use, passed directly to matplotlib if not None. If None, looks up the default cmap for self._data_type on config
log (bool, optional) – if True, plot on a log color scale
power (float, optional) – if not 1, plot on a power stretched color scale
interpolation (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – if True, draws the colorbar
show_axlabels (bool, optional) – if True, draws the axis labels
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

pv¶: Peak-to-Valley phase error. DIN/ISO St.

rms¶: RMS phase error. DIN/ISO Sq.

sample_spacing¶: center-to-center sample spacing.

samples_x¶: Number of samples in the x dimension.

samples_y¶: Number of samples in the y dimension.

semidiameter¶: Half of self.diameter.

shape¶: Proxy to phase or data shape.

size¶: Proxy to phase or data size.

slices(twosided=None)¶

Create a Slices instance from this instance.

Parameters: twosided (bool, optional) – if None, copied from self._default_twosided
Returns: a Slices object
Return type: Slices

spatial_unit¶: Unit used to describe the spatial phase.

std¶: Standard deviation of phase error.

strehl¶: Strehl ratio of the pupil.

top_n(n=5)¶

Identify the top n terms in the wavefront.

Parameters: n (int, optional) – identify the top n terms.
Returns: list of tuples (magnitude, index, term)
Return type: list

truncate(n)¶

Truncate the wavefront to the first n terms.

Parameters: n (int) – number of terms to keep.
Returns: modified FringeZernike instance.
Return type: self

truncate_topn(n)¶

Truncate the pupil to only the top n terms.

Parameters: n (int) – number of parameters to keep
Returns: modified FringeZernike instance.
Return type: self

class prysm.zernike.NollZernike(*args, **kwargs)¶

Bases: prysm.zernike.BaseZernike

Noll Zernike description of an optical pupil.

Sa¶: Sa phase error. DIN/ISO Sa.

barplot(orientation='h', buffer=1, zorder=3, number=True, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of coefficients and their names.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
number (bool, optional) – if True, plot numbers along the y=0 line showing indices
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_magnitudes(orientation='h', sort=False, buffer=1, zorder=3, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of magnitudes of coefficient pairs and their names.

E.g., astigmatism will get one bar.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
sort (bool, optional) – whether to sort the zernikes in descending order
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_topn(n=5, orientation='h', buffer=1, zorder=3, fig=None, ax=None)¶

Plot the top n terms in the wavefront.

Parameters

n (int, optional) – plot the top n terms.
orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

build()¶

Use the wavefront coefficients stored in this class instance to build a wavefront model.

Returns: self – this Zernike instance
Return type: BaseZernike

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_xy_unit(to, inplace=True)¶

Change the x/y unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray, numpy.ndarray – x, y from self, if inplace=False

change_z_unit(to, inplace=True)¶

Change the z unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray – data from self, if inplace=False

copy()¶: Return a (deep) copy of this instance.

diameter¶: Greater of (self.diameter_x, self.diameter_y).

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

exact_polar(rho, phi=None)¶

Retrieve data at the specified radial coordinates pairs.

Parameters

r (iterable) – radial coordinate(s) to sample
phi (iterable) – azimuthal coordinate(s) to sample

Returns

data at the given points

Return type

numpy.ndarray

exact_x(x)¶

Return data at an exact x coordinate along the y=0 axis.

Parameters: x (number or numpy.ndarray) – x coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

exact_xy(x, y=None)¶

Retrieve data at the specified X-Y frequency pairs.

Parameters

x (iterable) – X coordinate(s) to retrieve
y (iterable) – Y coordinate(s) to retrieve

Returns

data at the given points

Return type

numpy.ndarray

exact_y(y)¶

Return data at an exact y coordinate along the x=0 axis.

Parameters: y (number or numpy.ndarray) – y coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None, mask_phase=True)¶

Create a new Pupil instance from an interferogram.

Parameters

interferogram (Interferogram) – an interferogram object
wvl (float, optional) – wavelength of light, in micrometers, if not present in interferogram.meta

Returns

new Pupil instance

Return type

Pupil

Raises

ValueError – wavelength not present

interferogram(visibility=1, passes=2, interpolation='lanczos', fig=None, ax=None)¶

Create an interferogram of the Pupil.

Parameters

visibility (float) – Visibility of the interferogram
passes (float) – Number of passes (double-pass, quadra-pass, etc.)
interp_method (str, optional) – interpolation method, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional) – Figure to draw plot in
ax (matplotlib.axes.Axis) – Axis to draw plot in

Returns

fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

magnitudes¶: Return the magnitude and angles of the zernike components in this wavefront.

names¶: Names of the terms in self.

phase¶: phase is the Z (“height” or “opd”) data.

phase_unit¶: Unit used to describe the optical phase.

plot2d(xlim=None, ylim=None, clim=None, cmap=None, log=False, power=1, interpolation=None, show_colorbar=True, show_axlabels=True, fig=None, ax=None)¶

Plot the data in 2D.

Parameters

xlim (float or iterable, optional) – x axis limits. If not iterable, symmetric version of the single value
ylim (float or iterable, optional) – y axis limits. If None and xlim is not None, copied from xlim. If not iterable, symmetric version of the single value.
clim (iterable, optional) – clim passed directly to matplotlib. If None, looked up on self._default_clim.
cmap (str, optional) – colormap to use, passed directly to matplotlib if not None. If None, looks up the default cmap for self._data_type on config
log (bool, optional) – if True, plot on a log color scale
power (float, optional) – if not 1, plot on a power stretched color scale
interpolation (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – if True, draws the colorbar
show_axlabels (bool, optional) – if True, draws the axis labels
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

pv¶: Peak-to-Valley phase error. DIN/ISO St.

rms¶: RMS phase error. DIN/ISO Sq.

sample_spacing¶: center-to-center sample spacing.

samples_x¶: Number of samples in the x dimension.

samples_y¶: Number of samples in the y dimension.

semidiameter¶: Half of self.diameter.

shape¶: Proxy to phase or data shape.

size¶: Proxy to phase or data size.

slices(twosided=None)¶

Create a Slices instance from this instance.

Parameters: twosided (bool, optional) – if None, copied from self._default_twosided
Returns: a Slices object
Return type: Slices

spatial_unit¶: Unit used to describe the spatial phase.

std¶: Standard deviation of phase error.

strehl¶: Strehl ratio of the pupil.

top_n(n=5)¶

Identify the top n terms in the wavefront.

Parameters: n (int, optional) – identify the top n terms.
Returns: list of tuples (magnitude, index, term)
Return type: list

truncate(n)¶

Truncate the wavefront to the first n terms.

Parameters: n (int) – number of terms to keep.
Returns: modified FringeZernike instance.
Return type: self

truncate_topn(n)¶

Truncate the pupil to only the top n terms.

Parameters: n (int) – number of parameters to keep
Returns: modified FringeZernike instance.
Return type: self

class prysm.zernike.ANSI1TermZernike(*args, **kwargs)¶

Bases: prysm.zernike.BaseZernike

1-term ANSI Zernike description of an optical pupil.

Sa¶: Sa phase error. DIN/ISO Sa.

barplot(orientation='h', buffer=1, zorder=3, number=True, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of coefficients and their names.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
number (bool, optional) – if True, plot numbers along the y=0 line showing indices
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_magnitudes(orientation='h', sort=False, buffer=1, zorder=3, offset=0, width=0.8, fig=None, ax=None)¶

Create a barplot of magnitudes of coefficient pairs and their names.

E.g., astigmatism will get one bar.

Parameters

orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
sort (bool, optional) – whether to sort the zernikes in descending order
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
offset (float, optional) – offset to apply to bars, useful for before/after Zernike breakdowns
width (float, optional) – width of bars, useful for before/after Zernike breakdowns
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

barplot_topn(n=5, orientation='h', buffer=1, zorder=3, fig=None, ax=None)¶

Plot the top n terms in the wavefront.

Parameters

n (int, optional) – plot the top n terms.
orientation (str, {‘h’, ‘v’, ‘horizontal’, ‘vertical’}) – orientation of the plot
buffer (float, optional) – buffer to use around the left and right (or top and bottom) bars
zorder (int, optional) – zorder of the bars. Use zorder > 3 to put bars in front of gridlines
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

build()¶

Use the wavefront coefficients stored in this class instance to build a wavefront model.

Returns: self – this Zernike instance
Return type: BaseZernike

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_xy_unit(to, inplace=True)¶

Change the x/y unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray, numpy.ndarray – x, y from self, if inplace=False

change_z_unit(to, inplace=True)¶

Change the z unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray – data from self, if inplace=False

copy()¶: Return a (deep) copy of this instance.

diameter¶: Greater of (self.diameter_x, self.diameter_y).

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

exact_polar(rho, phi=None)¶

Retrieve data at the specified radial coordinates pairs.

Parameters

r (iterable) – radial coordinate(s) to sample
phi (iterable) – azimuthal coordinate(s) to sample

Returns

data at the given points

Return type

numpy.ndarray

exact_x(x)¶

Return data at an exact x coordinate along the y=0 axis.

Parameters: x (number or numpy.ndarray) – x coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

exact_xy(x, y=None)¶

Retrieve data at the specified X-Y frequency pairs.

Parameters

x (iterable) – X coordinate(s) to retrieve
y (iterable) – Y coordinate(s) to retrieve

Returns

data at the given points

Return type

numpy.ndarray

exact_y(y)¶

Return data at an exact y coordinate along the x=0 axis.

Parameters: y (number or numpy.ndarray) – y coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None, mask_phase=True)¶

Create a new Pupil instance from an interferogram.

Parameters

interferogram (Interferogram) – an interferogram object
wvl (float, optional) – wavelength of light, in micrometers, if not present in interferogram.meta

Returns

new Pupil instance

Return type

Pupil

Raises

ValueError – wavelength not present

interferogram(visibility=1, passes=2, interpolation='lanczos', fig=None, ax=None)¶

Create an interferogram of the Pupil.

Parameters

visibility (float) – Visibility of the interferogram
passes (float) – Number of passes (double-pass, quadra-pass, etc.)
interp_method (str, optional) – interpolation method, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional) – Figure to draw plot in
ax (matplotlib.axes.Axis) – Axis to draw plot in

Returns

fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

magnitudes¶: Return the magnitude and angles of the zernike components in this wavefront.

names¶: Names of the terms in self.

phase¶: phase is the Z (“height” or “opd”) data.

phase_unit¶: Unit used to describe the optical phase.

plot2d(xlim=None, ylim=None, clim=None, cmap=None, log=False, power=1, interpolation=None, show_colorbar=True, show_axlabels=True, fig=None, ax=None)¶

Plot the data in 2D.

Parameters

xlim (float or iterable, optional) – x axis limits. If not iterable, symmetric version of the single value
ylim (float or iterable, optional) – y axis limits. If None and xlim is not None, copied from xlim. If not iterable, symmetric version of the single value.
clim (iterable, optional) – clim passed directly to matplotlib. If None, looked up on self._default_clim.
cmap (str, optional) – colormap to use, passed directly to matplotlib if not None. If None, looks up the default cmap for self._data_type on config
log (bool, optional) – if True, plot on a log color scale
power (float, optional) – if not 1, plot on a power stretched color scale
interpolation (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – if True, draws the colorbar
show_axlabels (bool, optional) – if True, draws the axis labels
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

pv¶: Peak-to-Valley phase error. DIN/ISO St.

rms¶: RMS phase error. DIN/ISO Sq.

sample_spacing¶: center-to-center sample spacing.

samples_x¶: Number of samples in the x dimension.

samples_y¶: Number of samples in the y dimension.

semidiameter¶: Half of self.diameter.

shape¶: Proxy to phase or data shape.

size¶: Proxy to phase or data size.

slices(twosided=None)¶

Create a Slices instance from this instance.

Parameters: twosided (bool, optional) – if None, copied from self._default_twosided
Returns: a Slices object
Return type: Slices

spatial_unit¶: Unit used to describe the spatial phase.

std¶: Standard deviation of phase error.

strehl¶: Strehl ratio of the pupil.

top_n(n=5)¶

Identify the top n terms in the wavefront.

Parameters: n (int, optional) – identify the top n terms.
Returns: list of tuples (magnitude, index, term)
Return type: list

truncate(n)¶

Truncate the wavefront to the first n terms.

Parameters: n (int) – number of terms to keep.
Returns: modified FringeZernike instance.
Return type: self

truncate_topn(n)¶

Truncate the pupil to only the top n terms.

Parameters: n (int) – number of parameters to keep
Returns: modified FringeZernike instance.
Return type: self

class prysm.zernike.ANSI2TermZernike(*args, **kwargs)¶

Bases: prysm.pupil.Pupil

2-term ANSI Zernike description of an optical pupil.

Sa¶: Sa phase error. DIN/ISO Sa.

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_xy_unit(to, inplace=True)¶

Change the x/y unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray, numpy.ndarray – x, y from self, if inplace=False

change_z_unit(to, inplace=True)¶

Change the z unit to a new one, scaling the data in the process.

Parameters

to (astropy.unit or str) – if not an astropy unit, a string that is a valid attribute of astropy.units.
inplace (bool, optional) – if True, returns self. Otherwise returns the modified data.

Returns

RichData – self, if inplace=True
numpy.ndarray – data from self, if inplace=False

copy()¶: Return a (deep) copy of this instance.

diameter¶: Greater of (self.diameter_x, self.diameter_y).

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

exact_polar(rho, phi=None)¶

Retrieve data at the specified radial coordinates pairs.

Parameters

r (iterable) – radial coordinate(s) to sample
phi (iterable) – azimuthal coordinate(s) to sample

Returns

data at the given points

Return type

numpy.ndarray

exact_x(x)¶

Return data at an exact x coordinate along the y=0 axis.

Parameters: x (number or numpy.ndarray) – x coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

exact_xy(x, y=None)¶

Retrieve data at the specified X-Y frequency pairs.

Parameters

x (iterable) – X coordinate(s) to retrieve
y (iterable) – Y coordinate(s) to retrieve

Returns

data at the given points

Return type

numpy.ndarray

exact_y(y)¶

Return data at an exact y coordinate along the x=0 axis.

Parameters: y (number or numpy.ndarray) – y coordinate(s) to return
Returns: ndarray of values
Return type: numpy.ndarray

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None, mask_phase=True)¶

Create a new Pupil instance from an interferogram.

Parameters

interferogram (Interferogram) – an interferogram object
wvl (float, optional) – wavelength of light, in micrometers, if not present in interferogram.meta

Returns

new Pupil instance

Return type

Pupil

Raises

ValueError – wavelength not present

interferogram(visibility=1, passes=2, interpolation='lanczos', fig=None, ax=None)¶

Create an interferogram of the Pupil.

Parameters

visibility (float) – Visibility of the interferogram
passes (float) – Number of passes (double-pass, quadra-pass, etc.)
interp_method (str, optional) – interpolation method, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional) – Figure to draw plot in
ax (matplotlib.axes.Axis) – Axis to draw plot in

Returns

fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

phase¶: phase is the Z (“height” or “opd”) data.

phase_unit¶: Unit used to describe the optical phase.

plot2d(xlim=None, ylim=None, clim=None, cmap=None, log=False, power=1, interpolation=None, show_colorbar=True, show_axlabels=True, fig=None, ax=None)¶

Plot the data in 2D.

Parameters

xlim (float or iterable, optional) – x axis limits. If not iterable, symmetric version of the single value
ylim (float or iterable, optional) – y axis limits. If None and xlim is not None, copied from xlim. If not iterable, symmetric version of the single value.
clim (iterable, optional) – clim passed directly to matplotlib. If None, looked up on self._default_clim.
cmap (str, optional) – colormap to use, passed directly to matplotlib if not None. If None, looks up the default cmap for self._data_type on config
log (bool, optional) – if True, plot on a log color scale
power (float, optional) – if not 1, plot on a power stretched color scale
interpolation (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – if True, draws the colorbar
show_axlabels (bool, optional) – if True, draws the axis labels
fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

Returns

fig (matplotlib.figure.Figure) – Figure containing the plot
ax (matplotlib.axes.Axis) – Axis containing the plot

pv¶: Peak-to-Valley phase error. DIN/ISO St.

rms¶: RMS phase error. DIN/ISO Sq.

sample_spacing¶: center-to-center sample spacing.

samples_x¶: Number of samples in the x dimension.

samples_y¶: Number of samples in the y dimension.

semidiameter¶: Half of self.diameter.

shape¶: Proxy to phase or data shape.

size¶: Proxy to phase or data size.

slices(twosided=None)¶

Create a Slices instance from this instance.

Parameters: twosided (bool, optional) – if None, copied from self._default_twosided
Returns: a Slices object
Return type: Slices

spatial_unit¶: Unit used to describe the spatial phase.

std¶: Standard deviation of phase error.

strehl¶: Strehl ratio of the pupil.

build()¶

Use the wavefront coefficients stored in this class instance to build a wavefront model.

Returns: self – this Zernike instance
Return type: BaseZernike

prysm.zernike.zernikefit(data, x=None, y=None, rho=None, phi=None, terms=16, norm=False, residual=False, round_at=6, map_='Fringe')¶

Fits a number of Zernike coefficients to provided data.

Works by minimizing the mean square error between each coefficient and the given data. The data should be uniformly sampled in an x,y grid.

Parameters

data (numpy.ndarray) – data to fit to.
x (numpy.ndarray, optional) – x coordinates, same shape as data
y (numpy.ndarray, optional) – y coordinates, same shape as data
rho (numpy.ndarray, optional) – radial coordinates, same shape as data
phi (numpy.ndarray, optional) – azimuthal coordinates, same shape as data
terms (int or iterable, optional) – if an int, number of terms to fit, otherwise, specific terms to fit. If an iterable of ints, members of the single index set map_, else interpreted as (n,m) terms, in which case both m+ and m- must be given.
norm (bool, optional) – if True, normalize coefficients to unit RMS value
residual (bool, optional) – if True, return a tuple of (coefficients, residual)
round_at (int, optional) – decimal place to round values at.
map (str, optional, {‘Fringe’, ‘Noll’, ‘ANSI’}) – which ordering of Zernikes to use

Returns

coefficients (numpy.ndarray) – an array of coefficients matching the input data.
residual (float) – RMS error between the input data and the fit.

Raises

ValueError – too many terms requested.

prysm.zernike¶

prysm

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