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.secondary_astigmatism_00(rho, phi)¶: Zernike secondary astigmatism 0°.

prysm.zernike.secondary_astigmatism_45(rho, phi)¶: Zernike secondary astigmatism 45°.

prysm.zernike.secondary_coma_y(rho, phi)¶: Zernike secondary coma Y.

prysm.zernike.secondary_coma_x(rho, phi)¶: Zernike secondary coma X.

prysm.zernike.secondary_spherical(rho, phi)¶: Zernike secondary spherical.

prysm.zernike.primary_tetrafoil_y(rho, phi)¶: Zernike primary tetrafoil Y.

prysm.zernike.primary_tetrafoil_x(rho, phi)¶: Zernike primary tetrafoil X.

prysm.zernike.secondary_trefoil_y(rho, phi)¶: Zernike secondary trefoil Y.

prysm.zernike.secondary_trefoil_x(rho, phi)¶: Zernike secondary trefoil X.

prysm.zernike.tertiary_astigmatism_00(rho, phi)¶: Zernike tertiary astigmatism 0°.

prysm.zernike.tertiary_astigmatism_45(rho, phi)¶: Zernike tertiary astigmatism 45°.

prysm.zernike.tertiary_coma_y(rho, phi)¶: Zernike tertiary coma Y.

prysm.zernike.tertiary_coma_x(rho, phi)¶: Zernike tertiary coma X.

prysm.zernike.tertiary_spherical(rho, phi)¶: Zernike tertiary spherical.

prysm.zernike.primary_pentafoil_y(rho, phi)¶: Zernike primary pentafoil Y.

prysm.zernike.primary_pentafoil_x(rho, phi)¶: Zernike primary pentafoil X.

prysm.zernike.secondary_tetrafoil_y(rho, phi)¶: Zernike secondary tetrafoil Y.

prysm.zernike.secondary_tetrafoil_x(rho, phi)¶: Zernike secondary tetrafoil X.

prysm.zernike.tertiary_trefoil_y(rho, phi)¶: Zernike tertiary trefoil Y.

prysm.zernike.tertiary_trefoil_x(rho, phi)¶: Zernike tertiary trefoil X.

prysm.zernike.quaternary_astigmatism_00(rho, phi)¶: Zernike quaternary astigmatism 0°.

prysm.zernike.quaternary_astigmatism_45(rho, phi)¶: Zernike quaternary astigmatism 45°.

prysm.zernike.quaternary_coma_y(rho, phi)¶: Zernike quaternary coma Y.

prysm.zernike.quaternary_coma_x(rho, phi)¶: Zernike quaternary coma X.

prysm.zernike.quaternary_spherical(rho, phi)¶: Zernike quaternary spherical.

prysm.zernike.primary_hexafoil_y(rho, phi)¶: Zernike primary hexafoil Y.

prysm.zernike.primary_hexafoil_x(rho, phi)¶: Zernike primary hexafoil X.

prysm.zernike.secondary_pentafoil_y(rho, phi)¶: Zernike secondary pentafoil Y.

prysm.zernike.secondary_pentafoil_x(rho, phi)¶: Zernike secondary pentafoil X.

prysm.zernike.tertiary_tetrafoil_y(rho, phi)¶: Zernike tertiary tetrafoil Y.

prysm.zernike.tertiary_tetrafoil_x(rho, phi)¶: Zernike tertiary tetrafoil X.

prysm.zernike.quaternary_trefoil_y(rho, phi)¶: Zernike quaternary trefoil Y.

prysm.zernike.quaternary_trefoil_x(rho, phi)¶: Zernike quaternary trefoil X.

prysm.zernike.quinternary_astigmatism_00(rho, phi)¶: Zernike quinternary astigmatism 0°.

prysm.zernike.quinternary_astigmatism_45(rho, phi)¶: Zernike quinternary astigmatism 45°.

prysm.zernike.quinternary_coma_y(rho, phi)¶: Zernike quinternary coma Y.

prysm.zernike.quinternary_coma_x(rho, phi)¶: Zernike quinternary coma X.

prysm.zernike.quinternary_spherical(rho, phi)¶: Zernike quinternary spherical.

prysm.zernike.primary_septafoil_y(rho, phi)¶: Zernike primary septafoil.

prysm.zernike.primary_septafoil_x(rho, phi)¶: Zernike primary septafoil.

prysm.zernike.compfunc(rho, phi)¶: Zernike primary septafoil.

prysm.zernike.change_backend(to)¶: Change the backend between cuda/cupy and CPU.

prysm.zernike.zernikename(idx, base, map_)¶: Return the name of a Fringe Zernike with the given index and base.

prysm.zernike.zernikes_to_magnitude_angle(coefs, namer)¶: Convert Fringe Zernike polynomial set to a magnitude and phase representation.

class prysm.zernike.ZCache¶

Bases: object

Cache of Zernike terms evaluated over the unit circle.

get_zernike(number, norm, samples)¶: Get an array of phase values for a given index, norm, and number of samples.

clear(*args)¶: Empty the cache.

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.phase (numpy.ndarray) – arrays containing the phase associated with the pupil
self.fcn (numpy.ndarray) – array containing the wavefunction of the pupil plane

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_phase_unit(to, inplace=True)¶

Change the units used to describe the phase.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.phase, if False, returns updated phase, if True, returns self.

Returns

`new_phase` (np.ndarray) – new phase data
OR
`self` (OpticalPhase) – self

change_spatial_unit(to, inplace=True)¶

Change the units used to describe the spatial dimensions.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.x and self.y. If False, returns updated phase, if True, returns self

Returns

`new_ux` (np.ndarray) – new ordinate x axis
`new_uy` (np.ndarray) – new ordinate y axis
OR
`self` (OpticalPhase) – self

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.

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None)¶

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, interp_method='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

mask(mask, target, nanify=True)¶

Apply a mask to the pupil.

Used to implement vignetting, chief ray angles, etc.

Parameters

mask (str or numpy.ndarray) – if a string, uses geometry.mcache for high speed access to a mask with a given shape, e.g. mask=’circle’ or mask=’hexagon’. If an ndarray, directly use the mask.
target (str, {‘phase’, ‘fcn’, ‘both’}) – which array to mask
nanify (bool, optional) – if True, make (target) equal to NaN where the mask is zero.

Returns

self, the pupil instance

Return type

Pupil

phase_unit¶: Unit used to describe the optical phase.

plot2d(cmap='inferno', clim=(None, None), interp_method='lanczos', show_colorbar=True, fig=None, ax=None)¶

Plot the phase in 2D.

Parameters

cmap (str) – colormap to use, passed directly to matplotlib
interp_method (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – whether to draw the colorbar
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

plot_slice_xy(lw=3, zorder=3, fig=None, ax=None)¶

Create a plot of slices through the X and Y axes of the Pupil.

Parameters

lw (float, optional) – line width
zorder (int, optional) – zorder
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

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.

slice_x¶

Retrieve a slice through the X axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

slice_y¶

Retrieve a slice through the Y axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

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.phase (numpy.ndarray) – arrays containing the phase associated with the pupil
self.fcn (numpy.ndarray) – array containing the wavefunction of the pupil plane

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_phase_unit(to, inplace=True)¶

Change the units used to describe the phase.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.phase, if False, returns updated phase, if True, returns self.

Returns

`new_phase` (np.ndarray) – new phase data
OR
`self` (OpticalPhase) – self

change_spatial_unit(to, inplace=True)¶

Change the units used to describe the spatial dimensions.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.x and self.y. If False, returns updated phase, if True, returns self

Returns

`new_ux` (np.ndarray) – new ordinate x axis
`new_uy` (np.ndarray) – new ordinate y axis
OR
`self` (OpticalPhase) – self

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.

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None)¶

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, interp_method='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.

mask(mask, target, nanify=True)¶

Apply a mask to the pupil.

Used to implement vignetting, chief ray angles, etc.

Parameters

mask (str or numpy.ndarray) – if a string, uses geometry.mcache for high speed access to a mask with a given shape, e.g. mask=’circle’ or mask=’hexagon’. If an ndarray, directly use the mask.
target (str, {‘phase’, ‘fcn’, ‘both’}) – which array to mask
nanify (bool, optional) – if True, make (target) equal to NaN where the mask is zero.

Returns

self, the pupil instance

Return type

Pupil

names¶: Names of the terms in self.

phase_unit¶: Unit used to describe the optical phase.

plot2d(cmap='inferno', clim=(None, None), interp_method='lanczos', show_colorbar=True, fig=None, ax=None)¶

Plot the phase in 2D.

Parameters

cmap (str) – colormap to use, passed directly to matplotlib
interp_method (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – whether to draw the colorbar
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

plot_slice_xy(lw=3, zorder=3, fig=None, ax=None)¶

Create a plot of slices through the X and Y axes of the Pupil.

Parameters

lw (float, optional) – line width
zorder (int, optional) – zorder
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

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.

slice_x¶

Retrieve a slice through the X axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

slice_y¶

Retrieve a slice through the Y axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

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 deswcription 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.phase (numpy.ndarray) – arrays containing the phase associated with the pupil
self.fcn (numpy.ndarray) – array containing the wavefunction of the pupil plane

center_x¶: Center “pixel” in x.

center_y¶: Center “pixel” in y.

change_phase_unit(to, inplace=True)¶

Change the units used to describe the phase.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.phase, if False, returns updated phase, if True, returns self.

Returns

`new_phase` (np.ndarray) – new phase data
OR
`self` (OpticalPhase) – self

change_spatial_unit(to, inplace=True)¶

Change the units used to describe the spatial dimensions.

Parameters

to (str) – new unit, a member of OpticalPhase.units.keys()
inplace (bool, optional) – whether to change self.x and self.y. If False, returns updated phase, if True, returns self

Returns

`new_ux` (np.ndarray) – new ordinate x axis
`new_uy` (np.ndarray) – new ordinate y axis
OR
`self` (OpticalPhase) – self

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.

fcn¶: Complex wavefunction associated with the pupil.

static from_interferogram(interferogram, wvl=None)¶

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, interp_method='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.

mask(mask, target, nanify=True)¶

Apply a mask to the pupil.

Used to implement vignetting, chief ray angles, etc.

Parameters

mask (str or numpy.ndarray) – if a string, uses geometry.mcache for high speed access to a mask with a given shape, e.g. mask=’circle’ or mask=’hexagon’. If an ndarray, directly use the mask.
target (str, {‘phase’, ‘fcn’, ‘both’}) – which array to mask
nanify (bool, optional) – if True, make (target) equal to NaN where the mask is zero.

Returns

self, the pupil instance

Return type

Pupil

names¶: Names of the terms in self.

phase_unit¶: Unit used to describe the optical phase.

plot2d(cmap='inferno', clim=(None, None), interp_method='lanczos', show_colorbar=True, fig=None, ax=None)¶

Plot the phase in 2D.

Parameters

cmap (str) – colormap to use, passed directly to matplotlib
interp_method (str, optional) – interpolation method to use, passed directly to matplotlib
show_colorbar (bool, optional) – whether to draw the colorbar
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

plot_slice_xy(lw=3, zorder=3, fig=None, ax=None)¶

Create a plot of slices through the X and Y axes of the Pupil.

Parameters

lw (float, optional) – line width
zorder (int, optional) – zorder
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

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.

slice_x¶

Retrieve a slice through the X axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

slice_y¶

Retrieve a slice through the Y axis of the phase.

Returns

self.unit (numpy.ndarray) – ordinate axis
slice of self.phase or self.data (numpy.ndarray)

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

prysm.zernike.func(rho, phi)¶: Zernike primary septafoil.

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, optional) – number of terms to fit, fits terms 0~terms
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’}) – 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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