prysm.psf¶
A base point spread function interface.

class
prysm.psf.
PSF
(x, y, data)¶ Bases:
prysm.convolution.Convolvable
A Point Spread Function.

center_x
¶ center sample along x
 Type
int

center_y
¶ center sample along y
 Type
int

data
¶ PSF normalized intensity data
 Type
numpy.ndarray

sample_spacing
¶ center to center spacing of samples
 Type
float

x
¶ x Cartesian axis locations of samples, 1D ndarray
 Type
numpy.ndarray

y `numpy.ndarray`
y Cartesian axis locations of samples, 1D ndarray

encircled_energy
(radius)¶ Compute the encircled energy of the PSF.
 Parameters
radius (float or iterable) – radius or radii to evaluate encircled energy at
 Returns
if radius is a float, returns a float, else returns a list.
 Return type
encircled energy
Notes
implementation of “Simplified Method for Calculating Encircled Energy,” Baliga, J. V. and Cohn, B. D., doi: 10.1117/12.944334

ee_radius
(energy=0.8377850436212378)¶ Radius associated with a certain amount of enclosed energy.

ee_radius_diffraction
(energy=0.8377850436212378)¶ Radius associated with a certain amount of enclosed energy for a diffraction limited circular pupil.

ee_radius_ratio_to_diffraction
(energy=0.8377850436212378)¶ Ratio of this PSF and the diffraction limited PSFs’ radii enclosing a certain amount of energy.

plot2d
(axlim=25, power=1, clim=(None, None), interp_method='lanczos', pix_grid=None, cmap='Greys_r', fig=None, ax=None, show_axlabels=True, show_colorbar=True, circle_ee=None, circle_ee_lw=None)¶ Create a 2D plot of the PSF.
 Parameters
axlim (float) – limits of axis, symmetric. xlim=(axlim,axlim), ylim=(axlim, axlim)
power (float) – power to stretch the data by for plotting
clim (iterable) – limits to use for log color scaling. If power != 1 and clim != (None, None), clim (log axes) takes precedence
interp_method (string) – method used to interpolate the image between samples of the PSF
pix_grid (float) – if not None, overlays gridlines with spacing equal to pix_grid. Intended to show the collection into camera pixels while still in the oversampled domain
cmap (str, optional) – colormap, passed directly to matplotlib
fig (matplotlib.figure.Figure, optional:) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot
show_axlabels (bool) – whether or not to show the axis labels
show_colorbar (bool) – whether or not to show the colorbar
circle_ee (float, optional) – relative encircled energy to draw a circle at, in addition to diffraction limited airy radius (1.22*λ*F#). First airy zero occurs at circle_ee=0.8377850436212378
circle_ee_lw (float, optional) – linewidth passed to matplotlib for the encircled energy circles
 Returns
fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional) – Axis containing the plot

plot_encircled_energy
(axlim=None, npts=50, lw=3, zorder=3, fig=None, ax=None)¶ Make a 1D plot of the encircled energy at the given azimuth.
 Parameters
azimuth (float) – azimuth to plot at, in degrees
axlim (float) – limits of axis, will plot [0, axlim]
npts (int, optional) – number of points to use from [0, axlim]
lw (float, optional) – line width
zorder (int optional) – zorder
fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot
 Returns
fig (matplotlib.figure.Figure, optional) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

static
from_pupil
(pupil, efl, Q=2, norm='max')¶ Use scalar diffraction propogation to generate a PSF from a pupil.
 Parameters
pupil (Pupil) – Pupil, with OPD data and wavefunction
efl (int or float) – effective focal length of the optical system
Q (int or float) – ratio of pupil sample count to PSF sample count; Q > 2 satisfies nyquist
 Returns
A new PSF instance
 Return type
PSF

static
polychromatic
(psfs, spectral_weights=None, interp_method='linear')¶ Create a new PSF instance from an ensemble of monochromatic PSFs given spectral weights.
The new PSF is the polychromatic PSF, assuming the wavelengths are sufficiently different that they do not interfere and the mode of imaging is incoherent.

center_x
Center “pixel” in x.

center_y
Center “pixel” in y.

conv
(other)¶ Convolves this convolvable with another.
 Parameters
other (Convolvable) – A convolvable object
 Returns
a convolvable object
 Return type
Convolvable
Notes
If self and other both have analytic Fourier transforms, no math will be done and the aFTs are merged directly.
If only one of self or other has an analytic Fourier transform, the output grid will be defined by the object which does not have an analytic Fourier transform.
If neither has an analytic transform, the output grid will:  span max(self.support, other.support)  have sample spacing min(self.sample_spacing, other.sample_spacing)
This ensures the signal remains Nyquist sampled and (probably) doesn’t expand beyond the extent of the output window. The latter condition will be violated when two large convolvables are convolved.

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

deconv
(other, balance=1000, reg=None, is_real=True, clip=False, postnormalize=True)¶ Perform the deconvolution of this convolvable object by another.
 Parameters
other (Convolvable) – another convolvable object, used as the PSF in a Wiener deconvolution
balance (float, optional) – regularization parameter; passed through to skimage
reg (numpy.ndarray, optional) – regularization operator, passed through to skimage
is_real (bool, optional) – True if self and other are both real
clip (bool, optional) – clips self and other into (0,1)
postnormalize (bool, optional) – normalize the result such that it falls in [0,1]
 Returns
a new Convolable object
 Return type
Convolvable
Notes
See skimage: http://scikitimage.org/docs/dev/api/skimage.restoration.html#skimage.restoration.wiener

static
from_file
(path, scale)¶ Read a monochrome 8 bit per pixel file into a new Image instance.
 Parameters
path (string) – path to a file
scale (float) – pixel scale, in microns
 Returns
a new image object
 Return type
Convolvable

plot_slice_xy
(axlim=20, lw=3, zorder=3, fig=None, ax=None)¶ Create a plot of slices through the X and Y axes of the PSF.
 Parameters
axlim (float or int, optional) – axis limits, in microns
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

renorm
()¶ Renormalize so that the peak is at a value of unity.

sample_spacing
centertocenter sample spacing.

samples_x
¶ Number of samples in the x dimension.

samples_y
¶ Number of samples in the y dimension.

save
(path, nbits=8)¶ Write the image to a png, jpg, tiff, etc.
 Parameters
path (string) – path to write the image to
nbits (int) – number of bits in the output image

shape
¶ Proxy to phase or data shape.

show
(xlim=None, ylim=None, interp_method=None, power=1, show_colorbar=True, fig=None, ax=None)¶ Display the image.
 Parameters
xlim (iterable, optional) – x axis limits
ylim (iterable,) – y axis limits
interp_method (string) – interpolation technique used in display
power (float) – inverse of power to stretch image by. E.g. power=2 will plot img ** (1/2)
show_colorbar (bool) – whether to show the colorbar or not.
fig (matplotlib.figure.Figure, optional:) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot
 Returns
fig (matplotlib.figure.Figure, optional:) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

show_fourier
(freq_x=None, freq_y=None, interp_method='lanczos', fig=None, ax=None)¶ Display the fourier transform of the image.
 Parameters
interp_method (string) – method used to interpolate the data for display.
freq_x (iterable) – x frequencies to use for convolvable with analytical FT and no data
freq_y (iterable) – y frequencies to use for convolvable with analytic FT and no data
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
Notes
freq_x and freq_y are unused when the convolvable has a .data field.

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)

support
¶ Width of the domain.

support_x
¶ Width of the domain in X.

support_y
¶ Width of the domain in Y.


class
prysm.psf.
AiryDisk
(fno, wavelength, extent=None, samples=None)¶ Bases:
prysm.convolution.Convolvable
An airy disk, the PSF of a circular aperture.

analytic_ft
(x, y)¶ Analytic fourier transform of an airy disk.
 Parameters
x (numpy.ndarray) – sample points in x axis
y (numpy.ndarray) – sample points in y axis
 Returns
2D numpy array containing the analytic fourier transform
 Return type
numpy.ndarray

center_x
¶ Center “pixel” in x.

center_y
¶ Center “pixel” in y.

conv
(other)¶ Convolves this convolvable with another.
 Parameters
other (Convolvable) – A convolvable object
 Returns
a convolvable object
 Return type
Convolvable
Notes
If self and other both have analytic Fourier transforms, no math will be done and the aFTs are merged directly.
If only one of self or other has an analytic Fourier transform, the output grid will be defined by the object which does not have an analytic Fourier transform.
If neither has an analytic transform, the output grid will:  span max(self.support, other.support)  have sample spacing min(self.sample_spacing, other.sample_spacing)
This ensures the signal remains Nyquist sampled and (probably) doesn’t expand beyond the extent of the output window. The latter condition will be violated when two large convolvables are convolved.

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

deconv
(other, balance=1000, reg=None, is_real=True, clip=False, postnormalize=True)¶ Perform the deconvolution of this convolvable object by another.
 Parameters
other (Convolvable) – another convolvable object, used as the PSF in a Wiener deconvolution
balance (float, optional) – regularization parameter; passed through to skimage
reg (numpy.ndarray, optional) – regularization operator, passed through to skimage
is_real (bool, optional) – True if self and other are both real
clip (bool, optional) – clips self and other into (0,1)
postnormalize (bool, optional) – normalize the result such that it falls in [0,1]
 Returns
a new Convolable object
 Return type
Convolvable
Notes
See skimage: http://scikitimage.org/docs/dev/api/skimage.restoration.html#skimage.restoration.wiener

static
from_file
(path, scale)¶ Read a monochrome 8 bit per pixel file into a new Image instance.
 Parameters
path (string) – path to a file
scale (float) – pixel scale, in microns
 Returns
a new image object
 Return type
Convolvable

plot_slice_xy
(axlim=20, lw=3, zorder=3, fig=None, ax=None)¶ Create a plot of slices through the X and Y axes of the PSF.
 Parameters
axlim (float or int, optional) – axis limits, in microns
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

renorm
()¶ Renormalize so that the peak is at a value of unity.

sample_spacing
¶ centertocenter sample spacing.

samples_x
¶ Number of samples in the x dimension.

samples_y
¶ Number of samples in the y dimension.

save
(path, nbits=8)¶ Write the image to a png, jpg, tiff, etc.
 Parameters
path (string) – path to write the image to
nbits (int) – number of bits in the output image

shape
¶ Proxy to phase or data shape.

show
(xlim=None, ylim=None, interp_method=None, power=1, show_colorbar=True, fig=None, ax=None)¶ Display the image.
 Parameters
xlim (iterable, optional) – x axis limits
ylim (iterable,) – y axis limits
interp_method (string) – interpolation technique used in display
power (float) – inverse of power to stretch image by. E.g. power=2 will plot img ** (1/2)
show_colorbar (bool) – whether to show the colorbar or not.
fig (matplotlib.figure.Figure, optional:) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot
 Returns
fig (matplotlib.figure.Figure, optional:) – Figure containing the plot
ax (matplotlib.axes.Axis, optional:) – Axis containing the plot

show_fourier
(freq_x=None, freq_y=None, interp_method='lanczos', fig=None, ax=None)¶ Display the fourier transform of the image.
 Parameters
interp_method (string) – method used to interpolate the data for display.
freq_x (iterable) – x frequencies to use for convolvable with analytical FT and no data
freq_y (iterable) – y frequencies to use for convolvable with analytic FT and no data
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
Notes
freq_x and freq_y are unused when the convolvable has a .data field.

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)

support
¶ Width of the domain.

support_x
¶ Width of the domain in X.

support_y
¶ Width of the domain in Y.


prysm.psf.
airydisk
(unit_r, fno, wavelength)¶ Compute the airy disk function over a given spatial distance.
 Parameters
unit_r (numpy.ndarray) – ndarray with units of um
fno (float) – F/# of the system
wavelength (float) – wavelength of light, um
 Returns
ndarray containing the airy pattern
 Return type
numpy.ndarray