prysm.propagation¶

Numerical optical propagation.

prysm.propagation.focus(wavefunction, Q, incoherent=True, norm=None)¶

Propagate a pupil plane to a PSF plane.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
Q (float) – oversampling / padding factor
incoherent (bool, optional) – whether to return the incoherent (real valued) PSF, or the coherent (complex-valued) PSF. Incoherent = |coherent|^2
norm (str, {None, ‘ortho’}) – normalization parameter passed directly to numpy/cupy fft

Returns

psf – point spread function

Return type

numpy.ndarray

prysm.propagation.unfocus(wavefunction, Q, norm=None)¶

Propagate a PSF plane to a pupil plane.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
Q (float) – oversampling / padding factor
norm (str, {None, ‘ortho’}) – normalization parameter passed directly to numpy/cupy fft

Returns

pupil – field in the pupil plane

Return type

numpy.ndarray

prysm.propagation.focus_fixed_sampling(wavefunction, input_sample_spacing, prop_dist, wavelength, output_sample_spacing, output_samples, coherent=False, norm=False)¶

Propagate a pupil function to the PSF plane with fixed sampling.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
input_sample_spacing (float) – spacing between samples in the pupil plane, millimeters
prop_dist (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
output_sample_spacing (float) – sample spacing in the output plane, microns
output_samples (int) – number of samples in the square output array
coherent (bool) – if True, returns the complex array. Else returns its magnitude squared.

Returns

data – 2D array of data

Return type

numpy.ndarray

prysm.propagation.unfocus_fixed_sampling(wavefunction, input_sample_spacing, prop_dist, wavelength, output_sample_spacing, output_samples, norm=False)¶

Propagate an image plane field to the pupil plane with fixed sampling.

Parameters

wavefunction (numpy.ndarray) – the image plane wavefunction
input_sample_spacing (float) – spacing between samples in the pupil plane, millimeters
prop_dist (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
output_sample_spacing (float) – sample spacing in the output plane, microns
output_samples (int) – number of samples in the square output array

Returns

x (numpy.ndarray) – x axis unit, 1D ndarray
y (numpy.ndarray) – y axis unit, 1D ndarray
data (numpy.ndarray) – 2D array of data

prysm.propagation.Q_for_sampling(input_diameter, prop_dist, wavelength, output_sample_spacing)¶

Value of Q for a given output sampling, given input sampling.

Parameters

input_diameter (float) – diameter of the input array in millimeters
prop_dist (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
output_sample_spacing (float) – sampling in the output plane, microns

Returns

requesite Q

Return type

float

prysm.propagation.focus_units(wavefunction, input_sample_spacing, efl, wavelength, Q)¶

Compute the ordinate axes for a pupil plane to PSF plane propagation.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
input_sample_spacing (float) – spacing between samples in the pupil plane
efl (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
Q (float) – oversampling / padding factor

Returns

x (numpy.ndarray) – x axis unit, 1D ndarray
y (numpy.ndarray) – y axis unit, 1D ndarray

prysm.propagation.unfocus_units(wavefunction, input_sample_spacing, efl, wavelength, Q)¶

Compute the ordinate axes for a PSF plane to pupil plane propagation.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
input_sample_spacing (float) – spacing between samples in the PSF plane
efl (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
Q (float) – oversampling / padding factor

Returns

x (numpy.ndarray) – x axis unit, 1D ndarray
y (numpy.ndarray) – y axis unit, 1D ndarray

prysm.propagation.pupil_sample_to_psf_sample(pupil_sample, samples, wavelength, efl)¶

Convert pupil sample spacing to PSF sample spacing. fλ/D or Q.

Parameters

pupil_sample (float) – sample spacing in the pupil plane
samples (int) – number of samples present in both planes (must be equal)
wavelength (float) – wavelength of light, in microns
efl (float) – effective focal length of the optical system in mm

Returns

the sample spacing in the PSF plane

Return type

float

prysm.propagation.psf_sample_to_pupil_sample(psf_sample, samples, wavelength, efl)¶

Convert PSF sample spacing to pupil sample spacing.

Parameters

psf_sample (float) – sample spacing in the PSF plane
samples (int) – number of samples present in both planes (must be equal)
wavelength (float) – wavelength of light, in microns
efl (float) – effective focal length of the optical system in mm

Returns

the sample spacing in the pupil plane

Return type

float

prysm.propagation.fresnel_number(a, L, lambda_)¶

Compute the Fresnel number.

Notes

if the fresnel number is << 1, paraxial assumptions hold for propagation

Parameters

a (float) – characteristic size (“radius”) of an aperture
L (float) – distance of observation
lambda (float) – wavelength of light, same units as a

Returns

the fresnel number for these parameters

Return type

float

prysm.propagation.talbot_distance(a, lambda_)¶

Compute the talbot distance.

Parameters

a (float) – period of the grating, units of microns
lambda (float) – wavleength of light, units of microns

Returns

talbot distance, units of microns

Return type

float

prysm.propagation.angular_spectrum(field, wvl, sample_spacing, z, Q=2)¶

Propagate a field via the angular spectrum method.

Parameters

field (numpy.ndarray) – 2D array of complex electric field values
wvl (float) – wavelength of light, microns
z (float) – propagation distance, units of millimeters
sample_spacing (float) – cartesian sample spacing, units of millimeters
Q (float) – sampling factor used. Q>=2 for Nyquist sampling of incoherent fields

Returns

2D ndarray of the output field, complex

Return type

numpy.ndarray

class prysm.propagation.Wavefront(x, y, fcn, wavelength, space='pupil')¶

Bases: prysm._richdata.RichData

(Complex) representation of a wavefront.

fcn¶: Complex field / wavefunction.

diameter_x¶: Diameter of the data in x.

diameter_y¶: Diameter of the data in y.

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

semidiameter¶: Half of self.diameter.

free_space(dz, Q=2)¶

Perform a plane-to-plane free space propagation.

Uses angular spectrum and the free space kernel.

Parameters

dz (float) – inter-plane distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048.

Returns

the wavefront at the new plane

Return type

Wavefront

focus(efl, Q=2)¶

Perform a “pupil” to “psf” plane propgation.

Uses an FFT with no quadratic phase.

Parameters

efl (float) – focusing distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048. To avoid aliasng, the array must be padded such that Q is at least 2 this may happen organically if your data does not span the array.

Returns

the wavefront at the focal plane

Return type

Wavefront

unfocus(efl, Q=2)¶

Perform a “psf” to “pupil” plane propagation.

uses an FFT with no quadratic phase.

Parameters

efl (float) – un-focusing distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048. To avoid aliasng, the array must be padded such that Q is at least 2 this may happen organically if your data does not span the array.

Returns

the wavefront at the pupil plane

Return type

Wavefront

focus_fixed_sampling(efl, sample_spacing, samples)¶

Perform a “pupil” to “psf” propagation with fixed output sampling.

Uses matrix triple product DFTs to specify the grid directly.

Parameters

efl (float) – focusing distance, millimeters
sample_spacing (float) – output sample spacing, microns
samples (int) – number of samples in the output plane. If int, interpreted as square else interpreted as (x,y), which is the reverse of numpy’s (y, x) row major ordering

Returns

the wavefront at the psf plane

Return type

Wavefront

astype(other_type)¶

Change this instance of one type into another.

Useful to access methods of the other class.

Parameters: other_type (object) – the name of the other type to “cast” to, e.g. Interferogram. Not a string.
Returns: type-converted to the other type.
Return type: self

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.

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

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

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.

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

unfocus_fixed_sampling(efl, sample_spacing, samples)¶

Perform a “psf” to “pupil” propagation with fixed output sampling.

Uses matrix triple product DFTs to specify the grid directly.

Parameters

efl (float) – un-focusing distance, millimeters
sample_spacing (float) – output sample spacing, millimeters
samples (int) – number of samples in the output plane. If int, interpreted as square else interpreted as (x,y), which is the reverse of numpy’s (y, x) row major ordering

Returns

wavefront at the pupil plane

Return type

Wavefront

prysm.propagation¶

prysm

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