open_viewmin.nematic.jones

open_viewmin.nematic.jones#

Jones matrix calculations for transmission of polarized light through the nematic liquid crystal.

Adapted from code originally written by Sophie Ettinger and adapted for open-Qmin data by Yvonne Zagzag.

Functions#

`_add_jones_arrows`(plotter, coord_index, center, actor_name)	Add arrows for polarizer and analyzer directions and, if applicable,
`_add_jones_lambda_arrow`(plotter, p_dir, a_dir, ...)	Add arrow indicating orientation of quarter-wave plate
`_double_headed_arrow`(center, direction, **kwargs)
`add_jones_to_plotter`(plotter[, n, site_types])	Add planes to back of box, colored by RGB Jones matrix transmission
`add_jones_toolbar_to_plotter`(plotter[, n, site_types])	Add planes to back of box, colored by RGB Jones matrix transmission
`get_director_data_from_plotter`(plotter, n, site_types)	Use plotter's existing nematic director data for Jones matrix
`get_quarter_wave_plate_jones`(angle)	Apply quarter-wave plate transformation to Jones matrix
`jones_light_propagation_through_sample`(director, ...)	Calculate Jones matrix product for light propagation through nematic
`jones_matrices_multiple_wavelengths`(n, site_types[, ...])	Calculate list of Jones matrices for a sequence of wavelengths.
`jones_matrix`(n_phi, phi_ext, phi_ord)	Calculate Jones matrix array for one slice at constant z.
`list_to_xyz_mat`(data, dims)	Convert a flattened data array to shape (Lx, Ly, Lz, ...).
`n_and_site_types_from_open_qmin`(filename)	Import Q-tensor data in the open-Qmin data_format
`permute_axes`(arr, axis_name)	Permute coordinate axes so that the optical axis corresponds to
`polarizer_matrix_from_angle`(angle)	Calculate projection matrix along a polarizer's direction in the xy
`pom_animation_rotate_polarizers`(plotter[, n, ...])	Create video of simulated polarized optical microscopy images
`pom_image_color`(jones_mats[, polarizer_angle, ...])	Given Jones matrices for red, green, and blue light propagation,
`pom_image_one_wavelength`(jones_mat_product, p_angle, ...)	Simulated polarized optical microscopy image using a single wavelength
`pom_image_sequence_rotate_polarizers`(ax, n, site_types)	Create image sequence of simulated polarized optical microscopy images
`rgb_to_texture`(rgb_data[, sigma])	Transform 2D NumPy float rgb array to PyVista texture
`rotation_matrix_2d`(angle)	Calculate 2x2 rotation matrix
`rotation_transform`(mat, rot_mat)	Calculate M' = R M R^T for given matrix M and rotation matrix R.
`save_jones_data`(plotter, filename)	Saves numerical Jones matrix data to files
`save_jones_data_gui`(plotter[, filename])	Launch dialog to save numerical Jones matrix data to files
`save_jones_images`(plotter, filename)	Save Jones matrix images to files
`save_jones_images_gui`(plotter[, filename])	Launch dialog to save Jones matrix images to files

Module Contents#

_add_jones_arrows(plotter, coord_index, center, actor_name)#

Add arrows for polarizer and analyzer directions and, if applicable, quarter-wave plate direction

Parameters:

plotter (NematicPlotNoQt)
coord_index (int)
center (Iterable of [float])
actor_name (str)

_add_jones_lambda_arrow(plotter, p_dir, a_dir, jones_arrows_scale, arrows_center, lambda_arrow_actor_name)#

Add arrow indicating orientation of quarter-wave plate

Parameters:

plotter (NematicPlotNoQt)
p_dir (Iterable of [float])
a_dir (Iterable of [float])
jones_arrows_scale (float)
arrows_center (Iterable of [float])
lambda_arrow_actor_name (str)

_double_headed_arrow(center, direction, **kwargs)#

Parameters:

center (Iterable of [float])
direction (Iterable of [float])
kwargs (dict, optional) – Keyword arguments to pyvista.Arrow

Return type:

(pyvista.Arrow, pyvista.Arrow)

add_jones_to_plotter(plotter, n=None, site_types=None)#

Add planes to back of box, colored by RGB Jones matrix transmission and normal to x, y, z.

Parameters:

plotter (NematicPlot or NematicPlotNoQt)
n (numpy.ndarray or None, optional) – director data; if None, director will be taken from plotter
site_types (numpy.ndarray, “off”, or None) – site types data; if “off”, all sites are taken to be bulk; if None, site types data will be taken from plotter

add_jones_toolbar_to_plotter(plotter, n=None, site_types=None)#

Add planes to back of box, colored by RGB Jones matrix transmission and normal to x, y, z, with polarizer/analyzer angles and brightness controlled by sliders.

Parameters:

plotter (open_viewmin.NematicPlot)
n (numpy.ndarray or None, optional) – director data; if None, director will be taken from plotter
site_types (numpy.ndarray, “off”, or None) – site types data; if “off”, all sites are taken to be bulk; if None, site types data will be taken from plotter

Returns:

callback that refreshes Jones planes by re-applying the control slider widgets

Return type:

callable()

get_director_data_from_plotter(plotter, n, site_types)#

Use plotter’s existing nematic director data for Jones matrix calculations

Parameters:

plotter (open_viewmin.NematicPlot or open_viewmin.NematicPlotNoQt)
n (numpy.ndarray or None) – nematic director field in flattened array; if None, data is taken from plotter
site_types (numpy.ndarray, “off”, or None) – site types in flattened array; if “off”, all sites are treated as bulk; if None, data is taken from plotter

Returns:

reshaped arrays of nematic director and site types data

Return type:

numpy.ndarray, numpy.ndarray

get_quarter_wave_plate_jones(angle)#

Apply quarter-wave plate transformation to Jones matrix

Parameters:: angle (float)
Return type:: numpy.ndarray

jones_light_propagation_through_sample(director, site_types, wavelength=6.6e-07, res=4.5e-08, n_ord=1.55, n_ext=1.7, optical_axis='z', n_bdy=1.333)#

Calculate Jones matrix product for light propagation through nematic sample.

Parameters:

director (numpy.ndarray) – nematic director field
site_types (numpy.ndarray) – array of site types (bulk, boundary, or surface) for the lattice
wavelength (float) – wavelength of incident light, in meters
res (float) – lattice resolution, in meters
n_ord (float) – ordinary index of refraction
n_ext (float) – extraordinary index of refraction
optical_axis ('x', 'y', or 'z', optional) – light propagation direction
n_bdy (float or sequence of floats) – isotropic index of refraction inside boundary

Returns:

Jones matrix for light propagation through the entire simulation box

Return type:

numpy.ndarray

jones_matrices_multiple_wavelengths(n, site_types, wavelengths=(6.38e-07, 5.32e-07, 4.65e-07), **kwargs)#

Calculate list of Jones matrices for a sequence of wavelengths.

Parameters:

n (numpy.ndarray) – nematic director field
site_types (numpy.ndarray) – array of site types (bulk, boundary, surface)
wavelengths (sequence of floats) – wavelengths in meters
**kwargs – keyword arguments accepted by jones_light_propagation_through_sample

Returns:

list of Jones matrix arrays

Return type:

list(numpy.ndarray)

jones_matrix(n_phi, phi_ext, phi_ord)#

Calculate Jones matrix array for one slice at constant z.

Parameters:

n_phi (numpy.ndarray) – azimuthal angle of director in plane transverse to light propagation
phi_ext (numpy.ndarray) – array of local-frame complex Jones matrices for effective extraordinary index of refraction
phi_ord (numpy.ndarray) – local-frame complex Jones matrix for ordinary index of refraction

Returns:

array of lab-frame complex Jones matrices

Return type:

numpy.ndarray

list_to_xyz_mat(data, dims)#

Convert a flattened data array to shape (Lx, Ly, Lz, …).

Parameters:

data (numpy.ndarray)
dims ((int, int, int))

Return type:

numpy.ndarray

n_and_site_types_from_open_qmin(filename)#

Import Q-tensor data in the open-Qmin data_format

Parameters:: filename (str) – Filename of open-Qmin-style data.
Returns:: director, site_types arrays
Return type:: numpy.ndarray, numpy.ndarray

permute_axes(arr, axis_name)#

Permute coordinate axes so that the optical axis corresponds to axis_name

Parameters:

arr (numpy.ndarray)
axis_name ('x', 'y', or 'z')

Return type:

numpy.ndarray

polarizer_matrix_from_angle(angle)#

Calculate projection matrix along a polarizer’s direction in the xy plane.

Parameters:: angle (float) – angle of polarizer with respect to x-axis (after permuting axes so that z is the light propagation direction)
Returns:: polarizer projection matrix
Return type:: numpy.ndarray

pom_animation_rotate_polarizers(plotter, n=None, site_types='off', interval=50, filename=None, **kwargs)#

Create video of simulated polarized optical microscopy images with polarizer and analyzer rotating linearly in time through total angle pi/2.

Parameters:

plotter (open_viewmin.NematicPlot or open_viewmin.NematicPlotNoQt)
n (numpy.ndarray or None, optional) – nematic director data; if None, this data is taken from the plotter
site_types (numpy.ndarray, “off”, or None, optional) – site types data; if “off”, all sites are treated as bulk; if None, data is taken from plotter
interval (int, optional) – number of milliseconds between frames of animation
filename (str or None, optional) – filename for exported video; if None, no export occurs and the function returns the full HTML string for the video
kwargs (dict, optional) – keyword arguments accepted by pom_image_sequence_rotate_polarizers

Returns:

filename of exported video or full HTML string defining the video

Return type:

str

pom_image_color(jones_mats, polarizer_angle=0.0, analyzer_angle=None, brightness_factor=1, use_quarter_wave_plate=False)#

Given Jones matrices for red, green, and blue light propagation, generate rgb array (float values in [0, 1]) for a simulated color polarized optical microscopy image.

Parameters:

jones_mats (Iterable of [numpy.ndarray]) – list of three Jones matrix products for propagation of red, green, and blue light (respectively) through the entire sample
polarizer_angle (float) – angle of polarizer
analyzer_angle (float) – angle of analyzer
brightness_factor (float) – multiplier for intensity
use_quarter_wave_plate (bool, optional) – whether to insert a quarter wave plate, oriented at a 45-degree counterclockwise rotation from the polarizer, between the polarizer and the sample

Returns:

2D array of rgb values for transmitted light

Return type:

numpy.ndarray

pom_image_one_wavelength(jones_mat_product, p_angle, a_angle, use_quarter_wave_plate=False)#

Simulated polarized optical microscopy image using a single wavelength of light.

Parameters:

jones_mat_product (numpy.ndarray) – array of Jones matrix products for light propagation through the entire sample
p_angle (float) – angle of polarizer with respect to x-axis (after permuting axes so that light propagates along z)
a_angle (float) – angle of analyzer with respect to x-axis (after permuting axes so that light propagates along z)
use_quarter_wave_plate (bool, optional) – whether to insert a quarter wave plate, oriented at a 45-degree counterclockwise rotation from the polarizer, between the polarizer and the sample

Returns:

2D array of transmitted intensities

Return type:

numpy.ndarray

pom_image_sequence_rotate_polarizers(ax, n, site_types, num_frames=10, brightness_factor=1, **kwargs)#

Create image sequence of simulated polarized optical microscopy images with polarizer and analyzer rotating linearly in time through total angle pi/2.

Parameters:

ax (matplotlib.axes) – figure axes
n (numpy.ndarray or None) – nematic director field in flattened array; if None, data is taken from plotter
site_types (numpy.ndarray, “off”, or None) – site types in flattened array; if “off”, all sites are treated as bulk; if None, data is taken from plotter
num_frames (int, optional) – number of subdivisions of the [0, pi/2] interval for the polarizer angle, and thus the number of frames in the animation
brightness_factor (float, optional) – multiplier for intensity
kwargs (dict, optional) – keyword arguments accepted by jones_matrices_multiple_wavelengths

Returns:

list of transmitted intensity images

Return type:

list(matplotlib.axes.Axes.imshow)

rgb_to_texture(rgb_data, sigma=1.0)#

Transform 2D NumPy float rgb array to PyVista texture

Parameters:

rgb_data (numpy.ndarray) – 2D array of (red, green, blue) intensities, each in the interval [0, 1]
sigma (float, optional) – smoothing factor for Gaussian filter; set to 1. for no filter.

Return type:

pyvista.Texture

rotation_matrix_2d(angle)#

Calculate 2x2 rotation matrix

Parameters:: angle (float or numpy.ndarray) – rotation angle or array thereof
Returns:: rotation matrix or array thereof
Return type:: numpy.ndarray

rotation_transform(mat, rot_mat)#

Calculate M’ = R M R^T for given matrix M and rotation matrix R.

Parameters:

mat (numpy.ndarray) – Array of matrices M.
rot_mat (numpy.ndarray) – Rotation matrix R.

Returns:

Array of rotated matrices

Return type:

numpy.ndarray

save_jones_data(plotter, filename: str)#

Saves numerical Jones matrix data to files

Parameters:

plotter (NematicPlotNoQt)
filename (str)

save_jones_data_gui(plotter, filename=None)#

Launch dialog to save numerical Jones matrix data to files

Parameters:

plotter (NematicPlot)
filename (str | None)

save_jones_images(plotter, filename: str)#

Save Jones matrix images to files

Parameters:

plotter (NematicPlotNoQt)
filename (str)

save_jones_images_gui(plotter, filename=None)#

Launch dialog to save Jones matrix images to files

Parameters:

plotter (NematicPlot)
filename (str | None)