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.
Module Contents#
Functions#
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Add planes to back of box, colored by RGB Jones matrix transmission |
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Add planes to back of box, colored by RGB Jones matrix transmission |
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Use plotter's existing nematic director data for Jones matrix |
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Calculate Jones matrix product for light propagation through nematic |
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Calculate list of Jones matrices for a sequence of wavelengths. |
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Calculate Jones matrix array for one slice at constant z. |
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Convert a flattened data array to shape (Lx, Ly, Lz, ...). |
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Import Q-tensor data in the open-Qmin data_format |
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Permute coordinate axes so that the optical axis corresponds to |
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Calculate projection matrix along a polarizer's direction in the xy |
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Create video of simulated polarized optical microscopy images |
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Given Jones matrices for red, green, and blue light propagation, |
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Simulated polarized optical microscopy image using a single wavelength |
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Create image sequence of simulated polarized optical microscopy images |
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Transform 2D NumPy float rgb array to PyVista texture |
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Calculate 2x2 rotation matrix |
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Calculate M' = R M R^T for given matrix M and rotation matrix R. |
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- open_viewmin.nematic.jones._add_jones_arrows(plotter, coord_index, center, actor_name)#
- open_viewmin.nematic.jones._add_jones_lambda_arrow(plotter, p_dir, a_dir, jones_arrows_scale, arrows_center, lambda_arrow_actor_name)#
- open_viewmin.nematic.jones._double_headed_arrow(center, direction, **kwargs)#
- open_viewmin.nematic.jones.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 (open_viewmin.NematicPlot or open_viewmin.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
- open_viewmin.nematic.jones.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()
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.get_quarter_wave_plate_jones(angle)#
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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)
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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 ([numpy.ndarray, numpy.ndarray, 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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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)
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.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
- open_viewmin.nematic.jones.save_jones_data(plotter, filename: str)#
- open_viewmin.nematic.jones.save_jones_data_GUI(plotter, filename=None)#
- open_viewmin.nematic.jones.save_jones_images(plotter, filename: str)#
- open_viewmin.nematic.jones.save_jones_images_GUI(plotter, filename=None)#