odak.learn.wave.gerchberg_saxton¶

Definition to compute a hologram using an iterative method called Gerchberg-Saxton phase retrieval algorithm. For more on the method, see: Gerchberg, Ralph W. "A practical algorithm for the determination of phase from image and diffraction plane pictures." Optik 35 (1972): 237-246.

Parameters:

Name	Type	Description	Default
`field`	`torch.cfloat`	Complex field (MxN).	required
`distance`	`float`	Propagation distance.	required
`dx`	`float`	Size of one single pixel in the field grid (in meters).	required
`wavelength`	`float`	Wavelength of the electric field.	required
`slm_range`	`float`	Typically this is equal to two pi. See odak.wave.adjust_phase_only_slm_range() for more.	`6.28`
`propagation_type`	`str`	Type of the propagation (IR Fresnel, TR Fresnel, Fraunhofer).	`'IR Fresnel'`

Returns:

Type	Description
`torch.cfloat`	Calculated complex hologram.

Source code in odak/learn/wave/classical.py

def gerchberg_saxton(field, n_iterations, distance, dx, wavelength, slm_range=6.28, propagation_type='IR Fresnel'):
    """
    Definition to compute a hologram using an iterative method called Gerchberg-Saxton phase retrieval algorithm. For more on the method, see: Gerchberg, Ralph W. "A practical algorithm for the determination of phase from image and diffraction plane pictures." Optik 35 (1972): 237-246.

    Parameters
    ----------
    field            : torch.cfloat
                       Complex field (MxN).
    distance         : float
                       Propagation distance.
    dx               : float
                       Size of one single pixel in the field grid (in meters).
    wavelength       : float
                       Wavelength of the electric field.
    slm_range        : float
                       Typically this is equal to two pi. See odak.wave.adjust_phase_only_slm_range() for more.
    propagation_type : str
                       Type of the propagation (IR Fresnel, TR Fresnel, Fraunhofer).

    Returns
    -------
    hologram         : torch.cfloat
                       Calculated complex hologram.
    reconstruction   : torch.cfloat
                       Calculated reconstruction using calculated hologram. 
    """
    k = wavenumber(wavelength)
    reconstruction = field
    for i in range(n_iterations):
        hologram = propagate_beam(
            reconstruction, k, -distance, dx, wavelength, propagation_type)
        hologram, _ = produce_phase_only_slm_pattern(hologram, slm_range)
        reconstruction = propagate_beam(
            hologram, k, distance, dx, wavelength, propagation_type)
        reconstruction = set_amplitude(reconstruction, field)
    reconstruction = propagate_beam(
        hologram, k, distance, dx, wavelength, propagation_type)
    return hologram, reconstruction

Notes¶

To optimize a phase-only hologram using Gerchberg-Saxton algorithm, please follow and observe the below example:

import torch
from odak.learn.wave import gerchberg_saxton
from odak import np
wavelength              = 0.000000532
dx                      = 0.0000064
distance                = 0.2
target_field            = torch.zeros((500,500),dtype=torch.complex64)
target_field[0::50,:]  += 1
iteration_number        = 3
hologram,reconstructed  = gerchberg_saxton(
                                           target_field,
                                           iteration_number,
                                           distance,
                                           dx,
                                           wavelength,
                                           np.pi*2,
                                           'TR Fresnel'
                                          )

odak.learn.wave.gerchberg_saxton¶

Notes¶

See also¶