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odak.wave.band_limited_angular_spectrum

A definition to calculate bandlimited angular spectrum based beam propagation. For more Matsushima, Kyoji, and Tomoyoshi Shimobaba. "Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields." Optics express 17.22 (2009): 19662-19673.

Parameters:

Name Type Description Default
field np.complex

Complex field (MxN).

required
k odak.wave.wavenumber

Wave number of a wave, see odak.wave.wavenumber for more.

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

Returns:

Type Description
np.complex

Final complex field (MxN).

Source code in odak/wave/classical.py
def band_limited_angular_spectrum(field, k, distance, dx, wavelength):
    """
    A definition to calculate bandlimited angular spectrum based beam propagation. For more Matsushima, Kyoji, and Tomoyoshi Shimobaba. "Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields." Optics express 17.22 (2009): 19662-19673.

    Parameters
    ----------
    field            : np.complex
                       Complex field (MxN).
    k                : odak.wave.wavenumber
                       Wave number of a wave, see odak.wave.wavenumber for more.
    distance         : float
                       Propagation distance.
    dx               : float
                       Size of one single pixel in the field grid (in meters).
    wavelength       : float
                       Wavelength of the electric field.

    Returns
    -------
    result           : np.complex
                       Final complex field (MxN).
    """
    nv, nu = field.shape
    x = np.linspace(-nu/2*dx, nu/2*dx, nu)
    y = np.linspace(-nv/2*dx, nv/2*dx, nv)
    X, Y = np.meshgrid(x, y)
    Z = X**2+Y**2
    h = 1./(1j*wavelength*distance)*np.exp(1j*k*(distance+Z/2/distance))
    h = np.fft.fft2(np.fft.fftshift(h))*dx**2
    flimx = np.ceil(1/(((2*distance*(1./(nu)))**2+1)**0.5*wavelength))
    flimy = np.ceil(1/(((2*distance*(1./(nv)))**2+1)**0.5*wavelength))
    mask = np.zeros((nu, nv), dtype=np.complex64)
    mask = (np.abs(X) < flimx) & (np.abs(Y) < flimy)
    mask = set_amplitude(h, mask)
    U1 = np.fft.fft2(np.fft.fftshift(field))
    U2 = mask*U1
    result = np.fft.ifftshift(np.fft.ifft2(U2))
    return result

See also