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

odak.wave.band_limited_angular_spectrum¶

See also¶