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odak.wave.transfer_function_fresnel

A definition to calculate convolution based Fresnel approximation for beam propagation.

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 transfer_function_fresnel(field, k, distance, dx, wavelength):
    """
    A definition to calculate convolution based Fresnel approximation for beam propagation.

    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
    fx = np.linspace(-1./2./dx, 1./2./dx, nu)
    fy = np.linspace(-1./2./dx, 1./2./dx, nv)
    FX, FY = np.meshgrid(fx, fy)
    H = np.exp(1j*k*distance*(1-(FX*wavelength)**2-(FY*wavelength)**2)**0.5)
    U1 = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(field)))
    U2 = H*U1
    result = np.fft.ifftshift(np.fft.ifft2(np.fft.ifftshift(U2)))
    return result

See also