import numpy as np

def calctav(alfa, nr):
    """
    Calculate average transmittance of isotropic light across a dielectric surface.
    Translated from MATLAB version of calctav.m.

    Parameters:
        alfa : incidence angle in degrees (scalar or array)
        nr   : refractive index of second medium (scalar or array of same shape as alfa)

    Returns:
        tav : average transmittance (same shape as alfa)
    """
    alfa = np.asarray(alfa)
    nr = np.asarray(nr)
    rd = np.pi / 180.0

    n2 = nr ** 2
    np_ = n2 + 1
    nm = n2 - 1
    a = ((nr + 1) ** 2) / 2
    k = -((n2 - 1) ** 2) / 4
    sa = np.sin(alfa * rd)

    b1 = np.where(alfa != 90,
                  np.sqrt((sa ** 2 - np_ / 2) ** 2 + k),
                  0.0)
    b2 = sa ** 2 - np_ / 2
    b = b1 - b2
    b3 = b ** 3
    a3 = a ** 3

    ts = (k ** 2 / (6 * b3) + k / b - b / 2) - (k ** 2 / (6 * a3) + k / a - a / 2)

    tp1 = -2 * n2 * (b - a) / (np_ ** 2)
    tp2 = -2 * n2 * np_ * np.log(b / a) / (nm ** 2)
    tp3 = n2 * (1 / b - 1 / a) / 2
    tp4 = 16 * n2 ** 2 * (n2 ** 2 + 1) * np.log((2 * np_ * b - nm ** 2) / (2 * np_ * a - nm ** 2)) / (np_ ** 3 * nm ** 2)
    tp5 = 16 * n2 ** 3 * (1 / (2 * np_ * b - nm ** 2) - 1 / (2 * np_ * a - nm ** 2)) / (np_ ** 3)

    tp = tp1 + tp2 + tp3 + tp4 + tp5
    tav = (ts + tp) / (2 * sa ** 2)

    return tav