def transform_angular_variance_lens_1d(k, var_r, phi_c, var_q, f):
    """Calculate the angular variance of a beam that has passed through a lens.

    The lens phase is -k*r**2/(2*f). The formula used is (15) of Siegman IEEE J. Quantum Electronics,  vol. 27 1991,  with
    k = 2*pi/lambda and opposite sign convention for f. It is valid for any refractive index.

    Args:
        var_r (scalar): real space variance.
        phi_c (scalar): real-space curvature
        var_q (scalar): angular variance of the beam before the lens.
        f (scalar): focal length of the lens - positive = converging lens.

    Returns:
        var_qp (scalar): angular variance of the beam after the lens.
    """
    return var_q - 4*k*phi_c/f + var_r*k**2/f**2