def effective_einstein_radius(self, kwargs_lens_list, k=None, spacing=1000):
        """
        computes the radius with mean convergence=1

        :param kwargs_lens:
        :param spacing: number of annular bins to compute the convergence (resolution of the Einstein radius estimate)
        :return:
        """
        if 'center_x' in kwargs_lens_list[0]:
            center_x = kwargs_lens_list[0]['center_x']
            center_y = kwargs_lens_list[0]['center_y']
        elif self._lensModel.lens_model_list[0] in ['INTERPOL', 'INTERPOL_SCALED']:
            center_x, center_y = 0, 0
        else:
            center_x, center_y = 0, 0
        numPix = 200
        deltaPix = 0.05
        x_grid, y_grid = util.make_grid(numPix=numPix, deltapix=deltaPix)
        x_grid += center_x
        y_grid += center_y
        kappa = self._lensModel.kappa(x_grid, y_grid, kwargs_lens_list, k=k)
        if self._lensModel.lens_model_list[0] in ['INTERPOL', 'INTERPOL_SCALED']:
            center_x = x_grid[kappa == np.max(kappa)]
            center_y = y_grid[kappa == np.max(kappa)]
        kappa = util.array2image(kappa)
        r_array = np.linspace(0.0001, numPix*deltaPix/2., spacing)
        for r in r_array:
            mask = np.array(1 - mask_util.mask_center_2d(center_x, center_y, r, x_grid, y_grid))
            sum_mask = np.sum(mask)
            if sum_mask > 0:
                kappa_mean = np.sum(kappa*mask)/np.sum(mask)
                if kappa_mean < 1:
                    return r
        print(kwargs_lens_list, "Warning, no Einstein radius computed!")
        return r_array[-1]
computes the radius with mean convergence=1

        :param kwargs_lens:
        :param spacing: number of annular bins to compute the convergence (resolution of the Einstein radius estimate)
        :return: