def ray_shooting(self, x, y, kwargs, k=None):
        """
        maps image to source position (inverse deflection)
        :param x: x-position (preferentially arcsec)
        :type x: numpy array
        :param y: y-position (preferentially arcsec)
        :type y: numpy array
        :param kwargs: list of keyword arguments of lens model parameters matching the lens model classes
        :param k: only evaluate the k-th lens model
        :return: source plane positions corresponding to (x, y) in the image plane
        """
        dx, dy = self.alpha(x, y, kwargs, k=k)
        return x - dx, y - dy
maps image to source position (inverse deflection)
        :param x: x-position (preferentially arcsec)
        :type x: numpy array
        :param y: y-position (preferentially arcsec)
        :type y: numpy array
        :param kwargs: list of keyword arguments of lens model parameters matching the lens model classes
        :param k: only evaluate the k-th lens model
        :return: source plane positions corresponding to (x, y) in the image plane