get_categories() / Order of product categories?

Hello,
I use this function to get all product categories on the frontend:

$product_categories = get_categories( array( 'taxonomy' => 'product_cat', 'child_of' => $parent_id, 'orderby' => 'menu_order', 'order' => 'asc' ));

But the order of the elements in $product_categories do not reflect the order that I can see in the WP Backend. I can reorder product categories in the backend via Drag n Drop, but how can I get a list of the product categories in that order on the frontend?

Thanks!