Facebook GRAPH API + PHP SDK: get the URL of the large user picture

Question

I'm trying to rewrite a Facebook app (a PHP script embedding a small multiplayer Flash game) from old FBML to new iFrame type and it kind of works:

<?php

require_once('facebook.php');

define('FB_API_ID', '182820975103876');
define('FB_AUTH_SECRET', 'XXX');

$facebook = new Facebook(array(
            'appId'  => FB_API_ID,
            'secret' => FB_AUTH_SECRET,
            'cookie' => true,
            ));

if (! $facebook->getSession()) {
    printf('<script type="text/javascript">top.location.href="%s";</script>',
        $facebook->getLoginUrl(
                array('canvas'    => 1,
                      'fbconnect' => 0,
                      #'req_perms' => 'user_location',
        )));

} else {
    try {
        $me = $facebook->api('/me');

        $first_name = $me['first_name'];
        $city       = $me['location']['name'];
        $female     = ($me['gender'] != 'male');
        $fields     = $facebook->api('/me', array(
                          'fields' => 'picture',
                          'type'   => 'large'
                      ));
        $avatar     = $fields['picture'];

        # then I print swf tag and pass first_name;city;avatar to it

    } catch (FacebookApiException $e) {
        print('Error: ' . $e);
    }
}

?>

but I think that the call to get the user profile picture causes my script to perform a 2nd CURL fetch, which is probably avoidable? And also I'd like to use the new GRAPH API and not the old REST API - but I'm not sure how to rewrite that call (and I need to get the large and direct user picture).