Как сделать фон капчи прозрачным

<?php
session_start();
$string = "";
for ($i = 0; $i < 4; $i++)
$string .= chr(rand(97, 122));
 
$_SESSION['rand_code'] = $string;
 
$dir = "fonts/";
 
$image = imagecreatetruecolor(60, 30);
$black = imagecolorallocate($image, 0, 0, 0);
$color = imagecolorallocate($image, 79,79,79);
$white = imagecolorallocate($image, 245,245,245);
 
imagefilledrectangle($image,0,0,399,99,$white);
imagettftext ($image, 17, 0, 0, 22, $color, $dir."nautilus.ttf", $_SESSION['rand_code']);
 
header("Content-type: image/png");
imagepng($image);
?>

<?php
session_start();
$string = "";
for ($i = 0; $i < 4; $i++)
    $string .= chr(rand(97, 122));
$_SESSION['rand_code'] = $string;
$dir = "fonts/";
$image = imagecreatetruecolor(60, 30);
$color = imagecolorallocate($image, 79,79,79);
$alpha = imagecolorallocatealpha($image, 245,245,245, 127);
imagesavealpha($image, true);
imagefill($image, 0, 0, $alpha);
imagettftext ($image, 17, 0, 0, 22, $color, $dir."nautilus.ttf", $_SESSION['rand_code']);
header("Content-type: image/png");
imagepng($image);
imagedestroy($image);
?>