使用GDPHP创建带文本和透明背景的图像

一切都可以在该图像中旋转和居中文本，但imagecolortransparent函数创建的文本周围有一个黑色边框。如何创建一个带有文本和透明背景的图像？这是代码：

header('Content-Type: image/png');
$title = "test text";
$im = imagecreatetruecolor(87, 80);
$white = imagecolorallocate($im, 255, 255, 255);
$black = imagecolorallocate($im, 0, 0, 0);
imagefill($im, 87, 80, $black);
imagecolortransparent($im, $black);
$white = imagecolorallocate($im, 255, 255, 255);
$font = "../fonts/arial.ttf";
$bbox = imagettfbbox(12,-40,"../fonts/arial.ttf", $title);
$width = $bbox[2]-$bbox[0];
$height = ceil(($bbox[6]-$bbox[0])/2);
$pos = ceil((87-$width)/2);
$posx = $pos-$height;
$posy = $pos+$height;
imagettftext($im, 12, -45, $posx, $posy, $white, $font, $title);
imagepng($im);
imagedestroy($im);