Do you mean something like this:
$ch = curl_init();
// Authentication
curl_setopt($ch, CURLOPT_HTTPAUTH, CURLAUTH_BASIC);
curl_setopt($ch, CURLOPT_USERPWD, 'username:password');
// Fetch content as binary data
curl_setopt($ch, CURLOPT_URL, $urlToImage);
curl_setopt($ch, CURLOPT_BINARYTRANSFER, 1);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
// Fetch image data
$imageData = curl_exec($ch);
curl_close($ch);
// Encode returned data with base64
echo base64_encode($imageData);