With PHP
echo urlencode("http://www.image.com/?username=unknown&password=unknown");
Result
http%3A%2F%2Fwww.image.com%2F%3Fusername%3Dunknown%26password%3Dunknown
With Javascript:
var myUrl = "http://www.image.com/?username=unknown&password=unknown";
var encodedURL= "http://www.foobar.com/foo?imageurl=" + encodeURIComponent(myUrl);