To set the HTTP Header for a request using AngularJs you can use the following snippet.
$http({method: 'GET', url: 'www.fesslersoftexample.com/api', headers: { 'Authorization': 'Basic YmVlcDpib29w'} });
Use the headers parameter in the config object you pass to $http.
For more informations see the AngularJs API Reference