Programatically added custom fields don't show up

Question

I'm adding new fields to views through a custom module.

When I open the view page UI, the field is not shown. However, If I edit the view from the user interface, and click on Add field, the custom field is available.

How can I automatically add those fields to the list of fields to display on a view?

function mymodule_views_default_views() {
  // …
  $handler->display->display_options['fields']['myfield']['id'] = 'fieldname';
  $handler->display->display_options['fields']['myfield']['table'] = 'databaseTableName';
  $handler->display->display_options['fields']['myfield']['field'] = 'fieldname';
  // …
}