Showing datepicker calendar in modal box with overlay

Showing datepicker calendar in modal box with overlay

I am using the jQuery UI datepicker in a website. I am using the "dialog" method, so that the calendar opens in the center of the screen. However, what I'd really like would be to use the "modal" method ( http://jqueryui.com/demos/dialog/#modal) so that the background behind the calendar is dimmed.

Here is my current code:

$(function() {
      $("#dateInput").click(function() {  
          $("#dateInput").datepicker("dialog", "", updateDate);  
          function updateDate(date) {
            $('#dateInput').text(date);
          }
        });
    });

Anyone have any suggestions for how one might go about this? Is this possible?