JTable in JScrollPane, how to set background?

I am using a JScrollPane to wrap a JTable. Depending on the configuration, there is some space that is not occupied by the table. It is drawn gray (it looks like it is transparent and you can just see the component in the back). How can I set this area to be a certain color?

Here is a SSCCE to illustrate.

import java.awt.Color;
import java.util.Vector;

import javax.swing.JDialog;
import javax.swing.JScrollPane;
import javax.swing.JTable;

public class DialogDemo extends JDialog {
    public static void main(final String[] args) {
        final DialogDemo diag = new DialogDemo();
        diag.setVisible(true);
    }

    public DialogDemo() {
        super();
        setTitle("SSCCE");

        final Vector<Vector<String>> rowData = new Vector<Vector<String>>();
        final Vector<String> columnNames = new VectorBuilder<String>().addCont("Property").addCont("Value");
        rowData.addElement(new VectorBuilder<String>().addCont("lorem").addCont("ipsum"));
        rowData.addElement(new VectorBuilder<String>().addCont("dolor").addCont("sit amet"));
        rowData.addElement(new VectorBuilder<String>().addCont("consectetur").addCont("adipiscing elit."));
        rowData.addElement(new VectorBuilder<String>().addCont("Praesent").addCont("posuere..."));

        final JTable table = new JTable(rowData, columnNames);
        JScrollPane pane = new JScrollPane(table);

        // ************* make that stuff white! *******************
        table.setBackground(Color.white);
        table.setOpaque(true);
        pane.setBackground(Color.white);
        pane.setOpaque(true);
        // ************* make that stuff white! *******************

        add(pane);
        pack();

        setLocationRelativeTo(null);
        setDefaultCloseOperation(JDialog.DISPOSE_ON_CLOSE);
    }

    class VectorBuilder<T> extends Vector<T> {
        public VectorBuilder<T> addCont(final T elem) {
            addElement(elem);
            return this;
        }
    }
}

And here you can see the area, which I want to "colorize". In the SSCCE, I try to do that by using setOpaque(boolean) and setBackgroundColor(Color) of the table and scroll pane, with no success.

Can you tell me, what I am doing wrong?

Instead of this:

table.setBackground(Color.white);
table.setOpaque(true);
pane.setBackground(Color.white);
pane.setOpaque(true);

call:

pane.getViewport().setBackground(Color.WHITE);