The basic (internal) feeder is fairly standard, 3 inches in diameter and 16 inchs long. The pigeons are kept away by a wire screen cylinder. Construction is made simple by the Lucite (acrylic) disk at the top.
The acrlic disk has a 24 in diameter, and is 1/8 or 3/16 in thick. The center is reinforced by a 8x8 in square on the bottom and 4x4 square on top, both about 1/4 in thick (ideally they would be cut to make circles, thus distributing the stress more evenly, but I was lazy). They are cemented to the large disk, and a 3/8 in hole drilled in the center. A 3/8 in through bolt is inserted in the hole, with the loop at the top, and the 3 acrlic layer sandwich held together with bolts and washers on each side. A hook is fashened from a small piece of copper wire (or coat hanger) and fastened to the bottom with another bolt. Make small (1/8 th in) holes around the edge of the disk every 3 in or so. Copper wire will be threaded through these holes to hold the screen cylinder in place.
The outer wire screen should have openings of about 4x4 or 4x6, and be 24 in long. I used some left over screen from a fence around a garden plot that was to keep the dogs out. It had a complex pattern, so I had to cut out many links to create larger openings. It's important to have large openings at the very top, because small birds fly up to excape and you don't want them to be trapped there.
Bend the wire screen in a circle that is just larger than the acrylic disk and fasten the edges of the screen together with copper wire. Insert the acrylic disk through the top and bend the wire screen at the top edge so it will hold the screen when the feeder is hung. Then attach the disk to the screen with copper wire segments using the holes you have drilled along the edge of the disk. Now when the cadge is hung the screen will be held both by the copper wire and by the fact that the edge of the screen has be bent inward toward the center. The acrylic disk not only holds the wire screen, but protects the feeder from rain (you don't want the seed to get wet and mold to grow). It may cost $30, and could be replaced with a strong wire frame, but the solid acrylic disk shields the feeder from the rain and is worth the cost in my opinion.
Birds as large as bluejays can easily get through the holes in the screen or fly in from the bottom.