I didn't want a gap under my top door, so I took scraps of plywood, and filled in the space to the beam, as shown in the picture.
You will be making the door out of 1"x2" beams.
When measuring for the door, make sure you insert a tile on the shelf so you take the proper measurement.
Make the left and right door beams measure from the shelf floor (with tile) to the top beam, minus about 1/8" to allow the door to swing without scraping the shelf or ceiling.
When measuring the top and bottom beam for the door, remember to subtract the side beams from the measurement. Again, subtract about 1/8" so the door has room to open.
This next part is a matter of preference. For this door, I decided to attach the side of the door to the hinges first. This means that you have to take the door side off when you attach it to the rest of the door. I suggest building the door, and then clamping the whole assembly to the cage beam.
With the door firmly clamped in place, attach a pair of small hinges, being careful to keep the hinge centered between the the door board and cage board.
It is important to keep the screws in the centers of the holes in the hinge. If the screw is too far toward the inside of the hinge, then the pressure created will cause the door to pop open.
This is a picture of the side beam of the door attached to the cage.
Test to make sure that the door will be able to swing all the way open.
Start to assemble the door, making sure that the top and bottem beams go between the side beams of the door, and not on top and bottom of the side beams.
If you attached the side beam to the hinges already, take it off. You will want to mark which end is up with a wood pencil, and then attach the rest of the door frame on the left side of this beam.
Attach the door.
You can go ahead and attach chicken wire to the door now. This can help you feel like you are making progress, because the door will be completely finished.
When unwrapping the chicken wire, wear your safety goggles. These rolls are usually wrapped in a thin wire that can unexpectedly whip around and hit you in the eye. It is also a good idea to wear gloves, as chicken wire has a lot of sharp ends.
Cut out a piece of chicken wire bigger than the door. Attach the wire, then use your fence cutters to trim off the excess. Use a pair of pliers to bend back any wires that are sticking out so no one cuts theirself while opening the door. There will probably be a lot of wire to bend back, but it's worth the effort.
Install the latch on the door and side beam.
Congratulations. You have finished the top door.