Is it safe to travel through Tokyo?

Question:

My family is flying from Taipei to Seattle via Tokyo airport.
I'm worried about being exposed to radiation if we travel through the airport or through Japanese airspace.
Any route that avoids the Tokyo airport is more expensive to the tune of at least US$1500.
That's a lot money to throw away based on an unsubstantiated fear of radiation exposure.
At the same time, I am uncomfortable ignoring the risk of radiation exposure while walking through the Japanese airport or flying through Japanese airspace, when I really don't know how dangerous it might be.
Where can I find reliable information that addresses this issue?
I am not asking for off-the-cuff opinions, I am asking for research/statistics/facts.
Anybody have information that will ease my Japan-o-phobia?

Answer:

Don't be silly Tokyo is fine and besides you are only transiting and you don't have to leave the airport. If there was radiation in the airport don't you think that it would have been evacuated long time ago? and how would you guys even land there when it is closed? don't listen to scaremongering it ain't good