Failure to Observe Traffic Signal?

I got a ticket in the mail from supposedly running a red light two weeks ago. Let me pain the picture: One minute I look up and the light is green. I look up again when I'm about 10 feet closer to the light (2 seconds later) and it's already red. So I slam on the breaks but I see the camera take a snapshot of me. The thing is that I actually stopped on the crosswalk (this was at night so nobody was there), so I technically didn't run the light. In fact I could still see the light in front of me. This was in New Brunswick, NJ so the fine is $85. Should I pay it, or can I fight it in court???