It's pretty easy to fight it. I think it is good that it's a LH turn violation and NOT a speeding ticket, since there is no OBJECTIVE evidence. Although, it would be interesting to know whether he had a camera.
Anyway, this is not legal advice of course, but ... in my opinion ... if you want to fight it, check not-guilty, show up at the court date or the pre-trial, and just be honest, sincere, RESPECTFUL, and state that this is NOT worth $140.00 to fight about, but you simply cannot in good conscious pay a ticket for a violation that you did not commit.
Explain that you were looking AT the light, and had a head on viewing angle (assuming this is the fact) and that he was NOT looking at the light, and had a poor viewing angle (again, assuming this is the fact), and that you regret wasting the court's time, but nevertheless, respectfully request that they dismiss the case in your favor.
It's as simple as that. Yes, it's his word against yours, but use the facts in your favor. You were looking at the light, and paying attention to the light, and he was not looking at the light, nor was he likely dedicating his attention to the light as he was not waiting to turn safely, but rather, he was working as a cop ... which means he was doing 10 things at once, working on the computer, trying to get home safe, talking to the dispatcher, looking for criminals, etc.
You could even say, look, this seems like an honest misunderstanding on his part, which is understandable, but I just cannot look the other way and admit to a violation that I did not commit. That seems more wrong than actually running a red light.
In my experience, deference and honesty will give you credibility. Credibility will swing the presumption in your favor.
If you want to make a federal case out of it, which I do not recommend, you could start trying to subpoena any video footage he has, logs from his radar, computer activity logs, dispatch recording/logs for the time, cell phone usage logs for the time in question, GPS data/logs for the time in question, his shifts for the week (e.g. maybe he was tired), repair info for the light, and all sorts of stuff.
Hell, you could even request a deposition.
All that stuff is fun, and will really piss off the cops, and annoy the court, but much of it could be used in your favor. If you were a professional driver of some sorts, this might be advisable, but here, I'd just tell your story and be respectful.
Ugh ... ok, rant over.