You can have a different perspective of a phenomenon if you are using the "perception" meaning of perspective.
Members of the audience had different perspectives of the stage, depending on their seat.
If instead you want to use the "opinion" meaning of perspective, then you would have a perspective on a phenomenon (with the implication that you want to share and argue in support of your perspective).
Members of the audience had different perspectives on the performance as they left the theatre, depending on their tastes.
You can't have a perspective at a phenomenon without a fairly strange set of circumstances and taking a bit of poetic license with the language. Such a construction simply sounds wrong, unless the context strongly indicates that having a perspective can somehow have and effect on the phenomenon being focused upon. Such a context might happen in a fantasy novel where mental powers can change the world, but wouldn't be correct in more mundane writing contexts. Even in a fantastical context, it would take a better writer than I to craft such a sentence that didn't sound awkward:
I forcefully thought my different perspective at the magical wildfire, trying to impose my will on reality and extinguish the flames.