Led Driver Rise time
I'd suspect your detector circuit. What is your feedback resistance, and what feedback capacitance are you using? What bias are you using on the photodiode? Getting 50 nsec rise times from a photodiode/transimpedance amplifier is rather tricky, and I'd suspect that you aren't aware of the pitfalls.

It would be nice if, instead of a general description of your setup, you provided a schematic with part numbers both for your photodiode and your op amp.

For fast detection, particularly of relatively high light levels such as you can get at the output of your LED, a more direct approach is a good idea. Consider



This is from Thorlabs (Thorlabs.com), and can be used to produce GHz response (from the right detectors). It assumes that you can handle a fairly low signal, typically less than 1 volt. You get better response times by decreasing Rload, but less signal. Norm for best response times is a 50 ohm load, which has the added advantage of providing a proper termination of the coax used to connect the photodiode to the load/scope. In your case you can probably get away with a load resistor at the photodiode and a good 10x probe from the load to the scope.