There are plenty of logic level FETs which will do the job, they will drive directly from TTL.
Are you using the led to transmit data?
Del

No, it is for some scientific experiment. The LED illuminates a sample for a few seconds and exactly the moment the LED switches on and off are the region of interest (measurements are taken).

So: TTL high: LED on, stays on for a few seconds, TTL low, LED off. So the circuit should be able to switch the 0.5A UV LED in a few microseconds, using 12, 15 or 24V as input.

specs of the LED http://www.nichia.co.jp/specification/led_09/NCSU034AT-E.pdf

I assume that the LED switching on/off time is not the limiting factor, but I'm not sure. Can you give an example of a good FET which could do the job?

Just contacted the manufacturer, the LED switching time is sub microseconds (just to be sure). (BTW, sorry, cannot find edit button here).

RFD14N05L will do it, it's cheap readilly available (google will bring up data) and can take loads of current. We use 'em here and I drive 'em from a microcontoller no problem.
I'd have though you could adjust for any delay in switch off with the logic, but the FET should be quick enough anyhow, microseconds isn't considered fast these days.

Del

My suggestion is you just spelled out the spec. for this LED driver why not design your own driver instead of spending money on something maybe made in China LOL (sorry).

Any normal NPN transistor should be able to do this providing it can handle 500mA current. Something like a BD139 should be ideal. Put a resistor of about 470 ohm from your TTL output to the transistor base. Ground the emitter and connect the LED between 3.75V source and the collector. (I assume you get the 3.75V from a current limited circuit suitable to drive such LED's) Yes a logic level MOSFET is better. Infact a normal N-ch MOSFET should work too, a resistor isn't required.

You should check one of these:

http://www.motien.com.tw/led.html

This Nat Semiconductor site might give you some ideas,

http://www.national.com/pf/LM/LM3423.html

Garth.