The voltage across an LED changes with temperature. It is relatively easy to get a constant current, but are you sure that the light output is absolutely linked to the current? i.e. for a constant current over the temperature range that the light output will also be constant?
For a very stable current, drive the LED from a NPN transistors collector. Put a current metering resistor in the emitter circuit to earth. A good value would be 82 ohms (82 X .025 = ~ 1V). Now use a Op-amp with a bandgap reference (or a pot across the +5V) on its positive input, via a 10K, and return the negative input to the 82 ohms via 10K. The op amp will try to make the volt drop across the 82 ohm the same as the positive input, so the ability to adjust this must be designed in (10 turn pot?). It would be a good idea to put a temporary resistor in series with the LED ( say 180 ohms) tp protect the LED against current overload during setting up.
Frank