These LEDs should never used at 0.5 to 1A continuous or even past the absolute max power of 180mW.
But 150mW may be ok for continuous used if adequate cooling is provided. 1A can only be used for very low duty cycles or 100us max.
Final edit Assume I meant 3 R's in schematic or choose one 3 Ohm part but 1/2W. Choose R's with Ohmmeter for best accuracy.
- revised to 100mA max per LED with 3.125 fixed R using 3x1 Ohm resistors same as string "equalization" resistors. Choose ANY combination of 1 OHm parts for max current. The variable R controlled by Darlington bias controls constant current setting. Since LED Vf min is unknown for your parts, Imin may be <50mA, which can be nulled with 3k bias instead of 2k.. If you want to change string array to 6P4S to drive more LEDs adjust the fixed R of 3 down according to 1.25V/Icc. Visible light indicator added for 20mA.
Efficiency = ~1.8*4/12= 60% , luminous intensity variation , accuracy depends on focus of LEDs in housing.
A much better choice of LED is SFH4525 rated at same 940 nmP , 10deg for 550 mW/sr @100 mA continuous in the same 5mm package with over 5x the efficacy at 1/10th of the current 1.8V max 1.5 V typ.
For power, DC constant current is best, which means if you have 12V only, you can use a 3 terminal regulator such as LM317 which has a minimum drop of 2.2V drop @1A. Thus depending on your max, min Vinput, you can choose suitable strings of 4 or 5 in series. Using 5 strings in parallel of 4 in series , or an array of 5P4S (parallel,serial) you need 500mA @ 4x 1.8V min. from the adjustable current mode of LM317 below.
Adding 0.1V min. drop to each string to prevent thermal runaway, this means each string has a 1 Ohm in series x 5strings with power dissipated only = 0.05W @ 0.5A
R adj I (mA).
This might be done with fixed resistors or 2.5 Ohm + 10 Ohm Pot, wire wound ($) and added caps to stabilize regulator or a cheap pot with a NPN transistor in place of the WW pot. There are many other ways to do this depending on the accuracy you need.