LED s calculation of beam area, dosage and energy from data sheet information
Assuming that you only care about the energy within the half angle (angle at which the magnitude is 50%), here is what I come up with. Without a curve of brightness vs angle the amount within the half angle can't be determined. I made a wild guess. With the curve, you will need to integrate in polar coordinates, something I might have been able to do 40 years ago, no chance now without many hours of research. 

I am guessing that you will need multiple IR LEDs for your application, to calculate the optical power with overlapping curves will probably be necessary.