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Sensor is 320 um thick, so MIP = 124 keV, or 2e-14 J.

840 um light is above bandgap so ~1/4 of the energy is wasted; 1060 um light has 150 um attenuation length so ~1/8 of energy is lost out the back. Ignore both effects.

Assume 2 ns pulse width, then we need 2e-14 J/2e-9 s = 1e-5 W, or 10 uW. If we use wider pulses we need to attenuate more.

Filter damage: the narrower and more powerful of the two beams (1060 nm) is 2.4 mm diameter, so area is 4.5 mm^2; peak power density (factor of 2 is what Thorlabs says you should use for a Gaussian peak) is 2*10 mW/A = 0.4 W/cm^2. No actual spec on damage threshold for the AR coating, but the glass is definitely fine.