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Referring to your original problem statement:
I don't know the exact data of your diode, but I see a sensitivity in a 10 pA order of magnitude for 1 Hz bandwidth and room temperature according to NEP numbers of similar diodes. But I don't think that you'll be able to achieve it down to DC signals.Summarily, how do you get high-sensitivity readings off an InAs photodiode?
It should be useful well into pA range, according to the descriptions.