Regarding high input resistance in the FP-AI-110

Hello.
I'm struggling to measure the uA or low mA level of current from my micro power source by means of FP-AI-110. However, current values produced with less than 100 ohm of the external load applied is not correct since it is influenced by the module's input impedance (100 ohm, according to its circuitry given via the instruction manual), I guess. I tried to connect much smaller resistor like 1 ohm in parallel to reduce total input impedance but it appeared not to work out. Is there any way to resolve this or these kinds of a module (FP-AI-100, 100) is not just proper for measuring small currents?
Thanks for reading.

If the internal resistance of the load is small compare to the input resistance of the DAQ (100 Ohm), the load resistance will have most of the current flowing through it and the measurement will not be accurate. Attached is a drawing that will explain a little more what is happening.
Attachments:
input impedance.JPG ‏40 KB

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Regarding high input resistance in the FP-AI-110

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