Measuring integrated current
The standard method of performing this measurement is to use a transimpedance amplifier to convert the current into a voltage which is then sampled rapidly throughout the time period and integrated. However, there are lots of places for noise to creep in.


Reducing the places for noise to creep in is exactly why you would want to digitize your signal as soon as possible, and use as few analog processing stages as you can.


  Each of the measurements is quite noisy, and this get integrated up.


Integration will tend to reduce noise, not increase it, because integration is inherently bandwidth-limiting.

It's differentiation that tends to enhance noise.

You can certainly build an integrating response into your transimpedance amplifier:







simulate this circuit &ndash; Schematic created using CircuitLab

If R1 is very high, then the integrating response provided by C1 will tend to dominate the TIA response, and you will effective have an integrating TIA. In fact, this configuration is often used because the capacitive feedback path can improve the amplifier's stability, even when an integrating response is not desired. The integrating version is essentially just over-compensating this common circuit.

If you need to reset the output, you will need some additional circuitry to discharge C1 (without letting the op-amp go into saturation).