Op-Amp circuits always manage to look similar, even with subtleties.
Yes - we do have a trans-impedance amplifier. The one you posted is exactly What it says. It is a "detector". It counts pulses it makes, hence the differentiator, which basically signals a waveform has changed at some rate faster than usual. My TIA amplifier is different.
Back in the thread, we have had discussions and many simulations. None of it is "private", though it has occurred to me that if we make something ragingly successful, some oriental git will produce a version in a plastic box with nickel paint on the inside. I am open source.
Post #403 on page 41 shows us noise modeling.
Post #421 on page 43 shows Mark's first explorations of signal on the Pocket-Geiger board.
Post #425 was me simulating the front-end circuit gragment with an artificial photon current. Note the new gain distribution, and bandwidth sufficient to preserve the pulse shape, and hence its area energy analogue.
Here is the image..
View attachment 392590
I went for complete recovery of all the photon energy the diode would give up, it's amplitude, and it's duration, with an integrated area under it's curve either fully calculated, or (better), maybe high-speed peak-detect approximated, and it's amplitude captured. The intent is to be able to tell what mix of energies were in there, and apply some discrimination logic to assigning counts.
I went for as low noise as possible, with enough gain in the first stage to put the (amplified) noise beyond being increased by subsequent gain stages, so locking in the signal-to-noise ratio. The subsequent stages provide differential gain to drive the ADC, which is 16-bit, sampling fast enough to get the pulse captured. They can also incorporate a 50/60 Hz notch filter. In my circuit, I use every trick I can to shunt the noise, and avoid overshoots at zero. I will post the whole thing, when I have done making mistakes with it.