I'll use an IR LED modulated at 44 kHz to illuminate particles in air or water, and will use a silicon photodiode to detect weak pulses of scattered light as they pass through the LED's collimated beam.
Photodiode is shielded from direct light, so it will exhibit only dark current except for say roughly 5 ms pulses, when light scattered by the particle illuminates the detector.
An example of a detector's specs are shown below, it needs to be a large area detector for geometrical reasons.
I'm trying to make a ballpark estimate of how weak of a pulse I can reliably detect without getting a lot of false positives from noise.
I'll amplify the signal then use a simple diode + bandpass filter (say 100 Hz to 1 kHz) to remove the 44 kHz but pass the envelope of the 5 ms pulses.
With a bandwidth of ~1 kHz, detectors dark current of 200 pA means every 5 milliseconds there will be about 6 million electrons, with an RMS (shot noise) of about 2500 e-. So if my 5 ms light pulses produce say 10,000 or 20,000 e-h pairs and I set a threshold there, I'm in the right ballpark.
The 0.55 A/W at 850nm means each photon has about an 80% chance of making an e-h pair.
However, I haven't used the capacitance of the photodiode at all, nor the NEP (1.5E-14 W/Hz^1/2 @ 1550 nm) which curiously is specified at a wavelength for which silicon is blind. In other words, I haven't designed an amplifier and threshold discriminator yet.
Is disaster waiting for me around the bend, or is this likely to work with a reasonable low nose amplifier and bandpass filter?
Some spec data for an example 10x10mm PIN photodiode: https://www.thorlabs.com/thorproduct.cfm?partnumber=FDS10X10