My approach to this problem is to use photo diode in reverse-biased configuration (the fastest), and use a modified transimpedance
amp configuration using multiple pn-diodes to produce a logarithmic response to the photo-diode current - this automatically
compensates for the change in ambient lighting and makes the signal dependent only on the fraction of lost-light during the over-pass
of the object. Then a high pass filter (remove mains hum) and differentiator follow to pick up the rapid changes due to the
rapid occultations. You can then either sample that at a suitable high speed, or put through a comparator to threshold the
pulses.
I've built this and simulated it, circuit:
In place of the simulated pulse stuff you should place the reverse-biased photodiode (anode to ground).
Of course a real chronograph needs two copies of the circuit for the two gates, and carefully aligned optics to
ensure each photodiode sees a narrow vertical slice of space directly above it.
Raw voltage after the trans-impedance amp, with simulated noise and mains hum visible:
And the differentiator and comparator outputs super-posed:
For an arrow the biggest, negative, pulse is due to the abrupt end of the fletching passing, causing a rapid increase
in light. An opamp differentiator stage has negative gain which is why this then appears negative.
The choice of opamps and comparators will depend on the speed/bandwidth you are looking for, for archery its
less demanding. If you use a comparator you have the issue of deciding on a suitable threshold that produces
reliable results. If you sample the waveforms you'll need a suitably high sample rate and be able to both trigger
live and then have enough samples to perform the autocorrelation to measure the delay time.
In low light photodiodes produce more noise (as a proportion of wanted signal), which will limit the operation.
Larger area PIN photodiodes are probably the way to go, as they maintain good response speed at low light.
My circuit could benefit from putting more voltage across the diode to reduce its capacitance and increase its
speed (that would need a -5V rail perhaps).