Process Improvement Due to PLC Jitter

Possibly a crystal based timer....

https://en.wikipedia.org/wiki/Crystal_oscillator

That is a step in the right direction, dividing time into smaller and smaller segments, but it does not guarantee synchronization to mechanical motion. It only reduces the error slightly. The error will always be plus or minus half of the LSB (least significant bit) which can be pretty small compared to the overall requirement but the cost will be fairly high. A pair of photo eyes can be used with an AND gate to provide microsecond accuracy for a fraction of the cost but one must choose an appropriate AND gate to accomplish such a task. And the photo eyes must have a high speed response to keep the error rate low but synchronization can be easier and less expensive than some other solutions.

Even when one pre-triggers on an earlier event using purely analog technology (no timing clock) to compensate for propagation delays there will always be random things happening.

From a purely mathematical perspective, here from Wikipedia is the continuous probability distribution function:

with f(x) being whatever probability distribution is applicable to the process. From the same article is this quote:

In particular, the probability for X to take any single value a (that is a ≤ X ≤ a) is zero, because an integral with coinciding upper and lower limits is always equal to zero.

What you desire is not possible. You must have some non-zero width interval where the event can reside to have any probability to trigger.

If you want high precision triggering on a rotary output then might I suggest using a grey scale encoder with however many bit as you think you need.

A 16 bit grey scale encoder will give a resolution to 65536 parts per revolution or 182 parts per degree. If this is coupled with a high speed counter with a switched fet output then that is a reasonable accuracy.

I have used high speed plc input cards that run independent of the main plc having their own clock running at 4 or 16 MHZ and used it to count not teeth as you suggested but the interval between teeth such that the tooth rise starts the timer and the next tooth stops the timer, loads the time interval into a memory Location, resets the timer and restarts the timer.When I say timer, it is actually a counter counting clock cycles. The memory location values can be arithmetically operated on to give the desired time interval.

This method can also be triggered by the tooth width but the mark space ratio as used firstly helps to get around any small tooth/gap variations.

<...teeth on a gear...>

One must remember that when looking at something that has a frequency with something else that has a frequency, there are two resulting additional frequency signals: one that is the sum of the two frequencies and the other that is the difference between them. These can confuse control action leading to unexpected outcomes. Many PLC manufacturers offer high-speed input cards in an attempt to overcome this problem.

In the process industries, "If it happens in less than a second, it isn't real". Digital input de-bounce timers, either in the input cards' firmware or in the PLC input mapping logic, kick the perceived problem into the long grass, where it usually remains.