Let me see if I can make a simple recount of what Chuck is explaining:
If you have an oscilloscope and a function generator able to output a sine wave of about 100 kHz, you have everything you need to make simple, quick ESR measurements in situ.
- Connect the ground and tip of the oscilloscope probe on both ends of the capacitor.
- Inject as a current the 100 kHz AC signal into the capacitor side that has the oscilloscope tip.
- Observe and estimate on the oscilloscope the voltage this AC current creates on the capacitor.
I set the function generator to 10 V, then connect this output to a 1 K resistor, and touch the capacitor with the other end of the resistor. This will create an AC current of 10 mA.
If the ERS of the cap is 1 ohm, the measured voltage will be 10 mV, something that can be recognized on the oscilloscope set to its high sensitivity of direct input.
It is not necessary to measure the value of ERS precisely, but only to get an idea whether the capacitor is good or not.
"Acceptable ESR" is also a function of the capacitance. In a large cap, a fraction of an ohm can be fine. In a small one, one ohm or larger can be acceptable.
Electrolytics are polarized. If you are a meticulous person, you will put the ground of the scope on the negative of the cap, and will see that the AC signal has a positive offset.
If you are a practical person, you realize that a small negative AC does not affect the response of the electrolytic cap. They are not like schottky diodes.
For this measurement, the less noise and less bandwidth your oscilloscope has, the better. And use a direct probe instead of a x10 probe. If you can trigger the scope on the AC signal (at the generator) like Chuck recommends, it is easier to evaluate the AC signal in the noise.
But the use of protective diodes may not necessary, since a few tens of millivolts with good ESR on the cap will not damage it, and several volts on a bad cap, won't make it worse. If the diodes are used to protect other components in the circuit, they won't interfere in the measurement because the signal on a good capacitor is so low.