Another question I asked about Power Supply Noise pushed me to ask this question. 

The background is as follows: I have a design with PD (Photodetector) and Opamp at medium frequency (couple hundred KHz). I am trying to test my design when it come back. I am looking at power supply noise, opamp supply noise and opamp output noise. I realized, there is more to it than just touching the probe. People talk about power loops, having special cables etc. 

I will spin another board in two weeks and I wanted to ask, if you are designing your board now, what type of test points or elements you place on your board so that you can measure the noise accurately. We are talking about <20mV type signals.

Bonus question: The output of the opamp is connected to an ADC of the processor. Could I simply run the ADC and plot that to gain a deeper understanding of the noise compared to connecting my cheap scope?
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Typically you design some parts on the first spins of the board to help measure stuff like this. Be generous with footprints for bypass caps and filters, and put for example SMA coaxial contacts at key places in the signal chain, but put them with a removable SMD 0-ohm resistor at the T-junction so the stub doesn't have to affect the signal chain if not used.

For low-frequency signals you could hook this directly to the scope, but the SMA coaxes have a good feature in that some of the probes with the ground-lead built into the tip can be stuck into the center position of the coax connector and the ground lead will or can be made to touch the shielding.. note though that for best results with a probe it need to be active, and then the probe itself will cost 3000 dollars :/

With photodiodes and transimpedance amplifiers you have the problem that for a typical setup (you don't specify your parameters..) you have only a couple of microamps and a transimpedance gain of several hundred thousand. Inserting elements at the PD-side of the opamp, and indeed just having PCB traces in the vicinity might disrupt your precision and noiselevels. The solder resist coating has a non-infinite resistance for example.

Therefore if you can control the gain of the ADC and know you have designed a very good ADC circuit (this you can test separately, with separate SMA coax inputs to it for example) you can use that as a probe replacement yes if the sample rate is high enough. This is a good solution and postpones the need for the more expensive scope (you can rent these if you really need it sometime though).
Stevenvh is correct that noise can be very hard to measure, but I would like to point out a different point of view.

The only time that noise really matters to you is when it affects your readings. This means that you can just take an ADC of your input, pass it off to a computer, and then do some math on it. I am not entirely up to speed on your project, but I assume that you "know" what your signal is that you are receiving.

You can come up with an SNR figure by calculating the average power of your signal and then to get your noise, just subtract the known signal from your ADC signal, find the power of the resulting noise, and then divide the two. Most systems tend to convert this to a dB scale.
This won’t tell you anything about what part of the system the noise is coming from, but it will allow you to have an idea as to how well your system will function overall.