The classical instrument to measure small AC signals including phase to a reference is a lock in amplifier, especially the better 2 phase version. Compared to an DSO modern digital Lock-ins tend to use higher resolution ADCs, but lower speed. The other related old time instrument is a box car integrator - the equivalent to the averaging mode one an DSO. This one could also be done in analog for a limited number of channels.
A good working averaging mode can be an important and very useful feature on an DSO.
Using a DSO, you can act as a "human lock-in amplifier" by varying the capacitance across one of the bridge arms until the waveforms show that you have nulled out both the real and quadrature currents. You can even act as a human capacitor if the circuit is somewhat high impedance (e.g. 100K), playing it like a Theremin to balance it out!

Ghetto metrology!

Just for fun, I tried inputting a nice noisy 100uV signal on an Agilent 54622D, which (unlike the Siglent) only has a 2mV/division vertical amplifier (the 1mV setting is "faked").
Without averaging:

With averaging:

100uV amplitude is too low to measure properly - but good enough to see the phase!
Further experiments showed that you can get down to about 5uV - 10uV and still just about make out that there is a signal there...
If you put Dave Jones' uCurrent in front of this not particularly sensitive scope, with accurate amplification of x100, you can actually peek into the nanovolt region!
7 digit resolution is possible (has been achieved in the basement) this way, and with another x10 more amplification, that elusive 8:th digit might be within reach using the DSO method...
But, who knows, perhaps there is a lock in amplifier or a box car averager in the future!
