Explanation for circuit with 2-stage op-amp, with diode in between first output and second input
Very interesting. It looks like an input stage to something equivalent to a theremin although it could just be a capacitive sensor used for other applications. I'm guessing that U17 and U18 (the green plates) are in fact sensor plates and are used to detect the presence of hand movement or some other fairly conductive material that might bridge the plates.

Anyway, enough speculation; the plates (and whatever bridges them) and C16/C17 will form a variable capacitance and inject current into the inverting node of the 1st opamp. The diode (D1) and capacitor (C19) will attempt to resolve the amplitude of the disturbance of this "variable capacitor" and in doing so will also filter high frequency noise.

D1 and C19 form what is known as an envelope detector and this sort of circuit is used in AM radios to demodulate a radio frequency carrier and deliver the audio. I don't think audio is being demodulated but I do suspect that there is a lot of RF that could be present in the signal.

The pot (R17) might be used to set the decay time of the envelope detector.