Our custom design from a few years ago used a high impedance bipolar transistor output to drive the capacitive load, and OP-27 or OP-07 was the center of the amp design and the feedback was thru another amp, differential configured OP-07 or OP-27. The position feedback bridge wasn't located on the piezo elements, but along the movement "path"...so some mechanical delay involved. The driver amp was configured as an asymmetrical output (capable of +200V to -30V) to limit the negative swing, which can cause damage to piezo elements when they compress. These are under compression in the "forward" direction, and should be operated in compression. Initially we were going to use a 20 bit DAC, but decided on a 16Bit which worked well.
The Physik Instrumente OEM driver amp was based upon a low impedance MOS output, also worked well and was quicker in response than the high impedance amp. We designed a custom 16bit DAC based interface for this OEM amp, and all the "systems" worked with a RPi.
The piezo elements have huge hysteresis, highly non-linear capacitance, highly temperature dependent and work in reverse (produce an output with applied force), so fixturing, loading, orientation and external vibration must be carefully considered.
The optical technique we utilized to verify nanometer levels of position was based upon image correlation, not laser techniques. A grey scale print produces random laser printed patterns with tiny fused plastic/carbon high contrast particles on white print paper. This paper was bonded to a low TC glass slide and allowed to "settle" for a few weeks. After this the slide was placed orthogonal to the optical imaging axis, a series of high resolution images (~45MP per image) captured with a high resolution objective lens (Mitutoyo 10, 20 50X). The piezo element was commanded between images and allowed to settle, both high speed strobe and continuous (LED) illumination were tried. A carefull setup is required to reduce any temperature, air flow, vibration, movement, and other issues which would corrupt the results, including the minute thermal effects of illumination.
After the images were collected, they were processed in an image stacking package called Zerene we used for our high resolution chip images. This technique looks at in-focus areas and attempts to align features mainly to increase DoF, however our use was to align high contrast features of the tiny print particles randomly scattered throughout the images. By correlating each image, and recording the alignment parameters, the amount of movement can be reveled necessary for realignment of each image, one on top of the other. This technique worked very well, can resolve small fractions of an image pixel, allowing image position movement resolutions in nanometers regions, and required no expensive or additional measurement equipment, in fact we already had everything necessary to do such

Anyway, hope some of this helps.
Good luck with your project, sounds like an interesting endeavor.
Best,