The circle in the square on the ILDA test pattern is a measure of the 3dB small signal bandwidth of a galvo. You scan the ILDA pattern at 8 degrees angle and increase your point or vector rate until the circle collapses to just inside the square. The points per second update rate at that point is your galvo's speed rating for that combination of galvo, mirror size, and amplifier tuning.
As for the 80 Khz, your modern galvos have a low pass filter/integrator and or notch filter as part of the analog servo loop. Its rolling off the parts of your waveform it does not like. Be thankful for not all of them do that. A 30K galvo at 8' has a typical small jump bandwidth of 2.5 Khz or so. The large jump bandwidth is much less then this. Jump speed is determined by the shaft inertia and the mirror inertia and inductance limits in the coil, so by basic physics, it takes a long time to move on a larger angle.
Single ended is safer because it keeps the scan magnitude down. Its best when creating new hardware to have a potentiometer to set the image size smaller to prevent "slamming or oscillations". Some Chinese clone galvos have the power limiter circuits that US made galvo amps have, some dont. The power limiter will "shrink" the image if the galvo core is getting hot. Its a not really a sensor, its a "coil temperature calculator" that is a analog averaging circuit, and it looks at the feedback signal.
Galvo damage happens when you "Slam" against the stops or cause the galvo driver to oscilliate with a resonant excitation. Its possible to tune a galvo amp to a critical point with poles and zeros in the feedback that resonate. Some cheaper galvo amps are very susceptible to this. The closer your signals are to a sine wave or a trapazodial ramp, the happier and faster the galvos will be.
From basic physics, the quickest way to make a small jump is to accelerate linearly to max drive for 1/2 the time, then to apply a equal and opposite linear deceleration. (when you take the class, its defined as slam to slam, no linear... However this gets you high order harmonics in your signal, which is bad for galvos)
For large jumps, keep in mind it is wise to add (in software) evenly spaced "guide points" in between image points with large spacing.
Anchor and blanking points are added for sharp corners and for black spaces in the images, as needed. Ie at a 90' turn you might add 3 extra points to the image at that point.
Anchor/Blanking/Guide points are usually a user selectable setting in software, so users have a small amount of compensation for different types of galvo.
If you have a true oscilloscope with at least a 1 Megohm input impedance, it is wise to carefully connect it to the galvo feedback signal, which a lot of Asian amps bring out as two white, unconnected, wires. You can then see the settling time, and small position oscillations (ringing) that occur as the servo system tries to stop on a dime. Good, well tuned, galvo amps show about two or three cycles of a decaying, ringing, waveform in response to a sharp step input. The ILDA pattern shows that at the corners of the outer and inner boxes.
If your going to distribute your software, it is wise to have it checked by some one with Galvo tuning experience, as while not easy, it is possible to damage lower cost galvos or some older systems with bad waveforms. Random, fast, square waves with no anchor/guide points are something to avoid in this regard. Software RNGs/Digital Noise sources/Fast PWM are great at making that dangerous waveform.
The ILDA test pattern was carefully designed by a bunch of now retired scanner engineers, artists, and programmers, it is not ideal, it is a compromise, but it is one that has worked well for 20+ years.
Good software systems offer about 10 different tuning test patterns. Grids, and the "Laser Media" pattern are also critical for tuning. The LM pattern lets you match your X and Y galvo speeds, it has diagonal lines that "bow" if the speeds are different. It has corners designed to show overshoot/undershoot.
Laser Show Systems - Scanning Systems - www.LaserFX.com
Since you sound like a good engineer, here is optional reading:
While Mini_Sax is not a typical laser show galvo amp, chapter 10, "Tuning Stratagies" is a good read for advanced students.
http://www.camtech.com/archive/176-25016_MiniSAX_Manual_G.pdf
Dont expect users to retune their galvos to match your system, not many people can handle 6 dimensional problems without some training.
Thats not to insult users, but the truth is a "first tune" for a beginner can take hours. Unless you have Pangolin/LSX or some other"KNOWN GOOD" package to create the various patterns, getting back to good images is difficult.
I went to classes for this, its not "hidden" knowledge, its just that tuning classes are rare beasts, only happening at conferences/LEMS. When entertainment was still a large market for Cambridge, they came and gave classes and handed out study guides, based on factory initial tuning using 50 Hz square waves and a dual trace oscilloscope.
PS, whatever you do, stay away from the "Scale factor" potentiometers for the position sensors. That is a "factory only" adjustment.
Just about any "double buffered" dac will do, ie a dac that both x and y update at the same time. At 30 K, you can see it in the image if they dont. 12 Bits is great, 16 is fine, anything more then that is OVERKILL. 8 Bit is a horrid mistake these days.
As for using the LM675s, skip em. The ilda standard only specs the amps for +/- 10V DIFFERENTIAL, which is peak to peak. Most galvos are set up so +8 on one line and -8 on the other is full scale delection to one side. 24V from a circuit error would easily kill the TL084 clone used as the average galvo input amp, the clipping zeners that would protect the inputs are just not installed on the Asian clones. Use some TL084s with their inherent 20 mA output limit and use 12 or 15 volt rails, this is for "common mode" limitations on the differential inputs.
Steve