jahonen & alm, awesome posts as always, more comments later, jahonen your Agilent grabs just blows me away. This XY Rigol mode got me in tizzy but it had a good result. I think the readers/hackers should know the following as it salvages the XY mode usability if some features are known and used together.
The manual doesn't have much to describe in XY mode. It states 100Ms/s is
not available, and when you engage XY mode in the Rigol, it stated maximum is 1Ms/s, and thus the crawling and dotty image when viewing Lissajous figures, once it reaches 100kHz, ~ 1/10 the sampling rate.
Slow sampling rates are fairly useless when trying to adjust 2 out of phase signals and tuning the Lissajous figure to stability. However, all is not lost.
I found the following undocumented control:
Acquire Button
MemDepth:
select Long Mem will switch to 100Ms/s real time sampling rate
The other Menu items have no effect:
Sinx/x
Sampling
Horizontal Controls now are enhanced.
Position: disabled
Scale: adjusts Sampling Rate as follows:
Long Mem = Scale from 1Ms/s to 100Ms/s
Normal = Scale from 10ks/s to 1Ms/s
Vertical Controls, all work, but these shortcut help:
CH1+ Press Position button: centers X on screen
CH2+ Press Position button: centers Y on screen
The input amps can clearly go to the rated bandwidth of 50 MHz at -3dB, I checked each channel separately by measuring the length of each of the X & Y excursions, but how useful XY or Lissajou figures will be depends on purpose.
Photos:
A most practical use today is measuring phase shift, so even low sampling rates work using "persistence" to draw an image but it has to be stable, it tends to 'fatten' from noise, making more accurate measures difficult. Here the small circle is 75 MHz, the wide one is 7.5 MHz and narrow long one is 750kHz. One 'feature' of the persistence is you can follow shifts as you adjust. You can increase the gain on the image to make manual measurements as best possible, and clear the screen to erase the unneeded image. Phase shift is ~ 135, 45, and 20 degrees, by 'eyeball.'

For measuring frequency using Lissajous figures with unknown phase relationships, you can increase the sampling rate for a viable image, but it depends on the ratio of X/Y you use, and it can be awkward in dot mode. here is a sample comparing 1 MHz to 5 MHz resulting in the 5-1 lobed figure that is usually moving and unstable until ratios synch and 'lock in'. I used to do this with a stable reference, but a good frequency counter can replace this task easily.

Realtime sampling of 3 MHz 1:1, ~ 135 deg off phase.