Do you know of any company providing eye-tracking solutions (for whichever application, no matter whether commercial or only OEM) with acquisition rates over 1KHz and latency times below 3ms?
Dual-Purkinje image eye-trackers should meet your requirements. Me, I did not work with that technology. Instead I worked with video-camera-based pupil-tracking: The system of http://eyeseecam.com has up to 600Hz and 4ms latency and comes relatively close to your requirements.
The only system that I know of that can meet the performance rates and latency times you are looking for would be search coils. Not inexpensive nor useful for long durations. There are other magnetic imaging techniques that are tracking the retina (or could track the retina) with data rates and latency times that far exceed anything on the market.
Dear Samuel, in my lab we have two EyeLink 1000 from SR-Research that I think is what you are looking for. The 2000 Hz camera upgrade allows the EyeLink 1000 Plus camera to sample at an even higher frequency than its 1000 Hz default, making it the fastest eye-tracking camera in the world. Latency at 1000 Hz is 1.8 msec (SD < 0.8 msec). http://www.sr-research.com/
For the newest hardware on the market, the Tobii Pro Spectrum samples up to 1200 Hz, has < 3 ms system latency, binocular bright and dark pupil illumination, and excellent tolerance for head movement (no chin rest needed): https://www.tobiipro.com/product-listing/tobii-pro-spectrum/#Specifications
I can recommend the Jazz Novo eye tracker (http://www.ober-consulting.com/9/lang/1/). It samples at 1000Hz and does not use any camera (IROG technique). The method is very promising if speed is your concern because the device consists only of the IR emitter and receiver. I used a similar device (a prototype) that sampled at 4kHz.